Backcalculation of Pavement Layers Moduli Using 3D Nonlinear Explicit FEM

BACKCALCULATION OF PAVEMENT LAYERS MODULIUSING 3D NONLINEAR EXPLICIT

FINITE ELEMENT ANALYSIS

ByGergis W. William

Thesis Submitted to the College ofEngineering and Mineral Resources

at West Virginia Universityin Partial Fulfillment of the Requirements

for the Degree of

Master of Science in

Civil Engineering

Samir N. Shoukry, Ph.D., ChairDavid R. Martinelli, Ph.D.

W. J. Head, Ph. D.

Morgantown, West Virginia 1999

ii

ACKNOWLEDGMENTS

For his excellent support and advice in both my academic and research works, for many hours

spent improving, evaluating, correcting my work, and his friendship, I would like to express my

gratitude to Dr. Samir N. Shoukry whose assistance and guidance made this work feasible.

Appreciation is also extended to Dr. David Martinelli and Dr. W. J. Head for serving on the

examining Committee.

Thanks to Mr. George Hanna, West Virginia Division of Highways, who performed the field

tests using FWD. I would like also to thank Professor Per Ullidtz, Technical University of Denmark,

who provided some of his results for comparison with my results listed in Chapter 8, Table 8.2.

I would like thank to my parents for their love, support, and understanding and for being there

when times were rough. I would like also to thank my sister and my grand father for their love and

support Thanks are also extended to my friends for their encouragement and help.

The author gratefully acknowledges the financial support for this research from West Virginia

Division of Highways, and Mid Atlantic Universities Transportation Center.

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ABSTRACT

BACKCALCULATION OF PAVEMENT LAYERS MODULI USING3D NONLINEAR EXPLICIT FINITE ELEMENT ANALYSIS

by:

GERGIS W. WILLIAM

After reviewing the existing literature on FWD testing and backcalculation algorithms, a newbackcalculation approach based on Three Dimensional Finite Element Modeling (3D FEM) wasdeveloped. This approach accounts for the transient dynamic nature of FWD load, the threedimensional geometry of the pavement structure, and the friction and bonding characteristics ofpavement layers interfaces. The 3D FEM backcalculation approach was used to backcalculate thelayers moduli of flexible, rigid, and composite pavement sites located in West Virginia. The layersmoduli of each site were also evaluated using three widely used backcalculation algorithms:MODULUS, EVERCALC, and MODCOMP. Comparison of their results with those obtained using3D FEM revealed that the former should be multiplied by correction factors in order to match thelatter. Using 3D FEM backcalculation results as reference values, correction factors were developedfor each program and pavement type. The mechanistically evaluated correction factors were foundto be in close agreement with the experience-based factors recommended for flexible and rigidpavements in the American Association of State Highway and Transportation Officials (AASHTO)Pavement Design Guide.

The 3D FEM approach was also used to predict the apparent depth to bedrock. The decayof vertical stress and displacement in the subgrade layer were examined and used to predict theapparent depths to bedrock for four pavement sites located in Texas. The 3D FEM results werefound to be in good agreement with the measured values provided by Texas DOT.

A parametric study was conducted to evaluate the effect of the subgrade layer thickness(assumed in the finite element pavement structural model) on the stress and deformation obtained ontop of the subgrade layer and on the 3D FEM-generated deflection basin. It was found that asubgrade layer thickness of 6 ft. would produce satisfactory results.

The effect of concrete slab length on the deflection basin was examined for both doweled andundoweled concrete slabs. For doweled concrete pavements, slab length has no effect on thedeflection basin. For broken slabs or undoweled ones, the minimum slab length required to producean acceptable deflection basin was found to be 10 ft.

KEYWORDS:Falling Weight Deflectometer, Pavement Evaluation, Nondestructive testing, Backcalculation, FiniteElement Analysis of Pavements.

