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Faculty of the Built Environment and Engineering
AN INVESTIGATION OF THE AUSTRALIAN LAYERED ELASTIC TOOL FOR FLEXIBLE AIRCRAFT PAVEMENT THICKNESS DESIGN By Gregory William White BE(Civil,Hons 1), MEng(UoN), ME(UNSW), MTech(Pvmts), Grad Cert(App Stats), Cert IV(A&WT), CPEng, MIEAust. With the assistance of: Sinclair Knight Merz For the award of Master of Engineering Submitted for examination in July 2007
Queensland University of Technology
Preliminaries Key Words
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
i
KEY WORDS
Aircraft Pavement Structural Design System.
Layered Elastic Thickness Design.
Flexible Aircraft Pavement.
Sensitivity Analysis.
Proof Rolling.
Material Equivalence.
Preliminaries Publications
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design ii
PUBLICATIONS
The following works have been published based on the research contained in
this thesis.
WHITE, G. (2005). ‘A Sensitivity Analysis of APSDS, an Australian
Mechanistic Design Tool for Flexible Aircraft Pavement Thickness
Determination’. Proceedings First European Aircraft Pavement Workshop. The
National Information and Technology Platform for Infrastructure, Traffic,
Transport and Public Space (CROW). Amsterdam, Netherlands. 11-12 May.
WHITE, G. W. (2005). ‘Selection of Input Parameters for Layered Elastic
Design of Flexible Aircraft Pavements‘. Proceedings 7th International
Conference on the Bearing Capacity of Roads, Railways and Airfields. Paper
Number 49. NTNU, NPRA, NNRA and AVINOR. Trondheim, Norway. 27-29
June.
WHITE, G. W. (2005). ‘Design of Proof Rolling Regimes for Heavy Duty
Aircraft Pavements‘. Proceedings 7th International Conference on the Bearing
Capacity of Roads, Railways and Airfields. Paper Number 26. NTNU, NPRA,
NNRA and AVINOR. Trondheim, Norway. 27-29 June.
WHITE, G. W. (2006). ‘Material Equivalence for Flexible aircraft Pavement
Thickness Design’. Proceedings 2006 Airfield and Highway Pavements
Specialty Conference. Refereed paper number 17121. American Society of
Civil Engineers. Atlanta, United States of America. 1-3 May.
Preliminaries Abstract
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
iii
ABSTRACT
APSDS is a layered elastic tool for aircraft pavement thickness determination
developed and distributed by Mincad Systems and based on the sister software
Circly. As aircraft pavement thickness determination remains an empirical
science, mechanistic-empirical design tools such as APSDS require calibration
to full scale pavement performance, via the S77-1 curve. APSDS provides the
unique advantage over other tools that it models all the aircraft in all their
wandering positions, negating the need for designers to use pass to cover ratios
and acknowledging that different aircraft have their wheels located at difference
distances from the aircraft centerline.
APSDS requires a range of input parameters to be entered, including subgrade
modulus, aircraft types, masses and passes and a pavement structure. A
pavement thickness is then returned which has 50% design reliability. Greater
levels of reliability are obtained by conservative selection of input values. Whilst
most input parameters have a linear influence on pavement thickness,
subgrade modulus changes have a greater influence at lower values and less
influence at higher values. When selecting input values, designers should
concentrate their efforts on subgrade modulus and aircraft mass as these have
the greatest influence on the required pavement thickness. Presumptive or
standard values are generally acceptable for the less influential parameters.
S77-1 pavement thicknesses are of a standard composition with only the sub-
base thickness varying. Non-standard pavement structures are determined
using the principle of material equivalence and the FAA provides range of
material equivalence factors, of which the mid-range values are most commonly
used. APSDS allows direct modelling of non-standard pavement structures. By
comparing different APSDS pavements of equal structural capacity, implied
material equivalences can be calculated. These APSDS implied material
equivalences lie at the lower end of the ranges published by FAA.
Preliminaries Abstract
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design iv
In order to obtain consistence between APSDS and the FAA guidance, the
following material equivalence values are recommended:
• Asphalt for Crushed Rock. 1.3.
• Crushed Rock for Uncrushed Gravel. 1.2.
• Asphalt for Uncrushed Gravel. 1.6.
Proof rolling regimes remain an important part of the design and construction of
flexible aircraft pavements. Historically, designers relied on Bousinesq’s
equation and the assumption of point loads on semi-finite homogenous
materials to determine proof rolling regimes using stress as the indicator of
damage. The ability of APSDS to generate stress, strain and deflection at any
depth and any location across the pavement allows these historical
assumptions to be tested. As the design of a proof rolling regime is one of
comparing damage indicators modelled under aircraft loads to those under
heavy roller loads, the historical simplifications are generally valid for practical
design scenarios. Where project specific data is required, APSDS can readily
calculate stresses induced by proof rollers and aircraft at any location and depth
for comparison.
APSDS is a leading tool for flexible aircraft pavement thickness determination
due to its flexibility, transparency and being free from bias. However, the
following possible areas for improvement are considered worthy of future
research and development:
• Improvements to the user interface.
• Ability to model aircraft masses as frequency distributions.
• Ability to copy stress with depth data to Excel™ spreadsheets.
• Ability to perform parametric runs.
• Inclusion of a reliability based design module.
Preliminaries Table of Contents
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
v
TABLE OF CONTENTS
Section Page
KEY WORDS ...................................................................................................................I PUBLICATIONS ..............................................................................................................II ABSTRACT ....................................................................................................................III TABLE OF CONTENTS ................................................................................................. V LIST OF TABLES ......................................................................................................... VII LIST OF FIGURES...................................................................................................... VIII LIST OF ABBREVIATIONS........................................................................................... IX STATEMENT OF ORIGINAL AUTHORSHIP................................................................ XI ACKNOWLEDGEMENTS............................................................................................. XII 1. INTRODUCTION...................................................................................................1
1.1 General ........................................................................................................................1 1.2 The Early Days ............................................................................................................ 1 1.3 The Original CBR Method............................................................................................ 1 1.4 US Corps of Engineer Full Scale Aircraft Tests........................................................... 2 1.5 Material Equivalence Factors ...................................................................................... 4 1.6 The ICAO Pavement Rating System........................................................................... 5 1.7 Layered Elastic Design ................................................................................................ 6 1.8 New Generation Large Aircraft .................................................................................... 9 1.9 Future Developments ................................................................................................10 1.10 Aims and Methods .....................................................................................................12
2. AIRCRAFT PAVEMENT STRUCTURAL DESIGN SYSTEM..............................15 2.1 General ......................................................................................................................15 2.2 Inception and Development .......................................................................................15 2.3 Overview and Operation ............................................................................................17 2.4 Advantages and Benefits...........................................................................................26 2.5 Potential Improvements .............................................................................................28 2.6 Summary....................................................................................................................31
3. VALIDATION OF APSDS....................................................................................33 3.1 General ......................................................................................................................33 3.2 Validation Process .....................................................................................................33 3.3 Analysis of Results ....................................................................................................35 3.4 Summary....................................................................................................................36
4. INPUT PARAMETER SELECTION.....................................................................37 4.1 General ......................................................................................................................37 4.2 Input Parameters .......................................................................................................37 4.3 Subgrade Strength.....................................................................................................37 4.4 Aircraft Wander..........................................................................................................41 4.5 Aircraft Mass..............................................................................................................42 4.6 Aircraft Tyre Pressure................................................................................................43 4.7 Number of Passes .....................................................................................................43 4.8 Asphalt Modulus ........................................................................................................44 4.9 Pavement Structure ...................................................................................................45 4.10 Design Traffic Mix ......................................................................................................46
Preliminaries Table of Contents
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design vi
4.11 Summary ................................................................................................................... 47 5. SENSITIVITY ANALYSIS ................................................................................... 49
5.1 General...................................................................................................................... 49 5.2 Investigation Undertaken........................................................................................... 49 5.3 Sensitivity Analysis.................................................................................................... 52 5.4 Analysis of Results .................................................................................................... 62 5.5 Summary ................................................................................................................... 63
6. MATERIAL EQUIVALENCE ............................................................................... 65 6.1 General...................................................................................................................... 65 6.2 S77-1 and FAA Pavement Design ............................................................................ 65 6.3 Investigation undertaken ........................................................................................... 67 6.4 Practical Pavement Equivalences............................................................................. 69 6.5 Isolated pavement equivalences............................................................................... 80 6.6 Thickness Comparison Examples............................................................................. 84 6.7 Summary ................................................................................................................... 88
7. DESIGN OF PROOF ROLLING REGIMES........................................................ 91 7.1 General...................................................................................................................... 91 7.2 Design of Proof Rolling Regimes .............................................................................. 91 7.3 Australian Proof Rolling Fleet.................................................................................... 92 7.4 Damage Indicator Calculation ................................................................................... 92 7.5 Investigation Undertaken........................................................................................... 94 7.6 Proof Rolling Regime Design .................................................................................. 101 7.7 Practical Limitations ................................................................................................ 106 7.8 Examples of Application.......................................................................................... 107 7.9 Summary ................................................................................................................. 111
8. SUMMARY AND CONCLUSIONS ................................................................... 113 8.1 General.................................................................................................................... 113 8.2 Summary ................................................................................................................. 113 8.3 Conclusions............................................................................................................. 115
APPENDIX 1. S77-1 THICKNESS RESULTS APPENDIX 2. SENSITIVITY ANALYSIS DESIGN APPENDIX 3. SENSITIVITY ANALYSIS RESULTS APPENDIX 4. MATERIAL EQUIVALENCE DESIGN APPENDIX 5. MATERIAL EQUIVALENCE RESULTS APPENDIX 6. DAMAGE INDICATORS WITH DEPTH APPENDIX 7. PROOF ROLLING REGIMES BIBLIOGRAPHY
Preliminaries List of Tables
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
vii
LIST OF TABLES
Table Name Page
Table 1 Chicago failure criteria. ........................................................................26 Table 2 Input Parameters. ................................................................................34 Table 3 Aircraft Wander Standard Deviation. ...................................................42 Table 4 Typical asphalt moduli. ........................................................................45 Table 5 Aircraft Information...............................................................................50 Table 6 Input Parameters. ................................................................................51 Table 7 Normalised Linear Influence and Importance ......................................62 Table 8 FAA Material Equivalence Guidance. ..................................................67 Table 9 Number of Practical Equivalence Determinations................................70 Table 10 Design Parameter Values for Practical Equivalence. ..........................70 Table 11 Summary Statistics for Practical Equivalence......................................73 Table 12 Recommended Material Equivalences. ...............................................79 Table 13 Design Parameters for Isolated Equivalence.......................................81 Table 14 Equivalence Examples Input Parameters. ...........................................85 Table 15 Equivalence Examples Summary Statistics.........................................87 Table 16 Proof Rolling Regimes for B767, B747 and F111. .............................109
Preliminaries List of Figures
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design viii
LIST OF FIGURES
Figure Name Page
Figure 1 US Corps of Engineers CBR Curve....................................................... 3 Figure 2 S77-1 versus APSDS Thicknesses. .................................................... 35 Figure 3 S77-1 versus APSDS Differences. ...................................................... 36 Figure 4 Pavement Structure............................................................................. 51 Figure 5 General Model Results ........................................................................ 54 Figure 6 General Model Residuals .................................................................... 55 Figure 7 Specific Model Results ........................................................................ 56 Figure 8 Residuals for General and Specific Subgrade Models for B747 ......... 57 Figure 9 Residuals for General and Specific Subgrade Models for B767 ......... 57 Figure 10 Residuals for General and Specific Subgrade Models for B737 ......... 58 Figure 11 Thickness Ratio Consistency. ............................................................. 59 Figure 12 Relative Influence of Design Inputs for B747. ..................................... 60 Figure 13 Relative Influence of Design Inputs for B767 ...................................... 60 Figure 14 Relative Influence of Design Inputs for B737. ..................................... 61 Figure 15 Standard S77-1 Pavement Structure................................................... 66 Figure 16 Practical Equivalence for Asphalt and Crushed Rock. ........................ 72 Figure 17 Practical Equivalence for Crushed Rock and Uncrushed Gravel. ....... 72 Figure 18 Practical Equivalence for Asphalt and Uncrushed Gravel. .................. 73 Figure 19 Summary of Asphalt and Crushed Rock Equivalences ....................... 75 Figure 20 Summary of Crushed Rock and Uncrushed Gravel Equivalences ...... 75 Figure 21 Summary of Asphalt and Uncrushed Gravel Equivalences................. 76 Figure 22 Practical Equivalence Results ............................................................. 78 Figure 23 Practical Equivalence Residuals ......................................................... 79 Figure 24 Isolated Equivalence Residuals........................................................... 82 Figure 25 Effect of modulus ratio, thickness and location on equivalence. ......... 83 Figure 26 B737 Vertical Stress with depth for various pavements. ..................... 95 Figure 27 B737 Vertical Strain with depth for various pavements. ...................... 96 Figure 28 B737 Vertical Deflection with depth for various pavements. ............... 97 Figure 29 Comparison of Pavement and Single Material Stresses. .................... 99 Figure 30 Asphalt thickness and modulus effects. ............................................ 100 Figure 31 Allowable Macro Roller Tyre Pressures and Masses. ....................... 102 Figure 32 Allowable Test Rig Roller Tyre Pressures and Masses..................... 102 Figure 33 Porter Supercompactor Tyre Pressures and Masses........................ 103 Figure 34 Vertical Stress with Depth for Various Rollers................................... 103 Figure 35 Macro Roller Vertical Stress with Depth at various roller masses. .... 104 Figure 36 Vertical Stresses with Depth for various Aircraft. .............................. 105 Figure 37 B737 proof rolling regime. ................................................................. 108 Figure 38 B767 proof rolling regime. ................................................................. 110 Figure 39 B747 proof rolling regime. ................................................................. 110 Figure 40 F111 proof rolling regime................................................................... 111
Preliminaries List of Abbreviations
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
ix
LIST OF ABBREVIATIONS
ACN. Aircraft Classification Number.
ANOVA. Analysis of Variance.
APSDS. Aircraft Pavement Structural Design System.
CBR. Californian Bearing Ratio.
CDF. Cumulative Damage Factor.
CSIRO. Commonwealth Scientific and Industrial Research Organisation.
DCP. Dynamic Cone Penetrometer.
DF. Damage Factor.
ESWL. Equivalent Single Wheel Load.
FAA. Federal Aviation Administration (of the USA).
FAC. Federal Airports Corporation (of Australia).
FEDFAA. Finite Element Design Federal Aviation Administration.
FEM. Finite Element Methods.
HIPAVE. Heavy Industrial Pavement Design.
ICAO. International Civil Aviation Organisation.
kPa. Kilopascals.
LCN. Load Classification Number.
Preliminaries List of Abbreviations
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design x
LEDFAA. Layered Elastic Design Federal Aviation Administration.
m. Metre.
MAUM. Maximum All Up Mass.
mm. Millimetre.
MPa. Megapascal.
NAPTF. National Airport Pavement Testing Facility.
NIGS. Nose In Guidance System.
PCN. Pavement Classification Number.
PCR. Pass to Coverage Ratio
PRS. Pioneer Road Services.
t. Tonnes.
με. Microstrain.
μm. Micrometre.
Preliminaries Statement of Original Authorship
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
xi
STATEMENT OF ORIGINAL AUTHORSHIP
The work contained in this thesis has not been previously submitted for a
degree or diploma at any other higher education institution. To the best of my
knowledge and belief, the thesis contains no material previously published or
written by another person except where due reference is made.
Gregory William White BE(Civil,Hons 1), MEng(UoN), ME (UNSW), MTech(Pvmts),
Grad Cert(App Stats), CertIV(A&WT), CPEng, MIEAust.
Preliminaries Acknowledgements
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design xii
ACKNOWLEDGEMENTS
I would like to thank the following individuals and organisations for their
assistance with this research project. Such an undertaken can not be achieved
by an individual working alone and its completion is a reflection of the level of
support that the following have provided.
• Bruce Rodway of Bruce Rodway and Associates for his assistance with the
technical aspects of this project, access to various historical and technical
documents and his ongoing contribution to the development of my
pavement engineering career.
• Leigh Wardle of MINCAD Systems for his contribution to this project and
technical review of elements of this thesis.
• My QUT supervisor, Dr Andreas Nata-atmadja for his review of this thesis.
• My wife Claire who tolerates my moods, distraction and the time it takes to
undertake such a research program.
• My employer, Sinclair Knight Merz, for the corporate support of this research
project and financial assistance in attending conferences to present the
outcomes.
Without your help, this thesis would never have come to fruition. Thank you all.
Chapter 1 Introduction
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
1
1. INTRODUCTION
1.1 GENERAL
Aircraft and airports have developed dramatically since the maiden flight of the
Wright brothers at Kitty Hawk in 1903. Aircraft have increased in mass from
hundreds of kilograms to hundreds of tonnes. With this dramatic increase in
aircraft size, the requirement for high strength, flat and smooth airfield operating
surfaces also became a reality. Methods for the reliable design of pavements
for supporting aircraft operations have therefore been developed over a number
of years. The more recent of these design developments include advanced
computer based design tools which are calibrated to the performance of
pavements tested under repeated full scale aircraft loading.
1.2 THE EARLY DAYS
Prior to WWII, aircraft did not generally require any specific airfield to be
provided for operations. These aircraft were generally operated from farm
paddocks or from road pavements. The aircraft were light enough at that time
to not require specifically designed pavements to operate from. Operations
were so few and speeds so low that air traffic control was not necessary.
As aircraft grew in size and with the introduction of higher performance aircraft
associated with the war effort, an aircraft pavement design method was
considered to be necessary. As well as greater pavement thicknesses, the
war-time aircraft started to require smoother and flatter surfaces to operate
from. Increased frequency of operations and operating speeds also required
controlled air space and ground movement on formalised airfields.
1.3 THE ORIGINAL CBR METHOD
Prior to the 1920s, all pavements were designed based on experience alone.
In 1929, the first empirical design method, which incorporated a strength or
bearing test for the assessment of the subgrade, was introduced by the
California Highway Department (Porter, 1950) in the USA.
Chapter 1 Introduction
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 2
In 1942, the empirical road pavement design method, known as the California
Bearing Ratio (CBR) method was adapted to aircraft pavements and
extrapolated to incorporate higher wheel loads (Rodway, 2003). This
adaptation utilised the single elastic layer theory of Boussinesq (1885) and only
considered stress, strain and deflection directly under a single wheel load.
The CBR method of aircraft pavement design is an empirical method that
relates the required pavement thickness for a prescribed number of load
coverages to the CBR assigned to the subgrade under the pavement and the
aircraft wheel load (Rodway, 2003). The CBR design method provides for
increased aircraft loading by increasing the thickness between the subgrade
and the aircraft wheel.
The CBR design method assumes that the pavement fails through accumulated
vertical deformation in the subgrade. This implies that only minimal
deformation occurs within the various pavement layers. As these layers are not
specifically assessed in the design method, designers must assume that high
quality materials are used and adequate compaction is achieved during
construction. Otherwise, these layers may have a significant contribution to the
failure of the pavement, rather than failure by subgrade deformation.
1.4 US CORPS OF ENGINEER FULL SCALE AIRCRAFT TESTS
The CBR design method was further developed by the re-determination of the
empirical relationships through full scale testing from the 1940s to the early
1970s (Barker and Gonzalez, 1994). The last of these tests included the B747
four wheel landing gear and were reported in detail by Ahlvin, et al (1971). The
revised CBR-pavement thickness curve became known as the S77-1 curve
(Pereira, 1977) and this remains the primary empirical relationship to which
today’s computer-based aircraft pavement design tools are calibrated. Whilst it
would be preferable to calibrate directly to the empirical data, the limited
amount of empirical data and requirement for interpretation of the data has led
to all design tools being calibrated against S77-1. This has resulted in greater
Chapter 1 Introduction
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
3
consistence across the various design tools. The S77-2 curve is shown in
Figure 1.
Figure 1 US Corps of Engineers CBR Curve. 0
1
2
3
4
5
6
70.001 0.01 0.1 1
CBR/Pe
T/Sq
rt(A
c)
Where: CBR = California Bearing Ratio for the subgrade.
Pe = Tire pressure of an equivalent single wheel in PSI.
T = Thickness of pavement required in inches.
Ac = Tire contact area for one wheel in square inches.
To allow the S77-1 design curve to be plotted on a single two dimensional
chart, the tyre pressure was normalised with regards to CBR and the tyre
contact area was normalised with regards to the pavement thickness required
(Ahlvin, 1991). Any combination of tyre pressure and contact area can be
related to a unique single wheel aircraft load.
Factors (known as Alpha Factors) were introduced in 1971 which reduced the
required pavement thickness based on the number of wheels on the aircraft
landing gear and the number of coverages to be designed for. These Alpha
Factors were introduced to offset the finding that the damage caused by
multiple wheel landing gear was less than previously modelled under the
Chapter 1 Introduction
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 4
Equivalent Single Wheel Load (ESWL). This over statement of ESWL damage
is a result of the over estimation of wheel interaction caused by adopting
deflection as the measure of ‘equivalent’ rather than stress or strain (Rodway,
2000).
Whilst Alpha Factors were introduced for aircraft with up to 24 wheels in total,
only those with 1 to 4 wheels per landing gear were used in practice as no
commercial aircraft then had more than four wheels on any one landing gear.
The only wheel configuration with more wheels included in the full scale testing
was that of the 24-wheeled military C5A. This aircraft was initially considered
as two 12-wheeled gears (each comprising two actual 6-wheel gears behind
each other) but was subsequently amended for design purposes to be modeled
as separate 6-wheel gears. As the full scale testing did not incorporate landing
gear configurations in the conventional dual tridem arrangement, the extension
of the Corps’ full scale test results to the new large aircraft (A380 and B777)
was considered too great an extrapolation.
The concept of the Pass to Cover Ratio (PCR) was also introduced to enable a
logical conversion between aircraft passes and coverages based on the aircraft
wheel configuration and the spread of aircraft across the width of the pavement
(Rodway, 2003b).
1.5 MATERIAL EQUIVALENCE FACTORS
The result of the full scale tests, the S77-1 design curve, relates aircraft load to
pavement thickness required. This thickness is for a ‘standard’ pavement
composition as used in the full-scale tests. It does not take into account the
nature of the actual pavement structure, except for the underlying subgrade
strength. When a designer wishes to determine the required pavement
thickness of an alternate pavement structure, the principle of material
replacement equivalence must be used. The factors used to replace a known
thickness of one pavement material with an equivalent thickness of alternate
material are called ‘material equivalences’ as they relate the required thickness
Chapter 1 Introduction
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
5
of two difference materials in order to achieve a structurally equivalent
pavement.
The later full scale tests allowed some assessment to be made of the
comparative benefit of pavement materials other than those adopted in the
S77-1 pavement structures. These material equivalences were accepted by
the US Corps of Engineers in 1977 but significantly less than the equivalences
applied to road pavements.
These material equivalences are utilised to convert any pavement structure to
an equivalent thickness of S77-1 pavement, which comprised of 75 mm of
asphalt on 150 mm of fine crushed rock base on variable thickness of natural
gravel sub-base on subgrade of variable CBR (Wardle, et al, 2002). Guideline
material equivalence factors are published by the US Federal Aviation Authority
(FAA) (FAA, 1995). This guide covers a range of materials. However, for most
design scenarios, the equivalences covering fine crushed rock, natural
uncrushed gravel and asphalt are of most interest. The use of these material
equivalence factors is straight forward as demonstrated by Rodway (2003a).
The FAA document provides ranges of equivalence between various pairs of
material. No specific guidance is provided, however, as to which value in the
range is appropriate for any given deign scenario. The basis for the
determination of these factors could not be determined and they are considered
to be a weak link in the CBR design method for pavement structures which
differ significantly from the standard S77-1 test pavement.
1.6 THE ICAO PAVEMENT RATING SYSTEM
Whilst not a pavement design tool, the Aircraft Classification Number –
Pavement Classification Number (ACN – PCN) system for pavement strength
rating is a significant contributor to aircraft pavement engineering’s history. The
ACN – PCN system was introduced by the International Civil Aviation
Organisation (ICAO) in 1981 as the standard system for rating the strength of
aircraft pavements (CROW, 2003). The ACN is defined as twice the wheel load
Chapter 1 Introduction
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 6
in tonnes, which on a single wheel, inflated to 1.25 MPa, would cause
pavement damage equal to that caused by the aircraft’s actual multi-wheel gear
at its actual gear load and its actual tyre pressure (Rodway, 2003c). The PCN,
however, remains an airport owner derived value which is essentially an
advertisement to aircraft operators as to which aircraft are welcome to operate
at an unrestricted frequency from the airfield. The PCN should be selected to
be equal to the largest ACN of all the aircraft (at their respective masses) which
the airport owner will allow to operate in an unrestricted (from a pavement
strength view) manner.
With around 75% of the world’s airports utilising the ACN – PCN system (Loizos
and Charonitis, 2004), this system has largely replaced previous systems of
reporting and assessing aircraft pavement strength, such as the Load
Classification Number (LCN). The ACN derivation does not require the actual
pavement thickness or structure to be known, making the ACN of any aircraft
essentially independent of the actual pavement it is to operate on. It does
however depend upon the subgrade strength category and whether the
pavement is of flexible or rigid construction. Guidelines are generally available
which relate ratios of differing ACNs to relative amounts of pavement damage
induced. This relationship is not consistent for all aircraft and is not linear. Two
aircraft with an ACN ratio of 1.5 will have a damage ratio close to nine
(Defence, 2003a). The actual damage ratio is dependent upon the actual
pavement thickness required by the specific aircraft being considered.
1.7 LAYERED ELASTIC DESIGN
The first mechanistic-empirical design methods were developed in the 1950s
(Huang, 1993). The first, computer based layered elastic design tool for
pavements was developed in 1963 and reported by Warren and Dieckmann,
1963). This program was based on Burmister’s layered theory (Burmister,
1943).
With the increases in computer power in the 1980s and 1990s, layered elastic
design methods became commonly available to pavement designers. The
Chapter 1 Introduction
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
7
adoption of layered elastic design methods requires pavement structures to be
modelled as finitely thick and infinitely long/wide layers of elastic materials.
Each layer of material may be divided into sub-layers, each of uniform elastic
stiffness (modulus). Each material’s assigned modulus depends on both the
pavement material as well as its location within the pavement (as modulus of
granular pavement materials is dependent upon the stress conditions applied to
them) (Holtz and Kovacs, 1981). In 1975 a method of dividing layers into sub-
layers of uniform modulus and assignment of modulus values was developed
(Barker and Brabston, 1977). This method is understood to be used by all
layered elastic aircraft pavement design tools.
Mechanistic-empirical design allows the removal of the empirical load versus
thickness curve. However, one or more failure criteria are required to relate the
modelled single load stress, strain or other damage indicator, to the number of
allowable load applications of that magnitude. The modes of failure modelled
generally include vertical deformation in the subgrade (rutting) and tensile
cracking of all bound layers (fatigue). Of these, the subgrade deformation
(rutting) mode is generally the critical failure mechanism for aircraft pavements.
Failure criteria for layered elastic design tools are generally developed by
calibration against the results of the S77-1 design curve to provide a tie to
reality. This should result in the various tools returning essentially the same
thickness requirements.
Layered Elastic Design Federal Aviation Administration (LEDFAA) is the FAA’s
layered elastic design tool. LEDFAA was originally released in 1995 and
updated in 2004. The 2004 updated included the following changes (Hayhoe,
et al, 2004):
• The strain-repetitions failure criterion became independent of the subgrade
modulus.
• Full scale test data for six wheel aircraft were added to the failure criterion
calibration.
Chapter 1 Introduction
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 8
• The sensitivity of the model was reduced with respect to changes in aircraft
passes.
• All wheels were used for the strain calculations instead of just a single
gear’s wheels.
Whilst LEDFAA allows significant flexibility in the input of various pavement
design parameters, it lacks transparency. One cannot change the failure
criteria and the stresses, strains and deflections are not readily visible. Also, as
the FAA required LEDFAA to produce the same thicknesses as the chart-based
CBR methods, the resultant pavement thicknesses are ‘corrected’ to provide
consistent outputs within the range of traffic mixes considered in the
development of the failure criteria.
Aircraft Pavement Structural Design System (APSDS) is the Australian layered
elastic design tool for aircraft pavements and is based on the road pavement
design tool CIRCLY (MINCAD, 2000). CIRCLY, was developed by the
Commonwealth Scientific and Industrial Research Organisation, Australia
(CSIRO) in the 1970s (Wardle, 1976) and commercialised by MINCAD Systems
in the 1980s.
APSDS calibration processes are detailed by Wardle, et al (2001) and this
calibration is considered compulsory for aircraft pavement design. APSDS
offers the advantage of being able to be tailored by the designer, as well as
including the explicit modelling of aircraft wander. Unlike LEDFAA, APSDS
provides the designer with complete flexibility in the selection of all input
parameters and failure criteria as well as providing ready access to all the
calculated stresses, strains and deflections.
Layered elastic design tools such as APSDS include the ability to generate
damage indicator (stress, strain or deflection) with depth curves (MINCAD,
2000). These damage indicators with depth can be utilised for detailed analysis
of modelled pavement behavior. They can also be used for other purposes,
such as the determination of proof rolling regimes during new pavement
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9
construction. Similarly, comparative assessments of stresses or strains with
depth can reveal the ordinal relative damage caused by two or more aircraft
with seemingly different loading regimes.
1.8 NEW GENERATION LARGE AIRCRAFT
Increasing congestion and predicted growth in air travel influenced the
development of new larger aircraft. The demand for larger aircraft lead Boeing
to design the B777 and Airbus to design the A380. Both of these new large
aircraft include six wheel (in a dual tridem arrangement) landing gear (Drenth,
2002). The B777 was introduced into service in the 1990s whilst the A380
maiden voyage occurred in April 2005.
The extrapolation of the original US Corps of Engineers full scale test result to
the B777 and A380 was considered beyond justification (Rodway, 2003). As a
result, a new phase of full scale aircraft pavement testing was planned. The
National Airport Pavement Test Facility (NAPTF) in Atlantic City, USA, aimed at
developing new design procedures for B777 and A380 aircraft (Drenth, 2002),
was constructed in the 1990s. Testing at the facility continues and to date has
included preliminary testing as well as flexible and rigid pavement performance
tests.
In addition to the US efforts, a program of testing of various A380 wheel
configurations and their comparison to B777 and B747 aircraft have
commenced at Toulouse Blagnac airport in France. The study includes static
and repeated load testing of various pavements of flexible and rigid
construction (Petitjean, et al, 2002). The pavement experimental program at
Toulouse was designed to correlate the extrapolated finite element and layered
elastic theoretical pavement response to full scale A380 loadings (Fabre, 2005).
Prior to the introduction of these large aircraft, designers accepted that the
various landing gear for a particular aircraft had little or no interaction. That is,
the damage caused by one landing gear was sufficiently isolated from the
damage caused by the other landing gears to ignore them. Whilst the fact that
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S77-1 has Alpha curves for up to 24 wheels indicates that the Corps allowed for
gear interaction to be modelled, this was when pavement design was based on
deflection criteria. As vertical strains erode much quicker than vertical
deflections (as one moves horizontally away from the point of load application)
strain based design methods imply less interaction than deflection based
methods would.
The large number of gears and wheels, the close proximity of the various
landing gear and the large mass of the B777 and A380, has seen this premise
be revisited and some design methods such as the FAA’s LEDFAA 1.3, now
utilise all aircraft wheels for design purposes (Hayhoe, et al, 2004). There is
currently no justification for modelling all the wheels of these aircraft, which
results in significantly thicker pavement designs.
A study of comparative subgrade vertical strain under six and four wheel gear
loadings found that subgrade response is more complex than traditional layered
elastic analysis allows. Temperature, wander, accumulated damage and
position of previous loading were all found to affect the recovered and un-
recovered strain under the next load cycle (Hayhoe and Garg, 2002).
1.9 FUTURE DEVELOPMENTS
The introduction of the large B777 and A380 aircraft provide challenges into the
future. The following developments are expected to be issues for flexible
aircraft pavement designers in the near future.
1.9.1 Finite Element Methods
As computer power increases and research into modelling pavement structures
by Finite Element Methods (FEM) improves, the move towards finite element
design methods will continue. Currently, design tools are available which utilise
FEM to calculate the stresses and strains at critical positions in the pavement.
These calculated stresses and strains are, however, generally still related to an
allowable number of load repetitions through empirical performance criteria.
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Whilst it would be advantageous to develop a fully mechanistic design tool, this
is considered to be unlikely in the foreseeable future. A fully mechanistic
design tool would be free of empirical relationships and would be expected to
include additional failure mechanisms such as asphalt deformation and granular
material densification. Whilst the computer power and analytical methods are
available for such a design tool, the ability to accurately model the plastic
stress, strain and deformation states of each element in the mesh of each
pavement layer remains the weak link. The variable nature of crushed
aggregates, the difficulty in producing consistent material samples for
characterisation testing and the variability of characterisation testing results
further complicates this challenge. It would be more reasonable to expect that
FEM design tools with elastic material parameters would be developed in the
near future. Such a tool would allow the granular materials’ stress dependence
to be modelled and the modulus values assigned based on the material type as
well as the stress state. As such a model would be restricted to elastic
response of the materials, a failure criterion for plastic deformation of the
subgrade would still be required and would remain an empirical relationship.
1.9.2 Replacement of S77-1 design curve
With additional full scale testing being undertaken at Atlantic City as well as
Toulouse, the generation of a replacement S77-1 design curve would be
appropriate. This replacement curve would include the impact on flexible
aircraft pavements of the B777 and A380 aircraft which impose aircraft loading
regimes that greatly exceed the reliability of the original full scale testing of the
US Corps of Engineers. Following the ratification of a replacement S77-1
curve, re-calibration of design tools such as APSDS would be required.
1.9.3 Modelling of alternate materials
The characterisation of pavement materials such as cemented base and sub-
base layers continues (White and Gnanendran, 2005). Improved methods of
determining the modulus of these materials and improved fatigue life models
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are expected to find their way into APSDS and other layered elastic design
tools.
1.10 AIMS AND METHODS
1.10.1 Aims
The aim of this research was to identify and provide potential solutions to a
number of weaknesses in the current operation and use of APSDS. This
overarching aim has resulted in a number of sub-aims that include:
• Review the existing software and identify potential improvements.
• Validate the software to confirm its suitability for aircraft pavement design.
• Present general guidance to designers on the selection of input parameters.
• Determine which of the input parameters that pavement thickness is most
and least sensitive to.
• Provide material equivalence factors that are implied by APSDS and
compare them to those recommended by the FAA.
• Develop a methodology for determining proof rolling regimes for aircraft
pavement construction using the stress with depth function of APSDS.
1.10.2 Methods
In achieving these aims, a range of methods have been employed. Literature
searches have been undertaken and the empirical basis of aircraft pavement
thickness determination established. A review of the software was conducted
based on experience with its use for practical engineering purposes.
Significant numbers of parametric runs have been performed to calculate many
pavement thicknesses for a range of aircraft, subgrades and other input
parameters. These parametric runs were designed to allow each of the aims of
the research to be achieved. The runs were generally developed using
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statistical methods of experimental design. Statistical analysis of the pavement
thicknesses calculated was employed in each stage of the investigation. This
provided for statistically sound conclusions to be drawn.
Stress, strain and deflection with depth data was calculated using appropriate
functions within APSDS. This data was generated for aircraft and common
proof rollers so that proof rolling could be determined by comparing the effects
of the two loads.
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Chapter 2 Aircraft Pavement Structural Design System
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2. AIRCRAFT PAVEMENT STRUCTURAL DESIGN SYSTEM
2.1 GENERAL
APSDS is a layered elastic design tool for the thickness determination of
flexible aircraft pavements. APSDS is based on the road thickness design tool
Circly, which was developed in Australia in the 1970s. Whilst a tool with many
advantages, APSDS also has room for improvement. The inception and
development of Circly is presented along with the implementation of APSDS.
The inputs and outputs are described along with the calibration of the software
to empirical full scale testing. Advantages over other aircraft pavement
thickness design tools are presented as well as areas for potential future
developments.
2.2 INCEPTION AND DEVELOPMENT
2.2.1 Origins
The first mechanistic-empirical design methods were developed in the 1950s.
An Australian layered elastic tool was developed in the 1970 and became
known as Circly.
The Circly layered elastic algorithm was developed by Gerrard and Harrison
(1971) at the CSIRO. This program allowed an extension of Boussinesq’s
(1885) work to calculate stresses, strains and deflections at various depths,
induced by circular loads of uniform contact pressure. Gerrard and Harrison’s
work was furthered by Wardle (1976) and the first Circly user’s manual was
published in 1977 (Wardle, 1977). In these early stages, the Circly program
was a main-frame based program and ran at the limits of the then available
computer power.
2.2.2 Circly
In 1988 Circly was commercialised by Mincad Systems (Mincad, 1999). This
early version of the commercialised Circly was a PC DOS based program. The
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program Circly, which was a complete design tool, included a modified version
of the layered elastic algorithm of the same name.
Circly was re-released (Version 2.4) as a Windows based program in 1996.
Later in 1996, Version 3 was released and this included many improvements
such as a revised algorithm for the stress and strain calculations as well as
automation of the sub-layering systems for granular materials (Mincad, 1999).
In 1999, Version 4 was released and saw the inclusion of automated thickness
determination options as well as the generation of the Cumulative Damage
Factor (CDF) for multiple layers in one run.
Most recently, Circly Version 5 was released in 2004 (Wardle and Copley,
2004) and included many improvements consistent with the revision of the
Australian road pavement design guide (Austroads, 2004). This version of
Circly also included features for direct input of weigh-in-motion traffic data and
economical analysis of pavement design options based on user defined
construction and maintenance costs (Wardle and Copley, 2004).
2.2.3 APSDS
APSDS was initially developed in response to a request by the Australian
Federal Airports Corporation (FAC). The initial development was funded by
Pioneer Road Services Pty Ltd (PRS) and a prototype computer program was
produced by PRS’s Ian Rickards. Whilst the user interface and some inputs
were modified to suit the requirements of aircraft pavement design, the layered
elastic module is the same Circly algorithm. APSDS was first released by
Mincad Systems in a Windows based version in 1996. The revisions then
closely followed the release of Circly Version 2.4. The current version of
APSDS, Version 4, was released in mid 2000 and is currently under revision.
2.2.4 HIPAVE
Heavy Industrial Pavement Design System (HIPAVE) is a sister program of
APSDS. It is specifically designed to cater for the unique (variable container
mass on standard vehicle/wheel configuration) loading regime of container
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terminals. HIPAVE is also based on the Circly layered elastic algorithm.
HIPAVE was released as a test version in 2004 (Wardle and Oldfield, 2005).
2.3 OVERVIEW AND OPERATION
APSDS, like most layered elastic tools for flexible pavement thickness design,
calculates indicators of damage induced in the modelled pavement by a single
load application. The single load induced damage indicator is then related to
an allowable number of load repetitions of the same magnitude. This
relationship, known as the performance relationship or failure criterion, remains
an empirical tie to full scale pavement performance.
The use of the program is relatively straightforward. One selects and inputs a
series of parameters and then the software generates the stresses and strains
induced in the pavement. The effects of all aircraft in the traffic mix are
determined and a CDF is computed for each nominated transverse distance
from the centerline. If the CDF computed is 1.0, then the pavement is modelled
to fail at the end of the nominated design life. If the CDF exceeds 1.0, the
pavement is modelled to fail before the design life has expired.
Due to the accurate nature of the inputs and outputs associated with layered
elastic design, there is a risk of users interpreting the results as being similarly
accurate. However, the accuracy of APSDS can not be any better than the
accuracy and interpretation of the full scale testing to which it is calibrated
through the various failure criteria. Users therefore require an understanding of
the appropriateness of the value selected for each of the various inputs. The
limitations of the data to which the program is calibrated and the practical
accuracies that can be expected for the outputs is also important to understand.
2.3.1 Inputs
Some inputs are specific to the design scenario being considered whilst others
are more general in nature and would normally be common to all reasonable
design scenarios. APSDS allows modification of almost all inputs, including
those considered to be standard and not design scenario specific. Some inputs
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are stored in libraries within APSDS whilst other information is input for each
design scenario. These are described in the following sections.
2.3.1.1 Library Inputs
APSDS contains two libraries of data, one for layers and the other for loads.
Each is stored as a Microsoft Access database file.
The ‘layers’ database contains material information. The information stored for
each material is dependent upon the material type. Materials include:
• Asphalt.
• Cemented.
• Unbound granular.
• Subgrade.
For each material, the user can assign or modify the modulus and Poissons’
ratio values and choose either isotropic or cross anisotropic conditions. Whilst
asphalt, cemented materials and subgrades are considered to be homogenous
and isotropic, granular materials can be sub-layered to help address the stress
dependency issue. A single modulus can also be assigned to a non-sub-
layered granular material.
The requirement for sub-layering reflects the stress dependence of these
materials and is well documented in literature such as Barker and Brabston
(1975). A number of options for sub-layering of granular materials is available,
however, because APSDS (as with most other pavement design procedures)
relies on calibration to empirical performance data, the sub-layering system
used in design must be the same as that used in the calibration process. In the
case of aircraft pavements, the Barker and Brabston (1975) sub-layering
routine has been accepted as being suitable and was used for the APSDS
calibration process (Wardle, et al, 2001). Therefore, this sub-layering system
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must be used to ensure consistence between the model and the empirical data
against which the tool was calibrated.
Once any given layer is identified as a material type, the layer is provided with a
thickness as well as a boundary condition (rough or smooth). In the case of
subgrades, the layer is considered to be semi-infinite in the vertical direction.
Each material can be assigned a performance criterion. Current layered elastic
design protocol is to consider the following performance criteria (Huang, 1993):
• Cumulative vertical deformation at the top of the subgrade (rutting).
• Horizontal tensile fatigue initiating at the bottom of bound layers (fatigue).
Other potential failure mechanisms are assumed to be taken into account and
prevented from occurring by suitable material selection and adequate
construction. For example, internal vertical deformation within asphalt is
assumed not to occur through suitable asphalt mix design and compaction
during construction.
APSDS stores aircraft load information in the ‘loads’ library. Whilst a number of
aircraft come built-in to APSDS, additional aircraft are commonly required. The
loads database includes the following database hierarchy:
• Aircraft.
• Load groups.
• Load locations.
‘Aircraft’ are those aeroplanes being considered in any given design scenario.
Unlike the materials which may be encountered, aircraft are clearly defined and
limited in number. For each aircraft, a number of load groups may be
considered. Many aircraft have only two load groups (the nose wheel group
and the main gear groups). Because the main gears are generally assumed
not to interact, only one main gear group is defined and only one half of the
Chapter 2 Aircraft Pavement Structural Design System
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pavement structure is considered. However, some aircraft, such as the B747,
have more than one main gear on each side of the aircraft and the MD-11
aircraft has a significant centrally located belly gear. As some 95% of aircraft
mass is carried by the main gears, the nose gear group is generally ignored in
design. Each modelled load group has a constant contact tyre pressure
assigned and a portion of the total aircraft mass nominated.
For each load group, the actual load locations are also defined. These load
locations represent the location of each of the aircraft tyres. Each aircraft tyre
is assumed to carry an equal share of the load group’s portion of the aircraft
mass.
Whilst it is common to assume a constant contact pressure over the area of
each aircraft tyre, APSDS provides for complex load distributions with non-
constant contact pressure. The complex loading options also provide for
horizontal stresses to be modelled. These are, however, not considered to be
an advantageous addition for aircraft pavement thickness design as subgrade
deformation almost always governs thickness requirements. Therefore,
horizontal stresses are not commonly used.
2.3.1.2 Design Specific Inputs
A number of design specific inputs are required and these are generally not
retained in libraries. Rather, they are stored in an inputs (.cli) file. These
design specific inputs generally define the pavement structure and aircraft
traffic for any design scenario.
Within the pavement structure definition, the following inputs are required:
• Subgrade modulus. The modulus (in MPa) is representative of the elastic
stiffness of the natural ground or fill on which the pavement is to be
constructed. The assignment of subgrade modulus is actually only the
selection of a subgrade material of specific modulus from the ‘materials’
library, rather than an actual modulus entry.
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• Layer thicknesses and materials. The number of material layers, material
types and thicknesses are all definable. Where a design is being prepared,
the thickness of one layer, usually the sub-base, is determined to meet the
aircraft traffic requirements. Under an existing pavement evaluation
scenario, all layer thicknesses (in mm) are defined. For Barker and
Brabston base and sub-base type materials, the modulus is automatically
generated by the software, and is not selected by the designer.
• Asphalt modulus. Whilst defined in the ‘layers’ database, the selection of
an asphalt which represents, primarily through its modulus (in MPa), the
material characteristics and environmental conditions associated with the
design scenario.
• Cemented material modulus. Where cemented materials are considered,
they too are selected to reflect the materials available for the specific design
scenario even though their modulus (in MPa) is actually defined in the
‘layers’ library.
Aircraft traffic for any given design scenario is stored within the ‘loads’ library.
This allows use of a common traffic spectrum across a wide range of pavement
designs. However, the development of an aircraft traffic spectrum is a design
scenario specific input. The elements of an aircraft traffic spectrum include:
• Aircraft. The actual aircraft to be modelled are selected from the ‘loads’
library.
• Aircraft Mass. Whilst the maximum mass of each aircraft (in tonnes) is
commonly input into the ‘loads’ library, often a lesser mass is required for
the design scenario. In some instances, the same aircraft will be modelled
at a number of aircraft masses.
• Aircraft Passes. Each aircraft is assigned a number of aircraft passes.
Aircraft passes is defined as the number of times the aircraft passes a given
cross section of pavement. This is noted as being distinctly different from
coverages, operations or movements.
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• Aircraft wander. Aircraft wander across the width of a pavement from one
aircraft pass to the next. Aircraft wander is defined as the standard
deviation (in mm) of the distribution of aircraft centerlines. Whilst different
aircraft may be considered to wander to different extents, the location of the
pavement at the airfield (runway, taxiway or apron) is considered to govern
the degree of wander and therefore a single standard deviation of wander is
assigned for each design scenario. This is applied to all aircraft in the traffic
spectrum.
2.3.2 Layered Elastic Solution
The layered elastic component of any aircraft pavement design tool is the
method for the calculation of the damage indicators (stresses, strains and
deflections) at pre-determined locations, induced by a single load application.
APSDS uses the Circly algorithm for this purpose. The Circly algorithm is
based on integral transform methods and Bessel functions. This algorithm
computes the principal as well as shear stresses, strains and deflections.
Whilst some previous design methods have used stress and deflection as the
indicator of damage, APSDS uses strain in an effort to alleviate the
overstatement of wheel interaction associated with using stress as the damage
indicator.
The calculated strains of greatest interest are those that occur at points where
performance criteria have been assigned. This is generally the vertical
compressive strain at the top of the subgrade as well as the horizontal tensile
strain at the bottom of the bound layers.
The important unique feature of APSDS is that subgrade strain, or alternative
damage indicator, is computed at all nominated points across the pavement
width in order to capture all damage contributions from all the aircraft, in all their
wandering positions.
Each of the calculated single load event strains is used to calculate an
allowable number of repetitions of that same strain magnitude. This
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relationship between induced strain and allowable number of strain repetitions
is the failure criterion. Whilst other design tools, such as LEDFAA 1.3, have a
single, modulus independent, failure criterion for subgrade rutting (Garg, et al,
2005), APSDS has a separate failure criterion for each subgrade modulus. The
general form of the failure criteria is detailed in Equation 1.
N = (k/ε)b ..............................................................................................Equation 1
Where: N = allowable number of repetitions of strain E.
k = a material constant.
b = damage exponent of the material.
ε = the load induced strain.
More complex forms of the failure criteria are applied to most bound materials.
The damage factor is then calculated based on the modelled and allowable
number of load repetitions of the calculated magnitude of strain using Miner’s
Law. Miner’s Law is detailed as Equation 2.
Damage Factor (DF) = n/N ..................................................................Equation 2
Where: n = modelled number of load repetitions of a given magnitude.
N = allowable number of load repetitions of the same magnitude.
The damage contribution by each aircraft load at each wandering position is
then summed into the CDF for each location across the pavement width. The
pavement is assumed to have reached its end-of-life when the CDF equals 1.0.
2.3.3 Outputs
With all input parameters assigned, the designer runs the software and a range
of computations are performed and a range of outputs are generated.
However, prior to this, the designer is able to select the coordinates and format
of the outputs. Any range of coordinates can be selected for the location of
damage indicator calculation and a range of damage indicators can be selected
Chapter 2 Aircraft Pavement Structural Design System
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for graphical output. In addition, an option to design the required thickness of a
given pavement layer can be used.
Following the operation of the software, the following outputs are generated:
• Printable results file. The output (.clo) file contains the output from the
analysis.
• Job summary file. For record retention, the job summary text file (.txt)
provides a summary of the inputs and outputs. This includes the pavement
structure, aircraft traffic spectrum and CDFs for each pavement layer with
an assigned performance criterion.
• Raw results file. The raw results file (.prn) contains the stresses, strains
and deflections generated by the Circly algorithm.
• Plot files. The DFs for each aircraft and CDF are transferred to a Microsoft
Excel™ spreadsheet for the designated pavement layer. These CDFs are
then used to generate a plots at the selected locations across the width of
the pavement as well as the contribution to the total CDF attributed to each
aircraft load in the traffic spectrum.
In addition to these computer file outputs, the CDFs of the pavement layers with
failure criteria assigned are also displayed within the software. Where the
design layer thickness option is utilised, the determined pavement thickness is
also shown.
2.3.4 Empirical Basis
As described above, the relationship between the induced strain (or alternate
damage indicator) and the allowable number of repetitions of the same
magnitude of strain is known as the material performance relationship or failure
criterion. These failure criteria are generally material modulus specific and
provide the tie between the mechanistic element of the design process and ‘real
life’. For asphalt and cemented materials, relationships based on material
specific testing can be utilised. However, for subgrade materials, the failure
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criteria are based on the results of the full scale testing conducted by the US
Corps of Engineers during the 1940s to 1970s. The combined outcome of the
US Corps of Engineers’ full scale tests is known as the S77-1 design curve as
reported by Pereira (1977). It is to this curve, following adjustment to thickness
for the Corps’ Alpha factors, that APSDS and most other flexible aircraft
pavement design tools are calibrated. The S77-1 curve is shown in Figure 1. It
is recognized that the S77-1 curve is empirical in nature, however it remains the
best international reference for designers and provides a common basis for the
calibration of all current aircraft pavement thickness design methodologies.
2.3.5 Calibration
APSDS is based on the empirical relationships between damage by a single
load application and the number of repetitions until failure. The software must
therefore be calibrated against the original empirical performance relationships
by generation of appropriate failure criteria. For traditional flexible pavements
the most common governing failure criterion is vertical deformation (rutting) of
the subgrade (Rodway and Wardle, 1998). The calibration of the APSDS
subgrade failure criteria to the S77-1 design curve is detailed in Wardle, et al
(2001). Use of these calibrated failure criteria (known as the Chicago Criteria)
is essential to obtaining consistence between APSDS and the S77-1 design
method.