iv

TABLE OF CONTENTS

ACKNOWLEDGMENT ii

ABSTRACT iii

TABLE OF CONTENTS iv

LIST OF TABLES vi

LIST OF FIGURES vii

CHAPTER 1

INTRODUCTION 1

1.1 BACKGROUND 1

1.2 BACKCALCULATION PROBLEMS 4

1.3 OBJECTIVE OF THIS THESIS 5

1.3.1 Organization of this Thesis 6

CHAPTER 2

LITERATURE REVIEW 8

2.1 BACKCALCULATION PROGRAMS 8

2.2 PROGRAM SELECTION 9

2.3 DESCRIPTION OF SELECTED BACKCALCULATION PROGRAMS 10

2.3.1 Description of MODCOMP3 Program 11

2.3.2 Description of MODULUS5.0 Program 12

2.3.3 Description of EVERCALC4.0 Program 13

2.3.4 Description of ELMOD4 Program 15

CHAPTER 3

COMPARISON OF BACKCALCULATION RESULTS FOR SHRP TEST SECTIONS 20

CHAPTER 4

COMPARISON OF BACKCALCULATION RESULTS FOR SEVEN SELECTED SITES

IN WEST VIRGINIA 34

CHAPTER 5

FIELD TESTING 66

5.1 PAVEMENT SITES 66

5.2 MEASUREMENTS 67

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5.3 DEFLECTION TESTING 69

5.4 EVALUATION OF BACKCALCULATED MODULI 70

5.5 CONCLUSIONS 70

CHAPTER 6

EVALUATION OF BACKCALCULATION ALGORITHMS THROUGH

FINITE ELEMENT MODELING OF FWD TEST 76

6.1 INTRODUCTION 76

6.2 REVIEW OF FINITE ELEMENT MODELING OF PAVEMENTS 76

6.3 GUIDELINES FOR 3D-FEM OF PAVEMENT STRUCTURES 78

6.4 FINITE ELEMENT MODELS OF EXPERIMENTAL TEST SITES 81

6.4.1 Flexible Pavement Model 81

6.4.2 Rigid Pavement Model 81

6.4.3 Composite Pavement Model 82

6.5 STRUCTURAL MATERIAL MODELING 83

6.6 LAYERS MODULI EVALUATION FROM FE MODEL RESULTS 84

6.7 VERIFICATION OF FINITE ELEMENT MODELS 85

6.7.1 Deflection basins 85

6.7.2 Displacement time-history 86

6.8 EVALUATION OF BACKCALCULATION PROGRAMS 87

CHAPTER 7

SOME FACTORS INFLUENCE BACKCALCULATIONS OF RIGID PAVEMENTS 103

7.1 INTRODUCTION 103

7.2 FINITE ELEMENT STRUCTURAL MODEL 103

7.2.1 Model Loading and Material Model 105

7.2.2 Model Verification 106

7.3 PERFORMANCE ASSESSMENT OF BACKCALCULATION PROGRAMS 107

7.4 EFFECT OF SLAB LENGTH AND DOWEL BARS 108

7.5 CONCLUSIONS 109

CHAPTER 8

EFFECT OF 3D FEM MODEL DEPTH ON BACKCALCULATIONS OF FLEXIBLE PAVEMENTS 117

8.1 INTRODUCTION 117

8.2 FINITE ELEMENT STRUCTURAL MODELS 121

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8.3 EVALUATION OF LAYERS’ MODULI 122

8.4 EVALUATION OF DEPTH TO BEDROCK 123

8.5 EFFECT OF 3D FE MODEL DEPTH ON 3D FEM RESULTS 125

8.5.1 Effect of Model Depth on Deflection Basin 126

8.5.2 Effect of Stress Wave Reflection from Model Bottom on Deflection Basin 126

8.5.3 Effect of Model Depth on the 3D FEM-Calculated Depth to Bedrock 126

8.5.4 Effect of Model Depth on Stresses Induced in Subgrade 127

8.6 EFFECT OF LOAD DURATION ON THE DEFLECTION BASIN 128

8.7 CONCLUSION 128

CHAPTER 9

CONCLUSIONS 144

REFERENCES 148

APPENDIX A PARAMETRIC INPUT FILE TO GENERATE FLEXIBLE PAVEMENT MODEL 158

VITA 166

vii

LIST OF TABLES

TABLE 2.1 Available Backcalculation Programs. 18

TABLE 2.2 Comparison of Selected Backcalculation Programs. 19

TABLE 3.1 Moduli Range and Poisson’s Ratio for Backcalculation Inputs. 23

TABLE 3.2 Backcalculated Layer Moduli (Ksi) for SHRP Sections. 24

TABLE 4.1 Assumptions Used in Different Backcalculation Algorithms. 38

TABLE 4.2a Backcalculated Layer Moduli (Ksi) for Flexible Pavement Sections. 40

TABLE 4.2b Backcalculated Layer Moduli (Ksi) for Composite Pavement Sections. 41

TABLE 4.2c Backcalculated Layer Moduli (Ksi) for Rigid Pavement Sections. 42

TABLE 4.3 Comparison of Pavement Moduli Backcalculated by Different Programs. 43

TABLE 4.4 Number of Backcalculated Out of Range Moduli. 45

TABLE 5.1 Deflection Data Collected from Field Tests. 72

TABLE 5.2 Backcalculated Layer Moduli (Ksi) for Tested Pavement Sections. 73

TABLE 6.1 Correction Factors for Backcalculated Subgrade Modulus. 90

TABLE 7.1 Properties of Pavement Materials. 105

TABLE 8.1 Layer Thicknesses and Temperature Measurements. 130

TABLE 8.2 Backcalculated Pavement Layers’ Moduli, Ksi. 131

TABLE 8.3 Comparison Between Measured and Calculated Depth to Bedrock. 132

TABLE 8.4 Effect of Assumed Model Depth on the Calculated Depth to Bedrock. 133

viii

LIST OF FIGURES

FIGURE 1.1 FWD setup and schematic presentation of stress bulb. 8

FIGURE 3.1 SHRP sections data used for backcalculations. 25

FIGURE 3.2 Comparison of backcalculated moduli for SHRP section A. 26

FIGURE 3.3 Comparison of backcalculated moduli for SHRP section B. 27

FIGURE 3.4 Comparison of backcalculated moduli for SHRP section C. 28

FIGURE 3.5 Comparison of backcalculated moduli for SHRP section D. 29

FIGURE 3.6 Comparison of backcalculated moduli for SHRP section E. 30

FIGURE 3.7 Comparison of backcalculated moduli for SHRP section F. 31

FIGURE 3.8 Comparison of backcalculated moduli for SHRP section G. 32

FIGURE 3.9 Comparison of backcalculated moduli for SHRP section H. 33

FIGURE 4.1 Backcalculated layer moduli (Ksi) for flexible pavement section US52_pre station 16.250. 46

FIGURE 4.2 Backcalculated layer moduli (Ksi) for composite pavement section US52_pre station 18.360. 47

FIGURE 4.3 Backcalculated layer moduli (Ksi) for composite pavement section US52_pre station 19.179. 48

FIGURE 4.4 Backcalculated layer moduli (Ksi) for composite pavement section US60_smi station 1.230. 49



FIGURE 4.7 Backcalculated layer moduli (Ksi) for composite pavement section WV2_frie station 4.296. 52



FIGURE 4.10 Backcalculated layer moduli (Ksi) for flexible pavement section WV3_whit station 40.806. 55



FIGURE 4.13 Backcalculated layer moduli (Ksi) for flexible pavement section WV71_blu station 0.009. 58



FIGURE 4.16 Backcalculated layer moduli (Ksi) for rigid pavement section US2_moun station 18.250. 61

FIGURE 4.17 Backcalculated layer moduli (Ksi) for rigid pavement section US2_moun station 19.028. 62

FIGURE 4.18 Backcalculated layer moduli (Ksi) for rigid pavement section US19_hic station 20.856. 63



FIGURE 5.1 Flexible pavement section. 74

FIGURE 5.2 Rigid pavement section. 74

FIGURE 5.3 Composite pavement section. 74

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FIGURE 5.4 Instrumentation layout. 75

FIGURE 6.1 Finite element mesh of the flexible pavement model. 91

FIGURE 6.2 Finite element mesh of the rigid pavement model. 92

FIGURE 6.3 Finite element mesh of the composite pavement model. 93

FIGURE 6.4 Impact loading curves used in different finite element models. 94

FIGURE 6.5 Load-Deflection relation for different types of pavements. 95

FIGURE 6.6 Fringes of vertical Stress at time of maximum FWD load. 96

FIGURE 6.7 Vertical stresses in different types of pavements due to FWD load. 97

FIGURE 6.8 Comparison between experimental and FE deflection basins for different pavements models.. 98