The calibrated subgrade failure criteria are all of the form of Equation 1. The
Chicago Criteria are shown in Table 1 for common subgrade moduli.
Whilst the Chicago Criteria provide a best fit to the S77-1 design curve, which in
turn is a best fit to the combined data from the full scale testing effort,
discrepancies between the S77-1 curve and APSDS (when calibrated with the
Chicago Criteria) occur. Such discrepancies are not unexpected and are
generally minor. This discrepancy is believed to be the result of deflection
being used as the performance indicator in the S77-1 curve whilst strains are
utilised in APSDS (Wardle, et al, 2001).
Chapter 2 Aircraft Pavement Structural Design System
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Table 1 Chicago failure criteria.
Subgrade Modulus (MPa) k b 30 0.0032 9.5 40 0.0032 9.8 50 0.0031 10.3 60 0.0030 10.9 70 0.0029 11.7 80 0.0027 12.6 90 0.0026 13.7
100 0.0024 15.0 110 0.0023 16.4 120 0.0021 18.0 130 0.0020 19.7 140 0.0020 21.6 150 0.0020 23.6
2.3.6 Design Reliability
The S77-1 design curve is a best-fit to the full scale test results. The S77-1
curve and therefore the calibrated APSDS program, is expected to return
designs with a reliability of 50% unless the designer applies factors of safety by
using conservative design input parameter values. There are no built-in factors
of safety in either the design tool or the failure criteria.
2.4 ADVANTAGES AND BENEFITS
APSDS has a number of unique characteristics which give it significant
advantage over other flexible aircraft pavement design tools. These
advantages are considered likely to be the reason for its popularity and are
described in the following sections.
2.4.1 Fully Transparent
Every aspect of the system, with the exception of the calculation of the
stresses, strains and deflections, is fully transparent and able to be modified.
Whilst the damage indicator calculations are not available, all of the calculated
values of stress, strain and deflection are visible at all nominated pavement
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locations and depths. This allows stress with depth and other similar plots to be
readily generated. The modelling of materials is completely flexible in all
aspects. The location, composition and interaction of loads are also completely
visible and adjustable.
This transparency and ability to control all the inputs parameters provides for
rapid assessment of ‘what if’ scenarios. Designers can very rapidly determine
what effect the change of one or more input parameters can have on the
required thickness design or the life of the pavement at the same thickness.
This provides great advantage in considering the reliability of design solutions
and investigation of the impact of selecting certain values for the various input
parameters.
2.4.2 Aircraft Wander
The incorporation of aircraft wander allows the contribution to damage of all
aircraft in the traffic spectrum, in all their wandering positions, to be calculated
at all locations across the pavement. This contrasts with most previous design
methods which computed single maximum values (under a single tyre or
centroid of a single wheel group) of the damage indicator only. It is this feature
that eliminates the need for the traditional pass-to-coverage concept and allows
the designer to specify any degree of aircraft wander (Mincad, 2000).
2.4.3 Cumulative Damage Factor
The calculation and visibility of the CDF at all locations across the pavement
width and the contribution to the CDF of all aircraft in the traffic spectrum is
highly advantageous. This allows the more critical aircraft to be easily identified
as well as revealing the areas of the pavement which are most likely to fail first.
The graphical output of the CDF across the pavement width makes the
interpretation of this information very easy. This allows non-technical staff to
readily interpret the output of the pavement design process.
Chapter 2 Aircraft Pavement Structural Design System
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2.4.4 Thickness Design Option
By utilising the thickness design option, the selected pavement layer is
automatically selected, trialed and adjusted until a CDF of 1.0 is returned. This
allows quick and easy design of pavements without requiring manual trial and
adjustment runs of the software.
2.4.5 Free from Bias
The freedom and flexibility of the software is allowed as it is not intended to
implement any particular or regulated design procedure. Other software, such
as LEDFAA, is designed to automate the FAA chart based design method and
therefore restricts layer thickness and moduli values to those allowed by the
chart-based methods.
Further, programs such as LEDFAA are forced to return design thicknesses
which are consistent with the FAA chart based design method for ‘typical’
aircraft traffic mixes. This means that any difference between the S77-1 and
the layered elastic thicknesses are ‘corrected’ to provide consistency between
the chart-based and layered elastic solutions (Hayhoe, et al, 2004).
APSDS’ freedom from factors of safety or bias means that the designer can
obtain 50% reliability or ‘best-fit’ thickness designs. The designer can then
utilise judgment and experience in selecting input parameters and observing
their effect on the design thickness and subsequent pavement design reliability.
2.5 POTENTIAL IMPROVEMENTS
Whilst the many advantages of APSDS make it a very attractive pavement
design tool, there remains room for improvement within the software. Some of
the potential areas for improvement are detailed in the following sections.
2.5.1 User Interface
Since the conversion of APSDS to a Windows based tool in 1996, the user
interface has become increasingly simple and familiar to users of other
Chapter 2 Aircraft Pavement Structural Design System
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29
Windows-based applications. The format and accessibility of the output is,
however, an area that could be improved.
The basic output for any given design scenario should be printed and stored on
file if replication or confirmation is ever required in the future. The formatting of
the output files are such that this is not readily achievable in an efficient
manner. For example, the output is formatted with a large number of spaces,
rather than tab stops, making reading of any output report difficult as the
columns of data rarely align.
Benefit would also be gained from the ability to cut and paste the computed
stresses, strains and deflections. This would be especially useful where stress
with depth analyses are being undertaken, and the stress at a range of pre-
specified depths below the pavement surface is required to be copied into an
Excel™ spreadsheet or similar application. Currently, to use a spreadsheet
program, one is required to manually enter the data. This is both laborious and
error prone.
2.5.2 Out of Range Calculations
With the ability to input almost any combination of input parameters and
pavement structures, the ability to stretch the range of the reliability of the
design method is also possible. Whilst this in itself is not considered a problem,
the tendency to create non-solvable situations is. For example, the Barker and
Brabston (1975) sub-layering procedures are modelled by mathematical
equations relating the underlying layer’s stiffness and the next layer’s stiffness.
This procedure has a limit to the modulus that can be assigned any given layer.
This limit is not truly reflected in the software and by selecting certain
combinations of material in various layers, one can exceed the automated
limits. In particular, by modelling a layer of natural gravel over a layer of fine
crushed rock, negative modulus values of the natural gravel can be calculated.
This is clearly nonsensical but no ‘out of range’ error message is generated.
The addition of out of range errors in this and other scenarios would be of
benefit.
Chapter 2 Aircraft Pavement Structural Design System
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 30
2.5.3 Parametric Run Automation
When performing a large number of designs or when performing parametric
runs of the software for research or investigatory purposes, one is required to
input the parameters, manually run the software, change the parameters and
continue. There is no automation tool. Such a tool would allow a large range of
parameter combinations to be automatically run without human interaction.
This would potentially save researchers significant time, as well as allowing the
number of parametric runs being performed to be increased and subsequently
increase the number of results and the associated value of the research
conclusions.
2.5.4 Reliability Based Design
The S77-1 design curve is a best fit curve. Therefore, the calibrated APSDS is
a best fit design tool. That is, the model will return a 50% design reliability for
any given set of input parameters where vertical subgrade deformation is the
governing failure mode. This also may not take into account the variability of
assigned material properties. However, the failure criteria for bound materials,
such as cement stabilised and asphalt materials, are generally not a best fit
curve as they have been developed with in-built factors of safety based on
laboratory and field performance. This mixing of best fit and higher reliability
failure criteria is not considered appropriate but is generally accepted on the
basis that subgrade deformation is commonly the governing failure mode.
The calibration of APSDS to the best fit S77-1 curve means that designers are
required to increase the reliability of their designs through the selection of
conservative input parameters. A more formal approach to design reliability
could be achieved through the re-calibration of the failure criteria to a modified
version of the S77-1 curve with 90% (or some other) level of reliability assigned.
Alternatively, a Monte-Carlo or other simulation could be developed which
would allow the designer to gain an appreciation of the design outcome’s
probability of success and the gain in reliability achieved with any given
increase in pavement thickness. Given the advantage provided by the
Chapter 2 Aircraft Pavement Structural Design System
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
31
unbiased nature of the software, the latter is considered to be the preferred
approach.
2.5.5 Aircraft Mass Distributions
Aircraft in APSDS are assigned a specific operating mass. Whilst any given
aircraft can be assigned any specific mass, modelling of two masses for the
same aircraft (say landing mass and take off mass) requires that the aircraft be
modelled as two separate aircraft of the same type. With the introduction of a
container mass distribution input tool for HIPAVE (Wardle and Oldfield, 2005), it
would be relatively simple to incorporate an aircraft mass distribution input for
APSDS. This would allow more accurate modelling of the range of aircraft
operating masses to be incorporated, where that information is available to the
designer.
2.6 SUMMARY
APSDS is a layered elastic design tool for flexible aircraft pavement thickness
determination which is based on the road pavement design tool Circly. The
designer inputs a range of design parameters and the software perform a
number of calculations and produces design outputs. The calculations
performed are the determination of a damage indicator which is then related to
an allowable number of magnitudes of that load. This relationship is known as
the failure criteria and provides the tool a tie to full scale empirical test results.
Whilst APSDS offers many advantages, there are specific issues which could
also be improved to make the tool even more valuable to designers.
The advantages that APSDS holds over other design tools for flexible aircraft
pavements are many. These include being fully transparent, being free from
bias and uniquely catering for aircraft wander to avoid to PCR concept. Areas
where the tool could be improved in the future include:
• Improvement of the user interface.
• Provision of out of range calculations where appropriate.
Chapter 2 Aircraft Pavement Structural Design System
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 32
• Allowing automation of parametric runs for research purposes.
• Incorporation of a reliability based design output.
• Allowing input of variable aircraft masses for a single load group.
Chapter 3 Validation of APSDS
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
33
3. VALIDATION OF APSDS
3.1 GENERAL
To confirm the applicability of this investigation, which included using APSDS to
generate pavement thicknesses, a validation was required to confirm its
operation. APSDS comes ready to use from MINCAD Systems and requires
little set-up. However, APSDS does not come with the Chicago Criteria built-in.
It was therefore necessary to enter these calibration constants and perform a
validation of the software.
3.2 VALIDATION PROCESS
In order to validate the software, the following steps were undertaken:
• Entering the Chicago Criteria calibration constants.
• Selection of inputs.
• Calculation of a number of pavement thicknesses using APSDS.
• Calculation of equivalence pavement thicknesses using S77-1.
• Comparison of thicknesses generated by the two methods.
Each of these steps is discussed in the following sections.
3.2.1 The Chicago Criteria
Wardle, et al (2001) provides subgrade calibration constants for APSDS at
subgrade moduli values of 30, 60, 100 and 150 MPa. Formulae are provided to
allow the calculation of calibration constants at other subgrade modulus values.
These formulae were utilised to calculate the calibration constants contained in
Table 1. These values were entered into APSDS and new subgrade materials
created which utilised these calibration constants.
Chapter 3 Validation of APSDS
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 34
3.2.2 Selection in Inputs
The validation was performed following the bulk of the research presented in
this thesis. This meant that the validation was considered to be a confirmatory
process more than an active validation. The input parameters were therefore
selected from the inputs adopted for the various investigations undertaken as
part of this project, specifically the sensitivity analysis.
The inputs parameters selected are detailed in Table 2.
Table 2 Input Parameters.
Design input parameter Units Values Subgrade Modulus MPa 30, 60, 100, 150
Aircraft Type Not Applicable B747, B767, B737 Aircraft Mass % of maximum 60, 80, 100
Aircraft Passes Number 5000, 10000, 20000
3.2.3 Calculation of APSDS thicknesses
The APSDS pavement thicknesses were adopted from those calculated for
other stages of this investigation based on the input parameters detailed above
and using the Chicago Criteria.
3.2.4 Calculation of S77-1 thicknesses
S77-1 thicknesses were calculated using the software COMFAA. These were
recorded and entered into an Excel™ spreadsheet. The COMFAA determined
S77-1 thicknesses are contained in Appendix 1.
3.2.5 Comparison of APSDS and S77-1
Figure 2 shows the APSDS thicknesses against the S77-1 thicknesses. This
figure shows general agreement between the two design tools.
Chapter 3 Validation of APSDS
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
35
Figure 2 S77-1 versus APSDS Thicknesses.
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600 1800 2000S77-1 Thickness (mm)
APS
DS
Thi
ckne
ss (m
m)
B747 B767 B737 Unity
3.3 ANALYSIS OF RESULTS
The residuals are shown in Figure 3. These show that the magnitude of the
difference between S77-1 and APSDS was up to 90 mm for the 108 design
scenarios considered. The mean difference was 36 mm (6.7% of the S77-1
thickness) whilst the median difference was 33 mm (4.8% of the S77-1
thickness).
This analysis shows that APSDS has generally good agreement (R2 = 0.82)
with S77-1 when the Chicago Criteria are used. This analysis has been
performed for B737, B767 and B747 aircraft which span the range of common
commercial jet aircraft in Australia.
Chapter 3 Validation of APSDS
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 36
Figure 3 S77-1 versus APSDS Differences.
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120
Run
Res
idua
l (m
m)
3.4 SUMMARY
A validation of APSDS was performed by comparing thickness calculated from
this software to those calculated from the original S77-1 empirical design curve.
The comparison covered a range of 108 design scenarios, including medium to
large passenger jet aircraft in Australia and a wide range of subgrade moduli.
The analysis showed good general agreement between APSDS and S77-1 with
a median difference of 36 mm (or 6.7% of the S77-1 thickness).
Based on this analysis, it is considered that S77-1 is confirmed as being a valid
tool for aircraft pavement thickness design. This serves to validate the use of
the software for the remaining research presented in this thesis.
Chapter 4 Input Parameter Selection
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4. INPUT PARAMETER SELECTION
4.1 GENERAL
APSDS, like all computer-based design tools, is only a tool for the conversion of
design input parameters to design outputs. In the case of flexible aircraft
pavement thickness design, the outputs are pavement layer thicknesses or an
indication of pavement adequacy for a given thickness. The selection of input
parameters, which are appropriate is therefore the focus of the designer.
4.2 INPUT PARAMETERS
The inputs required to conduct an aircraft pavement design in APSDS are:
• Subgrade modulus. In MPa.
• Aircraft wander. As a standard deviation of wander in mm.
• Aircraft data. Including mass (in t), tyre pressure (in MPa) and number of
passes.
• Pavement structure. Including the type and thickness of each layer as well
as the modulus for materials which are not automatically sub-layered by the
Barker and Brabston (1975) method. For flexible pavements, this is
generally only the asphalt surface layer.
Appropriate input parameter value selection for any design scenario, should
concentrate on the parameters which have the greatest influence on the
required pavement thickness. The selection of an appropriate value of each
input parameter is described in the following sections.
4.3 SUBGRADE STRENGTH
The purpose of a pavement is to protect the subgrade from the loads imposed
by aircraft and other traffic (Pereira, 1977). The loads are applied to the
pavement surface through the aircraft tyres and then the pavement layers
spread the load until the stresses and strains induced by the load are small
Chapter 4 Input Parameter Selection
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 38
enough to be accommodated by the next lower layer. The deepest portion of
the pavement structure is the subgrade and therefore pavement design focuses
on the load which can be accommodated by the subgrade material. It is
however acknowledged that in reality, damage accumulation can occur within
the pavement layers.
The development of the S77-1 design curves by the US Corps of Engineers in
the 1960s and 1970s expressed subgrade strength by the CBR. CBR is a
dimensionless unit calculated as being the resistance of a soil to the penetration
of a standard piston, as a percentage of the resistance offered by a reference
material (Californian Limestone) (DOD, 1964).
The actual field CBR test is cumbersome, expensive and for existing
pavements, requires significant disturbance of the insitu structures. Therefore,
a number of alternate test methods have been developed in order to simplify the
field work whilst maintaining some correlation to the original test method (Holtz
and Kovacs, 1981). Alternatives to the insitu field CBR test, commonly
available in Australia, include:
4.3.1 Laboratory CBR
Whilst this is a less expensive and relatively simple test, the problem of
obtaining a sample which is representative of the moisture conditions, density
and soil structure in the field is problematic. Soaked (usually 4 or 7 days) and
unsoaked tests are available with varying degrees of overpressure.
4.3.2 Dynamic Cone Penetrometer
The Dynamic Cone Penetrometer (DCP) is a device designed for field
determination of subgrade stiffness which is measured through resistance to
penetration of a standard cone. This cone is dynamically penetrated by the
dropping of a standard weight over a standard height. Guidance for the
conversion of penetration (blows per mm of penetration) to subgrade CBR is
provided but this conversion was derived for fine grained cohesive soils only
Chapter 4 Input Parameter Selection
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39
(AS 1289, 1997). Similar penetrometers are available in other countries under
different names.
4.3.3 Associated material characteristics
By measuring associated material characteristics, an indicative CBR can be
assigned by comparison to the CBR of materials with similar properties.
Commonly used characteristics are the particle size distribution and the
plasticity of the fines (Holtz and Kovacs, 1981).
Of these, the laboratory CBR is the most common test for the determination of
material CBR on green field sites, where materials will be moistened and
compacted and therefore representation of field conditions at the time of
sampling is not appropriate. For existing pavement investigations, the
remolding of laboratory samples to an appropriate density and moisture content
is common and is often supplemented by insitu DCP tests.
It is normal to soak a CBR sample for four days prior to conducting the CBR test
(Huang, 1993). Common Australian practice has been to either adopt the four
day soaked test result or, where existing pavements are available on the same
site, test at the equilibrium moisture content identified under the existing
pavements.
US Corps of Engineer practice is to conduct laboratory CBR tests in a soaked
state, at a range of densities. The design CBR is then read from a plot of
density versus CBR, for a density equivalent to 95% of the maximum density.
The US Corps of Engineers also allow an un-soaked CBR determination in arid
regions (Ahlvin, 1991). Recent US FAA guidelines stipulate the use of a four-
day soaked test for laboratory CBR determination. This is based on the
premise that subgrades reach near saturation under pavements within about
three years of construction (FAA, 1989). The four-day soaked CBR test does
not, however, take into account the pore pressure state of the subgrade under
the pavement.
Chapter 4 Input Parameter Selection
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 40
Take two specimens of identical subgrade material compacted to the same
density at precisely the same moisture content. One sample is retained at zero
pore pressure whilst the other has a negative pore pressure applied. The
sample with negative pore pressure would behave as a significantly stiffer and
stronger subgrade than the zero pore pressure sample. Similarly, a sample
with positive pore pressure would perform more poorly than both samples.
Pore pressures are generally induced in subgrade materials by the relative
height of the water table to the material. No method for incorporating pore
pressure into subgrade CBR selection was identified. Engineering judgment
and experience must be applied in this regard or it must be nominated.
Regardless of the method of selection of subgrade strength in terms of CBR, it
must be converted to a modulus for use in APSDS. The conversion from CBR
to modulus utilised is an inherent part of the S77-1 design model and was
formalised by Barker and Brabston (1975). The conversion is shown in
Equation 3.
M = 10 × CBR...................................................................................... Equation 3
Where: M = Modulus of the Subgrade in MPa
CBR = Californian Bearing Ratio of the Subgrade as a percentage
Whilst other methods for converting from CBR to modulus are available, the
current version of APSDS was calibrated using this conversion. Therefore, this
empirical conversion must also be used for practical purposes.
Given the high influence of subgrade CBR on thickness required, the selection
of an appropriate subgrade CBR is critical to pavement design. This is
especially the case for low subgrades where a change of one CBR unit can
have a great impact on pavement thickness.
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41
4.4 AIRCRAFT WANDER
Unlike road and highway pavements, aircraft pavements are subjected to a
significant transverse distribution of loads. This distribution of loads is
commonly referred to as aircraft wander. An issue related to aircraft wander is
that aircraft have significantly different wheel configurations, and therefore, even
at zero aircraft wander, the point of load application transversely across the
pavement can be significantly different for different aircraft types. The effect of
aircraft wheel configuration and aircraft wander combine to distribute damage
across the width of the aircraft pavement and effectively increases the service
life compared to that which would be expected under channelised traffic.
APSDS caters for aircraft wander by applying the nominated number of load
repetitions across the width of the pavement, based on a nominated standard
deviation of aircraft wander, assuming traffic is normally distributed (MINCAD,
2000). The incorporation of aircraft wander into aircraft pavement design tools
negates the requirement to utilise PCR. PCRs are necessary to relate passes
to coverages for other design tools such as LEDFAA (FAA, 1995a) and the
FAA’s chart based methods (FAA, 1995).
A number of studies have been undertaken to measure the actual wander of
aircraft on pavements. These studies have concluded that the wander of
aircraft changes with the pavement area being considered. For example,
aircraft on a runway will land and takeoff with a greater degree of wander
across the pavement than aircraft moving slowly along a straight taxiway
pavement. Under marshal or Nose In Guidance Systems (NIGS) aircraft
parking on aprons, or at aerobridges, would be expected to have the smallest
degree of wander.
Table 3 provides the findings of two studies regarding the degree of aircraft
wander on different areas of aircraft pavement. They are considered
appropriate where site or project specific information is not available, which it
rarely is.
Chapter 4 Input Parameter Selection
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 42
Table 3 Aircraft Wander Standard Deviation.
Pavement Area HoSang (1975) US Army/Air Force (1988) Runway 1800 mm – 3400 mm 1550 mm Taxiway 800 mm – 1800 mm 770 mm
Whilst no specific literature was located, MINCAD (2000) suggests that 200 mm
may be an appropriate standard deviation of wander for parking positions. The
following wander standard deviations are commonly used in Australia:
• Runway. 1550 mm
• Taxiway. 773 mm
• Apron. 200 mm
4.5 AIRCRAFT MASS
Each aircraft has a measurable and exact mass at which it operates on any
given area of aircraft pavement. In addition, all aircraft have published,
certified, maximum operating masses, referred to as the Maximum All Up Mass
(MAUM). Aircraft rarely operate at their MAUM and therefore, to utilise their
MAUM in pavement design is a conservative approach, especially given their
high influence on pavement thickness. Mass can vary significantly for any given
aircraft make, type and variant. In commercial operations, additional weight
implies greater fuel burn and therefore more expensive operations. Also, at
many airfields, large aircraft cannot operate at their MAUM due to runway
length requirements on takeoff.
APSDS allows the input of any aircraft mass. Therefore the effect of different
assumed operating masses can be readily assessed. The mass should be
selected to be within the range of operating masses for the design aircraft and
should be based on some sensible estimate of the likely mass for the majority of
operations. Aircraft operators record aircraft masses for each and every flight
and therefore the actual information is available but may need to be
Chapter 4 Input Parameter Selection
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43
summarised or combined into a number of operations of aircraft at one or two
typical or characteristic masses.
4.6 AIRCRAFT TYRE PRESSURE
Just as each aircraft is certified to operate at a published MAUM, it is also
published with a standard operating tyre pressure. However, in practice, aircraft
maintainers will adjust the tyre pressure to provide an appropriate mass/tyre
pressure combination. This is done to limit the amount by which a tyre deforms
during operations. APSDS allows the input of any tyre pressure for each
aircraft being designed for. However, it is common practice to adopt the
standard operating tyre pressure at all operating weights of the aircraft. This is
a slightly conservative approach to pavement design. Tyre pressures generally
have little effect on pavement thickness required but do cause problems within
the asphalt surfacing.
4.7 NUMBER OF PASSES
The number of aircraft passes is the number of times the design aircraft travels
past any given cross section of aircraft pavement during the design life. This is
distinctly different from coverages, operations, movements and departures. The
number of passes of each of the design aircraft must be determined based on:
• Design life of the pavement. Typically 10 or 15 years is adopted for
flexible aircraft pavements based on the time between asphalt overlays
being required due to environmental degradation.
• Configuration of the pavement. The ratio between departures and passes
will be affected by the airfield layout, including the number of runways,
parallel taxiway and parking arrangements.
• Traffic growth. Like road traffic, aircraft traffic is assumed to grow over
time with an annual growth rate of 3% being a reasonable approximation (in
Australia) in the absence of project specific information.
Chapter 4 Input Parameter Selection
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 44
APSDS allows any number of passes to be assigned for each aircraft
considered in the design traffic.
4.8 ASPHALT MODULUS
As for all materials used to model aircraft pavements in APSDS, asphalt is
assigned a modulus. This modulus is considered to be an elastic resilient
modulus. The measurement of asphalt modulus is not an exact science. Its
measurement is expensive and time consuming and is generally not justified on
a project basis (Sukumaran, et al, 2002). Unlike base and sub-base materials,
which have an automated method for modulus assignment within APSDS
(based on Barker and Brabston (1975)) asphalt moduli are assigned by the
designer for each design scenario.
Asphalt modulus varies with pavement temperature, load duration, asphalt age
and induced confining stress. Therefore, any particular asphalt mix will exhibit a
large range of moduli during its life. However, a constant asphalt modulus (per
design scenario) is required by APSDS.
Procedures are available which relate air temperature to pavement
temperature, and in conjunction with bitumen penetration data, to asphalt
modulus. One method was developed by Heukelom and Klomp (1964) and
described in Brabston, et al (1975). Due to the cost associated with such
methods, it is normal for designers to assume a typical value of asphalt
modulus. Table 4 provides some guidance on typical asphalt moduli values in
various Australian environmental conditions. Given the low influence of asphalt
modulus on pavement thickness, adoption of presumptive or typical values is
generally appropriate.
Chapter 4 Input Parameter Selection
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45
Table 4 Typical asphalt moduli.
Environment Moduli Asphalt in northern and tropical regions.
Young asphalt in moderate regions. 1000 MPa
Mature asphalt in moderate regions. Young asphalt in southern and alpine regions.
2000 MPa
Mature asphalt in southern and alpine regions. 3000 MPa
4.9 PAVEMENT STRUCTURE
The pavement structure is clearly a design specific issue and guidance can not
readily be provided as to what pavement structure is suitable in the various
design environments one might encounter. Therefore, the following issues are
identified for consideration only.
4.9.1 Cemented materials
Whilst cemented materials are available and have been used on Australia
aircraft pavement design practice, they are less common. The concern with
cemented materials is their tendency to crack, due to local and environmental
factors, and the potential for cracks to reflect into the bound asphalt layer.
Where cemented materials have been used, they have commonly been overlain
by an unbound granular layer which acts as a stress dissipater and retards the
reflection of cracks into the asphalt surface.
4.9.2 Asphalt thickness
The thickness of asphalt surfacing in Australian aircraft pavement design
practice is generally 40 mm to 60 mm as this provides a generally economical
pavement structure. In the USA and other countries, thicker asphalt layers are
common. However, a significant number of Australian pavements that have
been subject to multiple overlays have 200 mm or more of asphalt.
Chapter 4 Input Parameter Selection
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 46
4.9.3 Base course thickness
Base course materials are commonly utilised in thicknesses of between
100 mm and 400 mm, depending on the size of the aircraft. The larger the
aircraft the thicker the base course required to protect to sub-base material from
over stressing.
4.9.4 Fill layers
Fill layers have been used in instances where great thicknesses are required
over the subgrade. This is generally associated with weak subgrades or where
the finished surface level greatly exceeds the natural surface level and full
pavement depth is governed by geometric requirements rather than pavement
strength.
4.10 DESIGN TRAFFIC MIX
The aircraft traffic mix or spectrum is clearly a design specific issue. Little
guidance can therefore be provided. The aircraft traffic spectrum includes the
following elements which are discussed for consideration only.
4.10.1 Aircraft Variants
Aircraft often have a number of variants. These variants can have significantly
different load characteristics. For example, the B737-100 has a maximum mass
of 45.4 t and tyre pressure of 1.02 MPa. In contrast, the B737-800 has a mass
of 79.2 t and a tyre pressure of 1.30 MPa. These two variants of the B737 also
have slightly different wheel configurations, with the space between the dual
tyres of the B737-300 being 775 mm but 864 mm for the B737-800. Further,
the B737-500, which has a maximum mass of 60.8 t and tyre pressure of
1.34 MPa, has the B737-300’s wheel spacing.
4.10.2 Masses and Tyre Pressures
As previously discussed, the mass and tyre pressure of the aircraft in the traffic
mix is required. Any number of masses and tyre pressures can be entered by
Chapter 4 Input Parameter Selection
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47
each additional combination requires an additional entry in the aircraft load
table. It is therefore normal for designers to adopt the standard tyre pressure
and to rationalise all aircraft traffic to one or two representative masses.
4.10.3 Number of Aircraft Passes
APSDS allows any number of passes to be assigned for each aircraft
considered in the design traffic. These should be selected based on information
from the airport operator.
4.11 SUMMARY
The use of APSDS is relatively simple but if the input parameters are not
appropriately selected, gross errors in the resulting design thickness can occur.
Therefore, the following input parameters should be appropriately selected
based on the design scenario and experience:
• Subgrade Strength.
• Aircraft Wander.
• Aircraft Mass.
• Aircraft Tyre Pressure.
• Number of Passes.
• Asphalt Modulus.
The aircraft traffic mix and pavement composition (base course thickness and
asphalt thickness) must also be determined. When a designer selects these
input parameters, effort should be concentrated on the parameters that have
the greatest influence on pavement thickness required. Less effort or
conservative estimates would be generally acceptable for the less influential
parameters. To determine the relative influence of the various input
parameters, a sensitivity analysis of APSDS is required.
Chapter 4 Input Parameter Selection
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 48
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
49
5. SENSITIVITY ANALYSIS
5.1 GENERAL
The key to successful aircraft pavement design using APSDS is the selection of
input parameters. With a general guide for the selection of the main parameters
provided, a designer may ask which of these to concentrate on. Using the
Pareto principle (Lawson and Erjavec, 2001), the parameters which should be
concentrated on are those which have the greatest influence on the outcome.
An understanding of the sensitivities of flexible aircraft pavement thickness to
the various input parameters is therefore desired.
5.2 INVESTIGATION UNDERTAKEN
An investigation was undertaken to determine the effect of the various input
parameters on the total thickness of flexible aircraft pavements. The
investigation included the parametric operation of the program under a range of
reasonable values of each input parameter. The combination of these input
parameters resulted in some impractical pavement solutions. Therefore, these
investigations should not be used as the basis of any pavement design.
During these investigations, some aspects of the input parameters were held
constant. These constants are discussed below.
5.2.1 Aircraft Traffic
For this investigation three aircraft were selected to represent the range of
medium to large domestic and international passenger jet aircraft currently in
operation. These were the B737, B767 and B747. The selected aircraft, their
MAUM and standard tyre pressure, are shown in Table 5. The selection of
Boeing aircraft is representative of their current dominance in the Australian
aviation industry. However, the analysis is equally applicable to similarly sized
alternate aircraft such as the Airbus A340, A300 and A320.
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 50
The B747 has outer and inner main landing gears. These gears are modelled
separately in APSDS and their separate contributions to pavement damage are
summed. The B777 and the A380 were specifically excluded from the analysis
as their six-wheel landing gear configurations were not included in the
calibration of the program to the S77-1 design curves (Wardle, et al, 2001) and
therefore the subgrade failure criteria do not adequately model these aircraft.
Table 5 Aircraft Information.
Aircraft MAUM (t) Standard Tyre Pressure (kPa) B747-400 397 1380 B767-300 180 1240 B737-800 79 1360
5.2.2 Pavement Structure
The standard pavement structure utilised during the testing in the US by the
Corps of Engineers to develop the S77-1 design procedure was (Pereira, 1977):
• 75 mm asphalt.
• 150 mm P209 (fine crushed rock base).
• Variable thickness of P154 (natural gravel sub-base).
• Variable CBR subgrade.
P209 (crushed aggregate base course) and P154 (sub-base course) are US
FAA specifications for airfield pavement materials (FAA, 1989). For this
investigation, the pavement structure illustrated in Figure 4 was adopted.
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
51
Figure 4 Pavement Structure.
5.2.3 Input Parameters
For this sensitivity analysis, values of the various input parameters required by
the program were selected to span the range normally encountered in practice.
The combination of parameter values for any given run was not necessarily
giving valid results, with some combinations returning non-solutions
(theoretically negative thicknesses of sub-base). The input parameters and the
values adopted for this investigation one detailed in Table 6.
Table 6 Input Parameters.
Design input parameter Units Values Subgrade Modulus (SM) MPa 30, 60, 100, 150
Aircraft Wander (W) mm 200, 800, 1400, 2000 Aircraft Mass (M) % of maximum 60, 80, 100
Tyre Pressure (TP) % of standard 80, 90, 100 Aircraft Passes (P) Number 5000, 10000, 20000
Asphalt Modulus (AM) MPa 1000, 2000, 3000 Asphalt Thickness (AT) mm 20, 40, 100 Base Thickness (BT) mm 100, 300, 500
It is noted that the Aircraft Mass were set to percentages of the MAUM of each
aircraft and that Tyre Pressures were set to percentages of the standard tyre
pressure for each aircraft.
20, 40 or 100 mm of asphalt of modulus 1000, 2000 or 3000 MPa
100, 300 or 500 mm of P209 B&B Base
Variable thickness (mm) of P154 B&B Sub-base
Variable CBR (%) Subgrade
Note: ‘B&B’ denotes a sub-
layering and modulus
assignment method in
accordance with Barker
and Brabston (1975).
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 52
5.3 SENSITIVITY ANALYSIS
The sensitivity analysis undertaken was based on statistical experimental
design and analysis methods. In particular, the analysis included linear
regression modelling and Analysis of Variance (ANOVA) tools (Lawson and
Erjavec, 2001). The statistical analysis of all data was performed using the tool
MINITAB (MINITAB, 2000). The sensitivity analysis is described in the following
sections.
5.3.1 Investigation Design
Initially, every combination of input parameters values was intended to be
utilised and for each, a total pavement thickness determined. However, for the
input parameter levels detailed in Table 6, this would require 42 × 36 = 11,664
runs of the program, for each aircraft considered, to cover all combinations.
Therefore, a fractional analysis was designed to allow the main effects and
influences of the parameters on total pavement thickness to be determined with
only 512 runs of the program, for each aircraft. The number of runs, 512, was
selected as a reasonable number that could be performed whilst allowing clear
identification of each input’s influence on pavement thickness. The parametric
run design is contained in Appendix 2.
5.3.2 Parametric Runs
Each of the 512 combinations of input parameter values was used to generate a
pavement thickness in APSDS for each of the three aircraft. Each run was
performed using the ‘determine design thickness’ function of the program for the
sub-base course and then the Total Thickness in mm of pavement was
calculated by adding the relevant thickness of asphalt and base course to the
sub-base thickness returned.
The total thickness of pavement was recorded for each run and then input into
MINITAB for analysis. The sub-base thicknesses ranged from ‘Not Applicable’
(where the pavement was more than sufficient without any sub-base course) up
to 1657 mm (a 1,777 mm total pavement thickness). Where a theoretically
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
53
negative sub-base thickness was returned for the B747 aircraft, the base and
asphalt thicknesses were amended to require some sub-base thickness.
Where B737 or B767 aircraft returned a theoretically negative sub-base
thickness for the B747 adopted base and asphalt thicknesses, a ‘Not
Applicable’ result was recorded. In total, 81 runs required changes to the base
and asphalt thickness for the B747. For the B767 and B737, 22 and 43 runs of
the program returned a ‘Not Applicable’ respectively. The results from the
parametric runs are contained in Appendix 3.
5.3.3 Simple Linear Regressions
Initially, simple linear regressions were performed on the total pavement
thickness for each aircraft. This was aimed at determining the consistency
between sensitivity of the pavement thickness to the various aircraft considered.
The linear regression models detailed as Equations 4 to 6 were derived for the
B747, B767 and B737 respectively.
TTB747 =1145 - 6.65 × SM - 0.0349 × W + 5.80 × M - 1.24 × TP + 0.00409 × P
- 0.0318 × AM - 0.797 × AT - 0.260 × BT (R2 = 0.81)..........................Equation 4
TTB767 = 1038 - 5.93 × SM - 0.0370 × W + 5.67 × M - 1.34 × TP + 0.00327 × P
- 0.0318 × AM - 0.813 × AT - 0.225 × BT (R2 = 0.80)..........................Equation 5
TTB737 = 837 - 4.62 × SM - 0.0321 × W + 4.61 × M - 0.564 × TP + 0.00309 × P
- 0.0264 × AM - 0.698 × AT - 0.210 × BT (R2 = 0.89)..........................Equation 6
Where: TTBXXX = Total thickness (for aircraft type)
SM = Subgrade modulus in MPa
W = Standard deviation of aircraft wander in mm
TP = Tyre pressure in MPa
P = Aircraft passes
AM = Asphalt modulus in MPa
AT = Asphalt thickness in mm
BT = Base course thickness in mm
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 54
The R2 (coefficient of determination) values are indicators of the goodness of fit
of the data to the linear models. The results are plotted against their modelled
values in Figure 5. The line of unity is also shown.
Figure 5 General Model Results
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600 1800 2000
APSDS thickness (mm)
Mod
elle
d th
ickn
ess
(mm
)
B747 B767 B737 Unity
The residuals for each model are shown in Figure 6, plotted against the order of
the runs. This figure clearly shows the non-linear nature of the data and the
associated positive residuals for subgrade modulus of 30 (first 128 runs) and
150 (last 128 runs). Residuals generally had a magnitude of less than 200 mm
with some as large as 400 mm.
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
55
Figure 6 General Model Residuals
-300
-200
-100
0
100
200
300
400
500
0 128 256 384 512
Run
Res
idua
l (m
m)
B747 B767 B737
5.3.4 Separate Subgrade Linear Regressions
For each aircraft, four additional linear regressions were performed. These
provided linear relationships between pavement thickness and the input
parameters for each subgrade modulus. For the B767 aircraft, the regression
models are expressed as Equations 7 to 10. The APSDS thicknesses are
plotted against in modelled thicknesses in Figure 7. Each model’s residuals are
plotted against the general subgrade model (Equation 4 to Equation 6) residuals
in Figure 8, Figure 9 and Figure 10 for the B747, B767 and B737 respectively.
TT30 = 151 - 0.0376 × W + 13.8 × M - 0.374 × TP + 0.00847 × P - 0.0304 × AM
- 0.687 × AT - 0.204 × BT (R2 = 0.99) .................................................Equation 7
TT60 = 188 - 0.0447 × W + 7.64 × M - 0.420 × TP + 0.00563 × P - 0.0254 × AM
- 0.521 × AT - 0.205 × BT (R2 = 0.99) .................................................Equation 8
TT100 = 232 - 0.0148 × W + 4.01 × M - 0.606 × TP + 0.0023 × P - 0.0171 × AM
- 0.454 × AT - 0.158 × BT (R2 = 0.98) .................................................Equation 9
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 56
TT150 = 178 - 0.0143 × W + 2.99 × M - 0.910 × TP + 0.0012 × P - 0.0126 × AM
- 0.463 × AT - 0.158 × BT (R2 = 0.99) ...............................................Equation 10
Where: TTxx = Total thickness (for subgrade modulus for B767)
SM = Subgrade Modulus in MPa
W = Standard deviation of aircraft Wander in mm
TP = Tyre Pressure in MPa
P = Aircraft Passes
AM = Asphalt Modulus in MPa
AT = Asphalt Thickness in mm
BT = Base course Thickness in mm
Figure 7 Specific Model Results
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 200 400 600 800 1000 1200 1400 1600 1800 2000APSDS thickness (mm)
Mod
elle
d th
ickn
ess
(mm
)
B747 B767 B737 Unity
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
57
Figure 8 Residuals for General and Specific Subgrade Models for B747
-500
-400
-300
-200
-100
0
100
200
300
400
500
0 128 256 384 512
Run
Res
idua
l (m
m)
General Subgrade model Specific Subgrade Models
Figure 9 Residuals for General and Specific Subgrade Models for B767
-500
-400
-300
-200
-100
0
100
200
300
400
500
0 128 256 384 512Run
Res
idua
l (m
m)
General Subgrade model Specific Subgrade Models
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 58
Figure 10 Residuals for General and Specific Subgrade Models for B737
-500
-400
-300
-200
-100
0
100
200
300
400
500
0 128 256 384 512
Run
Res
idua
l (m
m)
General Subgrade model Specific Subgrade Models
Figure 8 to Figure 10 show that the adoption of four specific subgrade models
reduced the maximum residuals from around 400 mm to 70 mm for all three
aircraft considered. This is combined with improved R2 values for the subgrade
specific models, indicating that pavement thickness is, generally, linear with
respect to all input parameters (when subgrade modulus is removed).
5.3.5 Consistence across Aircraft
An assessment of the consistency of pavement thickness with regard to the
input parameters across the three aircraft types was performed by calculating
the ratio of pavement thickness between each pair of aircraft (B747 and B737,
B747 and B767 as well as B767 and B737) against the pavement thickness
(average for the aircraft in the ratio) with all other factors held constant.
Figure 11 illustrates these ratios for the three aircraft considered in this analysis.
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
59
Figure 11 Thickness Ratio Consistency.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Average Pavement Thickness (mm)
Thic
knes
s R
atio
B747 to B767 B747 to B737 B767 to B737
Figure 11 shows that the ratios between pavement thicknesses required for the
various aircraft are relatively consistent for all other combinations of the input
parameters. Therefore, the sensitivity of pavement thickness to the input
parameters is considered to be essentially independent of the aircraft being
considered. With consistence across aircraft confirmed, the examination of
sensitivities could be undertaken.
5.3.6 Normalised Sensitivities
To determine the comparative influence of the input parameters on the total
pavement thickness, each parameters’ values (ranging from the smallest to
greatest reasonable value) were given a scale ranging from one to five (1 =
minimum, 3 = average , 5 = maximum). This allowed comparison of all input
parameters on a single chart. These ‘normalized’ parameters were plotted on
the same axis against the total pavement thickness with all other parameters
held constant. The relative influence of the normalised parameters can be
inferred from the relative slope of the resulting lines, which are illustrated in
Figure 12, Figure 13 and Figure 14 for the B747, B767 and B737 aircraft
respectively.
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 60
Figure 12 Relative Influence of Design Inputs for B747.
0
200
400
600
800
1000
1200
1400
1600
0 1 2 3 4 5 6
Normalised Input Value
Tota
l Pav
emen
t Thi
ckne
ss (m
m)
Subgrade Modulus Aircraft Wander Aircraft Mass Tyre PressureAircraft Passes Asphalt Modulus Asphalt Thickness Base Thickness
Figure 13 Relative Influence of Design Inputs for B767
0
200
400
600
800
1000
1200
1400
1600
0 1 2 3 4 5 6
Normalised Input Value
Tota
l Pav
emen
t Thi
ckne
ss (m
m)
Subgrade Modulus Aircraft Wander Aircraft Mass Tyre PressureAircraft Passes Asphalt Modulus Asphalt Thickness Base Thickness
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
61
Figure 14 Relative Influence of Design Inputs for B737.
0
200
400
600
800
1000
1200
1400
1600
0 1 2 3 4 5 6
Normalised Input Value
Tota
l Pav
emen
t Thi
ckne
ss (m
m)
Subgrade Modulus Aircraft Wander Aircraft Mass Tyre PressureAircraft Passes Asphalt Modulus Asphalt Thickness Base Thickness
It can be seen from Figure 12 to Figure 14 that the relative influence of the input
parameters on total pavement thickness is consistent for all three aircraft
considered. It can also be seen that the subgrade modulus has the greatest
influence on pavement thickness (demonstrated by the greatest slope or
gradient).
5.3.7 Relative Influence
The gradient of each line represents the change in the modelled pavement
thickness resulting from a unit change in that input parameter’s normalised
value. Each gradient represents the relative ‘influence’ of that input parameter
on pavement thickness. The modelled linear influences of all input parameters
are summarised for each aircraft in Table 7. It is noted that the influence of
subgrade modulus is taken as the average gradient over the full length of the
curved line based on a straight line between the two ends.
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 62
Table 7 Normalised Linear Influence and Importance
Influence Importance Factor 1 normalised unit equals B747 B767 B737 B747 B767 B737
Subgrade Modulus
30 MPa 200 178 139 43.4 40.2 54.6
Aircraft Wander 450 mm 16 17 14 4.7 5.2 8.0 Aircraft Mass 10 % 58 57 46 14.6 14.8 21.4 Tyre Pressure 5 % 6 7 3 1.6 1.8 1.3 Aircraft Passes 3750 15 12 12 4.0 3.3 5.6
Asphalt Modulus
500 MPa 16 16 13 2.0 2.1 3.1
Asphalt Thickness
20 mm 16 16 14 4.1 4.4 6.7
Base Thickness 100 mm 26 23 21 5.8 5.1 8.4
Table 7 also contains an ‘importance’ value for each input parameter for each
aircraft model. Importance is used to express the statistical significance of the
parameter on the pavement thickness and is a measure of the probability that
the input parameter could be removed from the model. The larger the
importance (the t-statistics from the test for the hypothesis that the coefficient is
equal to zero) the more significant the parameter is in the model and the greater
the analysis suggests that it should not be removed.
5.4 ANALYSIS OF RESULTS
From the analysis undertaken, the input parameters which are most significant
in the linear models for total pavement thickness are subgrade modulus and
aircraft mass. Aircraft wander, aircraft passes, asphalt thickness and base
course thickness are also important whilst tyre pressure and asphalt modulus
are essentially insignificant (as expected).
The relative importance and influence of the input parameters on the total
pavement thickness is consistent for all three aircraft considered. This is shown
by the summary in Table 7 and confirmed by the thickness ratio plot in
Figure 11. Given that these aircraft all have differing wheel configurations and
span the breadth of size of medium to large jet aircraft currently in operation
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
63
(excluding the B777 and A380) this analysis is considered to be generally
applicable to all medium to heavy jet aircraft. Further, its general application to
all medium to heavy jet aircraft suggests its application to combinations of
aircraft (traffic mixes) for which pavement thickness is governed by one or more
medium to large aircraft within the mix.
With the exception of subgrade modulus, the influence of the various input
parameters on the total pavement thickness is essentially linear as shown in
Figure 12 to Figure 14. In the case of subgrade modulus, a small change is far
more influential on pavement thickness at low subgrade modulus values than at
higher ones. Therefore, a general linear model covering all subgrade values is
not appropriate. Linear models developed for specific subgrade modulus,
however, are far more accurate as all other input parameters influence
pavement thickness in a generally linear manner. This is demonstrated by the
comparison of general and specific model residuals in Figure 8 to Figure 10.
5.5 SUMMARY
An analysis was conducted to determine the sensitivity of APSDS calculated
pavement thicknesses to the various input parameters required. Each input
parameter was varied over the range of commonly encountered values.
Designers should concentrate their efforts on the determination of subgrade
modulus and aircraft mass, as these input parameters have the greatest
influence on the total pavement thickness. Less effort should be spent on the
other influential parameters, and the use of reasonably conservative estimates
are generally appropriate. Presumptive values of tyre pressure and asphalt
modulus are usually adequate because these factors have only minor impact on
computed pavement thickness when failure of the pavement is governed by
subgrade deformation.
Total pavement thickness is essentially linearly responsive to all the program
inputs except for subgrade modulus. The relationship between subgrade
Chapter 5 Sensitivity Analysis
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 64
modulus and pavement thickness is clearly nonlinear. Modulus changes are
more influential at lower values than at higher ones.
The sensitivity of total pavement thickness to the various input parameters is
essentially consistent for all three medium to large jet aircraft considered.
Because these aircraft cover the range common medium to large jet aircraft in
current use, this sensitivity analysis is also considered to be applicable to all
medium to large jet aircraft and aircraft traffic mixes containing significant
numbers of at least one medium to large jet. Therefore, for all design traffic
scenarios, the design inputs which should be given the most attention by the
designer are subgrade modulus and aircraft mass.
Whilst not the most influential input parameters, pavement composition (asphalt
thickness and base course thickness) are important input parameters. Where
consistence between APSDS and FAA design procedures (which are based on
material thickness equivalences instead of layered elastic methods) is desired,
the APSDS implied material equivalence is critical.
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
65
6. MATERIAL EQUIVALENCE
6.1 GENERAL
The S77-1 design curve provides the total pavement thickness required. This
thickness, however, is deemed to comprise of a standard S77-1 pavement
structure. Where alternate pavement structures are considered, their
equivalent thicknesses are determined using material equivalence principles.
Material equivalence factors required to perform these conversions are
contained in the FAA’s guide to aircraft pavement thickness design (FAA,
1995). The FAA guide provides ranges of equivalence factors between various
materials and these ranges are quite broad. Designers therefore tend to adopt
the mid-range values for most applications.
Layered elastic design tools have generally been calibrated to the S77-1 design
curve. These layered elastic design tools commonly use an automated sub-
layering routine which was developed by Barker and Brabston (1975) to divide
each granular material layer into a number of sub-layers and assign a modulus
value to each. Two values of equivalence could be selected from with the FAA
range and result is significantly different total pavement thicknesses.
There was believed to be an inconsistency between the FAA mid-range values
of material equivalence and those implied by layered elastic design using
Barker and Brabston sub-layering techniques. This study provides more
accurate material equivalences for crushed rock base course, uncrushed gravel
sub-base and asphalt, with the aim of providing consistence with APSDS
implied equivalences. These recommended new material equivalence values
could be included in future updates of the FAA guidance.
6.2 S77-1 AND FAA PAVEMENT DESIGN
Aircraft pavement thickness design originated as, and continues to be, an
empirical based design method. Even when so-called mechanistic design tools
are used, the performance relationship, or failure criterion, remains an empirical
relationship developed from full scale testing results. The failure criterion is a
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 66
mathematical relationship between the damage indicator (commonly stress,
strain or deflection) modelled under a single load event and the number of
allowable repetitions of that level of loading. The current design methods are
therefore more appropriately termed mechanistic-empirical.
For flexible aircraft pavement design, the governing failure mode is usually
vertical subgrade deformation (rutting). The empirical performance relationship
for subgrade deformation was derived from full scale testing conducted by the
US Corps of Engineers and reported by Pereira (1977). The relationship
between aircraft loading, subgrade strength and pavement thickness required is
known as the S77-1 curve and this remains the empirical basis for most flexible
aircraft pavement design tools today.
The S77-1 curve provides a pavement thickness of a pre-determined
composition. The standard S77-1 pavement structure is shown in Figure 15.
P401, P209 and P154 are standard designations for the described materials,
utilised by the FAA for design and specification purposes (FAA, 1995).
Figure 15 Standard S77-1 Pavement Structure.
Where other pavement structures are considered, they must be converted to
the equivalent thickness of S77-1 pavement. Material equivalence factors are
provided in the FAA design guide (FAA, 1995) as detailed in Table 8. The
guide also provides equivalence factors for others materials including lean mix
concrete, soil cement and cemented crushed rock.
75 mm of 1400 MPa Asphalt (P401)
150 mm of Crushed Rock (P209)
Variable Uncrushed Gravel (P154)
Variable CBR subgrade
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
67
Table 8 FAA Material Equivalence Guidance.
1 mm of this material Is equivalent to the following thickness (mm)
Of this material
Asphalt (P401) 1.2 to 1.6 Crushed rock (P209) Crushed rock (P209) 1.2 to 1.8 Uncrushed gravel (P154)
Asphalt (P401) 1.7 to 2.3 Uncrushed gravel (P154)
The FAA documentation provides little guidance on when the low, medium and
high values in the various ranges detailed in Table 8 should be used. In
practice, for materials at the same relative density, a range of equivalences
would be expected due to:
• Differences in the material quality. A good quality fine crushed rock
would be more beneficial, in comparison to a standard uncrushed gravel,
than a poor fine crushed rock would be. Therefore, a good fine crushed
rock would have a greater equivalent thickness of standard uncrushed
gravel than what the same thickness of a poor fine crushed rock would.
• Stress conditions. Given the stress dependent nature of granular
materials the equivalence between two materials would be expected to vary
depending on the loading applied as well as the depth within the pavement
that the replacement occurs. Both of these factors will affect the stress
conditions under which the material is required to perform.
Generally, without better guidance, designers will utilise the mean value of the
range of equivalences. This study examines the material equivalences implied
by APSDS and examines their consistence with the FAA guidance.
6.3 INVESTIGATION UNDERTAKEN
The investigation undertaken was designed to meet the following objectives:
• Confirm any inconsistence between S77-1 and APSDS pavement thickness
when adopting the mid-range of the FAA equivalence ranges.
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 68
• Determine alternate or specific equivalence factors to provide improved
consistence.
• Investigate the cause of any variability in the APSDS implied equivalences.
• Confirm the suitability of the recommended equivalence factors by
performing a number of example calculations.
As the investigation evolved, it comprised of three main stages. In all stages,
the general approach was to perform a number of parametric operations of
APSDS and determine the APSDS implied equivalence factors before
comparing them to the FAA provided values. The three stages of the
investigation were:
• Practical pavement equivalences. The material equivalences implied
from designing various practical or typical pavement structures was
determined. Typical pavements were determined for a range of typical
medium to large aircraft on commonly encountered subgrade conditions.
Different combinations of layer thicknesses were determined, each able to
cater for the modelled number of aircraft passes.
• Isolated pavement equivalences. In order to isolate layer properties from
aircraft and pavement variables, single wheel load was applied and granular
pavement layers were not sub-layered. Materials were modelled as
homogenous materials of a pre-determined modulus and compared to
materials of other moduli values. Pavement thicknesses were determined
so that the vertical compressive strains modelled at the top of the subgrade
were equal to those modelled by a standard layer thickness. The aim of this
portion of the study was to examine the replacement material properties
(modulus, thickness and location) that affect the implied material
equivalence.
• Equivalence Examples. A number of pavement structures were designed
directly by APSDS and by S77-1 and the two pavement thicknesses were
compared using the FAA mid-range equivalences and the recommended
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
69
equivalence factors. This was designed to confirm the appropriateness of
the recommended equivalence factors as well as demonstrating their
application.
The details of each stage of the investigation are described in the following
sections.
6.4 PRACTICAL PAVEMENT EQUIVALENCES
In order to assess material equivalence for practical use, the APSDS implied
equivalences were determined for common and realistic design scenarios. This
analysis is detailed as follows.
6.4.1 Aircraft Traffic
For this stage of the investigation, three aircraft were selected to represent the
range of medium to large domestic and international passenger jet aircraft
currently in operation in Australia. The selected aircraft, their maximum mass
and standard tyre pressure are shown in Table 5 for consistence with the
sensitivity analysis previously discussed.
6.4.2 Pavement Structure
For this investigation, the pavement structure illustrated in Figure 4 was
adopted. This pavement structure is that utilised for the sensitivity analysis
previously discussed. A consistent pavement structure was selected to allow
re-use of the raw data collected during the sensitivity analysis’ parametric runs
of APSDS.
The number of Asphalt versus Crushed Rock and asphalt versus Uncrushed
Gravel equivalence determinations for each aircraft considered is detailed in
Table 9. For these parametric runs, the ‘design layer thickness’ option was
utilised for the uncrushed gravel layer. Where crushed rock versus asphalt
equivalence was required, a constant uncrushed gravel thickness was needed.
This was not available from the sensitivity analysis data. Therefore the crushed
rock thickness was selected as the ‘design layer thickness’.
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 70
Table 9 Number of Practical Equivalence Determinations.
Aircraft Equivalence
B747-400 B767-300 B737-800 Asphalt and Crushed Rock 128 122 109
Crushed Rock and Uncrushed Gravel 245 223 202 Asphalt and Uncrushed Gravel 164 155 141
The difference in the number of equivalence determinations for each aircraft
exists as a result of some pavements not returning a positive pavement layer
thickness for the layer being designed. This was most pronounced for the
lighter B737 aircraft, which requires the thinnest pavement of the three aircraft.
6.4.3 Design Parameters
The values of each of the parameters considered in the parametric runs of
APSDS are detailed in Table 10. The combination of input parameters for each
parametric run of APSDS was derived using the Plackett-Burman method of
statistical experimental design (Lawson and Erjavec, 2001). The parametric
design is contained in Appendix 4 and the results are contained in Appendix 5.
Table 10 Design Parameter Values for Practical Equivalence.
Parameter Units Values Subgrade Modulus MPa 30, 60, 100, 150
Aircraft Wander Mm 200, 800, 1400, 2000 Aircraft Mass % of maximum 60, 80, 100 Tyre Pressure % of standard 80, 90, 100 Aircraft Passes Number 5000, 10000, 20000
Asphalt Modulus MPa 1000, 2000, 3000 Asphalt Thickness Mm 20, 40, 100
Crushed rock Thickness Mm 100, 200, 400
6.4.4 Material Equivalence
Material equivalence was determined for each pair of parametric runs where all
design parameters were identical, with the only difference being the
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
71
thicknesses of the two materials being considered. The equivalences were
calculated using Equation 11.
EA/B = (TA - TA2)/(TB2 - TB1) .................................................................Equation 11
Where: EA/B = Thickness of A that is equivalent to 1 mm of B
TA1 = Thickness of material A in pavement 1
TA2 = Thickness of material A in pavement 2
TB1 = Thickness of material B in pavement 1
TB2 = Thickness of material B in pavement 2
Where pavement 1 and pavement 2 are considered to be equivalent in
structural capacity and are identical in all aspects except for the thicknesses of
material A and material B. Equation 11 was utilised as it provides for the
thickness of one material that can be directly replaced by another material and
result in the same structural capacity pavement.
Graphical representations of the calculated material equivalence for the three
aircraft considered are shown in Figure 16, Figure 17 and Figure 18, for the
Asphalt and Crushed rock, Crushed rock and Uncrushed gravel and Asphalt
and Uncrushed Gravel respectively. Figure 16 to Figure 18 also contain the
minimum, maximum and mid-range value of the material equivalence guidance
provided by FAA (FAA, 1995).
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 72
Figure 16 Practical Equivalence for Asphalt and Crushed Rock.
1.0
1.2
1.4
1.6
1.8
2.0
2.2
0 20 40 60 80 100 120 140
Run
Equi
vale
nce
Rat
io
B747 B767 B737 FAA Max FAA Ave FAA Min
Figure 17 Practical Equivalence for Crushed Rock and Uncrushed Gravel.
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0 50 100 150 200 250
Run
Equi
vale
nce
Rat
io
B747 B767 B737 FAA Max FAA Ave FAA Min
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
73
Figure 18 Practical Equivalence for Asphalt and Uncrushed Gravel.
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
0 20 40 60 80 100 120 140 160
Run
Equi
vale
nce
Rat
io
B747 B767 B737 FAA Max FAA Ave FAA Min
These figures show that the material equivalence implied by layered elastic
design tools is consistently at the lower range of the FAA guidance for the
materials considered. Summary statistics for the three equivalences are shown
in Table 11.
Table 11 Summary Statistics for Practical Equivalence.
Statistic Asphalt and
Crushed Rock Crushed Rock and Uncrushed
Gravel
Asphalt and Uncrushed
Gravel Mean 1.33 1.19 1.57
Standard Deviation 0.17 0.04 0.21 Coefficient of Variation 12.7% 3.0% 13.3%
Maximum 2.10 1.32 2.50 Upper Quartile 1.37 1.21 1.65
Median 1.30 1.19 1.51 Lower Quartile 1.22 1.17 1.45
Minimum 0.90 1.04 1.15 Range 1.20 0.28 1.35
Inter-quartile range 0.15 0.04 0.20
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 74
As a check, the equivalence between Asphalt and Crushed Rock, when
multiplied by that for Crushed Rock and Uncrushed Gravel, should equal that
for Asphalt and Uncrushed Gravel. Based on the mean equivalences
presented in Table 11, this is 1.33 × 1.19 = 1.58, which is very close to 1.57.
Some impractical equivalences are returned such as 0.90 for the equivalence
between Asphalt and Crushed Rock as shown in Figure 16. This implies that
replacing a certain material (Asphalt) with a less stiff material (Crushed Rock)
will reduce the overall pavement thickness. This is not sensible and is the
result of anomalies created by the automatic sub-layering and stiffness
assignment caused by slight changes in the layer thicknesses requiring
different numbers of sub-layers.
Significant variability in the material equivalence is observed, especially for
thicker pavements, which generally relate to low subgrade modulus values.
Further analysis was required to explain the cause of this variance. This
included the preparation of box and whisker plots for each material equivalence
for each aircraft. These are shown in Figure 19 (Asphalt and Crushed
Rock),Figure 20 (Crushed Rock and Natural Gravel) and Figure 21 (Asphalt
and Natural Gravel).
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
75
Figure 19 Summary of Asphalt and Crushed Rock Equivalences
0.80
1.00
1.20
1.40
1.60
1.80
2.00
2.20
B747 B767 B737
Aircraft
Equi
vale
nce
Figure 20 Summary of Crushed Rock and Uncrushed Gravel Equivalences
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
B747 B767 B737
Aircraft
Equi
vale
nce
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 76
Figure 21 Summary of Asphalt and Uncrushed Gravel Equivalences
1.00
1.20
1.40
1.60
1.80
2.00
2.20
2.40
2.60
B747 B767 B737
Aircraft
Equi
vale
nce
Figure 19 to Figure 21 shows that whilst the range of equivalences is large (eg.
1.20 for Asphalt and Crushed Rock), the inter-quartile range (which represents
the range of the central 50% of values) is quite low (eg. 0.15 for Asphalt and
Crushed Rock).
The aircraft type (B747, B767 and B737) was not a statistically significant
predictor of material equivalence. This is clearly shown in the similarity
between the three box and whisker plots contained in each of Figure 19 to
Figure 21. As the equivalences are not generally affected by the aircraft and
therefore further analysis considers the combined data only.
A number of linear regressions were performed on the combined aircraft data
utilised to determine the various practical material equivalences. These
regressions showed that subgrade modulus, asphalt modulus, uncrushed
gravel thickness and crushed rock thickness were generally statistically
significant predictors of material equivalence. These significant parameters can
all be related to the thickness and modulus of the various layers in the
pavement structure.
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
77
The regressions also showed that aircraft wander, aircraft mass, number of
passes and tyre pressure were not statistically significant. These factors are
independent of the pavement composition and materials.
From the linear regressions performed, simple models for the prediction of
material equivalence were determined. These are detailed in Equation 12 (for
asphalt versus crushed rock), Equation 13 (for crushed rock versus uncrushed
gravel) and Equation 14 (for asphalt versus uncrushed gravel).
ECR/AC = 1.14 + 0.00099 × SM + 0.00014 × AM +0.00025 × ST
(R2 = 0.36) ........................................................................................Equation 12
EUG/CR = 1.20 – 0.00045 × SM + 0.00012 × AT (R2 = 0.34)................Equation 13
EUG/AC = 1.62 – 0.00311 × SM + 0.00014 × AM + 0.00047 × BT
(R2 = 0.49) .........................................................................................Equation 14
Where: ECR/AC = Thickness of CR which is equivalent to 1 mm of AC.
EUG/CR = Thickness of UG which is equivalent to 1 mm of CR.
EUG/AC = Thickness of UG which is equivalent to 1 mm of AC.
SM = Subgrade Modulus in MPa
AM = Asphalt Modulus in MPa
AT = Asphalt Thickness in mm
BT = Base Thickness in mm
ST = Sub-base Thickness in mm
CR = Crushed Rock
UG = Uncrushed Gravel
AC = Asphalt Concrete
The calculated equivalence and modelled equivalence values are shown in
Figure 22. The line of unity is also shown.
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 78
Figure 22 Practical Equivalence Results
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2Calculated Equivalence
Mod
elle
d E
quiv
alen
ce
Asphalt versus Crushed Rock Crushed Rock versus Natural GravelAspahlt versus Natural Gravel Unity
The residuals from the linear regressions performed to generate these
prediction models were examined. The residuals are shown for each pair of
materials in Figure 23. Analysis of residuals from the linear regressions
showed no evidence that the residuals were not distributed normally with a
mean close to zero. This suggests that the underlying assumptions of the
linear regressions were not contradicted and the analysis and its findings were
therefore appropriate.
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
79
Figure 23 Practical Equivalence Residuals
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 700
Order
Res
idua
l
Aspahlt versus Crushed Rock Crushed Rock versus Uncrushed Gravel Asphalt versus Uncrushed Gravel
6.4.5 Recommended Material Equivalences
Based on the analysis undertaken and the premise that the consistence across
the range of aircraft considered in this study suggests consistence across all
medium to large commercial aircraft, the material equivalences detailed in
Table 6 are recommended. The equivalences should be considered in place of
the broader ranges currently detailed in the FAA design guide (FAA, 1995) for
the conversion of non-standard pavement structures to the equivalent thickness
of standard S77-1 pavement (or vice versa). It is noted that the recommended
equivalence factors presented in Table 12 are generally close to the lower
value in each of the FAA recommended ranges.
Table 12 Recommended Material Equivalences.
Equivalence Symbol Value FAA range Asphalt and Crushed Rock ECR/AC 1.3 1.2 to 1.6
Crushed Rock and Uncrushed Gravel EUG/CR 1.2 1.2 to 1.8 Asphalt and Uncrushed Gravel EUG/AC 1.6 1.7 to 2.3
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 80
Whether the use of these equivalence factors will result in thinner or thicker
pavements than those obtained using FAA’s mid-range values is case specific.
Where an asphalt thickness greater than 75 mm (the thickness in the standard
S77-1 pavement) is designed, the revised equivalence factors will result in a
thicker pavement. Where an asphalt thickness of less than 75 mm is designed,
a thinner pavement results. Where a 75 mm asphalt thickness is designed,
there would be no difference as there is no need to use an equivalence factor.
The same trends would result for non-standard thicknesses of crushed rock.
6.5 ISOLATED PAVEMENT EQUIVALENCES
To explain the variability in the APSDS implied equivalences, the material
properties were isolated and uniform material moduli values were adopted. In
order to obtain uniform moduli values Barker and Brabston sub-layered
materials were omitted in favour of homogenous, single modulus layers. This
analysis is less applicable to typical design situations than the previous analysis
but was undertaken to explain the variance in the observed practical
equivalences. The analysis is detailed as follows.
6.5.1 Aircraft Traffic and Pavement Structure
In order to isolate the material properties and their effects, a simple wheel load
was utilised in the analysis. This simple load consisted of a 20 t load on a
single wheel of 1.25 MPa tyre pressure. In order to further isolate the material
effects, a single load application was assessed and vertical strain at the
subgrade level was utilised to determine the equivalence of various structures.
As the performance criteria for all subgrade materials in APSDS are based on
vertical subgrade strains, this approach is equivalent to the application of a
constant number of repetitions of the simple wheel load.
The reference material adopted was a homogenous layer with a modulus of
500 MPa which is close to the average maximum allowed by the Barker and
Brabston method for Crushed Rock (690 MPa) and Uncrushed Gravel
(275 MPa). For this material, the reference strains were calculated for each of
the subgrade moduli values considered.
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
81
The reference strains were:
• 30 MPa subgrade. 685 με.
• 60 MPa subgrade. 545 με.
• 100 MPa subgrade. 446 με.
• 150 MPa subgrade. 372 με.
6.5.2 Design Parameters
With the simplified aircraft traffic and pavement structure, the only factors to
consider were the subgrade modulus and replacement material layer. The
replacement material factors considered were the thickness, modulus and
location of the replacement material. The design parameters considered are
detailed in Table 13.
Table 13 Design Parameters for Isolated Equivalence.
Parameter Units Values Subgrade Modulus MPa 30, 60, 100, 150
Replacement Modulus MPa 50, 100, 250, 750, 1000, 2000, 4000 Replacement Thickness mm 100, 200, 400, full depth Replacement Location Type Top, bottom, full depth
6.5.3 Material Equivalence
The resulting 196 equivalence determinations were statistically analysed to
assess the factors which affected the equivalence of materials of variable
modulus. The analysis determined that the most influential predictor of material
equivalence was the ratio between the original and replacement material
moduli. The thickness of the replacement layer and its location within the
pavement were also found to be somewhat significant, but less so than the
modulus ratio. The resulting recommended model for the determination of
material equivalence is shown as Equation 15. Equation 16 includes a modulus
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 82
ratio squared terms also. Another version, which includes the position of the
replacement layer is shown as Equation 17.
EA/B = 0.822 + 0.186 × MR (R2 = 0.69)...............................................Equation 15
EA/B = 0.715 + 0.323 × MR - 0.017 × MR2 (R2 = 0.72)........................Equation 16
EA/B = 0.964 + 0.186 × MR - 0.284 × Top (R2 = 0.75) ........................Equation 17
Where: EA/B = Thickness of A that is equivalent to 1 mm of B.
MR = Modulus of Material B/Modulus of Material A.
Top = 1 when at the top and 0 when at the bottom
The residuals for the simplest of the three models (Equation 15) are shown in
Figure 24.
Figure 24 Isolated Equivalence Residuals.
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
0 20 40 60 80 100 120 140 160 180Run
Res
idua
l (m
m)
Figure 25 illustrates the influence of modulus ratio, location of replacement and
replacement thickness on determined material equivalence. The simplest
model (Equation 15) is also shown in this figure.
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
83
Figure 25 Effect of modulus ratio, thickness and location on equivalence.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 1 2 3 4 5 6 7 8 9
Modulus Ratio
Equi
vale
nce
100 mm at top 200 mm at top 400 mm at top 100 mm at bottom200 mm at bottom 400 mm at bottom
Subgrade modulus was specifically determined as being not statistically
significant with no significant improvement in the prediction models when the
various subgrade values were incorporated.
This isolated analysis of material equivalence does not improve upon the
recommended practical equivalences presented in Table 12. It does, however,
explain the variability in equivalences derived from practical design scenarios
and determines the factors which influence the layered elastic implied
equivalence factors.
The dominant factor of influence on material equivalence is the modulus ratio.
The relationship between equivalence and modulus ratio is approximately
linear. Whether the replacement occurs at the top or the bottom of a pavement
structure and the thickness of the replacement are both less influential but still
statistically significant. The subgrade is not statistically significant for material
equivalence. Based on this analysis, the recommended material equivalence
factors detailed in Table 12 could be adopted knowing that the observed
variability has been analysed and explained. It can also be concluded that
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 84
making an improvement to the lower part of a pavement structure produces a
greater increase in pavement life than making the same improvement further up
because of the greater equivalence (on average of 0.3) of the improved
material at that pavement location.
6.6 THICKNESS COMPARISON EXAMPLES
A number of example calculations were undertaken in order to demonstrate the
application of the revised equivalence factors as well as to determine the
factors which have a statistically significant affect on the difference in pavement
thickness returned using the mid-range FAA values and the recommended
values for equivalence.
As an example of the calculation, the S77-1 pavement thickness is first
determined. For 20,000 passes of a 397 t B747 on a pavement with subgrade
CBR 3, a standard S77-1 pavement thickness of 1720 mm is required. This
figure is obtained from the FAA’s COMFAA program and requires the
conversion of aircraft passes to coverages. In this case a PCR of 1.75 is used
for the B747.
A non-standard pavement thickness is determined using APSDS. In this case,
50 mm of Asphalt on 350 mm of Crushed Rock on 1290 mm of Uncrushed
Gravel. This is a total pavement thickness of 1690 mm which is 30 mm thinner
than the standard S77-1 pavement thickness.
The non-standard pavement structure is converted to an equivalent thickness of
S77-1 pavement. In this example, the mid-range equivalence values
recommended by FAA are used. Equally valid would be the conversion of the
S77-1 pavement structure to an equivalent thickness of the non-standard (the
APSDS) pavement with the Uncrushed Gravel thickness being the only
difference. Firstly, the deficiency or excess of Asphalt is calculated and the
equivalent thickness of Crushed Rock is determined. The equivalent thickness
of Crushed Rock is the difference between the S77-1 and the non-standard
pavement’s Asphalt thickness multiplied by the equivalence factor for
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
85
converting Asphalt to Crushed Rock. That is, (50 - 75) × 1.4 = -35 mm (in this
case a deficiency). The effective thickness of Crushed Rock is then calculated
(350 - 35 = 315 mm). The deficiency or excess of effective Crushed Rock is
then calculated and converted to an equivalent thickness of Uncrushed Gravel.
That is (315-150) × 1.5 = 248 mm. This equivalent Uncrushed Gravel thickness
is added to the actual Uncrushed Gravel of the equivalent non-standard
pavement. That is 248 + 1290 = 1538 mm. The total S77-1 pavement
thickness therefore becomes 75 + 150 + 1538 = 1763 mm. This thickness can
be compared to the actual S77-1 determined thickness of 1720 mm. A
difference of 43 mm.
The same conversion can be made for the non-standard pavement to an
equivalent S77-1 pavement thickness using the recommended equivalence
factors from Table 12. For this example, this is detailed in Equation 18.
((50-75) × 1.3 + (350-150)) × 1.2 + 1290 = 1716 mm ........................Equation 18
The equivalent thickness using the revised equivalence factors is only 4 mm
thinner than the actual S77-1 determined thickness. This is significantly less
different than that determined using the FAA mid-range equivalence factors.
A total of 324 such examples were performed with the FAA mid-range factors
and the recommended equivalence factors detailed in Table 12. These
examples covered the subgrade moduli, aircraft, aircraft masses and aircraft
passes detailed in Table 14.
Table 14 Equivalence Examples Input Parameters.
Parameter Units Values Subgrade Modulus MPa 30, 60, 100, 150
Aircraft Nil B747, B767, B737 Aircraft Mass % 100, 80, 60
Aircraft Passes Number 5000, 10000, 20000
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 86
For each combination of the inputs detailed in Table 14, the S77-1 pavement
thickness required was determined from COMFAA. For these thickness
determinations, the aircraft passes were converted to aircraft coverages using
the following PCRs which can be adopted from a range of literature or
calculated from first principles:
• B747. 1.75.
• B767. 1.90.
• B737. 3.70.
For each of the combinations of input parameters, three combinations of
Asphalt and Crushed Rock thickness were considered. In all cases, a standard
S77-1 pavement structure (75 mm Asphalt and 150 mm Crushed Rock) was
included. This allowed an evaluation of the level of agreement between the
S77-1 and APSDS thicknesses provided by the calibration process. The two
other pavement structures were selected at random and were generally within
the realm of practical pavement solutions. The Asphalt thickness ranged from
30 to 300 mm. The Crushed Rock thickness ranged from 80 mm to 600 mm.
Following the determination of the non-standard pavement thickness from
APSDS, each was converted to the S77-1 equivalent thickness using firstly the
mid-range FAA equivalence factors and then the recommended replacement
factors detailed in Table 12. The resulting magnitudes of the differences were
analysed using statistical techniques, primarily the generation of means and
standard deviations, as well as linear regressions. In order to remove the
influence of the accuracy of the calibration of APSDS to the S77-1 pavement
thicknesses, the equivalent pavement thicknesses were corrected (by
subtracting the difference between the APSDS and S77-1 thickness for the
standard pavement structure) and re-analysed. Table 15 details the relevant
summary statistics.
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
87
Table 15 Equivalence Examples Summary Statistics.
Difference between S77-1/FAA and APSDS Thickness (mm) Statistic Uncorrected
FAA mid-range Uncorrected
Recommended Corrected
FAA mid-range Corrected
Recommended Average 48 36 45 7 Std Dev 34 23 33 7 Median 41 32 36 6
Maximum 199 96 165 55
From Table 15, it is clear that the recommended equivalence factors detailed in
Table 12 provide for a closer agreement between S77-1 and APSDS returned
pavement thickness for the aircraft and design scenarios considered. When the
differences are corrected for the difference between S77-1 and APSDS
thicknesses for a standard S77-1 pavement structure, the revised equivalence
factors provide agreement with an average difference of 7 mm. The current
FAA mid-range equivalences have an average difference of 45 mm. The
maximum difference was reduced from 165 mm to 55 mm when using the
recommended equivalences.
This agreement, to an average of 7 mm, is significantly better than the
agreement commonly obtained between the S77-1 and APSDS thicknesses for
a standard S77-1 pavement structure. This implies that the calibration of
APSDS to S77-1 creates significantly more variability than the conversion to a
non-standard pavement structure does. This is considered to be the optimum
solution from a material equivalence point of view. The recommendation to
adopt the recommended equivalence factors presented in Table 12 in order to
achieve closer agreement between S77-1 and APSDS thickness
determinations is therefore reinforced.
Linear regressions performed on the differences determined when using the
FAA mid-range and recommended equivalence factors were performed. A
simple linear regression was performed and the residuals were analysed and
confirmed to not contravene the assumptions underlying the validity of the
statistical analysis. These regressions determined that the aircraft type, aircraft
mass and aircraft passes were all non-significant factors for the difference
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 88
between S77-1 and APSDS equivalent pavement thicknesses using the
recommended equivalence factors. The subgrade modulus was, however, a
statistically significant determinant. This is in apparent contrast to subgrade not
being significant when the non-sub-layered equivalences were determined.
This apparent contrast results from the influence of subgrade modulus on sub-
layer modulus when using the Barker and Brabston sub-layering regime. For
example, for a 1000 mm thick layer of crushed rock under a B737 aircraft load,
the lowest sub-layer moduli value can range from 116 MPa to 360 MPa for
underlying subgrade CBRs of 3% and 15% respectively. The apparent
influence of subgrade modulus is therefore explained by the subgrade’s impact
on the lower sub-layers’ modulus values. The subgrade modulus has a
significant impact on the lowest sub-layer’s modulus when using the Barker and
Brabston sub-layered and modulus assignment method. The modulus values
in turn impact on the implied material equivalence values as material modulus
is the most influential factor on material equivalence.
6.7 SUMMARY
When determined using S77-1, standard pavement structures are converted to
an equivalent structural thickness of non-standard composition using
equivalence factors. The FAA provides a range for equivalences of a number
of pavement materials. APSDS offers the advantage of direct thickness
determination without the need to separately apply equivalence factors.
Material quality is accounted for in the sub-layering modulus assignment
routines. Inconsistencies have been noted between the equivalent S77-1
thicknesses (after applying conversion using the FAA’s mid-range equivalence
factors) and directly determined APSDS designed pavements for the same
design scenario. It was found that:
• Inconsistence results between S77-1 and APSDS pavement thicknesses
when the FAA’s mid-range equivalence factors are used to convert non-
standard pavement structures.
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
89
• Recommended equivalence factors, which are generally at the lower end of
the FAA recommended ranges, are:
o Asphalt for Crushed Rock. 1.3.
o Crushed Rock for Uncrushed Gravel. 1.2.
o Asphalt for Uncrushed Gravel. 1.6.
• These equivalence factors are applicable to all medium to large jet aircraft
or traffic mixes governed by their presence in the fleet mix.
• Some variability exists in the implied APSDS equivalence factors. This is
largely explained by the influence of the Barker and Brabston sub-layering
regime and the location of the replacement layer in the pavement structure.
• The isolated pavement material investigation shows that the modulus ratio
of the original and the replacement material is the main influence on the
APSDS implied equivalence.
• Examples show that the recommended replacement equivalence factors
generally provide superior consistence between APSDS and S77-1
pavement thicknesses than the current FAA mid-range values do.
• The FAA should review the material equivalence factors contained in their
design guide, in light of the findings from the investigation undertaken. It is
acknowledged that the correctness of the APSDS implied equivalence
factors can not be confirmed. However, the FAA acknowledges that their
material equivalence guidance is highly questionable and APSDS implied
equivalence factors would at least provide consistence between the two
methods.
Chapter 6 Material Equivalence
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 90
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
91
7. DESIGN OF PROOF ROLLING REGIMES
7.1 GENERAL
Proof rolling of heavy duty aircraft pavements during their construction is
generally practiced in Australia. With the introduction of large commercial
aircraft, such as the B767 and B747, extra heavy duty proof rolling equipment
was designed and built by the Australian Commonwealth Department of
Housing and Construction from the 1950s.
The aim of proof rolling these heavy duty pavements is to expose the various
layers to a level of ‘damage’ (indicated by calculated stress, strain or deflection)
that is slightly greater than the maximum expected service ‘damage’, prior to
constructing the next layer of the pavement structure. By proving pavements in
this manner, the variability of the structural strength of the pavement is
significantly reduced, allowing thinner pavements to be constructed with equal
reliability.
7.2 DESIGN OF PROOF ROLLING REGIMES
The design of proof rolling regimes therefore comprises two steps:
• Calculating the values of the chosen indicator of damage at various depths
through the pavement layers.
• Selection of a proof rolling regime (mass and tyre pressure combination) to
be applied to the various layers of the pavement structure such that the
calculated maximum service damage indicator value is just exceeded.
APSDS has the ability to calculate normal and shear stresses, strains and
deflections at any location defined by the user. These indicators of damage
can be determined for any desired depths below the pavement surface.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 92
7.3 AUSTRALIAN PROOF ROLLING FLEET
The Australian Department of Defence owns eleven pneumatic-tyred heavy
aircraft pavement rollers. The first two of these rollers were purchased and
imported from the USA in the 1950s (Brown, 1966). These rollers, known as
Marco rollers, were capable of applying up to 50 t on four wheels with a tyre
pressure of up to 1.4 MPa. The Commonwealth then constructed, a number of
additional rollers, based on the US roller design, which became known as
Macro rollers.
One of these Macro rollers was converted to 50 t on two wheels, with tyre
pressures up to 1.65 MPa. The roller was designed to produce stresses
comparable to those induced by heavier commercial aircraft and high tyre
pressure military jets. This roller was known as the Test Rig. At around the
same time, the Commonwealth also constructed a number of 200 t rollers on
four wheels, with up to 1 MPa tyre pressure, known as the Porter
Supercompactor. Only one Porter Supercompactor remains in service in
Australia today. These Porter Supercompactors were specifically designed for
the compaction of deep dredged-sand fills and for proving of subgrades to large
depths.
7.4 DAMAGE INDICATOR CALCULATION
The layered elastic component of APSDS is used for the calculation of the
indicators of damage (stress, strain or deflection) modelled by a single load
application. Many other layered elastic aircraft pavement design tools are also
available for the generation of these pavement damage indicators.
During each design scenario APSDS calculates the stresses, strains and
deflections of the pavement at a range of depths, as well as at user defined
lateral and longitudinal coordinates. The ability to view all damage indicators
calculated at all pavement locations is not available in all layered elastic tools
and is one advantage of APSDS. This provides for the ability to easily generate
plots of stress, strain and deflection against depth under the aircraft wheels or
between aircraft wheels.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
93
In developing a methodology for the design of proof rolling regimes, the
damage indicator options include:
• Stress, strain or deflection as the indicator of pavement damage caused by
aircraft and rollers.
• Use of the actual pavement structure or a simple single layer of material.
• Use of actual or representative subgrade modulus value for all subgrades.
• Calculation of the damage indicator directly under a tyre or at the centre of a
wheel gear, or both.
7.4.1 Traditional Approach
Prior to the development of APSDS and other layered elastic pavement design
tools, proof rolling regimes were developed using stress as the damage
indicator. Standard charts for aircraft and various proof rollers were compared
to determine the proof rolling regime. Standard charts were used as their
generation was time consuming and these charts were generally developed
using Boussinesq’s (1885) formula for stress in a single elastic layer imposed
by a simple static load. The use of stress curves generated by single point
loads and uniform, single layer, pavement structures was not by choice but due
to the lack of any more accurate tool being available at the time. Practitioners
hoped that the forced simplifications were valid but this assumption remained
untested.
7.4.2 APSDS Generated Damage Indicators
With the advent of layered elastic design tools, the ability to generate stresses,
strains and deflections at a range of depths for complex loads and complex
pavement structures is readily available. Therefore, the options for comparing
aircraft and roller induced ‘damage’ is markedly expanded.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 94
7.5 INVESTIGATION UNDERTAKEN
An investigation was undertaken to assess the options for the design of proof
rolling regimes using layered elastic methods. APSDS was utilised to generate
various damage indicators with depth. The preferred damage indicator, and
pavement composition was investigated as detailed in the following sections.
7.5.1 Deflection, Stress and Strain
To compare the relative merits of using stress, strain or deflection as the
indicator of damage for proof rolling regimes, stresses, strains and deflections
were calculated under a B737 aircraft (between the tyres and directly under one
tyre) and plotted against depth for the following pavement structures:
• 1000 mm crushed rock base course material on CBR 6.
• 1000 mm crushed rock base course material on CBR 15.
• 1000 mm natural gravel sub base material on CBR 6.
• 1000 mm natural gravel sub base material on CBR 15.
The damage indicators with depth data is contained in Appendix 6. The
resulting plots of damage indicator with depth are shown in
Figure 26 to Figure 28 for stress, strain and deflection respectively.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
95
Figure 26 B737 Vertical Stress with depth for various pavements.
0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Stress (MPa)
Dep
th (m
)
Crushed rock on CBR 6 Under Wheel Crushed rock on CBR 6 Centre of GearCrushed rock on CBR 15 Under Wheel Crushed rock on CBR 15 Centre of GearNatural Gravel on CBR 6 Under Wheel Natural Gravel on CBR 6 Centre of GearNatural Gravel on CBR 15 Under Wheel Natural Gravel on CBR 15 Centre of Gear
From Figure 26 it can be seen that stress at the pavement surface is equal to
the tyre pressure (under a wheel) and zero between two tyres. At depth (in this
case below 0.8 m), stresses beneath and between the wheels are similar in all
cases. Irrespective of the pavement material adopted and the subgrade
strength selected, the stresses are similar at all depths.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 96
Figure 27 B737 Vertical Strain with depth for various pavements.
0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5
-1000 -500 0 500 1000 1500 2000 2500 3000 3500 4000Strain (uE)
Dep
th (m
)
Crushed rock on CBR 6 Under Wheel Crushed rock on CBR 6 Centre of GearCrushed rock on CBR 15 Under Wheel Crushed rock on CBR 15 Centre of GearNatural Gravel on CBR 6 Under Wheel Natural Gravel on CBR 6 Centre of GearNatural Gravel on CBR 15 Under Wheel Natural Gravel on CBR 15 Centre of Gear
From Figure 27, it can be seen that strains vary significantly with pavement
material as well as subgrade strength. Strains also show complex relationships
to depth and are less consistent than stress. They cannot readily be related to
aircraft loading (tyre pressure and load) at either the surface or at depth.
Further, at changes in pavement layers and sub-layers, calculated strains
increase sharply due to a continuously and smoothly decreasing stress and an
immediate (discontinuous) decrease in modelled material modulus.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
97
Figure 28 B737 Vertical Deflection with depth for various pavements.
0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Deflection (mm)D
epth
(m)
Crushed rock on CBR 6 Under Wheel Crushed rock on CBR 6 Centre of GearCrushed rock on CBR 15 Under Wheel Crushed rock on CBR 15 Centre of GearNatural Gravel on CBR 6 Under Wheel Natural Gravel on CBR 6 Centre of GearNatural Gravel on CBR 15 Under Wheel Natural Gravel on CBR 15 Centre of Gear
Deflections with depth are shown in Figure 28 to be simple in their shape but
vary significantly with subgrade strength and pavement material. There is also
comparatively small difference in the deflection at the top of the pavement to
that at depth.
Based on the analysis of Figure 26 to Figure 28, stress is selected as being the
preferred method for indicating damage in the design of proof rolling regimes.
Stress is selected as it provides the following advantages:
• Easy to visualise and understand compared to strain.
• Equal to tyre pressure at the pavement surface.
• Related to load per landing gear at depth.
• Essentially equal for all modelled subgrade strengths and granular
pavement materials.
• Essentially equal, at depth, under the tyre and in the centre of a multiple
wheel landing gear.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 98
• Decreases smoothly with increased depth from a maximum value at the
surface.
It is also concluded from Figure 26 that stresses should be calculated directly
under a tyre only. At the surface, the stress induced under a tyre is significantly
higher than that at the centre of the landing gear. At depth the under-tyre and
centre-gear stresses converge and whilst the centre-gear stress does exceed
the under-tyre stress at depth, it is essentially equal for comparative purposes.
The additional effort required to compare the greater of the under-tyre and
centre-gear stresses is not considered warranted.
7.5.2 Pavement Composition
Using stress under the tyre as the most appropriate indicator of damage, the
influence of pavement structure was considered. From Figure 26, it can be
seen that there is virtually no difference in the stress with depth for base or sub-
base materials on either a strong (CBR 15) or weaker (CBR 6) subgrade. The
damage indicators with depth data is contained in Appendix 6. The resulting
stress with depth plots are shown in Figure 29 with the equivalent plot for a
typical B737 capable pavement. The B737 pavement consisted of:
• 50 mm asphalt of 1500 MPa.
• 200 mm crushed rock base course material.
• 550 mm natural gravel sub-base material.
• CBR 6 subgrade.
Chapter 7 Design of Proof Rolling Regimes
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99
Figure 29 Comparison of Pavement and Single Material Stresses.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Stress (MPa)D
epth
(m)
Pavement on CBR 6 Crushed rock on CBR 6 Natural gravel on CBR 6
Significant variations from the B737 pavement adopted for the generation of
Figure 29 were also assessed. This focused on the asphalt layer and included
a higher modulus asphalt option (4000 MPa) and a thicker (200 mm – with the
sub-base reduced to maintain a consistent total pavement thickness) asphalt
layer option. A combined high modulus, thick asphalt option was also
assessed. The comparison of the stress with depth for each asphalt option is
illustrated in Figure 30.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 100
Figure 30 Asphalt thickness and modulus effects.
0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Stress (MPa)
Dep
th (m
)
50 mm 1500 MPa 50 mm 4000 MPa 200 mm 1500 MPa 200 mm 4000 MPa
Figure 29 and Figure 30 confirm the suggestion from Figure 26 that pavement
structure (material and subgrade strength) have little impact on the stress with
depth.
When it is considered that the proof rolling regime design is a comparison of
relative stress induced by aircraft and roller, the influence of materials or
pavement structure becomes even less important, as long as the same
pavement structure is adopted for both the aircraft and roller stress calculations.
Therefore, for practical purposes, a standard pavement of 1000 mm of crushed
rock base course on CBR 6 subgrade is selected for stress with depth
calculations. This selection is justified by:
• All materials having an essentially negligible differential effect.
• The relative or comparative (aircraft to roller) stress being more important
than the accuracy of any absolute stress values calculated.
• Base material having a modulus approximately equal to the mean of the
moduli of asphalt and subgrade.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
101
• CBR 6 being typical of many pavement subgrades at airports in Australia.
When absolute stresses or far from typical pavement structures are required, a
customised pavement may be justified for the determination of stress with
depth. Such a case may be the 200 mm thick of 4000 MPa asphalt surface
layer option shown in Figure 30. However, as the roller and the aircraft stress
with depth would be similarly affected by the non-standard pavement, it would
be inconsequential to use a single layer pavement in most practical
circumstances. Where required, customised stress with depth plots can readily
be generated for any pavement structure using APSDS. The customised
pavement structure must, however, be adopted for both the design aircraft and
the proposed proof rollers.
7.6 PROOF ROLLING REGIME DESIGN
Using the methodology developed above, proof rolling regimes can be
developed for a range of aircraft. All proof rolling regimes are based on the
determination of mass and tyre pressure combinations for proof rollers which
result in stresses with depth that just exceed those imposed by the design
aircraft during service.
7.6.1 Roller Configurations
There are three specifically designed roller types available in Australia for
proving heavy duty aircraft pavements. More conventional pneumatic-tyred
rollers can also be utilised but are less likely to induce stresses comparable to
those caused by the design aircraft. For each roller, there is a range of
acceptable mass and tyre pressure combinations (Defence, 2003) required to
control tyre distortion. The allowable tyre pressure and roller mass
combinations for the Macro, the Test Rig and the Porter Supercompactor are
shown in Figure 31, Figure 32 and Figure 33.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 102
Figure 31 Allowable Macro Roller Tyre Pressures and Masses.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
10 15 20 25 30 35 40 45 50Total Mass (t)
Tyre
Pre
ssur
e (M
Pa)
ACCEPTABLE
UNACCEPTABLE
Figure 32 Allowable Test Rig Roller Tyre Pressures and Masses.
0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.7
10 15 20 25 30 35 40 45 50Total Mass (t)
Tyre
Pre
ssur
e (M
Pa)
ACCEPTABLE
UNACCEPTABLE
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An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
103
Figure 33 Porter Supercompactor Tyre Pressures and Masses.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200Total Mass (t)
Tyre
Pre
ssur
e (M
Pa)
ACCEPTABLE
UNACCEPTABLE
7.6.2 Roller Generated Stresses
The stress, directly under a tyre, with depth (at maximum mass and tyre
pressure) for each of the three rollers is illustrated in Figure 34.
Figure 34 Vertical Stress with Depth for Various Rollers.
0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7Stress (MPa)
Dep
th (m
)
50 t Macro 50 t Test Rig 200 t Porter
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 104
Figure 34 shows that at the pavement surface, the high tyre pressure of the
Test Rig induces the greatest stress. At depth, the higher wheel load of the
Porter Supercompactor results in the greatest stress. Due to their availability
(through greater numbers), portability and versatility, the Macro is the most
practical roller to use for most projects. Other rollers may be preferred for very
large projects, specific project requirements or where they are locally available.
Based on Figure 31, the maximum allowable roller mass for a range of tyre
pressures can be determined for the Macro roller. The stress with depth curves
for each allowable combination is shown in Figure 35. Figure 35 forms the
basis of the roller induced stresses for a proof rolling regime design. The
damage indicators with depth data is contained in Appendix 6.
Figure 35 Macro Roller Vertical Stress with Depth at various roller masses.
0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5Stress (MPa)
Dep
th (m
)
15 t, 0.4 MPa 19 t, 0.5 MPa 22 t, 0.6 MPa 26 t, 0.7 MPa30 t, 0.8 MPa 33 t, 0.9 MPa 36 t, 1.0 MPa 40 t, 1.1 MPa43 t, 1.2 MPa 47 t, 1.3 MPa 50 t, 1.4 MPa
The ‘kinks’ which can be seen for all rollers configurations at 0.25 m depth are
caused by the large change in sub-layer modulus at this depth. The assigned
change in sub-layer modulus is generated by the Barker and Brabston sub-
layering system which is automated in APSDS.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
105
7.6.3 Aircraft Generated Stresses
Stress with depth plots for aircraft are generated by APSDS in a similar manner
to that for the rollers. Figure 36 shows stresses with depth for the following:
• B747 at 397 t and 1.38 MPa tyre pressure. A dual-tandem landing gear.
• B767 at 180 t and 1.24 MPa tyre pressure. A dual-tandem landing gear.
• B737 at 78.5 t and 1.36 MPa tyre pressure. A dual wheel landing gear.
• F111 at 50.8 t and 1.48 MPa tyre pressure. A single wheel landing gear.
The damage indicators with depth data is contained in Appendix 6.
Figure 36 Vertical Stresses with Depth for various Aircraft.
0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5Stress (MPa)
Dep
th (m
)
B737 78.5 t, 1.36 MPa B767 180 t, 1.24 MPaB747 397 t, 1.38 MPa F111 50.8 t, 1.48 MPa
These aircraft were chosen as they span the range of common medium to large
civil and military jet aircraft in terms of landing gear configurations, wheel loads
and tyre pressures.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 106
A proof rolling regime designed for any aircraft mix should accommodate the
envelope of maximum stress induced by all the aircraft in the mix. For the four
aircraft shown in Figure 36, the high tyre pressure of the F111 would govern in
the upper layers whilst the B747’s high mass per landing gear would dominate
at the lower levels and subgrade.
The B767 is approximately half the mass of the B747 but has half the number
of main wheels so induces similar stresses at depth to those of the larger
aircraft. The B747 and B767 aircraft induce pressures at 1.2 m that are
comparable to those induced by the F111 and B737 at around 0.9 m.
7.7 PRACTICAL LIMITATIONS
Each of the materials and layers encountered during the construction of an
aircraft pavement have limits to the stresses they can accommodate.
Therefore, the theoretically required 0.8 MPa tyre pressure rolling of the
subgrade for a B747 aircraft, may not be practical as the subgrade may fail in
shear with such a high tyre pressure being placed directly on this material. In
such circumstances, experience must be applied by the designer and
constructor to minimise the risk of unduly failing pavements and bogging rollers.
The development of the proof rolling regime should therefore take into account
the following general rules.
7.7.1 Sand Subgrades
Sand subgrades should be covered with a layer of granular material to provide
some confinement before rolling and proving.
7.7.2 Weak Clay Subgrades
Often, clay subgrades cannot be significantly improved by compaction because
they are saturated and impermeable. In such cases, proving provides a check
for weak spots only and pavements are designed to accommodate the poor
subgrade conditions.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
107
7.7.3 Over Proof Rolling
Clay and other weaker subgrades should be proved with lower tyre pressures
to prevent shear failures under high stresses.
7.8 EXAMPLES OF APPLICATION
A proof rolling regime is to be determined for each of the individual aircraft
whose stress with depth is illustrated in Figure 36. With the adoption of a
standard pavement (1000 mm crushed rock base course material on CBR 6
subgrade) the only pavement specific issue needing to be considered is the
layers (and their thickness) upon which the rollers are to be applied. The depth
from the finished surface level determines the portion of the aircraft induced
stress with depth plot to be considered. These are the stresses that need to be
exceeded by the chosen proof roller for proving that layer of the pavement.
7.8.1 Proof Rolling Regime Design
Example proof rolling regimes have been designed for three common aircraft.
The stress with depth data for these proof rolling regimes is contained in
Appendix 7.
For the B737 aircraft, the assumed pavement structure is as detailed for the
derivation of Figure 29.
Based on the stress with depth plot for the B737 aircraft and the application of
the proof rollers at finished subgrade, top of sub-base and top of base course
levels, the proof rolling regime becomes:
• Subgrade. 22 t at 0.6 MPa.
• Sub-base. 36 t at 1.0 MPa.
• Base. 50 t at 1.4 MPa.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 108
The stress with depth for the B737 aircraft and for the proof rollers (applied at
each pavement layer) is shown in Figure 37. The roller masses and pressures
were selected to allow the roller induced stresses to just exceed the aircraft
induced stresses in each layer being proved. The asphalt surface layer is not
proved because the required degree of compaction is only achievable when the
asphalt mix is at placing temperature, typically around 150°C. Proof rolling at
ambient temperatures would not correct low asphalt density or prove that the
required asphalt density had been achieved during construction.
Figure 37 B737 proof rolling regime.
0.0
0.10.2
0.3
0.40.5
0.6
0.70.8
0.9
1.01.1
1.2
1.31.4
1.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Stress (MPa)
Dep
th (m
)
B737 50 t at 1.4 MPa 36 t at 1.0 MPa 22 t at 0.6 MPa
Proof rolling regimes were also determined for B767, B747 and F111 aircraft. It
is noted that the pavement layer thicknesses needed to be determined in each
case as this determines the levels at which the rollers are applied. Table 16
details the adopted pavement structures and proof rolling regimes for each of
these aircraft (all with a 50 mm of 1500 MPa asphalt surface).
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
109
Table 16 Proof Rolling Regimes for B767, B747 and F111.
B767 B747 F111 Course
Thickness Roller Thickness Roller Thickness Roller Subgrade NA 19 t
0.5 MPa NA 30 t
0.8 MPa NA 19 t
0.5 MPa Sub-base 500 mm 26 t
0.7 MPa 400 mm 22 t
0.6 MPa 550 mm 30 t
0.8 MPa Base 400 mm 22 t
0.6 MPa 50 t
1.4 MPa
400 mm 26 t 0.7 MPa
50 t 1.4 MPa
200 mm 50 t 1.4 MPa
Two rolling configurations are required for the B767 and B747 base courses as
the Macro roller (at 50 t and 1.4 MPa) cannot match the aircraft induced
stresses at the bottom of the base course when applied at the top. The first of
the two roller configurations is applied to the bottom half of the base course and
the second configuration to the top of the base course. This is appropriate as
the 400 mm of base course would be placed in two layers in order to achieve
adequate compaction.
The rolling regimes and the associated stresses with depth, for the B767, B747
and F111 aircraft, are illustrated in Figure 25, Figure 39 and Figure 40.
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 110
Figure 38 B767 proof rolling regime.
0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Stress (MPa)
Dep
th (m
)
B767 50 t at 1.4 MPa 22 t at 0.6 MPa 26 t at 0.7 MPa 19 t at 0.5 MPa
Figure 39 B747 proof rolling regime.
0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Stress (MPa)
Dep
th (m
)
B747 50 t at 1.4 MPa 26 t at 0.7 MPa 22 t at 0.6 MPa 30 t at 0.8 MPa
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
111
Figure 40 F111 proof rolling regime.
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0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.11.2
1.3
1.4
1.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Stress (MPa)
Dep
th (m
)
F111 50 t at 1.4 MPa 30 t at 0.8 MPa 19 t at 0.5 MPa
From Figure 40 it can be seen that the maximum stress induced by the Macro
roller of 1.4 MPa (equal to the highest allowable tyre pressure) cannot equal the
stress induced at the pavement surface by the very high tyre pressure of the
F111 aircraft. However, the spreading of the stress through the asphalt surface
layer is such that the roller applied to the top of the base course produces
almost equal stress (1.40 MPa versus 1.46 MPa) to that induced by the aircraft
from the finished surface. This inability to exceed the very high stresses
induced in the upper layers by high tyre pressure military aircraft is one of the
reasons for the development of the higher tyre pressure Test Rig roller.
However, adequate specification and compaction of the crushed rock base
course just below the asphalt is generally able to provide suitable performance
without the need to fully prove the crushed rock with the higher tyre pressure
roller.
7.9 SUMMARY
Proof rolling remains an important aspect of heavy duty aircraft pavement
construction. Determination of suitable proof rolling regimes should be the
responsibility of pavement designers. In the past, simple equations (based on
Chapter 7 Design of Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 112
single point loads and single elastic layers) and standard plots of stress with
depth were utilised for proof loading regime design. Practitioners hoped that
these simplifications were appropriate. With the availability of stress, strain and
deflection at any position and depth in the pavement, more rigorous analysis is
possible and has indicated the suitability of the traditional assumptions for many
practical design scenarios.