FIGURE 6.9 Fringes of vertical displacement at time of maximum FWD load. 99

FIGURE 6.10 Deflection-time histories for different pavement models. 100

FIGURE 6.11 Comparison between backcalculated deflection basins and measured basins. 101

FIGURE 6.12 Comparison of backcalculated layer moduli for the three types of pavements. 102

FIGURE 7.1 Finite element mesh for a rigid pavement. 110

FIGURE 7.2 Cross section in a doweled joint. 110

FIGURE 7.3 Impact load curve used in finite element model (Ref. (48)). 111

FIGURE 7.4 Model Verification. (Slab length=20 ft) 112

FIGURE 7.5 Comparison between the results of backcalculation programs. 113

FIGURE 7.6 Effect of slab length on deflection basin. 114

FIGURE 7.7 Change of maximum deflection with slab length for undoweled pavement. 115

FIGURE 7.8 Effect of slab length on the backcalculation results ( Using MODULUS). 116

FIGURE 8.1 Finite element model. 134

FIGURE 8.2 Measured FWD impact load curves used in finite element models. 135

FIGURE 8.3 Measured and FE-calculated deflection basins. 136

FIGURE 8.4 Subgrade vertical displacement versus depth. 137

FIGURE 8.5 Subgrade vertical displacement on a logarithmic scale versus depth. 138

FIGURE 8.6 Decay of vertical stress and displacement in subgrade. 139

FIGURE 8.7 Effect of the depth to bedrock on the deflection basin. 140

FIGURE 8.8 Effect of reflective subgrade bottom on deflection basin. 141

FIGURE 8.9 Subgrade vertical displacement for different model depths. 142

FIGURE 8.10 Effect of model depth on vertical stress distribution for site 3. 143

FIGURE 8.11 Effect of load duration on the deflection basin. 144

Numbers in parentheses refer to numbers of references.1

1

CHAPTER 1

INTRODUCTION

1.1 BACKGROUND

Backcalculation is an analytical procedure in which the deflection data collected during a

Falling Weight Deflectometer (FWD) test are used to predict the moduli of different pavement layers.

The backcalculation procedure involves theoretical calculations of the deflections produced under a

known applied load using an assumed set of layers’ moduli. The theoretical deflections are then

compared with those measured during the test. In case of differences between the theoretical and

measured deflections, the assumed pavement layers moduli are adjusted and the process is repeated

until the differences between the theoretical and measured values fall within acceptable limits.

Techniques like iteration, database searching, regression analysis, and artificial intelligence (neural

networks) have been used as backcalculation tools (1,2) .1

Most of the existing backcalculation algorithms use iterative analysis. In this case, the

solution for the theoretical deflections is initiated at the distant sensor locations assuming that surface

deflections at the distant sensor positions are due to strains or deflections in the subgrade layer only

and independent of the overlaying layers (3-5). As shown in Figure 1.1, the stress zone intersects

the interface between the subbase and subgrade layers at the radial distance r = a . This means thate

any surface deflection value obtained from the deflection basin at or beyond the distance r = a is duee

only to the deformation within the subgrade layer. Thus, in-situ modulus of the subgrade can be

evaluated from the known values of measured deflections at the outer geophone positions. From the

above discussion, a value is obviously very important. The AASHTO Guide for Design of Pavemente

Structures (1993), Section 5.4.5, Step4: Deflection Testing points out that the deflection used to

backcalculate the subgrade modulus must be measured far enough from the center of load application

r � 0.7ae

ae a2� D(3

Ep

MR

)

2

2

so that it provides a good estimate of the subgrade modulus. The guide suggests that minimum

distance may be determined from the following relationship:

the following formula is provided for the determination of a (5):e

where a = radius of a stress bulb at the subgrade-pavement interface, inches;e

a = FWD load plate radius, inches;

D = total thickness of pavement layers above the subgrade, inches;

E = effective modulus of all pavement layers above the subgrade, psi;P

M = subgrade resilient modulus, psi.R

The AASHTO guide gives a graph for the determination of the ratio E / M for a six inchP R

radius loading plate, known total thickness of pavement layers above the subgrade, known maximum

deflection under the center of the loading plate, and known load magnitude.

The following aspects should be considered for the evaluation of subgrade modulus from

FWD data:

1. Different types of pavement structures produce a different spread of stress zone (stress bulb).

Flexible pavements are characterized by localized stress distribution while rigid pavements

have a wider spread of stress zone. The stress zone in composite pavements falls between the

above two, depending on: the type of overlay, construction practice, and condition of the

second layer (old top layer). Calculation of a is useful in the determination of geophonee

location for the evaluation of subgrade moduli.

3

2. Accuracy of measurement progressively diminishes at distant geophone locations due to the

fact that the displacement magnitude is close to the resolution accuracy of the geophone.

Measurements below 2.5 mils (0.0025 inch) should be processed with care.

3. High load magnitude could be an additional source of error in the evaluation of linear resilient

subgrade modulus since it is likely to produce nonlinear deformations in the soil layer.

AASHTO Guide for Design of Pavement Structures (1993), Section 5.4.5, suggests the use

of a load magnitude of approximately 9,000 lb to avoid nonlinearity of the subgrade response.

Subgrade layers are the most complex layers in the pavement structure due to their physical

nature and construction practices. Undisturbed natural soil deposits frequently reveal an increase in

the value of elastic modulus with depth, due to higher consolidation of geologic material. Therefore,

if such a soil sample is divided into layers, the top layers will have lower moduli than the lower ones.

The backcalculation process is based on the assumption that surface deflection at a certain offset is

characteristic of the elastic modulus at a certain depth. However, deflections measured at distant

locations are very small and cannot be measured accurately based on geophone resolution. Higher

loads can produce deflections of large magnitudes, but unfortunately they will also cause stresses in

the soil that fall into the nonlinear zone. This again alters the accuracy of linear elastic modulus

evaluation for deeper layers. The only subgrade modulus that can be accurately predicted by FWD

test is the resilient modulus of the top of the subgrade layer positioned right under a base-subgrade

interface.