When compared to strain and deflection, stress is the simplest damage
indicator to understand and the most consistent. Stress is therefore the
preferred indicator of damage for proof rolling regime design. Whilst APSDS
allows specific pavement materials to be modelled, comparison of a number of
scenarios has shown that the adoption of a single material on any particular
subgrade can adequately represent any pavement being analysed. A
pavement of 1000 mm of crushed rock on CBR 6 subgrade is recommended as
standard, as this is typical for many Australian design scenarios. The traditional
Boussinesq generated stress charts are also suitable, as long as the same
stress generation method is used for both the roller and the aircraft being
compared.
Regimes are readily able to be developed for proof rolling pavements by
comparing the calculated stresses induced by the aircraft and those calculated
for the proof rolling device for a number of tyre pressure and mass
combinations. Roller configurations that provide modelled stresses just
exceeding the aircraft induced stresses should be selected. Where a thicker
pavement course cannot be rolled to exceed the aircraft induced stresses,
rolling the course in two layers may be required.
In practice, proof rolling regimes must take into account the site constraints.
The rollers are large and expensive to transport and therefore the selection of a
roller must take this into consideration. Also, clays and sands require special
consideration and their proof rolling regimes should be determined by the
methods described in this paper and then checked by experienced personnel
and modified as required.
Chapter 8 Summary and Conclusions
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
113
8. SUMMARY AND CONCLUSIONS
8.1 GENERAL
A significant investigation into the use of APSDS for the calculation of aircraft
pavement thickness was conducted. This investigation focused on identifying
potential areas of improvement within the software and providing potential
solutions.
8.2 SUMMARY
8.2.1 Aircraft Pavement Design
Aircraft pavement design dates back to around WWII when aircraft increased in
size and complexity at an accelerated rate. This required appropriately
designed and constructed pavements with a sealed and uniformly graded
surface to be provided.
The determination of aircraft pavement thickness remains an empirical science.
The majority of the full scale testing that today’s design tools are reliant was
performed by the US Corps of Engineers in the 1940s and 1950s and
culminated in the publishing of the S77-1 curve. This remains the basis for
calibration of aircraft pavement design tools today.
8.2.2 Overview of APSDS
APSDS is a specialised version of the road pavement design software Circly.
APSDS uses a layered elastic system and has been calibrated to S77-1. As an
mechanistic-empirical tool, APSDS retains a largely empirical approach, albeit
an efficient one.
Whilst a very useful and effective tool for aircraft pavement thickness design,
APSDS contains a number of areas for potential improvement. These have
been investigated and potential improvements have been suggested for future
releases of the software.
Chapter 8 Summary and Conclusions
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 114
8.2.3 Validation of APSDS
The Chicago Criteria represent the current basis for calibration of APSDS. This
series of calibration constants were derived by comparison of pavement
thicknesses calculated by APSDS to those calculated from S77-1 (using
COMFAA) for a range of aircraft types, subgrade moduli and numbers of
aircraft passes.
A comparison between S77-1 and APSDS thicknesses was performed to
confirm that the Chicago Criteria provide a valid tie to the empirical
relationships between materials, loads and pavement thickness.
8.2.4 Selection of Inputs
Each of the input parameters required by APSDS for a pavement design were
described. Each parameter was detailed and guidance provided for their
selection.
8.2.5 Sensitivity Analysis
A statistically designed sensitivity analysis was performed for a range of
common medium to large commercial jet aircraft. This allowed the relative
influence of each input parameter on the required pavement thickness to be
determined.
Commonly accepted relative sensitivities were confirmed and designers were
provided with guidance as to which inputs parameters to focus on defining
accurately during design.
8.2.6 Materials Equivalence
Observations had suggested that the material equivalences implied by APSDS
were not always consistent with the mid-points of the ranges provided by the
FAA. Statistically designed parametric runs were performed to enable many
values of material equivalence to be calculated from similar pavements
designed for the same subgrade modulus and aircraft load. This analysis
Chapter 8 Summary and Conclusions
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
115
considered equivalence between asphalt, crushed rock (base) and natural
gravel (sub-base). Practical values of material equivalence were determined
although significant variation in material equivalence values was observed.
Aircraft were replaced by a single wheel load and the pavement structure
simplified to isolate the material stiffness effects on material equivalence. This
less practical analysis provided insight into why the practical material
equivalence values varied and provided confidence in the recommended
practical material equivalence values.
8.2.7 Proof Rolling
In order to assess the traditional methodologies for determining proof rolling
regimes during aircraft pavement construction, stresses, strains and deflections
were calculated by APSDS. These were assessed for different locations (under
versus between wheels), at various levels in the pavement, and for difference
pavement compositions (practical pavements versus uniform materials). Stress
was confirmed as being the most appropriate indicator of damage for the
determination of proof rolling regimes.
A number of stress with depth plots were generated for aircraft and common
proof rollers. These were compared to allow proof roller configurations to be
determined that would adequately prove the pavement layers for their design
aircraft loads. Example proof rolling regimes were determined for a number of
common aircraft.
8.3 CONCLUSIONS
Based on the investigations undertaken, a number of significant conclusions
have been made. These are detailed as follows.
• Aircraft pavement thickness design remains an empirical science with purely
mechanistic tools unlikely to replace mechanistic-empirical tools in the near
future.
Chapter 8 Summary and Conclusions
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design 116
• APSDS is the preferred software for aircraft pavement thickness design. It
provides a transparent and very flexible tool that easily provides for ‘what if’
analysis.
• The Chicago Criteria provide for a reasonable fit to S77-1 pavement
thickness requirements and therefore APSDS is a suitable software for
aircraft pavement thickness design using existing knowledge and methods.
• Designers should utilise commonly accepted practice to determine the
values of each and every input parameter for any APSDS design.
• Designers should focus their attention to the very influential input
parameters of subgrade modulus and aircraft mass. Tyre pressure and
asphalt modulus can be assigned presumptive values as they have very
little influence on typical aircraft pavement thicknesses.
• The mid-points of the FAA guidance of material equivalence are not
consistent with the values implied by APSDS. In order to provide for
consistence with APSDS, the FAA should consider adopting the following
material equivalence values:
o Asphalt for Crushed Rock. 1.3.
o Crushed Rock for Uncrushed Gravel. 1.2.
o Asphalt for Uncrushed Gravel. 1.6.
• Proof rolling regimes should be determined using stress as the indicator of
damage with depth. Pavements should be modelled as single layers of
uniform (but sub-layered) material with a presumptive value of subgrade
modulus.
This project investigated the strengths and weaknesses of APSDS as a tool for
aircraft pavement thickness design. The software was validated, methods for
determining proof rolling regimes were developed and implied material
equivalence factors were determined for common pavement materials.
Guidance on input parameter selection was also presented.
Appendix 1 S77-1 Thickness Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A1 - 1
APPENDIX 1. S77-1 THICKNESS RESULTS
Run SM (MPa) Aircraft M
(%) P
(no.) Thickness
(mm) 1 30 B747 100 5000 1545 2 30 B747 100 10000 1635 3 30 B747 100 20000 1720 4 30 B747 80 5000 1327 5 30 B747 80 10000 1409 6 30 B747 80 20000 1487 7 30 B747 60 5000 1070 8 30 B747 60 10000 1142 9 30 B747 60 20000 1212
10 30 B767 100 5000 1445 11 30 B767 100 10000 1532 12 30 B767 100 20000 1616 13 30 B767 80 5000 1235 14 30 B767 80 10000 1315 15 30 B767 80 20000 1392 16 30 B767 60 5000 993 17 30 B767 60 10000 1061 18 30 B767 60 20000 1130 19 30 B737 100 5000 1058 20 30 B737 100 10000 1124 21 30 B737 100 20000 1186 22 30 B737 80 5000 923 23 30 B737 80 10000 984 24 30 B737 80 20000 1040 25 30 B737 60 5000 769 26 30 B737 60 10000 821 27 30 B737 60 20000 870 28 60 B747 100 5000 931 29 60 B747 100 10000 994 30 60 B747 100 20000 1054 31 60 B747 80 5000 784 32 60 B747 80 10000 835 33 60 B747 80 20000 887 34 60 B747 60 5000 634 35 60 B747 60 10000 672
Appendix 1 S77-1 Thickness Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A1 - 2
Run SM (MPa) Aircraft M
(%) P
(no.) Thickness
(mm) 36 60 B747 60 20000 710 37 60 B767 100 5000 860 38 60 B767 100 10000 920 39 60 B767 100 20000 980 40 60 B767 80 5000 727 41 60 B767 80 10000 774 42 60 B767 80 20000 822 43 60 B767 60 5000 593 44 60 B767 60 10000 628 45 60 B767 60 20000 664 46 60 B737 100 5000 686 47 60 B737 100 10000 733 48 60 B737 100 20000 778 49 60 B737 80 5000 592 50 60 B737 80 10000 632 51 60 B737 80 20000 670 52 60 B737 60 5000 489 53 60 B737 60 10000 521 54 60 B737 60 20000 552 55 100 B747 100 5000 634 56 100 B747 100 10000 672 57 100 B747 100 20000 710 58 100 B747 80 5000 539 59 100 B747 80 10000 572 60 100 B747 80 20000 603 61 100 B747 60 5000 439 62 100 B747 60 10000 463 63 100 B747 60 20000 486 64 100 B767 100 5000 593 65 100 B767 100 10000 628 66 100 B767 100 20000 664 67 100 B767 80 5000 507 68 100 B767 80 10000 536 69 100 B767 80 20000 566 70 100 B767 60 5000 414 71 100 B767 60 10000 436 72 100 B767 60 20000 458 73 100 B737 100 5000 492
Appendix 1 S77-1 Thickness Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A1 - 3
Run SM (MPa) Aircraft M
(%) P
(no.) Thickness
(mm) 74 100 B737 100 10000 524 75 100 B737 100 20000 555 76 100 B737 80 5000 423 77 100 B737 80 10000 450 78 100 B737 80 20000 476 79 100 B737 60 5000 351 80 100 B737 60 10000 372 81 100 B737 60 20000 392 82 150 B747 100 5000 472 83 150 B747 100 10000 499 84 150 B747 100 20000 525 85 150 B747 80 5000 406 86 150 B747 80 10000 428 87 150 B747 80 20000 448 88 150 B747 60 5000 332 89 150 B747 60 10000 349 90 150 B747 60 20000 366 91 150 B767 100 5000 444 92 150 B767 100 10000 468 93 150 B767 100 20000 492 94 150 B767 80 5000 382 95 150 B767 80 10000 403 96 150 B767 80 20000 422 97 150 B767 60 5000 316 98 150 B767 60 10000 334 99 150 B767 60 20000 351
100 150 B737 100 5000 376 101 150 B737 100 10000 400 102 150 B737 100 20000 423 103 150 B737 80 5000 329 104 150 B737 80 10000 348 105 150 B737 80 20000 366 106 150 B737 60 5000 265 107 150 B737 60 10000 280 108 150 B737 60 20000 295
Appendix 1 S77-1 Thickness Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A1 - 4
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A2 - 1
APPENDIX 2. SENSITIVITY ANALYSIS DESIGN
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
1 30 2600 60 80 5000 1000 20 100 2 30 2600 60 80 5000 1000 20 300 3 30 2600 60 80 5000 1000 40 100 4 30 2600 60 80 5000 1000 40 500 5 30 2600 60 80 5000 1500 20 300 6 30 2600 60 80 5000 1500 20 500 7 30 2600 60 80 5000 1500 100 100 8 30 2600 60 80 5000 1500 100 300 9 30 2600 60 80 10000 1000 40 100
10 30 2600 60 80 10000 1000 40 500 11 30 2600 60 80 10000 1000 100 300 12 30 2600 60 80 10000 1000 100 500 13 30 2600 60 80 10000 2000 20 100 14 30 2600 60 80 10000 2000 20 300 15 30 2600 60 80 10000 2000 40 100 16 30 2600 60 80 10000 2000 40 500 17 30 2600 60 90 5000 1500 20 300 18 30 2600 60 90 5000 1500 20 500 19 30 2600 60 90 5000 1500 100 100 20 30 2600 60 90 5000 1500 100 300 21 30 2600 60 90 5000 2000 40 100 22 30 2600 60 90 5000 2000 40 500 23 30 2600 60 90 5000 2000 100 300 24 30 2600 60 90 5000 2000 100 500 25 30 2600 60 90 20000 1000 20 100 26 30 2600 60 90 20000 1000 20 300 27 30 2600 60 90 20000 1000 40 100 28 30 2600 60 90 20000 1000 40 500 29 30 2600 60 90 20000 1500 20 300 30 30 2600 60 90 20000 1500 20 500 31 30 2600 60 90 20000 1500 100 100 32 30 2600 60 90 20000 1500 100 300 33 30 2600 80 80 10000 1000 40 100 34 30 2600 80 80 10000 1000 40 500
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A2 - 2
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
35 30 2600 80 80 10000 1000 100 300 36 30 2600 80 80 10000 1000 100 500 37 30 2600 80 80 10000 2000 20 100 38 30 2600 80 80 10000 2000 20 300 39 30 2600 80 80 10000 2000 40 100 40 30 2600 80 80 10000 2000 40 500 41 30 2600 80 80 20000 1500 20 300 42 30 2600 80 80 20000 1500 20 500 43 30 2600 80 80 20000 1500 100 100 44 30 2600 80 80 20000 1500 100 300 45 30 2600 80 80 20000 2000 40 100 46 30 2600 80 80 20000 2000 40 500 47 30 2600 80 80 20000 2000 100 300 48 30 2600 80 80 20000 2000 100 500 49 30 2600 80 100 5000 1000 20 100 50 30 2600 80 100 5000 1000 20 300 51 30 2600 80 100 5000 1000 40 100 52 30 2600 80 100 5000 1000 40 500 53 30 2600 80 100 5000 1500 20 300 54 30 2600 80 100 5000 1500 20 500 55 30 2600 80 100 5000 1500 100 100 56 30 2600 80 100 5000 1500 100 300 57 30 2600 80 100 10000 1000 40 100 58 30 2600 80 100 10000 1000 40 500 59 30 2600 80 100 10000 1000 100 300 60 30 2600 80 100 10000 1000 100 500 61 30 2600 80 100 10000 2000 20 100 62 30 2600 80 100 10000 2000 20 300 63 30 2600 80 100 10000 2000 40 100 64 30 2600 80 100 10000 2000 40 500 65 30 1000 60 90 5000 1500 20 300 66 30 1000 60 90 5000 1500 20 500 67 30 1000 60 90 5000 1500 100 100 68 30 1000 60 90 5000 1500 100 300 69 30 1000 60 90 5000 2000 40 100 70 30 1000 60 90 5000 2000 40 500 71 30 1000 60 90 5000 2000 100 300
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A2 - 3
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
72 30 1000 60 90 5000 2000 100 500 73 30 1000 60 90 20000 1000 20 100 74 30 1000 60 90 20000 1000 20 300 75 30 1000 60 90 20000 1000 40 100 76 30 1000 60 90 20000 1000 40 500 77 30 1000 60 90 20000 1500 20 300 78 30 1000 60 90 20000 1500 20 500 79 30 1000 60 90 20000 1500 100 100 80 30 1000 60 90 20000 1500 100 300 81 30 1000 60 100 10000 1000 40 100 82 30 1000 60 100 10000 1000 40 500 83 30 1000 60 100 10000 1000 100 300 84 30 1000 60 100 10000 1000 100 500 85 30 1000 60 100 10000 2000 20 100 86 30 1000 60 100 10000 2000 20 300 87 30 1000 60 100 10000 2000 40 100 88 30 1000 60 100 10000 2000 40 500 89 30 1000 60 100 20000 1500 20 300 90 30 1000 60 100 20000 1500 20 500 91 30 1000 60 100 20000 1500 100 100 92 30 1000 60 100 20000 1500 100 300 93 30 1000 60 100 20000 2000 40 100 94 30 1000 60 100 20000 2000 40 500 95 30 1000 60 100 20000 2000 100 300 96 30 1000 60 100 20000 2000 100 500 97 30 1000 100 80 5000 1000 20 100 98 30 1000 100 80 5000 1000 20 300 99 30 1000 100 80 5000 1000 40 100
100 30 1000 100 80 5000 1000 40 500 101 30 1000 100 80 5000 1500 20 300 102 30 1000 100 80 5000 1500 20 500 103 30 1000 100 80 5000 1500 100 100 104 30 1000 100 80 5000 1500 100 300 105 30 1000 100 80 10000 1000 40 100 106 30 1000 100 80 10000 1000 40 500 107 30 1000 100 80 10000 1000 100 300 108 30 1000 100 80 10000 1000 100 500
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A2 - 4
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
109 30 1000 100 80 10000 2000 20 100 110 30 1000 100 80 10000 2000 20 300 111 30 1000 100 80 10000 2000 40 100 112 30 1000 100 80 10000 2000 40 500 113 30 1000 100 90 5000 1500 20 300 114 30 1000 100 90 5000 1500 20 500 115 30 1000 100 90 5000 1500 100 100 116 30 1000 100 90 5000 1500 100 300 117 30 1000 100 90 5000 2000 40 100 118 30 1000 100 90 5000 2000 40 500 119 30 1000 100 90 5000 2000 100 300 120 30 1000 100 90 5000 2000 100 500 121 30 1000 100 90 20000 1000 20 100 122 30 1000 100 90 20000 1000 20 300 123 30 1000 100 90 20000 1000 40 100 124 30 1000 100 90 20000 1000 40 500 125 30 1000 100 90 20000 1500 20 300 126 30 1000 100 90 20000 1500 20 500 127 30 1000 100 90 20000 1500 100 100 128 30 1000 100 90 20000 1500 100 300 129 60 200 80 80 10000 1000 40 100 130 60 200 80 80 10000 1000 40 500 131 60 200 80 80 10000 1000 100 300 132 60 200 80 80 10000 1000 100 500 133 60 200 80 80 10000 2000 20 100 134 60 200 80 80 10000 2000 20 300 135 60 200 80 80 10000 2000 40 100 136 60 200 80 80 10000 2000 40 500 137 60 200 80 80 20000 1500 20 300 138 60 200 80 80 20000 1500 20 500 139 60 200 80 80 20000 1500 100 100 140 60 200 80 80 20000 1500 100 300 141 60 200 80 80 20000 2000 40 100 142 60 200 80 80 20000 2000 40 500 143 60 200 80 80 20000 2000 100 300 144 60 200 80 80 20000 2000 100 500 145 60 200 80 100 5000 1000 20 100
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A2 - 5
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
146 60 200 80 100 5000 1000 20 300 147 60 200 80 100 5000 1000 40 100 148 60 200 80 100 5000 1000 40 500 149 60 200 80 100 5000 1500 20 300 150 60 200 80 100 5000 1500 20 500 151 60 200 80 100 5000 1500 100 100 152 60 200 80 100 5000 1500 100 300 153 60 200 80 100 10000 1000 40 100 154 60 200 80 100 10000 1000 40 500 155 60 200 80 100 10000 1000 100 300 156 60 200 80 100 10000 1000 100 500 157 60 200 80 100 10000 2000 20 100 158 60 200 80 100 10000 2000 20 300 159 60 200 80 100 10000 2000 40 100 160 60 200 80 100 10000 2000 40 500 161 60 200 100 90 5000 1500 20 300 162 60 200 100 90 5000 1500 20 500 163 60 200 100 90 5000 1500 100 100 164 60 200 100 90 5000 1500 100 300 165 60 200 100 90 5000 2000 40 100 166 60 200 100 90 5000 2000 40 500 167 60 200 100 90 5000 2000 100 300 168 60 200 100 90 5000 2000 100 500 169 60 200 100 90 20000 1000 20 100 170 60 200 100 90 20000 1000 20 300 171 60 200 100 90 20000 1000 40 100 172 60 200 100 90 20000 1000 40 500 173 60 200 100 90 20000 1500 20 300 174 60 200 100 90 20000 1500 20 500 175 60 200 100 90 20000 1500 100 100 176 60 200 100 90 20000 1500 100 300 177 60 200 100 100 10000 1000 40 100 178 60 200 100 100 10000 1000 40 500 179 60 200 100 100 10000 1000 100 300 180 60 200 100 100 10000 1000 100 500 181 60 200 100 100 10000 2000 20 100 182 60 200 100 100 10000 2000 20 300
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A2 - 6
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
183 60 200 100 100 10000 2000 40 100 184 60 200 100 100 10000 2000 40 500 185 60 200 100 100 20000 1500 20 300 186 60 200 100 100 20000 1500 20 500 187 60 200 100 100 20000 1500 100 100 188 60 200 100 100 20000 1500 100 300 189 60 200 100 100 20000 2000 40 100 190 60 200 100 100 20000 2000 40 500 191 60 200 100 100 20000 2000 100 300 192 60 200 100 100 20000 2000 100 500 193 60 1800 60 80 5000 1000 20 100 194 60 1800 60 80 5000 1000 20 300 195 60 1800 60 80 5000 1000 40 100 196 60 1800 60 80 5000 1000 40 500 197 60 1800 60 80 5000 1500 20 300 198 60 1800 60 80 5000 1500 20 500 199 60 1800 60 80 5000 1500 100 100 200 60 1800 60 80 5000 1500 100 300 201 60 1800 60 80 10000 1000 40 100 202 60 1800 60 80 10000 1000 40 500 203 60 1800 60 80 10000 1000 100 300 204 60 1800 60 80 10000 1000 100 500 205 60 1800 60 80 10000 2000 20 100 206 60 1800 60 80 10000 2000 20 300 207 60 1800 60 80 10000 2000 40 100 208 60 1800 60 80 10000 2000 40 500 209 60 1800 60 90 5000 1500 20 300 210 60 1800 60 90 5000 1500 20 500 211 60 1800 60 90 5000 1500 100 100 212 60 1800 60 90 5000 1500 100 300 213 60 1800 60 90 5000 2000 40 100 214 60 1800 60 90 5000 2000 40 500 215 60 1800 60 90 5000 2000 100 300 216 60 1800 60 90 5000 2000 100 500 217 60 1800 60 90 20000 1000 20 100 218 60 1800 60 90 20000 1000 20 300 219 60 1800 60 90 20000 1000 40 100
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A2 - 7
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
220 60 1800 60 90 20000 1000 40 500 221 60 1800 60 90 20000 1500 20 300 222 60 1800 60 90 20000 1500 20 500 223 60 1800 60 90 20000 1500 100 100 224 60 1800 60 90 20000 1500 100 300 225 60 1800 80 80 10000 1000 40 100 226 60 1800 80 80 10000 1000 40 500 227 60 1800 80 80 10000 1000 100 300 228 60 1800 80 80 10000 1000 100 500 229 60 1800 80 80 10000 2000 20 100 230 60 1800 80 80 10000 2000 20 300 231 60 1800 80 80 10000 2000 40 100 232 60 1800 80 80 10000 2000 40 500 233 60 1800 80 80 20000 1500 20 300 234 60 1800 80 80 20000 1500 20 500 235 60 1800 80 80 20000 1500 100 100 236 60 1800 80 80 20000 1500 100 300 237 60 1800 80 80 20000 2000 40 100 238 60 1800 80 80 20000 2000 40 500 239 60 1800 80 80 20000 2000 100 300 240 60 1800 80 80 20000 2000 100 500 241 60 1800 80 100 5000 1000 20 100 242 60 1800 80 100 5000 1000 20 300 243 60 1800 80 100 5000 1000 40 100 244 60 1800 80 100 5000 1000 40 500 245 60 1800 80 100 5000 1500 20 300 246 60 1800 80 100 5000 1500 20 500 247 60 1800 80 100 5000 1500 100 100 248 60 1800 80 100 5000 1500 100 300 249 60 1800 80 100 10000 1000 40 100 250 60 1800 80 100 10000 1000 40 500 251 60 1800 80 100 10000 1000 100 300 252 60 1800 80 100 10000 1000 100 500 253 60 1800 80 100 10000 2000 20 100 254 60 1800 80 100 10000 2000 20 300 255 60 1800 80 100 10000 2000 40 100 256 60 1800 80 100 10000 2000 40 500
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A2 - 8
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
257 100 2600 60 90 5000 1500 20 300 258 100 2600 60 90 5000 1500 20 500 259 100 2600 60 90 5000 1500 100 100 260 100 2600 60 90 5000 1500 100 300 261 100 2600 60 90 5000 2000 40 100 262 100 2600 60 90 5000 2000 40 500 263 100 2600 60 90 5000 2000 100 300 264 100 2600 60 90 5000 2000 100 500 265 100 2600 60 90 20000 1000 20 100 266 100 2600 60 90 20000 1000 20 300 267 100 2600 60 90 20000 1000 40 100 268 100 2600 60 90 20000 1000 40 500 269 100 2600 60 90 20000 1500 20 300 270 100 2600 60 90 20000 1500 20 500 271 100 2600 60 90 20000 1500 100 100 272 100 2600 60 90 20000 1500 100 300 273 100 2600 60 100 10000 1000 40 100 274 100 2600 60 100 10000 1000 40 500 275 100 2600 60 100 10000 1000 100 300 276 100 2600 60 100 10000 1000 100 500 277 100 2600 60 100 10000 2000 20 100 278 100 2600 60 100 10000 2000 20 300 279 100 2600 60 100 10000 2000 40 100 280 100 2600 60 100 10000 2000 40 500 281 100 2600 60 100 20000 1500 20 300 282 100 2600 60 100 20000 1500 20 500 283 100 2600 60 100 20000 1500 100 100 284 100 2600 60 100 20000 1500 100 300 285 100 2600 60 100 20000 2000 40 100 286 100 2600 60 100 20000 2000 40 500 287 100 2600 60 100 20000 2000 100 300 288 100 2600 60 100 20000 2000 100 500 289 100 2600 100 80 5000 1000 20 100 290 100 2600 100 80 5000 1000 20 300 291 100 2600 100 80 5000 1000 40 100 292 100 2600 100 80 5000 1000 40 500 293 100 2600 100 80 5000 1500 20 300
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A2 - 9
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
294 100 2600 100 80 5000 1500 20 500 295 100 2600 100 80 5000 1500 100 100 296 100 2600 100 80 5000 1500 100 300 297 100 2600 100 80 10000 1000 40 100 298 100 2600 100 80 10000 1000 40 500 299 100 2600 100 80 10000 1000 100 300 300 100 2600 100 80 10000 1000 100 500 301 100 2600 100 80 10000 2000 20 100 302 100 2600 100 80 10000 2000 20 300 303 100 2600 100 80 10000 2000 40 100 304 100 2600 100 80 10000 2000 40 500 305 100 2600 100 90 5000 1500 20 300 306 100 2600 100 90 5000 1500 20 500 307 100 2600 100 90 5000 1500 100 100 308 100 2600 100 90 5000 1500 100 300 309 100 2600 100 90 5000 2000 40 100 310 100 2600 100 90 5000 2000 40 500 311 100 2600 100 90 5000 2000 100 300 312 100 2600 100 90 5000 2000 100 500 313 100 2600 100 90 20000 1000 20 100 314 100 2600 100 90 20000 1000 20 300 315 100 2600 100 90 20000 1000 40 100 316 100 2600 100 90 20000 1000 40 500 317 100 2600 100 90 20000 1500 20 300 318 100 2600 100 90 20000 1500 20 500 319 100 2600 100 90 20000 1500 100 100 320 100 2600 100 90 20000 1500 100 300 321 100 1000 80 80 10000 1000 40 100 322 100 1000 80 80 10000 1000 40 500 323 100 1000 80 80 10000 1000 100 300 324 100 1000 80 80 10000 1000 100 500 325 100 1000 80 80 10000 2000 20 100 326 100 1000 80 80 10000 2000 20 300 327 100 1000 80 80 10000 2000 40 100 328 100 1000 80 80 10000 2000 40 500 329 100 1000 80 80 20000 1500 20 300 330 100 1000 80 80 20000 1500 20 500
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A2 - 10
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
331 100 1000 80 80 20000 1500 100 100 332 100 1000 80 80 20000 1500 100 300 333 100 1000 80 80 20000 2000 40 100 334 100 1000 80 80 20000 2000 40 500 335 100 1000 80 80 20000 2000 100 300 336 100 1000 80 80 20000 2000 100 500 337 100 1000 80 100 5000 1000 20 100 338 100 1000 80 100 5000 1000 20 300 339 100 1000 80 100 5000 1000 40 100 340 100 1000 80 100 5000 1000 40 500 341 100 1000 80 100 5000 1500 20 300 342 100 1000 80 100 5000 1500 20 500 343 100 1000 80 100 5000 1500 100 100 344 100 1000 80 100 5000 1500 100 300 345 100 1000 80 100 10000 1000 40 100 346 100 1000 80 100 10000 1000 40 500 347 100 1000 80 100 10000 1000 100 300 348 100 1000 80 100 10000 1000 100 500 349 100 1000 80 100 10000 2000 20 100 350 100 1000 80 100 10000 2000 20 300 351 100 1000 80 100 10000 2000 40 100 352 100 1000 80 100 10000 2000 40 500 353 100 1000 100 90 5000 1500 20 300 354 100 1000 100 90 5000 1500 20 500 355 100 1000 100 90 5000 1500 100 100 356 100 1000 100 90 5000 1500 100 300 357 100 1000 100 90 5000 2000 40 100 358 100 1000 100 90 5000 2000 40 500 359 100 1000 100 90 5000 2000 100 300 360 100 1000 100 90 5000 2000 100 500 361 100 1000 100 90 20000 1000 20 100 362 100 1000 100 90 20000 1000 20 300 363 100 1000 100 90 20000 1000 40 100 364 100 1000 100 90 20000 1000 40 500 365 100 1000 100 90 20000 1500 20 300 366 100 1000 100 90 20000 1500 20 500 367 100 1000 100 90 20000 1500 100 100
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A2 - 11
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
368 100 1000 100 90 20000 1500 100 300 369 100 1000 100 100 10000 1000 40 100 370 100 1000 100 100 10000 1000 40 500 371 100 1000 100 100 10000 1000 100 300 372 100 1000 100 100 10000 1000 100 500 373 100 1000 100 100 10000 2000 20 100 374 100 1000 100 100 10000 2000 20 300 375 100 1000 100 100 10000 2000 40 100 376 100 1000 100 100 10000 2000 40 500 377 100 1000 100 100 20000 1500 20 300 378 100 1000 100 100 20000 1500 20 500 379 100 1000 100 100 20000 1500 100 100 380 100 1000 100 100 20000 1500 100 300 381 100 1000 100 100 20000 2000 40 100 382 100 1000 100 100 20000 2000 40 500 383 100 1000 100 100 20000 2000 100 300 384 100 1000 100 100 20000 2000 100 500 385 150 200 60 80 5000 1000 20 100 386 150 200 60 80 5000 1000 20 300 387 150 200 60 80 5000 1000 40 100 388 150 200 60 80 5000 1000 40 500 389 150 200 60 80 5000 1500 20 300 390 150 200 60 80 5000 1500 20 500 391 150 200 60 80 5000 1500 100 100 392 150 200 60 80 5000 1500 100 300 393 150 200 60 80 10000 1000 40 100 394 150 200 60 80 10000 1000 40 500 395 150 200 60 80 10000 1000 100 300 396 150 200 60 80 10000 1000 100 500 397 150 200 60 80 10000 2000 20 100 398 150 200 60 80 10000 2000 20 300 399 150 200 60 80 10000 2000 40 100 400 150 200 60 80 10000 2000 40 500 401 150 200 60 90 5000 1500 20 300 402 150 200 60 90 5000 1500 20 500 403 150 200 60 90 5000 1500 100 100 404 150 200 60 90 5000 1500 100 300
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A2 - 12
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
405 150 200 60 90 5000 2000 40 100 406 150 200 60 90 5000 2000 40 500 407 150 200 60 90 5000 2000 100 300 408 150 200 60 90 5000 2000 100 500 409 150 200 60 90 20000 1000 20 100 410 150 200 60 90 20000 1000 20 300 411 150 200 60 90 20000 1000 40 100 412 150 200 60 90 20000 1000 40 500 413 150 200 60 90 20000 1500 20 300 414 150 200 60 90 20000 1500 20 500 415 150 200 60 90 20000 1500 100 100 416 150 200 60 90 20000 1500 100 300 417 150 200 80 80 10000 1000 40 100 418 150 200 80 80 10000 1000 40 500 419 150 200 80 80 10000 1000 100 300 420 150 200 80 80 10000 1000 100 500 421 150 200 80 80 10000 2000 20 100 422 150 200 80 80 10000 2000 20 300 423 150 200 80 80 10000 2000 40 100 424 150 200 80 80 10000 2000 40 500 425 150 200 80 80 20000 1500 20 300 426 150 200 80 80 20000 1500 20 500 427 150 200 80 80 20000 1500 100 100 428 150 200 80 80 20000 1500 100 300 429 150 200 80 80 20000 2000 40 100 430 150 200 80 80 20000 2000 40 500 431 150 200 80 80 20000 2000 100 300 432 150 200 80 80 20000 2000 100 500 433 150 200 80 100 5000 1000 20 100 434 150 200 80 100 5000 1000 20 300 435 150 200 80 100 5000 1000 40 100 436 150 200 80 100 5000 1000 40 500 437 150 200 80 100 5000 1500 20 300 438 150 200 80 100 5000 1500 20 500 439 150 200 80 100 5000 1500 100 100 440 150 200 80 100 5000 1500 100 300 441 150 200 80 100 10000 1000 40 100
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A2 - 13
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
442 150 200 80 100 10000 1000 40 500 443 150 200 80 100 10000 1000 100 300 444 150 200 80 100 10000 1000 100 500 445 150 200 80 100 10000 2000 20 100 446 150 200 80 100 10000 2000 20 300 447 150 200 80 100 10000 2000 40 100 448 150 200 80 100 10000 2000 40 500 449 150 1800 60 90 5000 1500 20 300 450 150 1800 60 90 5000 1500 20 500 451 150 1800 60 90 5000 1500 100 100 452 150 1800 60 90 5000 1500 100 300 453 150 1800 60 90 5000 2000 40 100 454 150 1800 60 90 5000 2000 40 500 455 150 1800 60 90 5000 2000 100 300 456 150 1800 60 90 5000 2000 100 500 457 150 1800 60 90 20000 1000 20 100 458 150 1800 60 90 20000 1000 20 300 459 150 1800 60 90 20000 1000 40 100 460 150 1800 60 90 20000 1000 40 500 461 150 1800 60 90 20000 1500 20 300 462 150 1800 60 90 20000 1500 20 500 463 150 1800 60 90 20000 1500 100 100 464 150 1800 60 90 20000 1500 100 300 465 150 1800 60 100 10000 1000 40 100 466 150 1800 60 100 10000 1000 40 500 467 150 1800 60 100 10000 1000 100 300 468 150 1800 60 100 10000 1000 100 500 469 150 1800 60 100 10000 2000 20 100 470 150 1800 60 100 10000 2000 20 300 471 150 1800 60 100 10000 2000 40 100 472 150 1800 60 100 10000 2000 40 500 473 150 1800 60 100 20000 1500 20 300 474 150 1800 60 100 20000 1500 20 500 475 150 1800 60 100 20000 1500 100 100 476 150 1800 60 100 20000 1500 100 300 477 150 1800 60 100 20000 2000 40 100 478 150 1800 60 100 20000 2000 40 500
Appendix 2 Sensitivity Analysis Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A2 - 14
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
BT (mm)
479 150 1800 60 100 20000 2000 100 300 480 150 1800 60 100 20000 2000 100 500 481 150 1800 100 80 5000 1000 20 100 482 150 1800 100 80 5000 1000 20 300 483 150 1800 100 80 5000 1000 40 100 484 150 1800 100 80 5000 1000 40 500 485 150 1800 100 80 5000 1500 20 300 486 150 1800 100 80 5000 1500 20 500 487 150 1800 100 80 5000 1500 100 100 488 150 1800 100 80 5000 1500 100 300 489 150 1800 100 80 10000 1000 40 100 490 150 1800 100 80 10000 1000 40 500 491 150 1800 100 80 10000 1000 100 300 492 150 1800 100 80 10000 1000 100 500 493 150 1800 100 80 10000 2000 20 100 494 150 1800 100 80 10000 2000 20 300 495 150 1800 100 80 10000 2000 40 100 496 150 1800 100 80 10000 2000 40 500 497 150 1800 100 90 5000 1500 20 300 498 150 1800 100 90 5000 1500 20 500 499 150 1800 100 90 5000 1500 100 100 500 150 1800 100 90 5000 1500 100 300 501 150 1800 100 90 5000 2000 40 100 502 150 1800 100 90 5000 2000 40 500 503 150 1800 100 90 5000 2000 100 300 504 150 1800 100 90 5000 2000 100 500 505 150 1800 100 90 20000 1000 20 100 506 150 1800 100 90 20000 1000 20 300 507 150 1800 100 90 20000 1000 40 100 508 150 1800 100 90 20000 1000 40 500 509 150 1800 100 90 20000 1500 20 300 510 150 1800 100 90 20000 1500 20 500 511 150 1800 100 90 20000 1500 100 100 512 150 1800 100 90 20000 1500 100 300
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A3 - 1
APPENDIX 3. SENSITIVITY ANALYSIS RESULTS
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 1 30 2600 60 80 5000 1000 20 100 899 1019 785 905 669 789 2 30 2600 60 80 5000 1000 20 300 661 981 548 868 427 747 3 30 2600 60 80 5000 1000 40 100 861 1001 748 888 632 772 4 30 2600 60 80 5000 1000 40 500 393 933 260 800 159 699 5 30 2600 60 80 5000 1500 20 300 648 968 535 855 413 733 6 30 2600 60 80 5000 1500 20 500 406 926 285 805 187 707 7 30 2600 60 80 5000 1500 100 100 761 961 643 843 539 739 8 30 2600 60 80 5000 1500 100 300 517 917 412 812 284 684 9 30 2600 60 80 10000 1000 40 100 928 1068 811 951 672 812
10 30 2600 60 80 10000 1000 40 500 443 983 326 866 204 744 11 30 2600 60 80 10000 1000 100 300 610 1010 481 881 349 749 12 30 2600 60 80 10000 1000 100 500 359 959 222 822 101 701 13 30 2600 60 80 10000 2000 20 100 940 1060 812 932 687 807 14 30 2600 60 80 10000 2000 20 300 704 1024 588 908 444 764 15 30 2600 60 80 10000 2000 40 100 894 1034 781 921 646 786 16 30 2600 60 80 10000 2000 40 500 406 946 289 829 169 709 17 30 2600 60 90 5000 1500 20 300 649 969 490 810 415 735 18 30 2600 60 90 5000 1500 20 500 406 926 240 760 189 709
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A3 - 2
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 19 30 2600 60 90 5000 1500 100 100 763 963 610 810 541 741 20 30 2600 60 90 5000 1500 100 300 519 919 364 764 286 686 21 30 2600 60 90 5000 2000 40 100 831 971 681 821 609 749 22 30 2600 60 90 5000 2000 40 500 354 894 204 744 129 669 23 30 2600 60 90 5000 2000 100 300 502 902 350 750 271 671 24 30 2600 60 90 5000 2000 100 500 240 840 104 704 44 644 25 30 2600 60 90 20000 1000 20 100 1033 1153 839 959 754 874 26 30 2600 60 90 20000 1000 20 300 802 1122 610 930 512 832 27 30 2600 60 90 20000 1000 40 100 1000 1140 811 951 716 856 28 30 2600 60 90 20000 1000 40 500 519 1059 325 865 221 761 29 30 2600 60 90 20000 1500 20 300 788 1108 598 918 499 819 30 30 2600 60 90 20000 1500 20 500 544 1064 350 870 246 766 31 30 2600 60 90 20000 1500 100 100 883 1083 703 903 610 810 32 30 2600 60 90 20000 1500 100 300 643 1043 454 854 371 771 33 30 2600 80 80 10000 1000 40 100 1218 1358 1063 1203 837 977 34 30 2600 80 80 10000 1000 40 500 735 1275 596 1136 357 897 35 30 2600 80 80 10000 1000 100 300 882 1282 743 1143 510 910 36 30 2600 80 80 10000 1000 100 500 632 1232 490 1090 252 852 37 30 2600 80 80 10000 2000 20 100 1219 1339 1074 1194 851 971 38 30 2600 80 80 10000 2000 20 300 989 1309 837 1157 610 930 39 30 2600 80 80 10000 2000 40 100 1174 1314 1024 1164 813 953
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A3 - 3
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 40 30 2600 80 80 10000 2000 40 500 691 1231 552 1092 319 859 41 30 2600 80 80 20000 1500 20 300 1073 1393 927 1247 668 988 42 30 2600 80 80 20000 1500 20 500 829 1349 683 1203 413 933 43 30 2600 80 80 20000 1500 100 100 1167 1367 1021 1221 783 983 44 30 2600 80 80 20000 1500 100 300 931 1331 791 1191 533 933 45 30 2600 80 80 20000 2000 40 100 1247 1387 1100 1240 853 993 46 30 2600 80 80 20000 2000 40 500 776 1316 616 1156 369 909 47 30 2600 80 80 20000 2000 100 300 907 1307 769 1169 515 915 48 30 2600 80 80 20000 2000 100 500 652 1252 511 1111 254 854 49 30 2600 80 100 5000 1000 20 100 1182 1302 1032 1152 833 953 50 30 2600 80 100 5000 1000 20 300 937 1257 802 1122 602 922 51 30 2600 80 100 5000 1000 40 100 1139 1279 1000 1140 804 944 52 30 2600 80 100 5000 1000 40 500 655 1195 519 1059 311 851 53 30 2600 80 100 5000 1500 20 300 923 1243 789 1109 589 909 54 30 2600 80 100 5000 1500 20 500 679 1199 544 1064 338 858 55 30 2600 80 100 5000 1500 100 100 1016 1216 882 1082 693 893 56 30 2600 80 100 5000 1500 100 300 787 1187 642 1042 441 841 57 30 2600 80 100 10000 1000 40 100 1220 1360 1066 1206 840 980 58 30 2600 80 100 10000 1000 40 500 737 1277 599 1139 362 902 59 30 2600 80 100 10000 1000 100 300 885 1285 745 1145 514 914 60 30 2600 80 100 10000 1000 100 500 634 1234 493 1093 256 856
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A3 - 4
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 61 30 2600 80 100 10000 2000 20 100 1222 1342 1077 1197 854 974 62 30 2600 80 100 10000 2000 20 300 991 1311 839 1159 611 931 63 30 2600 80 100 10000 2000 40 100 1176 1316 1027 1167 812 952 64 30 2600 80 100 10000 2000 40 500 694 1234 555 1095 322 862 65 30 1000 60 90 5000 1500 20 300 690 1010 556 876 469 789 66 30 1000 60 90 5000 1500 20 500 441 961 306 826 217 737 67 30 1000 60 90 5000 1500 100 100 801 1001 664 864 594 794 68 30 1000 60 90 5000 1500 100 300 561 961 414 814 341 741 69 30 1000 60 90 5000 2000 40 100 869 1009 743 883 660 800 70 30 1000 60 90 5000 2000 40 500 398 938 247 787 184 724 71 30 1000 60 90 5000 2000 100 300 543 943 406 806 325 725 72 30 1000 60 90 5000 2000 100 500 280 880 166 766 80 680 73 30 1000 60 90 20000 1000 20 100 1077 1197 914 1034 813 933 74 30 1000 60 90 20000 1000 20 300 836 1156 673 993 572 892 75 30 1000 60 90 20000 1000 40 100 1037 1177 874 1014 774 914 76 30 1000 60 90 20000 1000 40 500 566 1106 404 944 280 820 77 30 1000 60 90 20000 1500 20 300 822 1142 660 980 559 879 78 30 1000 60 90 20000 1500 20 500 591 1111 407 927 306 826 79 30 1000 60 90 20000 1500 100 100 925 1125 774 974 665 865 80 30 1000 60 90 20000 1500 100 300 686 1086 528 928 412 812 81 30 1000 60 100 10000 1000 40 100 974 1114 885 1025 731 871
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A3 - 5
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 82 30 1000 60 100 10000 1000 40 500 490 1030 407 947 236 776 83 30 1000 60 100 10000 1000 100 300 644 1044 569 969 407 807 84 30 1000 60 100 10000 1000 100 500 406 1006 313 913 162 762 85 30 1000 60 100 10000 2000 20 100 986 1106 898 1018 745 865 86 30 1000 60 100 10000 2000 20 300 749 1069 661 981 503 823 87 30 1000 60 100 10000 2000 40 100 938 1078 853 993 702 842 88 30 1000 60 100 10000 2000 40 500 449 989 380 920 203 743 89 30 1000 60 100 20000 1500 20 300 823 1143 743 1063 559 879 90 30 1000 60 100 20000 1500 20 500 592 1112 496 1016 307 827 91 30 1000 60 100 20000 1500 100 100 927 1127 839 1039 666 866 92 30 1000 60 100 20000 1500 100 300 687 1087 610 1010 413 813 93 30 1000 60 100 20000 2000 40 100 1009 1149 919 1059 745 885 94 30 1000 60 100 20000 2000 40 500 525 1065 430 970 245 785 95 30 1000 60 100 20000 2000 100 300 668 1068 595 995 406 806 96 30 1000 60 100 20000 2000 100 500 406 1006 335 935 165 765 97 30 1000 100 80 5000 1000 20 100 1472 1592 1369 1489 1038 1158 98 30 1000 100 80 5000 1000 20 300 1221 1541 1121 1441 802 1122 99 30 1000 100 80 5000 1000 40 100 1427 1567 1325 1465 1006 1146
100 30 1000 100 80 5000 1000 40 500 949 1489 840 1380 512 1052 101 30 1000 100 80 5000 1500 20 300 1216 1536 1107 1427 789 1109 102 30 1000 100 80 5000 1500 20 500 972 1492 863 1383 537 1057
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A3 - 6
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 103 30 1000 100 80 5000 1500 100 100 1295 1495 1199 1399 888 1088 104 30 1000 100 80 5000 1500 100 300 1057 1457 964 1364 639 1039 105 30 1000 100 80 10000 1000 40 100 1521 1661 1416 1556 1051 1191 106 30 1000 100 80 10000 1000 40 500 1029 1569 929 1469 568 1108 107 30 1000 100 80 10000 1000 100 300 1184 1584 1073 1473 721 1121 108 30 1000 100 80 10000 1000 100 500 940 1540 827 1427 462 1062 109 30 1000 100 80 10000 2000 20 100 1530 1650 1426 1546 1064 1184 110 30 1000 100 80 10000 2000 20 300 1284 1604 1182 1502 820 1140 111 30 1000 100 80 10000 2000 40 100 1470 1610 1366 1506 1016 1156 112 30 1000 100 80 10000 2000 40 500 997 1537 884 1424 526 1066 113 30 1000 100 90 5000 1500 20 300 1218 1538 1108 1428 790 1110 114 30 1000 100 90 5000 1500 20 500 974 1494 864 1384 539 1059 115 30 1000 100 90 5000 1500 100 100 1296 1496 1200 1400 890 1090 116 30 1000 100 90 5000 1500 100 300 1059 1459 965 1365 640 1040 117 30 1000 100 90 5000 2000 40 100 1389 1529 1280 1420 972 1112 118 30 1000 100 90 5000 2000 40 500 905 1445 812 1352 473 1013 119 30 1000 100 90 5000 2000 100 300 1034 1434 940 1340 621 1021 120 30 1000 100 90 5000 2000 100 500 795 1395 686 1286 379 979 121 30 1000 100 90 20000 1000 20 100 1657 1777 1547 1667 1150 1270 122 30 1000 100 90 20000 1000 20 300 1409 1729 1293 1613 903 1223 123 30 1000 100 90 20000 1000 40 100 1618 1758 1500 1640 1109 1249
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A3 - 7
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 124 30 1000 100 90 20000 1000 40 500 1126 1666 1016 1556 611 1151 125 30 1000 100 90 20000 1500 20 300 1395 1715 1278 1598 889 1209 126 30 1000 100 90 20000 1500 20 500 1149 1669 1032 1552 635 1155 127 30 1000 100 90 20000 1500 100 100 1469 1669 1364 1564 997 1197 128 30 1000 100 90 20000 1500 100 300 1231 1631 1128 1528 749 1149 129 60 200 80 80 10000 1000 40 100 736 876 664 804 612 752 130 60 200 80 80 10000 1000 40 500 254 794 194 734 131 671 131 60 200 80 80 10000 1000 100 300 410 810 342 742 285 685 132 60 200 80 80 10000 1000 100 500 176 776 105 705 47 647 133 60 200 80 80 10000 2000 20 100 751 871 679 799 626 746 134 60 200 80 80 10000 2000 20 300 513 833 439 759 392 712 135 60 200 80 80 10000 2000 40 100 715 855 645 785 594 734 136 60 200 80 80 10000 2000 40 500 228 768 168 708 105 645 137 60 200 80 80 20000 1500 20 300 576 896 494 814 434 754 138 60 200 80 80 20000 1500 20 500 331 851 251 771 196 716 139 60 200 80 80 20000 1500 100 100 688 888 611 811 556 756 140 60 200 80 80 20000 1500 100 300 442 842 371 771 304 704 141 60 200 80 80 20000 2000 40 100 765 905 690 830 627 767 142 60 200 80 80 20000 2000 40 500 279 819 214 754 142 682 143 60 200 80 80 20000 2000 100 300 429 829 358 758 291 691 144 60 200 80 80 20000 2000 100 500 193 793 116 716 49 649
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A3 - 8
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 145 60 200 80 100 5000 1000 20 100 729 849 663 783 614 734 146 60 200 80 100 5000 1000 20 300 490 810 423 743 380 700 147 60 200 80 100 5000 1000 40 100 695 835 631 771 584 724 148 60 200 80 100 5000 1000 40 500 215 755 161 701 101 641 149 60 200 80 100 5000 1500 20 300 480 800 413 733 368 688 150 60 200 80 100 5000 1500 20 500 238 758 184 704 125 645 151 60 200 80 100 5000 1500 100 100 602 802 536 736 485 685 152 60 200 80 100 5000 1500 100 300 356 756 290 690 235 635 153 60 200 80 100 10000 1000 40 100 742 882 671 811 617 757 154 60 200 80 100 10000 1000 40 500 261 801 202 742 137 677 155 60 200 80 100 10000 1000 100 300 417 817 350 750 291 691 156 60 200 80 100 10000 1000 100 500 183 783 113 713 52 652 157 60 200 80 100 10000 2000 20 100 757 877 687 807 631 751 158 60 200 80 100 10000 2000 20 300 519 839 447 767 396 716 159 60 200 80 100 10000 2000 40 100 721 861 652 792 598 738 160 60 200 80 100 10000 2000 40 500 235 775 178 718 110 650 161 60 200 100 90 5000 1500 20 300 659 979 569 889 498 818 162 60 200 100 90 5000 1500 20 500 411 931 326 846 245 765 163 60 200 100 90 5000 1500 100 100 770 970 681 881 612 812 164 60 200 100 90 5000 1500 100 300 528 928 437 837 367 767 165 60 200 100 90 5000 2000 40 100 843 983 759 899 688 828
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A3 - 9
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 166 60 200 100 90 5000 2000 40 500 363 903 274 814 203 743 167 60 200 100 90 5000 2000 100 300 512 912 424 824 353 753 168 60 200 100 90 5000 2000 100 500 259 859 188 788 99 699 169 60 200 100 90 20000 1000 20 100 1051 1171 940 1060 835 955 170 60 200 100 90 20000 1000 20 300 813 1133 702 1022 599 919 171 60 200 100 90 20000 1000 40 100 1016 1156 902 1042 803 943 172 60 200 100 90 20000 1000 40 500 535 1075 421 961 310 850 173 60 200 100 90 20000 1500 20 300 804 1124 691 1011 586 906 174 60 200 100 90 20000 1500 20 500 559 1079 444 964 334 854 175 60 200 100 90 20000 1500 100 100 903 1103 799 999 697 897 176 60 200 100 90 20000 1500 100 300 662 1062 559 959 445 845 177 60 200 100 100 10000 1000 40 100 942 1082 841 981 760 900 178 60 200 100 100 10000 1000 40 500 460 1000 365 905 267 807 179 60 200 100 100 10000 1000 100 300 617 1017 520 920 427 827 180 60 200 100 100 10000 1000 100 500 371 971 270 870 185 785 181 60 200 100 100 10000 2000 20 100 954 1074 854 974 774 894 182 60 200 100 100 10000 2000 20 300 719 1039 617 937 533 853 183 60 200 100 100 10000 2000 40 100 910 1050 814 954 733 873 184 60 200 100 100 10000 2000 40 500 424 964 333 873 233 773 185 60 200 100 100 20000 1500 20 300 805 1125 693 1013 589 909 186 60 200 100 100 20000 1500 20 500 561 1081 446 966 336 856
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A3 - 10
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 187 60 200 100 100 20000 1500 100 100 904 1104 802 1002 699 899 188 60 200 100 100 20000 1500 100 300 664 1064 561 961 447 847 189 60 200 100 100 20000 2000 40 100 983 1123 874 1014 776 916 190 60 200 100 100 20000 2000 40 500 497 1037 397 937 278 818 191 60 200 100 100 20000 2000 100 300 646 1046 545 945 431 831 192 60 200 100 100 20000 2000 100 500 395 995 290 890 189 789 193 60 1800 60 80 5000 1000 20 100 516 636 463 583 425 545 194 60 1800 60 80 5000 1000 20 300 274 594 222 542 193 513 195 60 1800 60 80 5000 1000 40 100 484 624 433 573 400 540 196 60 1800 60 80 5000 1000 40 500 27 567 NA NA NA NA 197 60 1800 60 80 5000 1500 20 300 265 585 216 536 184 504 198 60 1800 60 80 5000 1500 20 500 42 562 NA NA NA NA 199 60 1800 60 80 5000 1500 100 100 391 591 338 538 298 498 200 60 1800 60 80 5000 1500 100 300 147 547 95 495 60 460 201 60 1800 60 80 10000 1000 40 100 514 654 458 598 419 559 202 60 1800 60 80 10000 1000 40 500 46 586 NA NA NA NA 203 60 1800 60 80 10000 1000 100 300 194 594 136 536 99 499 204 60 1800 60 80 10000 1000 100 100 430 630 379 579 337 537 205 60 1800 60 80 10000 2000 20 100 531 651 475 595 434 554 206 60 1800 60 80 10000 2000 20 300 288 608 231 551 203 523 207 60 1800 60 80 10000 2000 40 100 499 639 443 583 407 547
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A3 - 11
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 208 60 1800 60 80 10000 2000 40 500 33 573 NA NA NA NA 209 60 1800 60 90 5000 1500 20 300 269 589 218 538 188 508 210 60 1800 60 90 5000 1500 20 500 45 565 NA NA NA NA 211 60 1800 60 90 5000 1500 100 100 395 595 341 541 301 501 212 60 1800 60 90 5000 1500 100 300 152 552 100 500 63 463 213 60 1800 60 90 5000 2000 40 100 474 614 423 563 388 528 214 60 1800 60 90 5000 2000 40 500 20 560 NA NA NA NA 215 60 1800 60 90 5000 2000 100 300 140 540 89 489 52 452 216 60 1800 60 90 5000 2000 100 100 383 583 329 529 289 489 217 60 1800 60 90 20000 1000 20 100 581 701 520 640 480 600 218 60 1800 60 90 20000 1000 20 300 341 661 279 599 240 560 219 60 1800 60 90 20000 1000 40 100 549 689 489 629 448 588 220 60 1800 60 90 20000 1000 40 500 77 617 29 569 NA NA 221 60 1800 60 90 20000 1500 20 300 332 652 270 590 231 551 222 60 1800 60 90 20000 1500 20 500 99 619 45 565 21 541 223 60 1800 60 90 20000 1500 100 100 451 651 394 594 354 554 224 60 1800 60 90 20000 1500 100 300 205 605 152 552 111 511 225 60 1800 80 80 10000 1000 40 100 668 808 593 733 546 686 226 60 1800 80 80 10000 1000 40 500 198 738 117 657 68 608 227 60 1800 80 80 10000 1000 100 300 347 747 265 665 217 617 228 60 1800 80 80 10000 1000 100 500 108 708 46 646 NA NA
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A3 - 12
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 229 60 1800 80 80 10000 2000 20 100 683 803 609 729 561 681 230 60 1800 80 80 10000 2000 20 300 444 764 369 689 321 641 231 60 1800 80 80 10000 2000 40 100 649 789 576 716 526 666 232 60 1800 80 80 10000 2000 40 500 172 712 96 636 48 588 233 60 1800 80 80 20000 1500 20 300 502 822 419 739 365 685 234 60 1800 80 80 20000 1500 20 500 257 777 181 701 123 643 235 60 1800 80 80 20000 1500 100 100 617 817 537 737 481 681 236 60 1800 80 80 20000 1500 100 300 377 777 290 690 232 632 237 60 1800 80 80 20000 2000 40 100 695 835 616 756 560 700 238 60 1800 80 80 20000 2000 40 500 208 748 124 664 75 615 239 60 1800 80 80 20000 2000 100 300 364 764 278 678 219 619 240 60 1800 80 80 20000 2000 100 500 122 722 52 652 NA NA 241 60 1800 80 100 5000 1000 20 100 665 785 596 716 553 673 242 60 1800 80 100 5000 1000 20 300 426 746 357 677 313 633 243 60 1800 80 100 5000 1000 40 100 633 773 565 705 520 660 244 60 1800 80 100 5000 1000 40 500 161 701 91 631 47 587 245 60 1800 80 100 5000 1500 20 300 416 736 348 668 303 623 246 60 1800 80 100 5000 1500 20 500 186 706 113 633 67 587 247 60 1800 80 100 5000 1500 100 100 540 740 467 667 421 621 248 60 1800 80 100 5000 1500 100 300 292 692 221 621 181 581 249 60 1800 80 100 10000 1000 40 100 675 815 601 741 552 692
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A3 - 13
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 250 60 1800 80 100 10000 1000 40 500 204 744 126 666 73 613 251 60 1800 80 100 10000 1000 100 300 354 754 274 674 227 627 252 60 1800 80 100 10000 1000 100 500 116 716 47 647 NA NA 253 60 1800 80 100 10000 2000 20 100 691 811 613 733 567 687 254 60 1800 80 100 10000 2000 20 300 451 771 377 697 327 647 255 60 1800 80 100 10000 2000 40 100 656 796 584 724 532 672 256 60 1800 80 100 10000 2000 40 500 180 720 106 646 53 593 257 100 2600 60 90 5000 1500 20 300 138 458 101 421 70 390 258 100 2600 60 90 5000 1500 20 100 378 498 338 458 303 423 259 100 2600 60 90 5000 1500 100 100 253 453 214 414 181 381 260 100 2600 60 90 5000 1500 100 300 26 426 NA NA NA NA 261 100 2600 60 90 5000 2000 40 100 340 480 303 443 269 409 262 100 2600 60 90 5000 2000 40 300 101 441 66 406 37 377 263 100 2600 60 90 5000 2000 20 300 133 453 96 416 65 385 264 100 2600 60 90 5000 2000 20 100 370 490 333 453 299 419 265 100 2600 60 90 20000 1000 20 100 410 530 372 492 337 457 266 100 2600 60 90 20000 1000 20 300 175 495 136 456 103 423 267 100 2600 60 90 20000 1000 40 100 383 523 343 483 308 448 268 100 2600 60 90 20000 1000 40 300 145 485 106 446 74 414 269 100 2600 60 90 20000 1500 20 300 167 487 128 448 96 416 270 100 2600 60 90 20000 1500 20 100 406 526 366 486 331 451
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A3 - 14
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 271 100 2600 60 90 20000 1500 100 100 284 484 243 443 207 407 272 100 2600 60 90 20000 1500 100 300 52 452 19 419 NA NA 273 100 2600 60 100 10000 1000 40 100 372 512 331 471 298 438 274 100 2600 60 100 10000 1000 40 300 135 475 94 434 65 405 275 100 2600 60 100 10000 1000 100 300 55 455 21 421 NA NA 276 100 2600 60 100 10000 1000 100 100 287 487 246 446 213 413 277 100 2600 60 100 10000 2000 20 100 390 510 350 470 317 437 278 100 2600 60 100 10000 2000 20 300 152 472 112 432 82 402 279 100 2600 60 100 10000 2000 40 100 359 499 319 459 286 426 280 100 2600 60 100 10000 2000 40 300 121 461 81 421 53 393 281 100 2600 60 100 20000 1500 20 300 172 492 131 451 100 420 282 100 2600 60 100 20000 1500 20 100 407 527 368 488 334 454 283 100 2600 60 100 20000 1500 100 100 288 488 244 444 211 411 284 100 2600 60 100 20000 1500 100 300 56 456 21 421 NA NA 285 100 2600 60 100 20000 2000 40 100 375 515 333 473 300 440 286 100 2600 60 100 20000 2000 40 300 135 475 94 434 65 405 287 100 2600 60 100 20000 2000 100 300 45 445 NA NA NA NA 288 100 2600 60 100 20000 2000 100 100 276 476 232 432 199 399 289 100 2600 100 80 5000 1000 20 100 549 669 486 606 462 582 290 100 2600 100 80 5000 1000 20 300 309 629 246 566 224 544 291 100 2600 100 80 5000 1000 40 100 518 658 456 596 432 572
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A3 - 15
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 292 100 2600 100 80 5000 1000 40 500 50 590 NA NA NA NA 293 100 2600 100 80 5000 1500 20 300 301 621 238 558 216 536 294 100 2600 100 80 5000 1500 20 500 70 590 NA NA NA NA 295 100 2600 100 80 5000 1500 100 100 422 622 363 563 337 537 296 100 2600 100 80 5000 1500 100 300 184 584 123 523 98 498 297 100 2600 100 80 10000 1000 40 100 542 682 478 618 451 591 298 100 2600 100 80 10000 1000 40 500 71 611 NA NA NA NA 299 100 2600 100 80 10000 1000 100 300 218 618 158 558 134 534 300 100 2600 100 80 10000 1000 100 100 460 660 398 598 372 572 301 100 2600 100 80 10000 2000 20 100 559 679 495 615 469 589 302 100 2600 100 80 10000 2000 20 300 318 638 253 573 230 550 303 100 2600 100 80 10000 2000 40 100 527 667 463 603 437 577 304 100 2600 100 80 10000 2000 40 500 55 595 NA NA NA NA 305 100 2600 100 90 5000 1500 20 300 308 628 247 567 222 542 306 100 2600 100 90 5000 1500 20 500 78 598 26 546 NA NA 307 100 2600 100 90 5000 1500 100 100 429 629 371 571 343 543 308 100 2600 100 90 5000 1500 100 300 192 592 131 531 105 505 309 100 2600 100 90 5000 2000 40 100 511 651 451 591 423 563 310 100 2600 100 90 5000 2000 40 500 42 582 NA NA NA NA 311 100 2600 100 90 5000 2000 100 300 180 580 120 520 93 493 312 100 2600 100 90 5000 2000 100 100 419 619 360 560 332 532
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A3 - 16
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 313 100 2600 100 90 20000 1000 20 100 605 725 537 657 510 630 314 100 2600 100 90 20000 1000 20 300 366 686 298 618 273 593 315 100 2600 100 90 20000 1000 40 100 574 714 507 647 480 620 316 100 2600 100 90 20000 1000 40 500 102 642 41 581 21 561 317 100 2600 100 90 20000 1500 20 300 356 676 289 609 264 584 318 100 2600 100 90 20000 1500 20 500 125 645 61 581 35 555 319 100 2600 100 90 20000 1500 100 100 478 678 411 611 385 585 320 100 2600 100 90 20000 1500 100 300 235 635 173 573 145 545 321 100 1000 80 80 10000 1000 40 100 462 602 420 560 395 535 322 100 1000 80 80 10000 1000 40 300 222 562 184 524 158 498 323 100 1000 80 80 10000 1000 100 300 143 543 102 502 77 477 324 100 1000 80 80 10000 1000 100 100 382 582 340 540 313 513 325 100 1000 80 80 10000 2000 20 100 479 599 438 558 411 531 326 100 1000 80 80 10000 2000 20 300 238 558 201 521 175 495 327 100 1000 80 80 10000 2000 40 100 448 588 407 547 382 522 328 100 1000 80 80 10000 2000 40 300 205 545 168 508 142 482 329 100 1000 80 80 20000 1500 20 300 264 584 221 541 199 519 330 100 1000 80 80 20000 1500 20 500 40 560 13 533 NA NA 331 100 1000 80 80 20000 1500 100 100 387 587 344 544 317 517 332 100 1000 80 80 20000 1500 100 300 149 549 107 507 80 480 333 100 1000 80 80 20000 2000 40 100 468 608 426 566 399 539
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A3 - 17
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 334 100 1000 80 80 20000 2000 40 300 225 565 186 526 160 500 335 100 1000 80 80 20000 2000 100 300 138 538 95 495 69 469 336 100 1000 80 80 20000 2000 100 100 377 577 333 533 305 505 337 100 1000 80 100 5000 1000 20 100 485 605 445 565 415 535 338 100 1000 80 100 5000 1000 20 300 244 564 205 525 182 502 339 100 1000 80 100 5000 1000 40 100 453 593 414 554 387 527 340 100 1000 80 100 5000 1000 40 300 215 555 179 519 151 491 341 100 1000 80 100 5000 1500 20 300 236 556 202 522 173 493 342 100 1000 80 100 5000 1500 20 100 476 596 437 557 408 528 343 100 1000 80 100 5000 1500 100 100 359 559 318 518 288 488 344 100 1000 80 100 5000 1500 100 300 122 522 83 483 56 456 345 100 1000 80 100 10000 1000 40 100 472 612 432 572 405 545 346 100 1000 80 100 10000 1000 40 300 233 573 196 536 168 508 347 100 1000 80 100 10000 1000 100 300 155 555 114 514 87 487 348 100 1000 80 100 10000 1000 100 100 393 593 352 552 322 522 349 100 1000 80 100 10000 2000 20 100 491 611 450 570 420 540 350 100 1000 80 100 10000 2000 20 300 249 569 209 529 186 506 351 100 1000 80 100 10000 2000 40 100 459 599 418 558 391 531 352 100 1000 80 100 10000 2000 40 300 216 556 181 521 152 492 353 100 1000 100 90 5000 1500 20 300 321 641 271 591 248 568 354 100 1000 100 90 5000 1500 20 500 90 610 45 565 25 545
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A3 - 18
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 355 100 1000 100 90 5000 1500 100 100 442 642 396 596 370 570 356 100 1000 100 90 5000 1500 100 300 203 603 156 556 130 530 357 100 1000 100 90 5000 2000 40 100 523 663 476 616 449 589 358 100 1000 100 90 5000 2000 40 500 52 592 NA NA NA NA 359 100 1000 100 90 5000 2000 100 300 193 593 145 545 119 519 360 100 1000 100 90 5000 2000 100 100 432 632 385 585 358 558 361 100 1000 100 90 20000 1000 20 100 616 736 564 684 541 661 362 100 1000 100 90 20000 1000 20 300 380 700 325 645 303 623 363 100 1000 100 90 20000 1000 40 100 588 728 534 674 509 649 364 100 1000 100 90 20000 1000 40 500 115 655 65 605 39 579 365 100 1000 100 90 20000 1500 20 300 371 691 317 637 294 614 366 100 1000 100 90 20000 1500 20 500 139 659 86 606 59 579 367 100 1000 100 90 20000 1500 100 100 492 692 438 638 413 613 368 100 1000 100 90 20000 1500 100 300 249 649 200 600 174 574 369 100 1000 100 100 10000 1000 40 100 568 708 517 657 491 631 370 100 1000 100 100 10000 1000 40 500 96 636 50 590 27 567 371 100 1000 100 100 10000 1000 100 300 244 644 198 598 172 572 372 100 1000 100 100 10000 1000 100 500 25 625 NA NA NA NA 373 100 1000 100 100 10000 2000 20 100 584 704 534 654 507 627 374 100 1000 100 100 10000 2000 20 300 344 664 293 613 268 588 375 100 1000 100 100 10000 2000 40 100 552 692 503 643 474 614
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A3 - 19
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 376 100 1000 100 100 10000 2000 40 300 309 649 259 599 232 572 377 100 1000 100 100 20000 1500 20 300 376 696 323 643 298 618 378 100 1000 100 100 20000 1500 20 500 144 664 92 612 64 584 379 100 1000 100 100 20000 1500 100 100 497 697 443 643 416 616 380 100 1000 100 100 20000 1500 100 300 254 654 203 603 179 579 381 100 1000 100 100 20000 2000 40 100 577 717 525 665 496 636 382 100 1000 100 100 20000 2000 40 500 103 643 55 595 28 568 383 100 1000 100 100 20000 2000 100 300 243 643 195 595 167 567 384 100 1000 100 100 20000 2000 100 100 487 687 433 633 406 606 385 150 200 60 80 5000 1000 20 100 301 421 273 393 248 368 386 150 200 60 80 5000 1000 20 300 67 387 41 361 21 341 387 150 200 60 80 5000 1000 40 100 272 412 244 384 220 360 388 150 200 60 80 5000 1000 40 300 40 380 17 357 NA NA 389 150 200 60 80 5000 1500 20 300 61 381 36 356 NA NA 390 150 200 60 80 5000 1500 20 100 294 414 267 387 243 363 391 150 200 60 80 5000 1500 100 100 175 375 147 347 122 322 392 150 200 60 80 5000 1500 40 100 266 406 238 378 215 355 393 150 200 60 80 10000 1000 40 100 280 420 252 392 228 368 394 150 200 60 80 10000 1000 40 300 48 388 23 363 NA NA 395 150 200 60 80 10000 1000 100 100 200 400 171 371 146 346 396 150 200 60 80 10000 1000 20 300 75 395 49 369 28 348
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A3 - 20
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 397 150 200 60 80 10000 2000 20 100 298 418 271 391 247 367 398 150 200 60 80 10000 2000 20 300 65 385 39 359 20 340 399 150 200 60 80 10000 2000 40 100 268 408 241 381 218 358 400 150 200 60 80 10000 2000 40 300 37 377 NA NA NA NA 401 150 200 60 90 5000 1500 20 300 69 389 45 365 22 342 402 150 200 60 90 5000 1500 20 100 301 421 277 397 249 369 403 150 200 60 90 5000 1500 100 100 182 382 157 357 129 329 404 150 200 60 90 5000 1500 40 100 273 413 248 388 221 361 405 150 200 60 90 5000 2000 40 100 267 407 244 384 216 356 406 150 200 60 90 5000 2000 40 300 36 376 16 356 NA NA 407 150 200 60 90 5000 2000 100 100 169 369 143 343 114 314 408 150 200 60 90 5000 2000 20 300 64 384 41 361 19 339 409 150 200 60 90 20000 1000 20 100 324 444 299 419 269 389 410 150 200 60 90 20000 1000 20 300 91 411 66 386 40 360 411 150 200 60 90 20000 1000 40 100 295 435 270 410 242 382 412 150 200 60 90 20000 1000 40 300 63 403 39 379 17 357 413 150 200 60 90 20000 1500 20 300 84 404 60 380 35 355 414 150 200 60 90 20000 1500 20 100 318 438 292 412 264 384 415 150 200 60 90 20000 1500 100 100 199 399 173 373 143 343 416 150 200 60 90 20000 1500 40 100 289 429 264 404 236 376 417 150 200 80 80 10000 1000 40 100 356 496 317 457 293 433
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A3 - 21
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 418 150 200 80 80 10000 1000 40 300 116 456 82 422 62 402 419 150 200 80 80 10000 1000 100 300 39 439 NA NA NA NA 420 150 200 80 80 10000 1000 100 100 269 469 235 435 212 412 421 150 200 80 80 10000 2000 20 100 369 489 336 456 312 432 422 150 200 80 80 10000 2000 20 300 133 453 100 420 79 399 423 150 200 80 80 10000 2000 40 100 339 479 306 446 282 422 424 150 200 80 80 10000 2000 40 300 102 442 69 409 50 390 425 150 200 80 80 20000 1500 20 300 147 467 113 433 92 412 426 150 200 80 80 20000 1500 20 100 383 503 349 469 326 446 427 150 200 80 80 20000 1500 100 100 265 465 230 430 206 406 428 150 200 80 80 20000 1500 100 300 35 435 NA NA NA NA 429 150 200 80 80 20000 2000 40 100 349 489 315 455 292 432 430 150 200 80 80 20000 2000 40 300 111 451 78 418 58 398 431 150 200 80 80 20000 2000 100 300 26 426 NA NA NA NA 432 150 200 80 80 20000 2000 100 100 253 453 218 418 195 395 433 150 200 80 100 5000 1000 20 100 384 504 353 473 326 446 434 150 200 80 100 5000 1000 20 300 150 470 118 438 95 415 435 150 200 80 100 5000 1000 40 100 355 495 323 463 297 437 436 150 200 80 100 5000 1000 40 300 121 461 89 429 67 407 437 150 200 80 100 5000 1500 20 300 142 462 111 431 88 408 438 150 200 80 100 5000 1500 20 100 378 498 346 466 320 440
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A3 - 22
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 439 150 200 80 100 5000 1500 100 100 259 459 226 426 201 401 440 150 200 80 100 5000 1500 100 300 32 432 NA NA NA NA 441 150 200 80 100 10000 1000 40 100 365 505 333 473 307 447 442 150 200 80 100 10000 1000 40 300 131 471 99 439 75 415 443 150 200 80 100 10000 1000 100 300 53 453 24 424 NA NA 444 150 200 80 100 10000 1000 100 100 283 483 250 450 224 424 445 150 200 80 100 10000 2000 20 100 383 503 351 471 325 445 446 150 200 80 100 10000 2000 20 300 148 468 116 436 93 413 447 150 200 80 100 10000 2000 40 100 353 493 321 461 295 435 448 150 200 80 100 10000 2000 40 300 117 457 85 425 63 403 449 150 1800 60 90 5000 1500 20 300 54 374 30 350 NA NA 450 150 1800 60 90 5000 1500 20 100 286 406 259 379 233 353 451 150 1800 60 90 5000 1500 100 100 167 367 139 339 111 311 452 150 1800 60 90 5000 1500 40 100 258 398 231 371 205 345 453 150 1800 60 90 5000 2000 40 100 253 393 227 367 202 342 454 150 1800 60 90 5000 2000 40 300 23 363 NA NA NA NA 455 150 1800 60 90 5000 2000 100 100 153 353 125 325 97 297 456 150 1800 60 90 5000 2000 20 100 282 402 256 376 230 350 457 150 1800 60 90 20000 1000 20 100 308 428 281 401 252 372 458 150 1800 60 90 20000 1000 20 300 76 396 49 369 25 345 459 150 1800 60 90 20000 1000 40 100 280 420 252 392 224 364
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A3 - 23
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 460 150 1800 60 90 20000 1000 40 300 48 388 16 356 NA NA 461 150 1800 60 90 20000 1500 20 300 70 390 44 364 21 341 462 150 1800 60 90 20000 1500 20 100 303 423 275 395 247 367 463 150 1800 60 90 20000 1500 100 100 183 383 155 355 126 326 464 150 1800 60 90 20000 1500 40 100 274 414 246 386 219 359 465 150 1800 60 100 10000 1000 40 100 277 417 248 388 222 362 466 150 1800 60 100 10000 1000 40 300 46 386 21 361 NA NA 467 150 1800 60 100 10000 1000 100 100 197 397 167 367 141 341 468 150 1800 60 100 10000 1000 20 100 306 426 277 397 251 371 469 150 1800 60 100 10000 2000 20 100 296 416 267 387 242 362 470 150 1800 60 100 10000 2000 20 300 63 383 37 357 17 337 471 150 1800 60 100 10000 2000 40 100 266 406 238 378 212 352 472 150 1800 60 100 10000 2000 40 300 35 375 NA NA NA NA 473 150 1800 60 100 20000 1500 20 300 75 395 48 368 25 345 474 150 1800 60 100 20000 1500 20 100 308 428 279 399 252 372 475 150 1800 60 100 20000 1500 100 100 189 389 159 359 131 331 476 150 1800 60 100 20000 1500 40 100 279 419 250 390 224 364 477 150 1800 60 100 20000 2000 40 100 274 414 246 386 220 360 478 150 1800 60 100 20000 2000 40 300 43 383 18 358 NA NA 479 150 1800 60 100 20000 2000 100 100 176 376 146 346 117 317 480 150 1800 60 100 20000 2000 20 100 304 424 274 394 249 369
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A3 - 24
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 481 150 1800 100 80 5000 1000 20 100 412 532 372 492 352 472 482 150 1800 100 80 5000 1000 20 300 176 496 135 455 118 438 483 150 1800 100 80 5000 1000 40 100 383 523 342 482 322 462 484 150 1800 100 80 5000 1000 40 300 146 486 106 446 88 428 485 150 1800 100 80 5000 1500 20 300 168 488 128 448 110 430 486 150 1800 100 80 5000 1500 20 100 406 526 365 485 345 465 487 150 1800 100 80 5000 1500 100 100 288 488 246 446 227 427 488 150 1800 100 80 5000 1500 100 300 55 455 19 419 NA NA 489 150 1800 100 80 10000 1000 40 100 394 534 353 493 333 473 490 150 1800 100 80 10000 1000 40 300 157 497 116 456 99 439 491 150 1800 100 80 10000 1000 100 300 79 479 39 439 24 424 492 150 1800 100 80 10000 1000 100 100 313 513 271 471 251 451 493 150 1800 100 80 10000 2000 20 100 412 532 371 491 352 472 494 150 1800 100 80 10000 2000 20 300 174 494 133 453 116 436 495 150 1800 100 80 10000 2000 40 100 382 522 341 481 321 461 496 150 1800 100 80 10000 2000 40 300 143 483 102 442 85 425 497 150 1800 100 90 5000 1500 20 300 179 499 139 459 119 439 498 150 1800 100 90 5000 1500 20 100 414 534 376 496 353 473 499 150 1800 100 90 5000 1500 100 100 297 497 257 457 234 434 500 150 1800 100 90 5000 1500 100 300 65 465 28 428 NA NA 501 150 1800 100 90 5000 2000 40 100 381 521 341 481 319 459
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A3 - 25
Factor Levels B747 B767 B737 Run
SM W M TP P AM AT BT ST TT ST TT ST TT 502 150 1800 100 90 5000 2000 40 300 142 482 103 443 84 424 503 150 1800 100 90 5000 2000 100 300 55 455 20 420 NA NA 504 150 1800 100 90 5000 2000 100 100 286 486 245 445 222 422 505 150 1800 100 90 20000 1000 20 100 444 564 404 524 380 500 506 150 1800 100 90 20000 1000 20 300 206 526 167 487 147 467 507 150 1800 100 90 20000 1000 40 100 414 554 374 514 351 491 508 150 1800 100 90 20000 1000 40 300 178 518 137 477 118 458 509 150 1800 100 90 20000 1500 20 300 201 521 159 479 139 459 510 150 1800 100 90 20000 1500 20 100 437 557 397 517 374 494 511 150 1800 100 90 20000 1500 100 100 320 520 278 478 255 455 512 150 1800 100 90 20000 1500 100 300 86 486 47 447 28 428
Notes
Bold denotes changed parameters to return a positive SB thickness for B747 aircraft.
NA denotes a combination of parameters for which no SB thickness was required to achieve a CDF of less than 1.0.
Appendix 3 Sensitivity Analysis Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A3 - 26
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 1
APPENDIX 4. MATERIAL EQUIVALENCE DESIGN
Practical Crushed Rock versus Uncrushed Gravel
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
1 30 2600 60 80 5000 1000 20 2 30 2600 60 80 5000 1000 40 3 30 2600 60 80 5000 1500 20 4 30 2600 60 80 5000 1500 100 5 30 2600 60 80 10000 1000 40 6 30 2600 60 80 10000 1000 100 7 30 2600 60 80 10000 2000 20 8 30 2600 60 80 10000 2000 40 9 30 2600 60 90 5000 1500 20
10 30 2600 60 90 5000 1500 100 11 30 2600 60 90 5000 2000 40 12 30 2600 60 90 5000 2000 100 13 30 2600 60 90 20000 1000 20 14 30 2600 60 90 20000 1000 40 15 30 2600 60 90 20000 1500 20 16 30 2600 60 90 20000 1500 100 17 30 2600 80 80 10000 1000 40 18 30 2600 80 80 10000 1000 100 19 30 2600 80 80 10000 2000 20 20 30 2600 80 80 10000 2000 40 21 30 2600 80 80 20000 1500 20 22 30 2600 80 80 20000 1500 100 23 30 2600 80 80 20000 2000 40 24 30 2600 80 80 20000 2000 100 25 30 2600 80 100 5000 1000 20 26 30 2600 80 100 5000 1000 40 27 30 2600 80 100 5000 1500 20 28 30 2600 80 100 5000 1500 100 29 30 2600 80 100 10000 1000 40 30 30 2600 80 100 10000 1000 100 31 30 2600 80 100 10000 2000 20 32 30 2600 80 100 10000 2000 40
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 2
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
33 30 1000 60 90 5000 1500 20 34 30 1000 60 90 5000 1500 100 35 30 1000 60 90 5000 2000 40 36 30 1000 60 90 5000 2000 100 37 30 1000 60 90 20000 1000 20 38 30 1000 60 90 20000 1000 40 39 30 1000 60 90 20000 1500 20 40 30 1000 60 90 20000 1500 100 41 30 1000 60 100 10000 1000 40 42 30 1000 60 100 10000 1000 100 43 30 1000 60 100 10000 2000 20 44 30 1000 60 100 10000 2000 40 45 30 1000 60 100 20000 1500 20 46 30 1000 60 100 20000 1500 100 47 30 1000 60 100 20000 2000 40 48 30 1000 60 100 20000 2000 100 49 30 1000 100 80 5000 1000 20 50 30 1000 100 80 5000 1000 40 51 30 1000 100 80 5000 1500 20 52 30 1000 100 80 5000 1500 100 53 30 1000 100 80 10000 1000 40 54 30 1000 100 80 10000 1000 100 55 30 1000 100 80 10000 2000 20 56 30 1000 100 80 10000 2000 40 57 30 1000 100 90 5000 1500 20 58 30 1000 100 90 5000 1500 100 59 30 1000 100 90 5000 2000 40 60 30 1000 100 90 5000 2000 100 61 30 1000 100 90 20000 1000 20 62 30 1000 100 90 20000 1000 40 63 30 1000 100 90 20000 1500 20 64 30 1000 100 90 20000 1500 100 65 60 200 80 80 10000 1000 40 66 60 200 80 80 10000 1000 100 67 60 200 80 80 10000 2000 20 68 60 200 80 80 10000 2000 40 69 60 200 80 80 20000 1500 20
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 3
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
70 60 200 80 80 20000 1500 100 71 60 200 80 80 20000 2000 40 72 60 200 80 80 20000 2000 100 73 60 200 80 100 5000 1000 20 74 60 200 80 100 5000 1000 40 75 60 200 80 100 5000 1500 20 76 60 200 80 100 5000 1500 100 77 60 200 80 100 10000 1000 40 78 60 200 80 100 10000 1000 100 79 60 200 80 100 10000 2000 20 80 60 200 80 100 10000 2000 40 81 60 200 100 90 5000 1500 20 82 60 200 100 90 5000 1500 100 83 60 200 100 90 5000 2000 40 84 60 200 100 90 5000 2000 100 85 60 200 100 90 20000 1000 20 86 60 200 100 90 20000 1000 40 87 60 200 100 90 20000 1500 20 88 60 200 100 90 20000 1500 100 89 60 200 100 100 10000 1000 40 90 60 200 100 100 10000 1000 100 91 60 200 100 100 10000 2000 20 92 60 200 100 100 10000 2000 40 93 60 200 100 100 20000 1500 20 94 60 200 100 100 20000 1500 100 95 60 200 100 100 20000 2000 40 96 60 200 100 100 20000 2000 100 97 60 1800 60 80 5000 1000 20 98 60 1800 60 80 5000 1000 40 99 60 1800 60 80 5000 1500 20
100 60 1800 60 80 5000 1500 100 101 60 1800 60 80 10000 1000 40 102 60 1800 60 80 10000 1000 100 103 60 1800 60 80 10000 2000 20 104 60 1800 60 80 10000 2000 40 105 60 1800 60 90 5000 1500 20 106 60 1800 60 90 5000 1500 100
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 4
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
107 60 1800 60 90 5000 2000 40 108 60 1800 60 90 5000 2000 100 109 60 1800 60 90 20000 1000 20 110 60 1800 60 90 20000 1000 40 111 60 1800 60 90 20000 1500 20 112 60 1800 60 90 20000 1500 100 113 60 1800 80 80 10000 1000 40 114 60 1800 80 80 10000 1000 100 115 60 1800 80 80 10000 2000 20 116 60 1800 80 80 10000 2000 40 117 60 1800 80 80 20000 1500 20 118 60 1800 80 80 20000 1500 100 119 60 1800 80 80 20000 2000 40 120 60 1800 80 80 20000 2000 100 121 60 1800 80 100 5000 1000 20 122 60 1800 80 100 5000 1000 40 123 60 1800 80 100 5000 1500 20 124 60 1800 80 100 5000 1500 100 125 60 1800 80 100 10000 1000 40 126 60 1800 80 100 10000 1000 100 127 60 1800 80 100 10000 2000 20 128 60 1800 80 100 10000 2000 40 129 100 2600 60 90 5000 1500 20 130 100 2600 60 90 5000 1500 100 131 100 2600 60 90 5000 2000 40 132 100 2600 60 90 5000 2000 20 133 100 2600 60 90 20000 1000 20 134 100 2600 60 90 20000 1000 40 135 100 2600 60 90 20000 1500 20 136 100 2600 60 90 20000 1500 100 137 100 2600 60 100 10000 1000 40 138 100 2600 60 100 10000 1000 100 139 100 2600 60 100 10000 2000 20 140 100 2600 60 100 10000 2000 40 141 100 2600 60 100 20000 1500 20 142 100 2600 60 100 20000 1500 100 143 100 2600 60 100 20000 2000 40
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 5
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
144 100 2600 60 100 20000 2000 100 145 100 2600 100 80 5000 1000 20 146 100 2600 100 80 5000 1000 40 147 100 2600 100 80 5000 1500 20 148 100 2600 100 80 5000 1500 100 149 100 2600 100 80 10000 1000 40 150 100 2600 100 80 10000 1000 100 151 100 2600 100 80 10000 2000 20 152 100 2600 100 80 10000 2000 40 153 100 2600 100 90 5000 1500 20 154 100 2600 100 90 5000 1500 100 155 100 2600 100 90 5000 2000 40 156 100 2600 100 90 5000 2000 100 157 100 2600 100 90 20000 1000 20 158 100 2600 100 90 20000 1000 40 159 100 2600 100 90 20000 1500 20 160 100 2600 100 90 20000 1500 100 161 100 1000 80 80 10000 1000 40 162 100 1000 80 80 10000 1000 100 163 100 1000 80 80 10000 2000 20 164 100 1000 80 80 10000 2000 40 165 100 1000 80 80 20000 1500 20 166 100 1000 80 80 20000 1500 100 167 100 1000 80 80 20000 2000 40 168 100 1000 80 80 20000 2000 100 169 100 1000 80 100 5000 1000 20 170 100 1000 80 100 5000 1000 40 171 100 1000 80 100 5000 1500 20 172 100 1000 80 100 5000 1500 100 173 100 1000 80 100 10000 1000 40 174 100 1000 80 100 10000 1000 100 175 100 1000 80 100 10000 2000 20 176 100 1000 80 100 10000 2000 40 177 100 1000 100 90 5000 1500 20 178 100 1000 100 90 5000 1500 100 179 100 1000 100 90 5000 2000 40 180 100 1000 100 90 5000 2000 100
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 6
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
181 100 1000 100 90 20000 1000 20 182 100 1000 100 90 20000 1000 40 183 100 1000 100 90 20000 1500 20 184 100 1000 100 90 20000 1500 100 185 100 1000 100 100 10000 1000 40 186 100 1000 100 100 10000 1000 100 187 100 1000 100 100 10000 2000 20 188 100 1000 100 100 10000 2000 40 189 100 1000 100 100 20000 1500 20 190 100 1000 100 100 20000 1500 100 191 100 1000 100 100 20000 2000 40 192 100 1000 100 100 20000 2000 100 193 150 200 60 80 5000 1000 20 194 150 200 60 80 5000 1000 40 195 150 200 60 80 5000 1500 20 196 150 200 60 80 10000 1000 40 197 150 200 60 80 10000 2000 20 198 150 200 60 80 10000 2000 40 199 150 200 60 90 5000 1500 20 200 150 200 60 90 5000 2000 40 201 150 200 60 90 20000 1000 20 202 150 200 60 90 20000 1000 40 203 150 200 60 90 20000 1500 20 204 150 200 80 80 10000 1000 40 205 150 200 80 80 10000 1000 100 206 150 200 80 80 10000 2000 20 207 150 200 80 80 10000 2000 40 208 150 200 80 80 20000 1500 20 209 150 200 80 80 20000 1500 100 210 150 200 80 80 20000 2000 40 211 150 200 80 80 20000 2000 100 212 150 200 80 100 5000 1000 20 213 150 200 80 100 5000 1000 40 214 150 200 80 100 5000 1500 20 215 150 200 80 100 5000 1500 100 216 150 200 80 100 10000 1000 40 217 150 200 80 100 10000 1000 100
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 7
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
AT (mm)
218 150 200 80 100 10000 2000 20 219 150 200 80 100 10000 2000 40 220 150 1800 60 90 5000 1500 20 221 150 1800 60 90 5000 2000 40 222 150 1800 60 90 20000 1000 20 223 150 1800 60 90 20000 1000 40 224 150 1800 60 90 20000 1500 20 225 150 1800 60 100 10000 1000 40 226 150 1800 60 100 10000 2000 20 227 150 1800 60 100 10000 2000 40 228 150 1800 60 100 20000 1500 20 229 150 1800 60 100 20000 2000 40 230 150 1800 100 80 5000 1000 20 231 150 1800 100 80 5000 1000 40 232 150 1800 100 80 5000 1500 20 233 150 1800 100 80 5000 1500 100 234 150 1800 100 80 10000 1000 40 235 150 1800 100 80 10000 1000 100 236 150 1800 100 80 10000 2000 20 237 150 1800 100 80 10000 2000 40 238 150 1800 100 90 5000 1500 20 239 150 1800 100 90 5000 1500 100 240 150 1800 100 90 5000 2000 40 241 150 1800 100 90 5000 2000 100 242 150 1800 100 90 20000 1000 20 243 150 1800 100 90 20000 1000 40 244 150 1800 100 90 20000 1500 20 245 150 1800 100 90 20000 1500 100
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 8
Practical Asphalt versus Uncrushed Gravel
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
BT (mm)
1 30 2600 60 80 5000 1000 100 2 30 2600 60 80 5000 1500 300 3 30 2600 60 80 10000 1000 500 4 30 2600 60 80 10000 2000 100 5 30 2600 60 90 5000 1500 300 6 30 2600 60 90 5000 2000 500 7 30 2600 60 90 20000 1000 100 8 30 2600 60 90 20000 1500 300 9 30 2600 80 80 10000 1000 500
10 30 2600 80 80 10000 2000 100 11 30 2600 80 80 20000 1500 300 12 30 2600 80 80 20000 2000 500 13 30 2600 80 100 5000 1000 100 14 30 2600 80 100 5000 1500 300 15 30 2600 80 100 10000 1000 500 16 30 2600 80 100 10000 2000 100 17 30 1000 60 90 5000 1500 300 18 30 1000 60 90 5000 2000 500 19 30 1000 60 90 20000 1000 100 20 30 1000 60 90 20000 1500 300 21 30 1000 60 100 10000 1000 500 22 30 1000 60 100 10000 2000 100 23 30 1000 60 100 20000 1500 300 24 30 1000 60 100 20000 2000 500 25 30 1000 100 80 5000 1000 100 26 30 1000 100 80 5000 1500 300 27 30 1000 100 80 10000 1000 500 28 30 1000 100 90 5000 1500 300 29 30 1000 100 90 5000 2000 500 30 30 1000 100 90 20000 1000 100 31 30 1000 100 90 20000 1500 300 32 60 200 80 80 10000 1000 500 33 60 200 80 80 10000 2000 100 34 60 200 80 80 20000 1500 300 35 60 200 80 80 20000 2000 500
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 9
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
BT (mm)
36 60 200 80 100 5000 1000 100 37 60 200 80 100 5000 1500 300 38 60 200 80 100 10000 1000 500 39 60 200 80 100 10000 2000 100 40 60 200 100 90 5000 1500 300 41 60 200 100 90 5000 2000 500 42 60 200 100 90 20000 1000 100 43 60 200 100 90 20000 1500 300 44 60 200 100 100 10000 1000 500 45 60 200 100 100 10000 2000 100 46 60 200 100 100 20000 1500 300 47 60 200 100 100 20000 2000 500 48 60 1800 60 80 5000 1000 100 49 60 1800 60 80 5000 1500 300 50 60 1800 60 80 10000 1000 100 51 60 1800 60 80 10000 2000 100 52 60 1800 60 90 5000 1500 300 53 60 1800 60 90 5000 2000 100 54 60 1800 60 90 20000 1000 100 55 60 1800 60 90 20000 1500 300 56 60 1800 80 80 10000 1000 500 57 60 1800 80 80 10000 2000 100 58 60 1800 80 80 20000 1500 300 59 60 1800 80 80 20000 2000 500 60 60 1800 80 100 5000 1000 100 61 60 1800 80 100 5000 1500 300 62 60 1800 80 100 10000 1000 500 63 60 1800 80 100 10000 2000 100 64 100 2600 60 90 5000 1500 100 65 100 2600 60 90 5000 1500 300 66 100 2600 60 90 5000 2000 100 67 100 2600 60 90 5000 2000 300 68 100 2600 60 90 20000 1000 100 69 100 2600 60 90 20000 1000 300 70 100 2600 60 90 20000 1500 100 71 100 2600 60 90 20000 1500 300 72 100 2600 60 100 10000 1000 100
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 10
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
BT (mm)
73 100 2600 60 100 10000 1000 300 74 100 2600 60 100 10000 2000 100 75 100 2600 60 100 10000 2000 300 76 100 2600 60 100 20000 1500 100 77 100 2600 60 100 20000 1500 300 78 100 2600 60 100 20000 2000 100 79 100 2600 60 100 20000 2000 300 80 100 2600 100 80 5000 1000 100 81 100 2600 100 80 5000 1500 300 82 100 2600 100 80 10000 1000 100 83 100 2600 100 80 10000 2000 100 84 100 2600 100 90 5000 1500 300 85 100 2600 100 90 5000 2000 100 86 100 2600 100 90 20000 1000 100 87 100 2600 100 90 20000 1500 300 88 100 1000 80 80 10000 1000 100 89 100 1000 80 80 10000 1000 300 90 100 1000 80 80 10000 2000 100 91 100 1000 80 80 10000 2000 300 92 100 1000 80 80 20000 1500 300 93 100 1000 80 80 20000 2000 100 94 100 1000 80 100 5000 1000 100 95 100 1000 80 100 5000 1000 300 96 100 1000 80 100 5000 1500 100 97 100 1000 80 100 5000 1500 300 98 100 1000 80 100 10000 1000 100 99 100 1000 80 100 10000 1000 300
100 100 1000 80 100 10000 2000 100 101 100 1000 80 100 10000 2000 300 102 100 1000 100 90 5000 2000 100 103 100 1000 100 90 20000 1000 100 104 100 1000 100 90 20000 1500 300 105 100 1000 100 100 10000 1000 500 106 100 1000 100 100 10000 2000 100 107 100 1000 100 100 10000 2000 300 108 100 1000 100 100 20000 1500 300 109 100 1000 100 100 20000 2000 100
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 11
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
BT (mm)
110 150 200 60 80 5000 1000 100 111 150 200 60 80 5000 1000 300 112 150 200 60 80 5000 1500 100 113 150 200 60 80 10000 1000 100 114 150 200 60 80 10000 1000 300 115 150 200 60 80 10000 2000 100 116 150 200 60 80 10000 2000 300 117 150 200 60 90 5000 1500 100 118 150 200 60 90 5000 2000 100 119 150 200 60 90 5000 2000 300 120 150 200 60 90 20000 1000 100 121 150 200 60 90 20000 1000 300 122 150 200 60 90 20000 1500 100 123 150 200 80 80 10000 1000 100 124 150 200 80 80 10000 1000 300 125 150 200 80 80 10000 2000 100 126 150 200 80 80 10000 2000 300 127 150 200 80 80 20000 1500 100 128 150 200 80 80 20000 1500 300 129 150 200 80 80 20000 2000 100 130 150 200 80 80 20000 2000 300 131 150 200 80 100 5000 1000 100 132 150 200 80 100 5000 1000 300 133 150 200 80 100 5000 1500 100 134 150 200 80 100 5000 1500 300 135 150 200 80 100 10000 1000 100 136 150 200 80 100 10000 1000 300 137 150 200 80 100 10000 2000 100 138 150 200 80 100 10000 2000 300 139 150 1800 60 90 5000 1500 100 140 150 1800 60 90 5000 2000 100 141 150 1800 60 90 20000 1000 100 142 150 1800 60 90 20000 1000 300 143 150 1800 60 90 20000 1500 100 144 150 1800 60 100 10000 1000 100 145 150 1800 60 100 10000 2000 100 146 150 1800 60 100 10000 2000 300
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 12
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
BT (mm)
147 150 1800 60 100 20000 1500 100 148 150 1800 60 100 20000 2000 100 149 150 1800 100 80 5000 1000 100 150 150 1800 100 80 5000 1000 300 151 150 1800 100 80 5000 1500 100 152 150 1800 100 80 5000 1500 300 153 150 1800 100 80 10000 1000 100 154 150 1800 100 80 10000 1000 300 155 150 1800 100 80 10000 2000 100 156 150 1800 100 80 10000 2000 300 157 150 1800 100 90 5000 1500 100 158 150 1800 100 90 5000 1500 300 159 150 1800 100 90 5000 2000 100 160 150 1800 100 90 5000 2000 300 161 150 1800 100 90 20000 1000 100 162 150 1800 100 90 20000 1000 300 163 150 1800 100 90 20000 1500 100 164 150 1800 100 90 20000 1500 300
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 13
Practical Asphalt versus Crushed Rock
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
ST (mm)
1 30 2600 60 80 5000 1000 200 2 30 2600 60 80 5000 1500 400 3 30 2600 60 80 10000 1000 200 4 30 2600 60 80 10000 2000 800 5 30 2600 60 90 5000 1500 400 6 30 2600 60 90 5000 2000 800 7 30 2600 60 90 20000 1000 200 8 30 2600 60 90 20000 2000 400 9 30 2600 80 80 10000 1500 200
10 30 2600 80 80 10000 2000 800 11 30 2600 80 80 20000 1000 400 12 30 2600 80 80 20000 1500 800 13 30 2600 80 100 5000 1500 200 14 30 2600 80 100 5000 2000 400 15 30 2600 80 100 10000 1000 200 16 30 2600 80 100 10000 1500 800 17 30 1000 60 80 5000 1000 400 18 30 1000 60 80 5000 2000 800 19 30 1000 60 80 20000 1000 200 20 30 1000 60 80 20000 1500 400 21 30 1000 60 90 10000 1000 200 22 30 1000 60 90 10000 2000 800 23 30 1000 60 90 20000 1500 400 24 30 1000 60 90 20000 2000 800 25 30 1000 100 80 5000 1000 200 26 30 1000 100 80 5000 2000 400 27 30 1000 100 80 10000 1500 200 28 30 1000 100 80 10000 2000 800 29 30 1000 100 100 5000 1000 400 30 30 1000 100 100 5000 1500 800 31 30 1000 100 100 20000 1500 200 32 30 1000 100 100 20000 2000 400 33 60 200 60 80 10000 1000 200 34 60 200 60 80 10000 1500 400 35 60 200 60 80 20000 1000 400
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 14
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
ST (mm)
36 60 200 60 80 20000 2000 400 37 60 200 60 90 5000 1000 200 38 60 200 60 90 5000 1500 400 39 60 200 60 90 10000 1000 200 40 60 200 60 90 10000 2000 400 41 60 200 80 80 5000 1500 400 42 60 200 80 80 5000 2000 200 43 60 200 80 80 20000 1000 200 44 60 200 80 80 20000 2000 400 45 60 200 80 100 10000 1500 200 46 60 200 80 100 10000 2000 400 47 60 200 80 100 20000 1000 400 48 60 200 80 100 20000 1500 200 49 60 1800 60 80 5000 1500 200 50 60 1800 60 80 5000 2000 400 51 60 1800 60 80 10000 1000 200 52 60 1800 60 80 10000 1500 400 53 60 1800 60 90 5000 1000 400 54 60 1800 60 90 5000 2000 200 55 60 1800 60 90 20000 1000 200 56 60 1800 60 90 20000 1500 400 57 60 1800 100 80 10000 1000 200 58 60 1800 100 80 10000 2000 800 59 60 1800 100 80 20000 1500 400 60 60 1800 100 80 20000 2000 800 61 60 1800 100 100 5000 1000 200 62 60 1800 100 100 5000 2000 400 63 60 1800 100 100 10000 1500 200 64 60 1800 100 100 10000 2000 800 65 100 2600 60 80 5000 1000 200 66 100 2600 60 80 5000 1500 200 67 100 2600 60 80 20000 1500 200 68 100 2600 60 80 20000 2000 200 69 100 2600 60 90 10000 1000 200 70 100 2600 60 90 10000 1500 200 71 100 2600 60 90 20000 1000 200 72 100 2600 60 90 20000 2000 200
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 15
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
ST (mm)
73 100 2600 80 80 5000 1000 200 74 100 2600 80 80 5000 1500 400 75 100 2600 80 80 10000 1000 200 76 100 2600 80 80 10000 2000 200 77 100 2600 80 100 5000 1500 400 78 100 2600 80 100 5000 2000 200 79 100 2600 80 100 20000 1000 200 80 100 2600 80 100 20000 2000 400 81 100 1000 60 80 10000 1500 200 82 100 1000 60 80 10000 2000 200 83 100 1000 60 80 20000 1000 400 84 100 1000 60 80 20000 1500 200 85 100 1000 60 90 5000 1500 200 86 100 1000 60 90 5000 2000 200 87 100 1000 60 90 10000 1000 200 88 100 1000 60 90 10000 1500 200 89 100 1000 100 80 5000 1000 400 90 100 1000 100 80 5000 2000 200 91 100 1000 100 80 20000 1000 200 92 100 1000 100 80 20000 1500 400 93 100 1000 100 100 10000 1000 200 94 100 1000 100 100 10000 2000 400 95 100 1000 100 100 20000 1500 400 96 100 1000 100 100 20000 2000 200 97 150 200 60 80 5000 1000 200 98 150 200 60 80 5000 2000 200 99 150 200 60 80 10000 1500 200
100 150 200 60 80 10000 2000 200 101 150 200 60 90 5000 1000 200 102 150 200 60 90 5000 1500 200 103 150 200 60 90 20000 1500 200 104 150 200 60 90 20000 2000 200 105 150 200 80 80 10000 1000 200 106 150 200 80 80 10000 1500 200 107 150 200 80 80 20000 1000 200 108 150 200 80 80 20000 2000 200 109 150 200 80 100 5000 1000 200
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 16
Factor Levels Run SM
(MPa) W
(mm) M
(%) TP (%)
P (no.)