During the 1998 annual Transportation Research Board (TRB) Meeting of the Committee on

Backcalculation of Pavement Moduli, a specific question regarding accuracy of subgrade moduli

calculation was addressed to L. Irwin, the developer of the MODCOMP3 backcalculation program.

He suggested improving accuracy of subgrade modulus evaluation by dividing the soil layer into a

larger number of thin sublayers. Regarding the depth of top subgrade layer, he suggested calculating

the depth by subtracting the height of pavement structure above the subgrade from the depth of frost

penetration value, which is 30 to 36 inches for West Virginia.

4

Assumption of a thicker layer in backcalculations consistently produced higher subgrade

modulus value. This observation shows that a thicker layer assumption leads to overestimation of

subgrade moduli, which is an undesirable outcome.

In the backcalculation procedure, the modulus of the lowest subgrade layer is changed in the

iterative procedures until such value is found that will produce surface deflection at the distant

geophone that agrees with the measured one, within a certain tolerance. Once the modulus value for

the lowest layer is found, it is assumed to be the “true” value and is used as a constant in the

evaluation of moduli for the upper layers. The solution progresses from the distant geophone

locations to the center of load application and the layers moduli are evaluated from the bottom to

top layers. Knowledge of existing pavement layer thicknesses, Poisson’s ratios, and load magnitude

are necessary conditions for the backcalculation procedure. The pavement layers moduli derived in

the above process are further used for the stress and strain analysis of the pavement structure. The

moduli are usually averaged from the results of several load drops in order to lower the weight of the

random error that is introduced during every FWD drop.

The major assumption used in backcalculation algorithms is that the amount of surface

deflection at any point is dependent on the stress-strain state in subsequent layers. This assumption

is true for static loading, but may be violated if the load is dynamic, or if there is discontinuity

(separation) at one or more interfaces.

1.2 BACKCALCULATION PROBLEMS

Although FWD load is an impact load by nature (6-9), most of available backcalculation

programs are based on the static multilayer elastic theoty. The major limitation of the elastostatic

analysis of the FWD load is that it does not account for factors such as material inertia and damping

. As noted by Hoffman and Thompson (10), inertial effects in the pavement layers subjected to FWD

impact may be significant and therefore need to be considered in the theoretical analysis.

5

As pointed out by Chou et al. (11), none of the programs based on the static multilayered

elastic theory could guarantee accurate results for every test section. Chou et al. stated that two

independent agencies who used the same backcalculation software to determine moduli for the same

pavement section produced different results. Therefore, engineering judgement plays an important

role in the evaluation of the test results.

Irwin et al. (12) reported that most errors occur during the evaluation of the surface layer

modulus and Huang (4) stated that this is especially true in the case of thin asphalt layers. One

reason may be the difference between patterns of dynamic and static deformations of the surface

layer.

1.3 OBJECTIVES OF THIS THESIS

Most of the existing backcalculation algorithms are based on simplifying approximations which

include that:

1. the pavement structure has infinite extension perpendicular and along the traffic direction,

3. all pavement layers are fully bonded, and

4. the short duration loading impulse (25 millisecond) applied by the FWD may be approximated as

a static applied load.

The work presented in this thesis is directed towards developing a backcalculation technique in which

the actual pavement geometry, the full FWD loading pulse time-history, and the properties of the

interfaces between pavement layers are accounted for in the backcalculation of the pavement moduli

profile. The structural moduli profile obtained using such a backcalculation technique could be used

to evaluate the performance of existing backcalculation programs. It could also be used in situations

where existing backcalculation algorithms would produce unrealistic results such as in the case of

composite pavements. To achieve this objective, Three Dimensional Finite Element Modeling (3D

FEM) was used to simulate the pavement structure. The use of 3D FEM allows loading the model

6

with the exact FWD loading-time history measured from FWD load cell, as well as representation of

the properties of interfaces between different layers. Although elastic material models were assumed

for all pavement layers (based on the experimental measurement of FWD load-deflection relation),

the 3D FEM approach allows the use of any nonlinear material models including thermo-elastic and

thermoplastic material models.

1.3.1 Organization of this Thesis

The work presented in this Thesis starts in Chapter Two which contains a review of the research

studies which aimed at evaluating the performance of existing backcalculation algorithms. Two major

studies were reviewed in some detail: the Strategic Highway Research Program ( SHRP) study whose

results were first published in 1993 and the MnDOT study published in 1996. The outcome of this

review was the selection of four major backcalculation programs that were the most widely used by

the pavement community. In Chapters Three and Four, the results from the four programs were

compared to each other using SHRP-LTPP data and using data for seven different roads measured

in West Virginia. Chapter Five outlines the FWD testing procedures used for testing three pavement

sites in West Virginia. 3D FEM backcalculation procedures were presented in Chapter Six. The 3D

FEM-backcalculated layer moduli were compared with those obtained using the previously selected

conventional backcalculation algorithms and correction factors were obtained. Some factors which

influence the results of backcalculation of rigid pavements were examined in Chapter Seven. The

factors which influence the backcalculation of flexible pavements were examined in Chapter Eight.

Chapter Nine presents the conclusions drawn from this work along with some points for future

research.

7

FIGURE 1.1 FWD setup and schematic presentation of stress bulb.

8

CHAPTER 2

LITERATURE REVIEW

2.1 BACKCALCULATION PROGRAMS

In 1993, a comprehensive review of existing software for backcalculation procedures was

published as a result of Project SHRP-90-P-001B, sponsored by the Strategic Highway Research

Program (13). After considering a large number of different backcalculation programs, the study was

narrowed down to the following three: MODULUS, WESDEF, and MODCOMP3. The programs

were tested by a group of independent researchers and practicing engineers for different types of

pavement structures. Evaluation criteria that were considered are the repeatability of results obtained

by different users, reasonableness of results, deflection matching errors, ability to match assumed

moduli from simulated deflection basins, and versatility.

As a result of this evaluation, the MODULUS program was judged to be the best and was

therefore chosen for routine use on SHRP and LTPP data. Nonetheless, the MODULUS program

had one drawback that it required deflections to be measured at the specific sensor locations. This

means that some of the points in the deflection basin will be excluded from the matching procedure.

The results from WESDEF program were found to have the highest level of sensitivity to user input.