AM (MPa)
ST (mm)
110 150 200 80 100 5000 1500 200 111 150 200 80 100 10000 1000 200 112 150 200 80 100 10000 2000 200 113 150 1800 60 80 5000 1500 200 114 150 1800 60 80 5000 2000 200 115 150 1800 60 80 20000 1000 200 116 150 1800 60 80 20000 2000 200 117 150 1800 60 90 10000 1500 200 118 150 1800 60 90 10000 2000 200 119 150 1800 60 90 20000 1000 200 120 150 1800 60 90 20000 1500 200 121 150 1800 100 80 5000 1500 200 122 150 1800 100 80 5000 2000 200 123 150 1800 100 80 10000 1000 200 124 150 1800 100 80 10000 1500 400 125 150 1800 100 100 5000 1000 200 126 150 1800 100 100 5000 2000 200 127 150 1800 100 100 20000 1000 200 128 150 1800 100 100 20000 1500 800
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 17
Isolated Material Equivalence
Factor Levels Run SM
(MPa) RL RM
(MPa) RT
(mm) 1 30 Full 50 Full 2 30 Full 100 Full 3 30 Full 250 Full 4 30 Full 750 Full 5 30 Full 1000 Full 6 30 Full 2000 Full 7 30 Full 4000 Full 8 60 Full 50 Full 9 60 Full 100 Full
10 60 Full 250 Full 11 60 Full 750 Full 12 60 Full 1000 Full 13 60 Full 2000 Full 14 60 Full 4000 Full 15 100 Full 50 Full 16 100 Full 100 Full 17 100 Full 250 Full 18 100 Full 750 Full 19 100 Full 1000 Full 20 100 Full 2000 Full 21 100 Full 4000 Full 22 150 Full 50 Full 23 150 Full 100 Full 24 150 Full 250 Full 25 150 Full 750 Full 26 150 Full 1000 Full 27 150 Full 2000 Full 28 150 Full 4000 Full 29 30 Top 50 100 30 30 Top 50 200 31 30 Top 50 400 32 30 Top 100 100 33 30 Top 100 200 34 30 Top 100 400 35 30 Top 250 100
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 18
Factor Levels Run SM
(MPa) RL RM
(MPa) RT
(mm) 36 30 Top 250 200 37 30 Top 250 400 38 30 Top 750 100 39 30 Top 750 200 40 30 Top 750 400 41 30 Top 1000 100 42 30 Top 1000 200 43 30 Top 1000 400 44 30 Top 2000 100 45 30 Top 2000 200 46 30 Top 2000 400 47 30 Top 4000 100 48 30 Top 4000 200 49 30 Top 4000 400 50 30 Bottom 50 100 51 30 Bottom 50 200 52 30 Bottom 50 400 53 30 Bottom 100 100 54 30 Bottom 100 200 55 30 Bottom 100 400 56 30 Bottom 250 100 57 30 Bottom 250 200 58 30 Bottom 250 400 59 30 Bottom 750 100 60 30 Bottom 750 200 61 30 Bottom 750 400 62 30 Bottom 1000 100 63 30 Bottom 1000 200 64 30 Bottom 1000 400 65 30 Bottom 2000 100 66 30 Bottom 2000 200 67 30 Bottom 2000 400 68 30 Bottom 4000 100 69 30 Bottom 4000 200 70 30 Bottom 4000 400 71 60 Top 50 100 72 60 Top 50 200
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 19
Factor Levels Run SM
(MPa) RL RM
(MPa) RT
(mm) 73 60 Top 50 400 74 60 Top 100 100 75 60 Top 100 200 76 60 Top 100 400 77 60 Top 250 100 78 60 Top 250 200 79 60 Top 250 400 80 60 Top 750 100 81 60 Top 750 200 82 60 Top 750 400 83 60 Top 1000 100 84 60 Top 1000 200 85 60 Top 1000 400 86 60 Top 2000 100 87 60 Top 2000 200 88 60 Top 2000 400 89 60 Top 4000 100 90 60 Top 4000 200 91 60 Top 4000 400 92 60 Bottom 50 100 93 60 Bottom 50 200 94 60 Bottom 50 400 95 60 Bottom 100 100 96 60 Bottom 100 200 97 60 Bottom 100 400 98 60 Bottom 250 100 99 60 Bottom 250 200
100 60 Bottom 250 400 101 60 Bottom 750 100 102 60 Bottom 750 200 103 60 Bottom 750 400 104 60 Bottom 1000 100 105 60 Bottom 1000 200 106 60 Bottom 1000 400 107 60 Bottom 2000 100 108 60 Bottom 2000 200 109 60 Bottom 2000 400
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 20
Factor Levels Run SM
(MPa) RL RM
(MPa) RT
(mm) 110 60 Bottom 4000 100 111 60 Bottom 4000 200 112 60 Bottom 4000 400 113 100 Top 50 100 114 100 Top 50 200 115 100 Top 50 400 116 100 Top 100 100 117 100 Top 100 200 118 100 Top 100 400 119 100 Top 250 100 120 100 Top 250 200 121 100 Top 250 400 122 100 Top 750 100 123 100 Top 750 200 124 100 Top 750 400 125 100 Top 1000 100 126 100 Top 1000 200 127 100 Top 1000 400 128 100 Top 2000 100 129 100 Top 2000 200 130 100 Top 2000 400 131 100 Top 4000 100 132 100 Top 4000 200 133 100 Top 4000 400 134 100 Bottom 50 100 135 100 Bottom 50 200 136 100 Bottom 50 400 137 100 Bottom 100 100 138 100 Bottom 100 200 139 100 Bottom 100 400 140 100 Bottom 250 100 141 100 Bottom 250 200 142 100 Bottom 250 400 143 100 Bottom 750 100 144 100 Bottom 750 200 145 100 Bottom 750 400 146 100 Bottom 1000 100
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 21
Factor Levels Run SM
(MPa) RL RM
(MPa) RT
(mm) 147 100 Bottom 1000 200 148 100 Bottom 1000 400 149 100 Bottom 2000 100 150 100 Bottom 2000 200 151 100 Bottom 2000 400 152 100 Bottom 4000 100 153 100 Bottom 4000 200 154 100 Bottom 4000 400 155 150 Top 50 100 156 150 Top 50 200 157 150 Top 50 400 158 150 Top 100 100 159 150 Top 100 200 160 150 Top 100 400 161 150 Top 250 100 162 150 Top 250 200 163 150 Top 250 400 164 150 Top 750 100 165 150 Top 750 200 166 150 Top 750 400 167 150 Top 1000 100 168 150 Top 1000 200 169 150 Top 1000 400 170 150 Top 2000 100 171 150 Top 2000 200 172 150 Top 2000 400 173 150 Top 4000 100 174 150 Top 4000 200 175 150 Top 4000 400 176 150 Bottom 50 100 177 150 Bottom 50 200 178 150 Bottom 50 400 179 150 Bottom 100 100 180 150 Bottom 100 200 181 150 Bottom 100 400 182 150 Bottom 250 100 183 150 Bottom 250 200
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 22
Factor Levels Run SM
(MPa) RL RM
(MPa) RT
(mm) 184 150 Bottom 250 400 185 150 Bottom 750 100 186 150 Bottom 750 200 187 150 Bottom 750 400 188 150 Bottom 1000 100 189 150 Bottom 1000 200 190 150 Bottom 1000 400 191 150 Bottom 2000 100 192 150 Bottom 2000 200 193 150 Bottom 2000 400 194 150 Bottom 4000 100 195 150 Bottom 4000 200 196 150 Bottom 4000 400
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 23
Equivalence Examples
Factor Levels Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) 1 30 B747 397 5,000 1.75 2,857 2 30 B747 397 5,000 1.75 2,857 3 30 B747 397 5,000 1.75 2,857 4 30 B747 397 10,000 1.75 5,714 5 30 B747 397 10,000 1.75 5,714 6 30 B747 397 10,000 1.75 5,714 7 30 B747 397 20,000 1.75 11,429 8 30 B747 397 20,000 1.75 11,429 9 30 B747 397 20,000 1.75 11,429
10 30 B747 318 5,000 1.75 2,857 11 30 B747 318 5,000 1.75 2,857 12 30 B747 318 5,000 1.75 2,857 13 30 B747 318 10,000 1.75 5,714 14 30 B747 318 10,000 1.75 5,714 15 30 B747 318 10,000 1.75 5,714 16 30 B747 318 20,000 1.75 11,429 17 30 B747 318 20,000 1.75 11,429 18 30 B747 318 20,000 1.75 11,429 19 30 B747 238 5,000 1.75 2,857 20 30 B747 238 5,000 1.75 2,857 21 30 B747 238 5,000 1.75 2,857 22 30 B747 238 10,000 1.75 5,714 23 30 B747 238 10,000 1.75 5,714 24 30 B747 238 10,000 1.75 5,714 25 30 B747 238 20,000 1.75 11,429 26 30 B747 238 20,000 1.75 11,429 27 30 B747 238 20,000 1.75 11,429 28 30 B767 180 5,000 1.90 2,632 29 30 B767 180 5,000 1.90 2,632 30 30 B767 180 5,000 1.90 2,632 31 30 B767 180 10,000 1.90 5,263 32 30 B767 180 10,000 1.90 5,263 33 30 B767 180 10,000 1.90 5,263 34 30 B767 180 20,000 1.90 10,526 35 30 B767 180 20,000 1.90 10,526
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 24
Factor Levels Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) 36 30 B767 180 20,000 1.90 10,526 37 30 B767 144 5,000 1.90 2,632 38 30 B767 144 5,000 1.90 2,632 39 30 B767 144 5,000 1.90 2,632 40 30 B767 144 10,000 1.90 5,263 41 30 B767 144 10,000 1.90 5,263 42 30 B767 144 10,000 1.90 5,263 43 30 B767 144 20,000 1.90 10,526 44 30 B767 144 20,000 1.90 10,526 45 30 B767 144 20,000 1.90 10,526 46 30 B767 108 5,000 1.90 2,632 47 30 B767 108 5,000 1.90 2,632 48 30 B767 108 5,000 1.90 2,632 49 30 B767 108 10,000 1.90 5,263 50 30 B767 108 10,000 1.90 5,263 51 30 B767 108 10,000 1.90 5,263 52 30 B767 108 20,000 1.90 10,526 53 30 B767 108 20,000 1.90 10,526 54 30 B767 108 20,000 1.90 10,526 55 30 B737 79 5,000 3.70 1,351 56 30 B737 79 5,000 3.70 1,351 57 30 B737 79 5,000 3.70 1,351 58 30 B737 79 10,000 3.70 2,703 59 30 B737 79 10,000 3.70 2,703 60 30 B737 79 10,000 3.70 2,703 61 30 B737 79 20,000 3.70 5,405 62 30 B737 79 20,000 3.70 5,405 63 30 B737 79 20,000 3.70 5,405 64 30 B737 63 5,000 3.70 1,351 65 30 B737 63 5,000 3.70 1,351 66 30 B737 63 5,000 3.70 1,351 67 30 B737 63 10,000 3.70 2,703 68 30 B737 63 10,000 3.70 2,703 69 30 B737 63 10,000 3.70 2,703 70 30 B737 63 20,000 3.70 5,405 71 30 B737 63 20,000 3.70 5,405 72 30 B737 63 20,000 3.70 5,405
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 25
Factor Levels Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) 73 30 B737 47 5,000 3.70 1,351 74 30 B737 47 5,000 3.70 1,351 75 30 B737 47 5,000 3.70 1,351 76 30 B737 47 10,000 3.70 2,703 77 30 B737 47 10,000 3.70 2,703 78 30 B737 47 10,000 3.70 2,703 79 30 B737 47 20,000 3.70 5,405 80 30 B737 47 20,000 3.70 5,405 81 30 B737 47 20,000 3.70 5,405 82 60 B747 397 5,000 1.75 2,857 83 60 B747 397 5,000 1.75 2,857 84 60 B747 397 5,000 1.75 2,857 85 60 B747 397 10,000 1.75 5,714 86 60 B747 397 10,000 1.75 5,714 87 60 B747 397 10,000 1.75 5,714 88 60 B747 397 20,000 1.75 11,429 89 60 B747 397 20,000 1.75 11,429 90 60 B747 397 20,000 1.75 11,429 91 60 B747 318 5,000 1.75 2,857 92 60 B747 318 5,000 1.75 2,857 93 60 B747 318 5,000 1.75 2,857 94 60 B747 318 10,000 1.75 5,714 95 60 B747 318 10,000 1.75 5,714 96 60 B747 318 10,000 1.75 5,714 97 60 B747 318 20,000 1.75 11,429 98 60 B747 318 20,000 1.75 11,429 99 60 B747 318 20,000 1.75 11,429
100 60 B747 238 5,000 1.75 2,857 101 60 B747 238 5,000 1.75 2,857 102 60 B747 238 5,000 1.75 2,857 103 60 B747 238 10,000 1.75 5,714 104 60 B747 238 10,000 1.75 5,714 105 60 B747 238 10,000 1.75 5,714 106 60 B747 238 20,000 1.75 11,429 107 60 B747 238 20,000 1.75 11,429 108 60 B747 238 20,000 1.75 11,429 109 60 B767 180 5,000 1.90 2,632
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 26
Factor Levels Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) 110 60 B767 180 5,000 1.90 2,632 111 60 B767 180 5,000 1.90 2,632 112 60 B767 180 10,000 1.90 5,263 113 60 B767 180 10,000 1.90 5,263 114 60 B767 180 10,000 1.90 5,263 115 60 B767 180 20,000 1.90 10,526 116 60 B767 180 20,000 1.90 10,526 117 60 B767 180 20,000 1.90 10,526 118 60 B767 144 5,000 1.90 2,632 119 60 B767 144 5,000 1.90 2,632 120 60 B767 144 5,000 1.90 2,632 121 60 B767 144 10,000 1.90 5,263 122 60 B767 144 10,000 1.90 5,263 123 60 B767 144 10,000 1.90 5,263 124 60 B767 144 20,000 1.90 10,526 125 60 B767 144 20,000 1.90 10,526 126 60 B767 144 20,000 1.90 10,526 127 60 B767 108 5,000 1.90 2,632 128 60 B767 108 5,000 1.90 2,632 129 60 B767 108 5,000 1.90 2,632 130 60 B767 108 10,000 1.90 5,263 131 60 B767 108 10,000 1.90 5,263 132 60 B767 108 10,000 1.90 5,263 133 60 B767 108 20,000 1.90 10,526 134 60 B767 108 20,000 1.90 10,526 135 60 B767 108 20,000 1.90 10,526 136 60 B737 79 5,000 3.70 1,351 137 60 B737 79 5,000 3.70 1,351 138 60 B737 79 5,000 3.70 1,351 139 60 B737 79 10,000 3.70 2,703 140 60 B737 79 10,000 3.70 2,703 141 60 B737 79 10,000 3.70 2,703 142 60 B737 79 20,000 3.70 5,405 143 60 B737 79 20,000 3.70 5,405 144 60 B737 79 20,000 3.70 5,405 145 60 B737 63 5,000 3.70 1,351 146 60 B737 63 5,000 3.70 1,351
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 27
Factor Levels Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) 147 60 B737 63 5,000 3.70 1,351 148 60 B737 63 10,000 3.70 2,703 149 60 B737 63 10,000 3.70 2,703 150 60 B737 63 10,000 3.70 2,703 151 60 B737 63 20,000 3.70 5,405 152 60 B737 63 20,000 3.70 5,405 153 60 B737 63 20,000 3.70 5,405 154 60 B737 47 5,000 3.70 1,351 155 60 B737 47 5,000 3.70 1,351 156 60 B737 47 5,000 3.70 1,351 157 60 B737 47 10,000 3.70 2,703 158 60 B737 47 10,000 3.70 2,703 159 60 B737 47 10,000 3.70 2,703 160 60 B737 47 20,000 3.70 5,405 161 60 B737 47 20,000 3.70 5,405 162 60 B737 47 20,000 3.70 5,405 163 100 B747 397 5,000 1.75 2,857 164 100 B747 397 5,000 1.75 2,857 165 100 B747 397 5,000 1.75 2,857 166 100 B747 397 10,000 1.75 5,714 167 100 B747 397 10,000 1.75 5,714 168 100 B747 397 10,000 1.75 5,714 169 100 B747 397 20,000 1.75 11,429 170 100 B747 397 20,000 1.75 11,429 171 100 B747 397 20,000 1.75 11,429 172 100 B747 318 5,000 1.75 2,857 173 100 B747 318 5,000 1.75 2,857 174 100 B747 318 5,000 1.75 2,857 175 100 B747 318 10,000 1.75 5,714 176 100 B747 318 10,000 1.75 5,714 177 100 B747 318 10,000 1.75 5,714 178 100 B747 318 20,000 1.75 11,429 179 100 B747 318 20,000 1.75 11,429 180 100 B747 318 20,000 1.75 11,429 181 100 B747 238 5,000 1.75 2,857 182 100 B747 238 5,000 1.75 2,857 183 100 B747 238 5,000 1.75 2,857
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 28
Factor Levels Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) 184 100 B747 238 10,000 1.75 5,714 185 100 B747 238 10,000 1.75 5,714 186 100 B747 238 10,000 1.75 5,714 187 100 B747 238 20,000 1.75 11,429 188 100 B747 238 20,000 1.75 11,429 189 100 B747 238 20,000 1.75 11,429 190 100 B767 180 5,000 1.90 2,632 191 100 B767 180 5,000 1.90 2,632 192 100 B767 180 5,000 1.90 2,632 193 100 B767 180 10,000 1.90 5,263 194 100 B767 180 10,000 1.90 5,263 195 100 B767 180 10,000 1.90 5,263 196 100 B767 180 20,000 1.90 10,526 197 100 B767 180 20,000 1.90 10,526 198 100 B767 180 20,000 1.90 10,526 199 100 B767 144 5,000 1.90 2,632 200 100 B767 144 5,000 1.90 2,632 201 100 B767 144 5,000 1.90 2,632 202 100 B767 144 10,000 1.90 5,263 203 100 B767 144 10,000 1.90 5,263 204 100 B767 144 10,000 1.90 5,263 205 100 B767 144 20,000 1.90 10,526 206 100 B767 144 20,000 1.90 10,526 207 100 B767 144 20,000 1.90 10,526 208 100 B767 108 5,000 1.90 2,632 209 100 B767 108 5,000 1.90 2,632 210 100 B767 108 5,000 1.90 2,632 211 100 B767 108 10,000 1.90 5,263 212 100 B767 108 10,000 1.90 5,263 213 100 B767 108 10,000 1.90 5,263 214 100 B767 108 20,000 1.90 10,526 215 100 B767 108 20,000 1.90 10,526 216 100 B767 108 20,000 1.90 10,526 217 100 B737 79 5,000 3.70 1,351 218 100 B737 79 5,000 3.70 1,351 219 100 B737 79 5,000 3.70 1,351 220 100 B737 79 10,000 3.70 2,703
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 29
Factor Levels Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) 221 100 B737 79 10,000 3.70 2,703 222 100 B737 79 10,000 3.70 2,703 223 100 B737 79 20,000 3.70 5,405 224 100 B737 79 20,000 3.70 5,405 225 100 B737 79 20,000 3.70 5,405 226 100 B737 63 5,000 3.70 1,351 227 100 B737 63 5,000 3.70 1,351 228 100 B737 63 5,000 3.70 1,351 229 100 B737 63 10,000 3.70 2,703 230 100 B737 63 10,000 3.70 2,703 231 100 B737 63 10,000 3.70 2,703 232 100 B737 63 20,000 3.70 5,405 233 100 B737 63 20,000 3.70 5,405 234 100 B737 63 20,000 3.70 5,405 235 100 B737 47 5,000 3.70 1,351 236 100 B737 47 5,000 3.70 1,351 237 100 B737 47 5,000 3.70 1,351 238 100 B737 47 10,000 3.70 2,703 239 100 B737 47 10,000 3.70 2,703 240 100 B737 47 10,000 3.70 2,703 241 100 B737 47 20,000 3.70 5,405 242 100 B737 47 20,000 3.70 5,405 243 100 B737 47 20,000 3.70 5,405 244 150 B747 397 5,000 1.75 2,857 245 150 B747 397 5,000 1.75 2,857 246 150 B747 397 5,000 1.75 2,857 247 150 B747 397 10,000 1.75 5,714 248 150 B747 397 10,000 1.75 5,714 249 150 B747 397 10,000 1.75 5,714 250 150 B747 397 20,000 1.75 11,429 251 150 B747 397 20,000 1.75 11,429 252 150 B747 397 20,000 1.75 11,429 253 150 B747 318 5,000 1.75 2,857 254 150 B747 318 5,000 1.75 2,857 255 150 B747 318 5,000 1.75 2,857 256 150 B747 318 10,000 1.75 5,714 257 150 B747 318 10,000 1.75 5,714
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 30
Factor Levels Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) 258 150 B747 318 10,000 1.75 5,714 259 150 B747 318 20,000 1.75 11,429 260 150 B747 318 20,000 1.75 11,429 261 150 B747 318 20,000 1.75 11,429 262 150 B747 238 5,000 1.75 2,857 263 150 B747 238 5,000 1.75 2,857 264 150 B747 238 5,000 1.75 2,857 265 150 B747 238 10,000 1.75 5,714 266 150 B747 238 10,000 1.75 5,714 267 150 B747 238 10,000 1.75 5,714 268 150 B747 238 20,000 1.75 11,429 269 150 B747 238 20,000 1.75 11,429 270 150 B747 238 20,000 1.75 11,429 271 150 B767 180 5,000 1.90 2,632 272 150 B767 180 5,000 1.90 2,632 273 150 B767 180 5,000 1.90 2,632 274 150 B767 180 10,000 1.90 5,263 275 150 B767 180 10,000 1.90 5,263 276 150 B767 180 10,000 1.90 5,263 277 150 B767 180 20,000 1.90 10,526 278 150 B767 180 20,000 1.90 10,526 279 150 B767 180 20,000 1.90 10,526 280 150 B767 144 5,000 1.90 2,632 281 150 B767 144 5,000 1.90 2,632 282 150 B767 144 5,000 1.90 2,632 283 150 B767 144 10,000 1.90 5,263 284 150 B767 144 10,000 1.90 5,263 285 150 B767 144 10,000 1.90 5,263 286 150 B767 144 20,000 1.90 10,526 287 150 B767 144 20,000 1.90 10,526 288 150 B767 144 20,000 1.90 10,526 289 150 B767 108 5,000 1.90 2,632 290 150 B767 108 5,000 1.90 2,632 291 150 B767 108 5,000 1.90 2,632 292 150 B767 108 10,000 1.90 5,263 293 150 B767 108 10,000 1.90 5,263 294 150 B767 108 10,000 1.90 5,263
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A4 - 31
Factor Levels Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) 295 150 B767 108 20,000 1.90 10,526 296 150 B767 108 20,000 1.90 10,526 297 150 B767 108 20,000 1.90 10,526 298 150 B737 79 5,000 3.70 1,351 299 150 B737 79 5,000 3.70 1,351 300 150 B737 79 5,000 3.70 1,351 301 150 B737 79 10,000 3.70 2,703 302 150 B737 79 10,000 3.70 2,703 303 150 B737 79 10,000 3.70 2,703 304 150 B737 79 20,000 3.70 5,405 305 150 B737 79 20,000 3.70 5,405 306 150 B737 79 20,000 3.70 5,405 307 150 B737 63 5,000 3.70 1,351 308 150 B737 63 5,000 3.70 1,351 309 150 B737 63 5,000 3.70 1,351 310 150 B737 63 10,000 3.70 2,703 311 150 B737 63 10,000 3.70 2,703 312 150 B737 63 10,000 3.70 2,703 313 150 B737 63 20,000 3.70 5,405 314 150 B737 63 20,000 3.70 5,405 315 150 B737 63 20,000 3.70 5,405 316 150 B737 47 5,000 3.70 1,351 317 150 B737 47 5,000 3.70 1,351 318 150 B737 47 5,000 3.70 1,351 319 150 B737 47 10,000 3.70 2,703 320 150 B737 47 10,000 3.70 2,703 321 150 B737 47 10,000 3.70 2,703 322 150 B737 47 20,000 3.70 5,405 323 150 B737 47 20,000 3.70 5,405 324 150 B737 47 20,000 3.70 5,405
Appendix 4 Material Equivalence Design
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A4 - 32
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 1
APPENDIX 5. MATERIAL EQUIVALENCE RESULTS
Practical Crushed Rock versus Uncrushed Gravel
Factor Levels Base Thickness Material Equivalence Run
SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 1 30 2600 60 80 5000 1000 20 100 300 1.19 1.19 1.21 2 30 2600 60 80 5000 1000 40 100 500 1.17 1.22 1.18 3 30 2600 60 80 5000 1500 20 300 500 1.21 1.25 1.13 4 30 2600 60 80 5000 1500 100 100 300 1.22 1.16 1.28 5 30 2600 60 80 10000 1000 40 100 500 1.21 1.21 1.17 6 30 2600 60 80 10000 1000 100 300 500 1.26 1.30 1.24 7 30 2600 60 80 10000 2000 20 100 300 1.18 1.12 1.22 8 30 2600 60 80 10000 2000 40 100 500 1.22 1.23 1.19 9 30 2600 60 90 5000 1500 20 300 500 1.22 1.25 1.13
10 30 2600 60 90 5000 1500 100 100 300 1.22 1.23 1.28 11 30 2600 60 90 5000 2000 40 100 500 1.19 1.19 1.20 12 30 2600 60 90 5000 2000 100 300 500 1.31 1.23 1.14 13 30 2600 60 90 20000 1000 20 100 300 1.16 1.15 1.21 14 30 2600 60 90 20000 1000 40 100 500 1.20 1.22 1.24 15 30 2600 60 90 20000 1500 20 300 500 1.22 1.24 1.27 16 30 2600 60 90 20000 1500 100 100 300 1.20 1.25 1.20
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 2
Factor Levels Base Thickness Material Equivalence Run
SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 17 30 2600 80 80 10000 1000 40 100 500 1.21 1.17 1.20 18 30 2600 80 80 10000 1000 100 300 500 1.25 1.27 1.29 19 30 2600 80 80 10000 2000 20 100 300 1.15 1.19 1.21 20 30 2600 80 80 10000 2000 40 100 500 1.21 1.18 1.24 21 30 2600 80 80 20000 1500 20 300 500 1.22 1.22 1.28 22 30 2600 80 80 20000 1500 100 100 300 1.18 1.15 1.25 23 30 2600 80 80 20000 2000 40 100 500 1.18 1.21 1.21 24 30 2600 80 80 20000 2000 100 300 500 1.28 1.29 1.31 25 30 2600 80 100 5000 1000 20 100 300 1.23 1.15 1.16 26 30 2600 80 100 5000 1000 40 100 500 1.21 1.20 1.23 27 30 2600 80 100 5000 1500 20 300 500 1.22 1.23 1.26 28 30 2600 80 100 5000 1500 100 100 300 1.15 1.20 1.26 29 30 2600 80 100 10000 1000 40 100 500 1.21 1.17 1.20 30 30 2600 80 100 10000 1000 100 300 500 1.26 1.26 1.29 31 30 2600 80 100 10000 2000 20 100 300 1.16 1.19 1.22 32 30 2600 80 100 10000 2000 40 100 500 1.21 1.18 1.23 33 30 1000 60 90 5000 1500 20 300 500 1.25 1.25 1.26 34 30 1000 60 90 5000 1500 100 100 300 1.20 1.25 1.27 35 30 1000 60 90 5000 2000 40 100 500 1.18 1.24 1.19 36 30 1000 60 90 5000 2000 100 300 500 1.32 1.20 1.23 37 30 1000 60 90 20000 1000 20 100 300 1.21 1.21 1.21
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 3
Factor Levels Base Thickness Material Equivalence Run
SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 38 30 1000 60 90 20000 1000 40 100 500 1.18 1.18 1.24 39 30 1000 60 90 20000 1500 20 300 500 1.16 1.27 1.27 40 30 1000 60 90 20000 1500 100 100 300 1.20 1.23 1.27 41 30 1000 60 100 10000 1000 40 100 500 1.21 1.20 1.24 42 30 1000 60 100 10000 1000 100 300 500 1.19 1.28 1.23 43 30 1000 60 100 10000 2000 20 100 300 1.19 1.19 1.21 44 30 1000 60 100 10000 2000 40 100 500 1.22 1.18 1.25 45 30 1000 60 100 20000 1500 20 300 500 1.16 1.24 1.26 46 30 1000 60 100 20000 1500 100 100 300 1.20 1.15 1.27 47 30 1000 60 100 20000 2000 40 100 500 1.21 1.22 1.25 48 30 1000 60 100 20000 2000 100 300 500 1.31 1.30 1.21 49 30 1000 100 80 5000 1000 20 100 300 1.26 1.24 1.18 50 30 1000 100 80 5000 1000 40 100 500 1.20 1.21 1.24 51 30 1000 100 80 5000 1500 20 300 500 1.22 1.22 1.26 52 30 1000 100 80 5000 1500 100 100 300 1.19 1.18 1.25 53 30 1000 100 80 10000 1000 40 100 500 1.23 1.22 1.21 54 30 1000 100 80 10000 1000 100 300 500 1.22 1.23 1.30 55 30 1000 100 80 10000 2000 20 100 300 1.23 1.22 1.22 56 30 1000 100 80 10000 2000 40 100 500 1.18 1.21 1.23 57 30 1000 100 90 5000 1500 20 300 500 1.22 1.22 1.26 58 30 1000 100 90 5000 1500 100 100 300 1.19 1.18 1.25
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 4
Factor Levels Base Thickness Material Equivalence Run
SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 59 30 1000 100 90 5000 2000 40 100 500 1.21 1.17 1.25 60 30 1000 100 90 5000 2000 100 300 500 1.20 1.27 1.21 61 30 1000 100 90 20000 1000 20 100 300 1.24 1.27 1.24 62 30 1000 100 90 20000 1000 40 100 500 1.23 1.21 1.25 63 30 1000 100 90 20000 1500 20 300 500 1.23 1.23 1.27 64 30 1000 100 90 20000 1500 100 100 300 1.19 1.18 1.24 65 60 200 80 80 10000 1000 40 100 500 1.21 1.18 1.20 66 60 200 80 80 10000 1000 100 300 500 1.17 1.19 1.19 67 60 200 80 80 10000 2000 20 100 300 1.19 1.20 1.17 68 60 200 80 80 10000 2000 40 100 500 1.22 1.19 1.22 69 60 200 80 80 20000 1500 20 300 500 1.23 1.22 1.19 70 60 200 80 80 20000 1500 100 100 300 1.23 1.20 1.26 71 60 200 80 80 20000 2000 40 100 500 1.22 1.19 1.21 72 60 200 80 80 20000 2000 100 300 500 1.18 1.21 1.21 73 60 200 80 100 5000 1000 20 100 300 1.20 1.20 1.17 74 60 200 80 100 5000 1000 40 100 500 1.20 1.18 1.21 75 60 200 80 100 5000 1500 20 300 500 1.21 1.15 1.22 76 60 200 80 100 5000 1500 100 100 300 1.23 1.23 1.25 77 60 200 80 100 10000 1000 40 100 500 1.20 1.17 1.20 78 60 200 80 100 10000 1000 100 300 500 1.17 1.19 1.20 79 60 200 80 100 10000 2000 20 100 300 1.19 1.20 1.18
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 5
Factor Levels Base Thickness Material Equivalence Run
SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 80 60 200 80 100 10000 2000 40 100 500 1.22 1.19 1.22 81 60 200 100 90 5000 1500 20 300 500 1.24 1.22 1.27 82 60 200 100 90 5000 1500 100 100 300 1.21 1.22 1.23 83 60 200 100 90 5000 2000 40 100 500 1.20 1.21 1.21 84 60 200 100 90 5000 2000 100 300 500 1.27 1.18 1.27 85 60 200 100 90 20000 1000 20 100 300 1.19 1.19 1.18 86 60 200 100 90 20000 1000 40 100 500 1.20 1.20 1.23 87 60 200 100 90 20000 1500 20 300 500 1.23 1.24 1.26 88 60 200 100 90 20000 1500 100 100 300 1.21 1.20 1.26 89 60 200 100 100 10000 1000 40 100 500 1.21 1.19 1.23 90 60 200 100 100 10000 1000 100 300 500 1.23 1.25 1.21 91 60 200 100 100 10000 2000 20 100 300 1.18 1.19 1.21 92 60 200 100 100 10000 2000 40 100 500 1.22 1.20 1.25 93 60 200 100 100 20000 1500 20 300 500 1.22 1.24 1.27 94 60 200 100 100 20000 1500 100 100 300 1.20 1.21 1.26 95 60 200 100 100 20000 2000 40 100 500 1.22 1.19 1.25 96 60 200 100 100 20000 2000 100 300 500 1.26 1.28 1.21 97 60 1800 60 80 5000 1000 20 100 300 1.21 1.21 1.16 98 60 1800 60 80 5000 1000 40 100 500 1.14 NA NA 99 60 1800 60 80 5000 1500 20 300 500 1.12 NA NA
100 60 1800 60 80 5000 1500 100 100 300 1.22 1.22 1.19
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 6
Factor Levels Base Thickness Material Equivalence Run
SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 101 60 1800 60 80 10000 1000 40 100 500 1.17 NA NA 102 60 1800 60 80 10000 1000 100 300 100 1.18 1.22 1.19 103 60 1800 60 80 10000 2000 20 100 300 1.22 1.22 1.16 104 60 1800 60 80 10000 2000 40 100 500 1.17 NA NA 105 60 1800 60 90 5000 1500 20 300 500 1.12 NA NA 106 60 1800 60 90 5000 1500 100 100 300 1.22 1.21 1.19 107 60 1800 60 90 5000 2000 40 100 500 1.14 NA NA 108 60 1800 60 90 5000 2000 100 300 100 1.22 1.20 1.19 109 60 1800 60 90 20000 1000 20 100 300 1.20 1.21 1.20 110 60 1800 60 90 20000 1000 40 100 500 1.18 1.15 NA 111 60 1800 60 90 20000 1500 20 300 500 1.17 1.13 1.05 112 60 1800 60 90 20000 1500 100 100 300 1.23 1.21 1.22 113 60 1800 80 80 10000 1000 40 100 500 1.18 1.19 1.20 114 60 1800 80 80 10000 1000 100 300 500 1.20 1.10 NA 115 60 1800 80 80 10000 2000 20 100 300 1.20 1.20 1.20 116 60 1800 80 80 10000 2000 40 100 500 1.19 1.20 1.20 117 60 1800 80 80 20000 1500 20 300 500 1.23 1.19 1.21 118 60 1800 80 80 20000 1500 100 100 300 1.20 1.24 1.25 119 60 1800 80 80 20000 2000 40 100 500 1.22 1.23 1.21 120 60 1800 80 80 20000 2000 100 300 500 1.21 1.13 NA 121 60 1800 80 100 5000 1000 20 100 300 1.20 1.20 1.20
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 7
Factor Levels Base Thickness Material Equivalence Run
SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 122 60 1800 80 100 5000 1000 40 100 500 1.18 1.19 1.18 123 60 1800 80 100 5000 1500 20 300 500 1.15 1.18 1.18 124 60 1800 80 100 5000 1500 100 100 300 1.24 1.23 1.20 125 60 1800 80 100 10000 1000 40 100 500 1.18 1.19 1.20 126 60 1800 80 100 10000 1000 100 300 500 1.19 1.14 NA 127 60 1800 80 100 10000 2000 20 100 300 1.20 1.18 1.20 128 60 1800 80 100 10000 2000 40 100 500 1.19 1.20 1.20 129 100 2600 60 90 5000 1500 20 300 100 1.20 1.19 1.17 130 100 2600 60 90 5000 1500 100 100 300 1.14 NA NA 131 100 2600 60 90 5000 2000 40 100 300 1.20 1.19 1.16 132 100 2600 60 90 5000 2000 20 300 100 1.19 1.19 1.17 133 100 2600 60 90 20000 1000 20 100 300 1.18 1.18 1.17 134 100 2600 60 90 20000 1000 40 100 300 1.19 1.19 1.17 135 100 2600 60 90 20000 1500 20 300 100 1.20 1.19 1.18 136 100 2600 60 90 20000 1500 100 100 300 1.16 1.12 NA 137 100 2600 60 100 10000 1000 40 100 300 1.19 1.19 1.17 138 100 2600 60 100 10000 1000 100 300 100 1.16 1.13 NA 139 100 2600 60 100 10000 2000 20 100 300 1.19 1.19 1.18 140 100 2600 60 100 10000 2000 40 100 300 1.19 1.19 1.17 141 100 2600 60 100 20000 1500 20 300 100 1.18 1.19 1.17 142 100 2600 60 100 20000 1500 100 100 300 1.16 1.12 NA
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 8
Factor Levels Base Thickness Material Equivalence Run
SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 143 100 2600 60 100 20000 2000 40 100 300 1.20 1.20 1.18 144 100 2600 60 100 20000 2000 100 300 100 1.16 NA NA 145 100 2600 100 80 5000 1000 20 100 300 1.20 1.20 1.19 146 100 2600 100 80 5000 1000 40 100 500 1.17 NA NA 147 100 2600 100 80 5000 1500 20 300 500 1.16 NA NA 148 100 2600 100 80 5000 1500 100 100 300 1.19 1.20 1.20 149 100 2600 100 80 10000 1000 40 100 500 1.18 NA NA 150 100 2600 100 80 10000 1000 100 300 100 1.21 1.20 1.19 151 100 2600 100 80 10000 2000 20 100 300 1.21 1.21 1.20 152 100 2600 100 80 10000 2000 40 100 500 1.18 NA NA 153 100 2600 100 90 5000 1500 20 300 500 1.15 1.11 NA 154 100 2600 100 90 5000 1500 100 100 300 1.19 1.20 1.19 155 100 2600 100 90 5000 2000 40 100 500 1.17 NA NA 156 100 2600 100 90 5000 2000 100 300 100 1.20 1.20 1.20 157 100 2600 100 90 20000 1000 20 100 300 1.20 1.20 1.19 158 100 2600 100 90 20000 1000 40 100 500 1.18 1.17 1.15 159 100 2600 100 90 20000 1500 20 300 500 1.16 1.14 1.15 160 100 2600 100 90 20000 1500 100 100 300 1.22 1.19 1.20 161 100 1000 80 80 10000 1000 40 100 300 1.20 1.18 1.19 162 100 1000 80 80 10000 1000 100 300 100 1.20 1.19 1.18 163 100 1000 80 80 10000 2000 20 100 300 1.21 1.19 1.18
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 9
Factor Levels Base Thickness Material Equivalence Run
SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 164 100 1000 80 80 10000 2000 40 100 300 1.22 1.20 1.20 165 100 1000 80 80 20000 1500 20 300 500 1.12 1.04 NA 166 100 1000 80 80 20000 1500 100 100 300 1.19 1.19 1.19 167 100 1000 80 80 20000 2000 40 100 300 1.22 1.20 1.20 168 100 1000 80 80 20000 2000 100 300 100 1.20 1.19 1.18 169 100 1000 80 100 5000 1000 20 100 300 1.21 1.20 1.17 170 100 1000 80 100 5000 1000 40 100 300 1.19 1.18 1.18 171 100 1000 80 100 5000 1500 20 300 100 1.20 1.18 1.18 172 100 1000 80 100 5000 1500 100 100 300 1.19 1.18 1.16 173 100 1000 80 100 10000 1000 40 100 300 1.20 1.18 1.19 174 100 1000 80 100 10000 1000 100 300 100 1.19 1.19 1.18 175 100 1000 80 100 10000 2000 20 100 300 1.21 1.21 1.17 176 100 1000 80 100 10000 2000 40 100 300 1.22 1.19 1.20 177 100 1000 100 90 5000 1500 20 300 500 1.16 1.13 1.12 178 100 1000 100 90 5000 1500 100 100 300 1.20 1.20 1.20 179 100 1000 100 90 5000 2000 40 100 500 1.18 NA NA 180 100 1000 100 90 5000 2000 100 300 100 1.20 1.20 1.20 181 100 1000 100 90 20000 1000 20 100 300 1.18 1.20 1.19 182 100 1000 100 90 20000 1000 40 100 500 1.18 1.17 1.18 183 100 1000 100 90 20000 1500 20 300 500 1.16 1.16 1.18 184 100 1000 100 90 20000 1500 100 100 300 1.22 1.19 1.20
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 10
Factor Levels Base Thickness Material Equivalence Run
SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 185 100 1000 100 100 10000 1000 40 100 500 1.18 1.17 1.16 186 100 1000 100 100 10000 1000 100 300 500 1.10 NA NA 187 100 1000 100 100 10000 2000 20 100 300 1.20 1.21 1.20 188 100 1000 100 100 10000 2000 40 100 300 1.22 1.22 1.21 189 100 1000 100 100 20000 1500 20 300 500 1.16 1.16 1.17 190 100 1000 100 100 20000 1500 100 100 300 1.22 1.20 1.19 191 100 1000 100 100 20000 2000 40 100 500 1.19 1.18 1.17 192 100 1000 100 100 20000 2000 100 300 100 1.22 1.19 1.20 193 150 200 60 80 5000 1000 20 100 300 1.17 1.16 1.14 194 150 200 60 80 5000 1000 40 100 300 1.16 1.14 NA 195 150 200 60 80 5000 1500 20 300 100 1.17 1.16 NA 196 150 200 60 80 10000 1000 40 100 300 1.16 1.15 NA 197 150 200 60 80 10000 2000 20 100 300 1.17 1.16 1.14 198 150 200 60 80 10000 2000 40 100 300 1.16 NA NA 199 150 200 60 90 5000 1500 20 300 100 1.16 1.16 1.14 200 150 200 60 90 5000 2000 40 100 300 1.16 1.14 NA 201 150 200 60 90 20000 1000 20 100 300 1.17 1.17 1.15 202 150 200 60 90 20000 1000 40 100 300 1.16 1.16 1.13 203 150 200 60 90 20000 1500 20 300 100 1.17 1.16 1.15 204 150 200 80 80 10000 1000 40 100 300 1.20 1.18 1.16 205 150 200 80 80 10000 1000 100 300 100 1.15 NA NA
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 11
Factor Levels Base Thickness Material Equivalence Run
SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 206 150 200 80 80 10000 2000 20 100 300 1.18 1.18 1.17 207 150 200 80 80 10000 2000 40 100 300 1.19 1.19 1.16 208 150 200 80 80 20000 1500 20 300 100 1.18 1.18 1.17 209 150 200 80 80 20000 1500 100 100 300 1.15 NA NA 210 150 200 80 80 20000 2000 40 100 300 1.19 1.19 1.17 211 150 200 80 80 20000 2000 100 300 100 1.14 NA NA 212 150 200 80 100 5000 1000 20 100 300 1.17 1.18 1.16 213 150 200 80 100 5000 1000 40 100 300 1.17 1.17 1.15 214 150 200 80 100 5000 1500 20 300 100 1.18 1.18 1.16 215 150 200 80 100 5000 1500 100 100 300 1.14 NA NA 216 150 200 80 100 10000 1000 40 100 300 1.17 1.17 1.16 217 150 200 80 100 10000 1000 100 300 100 1.15 1.13 NA 218 150 200 80 100 10000 2000 20 100 300 1.18 1.18 1.16 219 150 200 80 100 10000 2000 40 100 300 1.18 1.18 1.16 220 150 1800 60 90 5000 1500 20 300 100 1.16 1.15 NA 221 150 1800 60 90 5000 2000 40 100 300 1.15 NA NA 222 150 1800 60 90 20000 1000 20 100 300 1.16 1.16 1.14 223 150 1800 60 90 20000 1000 40 100 300 1.16 1.18 NA 224 150 1800 60 90 20000 1500 20 300 100 1.17 1.16 1.13 225 150 1800 60 100 10000 1000 40 100 300 1.16 1.14 NA 226 150 1800 60 100 10000 2000 20 100 300 1.17 1.15 1.13
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 12
Factor Levels Base Thickness Material Equivalence Run
SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 227 150 1800 60 100 10000 2000 40 100 300 1.16 NA NA 228 150 1800 60 100 20000 1500 20 300 100 1.17 1.16 1.14 229 150 1800 60 100 20000 2000 40 100 300 1.16 1.14 NA 230 150 1800 100 80 5000 1000 20 100 300 1.18 1.19 1.17 231 150 1800 100 80 5000 1000 40 100 300 1.19 1.18 1.17 232 150 1800 100 80 5000 1500 20 300 100 1.19 1.19 1.18 233 150 1800 100 80 5000 1500 100 100 300 1.17 1.14 NA 234 150 1800 100 80 10000 1000 40 100 300 1.19 1.19 1.17 235 150 1800 100 80 10000 1000 100 300 100 1.17 1.16 1.14 236 150 1800 100 80 10000 2000 20 100 300 1.19 1.19 1.18 237 150 1800 100 80 10000 2000 40 100 300 1.20 1.20 1.18 238 150 1800 100 90 5000 1500 20 300 100 1.18 1.19 1.17 239 150 1800 100 90 5000 1500 100 100 300 1.16 1.15 NA 240 150 1800 100 90 5000 2000 40 100 300 1.20 1.19 1.18 241 150 1800 100 90 5000 2000 100 300 100 1.16 1.13 NA 242 150 1800 100 90 20000 1000 20 100 300 1.19 1.19 1.17 243 150 1800 100 90 20000 1000 40 100 300 1.18 1.19 1.17 244 150 1800 100 90 20000 1500 20 300 100 1.18 1.19 1.18 245 150 1800 100 90 20000 1500 100 100 300 1.17 1.16 1.14
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 13
Practical Asphalt versus Uncrushed Gravel
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 1 30 2600 60 80 5000 1000 100 20 40 1.90 1.85 1.85 2 30 2600 60 80 5000 1500 300 20 100 1.64 1.54 1.61 3 30 2600 60 80 10000 1000 500 40 100 1.40 1.73 1.72 4 30 2600 60 80 10000 2000 100 20 40 2.30 1.55 2.05 5 30 2600 60 90 5000 1500 300 20 100 1.63 1.58 1.61 6 30 2600 60 90 5000 2000 500 40 100 1.90 1.67 1.42 7 30 2600 60 90 20000 1000 100 20 40 1.65 1.40 1.90 8 30 2600 60 90 20000 1500 300 20 100 1.81 1.80 1.60 9 30 2600 80 80 10000 1000 500 40 100 1.72 1.77 1.75
10 30 2600 80 80 10000 2000 100 20 40 2.25 2.50 1.90 11 30 2600 80 80 20000 1500 300 20 100 1.78 1.70 1.69 12 30 2600 80 80 20000 2000 500 40 100 2.07 1.75 1.92 13 30 2600 80 100 5000 1000 100 20 40 2.15 1.60 1.45 14 30 2600 80 100 5000 1500 300 20 100 1.70 1.84 1.85 15 30 2600 80 100 10000 1000 500 40 100 1.72 1.77 1.77 16 30 2600 80 100 10000 2000 100 20 40 2.30 2.50 2.10 17 30 1000 60 90 5000 1500 300 20 100 1.61 1.78 1.60 18 30 1000 60 90 5000 2000 500 40 100 1.97 1.35 1.73 19 30 1000 60 90 20000 1000 100 20 40 2.00 2.00 1.95
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 14
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 20 30 1000 60 90 20000 1500 300 20 100 1.70 1.65 1.84 21 30 1000 60 100 10000 1000 500 40 100 1.40 1.57 1.23 22 30 1000 60 100 10000 2000 100 20 40 2.40 2.25 2.15 23 30 1000 60 100 20000 1500 300 20 100 1.70 1.66 1.83 24 30 1000 60 100 20000 2000 500 40 100 1.98 1.58 1.33 25 30 1000 100 80 5000 1000 100 20 40 2.25 2.20 1.60 26 30 1000 100 80 5000 1500 300 20 100 1.99 1.79 1.88 27 30 1000 100 80 10000 1000 500 40 100 1.48 1.70 1.77 28 30 1000 100 90 5000 1500 300 20 100 1.99 1.79 1.88 29 30 1000 100 90 5000 2000 500 40 100 1.83 2.10 1.57 30 30 1000 100 90 20000 1000 100 20 40 1.95 2.35 2.05 31 30 1000 100 90 20000 1500 300 20 100 2.05 1.88 1.75 32 60 200 80 80 10000 1000 500 40 100 1.30 1.48 1.40 33 60 200 80 80 10000 2000 100 20 40 1.80 1.70 1.60 34 60 200 80 80 20000 1500 300 20 100 1.68 1.54 1.63 35 60 200 80 80 20000 2000 500 40 100 1.43 1.63 1.55 36 60 200 80 100 5000 1000 100 20 40 1.70 1.60 1.50 37 60 200 80 100 5000 1500 300 20 100 1.55 1.54 1.66 38 60 200 80 100 10000 1000 500 40 100 1.30 1.48 1.42 39 60 200 80 100 10000 2000 100 20 40 1.80 1.75 1.65 40 60 200 100 90 5000 1500 300 20 100 1.64 1.65 1.64
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 15
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 41 60 200 100 90 5000 2000 500 40 100 1.73 1.43 1.73 42 60 200 100 90 20000 1000 100 20 40 1.75 1.90 1.60 43 60 200 100 90 20000 1500 300 20 100 1.78 1.65 1.76 44 60 200 100 100 10000 1000 500 40 100 1.48 1.58 1.37 45 60 200 100 100 10000 2000 100 20 40 2.20 2.00 2.05 46 60 200 100 100 20000 1500 300 20 100 1.76 1.65 1.78 47 60 200 100 100 20000 2000 500 40 100 1.70 1.78 1.48 48 60 1800 60 80 5000 1000 100 20 40 1.60 1.50 1.25 49 60 1800 60 80 5000 1500 300 20 100 1.48 1.51 1.55 50 60 1800 60 80 10000 1000 100 40 100 1.40 1.32 1.37 51 60 1800 60 80 10000 2000 100 20 40 1.60 1.60 1.35 52 60 1800 60 90 5000 1500 300 20 100 1.46 1.48 1.56 53 60 1800 60 90 5000 2000 100 40 100 1.52 1.57 1.65 54 60 1800 60 90 20000 1000 100 20 40 1.60 1.55 1.60 55 60 1800 60 90 20000 1500 300 20 100 1.59 1.48 1.50 56 60 1800 80 80 10000 1000 500 40 100 1.50 1.18 NA 57 60 1800 80 80 10000 2000 100 20 40 1.70 1.65 1.75 58 60 1800 80 80 20000 1500 300 20 100 1.56 1.61 1.66 59 60 1800 80 80 20000 2000 500 40 100 1.43 1.20 NA 60 60 1800 80 100 5000 1000 100 20 40 1.60 1.55 1.65 61 60 1800 80 100 5000 1500 300 20 100 1.55 1.59 1.53
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 16
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 62 60 1800 80 100 10000 1000 500 40 100 1.47 1.32 NA 63 60 1800 80 100 10000 2000 100 20 40 1.75 1.45 1.75 64 100 2600 60 90 5000 1500 100 20 100 1.56 1.55 1.53 65 100 2600 60 90 5000 1500 300 20 100 1.40 NA NA 66 100 2600 60 90 5000 2000 100 40 20 1.50 1.50 1.50 67 100 2600 60 90 5000 2000 300 40 20 1.60 1.50 1.40 68 100 2600 60 90 20000 1000 100 20 40 1.35 1.45 1.45 69 100 2600 60 90 20000 1000 300 20 40 1.50 1.50 1.45 70 100 2600 60 90 20000 1500 100 20 100 1.53 1.54 1.55 71 100 2600 60 90 20000 1500 300 20 100 1.44 1.36 NA 72 100 2600 60 100 10000 1000 100 40 100 1.42 1.42 1.42 73 100 2600 60 100 10000 1000 300 40 100 1.33 1.22 NA 74 100 2600 60 100 10000 2000 100 20 40 1.55 1.55 1.55 75 100 2600 60 100 10000 2000 300 20 40 1.55 1.55 1.45 76 100 2600 60 100 20000 1500 100 20 100 1.49 1.55 1.54 77 100 2600 60 100 20000 1500 300 20 100 1.45 1.38 NA 78 100 2600 60 100 20000 2000 100 40 100 1.65 1.68 1.68 79 100 2600 60 100 20000 2000 300 40 100 1.50 NA NA 80 100 2600 100 80 5000 1000 100 20 40 1.55 1.50 1.50 81 100 2600 100 80 5000 1500 300 20 100 1.46 1.44 1.48 82 100 2600 100 80 10000 1000 100 40 100 1.37 1.33 1.32
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 17
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 83 100 2600 100 80 10000 2000 100 20 40 1.60 1.60 1.60 84 100 2600 100 90 5000 1500 300 20 100 1.45 1.45 1.46 85 100 2600 100 90 5000 2000 100 40 100 1.53 1.52 1.52 86 100 2600 100 90 20000 1000 100 20 40 1.55 1.50 1.50 87 100 2600 100 90 20000 1500 300 20 100 1.51 1.45 1.49 88 100 1000 80 80 10000 1000 100 40 100 1.33 1.33 1.37 89 100 1000 80 80 10000 1000 300 40 100 1.32 1.37 1.35 90 100 1000 80 80 10000 2000 100 20 40 1.55 1.55 1.45 91 100 1000 80 80 10000 2000 300 20 40 1.65 1.65 1.65 92 100 1000 80 80 20000 1500 300 20 100 1.44 1.43 1.49 93 100 1000 80 80 20000 2000 100 40 100 1.52 1.55 1.57 94 100 1000 80 100 5000 1000 100 20 40 1.60 1.55 1.40 95 100 1000 80 100 5000 1000 300 20 40 1.45 1.30 1.55 96 100 1000 80 100 5000 1500 100 20 100 1.46 1.49 1.50 97 100 1000 80 100 5000 1500 300 20 100 1.43 1.49 1.46 98 100 1000 80 100 10000 1000 100 40 100 1.32 1.33 1.38 99 100 1000 80 100 10000 1000 300 40 100 1.30 1.37 1.35
100 100 1000 80 100 10000 2000 100 20 40 1.60 1.60 1.45 101 100 1000 80 100 10000 2000 300 20 40 1.65 1.40 1.70 102 100 1000 100 90 5000 2000 100 40 100 1.52 1.52 1.52 103 100 1000 100 90 20000 1000 100 20 40 1.40 1.50 1.60
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 18
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 104 100 1000 100 90 20000 1500 300 20 100 1.53 1.46 1.50 105 100 1000 100 100 10000 1000 500 40 100 1.18 NA NA 106 100 1000 100 100 10000 2000 100 20 40 1.60 1.55 1.65 107 100 1000 100 100 10000 2000 300 20 40 1.75 1.70 1.80 108 100 1000 100 100 20000 1500 300 20 100 1.53 1.50 1.49 109 100 1000 100 100 20000 2000 100 40 100 1.50 1.53 1.50 110 150 200 60 80 5000 1000 100 20 40 1.45 1.45 1.40 111 150 200 60 80 5000 1000 300 20 40 1.35 1.20 NA 112 150 200 60 80 5000 1500 100 20 100 1.49 1.50 1.51 113 150 200 60 80 10000 1000 100 40 100 1.33 1.35 1.37 114 150 200 60 80 10000 1000 300 40 20 1.35 1.30 NA 115 150 200 60 80 10000 2000 100 20 40 1.50 1.50 1.45 116 150 200 60 80 10000 2000 300 20 40 1.40 NA NA 117 150 200 60 90 5000 1500 100 100 40 1.52 1.52 1.53 118 150 200 60 90 5000 2000 100 40 100 1.63 1.68 1.70 119 150 200 60 90 5000 2000 300 40 20 1.40 1.25 NA 120 150 200 60 90 20000 1000 100 20 40 1.45 1.45 1.35 121 150 200 60 90 20000 1000 300 20 40 1.40 1.35 1.15 122 150 200 60 90 20000 1500 100 20 100 1.49 1.49 1.51 123 150 200 80 80 10000 1000 100 40 100 1.45 1.37 1.35 124 150 200 80 80 10000 1000 300 40 100 1.28 NA NA
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 19
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 125 150 200 80 80 10000 2000 100 20 40 1.50 1.50 1.50 126 150 200 80 80 10000 2000 300 20 40 1.55 1.55 1.45 127 150 200 80 80 20000 1500 100 20 100 1.48 1.49 1.50 128 150 200 80 80 20000 1500 300 20 100 1.40 NA NA 129 150 200 80 80 20000 2000 100 40 100 1.60 1.62 1.62 130 150 200 80 80 20000 2000 300 40 100 1.42 NA NA 131 150 200 80 100 5000 1000 100 20 40 1.45 1.50 1.45 132 150 200 80 100 5000 1000 300 20 40 1.45 1.45 1.40 133 150 200 80 100 5000 1500 100 20 100 1.49 1.50 1.49 134 150 200 80 100 5000 1500 300 20 100 1.38 NA NA 135 150 200 80 100 10000 1000 100 40 100 1.37 1.38 1.38 136 150 200 80 100 10000 1000 300 40 100 1.30 1.25 NA 137 150 200 80 100 10000 2000 100 20 40 1.50 1.50 1.50 138 150 200 80 100 10000 2000 300 20 40 1.55 1.55 1.50 139 150 1800 60 90 5000 1500 100 100 40 1.52 1.53 1.57 140 150 1800 60 90 5000 2000 100 100 20 1.61 1.64 1.66 141 150 1800 60 90 20000 1000 100 20 40 1.40 1.45 1.40 142 150 1800 60 90 20000 1000 300 20 40 1.40 1.65 NA 143 150 1800 60 90 20000 1500 100 20 100 1.50 1.50 1.51 144 150 1800 60 100 10000 1000 100 40 100 1.33 1.35 1.35 145 150 1800 60 100 10000 2000 100 20 40 1.50 1.45 1.50
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 20
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 146 150 1800 60 100 10000 2000 300 20 40 1.40 NA NA 147 150 1800 60 100 20000 1500 100 20 100 1.49 1.50 1.51 148 150 1800 60 100 20000 2000 100 40 100 1.63 1.67 1.72 149 150 1800 100 80 5000 1000 100 20 40 1.45 1.50 1.50 150 150 1800 100 80 5000 1000 300 20 40 1.50 1.45 1.50 151 150 1800 100 80 5000 1500 100 20 100 1.48 1.49 1.48 152 150 1800 100 80 5000 1500 300 20 100 1.41 1.36 NA 153 150 1800 100 80 10000 1000 100 40 100 1.35 1.37 1.37 154 150 1800 100 80 10000 1000 300 40 100 1.30 1.28 1.25 155 150 1800 100 80 10000 2000 100 20 40 1.50 1.50 1.55 156 150 1800 100 80 10000 2000 300 20 40 1.55 1.55 1.55 157 150 1800 100 90 5000 1500 100 20 100 1.46 1.49 1.49 158 150 1800 100 90 5000 1500 300 20 100 1.43 1.39 NA 159 150 1800 100 90 5000 2000 100 40 100 1.58 1.60 1.62 160 150 1800 100 90 5000 2000 300 40 100 1.45 1.38 NA 161 150 1800 100 90 20000 1000 100 20 40 1.50 1.50 1.45 162 150 1800 100 90 20000 1000 300 20 40 1.40 1.50 1.45 163 150 1800 100 90 20000 1500 100 20 100 1.46 1.49 1.49 164 150 1800 100 90 20000 1500 300 20 100 1.44 1.40 1.39
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 21
Practical Asphalt versus Crushed Rock
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 1 30 2600 60 80 5000 1000 200 20 40 1.50 1.50 1.50 2 30 2600 60 80 5000 1500 400 40 100 1.30 1.25 1.20 3 30 2600 60 80 10000 1000 200 20 100 1.34 1.30 1.19 4 30 2600 60 80 10000 2000 800 20 40 1.90 1.75 NA 5 30 2600 60 90 5000 1500 400 40 100 1.30 1.23 1.20 6 30 2600 60 90 5000 2000 800 20 100 1.39 NA NA 7 30 2600 60 90 20000 1000 200 20 40 1.30 1.50 1.50 8 30 2600 60 90 20000 2000 400 40 100 1.32 1.30 1.25 9 30 2600 80 80 10000 1500 200 20 100 1.56 1.20 1.46
10 30 2600 80 80 10000 2000 800 20 40 2.05 1.90 1.80 11 30 2600 80 80 20000 1000 400 40 100 1.23 1.28 1.27 12 30 2600 80 80 20000 1500 800 20 100 1.50 1.46 1.39 13 30 2600 80 100 5000 1500 200 20 40 1.80 1.20 1.75 14 30 2600 80 100 5000 2000 400 40 100 1.48 1.35 1.30 15 30 2600 80 100 10000 1000 200 20 100 1.35 1.20 1.34 16 30 2600 80 100 10000 1500 800 20 40 1.80 1.75 1.75 17 30 1000 60 80 5000 1000 400 40 100 1.18 1.23 1.20 18 30 1000 60 80 5000 2000 800 20 100 1.43 1.36 NA 19 30 1000 60 80 20000 1000 200 20 40 1.45 1.50 1.45
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 22
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 20 30 1000 60 80 20000 1500 400 40 100 1.37 1.28 1.30 21 30 1000 60 90 10000 1000 200 20 100 1.29 1.30 1.18 22 30 1000 60 90 10000 2000 800 20 40 1.85 1.75 NA 23 30 1000 60 90 20000 1500 400 40 100 1.37 1.32 1.28 24 30 1000 60 90 20000 2000 800 20 100 1.50 1.40 NA 25 30 1000 100 80 5000 1000 200 20 40 1.50 0.95 0.90 26 30 1000 100 80 5000 2000 400 40 100 1.62 1.52 1.32 27 30 1000 100 80 10000 1500 200 20 100 1.66 1.51 1.36 28 30 1000 100 80 10000 2000 800 20 40 2.10 2.10 1.90 29 30 1000 100 100 5000 1000 400 40 100 1.32 1.28 1.27 30 30 1000 100 100 5000 1500 800 20 100 1.54 1.50 1.41 31 30 1000 100 100 20000 1500 200 20 40 1.90 1.95 1.80 32 30 1000 100 100 20000 2000 400 40 100 1.63 1.65 1.45 33 60 200 60 80 10000 1000 200 20 100 1.24 1.24 1.24 34 60 200 60 80 10000 1500 400 20 40 1.35 1.35 1.40 35 60 200 60 80 20000 1000 400 40 100 1.13 1.17 1.17 36 60 200 60 80 20000 2000 400 20 100 1.28 1.30 1.31 37 60 200 60 90 5000 1000 200 20 40 1.40 1.40 1.35 38 60 200 60 90 5000 1500 400 40 100 1.23 1.25 1.25 39 60 200 60 90 10000 1000 200 20 100 1.24 1.25 1.24 40 60 200 60 90 10000 2000 400 20 40 1.40 1.40 1.45
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 23
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 41 60 200 80 80 5000 1500 400 40 100 1.22 1.20 1.22 42 60 200 80 80 5000 2000 200 20 100 1.29 1.35 1.36 43 60 200 80 80 20000 1000 200 20 40 1.40 1.35 1.50 44 60 200 80 80 20000 2000 400 40 100 1.27 1.25 1.22 45 60 200 80 100 10000 1500 200 20 100 1.26 1.24 1.34 46 60 200 80 100 10000 2000 400 20 40 1.60 1.50 1.60 47 60 200 80 100 20000 1000 400 40 100 1.22 1.18 1.18 48 60 200 80 100 20000 1500 200 20 100 1.31 1.25 1.38 49 60 1800 60 80 5000 1500 200 20 40 1.40 1.35 1.40 50 60 1800 60 80 5000 2000 400 40 100 1.30 1.32 NA 51 60 1800 60 80 10000 1000 200 20 100 1.24 1.16 1.18 52 60 1800 60 80 10000 1500 400 20 40 1.40 1.30 NA 53 60 1800 60 90 5000 1000 400 40 100 1.17 1.17 1.17 54 60 1800 60 90 5000 2000 200 20 100 1.31 1.29 1.31 55 60 1800 60 90 20000 1000 200 20 40 1.40 1.35 1.40 56 60 1800 60 90 20000 1500 400 40 100 1.22 1.23 1.23 57 60 1800 100 80 10000 1000 200 20 100 1.26 1.16 1.20 58 60 1800 100 80 10000 2000 800 20 40 1.75 1.55 NA 59 60 1800 100 80 20000 1500 400 40 100 1.27 1.25 1.23 60 60 1800 100 80 20000 2000 800 20 100 1.39 NA NA 61 60 1800 100 100 5000 1000 200 20 40 1.40 1.35 1.40
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 24
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 62 60 1800 100 100 5000 2000 400 40 100 1.28 1.23 1.22 63 60 1800 100 100 10000 1500 200 20 100 1.39 1.28 1.29 64 60 1800 100 100 10000 2000 800 20 40 1.70 1.60 NA 65 100 2600 60 80 5000 1000 200 40 100 1.18 1.18 1.22 66 100 2600 60 80 5000 1500 200 20 100 1.28 1.30 1.33 67 100 2600 60 80 20000 1500 200 20 40 1.25 1.30 1.30 68 100 2600 60 80 20000 2000 200 40 100 1.38 1.38 1.43 69 100 2600 60 90 10000 1000 200 20 100 1.18 1.20 1.20 70 100 2600 60 90 10000 1500 200 20 40 1.20 1.25 1.30 71 100 2600 60 90 20000 1000 200 40 100 1.13 1.17 1.18 72 100 2600 60 90 20000 2000 200 20 100 1.33 1.36 1.39 73 100 2600 80 80 5000 1000 200 20 40 1.30 1.25 1.20 74 100 2600 80 80 5000 1500 400 40 100 1.22 NA NA 75 100 2600 80 80 10000 1000 200 20 100 1.14 1.15 1.16 76 100 2600 80 80 10000 2000 200 20 40 1.25 1.25 1.30 77 100 2600 80 100 5000 1500 400 40 100 1.22 NA NA 78 100 2600 80 100 5000 2000 200 20 100 1.25 1.29 1.31 79 100 2600 80 100 20000 1000 200 20 40 1.30 1.30 1.30 80 100 2600 80 100 20000 2000 400 40 100 1.28 1.30 NA 81 100 1000 60 80 10000 1500 200 20 100 1.25 1.29 1.30 82 100 1000 60 80 10000 2000 200 20 40 1.15 1.25 1.35
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 25
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 83 100 1000 60 80 20000 1000 400 40 100 1.13 NA NA 84 100 1000 60 80 20000 1500 200 20 100 1.25 1.28 1.30 85 100 1000 60 90 5000 1500 200 20 40 1.20 1.30 1.30 86 100 1000 60 90 5000 2000 200 40 100 1.40 1.40 1.47 87 100 1000 60 90 10000 1000 200 20 100 1.18 1.20 1.21 88 100 1000 60 90 10000 1500 200 20 40 1.20 1.30 1.30 89 100 1000 100 80 5000 1000 400 40 100 1.17 1.13 1.15 90 100 1000 100 80 5000 2000 200 20 100 1.31 1.23 1.28 91 100 1000 100 80 20000 1000 200 20 40 1.40 1.30 1.35 92 100 1000 100 80 20000 1500 400 40 100 1.20 1.20 1.22 93 100 1000 100 100 10000 1000 200 20 100 1.21 1.20 1.20 94 100 1000 100 100 10000 2000 400 20 40 1.35 1.35 1.45 95 100 1000 100 100 20000 1500 400 40 100 1.20 1.20 1.20 96 100 1000 100 100 20000 2000 200 20 100 1.33 1.33 1.33 97 150 200 60 80 5000 1000 200 20 40 1.25 1.20 1.20 98 150 200 60 80 5000 2000 200 40 100 1.42 1.45 NA 99 150 200 60 80 10000 1500 200 20 100 1.28 1.29 1.33
100 150 200 60 80 10000 2000 200 20 40 1.30 1.25 1.25 101 150 200 60 90 5000 1000 200 40 100 1.15 1.18 1.20 102 150 200 60 90 5000 1500 200 20 100 1.28 1.30 1.33 103 150 200 60 90 20000 1500 200 20 40 1.25 1.25 1.25
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 26
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 104 150 200 60 90 20000 2000 200 40 100 1.40 1.43 1.52 105 150 200 80 80 10000 1000 200 20 100 1.19 1.16 1.18 106 150 200 80 80 10000 1500 200 20 40 1.30 1.25 1.30 107 150 200 80 80 20000 1000 200 40 100 1.13 1.13 1.15 108 150 200 80 80 20000 2000 200 20 100 1.31 1.33 1.36 109 150 200 80 100 5000 1000 200 20 40 1.25 1.30 1.25 110 150 200 80 100 5000 1500 200 40 100 1.25 1.27 1.30 111 150 200 80 100 10000 1000 200 20 100 1.18 1.18 1.19 112 150 200 80 100 10000 2000 200 20 40 1.25 1.30 1.30 113 150 1800 60 80 5000 1500 200 40 100 1.30 1.33 NA 114 150 1800 60 80 5000 2000 200 20 100 1.40 1.41 NA 115 150 1800 60 80 20000 1000 200 20 40 1.25 1.20 1.15 116 150 1800 60 80 20000 2000 200 40 100 1.43 1.45 NA 117 150 1800 60 90 10000 1500 200 20 100 1.29 1.30 1.34 118 150 1800 60 90 10000 2000 200 20 40 1.30 1.30 1.25 119 150 1800 60 90 20000 1000 200 40 100 1.15 1.17 1.20 120 150 1800 60 90 20000 1500 200 20 100 1.28 1.30 1.34 121 150 1800 100 80 5000 1500 200 20 40 1.25 1.30 1.30 122 150 1800 100 80 5000 2000 200 40 100 1.28 1.30 1.37 123 150 1800 100 80 10000 1000 200 20 100 1.15 1.15 1.18 124 150 1800 100 80 10000 1500 400 20 40 1.25 1.20 1.20
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 27
Factor Levels Asphalt Thickness Material Equivalence Run
SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 125 150 1800 100 100 5000 1000 200 40 100 1.12 1.15 1.15 126 150 1800 100 100 5000 2000 200 20 100 1.29 1.33 1.34 127 150 1800 100 100 20000 1000 200 20 40 1.30 1.25 1.25 128 150 1800 100 100 20000 1500 800 40 100 1.22 NA NA
Notes
Bold denotes changed parameters to return a positive SB thickness for B747 aircraft.
NA denotes a combination of parameters for which no SB thickness was required to achieve a CDF of less than 1.0.
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 28
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 29
Isolated Material Equivalence
Factor Levels Run SM
(MPa) RL RM
(MPs) RT
(mm) E MR TR
1 30 Full 50 Full 0.50 0.1 NA 2 30 Full 100 Full 0.59 0.2 NA 3 30 Full 250 Full 0.78 0.5 NA 4 30 Full 750 Full 1.16 1.5 NA 5 30 Full 1000 Full 1.30 2.0 NA 6 30 Full 2000 Full 1.72 4.0 NA 7 30 Full 4000 Full 2.28 8.0 NA 8 60 Full 50 Full 0.57 0.1 NA 9 60 Full 100 Full 0.64 0.2 NA
10 60 Full 250 Full 0.80 0.5 NA 11 60 Full 750 Full 1.15 1.5 NA 12 60 Full 1000 Full 1.28 2.0 NA 13 60 Full 2000 Full 1.69 4.0 NA 14 60 Full 4000 Full 2.23 8.0 NA 15 100 Full 50 Full 0.63 0.1 NA 16 100 Full 100 Full 0.68 0.2 NA 17 100 Full 250 Full 0.82 0.5 NA 18 100 Full 750 Full 1.14 1.5 NA 19 100 Full 1000 Full 1.26 2.0 NA 20 100 Full 2000 Full 1.64 4.0 NA 21 100 Full 4000 Full 2.17 8.0 NA 22 150 Full 50 Full 0.68 0.1 NA 23 150 Full 100 Full 0.73 0.2 NA 24 150 Full 250 Full 0.84 0.5 NA 25 150 Full 750 Full 1.13 1.5 NA 26 150 Full 1000 Full 1.24 2.0 NA 27 150 Full 2000 Full 1.59 4.0 NA 28 150 Full 4000 Full 2.10 8.0 NA 29 30 Top 50 100 0.66 0.1 0.11 30 30 Top 50 200 0.65 0.1 0.23 31 30 Top 50 400 0.59 0.1 0.52 32 30 Top 100 100 0.71 0.2 0.11 33 30 Top 100 200 0.70 0.2 0.23 34 30 Top 100 400 0.66 0.2 0.54 35 30 Top 250 100 0.83 0.5 0.11
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 30
Factor Levels Run SM
(MPa) RL RM
(MPs) RT
(mm) E MR TR
36 30 Top 250 200 0.84 0.5 0.24 37 30 Top 250 400 0.82 0.5 0.60 38 30 Top 750 100 1.12 1.5 0.11 39 30 Top 750 200 1.12 1.5 0.26 40 30 Top 750 400 1.13 1.5 0.73 41 30 Top 1000 100 1.22 2.0 0.11 42 30 Top 1000 200 1.21 2.0 0.26 43 30 Top 1000 400 1.23 2.0 0.79 44 30 Top 2000 100 1.49 4.0 0.12 45 30 Top 2000 200 1.45 4.0 0.28 46 30 Top 2000 400 1.52 4.0 1.02 47 30 Top 4000 100 1.78 8.0 0.12 48 30 Top 4000 200 1.76 8.0 0.31 49 30 Top 4000 400 1.99 8.0 1.96 50 30 Bottom 50 100 0.43 0.1 0.10 51 30 Bottom 50 200 0.49 0.1 0.22 52 30 Bottom 50 400 0.51 0.1 0.50 53 30 Bottom 100 100 0.31 0.2 0.10 54 30 Bottom 100 200 0.44 0.2 0.22 55 30 Bottom 100 400 0.52 0.2 0.51 56 30 Bottom 250 100 0.53 0.5 0.11 57 30 Bottom 250 200 0.64 0.5 0.23 58 30 Bottom 250 400 0.72 0.5 0.56 59 30 Bottom 750 100 1.41 1.5 0.12 60 30 Bottom 750 200 1.28 1.5 0.27 61 30 Bottom 750 400 1.20 1.5 0.77 62 30 Bottom 1000 100 1.75 2.0 0.12 63 30 Bottom 1000 200 1.49 2.0 0.28 64 30 Bottom 1000 400 1.35 2.0 0.87 65 30 Bottom 2000 100 2.64 4.0 0.14 66 30 Bottom 2000 200 2.02 4.0 0.34 67 30 Bottom 2000 400 1.75 4.0 1.32 68 30 Bottom 4000 100 3.50 8.0 0.15 69 30 Bottom 4000 200 2.54 8.0 0.41 70 30 Bottom 4000 400 2.26 8.0 4.17 71 60 Top 50 100 0.74 0.1 0.11 72 60 Top 50 200 0.72 0.1 0.23
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 31
Factor Levels Run SM
(MPa) RL RM
(MPs) RT
(mm) E MR TR
73 60 Top 50 400 0.65 0.1 0.54 74 60 Top 100 100 0.78 0.2 0.11 75 60 Top 100 200 0.76 0.2 0.24 76 60 Top 100 400 0.71 0.2 0.56 77 60 Top 250 100 0.87 0.5 0.11 78 60 Top 250 200 0.87 0.5 0.24 79 60 Top 250 400 0.84 0.5 0.60 80 60 Top 750 100 1.09 1.5 0.11 81 60 Top 750 200 1.09 1.5 0.26 82 60 Top 750 400 1.12 1.5 0.72 83 60 Top 1000 100 1.17 2.0 0.11 84 60 Top 1000 200 1.17 2.0 0.26 85 60 Top 1000 400 1.22 2.0 0.78 86 60 Top 2000 100 1.38 4.0 0.12 87 60 Top 2000 200 1.40 4.0 0.28 88 60 Top 2000 400 1.52 4.0 1.02 89 60 Top 4000 100 1.62 8.0 0.12 90 60 Top 4000 200 1.70 8.0 0.30 91 60 Top 4000 400 1.98 8.0 1.92 92 60 Bottom 50 100 0.89 0.1 0.11 93 60 Bottom 50 200 0.81 0.1 0.24 94 60 Bottom 50 400 0.71 0.1 0.56 95 60 Bottom 100 100 0.57 0.2 0.11 96 60 Bottom 100 200 0.63 0.2 0.23 97 60 Bottom 100 400 0.65 0.2 0.54 98 60 Bottom 250 100 0.61 0.5 0.11 99 60 Bottom 250 200 0.71 0.5 0.23
100 60 Bottom 250 400 0.77 0.5 0.58 101 60 Bottom 750 100 1.37 1.5 0.12 102 60 Bottom 750 200 1.25 1.5 0.27 103 60 Bottom 750 400 1.18 1.5 0.76 104 60 Bottom 1000 100 1.68 2.0 0.12 105 60 Bottom 1000 200 1.45 2.0 0.28 106 60 Bottom 1000 400 1.33 2.0 0.85 107 60 Bottom 2000 100 2.53 4.0 0.13 108 60 Bottom 2000 200 1.96 4.0 0.33 109 60 Bottom 2000 400 1.72 4.0 1.28
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 32
Factor Levels Run SM
(MPa) RL RM
(MPs) RT
(mm) E MR TR
110 60 Bottom 4000 100 3.36 8.0 0.15 111 60 Bottom 4000 200 2.49 8.0 0.40 112 60 Bottom 4000 400 2.23 8.0 3.67 113 100 Top 50 100 0.80 0.1 0.11 114 100 Top 50 200 0.77 0.1 0.24 115 100 Top 50 400 0.69 0.1 0.55 116 100 Top 100 100 0.82 0.2 0.11 117 100 Top 100 200 0.80 0.2 0.24 118 100 Top 100 400 0.74 0.2 0.57 119 100 Top 250 100 0.89 0.5 0.11 120 100 Top 250 200 0.89 0.5 0.24 121 100 Top 250 400 0.86 0.5 0.61 122 100 Top 750 100 1.06 1.5 0.11 123 100 Top 750 200 1.08 1.5 0.25 124 100 Top 750 400 1.11 1.5 0.72 125 100 Top 1000 100 1.12 2.0 0.11 126 100 Top 1000 200 1.15 2.0 0.26 127 100 Top 1000 400 1.21 2.0 0.77 128 100 Top 2000 100 1.29 4.0 0.11 129 100 Top 2000 200 1.36 4.0 0.27 130 100 Top 2000 400 1.50 4.0 1.00 131 100 Top 4000 100 1.50 8.0 0.12 132 100 Top 4000 200 1.65 8.0 0.30 133 100 Top 4000 400 1.95 8.0 1.83 134 100 Bottom 50 100 1.35 0.1 0.12 135 100 Bottom 50 200 1.10 0.1 0.26 136 100 Bottom 50 400 0.88 0.1 0.62 137 100 Bottom 100 100 0.85 0.2 0.11 138 100 Bottom 100 200 0.82 0.2 0.24 139 100 Bottom 100 400 0.77 0.2 0.58 140 100 Bottom 250 100 0.70 0.5 0.11 141 100 Bottom 250 200 0.78 0.5 0.24 142 100 Bottom 250 400 0.81 0.5 0.59 143 100 Bottom 750 100 1.32 1.5 0.12 144 100 Bottom 750 200 1.22 1.5 0.26 145 100 Bottom 750 400 1.17 1.5 0.75 146 100 Bottom 1000 100 1.60 2.0 0.12
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 33
Factor Levels Run SM
(MPa) RL RM
(MPs) RT
(mm) E MR TR
147 100 Bottom 1000 200 1.40 2.0 0.28 148 100 Bottom 1000 400 1.30 2.0 0.83 149 100 Bottom 2000 100 2.41 4.0 0.13 150 100 Bottom 2000 200 1.88 4.0 0.32 151 100 Bottom 2000 400 1.68 4.0 1.22 152 100 Bottom 4000 100 3.22 8.0 0.15 153 100 Bottom 4000 200 2.41 8.0 0.39 154 100 Bottom 4000 400 2.18 8.0 3.08 155 150 Top 50 100 0.84 0.1 0.11 156 150 Top 50 200 0.82 0.1 0.24 157 150 Top 50 400 0.73 0.1 0.56 158 150 Top 100 100 0.87 0.2 0.11 159 150 Top 100 200 0.84 0.2 0.24 160 150 Top 100 400 0.77 0.2 0.58 161 150 Top 250 100 0.92 0.5 0.11 162 150 Top 250 200 0.91 0.5 0.24 163 150 Top 250 400 0.87 0.5 0.61 164 150 Top 750 100 1.05 1.5 0.11 165 150 Top 750 200 1.07 1.5 0.25 166 150 Top 750 400 1.11 1.5 0.72 167 150 Top 1000 100 1.10 2.0 0.11 168 150 Top 1000 200 1.13 2.0 0.26 169 150 Top 1000 400 1.20 2.0 0.77 170 150 Top 2000 100 1.24 4.0 0.11 171 150 Top 2000 200 1.33 4.0 0.27 172 150 Top 2000 400 1.49 4.0 0.99 173 150 Top 4000 100 1.42 8.0 0.12 174 150 Top 4000 200 1.62 8.0 0.30 175 150 Top 4000 400 1.93 8.0 1.74 176 150 Bottom 50 100 1.78 0.1 0.12 177 150 Bottom 50 200 1.35 0.1 0.27 178 150 Bottom 50 400 1.02 0.1 0.68 179 150 Bottom 100 100 1.13 0.2 0.11 180 150 Bottom 100 200 0.99 0.2 0.25 181 150 Bottom 100 400 0.87 0.2 0.61 182 150 Bottom 250 100 0.81 0.5 0.11 183 150 Bottom 250 200 0.85 0.5 0.24
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 34
Factor Levels Run SM
(MPa) RL RM
(MPs) RT
(mm) E MR TR
184 150 Bottom 250 400 0.85 0.5 0.61 185 150 Bottom 750 100 1.28 1.5 0.11 186 150 Bottom 750 200 1.19 1.5 0.26 187 150 Bottom 750 400 1.15 1.5 0.74 188 150 Bottom 1000 100 1.54 2.0 0.12 189 150 Bottom 1000 200 1.35 2.0 0.27 190 150 Bottom 1000 400 1.27 2.0 0.81 191 150 Bottom 2000 100 2.29 4.0 0.13 192 150 Bottom 2000 200 1.81 4.0 0.31 193 150 Bottom 2000 400 1.64 4.0 1.16 194 150 Bottom 4000 100 3.08 8.0 0.14 195 150 Bottom 4000 200 2.32 8.0 0.37 196 150 Bottom 4000 400 2.12 8.0 2.61
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 35
Equivalence Examples
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
1 30 B747 397 5,000 1.75 2,857 75 150 1305 1530 1545 1530 1530 2 30 B747 397 5,000 1.75 2,857 50 400 1050 1500 1545 1600 1535 3 30 B747 397 5,000 1.75 2,857 150 300 1016 1466 1545 1616 1541 4 30 B747 397 10,000 1.75 5,714 75 150 1397 1622 1635 1622 1622 5 30 B747 397 10,000 1.75 5,714 40 200 1407 1647 1635 1637 1636 6 30 B747 397 10,000 1.75 5,714 100 400 1048 1548 1635 1698 1613 7 30 B747 397 20,000 1.75 11,429 75 150 1481 1706 1720 1706 1706 8 30 B747 397 20,000 1.75 11,429 50 350 1290 1690 1720 1765 1715 9 30 B747 397 20,000 1.75 11,429 300 100 1220 1620 1720 1820 1745
10 30 B747 318 5,000 1.75 2,857 75 150 1061 1286 1327 1286 1286 11 30 B747 318 5,000 1.75 2,857 50 400 814 1264 1327 1364 1299 12 30 B747 318 5,000 1.75 2,857 150 300 783 1233 1327 1383 1308 13 30 B747 318 10,000 1.75 5,714 75 150 1142 1367 1409 1367 1367 14 30 B747 318 10,000 1.75 5,714 40 200 1148 1388 1409 1378 1377 15 30 B747 318 10,000 1.75 5,714 150 300 849 1299 1409 1449 1374 16 30 B747 318 20,000 1.75 11,429 75 150 1219 1444 1487 1444 1444 17 30 B747 318 20,000 1.75 11,429 50 400 972 1422 1487 1522 1457 18 30 B747 318 20,000 1.75 11,429 100 350 946 1396 1487 1521 1451 19 30 B747 238 5,000 1.75 2,857 75 150 796 1021 1070 1021 1021
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 36
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
20 30 B747 238 5,000 1.75 2,857 40 100 904 1044 1070 984 1013 21 30 B747 238 5,000 1.75 2,857 100 300 581 981 1070 1081 1026 22 30 B747 238 10,000 1.75 5,714 75 150 853 1078 1142 1078 1078 23 30 B747 238 10,000 1.75 5,714 60 400 587 1047 1142 1157 1088 24 30 B747 238 10,000 1.75 5,714 50 600 343 993 1142 1193 1068 25 30 B747 238 20,000 1.75 11,429 75 150 924 1149 1212 1149 1149 26 30 B747 238 20,000 1.75 11,429 150 300 634 1084 1212 1234 1159 27 30 B747 238 20,000 1.75 11,429 100 550 399 1049 1212 1274 1144 28 30 B767 180 5,000 1.90 2,632 75 150 1207 1432 1445 1432 1432 29 30 B767 180 5,000 1.90 2,632 50 400 954 1404 1445 1504 1439 30 30 B767 180 5,000 1.90 2,632 150 300 914 1364 1445 1514 1439 31 30 B767 180 10,000 1.90 5,263 75 150 1284 1509 1532 1509 1509 32 30 B767 180 10,000 1.90 5,263 40 200 1293 1533 1532 1523 1522 33 30 B767 180 10,000 1.90 5,263 150 400 868 1418 1532 1618 1513 34 30 B767 180 20,000 1.90 10,526 75 150 1374 1599 1616 1599 1599 35 30 B767 180 20,000 1.90 10,526 200 500 756 1456 1616 1756 1601 36 30 B767 180 20,000 1.90 10,526 100 200 1270 1570 1616 1620 1595 37 30 B767 144 5,000 1.90 2,632 75 150 974 1199 1235 1199 1199 38 30 B767 144 5,000 1.90 2,632 150 400 563 1113 1235 1313 1208 39 30 B767 144 5,000 1.90 2,632 40 100 1087 1227 1235 1167 1196 40 30 B767 144 10,000 1.90 5,263 75 150 1040 1265 1315 1265 1265
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 37
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
41 30 B767 144 10,000 1.90 5,263 40 350 867 1257 1315 1322 1276 42 30 B767 144 10,000 1.90 5,263 200 600 280 1080 1315 1430 1245 43 30 B767 144 20,000 1.90 10,526 75 150 1120 1345 1392 1345 1345 44 30 B767 144 20,000 1.90 10,526 60 400 846 1306 1392 1416 1347 45 30 B767 144 20,000 1.90 10,526 150 300 829 1279 1392 1429 1354 46 30 B767 108 5,000 1.90 2,632 75 150 712 937 993 937 937 47 30 B767 108 5,000 1.90 2,632 100 400 377 877 993 1027 942 48 30 B767 108 5,000 1.90 2,632 40 300 596 936 993 976 945 49 30 B767 108 10,000 1.90 5,263 75 150 777 1002 1061 1002 1002 50 30 B767 108 10,000 1.90 5,263 150 400 365 915 1061 1115 1010 51 30 B767 108 10,000 1.90 5,263 100 300 563 963 1061 1063 1008 52 30 B767 108 20,000 1.90 10,526 75 150 835 1060 1130 1060 1060 53 30 B767 108 20,000 1.90 10,526 50 350 637 1037 1130 1112 1062 54 30 B767 108 20,000 1.90 10,526 150 450 367 967 1130 1192 1072 55 30 B737 79 5,000 3.70 1,351 75 150 883 1108 1058 1108 1108 56 30 B737 79 5,000 3.70 1,351 40 100 1006 1146 1058 1086 1115 57 30 B737 79 5,000 3.70 1,351 60 300 727 1087 1058 1147 1108 58 30 B737 79 10,000 3.70 2,703 75 150 937 1162 1124 1162 1162 59 30 B737 79 10,000 3.70 2,703 100 250 779 1129 1124 1204 1164 60 30 B737 79 10,000 3.70 2,703 50 300 800 1150 1124 1200 1165 61 30 B737 79 20,000 3.70 5,405 75 150 992 1217 1186 1217 1217
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 38
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
62 30 B737 79 20,000 3.70 5,405 40 300 865 1205 1186 1245 1214 63 30 B737 79 20,000 3.70 5,405 100 200 888 1188 1186 1238 1213 64 30 B737 63 5,000 3.70 1,351 75 150 742 967 923 967 967 65 30 B737 63 5,000 3.70 1,351 100 300 519 919 923 1019 964 66 30 B737 63 5,000 3.70 1,351 200 500 122 822 923 1122 967 67 30 B737 63 10,000 3.70 2,703 75 150 791 1016 984 1016 1016 68 30 B737 63 10,000 3.70 2,703 50 300 639 989 984 1039 1004 69 30 B737 63 10,000 3.70 2,703 150 250 559 959 984 1084 1024 70 30 B737 63 20,000 3.70 5,405 75 150 830 1055 1040 1055 1055 71 30 B737 63 20,000 3.70 5,405 60 200 802 1062 1040 1072 1063 72 30 B737 63 20,000 3.70 5,405 100 400 480 980 1040 1130 1045 73 30 B737 47 5,000 3.70 1,351 75 150 581 806 769 806 806 74 30 B737 47 5,000 3.70 1,351 50 350 372 772 769 847 797 75 30 B737 47 5,000 3.70 1,351 150 300 273 723 769 873 798 76 30 B737 47 10,000 3.70 2,703 75 150 610 835 821 835 835 77 30 B737 47 10,000 3.70 2,703 40 250 553 843 821 858 842 78 30 B737 47 10,000 3.70 2,703 200 400 114 714 821 964 839 79 30 B737 47 20,000 3.70 5,405 75 150 654 879 870 879 879 80 30 B737 47 20,000 3.70 5,405 100 100 680 880 870 880 885 81 30 B737 47 20,000 3.70 5,405 150 350 293 793 870 968 878 82 60 B747 397 5,000 1.75 2,857 75 150 709 934 931 934 934
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 39
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
83 60 B747 397 5,000 1.75 2,857 50 100 806 956 931 906 931 84 60 B747 397 5,000 1.75 2,857 100 400 369 869 931 1019 934 85 60 B747 397 10,000 1.75 5,714 75 150 769 994 994 994 994 86 60 B747 397 10,000 1.75 5,714 50 250 687 987 994 1012 992 87 60 B747 397 10,000 1.75 5,714 100 400 423 923 994 1073 988 88 60 B747 397 20,000 1.75 11,429 75 140 828 1043 1054 1038 1041 89 60 B747 397 20,000 1.75 11,429 60 300 673 1033 1054 1093 1054 90 60 B747 397 20,000 1.75 11,429 150 250 609 1009 1054 1134 1074 91 60 B747 318 5,000 1.75 2,857 75 150 540 765 784 765 765 92 60 B747 318 5,000 1.75 2,857 40 200 532 772 784 762 761 93 60 B747 318 5,000 1.75 2,857 200 300 173 673 784 873 778 94 60 B747 318 10,000 1.75 5,714 75 150 586 811 835 811 811 95 60 B747 318 10,000 1.75 5,714 60 250 486 796 835 831 807 96 60 B747 318 10,000 1.75 5,714 100 400 240 740 835 890 805 97 60 B747 318 20,000 1.75 11,429 75 150 632 857 887 857 857 98 60 B747 318 20,000 1.75 11,429 100 300 412 812 887 912 857 99 60 B747 318 20,000 1.75 11,429 150 350 279 779 887 954 864
100 60 B747 238 5,000 1.75 2,857 75 150 392 617 634 617 617 101 60 B747 238 5,000 1.75 2,857 50 250 305 605 634 630 610 102 60 B747 238 5,000 1.75 2,857 100 300 173 573 634 673 618 103 60 B747 238 10,000 1.75 5,714 75 150 416 641 672 641 641
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 40
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
104 60 B747 238 10,000 1.75 5,714 60 200 382 642 672 652 643 105 60 B747 238 10,000 1.75 5,714 100 300 204 604 672 704 649 106 60 B747 238 20,000 1.75 11,429 75 150 449 674 710 674 674 107 60 B747 238 20,000 1.75 11,429 40 200 439 679 710 669 668 108 60 B747 238 20,000 1.75 11,429 100 250 295 645 710 720 680 109 60 B767 180 5,000 1.90 2,632 75 150 624 849 860 849 849 110 60 B767 180 5,000 1.90 2,632 50 100 720 870 860 820 845 111 60 B767 180 5,000 1.90 2,632 150 300 336 786 860 936 861 112 60 B767 180 10,000 1.90 5,263 75 150 678 903 920 903 903 113 60 B767 180 10,000 1.90 5,263 90 100 717 907 920 897 906 114 60 B767 180 10,000 1.90 5,263 120 300 431 851 920 971 908 115 60 B767 180 20,000 1.90 10,526 75 150 737 962 980 962 962 116 60 B767 180 20,000 1.90 10,526 60 200 699 959 980 969 960 117 60 B767 180 20,000 1.90 10,526 150 300 447 897 980 1047 972 118 60 B767 144 5,000 1.90 2,632 75 150 477 702 727 702 702 119 60 B767 144 5,000 1.90 2,632 50 200 451 701 727 701 696 120 60 B767 144 5,000 1.90 2,632 200 250 170 620 727 795 715 121 60 B767 144 10,000 1.90 5,263 75 150 516 741 774 741 741 122 60 B767 144 10,000 1.90 5,263 100 100 543 743 774 743 748 123 60 B767 144 10,000 1.90 5,263 200 200 265 665 774 815 750 124 60 B767 144 20,000 1.90 10,526 75 150 560 785 822 785 785
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 41
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
125 60 B767 144 20,000 1.90 10,526 40 100 667 807 822 747 776 126 60 B767 144 20,000 1.90 10,526 120 200 433 753 822 823 790 127 60 B767 108 5,000 1.90 2,632 75 150 347 572 593 572 572 128 60 B767 108 5,000 1.90 2,632 50 100 441 591 593 541 566 129 60 B767 108 5,000 1.90 2,632 100 300 129 529 593 629 574 130 60 B767 108 10,000 1.90 5,263 75 150 375 600 628 600 600 131 60 B767 108 10,000 1.90 5,263 100 200 275 575 628 625 600 132 60 B767 108 10,000 1.90 5,263 150 250 144 544 628 669 609 133 60 B767 108 20,000 1.90 10,526 75 150 406 631 664 631 631 134 60 B767 108 20,000 1.90 10,526 40 100 512 652 664 592 621 135 60 B767 108 20,000 1.90 10,526 60 300 238 598 664 658 619 136 60 B737 79 5,000 3.70 1,351 75 150 552 777 686 777 777 137 60 B737 79 5,000 3.70 1,351 60 200 512 772 686 782 773 138 60 B737 79 5,000 3.70 1,351 100 300 329 729 686 829 774 139 60 B737 79 10,000 3.70 2,703 75 150 591 816 733 816 816 140 60 B737 79 10,000 3.70 2,703 100 100 612 812 733 812 817 141 60 B737 79 10,000 3.70 2,703 150 250 360 760 733 885 825 142 60 B737 79 20,000 3.70 5,405 75 150 626 851 778 851 851 143 60 B737 79 20,000 3.70 5,405 60 100 709 869 778 829 850 144 60 B737 79 20,000 3.70 5,405 150 150 522 822 778 897 867 145 60 B737 63 5,000 3.70 1,351 75 150 430 655 592 655 655
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 42
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
146 60 B737 63 5,000 3.70 1,351 100 100 456 656 592 656 661 147 60 B737 63 5,000 3.70 1,351 50 250 349 649 592 674 654 148 60 B737 63 10,000 3.70 2,703 75 150 463 688 632 688 688 149 60 B737 63 10,000 3.70 2,703 40 100 577 717 632 657 686 150 60 B737 63 10,000 3.70 2,703 100 300 241 641 632 741 686 151 60 B737 63 20,000 3.70 5,405 75 150 499 724 670 724 724 152 60 B737 63 20,000 3.70 5,405 60 200 458 718 670 728 719 153 60 B737 63 20,000 3.70 5,405 100 250 343 693 670 768 728 154 60 B737 47 5,000 3.70 1,351 75 150 309 534 489 534 534 155 60 B737 47 5,000 3.70 1,351 50 200 285 535 489 535 530 156 60 B737 47 5,000 3.70 1,351 150 300 21 471 489 621 546 157 60 B737 47 10,000 3.70 2,703 75 150 335 560 521 560 560 158 60 B737 47 10,000 3.70 2,703 100 100 358 558 521 558 563 159 60 B737 47 10,000 3.70 2,703 150 200 161 511 521 611 566 160 60 B737 47 20,000 3.70 5,405 75 150 363 588 552 588 588 161 60 B737 47 20,000 3.70 5,405 50 100 455 605 552 555 580 162 60 B737 47 20,000 3.70 5,405 100 250 203 553 552 628 588 163 100 B747 397 5,000 1.75 2,857 75 150 428 653 634 653 653 164 100 B747 397 5,000 1.75 2,857 100 200 334 634 634 684 659 165 100 B747 397 5,000 1.75 2,857 150 250 203 603 634 728 668 166 100 B747 397 10,000 1.75 5,714 75 150 453 678 672 678 678
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 43
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
167 100 B747 397 10,000 1.75 5,714 60 200 413 673 672 683 674 168 100 B747 397 10,000 1.75 5,714 100 400 122 622 672 772 687 169 100 B747 397 20,000 1.75 11,429 75 150 479 704 710 704 704 170 100 B747 397 20,000 1.75 11,429 40 200 468 708 710 698 697 171 100 B747 397 20,000 1.75 11,429 100 300 260 660 710 760 705 172 100 B747 318 5,000 1.75 2,857 75 150 341 566 539 566 566 173 100 B747 318 5,000 1.75 2,857 100 100 363 563 539 563 568 174 100 B747 318 5,000 1.75 2,857 150 300 52 502 539 652 577 175 100 B747 318 10,000 1.75 5,714 75 150 360 585 572 585 585 176 100 B747 318 10,000 1.75 5,714 50 200 335 585 572 585 580 177 100 B747 318 10,000 1.75 5,714 90 300 160 550 572 640 589 178 100 B747 318 20,000 1.75 11,429 75 150 380 605 603 605 605 179 100 B747 318 20,000 1.75 11,429 40 100 489 629 603 569 598 180 100 B747 318 20,000 1.75 11,429 100 300 164 564 603 664 609 181 100 B747 238 5,000 1.75 2,857 75 150 247 472 439 472 472 182 100 B747 238 5,000 1.75 2,857 40 200 239 479 439 469 468 183 100 B747 238 5,000 1.75 2,857 150 100 183 433 439 483 468 184 100 B747 238 10,000 1.75 5,714 75 150 262 487 463 487 487 185 100 B747 238 10,000 1.75 5,714 50 100 361 511 463 461 486 186 100 B747 238 10,000 1.75 5,714 100 200 170 470 463 520 495 187 100 B747 238 20,000 1.75 11,429 75 150 278 503 486 503 503
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 44
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
188 100 B747 238 20,000 1.75 11,429 40 100 391 531 486 471 500 189 100 B747 238 20,000 1.75 11,429 60 300 123 483 486 543 504 190 100 B767 180 5,000 1.90 2,632 75 100 382 557 593 532 547 191 100 B767 180 5,000 1.90 2,632 50 250 297 597 593 622 602 192 100 B767 180 5,000 1.90 2,632 250 100 148 498 593 648 593 193 100 B767 180 10,000 1.90 5,263 75 150 404 629 628 629 629 194 100 B767 180 10,000 1.90 5,263 60 100 484 644 628 604 625 195 100 B767 180 10,000 1.90 5,263 120 300 159 579 628 699 636 196 100 B767 180 20,000 1.90 10,526 75 150 424 649 664 649 649 197 100 B767 180 20,000 1.90 10,526 100 100 449 649 664 649 654 198 100 B767 180 20,000 1.90 10,526 150 250 201 601 664 726 666 199 100 B767 144 5,000 1.90 2,632 75 150 300 525 507 525 525 200 100 B767 144 5,000 1.90 2,632 40 200 291 531 507 521 520 201 100 B767 144 5,000 1.90 2,632 60 300 145 505 507 565 526 202 100 B767 144 10,000 1.90 5,263 75 150 318 543 536 543 543 203 100 B767 144 10,000 1.90 5,263 50 100 414 564 536 514 539 204 100 B767 144 10,000 1.90 5,263 100 300 104 504 536 604 549 205 100 B767 144 20,000 1.90 10,526 75 150 337 562 566 562 562 206 100 B767 144 20,000 1.90 10,526 40 100 447 587 566 527 556 207 100 B767 144 20,000 1.90 10,526 60 400 65 525 566 635 566 208 100 B767 108 5,000 1.90 2,632 75 150 217 442 414 442 442