However, in the same report it was pointed out that this could have been due to the default depth to

bedrock that was not overridden by the users in cases of semi-infinite subgrade layers. The authors

concluded that the MODCOMP3 program tends to over predict subgrade modulus and under predict

base and subbase moduli.

Research was conducted recently by the Minnesota DOT to select a backcalculation software

for the Minnesota Road Research Project (14). The strategy of that study was to compare the

performance of the candidate programs for flexible pavement evaluation in terms of usability and

accuracy of backcalculation results. Four different programs were evaluated: EVERCALC3.3,

9

EVERCALC4.0. WESDEF, and MOCOMP3. All four programs were based on the multilayer linear

elasto-static forward calculation subroutines. As a result of this project, the EVERCALC4.0 program

was recommended for routine research of the Minnesota Road Research test sections.

2.2 PROGRAM SELECTION

Information about sixteen different backcalculation programs available on the market was

collected and is presented in summarized form in Table 2.1. The selection of programs to be

evaluated during the current project was based upon the following recommendations:

1. SHRP Report on Layer Moduli Backcalculation Procedure, 1993 (13).

2. Minnesota Road Research Project Report on Selection of Flexible Pavement

Backcalculation Software, 1996 (14).

As a result, four backcalculation programs were selected for evaluation:

� MODCOMP3 Developed at Cornell University

� MODULUS5.0 Developed by Texas Transportation Institute

� EVERCALC4.0 Used by Washington State DOT

� ELMOD4 Developed by Dynatest

Evaluation of the above programs using data from eight SHRP test sections and twenty-one

sections for seven different roads in West Virginia is presented in this report.

10

2.3 DESCRIPTION OF SELECTED BACKCALCULATION PROGRAMS

2.3.1 Description of MODCOMP3 Program

MODCOMP3 was initially developed by Irwin and Speck for the U.S. Army Cold Regions

Research and Engineering Laboratory. Later, MODCOMP3 was modified by Irwin and Szebenyi

(15) in 1991 at Cornell University.

The MODCOMP3 program uses CHEVRON computer code as a forward calculation

subroutine. This code is based on the multilayer linear elasto-static theory that is traditionally used

for flexible pavement analysis. Fitting the calculated results with the experimentally obtained ones

is implemented through an iterative analysis approach. The modulus of each layer is assumed to

affect the deflection measured at a certain distance from the load. The program first evaluates the

modulus of the deepest layer corresponding to the deflection reading at the farthest geophone

location specified and then it works upwards to calculate the moduli of near surface layers. The

drawback of the program is that the user is responsible for the accurate prediction of the exact

distance that would reveal the deflection characterizing the modulus of a particular layer.

The program can handle from two to fifteen layers, including the bottom layer that is treated

as a semi-infinite half space. Layers moduli can be treated both as known or unknown. No more than

five unknown layers are recommended for use in the analysis. Based on the readings at distant

geophone locations, the program has the ability to calculate the depth to bedrock. Up to ten

geophone locations can be included in backcalculation. The program can accept up to six different

loading cases in the analysis. Layers can be treated both as linear elastic or nonlinear elastic.

The backcalculation analysis is initiated by the set of initial seed moduli specified by the user.

Since no moduli range can be specified, therefore the algorithm has the potential of producing out

of range moduli.

11

The process of backcalculation terminates when one of the following conditions is met:

1. The deflection fit precision tolerance is satisfied.

2. The modulus convergence tolerance is satisfied.

3. The allowed number of iterations is exhausted.

At the end of each iteration, MODCOMP3 checks two tolerances before proceeding to the

next iteration. If either of the tolerances is satisfied, the calculations cease.

The deflection fit precision is a check on the match between the measured deflections and

the deflections that have been calculated at the same radii using the backcalculated moduli. Only the

sensors that are assigned to the layers are included in this check. This means that the whole deflection

basin may not be used in the backcalculation process. For example, if the pavement structure consists

of three layers and the FWD test setup has seven geophones, the user will need to choose three out

of seven geophone readings to backcalculate pavement moduli. In this case, initially, different

geophone selections will produce different sets of moduli; then, the deflection basin built using the

backcalculated moduli will fit the measured basin only at the selected points. So the program leaves

little opportunity to achieve a full match between measured and calculated basins. The accuracy of

the solution is highly dependant on the success in the selection of the “right” geophones for

backcalculation of pavement moduli.

The modulus convergence is a check on the rate of change of the backcalculated moduli

from one iteration to the next. A tolerance of 1.5 percent is typically assigned; but if a value close

to zero is used, this tolerance check is eliminated because it will not be satisfied before either the

deflection fit precision tolerance is achieved, or the allowed number of iterations is exhausted.

2.3.2 Description of MODULUS5.0 Program

MODULUS5.0 was developed by Texas Transportation Institute (16,17). This computer

12

code uses WESLEA program as a forward calculation subroutine. WESLEA is based on the

multilayer linear elasto-static theory that is traditionally used for the purposes of flexible pavement

analysis. The WESLEA subroutine is used to build a data base for the calculated deflection basins of

a given pavement system. A pattern search technique is then used to determine the set of layers

moduli that produce a deflection basin that fits the measured one.

The deflection data collected during the FWD test can be read directly from the DYNATEST

FWD field data diskette or manually typed by the user. Up to eight different load drops at each

station can be considered in the backcalculation analysis, and up to seven geophone locations can be

included in the backcalculation.

The maximum number of unknown layers is limited to four in order to minimize the errors and

produce acceptable results. The depth to the stiff layer can be automatically calculated in the

program. In addition, the user can specify different depth values.

MODULUS5.0 uses weighting factors assigned to each geophone deflection reading.

Different values of weighting factors can maximize or minimize the significance of a certain deflection

value in the backcalculation process. If the weighting factors are not specified by the user, the

program implements an automatic weighting factor determination algorithm. In this case, if a

nonlinear subgrade stiffening with depth is detected, the backcalculation program automatically drops

a maximum of one sensor reading by assigning to it a zero weighting factor.

The backcalculation program has two analysis options. In the first option called “Full

Analysis”, the program asks the user to specify the moduli range to be used in the backcalculation.