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 45
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
209 100 B767 108 5,000 1.90 2,632 60 120 275 455 414 425 440 210 100 B767 108 5,000 1.90 2,632 40 300 92 432 414 472 441 211 100 B767 108 10,000 1.90 5,263 75 150 230 455 436 455 455 212 100 B767 108 10,000 1.90 5,263 100 200 137 437 436 487 462 213 100 B767 108 10,000 1.90 5,263 200 100 73 373 436 473 438 214 100 B767 108 20,000 1.90 10,526 75 150 245 470 458 470 470 215 100 B767 108 20,000 1.90 10,526 50 200 222 472 458 472 467 216 100 B767 108 20,000 1.90 10,526 100 100 266 466 458 466 471 217 100 B737 79 5,000 3.70 1,351 75 150 358 583 492 583 583 218 100 B737 79 5,000 3.70 1,351 30 100 481 611 492 541 574 219 100 B737 79 5,000 3.70 1,351 150 150 243 543 492 618 588 220 100 B737 79 10,000 3.70 2,703 75 150 379 604 524 604 604 221 100 B737 79 10,000 3.70 2,703 60 200 339 599 524 609 600 222 100 B737 79 10,000 3.70 2,703 100 250 223 573 524 648 608 223 100 B737 79 20,000 3.70 5,405 75 150 402 627 555 627 627 224 100 B737 79 20,000 3.70 5,405 50 100 495 645 555 595 620 225 100 B737 79 20,000 3.70 5,405 100 200 305 605 555 655 630 226 100 B737 63 5,000 3.70 1,351 75 150 272 497 423 497 497 227 100 B737 63 5,000 3.70 1,351 40 100 384 524 423 464 493 228 100 B737 63 5,000 3.70 1,351 90 200 195 485 423 525 504 229 100 B737 63 10,000 3.70 2,703 75 150 289 514 450 514 514
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 46
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
230 100 B737 63 10,000 3.70 2,703 60 200 252 512 450 522 513 231 100 B737 63 10,000 3.70 2,703 100 250 140 490 450 565 525 232 100 B737 63 20,000 3.70 5,405 75 150 308 533 476 533 533 233 100 B737 63 20,000 3.70 5,405 50 100 405 555 476 505 530 234 100 B737 63 20,000 3.70 5,405 100 200 212 512 476 562 537 235 100 B737 47 5,000 3.70 1,351 75 150 190 415 351 415 415 236 100 B737 47 5,000 3.70 1,351 30 100 313 443 351 373 406 237 100 B737 47 5,000 3.70 1,351 50 300 51 401 351 451 416 238 100 B737 47 10,000 3.70 2,703 75 150 204 429 372 429 429 239 100 B737 47 10,000 3.70 2,703 60 100 283 443 372 403 424 240 100 B737 47 10,000 3.70 2,703 100 150 164 414 372 439 429 241 100 B737 47 20,000 3.70 5,405 75 150 214 439 392 439 439 242 100 B737 47 20,000 3.70 5,405 100 100 233 433 392 433 438 243 100 B737 47 20,000 3.70 5,405 150 200 42 392 392 492 447 244 150 B747 397 5,000 1.75 2,857 75 150 288 513 472 513 513 245 150 B747 397 5,000 1.75 2,857 40 90 410 540 472 475 507 246 150 B747 397 5,000 1.75 2,857 90 200 209 499 472 539 518 247 150 B747 397 10,000 1.75 5,714 75 150 300 525 499 525 525 248 150 B747 397 10,000 1.75 5,714 60 100 381 541 499 501 522 249 150 B747 397 10,000 1.75 5,714 100 300 89 489 499 589 534 250 150 B747 397 20,000 1.75 11,429 75 150 310 535 525 535 535
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 47
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
251 150 B747 397 20,000 1.75 11,429 50 100 407 557 525 507 532 252 150 B747 397 20,000 1.75 11,429 200 200 65 465 525 615 550 253 150 B747 318 5,000 1.75 2,857 75 150 226 451 406 451 451 254 150 B747 318 5,000 1.75 2,857 40 100 337 477 406 417 446 255 150 B747 318 5,000 1.75 2,857 90 200 148 438 406 478 457 256 150 B747 318 10,000 1.75 5,714 75 150 236 461 428 461 461 257 150 B747 318 10,000 1.75 5,714 50 120 308 478 428 438 457 258 150 B747 318 10,000 1.75 5,714 100 200 142 442 428 492 467 259 150 B747 318 20,000 1.75 11,429 75 150 245 470 448 470 470 260 150 B747 318 20,000 1.75 11,429 60 300 92 452 448 512 473 261 150 B747 318 20,000 1.75 11,429 100 100 266 466 448 466 471 262 150 B747 238 5,000 1.75 2,857 75 150 159 384 332 384 384 263 150 B747 238 5,000 1.75 2,857 40 80 291 411 332 341 376 264 150 B747 238 5,000 1.75 2,857 90 200 81 371 332 411 390 265 150 B747 238 10,000 1.75 5,714 75 150 166 391 349 391 391 266 150 B747 238 10,000 1.75 5,714 100 100 185 385 349 385 390 267 150 B747 238 10,000 1.75 5,714 40 200 159 399 349 389 388 268 150 B747 238 20,000 1.75 11,429 75 150 175 400 366 400 400 269 150 B747 238 20,000 1.75 11,429 60 100 254 414 366 374 395 270 150 B747 238 20,000 1.75 11,429 100 250 29 379 366 454 414 271 150 B767 180 5,000 1.90 2,632 75 150 252 477 444 477 477
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 48
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
272 150 B767 180 5,000 1.90 2,632 40 100 363 503 444 443 472 273 150 B767 180 5,000 1.90 2,632 100 300 44 444 444 544 489 274 150 B767 180 10,000 1.90 5,263 75 150 262 487 468 487 487 275 150 B767 180 10,000 1.90 5,263 40 100 374 514 468 454 483 276 150 B767 180 10,000 1.90 5,263 60 300 108 468 468 528 489 277 150 B767 180 20,000 1.90 10,526 75 150 273 498 492 498 498 278 150 B767 180 20,000 1.90 10,526 100 100 295 495 492 495 500 279 150 B767 180 20,000 1.90 10,526 150 150 158 458 492 533 503 280 150 B767 144 5,000 1.90 2,632 75 150 197 422 382 422 422 281 150 B767 144 5,000 1.90 2,632 50 100 291 441 382 391 416 282 150 B767 144 5,000 1.90 2,632 100 200 102 402 382 452 427 283 150 B767 144 10,000 1.90 5,263 75 150 204 429 403 429 429 284 150 B767 144 10,000 1.90 5,263 50 100 300 450 403 400 425 285 150 B767 144 10,000 1.90 5,263 150 200 35 385 403 485 440 286 150 B767 144 20,000 1.90 10,526 75 150 212 437 422 437 437 287 150 B767 144 20,000 1.90 10,526 40 100 323 463 422 403 432 288 150 B767 144 20,000 1.90 10,526 60 300 61 421 422 481 442 289 150 B767 108 5,000 1.90 2,632 75 150 133 358 316 358 358 290 150 B767 108 5,000 1.90 2,632 60 100 213 373 316 333 354 291 150 B767 108 5,000 1.90 2,632 40 200 125 365 316 355 354 292 150 B767 108 10,000 1.90 5,263 75 150 141 366 334 366 366
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A5 - 49
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
293 150 B767 108 10,000 1.90 5,263 50 100 235 385 334 335 360 294 150 B767 108 10,000 1.90 5,263 80 200 77 357 334 387 370 295 150 B767 108 20,000 1.90 10,526 75 150 149 374 351 374 374 296 150 B767 108 20,000 1.90 10,526 40 100 256 396 351 336 365 297 150 B767 108 20,000 1.90 10,526 70 250 45 365 351 410 382 298 150 B737 79 5,000 3.70 1,351 75 150 232 457 376 457 457 299 150 B737 79 5,000 3.70 1,351 60 100 313 473 376 433 454 300 150 B737 79 5,000 3.70 1,351 100 300 26 426 376 526 471 301 150 B737 79 10,000 3.70 2,703 75 150 241 466 400 466 466 302 150 B737 79 10,000 3.70 2,703 40 100 352 492 400 432 461 303 150 B737 79 10,000 3.70 2,703 150 200 74 424 400 524 479 304 150 B737 79 20,000 3.70 5,405 75 150 252 477 423 477 477 305 150 B737 79 20,000 3.70 5,405 50 100 348 498 423 448 473 306 150 B737 79 20,000 3.70 5,405 80 300 72 452 423 532 485 307 150 B737 63 5,000 3.70 1,351 75 150 173 398 329 398 398 308 150 B737 63 5,000 3.70 1,351 60 100 253 413 329 373 394 309 150 B737 63 5,000 3.70 1,351 100 200 80 380 329 430 405 310 150 B737 63 10,000 3.70 2,703 75 150 182 407 348 407 407 311 150 B737 63 10,000 3.70 2,703 40 100 290 430 348 370 399 312 150 B737 63 10,000 3.70 2,703 60 200 146 406 348 416 407 313 150 B737 63 20,000 3.70 5,405 75 150 191 416 366 416 416
Appendix 5 Material Equivalence Results
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A5 - 50
Factor Levels APSDS Thickness Equivalent Thickness Run SM
(MPa) Aircraft M
(t) P
(no.) PCR C
(no.) AT
(mm) BT
(mm) ST
(mm) TT
(mm) S77-1(mm)
FAA (mm)
Revised (mm)
314 150 B737 63 20,000 3.70 5,405 50 100 285 435 366 385 410 315 150 B737 63 20,000 3.70 5,405 100 250 44 394 366 469 429 316 150 B737 47 5,000 3.70 1,351 75 150 108 333 265 333 333 317 150 B737 47 5,000 3.70 1,351 40 100 217 357 265 297 326 318 150 B737 47 5,000 3.70 1,351 60 200 75 335 265 345 336 319 150 B737 47 10,000 3.70 2,703 75 150 116 341 280 341 341 320 150 B737 47 10,000 3.70 2,703 40 100 224 364 280 304 333 321 150 B737 47 10,000 3.70 2,703 80 200 54 334 280 364 347 322 150 B737 47 20,000 3.70 5,405 75 150 123 348 295 348 348 323 150 B737 47 20,000 3.70 5,405 60 100 204 364 295 324 345 324 150 B737 47 20,000 3.70 5,405 100 200 32 332 295 382 357
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A6 - 1
APPENDIX 6. DAMAGE INDICATORS WITH DEPTH
B737 at mass of 78.5 t and tyre pressure of 1.39 MPa
B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (uE)
Stress (MPa)
Deflection(mm)
Strain (uE)
Stress (MPa)
Deflection(mm)
0.00 836 1.360 2.320 -186 0.000 1.906 0.05 1197 1.339 2.269 -202 0.002 1.916 0.10 1350 1.237 2.220 -185 0.017 1.925 0.15 1293 1.064 2.137 -129 0.046 1.933 0.20 1134 0.871 2.076 -54 0.078 1.938 0.25 755 0.568 2.000 75 0.140 1.947 0.30 714 0.469 1.962 149 0.150 1.941 0.35 616 0.384 1.928 193 0.152 1.932 0.40 537 0.314 1.900 227 0.149 1.922 0.45 478 0.255 1.874 253 0.142 1.910 0.50 444 0.210 1.852 274 0.133 1.897 0.55 495 0.174 1.825 351 0.122 1.879 0.60 445 0.144 1.802 352 0.110 1.862 0.65 411 0.120 1.780 356 0.099 1.844 0.70 392 0.100 1.760 363 0.089 1.826 0.75 392 0.086 1.741 375 0.081 1.808 0.80 525 0.075 1.714 521 0.074 1.781 0.85 494 0.067 1.689 506 0.067 1.755 0.90 475 0.060 1.664 497 0.061 1.730 0.95 467 0.054 1.641 497 0.057 1.706 1.00 473 0.050 1.617 505 0.053 1.681 1.05 778 0.047 1.577 837 0.051 1.638 1.10 734 0.045 1.539 794 0.048 1.597 1.15 695 0.042 1.504 754 0.046 1.558 1.20 661 0.040 1.470 717 0.043 1.521 1.25 629 0.039 1.437 683 0.041 1.486 1.30 600 0.037 1.407 652 0.040 1.453 1.35 573 0.035 1.377 622 0.038 1.421 1.40 549 0.034 1.349 595 0.036 1.391 1.45 526 0.032 1.322 520 0.035 1.362 1.50 505 0.031 1.297 546 0.033 1.334
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A6 - 2
B737 at mass of 78.5 t and tyre pressure of 1.39 MPa
B&B Base on CBR 15 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Deflection(μm)
Strain (με)
Stress (MPa)
Deflection (μm)
0.00 942 1.360 1.398 -90 0.000 0.959 0.05 1281 1.341 1.342 -123 0.003 0.964 0.10 1418 1.244 1.273 -123 0.018 0.970 0.15 1349 1.078 1.203 -84 0.048 0.976 0.20 1178 0.893 1.140 -20 0.083 0.978 0.25 780 0.594 1.062 10 0.148 0.986 0.30 681 0.498 1.025 146 0.162 0.979 0.35 587 0.416 0.993 180 0.168 0.971 0.40 507 0.348 0.966 204 0.168 0.962 0.45 442 0.292 0.943 219 0.164 0.951 0.50 393 0.246 0.922 229 0.156 0.940 0.55 386 0.208 0.901 260 0.147 0.927 0.60 343 0.177 0.883 259 0.136 0.914 0.65 311 0.151 0.867 257 0.126 0.901 0.70 288 0.130 0.852 256 0.116 0.888 0.75 276 0.114 0.838 257 0.106 0.875 0.80 335 0.101 0.820 327 0.098 0.859 0.85 312 0.090 0.804 316 0.090 0.843 0.90 296 0.081 0.789 308 0.083 0.827 0.95 288 0.074 0.774 305 0.077 0.812 1.00 287 0.068 0.760 306 0.073 0.796 1.05 412 0.064 0.739 444 0.069 0.774 1.10 388 0.060 0.719 421 0.065 0.752 1.15 366 0.057 0.700 400 0.062 0.732 1.20 347 0.054 0.682 380 0.058 0.712 1.25 329 0.051 0.665 361 0.055 0.694 1.30 313 0.049 0.650 344 0.053 0.676 1.35 298 0.046 0.634 327 0.050 0.659 1.40 285 0.044 0.619 312 0.048 0.643 1.45 272 0.042 0.605 298 0.046 0.628 1.50 260 0.040 0.592 285 0.044 0.613
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A6 - 3
B737 at mass of 78.5 t and tyre pressure of 1.39 MPa
B&B Sub-base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Deflection(μm)
Strain (με)
Stress (MPa)
Deflection(μm)
0.00 2397 1.360 3.665 -241 0.000 2.518 0.05 3292 1.340 3.521 -324 0.003 2.532 0.10 3656 1.241 3.345 -317 0.019 2.549 0.15 3488 1.072 3.164 -207 0.049 2.562 0.20 2309 0.696 2.906 117 0.127 2.597 0.25 2114 0.585 2.793 293 0.149 2.586 0.30 1830 0.489 2.694 417 0.163 2.569 0.35 1585 0.408 2.609 509 0.169 2.545 0.40 1387 0.341 2.535 571 0.169 2.518 0.45 1308 0.287 2.465 670 0.164 2.486 0.50 1143 0.242 2.404 691 0.157 2.452 0.55 1017 0.205 2.350 701 0.148 2.417 0.60 929 0.175 2.301 707 0.138 2.382 0.65 972 0.151 2.250 811 0.128 2.340 0.70 886 0.131 2.204 793 0.118 2.300 0.75 825 0.115 2.161 780 0.108 2.261 0.80 790 0.102 2.121 774 0.100 2.222 0.85 943 0.092 2.072 957 0.093 2.174 0.90 889 0.083 2.026 925 0.086 2.127 0.95 853 0.076 1.982 903 0.080 2.081 1.00 835 0.071 1.940 893 0.076 2.036 1.05 1071 0.066 1.885 1157 0.071 1.977 1.10 1008 0.062 1.833 1096 0.068 1.920 1.15 952 0.059 1.784 1040 0.064 1.867 1.20 901 0.056 1.738 988 0.061 1.816 1.25 854 0.053 1.694 939 0.058 1.768 1.30 812 0.050 1.652 893 0.055 1.722 1.35 773 0.048 1.613 850 0.052 1.679 1.40 738 0.046 1.575 810 0.050 1.637 1.45 704 0.043 1.539 773 0.047 1.598 1.50 674 0.042 1.504 738 0.045 1.560
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A6 - 4
B737 at mass of 78.5 t and tyre pressure of 1.39 MPa
B&B Sub-base on CBR 15 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Deflection(μm)
Strain (με)
Stress (MPa)
Deflection (μm)
0.00 2503 1.360 2.482 -73 0.000 1.331 0.05 3342 1.342 2.335 -181 0.003 1.337 0.10 3672 1.246 2.157 -199 0.020 1.347 0.15 3490 1.082 1.976 -112 0.052 1.355 0.20 2322 0.710 1.720 188 0.131 1.385 0.25 2062 0.603 1.610 328 0.156 1.372 0.30 1789 0.510 1.514 434 0.173 1.353 0.35 1546 0.432 1.431 510 0.182 1.329 0.40 1340 0.368 1.359 559 0.185 1.303 0.45 1190 0.315 1.295 604 0.183 1.273 0.50 1038 0.271 1.239 616 0.178 1.242 0.55 915 0.234 1.190 616 0.171 1.212 0.60 816 0.205 1.147 608 0.162 1.181 0.65 770 0.180 1.107 627 0.153 1.149 0.70 695 0.160 1.070 607 0.144 1.118 0.75 635 0.143 1.037 587 0.135 1.089 0.80 590 0.128 1.006 569 0.126 1.060 0.85 609 0.117 0.975 610 0.118 1.028 0.90 568 0.107 0.945 585 0.110 0.999 0.95 537 0.098 0.918 564 0.104 0.970 1.00 514 0.091 0.891 547 0.098 0.942 1.05 535 0.085 0.864 576 0.092 0.913 1.10 503 0.080 0.838 548 0.087 0.885 1.15 474 0.075 0.813 520 0.082 0.858 1.20 448 0.071 0.790 494 0.078 0.833 1.25 425 0.069 0.769 470 0.074 0.808 1.30 403 0.064 0.748 447 0.070 0.786 1.35 383 0.060 0.728 425 0.066 0.764 1.40 365 0.057 0.709 405 0.063 0.743 1.45 348 0.054 0.692 385 0.060 0.723 1.50 332 0.052 0.675 367 0.057 0.704
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A6 - 5
B737 at mass of 78.5 t and tyre pressure of 1.39 MPa
B737 Pavement with 50 mm of 1500 MPa Asphalt
on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Deflection(μm)
Strain (με)
Stress (MPa)
Deflection(μm)
0.00 -728 1.360 -332 0.000 -728 1.360 0.05 -331 1.270 -297 0.040 -331 1.270 0.10 2232 1.117 -96 0.047 2232 1.117 0.15 2004 0.894 15 0.075 2004 0.894 0.20 1737 0.682 145 0.108 1737 0.682 0.25 1606 0.522 247 0.130 1606 0.522 0.30 2007 0.414 512 0.139 2007 0.414 0.35 1659 0.330 651 0.142 1659 0.330 0.40 1411 0.265 705 0.141 1411 0.265 0.45 1435 0.218 862 0.135 1435 0.218 0.50 1244 0.181 870 0.128 1244 0.181 0.55 1108 0.153 872 0.120 1108 0.153 0.60 1023 0.131 874 0.112 1023 0.131 0.65 1201 0.114 1097 0.105 1201 0.114 0.70 1106 0.101 1066 0.098 1106 0.101 0.75 1042 0.090 1043 0.096 1042 0.090 0.80 1010 0.083 1032 0.086 1010 0.083 0.85 1269 0.077 1322 0.081 1269 0.077 0.90 1182 0.072 1252 0.077 1182 0.072 0.95 1106 0.068 1186 0.072 1106 0.068 1.00 1038 0.064 1123 0.068 1038 0.064 1.05 978 0.060 1065 0.065 978 0.060 1.10 924 0.057 1011 0.061 924 0.057 1.15 876 0.054 960 0.058 876 0.054 1.20 831 0.051 912 0.055 831 0.051 1.25 790 0.048 868 0.053 790 0.048 1.30 753 0.046 827 0.050 753 0.046 1.35 719 0.044 788 0.048 719 0.044 1.40 687 0.042 752 0.045 687 0.042 1.45 657 0.040 718 0.043 657 0.040 1.50 629 0.038 687 0.041 629 0.038
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A6 - 6
B737 at mass of 78.5 t and tyre pressure of 1.39 MPa
B737 Pavement with 50 mm of 4000 MPa Asphalt
on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Deflection(μm)
Strain (με)
Stress (MPa)
Deflection (μm)
0.00 -732 1.360 -167 0.000 -732 1.360 0.05 441 1.260 -197 0.027 441 1.260 0.10 2249 1.057 -21 0.045 2249 1.057 0.15 1949 0.828 96 0.078 1949 0.828 0.20 1667 0.626 217 0.109 1667 0.626 0.25 1530 0.478 308 0.128 1530 0.478 0.30 1887 0.378 609 0.135 1887 0.378 0.35 1564 0.302 671 0.136 1564 0.302 0.40 1333 0.243 710 0.133 1333 0.243 0.45 1352 0.200 849 0.127 1352 0.200 0.50 1174 0.166 847 0.120 1174 0.166 0.55 1047 0.140 843 0.112 1047 0.140 0.60 967 0.120 840 0.104 967 0.120 0.65 1129 0.105 1042 0.097 1129 0.105 0.70 1040 0.093 1009 0.090 1040 0.093 0.75 980 0.084 985 0.084 980 0.084 0.80 948 0.077 971 0.079 948 0.077 0.85 1194 0.071 1246 0.075 1194 0.071 0.90 1111 0.066 1178 0.071 1111 0.066 0.95 1038 0.063 1113 0.066 1038 0.063 1.00 975 0.060 1052 0.063 975 0.060 1.05 918 0.056 996 0.060 918 0.056 1.10 867 0.054 946 0.056 867 0.054 1.15 820 0.051 897 0.054 820 0.051 1.20 778 0.048 852 0.051 778 0.048 1.25 740 0.046 810 0.048 740 0.046 1.30 704 0.044 771 0.046 704 0.044 1.35 672 0.042 735 0.044 672 0.042 1.40 642 0.040 701 0.042 642 0.040 1.45 614 0.038 669 0.040 614 0.038 1.50 588 0.035 640 0.038 588 0.035
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A6 - 7
B737 at mass of 78.5 t and tyre pressure of 1.39 MPa
B737 Pavement with 200 mm of 1500 MPa Asphalt
on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Deflection(μm)
Strain (με)
Stress (MPa)
Deflection(μm)
0.00 -417 1.360 -324 0.000 -417 1.360 0.05 82 1.280 -251 0.014 82 1.280 0.10 387 1.055 -146 0.054 387 1.055 0.15 598 0.765 -29 0.102 598 0.765 0.20 918 0.579 60 0.124 918 0.579 0.25 1298 0.442 356 0.135 1298 0.442 0.30 1074 0.338 434 0.140 1074 0.338 0.35 935 0.261 495 0.139 935 0.261 0.40 886 0.208 541 0.136 886 0.208 0.45 1163 0.174 833 0.126 1163 0.174 0.50 1026 0.146 830 0.117 1026 0.146 0.55 932 0.125 814 0.108 932 0.125 0.60 877 0.109 809 0.101 877 0.109 0.65 1022 0.097 993 0.094 1022 0.097 0.70 951 0.087 960 0.087 951 0.087 0.75 904 0.079 937 0.081 904 0.079 0.80 881 0.073 924 0.076 881 0.073 0.85 1126 0.068 1199 0.072 1126 0.068 0.90 1054 0.064 1134 0.068 1054 0.064 0.95 990 0.060 1074 0.065 990 0.060 1.00 934 0.056 1017 0.061 934 0.056 1.05 883 0.053 965 0.058 883 0.053 1.10 836 0.051 916 0.055 836 0.051 1.15 794 0.048 871 0.052 794 0.048 1.20 756 0.046 828 0.050 756 0.046 1.25 720 0.044 789 0.047 720 0.044 1.30 688 0.042 752 0.045 688 0.042 1.35 657 0.040 718 0.043 657 0.040 1.40 629 0.038 686 0.041 629 0.038 1.45 603 0.036 656 0.039 603 0.036 1.50 578 0.035 628 0.037 578 0.035
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A6 - 8
B737 at mass of 78.5 t and tyre pressure of 1.39 MPa
B737 Pavement with 200 mm of 4000 MPa Asphalt
on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Deflection(μm)
Strain (με)
Stress (MPa)
Deflection (μm)
0.00 -371 1.360 -255 0.000 -371 1.360 0.05 -76 1.239 -160 0.020 -76 1.239 0.10 -13 0.929 -52 0.069 -13 0.929 0.15 304 0.564 59 0.124 304 0.564 0.20 560 0.371 153 0.142 560 0.371 0.25 887 0.292 414 0.140 887 0.292 0.30 765 0.231 452 0.135 765 0.231 0.35 691 0.185 484 0.128 691 0.185 0.40 668 0.153 512 0.119 668 0.153 0.45 895 0.131 752 0.111 895 0.131 0.50 811 0.113 738 0.102 811 0.113 0.55 753 0.099 723 0.094 753 0.099 0.60 719 0.088 715 0.087 719 0.088 0.65 850 0.079 871 0.081 850 0.079 0.70 802 0.072 841 0.075 802 0.072 0.75 769 0.066 819 0.070 769 0.066 0.80 753 0.062 808 0.066 753 0.062 0.85 971 0.058 1050 0.063 971 0.058 0.90 914 0.055 995 0.059 914 0.055 0.95 864 0.052 943 0.056 864 0.052 1.00 819 0.049 896 0.053 819 0.049 1.05 778 0.047 851 0.051 778 0.047 1.10 740 0.045 810 0.048 740 0.045 1.15 705 0.042 771 0.046 705 0.042 1.20 673 0.041 735 0.044 673 0.041 1.25 643 0.039 702 0.042 643 0.039 1.30 616 0.037 671 0.040 616 0.037 1.35 591 0.035 642 0.038 591 0.035 1.40 567 0.034 614 0.037 567 0.034 1.45 544 0.033 589 0.035 544 0.033 1.50 523 0.031 565 0.033 523 0.031
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A6 - 9
50 t Macro at mass of 15 t and tyre pressure of 0.4 MPa
1000 mm of B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Strain (με)
Stress (MPa)
0.00 260 0.400 -36 0.000 0.05 377 0.390 -36 0.000 0.10 403 0.346 -34 0.001 0.15 357 0.281 -28 0.004 0.20 292 0.217 -20 0.007 0.25 187 0.138 -26 0.001 0.30 171 0.111 -8 0.008 0.35 143 0.089 7 0.013 0.40 122 0.071 19 0.016 0.45 106 0.057 28 0.018 0.50 97 0.046 36 0.019 0.55 107 0.038 52 0.019 0.60 96 0.032 56 0.018 0.65 88 0.026 60 0.017 0.70 84 0.022 64 0.017 0.75 84 0.019 68 0.016 0.80 112 0.017 100 0.015 0.85 110 0.016 100 0.014 0.90 106 0.014 100 0.013 0.95 105 0.013 102 0.013 1.00 107 0.013 104 0.012 1.05 180 0.011 178 0.012 1.10 172 0.011 172 0.011 1.15 165 0.010 167 0.011 1.20 159 0.010 161 0.011 1.25 153 0.010 156 0.010 1.30 148 0.009 152 0.010 1.35 144 0.009 147 0.010 1.40 139 0.009 143 0.009 1.45 135 0.009 139 0.009 1.50 131 0.009 135 0.009
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A6 - 10
50 t Macro at mass of 19 t and tyre pressure of 0.5 MPa
1000 mm of B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Strain (με)
Stress (MPa)
0.00 324 0.500 -46 0.000 0.05 470 0.488 -46 0.000 0.10 503 0.434 -43 0.002 0.15 448 0.352 -36 0.005 0.20 366 0.273 -25 0.009 0.25 235 0.173 -34 0.010 0.30 215 0.140 -11 0.001 0.35 180 0.112 8 0.016 0.40 153 0.090 24 0.021 0.45 134 0.072 36 0.023 0.50 122 0.059 45 0.024 0.55 135 0.048 66 0.024 0.60 121 0.040 72 0.023 0.65 111 0.034 77 0.022 0.70 106 0.028 81 0.021 0.75 106 0.025 86 0.020 0.80 146 0.022 127 0.019 0.85 139 0.020 126 0.018 0.90 135 0.018 127 0.017 0.95 133 0.017 129 0.016 1.00 135 0.016 132 0.015 1.05 227 0.015 225 0.015 1.10 218 0.014 218 0.014 1.15 209 0.014 211 0.014 1.20 201 0.013 204 0.013 1.25 194 0.013 198 0.013 1.30 188 0.012 192 0.013 1.35 182 0.012 186 0.012 1.40 176 0.012 181 0.012 1.45 171 0.011 176 0.011 1.50 166 0.011 171 0.011
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A6 - 11
50 t Macro at mass of 22 t and tyre pressure of 0.6 MPa
1000 mm of B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Strain (με)
Stress (MPa)
0.00 391 0.600 -53 0.000 0.05 568 0.585 -53 0.000 0.10 604 0.517 -50 0.002 0.15 533 0.418 -42 0.006 0.20 433 0.322 -29 0.011 0.25 280 0.205 -38 0.002 0.30 254 0.165 -12 0.012 0.35 212 0.132 10 0.019 0.40 180 0.105 28 0.024 0.45 156 0.084 42 0.027 0.50 143 0.068 52 0.028 0.55 158 0.056 76 0.027 0.60 141 0.047 83 0.027 0.65 129 0.039 89 0.026 0.70 123 0.033 94 0.025 0.75 123 0.029 100 0.023 0.80 170 0.025 147 0.022 0.85 161 0.023 146 0.021 0.90 156 0.021 147 0.020 0.95 154 0.019 149 0.019 1.00 156 0.018 153 0.018 1.05 263 0.017 261 0.017 1.10 252 0.017 252 0.017 1.15 242 0.016 244 0.016 1.20 233 0.015 237 0.016 1.25 225 0.015 229 0.015 1.30 218 0.014 222 0.015 1.35 211 0.014 216 0.014 1.40 204 0.013 209 0.014 1.45 198 0.013 203 0.013 1.50 193 0.013 198 0.013
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A6 - 12
50 t Macro at mass of 26 t and tyre pressure of 0.7 MPa
1000 mm of B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Strain (με)
Stress (MPa)
0.00 455 0.700 -63 0.000 0.05 661 0.683 -63 0.000 0.10 705 0.605 -59 0.002 0.15 624 0.489 -49 0.007 0.20 508 0.379 -35 0.013 0.25 327 0.240 -45 0.002 0.30 298 0.193 -14 0.014 0.35 249 0.155 12 0.023 0.40 211 0.124 33 0.028 0.45 184 0.099 49 0.031 0.50 168 0.081 62 0.033 0.55 186 0.067 90 0.032 0.60 166 0.055 98 0.031 0.65 153 0.046 105 0.030 0.70 146 0.039 111 0.029 0.75 146 0.034 118 0.027 0.80 200 0.030 173 0.026 0.85 190 0.027 173 0.024 0.90 184 0.025 174 0.023 0.95 182 0.023 176 0.022 1.00 185 0.021 180 0.021 1.05 311 0.020 308 0.020 1.10 280 0.019 298 0.020 1.15 286 0.018 289 0.019 1.20 276 0.017 279 0.018 1.25 266 0.017 271 0.018 1.30 257 0.016 263 0.017 1.35 249 0.016 255 0.017 1.40 241 0.015 247 0.016 1.45 234 0.015 240 0.016 1.50 228 0.015 234 0.015
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A6 - 13
50 t Macro at mass of 30 t and tyre pressure of 0.8 MPa
1000 mm of B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Strain (με)
Stress (MPa)
0.00 519 0.800 -72 0.000 0.05 754 0.781 -72 0.000 0.10 806 0.692 -68 0.003 0.15 714 0.561 -57 0.008 0.20 583 0.434 -40 0.015 0.25 375 0.276 -53 0.018 0.30 342 0.221 -17 0.002 0.35 287 0.178 13 0.026 0.40 243 0.143 38 0.033 0.45 212 0.114 57 0.038 0.50 194 0.093 71 0.037 0.55 214 0.077 104 0.036 0.60 191 0.063 113 0.035 0.65 176 0.053 121 0.033 0.70 168 0.045 129 0.031 0.75 168 0.039 136 0.030 0.80 231 0.035 200 0.028 0.85 219 0.031 200 0.027 0.90 212 0.028 201 0.025 0.95 210 0.026 203 0.024 1.00 213 0.025 208 0.024 1.05 359 0.024 356 0.023 1.10 343 0.023 344 0.022 1.15 330 0.022 333 0.022 1.20 318 0.021 322 0.021 1.25 307 0.020 312 0.019 1.30 297 0.019 303 0.090 1.35 287 0.019 294 0.018 1.40 278 0.018 285 0.018 1.45 270 0.018 277 0.017 1.50 263 0.017 270 0.017
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A6 - 14
50 t Macro at mass of 33 t and tyre pressure of 0.9 MPa
1000 mm of B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Strain (με)
Stress (MPa)
0.00 586 0.900 -79 0.000 0.05 852 0.878 -80 0.000 0.10 906 0.776 -75 0.003 0.15 800 0.626 -62 0.008 0.20 650 0.484 -44 0.016 0.25 419 0.308 -57 0.029 0.30 382 0.247 -18 0.002 0.35 319 0.198 15 0.029 0.40 269 0.158 42 0.036 0.45 234 0.127 63 0.040 0.50 214 0.103 79 0.042 0.55 237 0.085 114 0.041 0.60 211 0.070 124 0.040 0.65 194 0.058 133 0.038 0.70 185 0.049 141 0.037 0.75 185 0.043 150 0.035 0.80 255 0.038 220 0.033 0.85 241 0.034 220 0.031 0.90 234 0.031 221 0.029 0.95 231 0.029 224 0.028 1.00 235 0.027 229 0.027 1.05 395 0.026 391 0.026 1.10 378 0.025 379 0.025 1.15 363 0.024 366 0.024 1.20 350 0.023 355 0.023 1.25 337 0.022 344 0.023 1.30 326 0.021 333 0.022 1.35 316 0.021 323 0.022 1.40 306 0.020 314 0.021 1.45 297 0.019 305 0.020 1.50 289 0.019 297 0.019
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A6 - 15
50 t Macro at mass of 36 t and tyre pressure of 1.0 MPa
1000 mm of B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Strain (με)
Stress (MPa)
0.00 653 1.000 -86 0.000 0.05 949 0.975 -87 0.000 0.10 1007 0.859 -81 0.003 0.15 885 0.692 -68 0.009 0.20 717 0.532 -48 0.017 0.25 464 0.339 -61 0.004 0.30 421 0.272 -18 0.020 0.35 350 0.218 17 0.032 0.40 296 0.174 46 0.039 0.45 257 0.139 68 0.044 0.50 234 0.112 86 0.045 0.55 259 0.093 125 0.045 0.60 231 0.077 136 0.044 0.65 212 0.064 145 0.042 0.70 202 0.054 154 0.040 0.75 202 0.047 163 0.038 0.80 278 0.042 240 0.036 0.85 264 0.037 240 0.034 0.90 255 0.034 241 0.032 0.95 253 0.031 244 0.031 1.00 256 0.030 250 0.030 1.05 431 0.028 427 0.029 1.10 413 0.027 413 0.028 1.15 396 0.026 400 0.027 1.20 382 0.025 387 0.026 1.25 368 0.024 375 0.026 1.30 356 0.023 364 0.025 1.35 345 0.023 353 0.024 1.40 334 0.022 343 0.023 1.45 324 0.022 333 0.022 1.50 315 0.021 324 0.022
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A6 - 16
50 t Macro at mass of 40 t and tyre pressure of 1.1 MPa
1000 mm of B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Strain (με)
Stress (MPa)
0.00 717 1.100 -96 0.000 0.05 1042 1.073 -96 0.001 0.10 1108 0.947 -91 0.004 0.15 975 0.764 -76 0.010 0.20 792 0.589 -53 0.019 0.25 511 0.375 -68 0.004 0.30 465 0.301 -21 0.022 0.35 398 0.241 18 0.035 0.40 328 0.192 50 0.044 0.45 285 0.154 76 0.049 0.50 260 0.125 95 0.050 0.55 287 0.103 139 0.050 0.60 256 0.085 151 0.049 0.65 235 0.071 161 0.047 0.70 225 0.060 171 0.044 0.75 224 0.052 181 0.042 0.80 309 0.046 267 0.040 0.85 293 0.042 266 0.038 0.90 283 0.038 268 0.036 0.95 281 0.035 271 0.034 1.00 285 0.033 277 0.033 1.05 479 0.031 474 0.031 1.10 459 0.030 459 0.030 1.15 440 0.029 444 0.029 1.20 424 0.028 430 0.028 1.25 409 0.027 417 0.027 1.30 396 0.026 404 0.027 1.35 383 0.025 392 0.026 1.40 371 0.024 381 0.025 1.45 360 0.023 370 0.024 1.50 350 0.022 360 0.023
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A6 - 17
50 t Macro at mass of 43 t and tyre pressure of 1.2 MPa
1000 mm of B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Strain (με)
Stress (MPa)
0.00 784 1.200 -103 0.000 0.05 1140 1.170 -104 0.001 0.10 1209 1.030 -97 0.004 0.15 1061 0.829 -81 0.011 0.20 858 0.637 -58 0.021 0.25 556 0.406 -22 0.005 0.30 504 0.326 -22 0.024 0.35 420 0.260 20 0.038 0.40 354 0.208 55 0.047 0.45 307 0.166 82 0.052 0.50 280 0.134 103 0.054 0.55 309 0.111 149 0.054 0.60 276 0.092 162 0.054 0.65 253 0.076 173 0.052 0.70 242 0.064 184 0.050 0.75 241 0.056 195 0.048 0.80 332 0.050 287 0.042 0.85 315 0.045 287 0.040 0.90 305 0.041 288 0.039 0.95 302 0.038 292 0.036 1.00 306 0.035 298 0.035 1.05 515 0.034 510 0.034 1.10 493 0.032 493 0.033 1.15 473 0.031 477 0.032 1.20 456 0.030 462 0.030 1.25 440 0.029 448 0.029 1.30 425 0.028 434 0.029 1.35 412 0.027 421 0.028 1.40 399 0.026 409 0.027 1.45 387 0.025 398 0.026 1.50 376 0.024 387 0.025
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A6 - 18
50 t Macro at mass of 47 t and tyre pressure of 1.3 MPa
1000 mm of B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Strain (με)
Stress (MPa)
0.00 848 1.300 -113 0.000 0.05 1233 1.267 -113 0.001 0.10 1309 1.118 -106 0.004 0.15 1151 0.901 -89 0.012 0.20 933 0.693 -63 0.022 0.25 603 0.442 -50 0.005 0.30 548 0.355 -24 0.026 0.35 457 0.284 22 0.041 0.40 386 0.226 59 0.051 0.45 335 0.181 89 0.057 0.50 306 0.147 112 0.059 0.55 338 0.121 163 0.059 0.60 301 0.100 177 0.057 0.65 277 0.083 190 0.055 0.70 264 0.070 201 0.052 0.75 264 0.061 213 0.049 0.80 363 0.054 313 0.047 0.85 334 0.049 313 0.044 0.90 333 0.044 314 0.042 0.95 330 0.041 319 0.040 1.00 334 0.039 326 0.038 1.05 563 0.037 557 0.037 1.10 539 0.035 539 0.036 1.15 517 0.034 522 0.034 1.20 498 0.033 505 0.033 1.25 481 0.032 490 0.032 1.30 465 0.031 475 0.031 1.35 450 0.030 461 0.030 1.40 436 0.029 447 0.029 1.45 423 0.028 435 0.028 1.50 411 0.027 423 0.027
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A6 - 19
50 t Macro at mass of 50 t and tyre pressure of 1.4 MPa
1000 mm of B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Strain (με)
Stress (MPa)
0.00 915 1.400 -120 0.000 0.05 1331 1.364 -120 0.001 0.10 1420 1.201 -113 0.004 0.15 1236 0.966 -95 0.013 0.20 1000 0.742 -67 0.024 0.25 648 0.474 -83 0.006 0.30 587 0.380 -25 0.028 0.35 489 0.303 24 0.044 0.40 412 0.242 63 0.055 0.45 358 0.193 95 0.061 0.50 326 0.156 119 0.063 0.55 360 0.129 173 0.062 0.60 321 0.106 188 0.061 0.65 295 0.089 201 0.058 0.70 281 0.075 214 0.055 0.75 280 0.065 227 0.052 0.80 386 0.058 333 0.050 0.85 366 0.052 333 0.047 0.90 354 0.047 335 0.045 0.95 351 0.044 339 0.042 1.00 356 0.041 347 0.041 1.05 590 0.039 593 0.039 1.10 573 0.038 574 0.038 1.15 551 0.036 555 0.037 1.20 530 0.035 538 0.035 1.25 511 0.034 521 0.034 1.30 494 0.032 505 0.033 1.35 474 0.031 490 0.032 1.40 464 0.030 476 0.031 1.45 451 0.029 462 0.030 1.50 438 0.028 450 0.029
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A6 - 20
50 t Test Rig at mass of 50 t and tyre pressure of 1.65 MPa
1000 mm of B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Strain (με)
Stress (MPa)
0.00 1027 1.650 -170 0.000 0.05 1451 1.628 -162 0.001 0.10 1649 1.516 -150 0.003 0.15 1606 1.322 -130 0.009 0.20 1433 1.099 -100 0.017 0.25 910 0.686 -179 0.004 0.30 874 0.574 -115 0.002 0.35 763 0.475 -45 0.014 0.40 609 0.390 14 0.033 0.45 598 0.319 65 0.047 0.50 553 0.262 105 0.056 0.55 612 0.216 178 0.062 0.60 545 0.178 213 0.065 0.65 497 0.147 244 0.066 0.70 469 0.122 271 0.066 0.75 465 0.104 294 0.065 0.80 619 0.090 440 0.063 0.85 575 0.079 451 0.061 0.90 547 0.070 461 0.059 0.95 535 0.063 473 0.057 1.00 540 0.058 485 0.055 1.05 887 0.055 832 0.053 1.10 836 0.052 808 0.052 1.15 791 0.049 783 0.050 1.20 750 0.047 759 0.048 1.25 714 0.045 735 0.046 1.30 682 0.043 711 0.045 1.35 653 0.041 689 0.043 1.40 626 0.039 666 0.042 1.45 601 0.037 645 0.040 1.50 579 0.036 624 0.039
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A6 - 21
200 t Supercompactor at mass of 200 t and
tyre pressure of 1.65 MPa
1000 mm of B&B Base on CBR 6 Subgrade
Under Wheel Centre of Gear Depth
(m) Strain (με)
Stress (MPa)
Strain (με)
Stress (MPa)
0.00 279 1.000 -414 0.000 0.05 491 0.994 -421 0.003 0.10 660 0.969 -385 0.024 0.15 776 0.924 -300 0.061 0.20 842 0.860 -189 0.103 0.25 1029 0.822 -28 0.171 0.30 1054 0.764 92 0.191 0.35 974 0.658 182 0.204 0.40 908 0.564 262 0.211 0.45 862 0.483 333 0.214 0.50 843 0.416 395 0.212 0.55 1000 0.361 564 0.206 0.60 948 0.314 609 0.200 0.65 916 0.274 653 0.192 0.70 909 0.242 697 0.184 0.75 928 0.218 741 0.177 0.80 1316 0.199 1114 0.169 0.85 1277 0.183 1126 0.163 0.90 1256 0.170 1142 0.156 0.95 1258 0.159 1164 0.151 1.00 1279 0.151 1193 0.146 1.05 2178 0.146 2070 0.142 1.10 2100 0.140 2021 0.138 1.15 2028 0.135 1972 0.134 1.20 1962 0.130 1925 0.130 1.25 1902 0.127 1879 0.127 1.30 1845 0.123 1834 0.123 1.35 1792 0.119 1790 0.120 1.40 1743 0.115 1748 0.117 1.45 1696 0.112 1707 0.113 1.50 1651 0.109 1668 0.110
Appendix 6 Damage Indicators with Depth
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A6 - 22
Appendix 7 Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A7 - 1
APPENDIX 7. PROOF ROLLING REGIMES
B737 at mass of 78.5 t and tyre pressure of 1.39 MPa
Depth (m)
Pavement structure
Aircraft Stress (MPa)
Roller Stress (MPa)
Roller configuration
0.00 Asphalt 1.360 0.05 1.339 1.400 0.10 1.237 1.364 0.15 1.064 1.201 0.20 0.871 0.966 0.25
Base
0.568 0.742
50 t at 1.4 MPa
0.25 0.568 1.000 0.30 0.469 0.975 0.35 0.384 0.859 0.40 0.314 0.692 0.45 0.255 0.532 0.50 0.210 0.339 0.55 0.174 0.272 0.60 0.144 0.218 0.65 0.120 0.174 0.70 0.100 0.139 0.75 0.086 0.112 0.80
Sub-base
0.075 0.093
36 t at 1.0 MPa
0.80 0.075 0.600 0.85 0.067 0.585 0.90 0.060 0.517 0.95 0.054 0.418 1.00 0.050 0.322 1.05 0.047 0.205 1.10 0.045 0.165 1.15 0.042 0.132 1.20 0.040 0.105 1.25 0.039 0.084 1.30 0.037 0.068 1.35 0.035 0.056 1.40 0.034 0.047 1.45 0.032 0.039 1.50
Subgrade
0.031 0.033
22 t at 0.6 MPa
Appendix 7 Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A7 - 2
B767 at mass of 180 t and tyre pressure of 1.24 MPa
Depth (m)
Pavement structure
Aircraft Stress (MPa)
Roller Stress (MPa)
Roller configuration
0.00 Asphalt 1.240 0.05 1.225 1.400 0.10 1.153 1.364 0.15 1.021 1.201 0.20 0.864 0.966 0.25
Base 1
0.573 0.742
50 t at 1.4 MPa
0.25 0.573 0.600 0.30 0.482 0.585 0.35 0.402 0.517 0.40 0.333 0.418 0.45
Base 2
0.276 0.322
22 t at 0.6 MPa
0.45 0.276 0.700 0.50 0.230 0.683 0.55 0.193 0.605 0.60 0.162 0.489 0.65 0.137 0.379 0.70 0.117 0.240 0.75 0.103 0.193 0.80 0.092 0.155 0.85 0.083 0.124 0.90 0.076 0.099 0.95
Sub-base
0.070 0.081
26 t at 0.7 MPa
0.95 0.070 0.500 1.00 0.066 0.488 1.05 0.064 0.434 1.10 0.061 0.352 1.15 0.059 0.273 1.20 0.057 0.173 1.25 0.055 0.140 1.30 0.053 0.112 1.35 0.051 0.090 1.40 0.049 0.072 1.45 0.048 0.059 1.50
Subgrade
0.047 0.048
19 t at 0.5 MPa
Appendix 7 Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
A7 - 3
B747 at mass of 397 t and tyre pressure of 1.38 MPa
Depth (m)
Pavement structure
Aircraft Stress (MPa)
Roller Stress (MPa)
Roller configuration
0.00 Asphalt 1.380 0.05 1.364 1.400 0.10 1.282 1.364 0.15 1.134 1.201 0.20 0.958 0.966 0.25
Base 1
0.638 0.742
50 t at 1.4 MPa
0.25 0.638 0.700 0.30 0.536 0.683 0.35 0.446 0.605 0.40 0.369 0.489 0.45
Base 2
0.305 0.379
26 t at 0.7 MPa
0.45 0.305 0.600 0.50 0.254 0.585 0.55 0.213 0.517 0.60 0.179 0.418 0.65 0.151 0.322 0.70 0.129 0.205 0.75 0.113 0.165 0.80 0.101 0.132 0.85
Sub-base
0.091 0.105
22 t at 0.6 MPa
0.85 0.091 0.800 0.90 0.083 0.781 0.95 0.077 0.692 1.00 0.073 0.561 1.05 0.070 0.434 1.10 0.067 0.276 1.15 0.064 0.221 1.20 0.062 0.178 1.25 0.060 0.143 1.30 0.058 0.114 1.35 0.056 0.093 1.40 0.054 0.077 1.45 0.053 0.063 1.50
Subgrade
0.052 0.053
30 t at 0.8 MPa
Appendix 7 Proof Rolling Regimes
An Investigation of the Australian Layered Elastic Tool for
Flexible Aircraft Pavement Thickness Design A7 - 4
F111 at mass of 50.8 t and tyre pressure of 1.48 MPa
Depth (m)
Pavement structure
Aircraft Stress (MPa)
Roller Stress (MPa)
Roller configuration
0.00 Asphalt 1.480 0.05 1.461 1.400 0.10 1.368 1.364 0.15 1.203 1.201 0.20 1.009 0.966 0.25
Base
0.653 0.742
50 t at 1.4 MPa
0.25 0.653 0.800 0.30 0.545 0.781 0.35 0.450 0.692 0.40 0.368 0.561 0.45 0.299 0.434 0.50 0.244 0.276 0.55 0.200 0.221 0.60 0.162 0.178 0.65 0.131 0.143 0.70 0.107 0.114 0.75 0.089 0.093 0.80
Sub-base
0.076 0.077
30 t at 0.8 MPa
0.80 0.076 0.500 0.85 0.065 0.488 0.90 0.056 0.434 0.95 0.049 0.352 1.00 0.044 0.273 1.05 0.041 0.173 1.10 0.038 0.140 1.15 0.036 0.112 1.20 0.033 0.090 1.25 0.031 0.072 1.30 0.030 0.059 1.35 0.028 0.048 1.40 0.027 0.040 1.45 0.025 0.034 1.50
Subgrade
0.024 0.028
19 t at 0.5 MPa
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An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design
B - 1
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