The user can specify moduli ranges for up to three layers except the subgrade, and provides a seed

modulus value for the subgrade layer. This feature prevents the program from producing out-of-

range moduli for all layers except the subgrade. Although the program allows the user to enter up

to seven different locations, the manual has a note stating that in MODULUS5.0 the sensors must

be placed at 0, 12, 24, and 36 in..

13

In the second option called “Material Types,” the user is asked to input only the material types

and layers thicknesses and the program automatically selects acceptable ranges of moduli and

Poisson’s Ratios. Both options produce similar outputs for the same types of pavement layer

materials. However, it is worth noting that this program was designed in Texas and oriented to the

pavement design practices used there. Thus, the material selection table is limited to those materials

that are frequently used in Texas and cannot cover all the wide range of pavement materials used in

road construction in the USA. As a result, it is more appropriate to use the first option of the

program in the current backcalculation evaluation process.

Both computed and measured deflection basins can be plotted on the screen. This feature provides

the user with a visual assessment of the accuracy of the program.

2.3.3 Description of EVERCALC4.0 Program

EVERCALC4.0 was developed by J. Mahoney at the University of Washington for

Washington DOT (18). The EVERCALC4.0 uses the WESLEA computer code developed by

Waterways Experimental Station, U.S. Army Corps of Engineers, as a forward calculation subroutine

and a modified augmented Gauss-Newton algorithm for solution optimization. The WESLEA

computer code is based on the multilayer linear elasto-static theory that is traditionally used for

purposes of flexible pavement analysis. The fit of the calculated deflection basin with the

experimentally measured one is implemented through the iterative analysis approach.

The program can handle up to seven sensor measurements and eight drops per section.

Flexible pavement sections containing up to five layers can be evaluated.

To initialize the backcalculation process, initial moduli, as well as moduli ranges, need to be

specified for all the layers. This feature prevents the program from producing out-of-range moduli

for all the layers. At the end of each iteration, the deflections calculated by WESLEA are compared

14

with the measured ones. The discrepancies between the calculated and measured deflections are

characterized by Root Mean Square (RMS) error. The iterations are terminated when one of the

following three conditions are satisfied: (1) RMS falls within the allowable tolerance, (2) the changes

in modulus between two successive iterations fall within the allowable tolerance, or (3) the number

of iterations has reached the maximum limit. When two or more deflection data sets for the same

location are analyzed, the final moduli from the first deflection data is used as a seed moduli for the

next one.

If the pavement section contains no more than three layers, the program can assign the seed

moduli internally. In this case, a set of regression equations is used to determine a set of seed moduli

from the relationships between the layers moduli, surface deflections, applied load, and layer

thickness.

A stiff layer that has a known modulus can be included in the analysis. In this case, the depth

to the stiff layer will be calculated by the program. Inclusion of the stiff layer in the analysis normally

results in a decrease of the subgrade modulus and an increase of the modulus of the layer above the

subgrade (subbase or base) layer.

The program is also able to normalize the modulus of the Asphalt Concrete (AC) layer to that

evaluated at the standard laboratory conditions (for a temperature of 77 F and 100-millisecondo

loading time).

A disadvantage of the EVERCALC4.0 program is that the output files are stored in binary

format, which complicates the communication of EVERCALC4.0 with any other software when

needed (such as an external data base of deflection basins, etc.).

The FWD “raw” deflection data file can be used for the direct input if DYNATEST FWD

model 8000 is used. In this case, the EVERCALC4.0 program will internally convert FWD data to

the EVERCALC4.0 deflection data file. Otherwise, deflection data should be entered manually and

15

saved in a deflection data format provided by EVERCALC4.0. The EVERCALC4.0 program

provides excellent visualization of the results in a variety of graphs and bar charts. The program can

handle English or Metric units.

2.3.4 Description of ELMOD4 Program

ELMOD4 was developed by Dynatest Consulting Inc. ELMOD is an acronym for Evaluation

of Layer Moduli and Overlay Design. The program accepts DYNATEST-FWD file format. If such

a file does not exist, no means for manual input of deflection data is provided by the program. The

ELMOD4 program is capable of calculating pavement layer moduli using one of these two options:

the Odemark-Boussinesq transformed section approach or the deflection basin fit backcalculation.

The first method can be used for one to four layers pavement systems. The second method can

handle up to five layers. In both methods, the dependancy of AC material on temperature conditions

is accounted for. In order to use this feature of the program, the 24-hour air temperature should be

entered in the Structural Data input screen.

Odemark’s layer transformed (structural) section approach is used in conjunction with

Boussinesq’s equations to calculate deflections. An iterative procedure is used to determine layers

moduli which results in the same deflections as measured by a FWD. This method provides the

apparent moduli for the as-measured deflections at each FWD test point, it also takes the nonlinearity

of the subgrade into consideration. This approach is very reliable for flexible three layered pavement

systems that include an unbound base layer plus the bound surface layer . Four layer flexible systems

may also be evaluated using the Odemark-Boussinesq mode provided that the ratio E /E is known.2 3

The program includes a procedure for the automatic calculation of this ratio for granular materials

from the thickness of layers number two and three. For the backcalculation input, a “layer” can

consist of several materials. To better simulate the theoretical conditions on which the backcalculation

approach is based, the program developers suggest combining an asphalt layer with an adjacent gravel

layer or another stabilized layer.

16

A total of five layers, including the subgrade, may be backcalculated if the “deflection basin

fit” backcalculation option is utilized; however, many layers are not recommended unless one or more

of them are assigned some fixed modulus. The deflection basin fit backcalculation method is done

either by using the normal Odemark transformed section factors (0.8 for multi-layered systems and

0.9 for two-layered systems) and adjusting the moduli accordingly, or by recalculating the factors by

a numerical integration forward calculation procedure using a modified version of WES5 and then

performing the deflection basin fit backcalculation using “calibrated” transformed section factors.

The developers of the program recommend the use of the first approach for backcalculation.

ELMOD4 can also provide a theoretical estimate of the equivalent depth to a rigid layer from

the measured deflections. If this option is not chosen, ELMOD4 considers an infinitely thick

nonlinear subgrade. In case of a stiff layer input, linear elastic behavior of the finite subgrade layer

is assumed. ELMOD4 calculates the equivalent depth of an apparently stiff layer and compares this

calculated depth with the user’s maximum depth input; if it is less than the input depth it uses the

calculated depth to perform the analysis. If the calculated depth is greater than the input depth, the

analysis reverts to the consideration of a semi-infinite (nonlinear) subgrade.

ELMOD4 backcalculates the elastic moduli of up to five layers provided that the following

conditions are met:

1. The structure should contain only ONE bound upper (stiff) layer, where E /E �5. If the1 subgrade

structure contains more than one bound layer, they should be combined into one analysis for

the purpose of structural evaluation.

2. The moduli should decrease with depth by approximately E /E >2. Where E is the modulusi i+1 i

of the ith layer counted from the surface.

3. The thickness of the upper (bound) layer (H1) should be larger than half the radius of the

loading plate (generally > 75 mm or 3 inches).

17

4. For three layered structures, the thickness of the upper layer should be less than the diameter

of the loading plate and the thickness of layer one should be less than that of layer two (H1<

H2).

5. When testing on/near a joint, a very wide crack, on gravel surfaces, the structure should be

treated as a two-layer system.

Another limitation of the ELMOD4 program is that Poisson’s Ratios are assumed to be 0.35

for all layers. This is suitable for asphaltic and unbound granular materials, but different from the

values for the cohesive soils (0.42-0.45) and concrete (0.15-0.18).

The main features of the above four reviewed programs are summarized in Table 2.2.

18

TABLE 2.1 Available Backcalculation Programs.

Name of the Name of Theoretical Backcalculation Sourcemain program subroutine for method for method

pavement analysis pavement analysis

BISDEF BISAR Multilayer elastic Iterative USACE-WES

CHEVDEF CHEVRON Multilayer elastic Iterative USACE-WES

CLEVERCALC CHEVRON Multilayer elastic Iterative Royal Institute ofTechnology,

Sweden

COMDEF BISAR Multilayer elastic Data Base M. Anderson

ELSDEF ELSYM5 Multilayer elastic Iterative Texas A&MUniversity,

USACE-WES

EMOD CHEVRON Multilayer elastic Iterative PCS/LAW

EVERCALC CHEVRON Multilayer elastic Iterative J. Mahoney

FPEDDI BASINPT Multilayer elastic Iterative W. Uddin

ILLIBACK ILLIBACK Plate on elastic Closed form University offoundation theory solution Illinois

ILLI-CALC ILLIPAVE Nonlinear elasto- Iterative University ofstatic finite Illinois

element modeling

ISSEM4 ELSYM5 Multilayer elastic Iterative R. Stubstud

MODCOMP CHEVRON Multilayer elastic Iterative L. Irwin, Szebenyi

MODULUS WESLEA Multilayer elastic Data Base TexasTransportation

Institute

PADAL PADAL Multilayer elastic Iterative S.F.Brown et al.

WESDEF WESLEA Multilayer elastic Iterative USACE-WES

MICHBACK CHEVRON Multilayer elastic Iterative Michigan StateUniversity

19

TABLE 2.2 Comparison of Selected Backcalculation Programs.

Name of the Forward Theoretical Back- Maximum Number of sensors Maximum Use of bedrock Temperature Developed Operatingmain program back- method for calculation number of used in analysis number of in corrections by Environment

calculation pavement method unknown different backcalculationsolution analysis layers load levels

MODCOMP3 CHEVRON Multilayer Iterative Five Internally or user Six Calculates depth No l. Irwin, DOSelastic Analysis specified number to bedrock upon Szebenyi,

of layer-sensor users request. Cornellassignments,up to Universityten sensors

MODULUS5.0 WESLEA Multilayer Data Base Four Program selects No limit Automatically No Texas DOSelastic Search optimum number calculates depth Trasportation

of sensors to use to bedrock and Institute in backcalculation, includes it in thecan be overridden analysis, can beby user through overridden byspecification of user.weighting factorsfor up to sevensensors

EVERCALC4.0 WESLEA Multilayer Iterative Five Up to seven sensors Eight Calculates depth Yes J. Mahoney, Windowselastic Analysis to bedrock only if University of

bedrock modulus Washingtonis known.

ELMOD4 ELMOD4, Odemark- Iterative Five As provided in raw as provided Calculates depth Yes Dynatest WindowsWES5 Boussinesq Analysis FWD data file in raw to bedrock and

FWD data includes it in thefile. analysis, can be

overridden byuser.

20

CHAPTER 3

COMPARISON OF BACKCALCULATION RESULTS

FOR SHRP TEST SECTIONS

To evaluate the performance of backcalculation programs, the deflections and loadings

measured for eight different SHRP sections were used with each of the four selected programs. The

data required for the backcalculation were obtained from the SHRP-P-651 report. The types of

materials and thicknesses for all eight sections are given in Figure 3.1. Six of the SHRP sections were

for flexible pavement structures and the other two were for composite pavements constructed by

overlaying original plain Portland Cement Concrete (PCC) pavement structures with asphaltic

concrete. The moduli ranges for the different sections were obtained from the literature. The values

were those commonly used to characterize a particular type of geologic material. When the

information on a particular material type was not available in the literature, the modulus range for this

material was interpolated from the published SHRP backcalculation results. The ranges of pavement

layers moduli and Poisson’s Ratios are presented in Table 3.1.

All of the selected programs, MODCOMP3, MODULUS5.0, EVERCALC4.0, and ELMOD4

produced sets of pavement moduli that were within an acceptable match with the published results

of backcalculation obtained from the SHRP project report, as listed in Table 3.2.

During different backcalculation runs, it was found that the inclusion or omission of a stiff

layer resulted in different values for subgrade modulus and affected, to some extent, the

backcalculated values of other layers. Inclusion of the stiff layer results in evaluation of a lower

subgrade modulus. This dependancy was observed mainly in MODCOMP3 and MODULUS5.0

programs.

It was noted that the results from MODCOMP3 program were very sensitive to the

assignment of the deflection sensor reading to a particular layer. Different layer-deflection

21

assignments may result in different results. Another disadvantage is that when the number of

deflection sensors exceed the number of pavement layers, some of the deflection sensor readings are

ignored in the backcalculation; and instead of the whole calculated deflection basin fit, only the

chosen deflection sensor readings are fitted with the calculated ones. This limited approach makes

the task of deflection basin fitting extremely difficult. A possible solution is to divide one or two

layers into sublayers so that the number of sensors and layers will be equal. This approach has two

drawbacks. First, it is difficult to decide which layers to subdivide so that the surface deflection will

accurately predict their deflections. Second, division of a layer into sublayers may result in the

calculation of two completely different moduli for the same layer.

The EVERCALC4.0 program terminates as soon as a moduli tolerance of one percent is

satisfied. However, frequently this solution does not satisfy the deflection basin tolerances and has

a high Root Mean Square value (RMS) error between measured and calculated deflections. All the

attempts to override the default, one percent moduli tolerance, have failed. The program does not

save this change upon its exit from the data input file. For most of the eight SHRP sections, subgrade

moduli backcalculated by EVERCALC4.0 program were around the upper bound of the moduli range

obtained from SHRP report. This might mean that EVERCALC4.0 has a tendency to overestimate

the subgrade modulus.

The ELMOD4 program produced good results for the flexible pavement sections with

unbound granular bases. However, backcalculations for the sections that include a stabilized or

concrete layer under the surface AC layer resulted in over prediction of the surface layer modulus and

under prediction of the base layer modulus. This could be due to the limitations of the ELMOD4

forward calculation algorithm that were discussed previously in Section 2.4.

The results of backcalculations for the eight SHRP sections are presented in Figures 3.2

through 3.9 for SHRP sections A through H. Each figure contains bar charts for comparison between

pavement layers moduli evaluated by the above four backcalculation programs and the maximum and

minimum values of moduli produced for the same layers during the SHRP project evaluation. All the

22

tested programs produced results that fall within the range obtained during SHRP project program

evaluation.

Out of the four tested programs, MODCOMP3 program proved to be the most user-sensitive

and required more engineering judgement. The approach of using seed moduli only, without

specifying the acceptable moduli range, can lead to the calculation of unexpectably high or low

moduli in different layers. The accuracy of the solution is highly dependent on the layer-deflection

assignments. Totally different sets of moduli can be backcalculated for different layer-deflection

assignments.

The ELMOD4 program failed to perform well on the sections that contained a stiff layer

under the AC surface. However, it produced good results for flexible pavement sections with

unbound granular bases.

Both MODULUS5.0 and EVERCALC4.0 are user-friendly and capable of producing

pavement moduli within an acceptable range. MODULUS5.0 program allows to internally assign

layer moduli based on the material types specified by the user. This feature can be advantageous if

the material type is known and supported by the program. The EVERCALC4.0 program is fitted

with a temperature correction option. This feature enables the user to adjust the backcalculated

modulus of the AC layer to the modulus value measured at the standard temperature testing

conditions.

23

TABLE 3.1 Moduli Range and Poisson’s Ratio for Backcalculation Inputs.

Material Type Moduli Range Poisson’s(Ksi) Ratio

Portland Cement Concrete 1000 - 10000 0.15

Asphalt Concrete (cold->hot) 200 - 2,500 0.25 - 0.35

Unstabilized Crushed Stone or Gravel Base Course (well drained) 10 - 160 0.35 - 0.40

Unstabilized Crushed Stone or Gravel Subbase (poorly drained) 10 - 100 0.40 - 0.42

Asphalt Treated Base 10 - 90 0.35

Sand Base 5 - 80 0.35

Sand Subbase 5 - 80 0.35

Cement-Stabilized Base and Subbase 500 - 2,500 0.25 - 0.35

Lime-Stabilized Base and Subbase 5 - 200 0.25 - 0.35

Subgrade Soil Cohesive Clay 3 - 4 0.42- 0.45

Subgrade Soil Fine-Grained Sands 25 - 30 0.42 - 0.45

Cement Stabilized Soil and Bedrock 100 - 1000 0.20

Lime Stabilized Soil 100 - 400 0.25

24

TABLE 3.2 Backcalculated Layer Moduli (ksi) for SHRP Sections.

Surface Layer Base Layer Subbase Layer Subgrade

SHRP Section AMODULUS 993 65.8 16.8 36.4

EVERCALC 918 70 14 39

MODCOMP3 1000 80.4 16.7 29.6

SHRP MAX 1320 92 92 40

SHRP MIN 720 10 10 13

SHRP Section B

MODULUS 1009 57.4 27.6

EVERCALC 813 87 23

MODCOMP3 547 175 24.2

SHRP MAX 1420 155 27

SHRP MIN 500 85 22

SHRP Section CMODULUS 566 500 36.5

EVERCALC 572 447 36

MODCOMP3 613 537 36.4

SHRP MAX 630 1020 37

SHRP MIN 450 400 26

SHRP Section DMODULUS 2526 678.7 20.1

EVERCALC 1933 967 20

MODCOMP3 2230 870 19.1

SHRP MAX 3050 2510 21

SHRP MIN 1400 430 12

SHRP Section EMODULUS 991 753.3 51.8 33.6

EVERCALC 1034 689 11 79

MODCOMP3 1090 696 157 63.3

SHRP MAX 2310 890 182 52

SHRP MIN 850 90 34 32

SHRP Section FMODULUS 1069 79.4 32.5

EVERCALC 1015 77 44

MODCOMP3 1180 50.3 41.3

SHRP MAX 1300 178 45

SHRP MIN 720 37 28

SHRP Section GMODULUS 1426 8311.8 19.5 21.6

EVERCALC 1248 7470 133 31

MODCOMP3 1050 7130 30 30.6

SHRP MAX 2440 11400 133 31

SHRP MIN 820 3900 19 18

SHRP Section HMODULUS 282 4272.3 26.1

EVERCALC 308 3789 25

MODCOMP3 239 6140 15.1

SHRP MAX 7761 6300 36

SHRP MIN 200 0 19

25

FIGURE 3.1 SHRP sections data used for backcalculations.

26

SHRP SECTION A

0

5

10

15

20

25

30

35

40

45

Subgrade

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION A

0

10

20

30

40

50

60

70

80

90

100

Subbase layer

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION A

0

10

20

30

40

50

60

70

80

90

100

Base layer

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION A

0

200

400

600

800

1000

1200

1400

Surface layer

Bac

kcal

cula

ted

mod

uli,

Ksi

FIGURE 3.2 Comparison of backcalculated moduli for SHRP section A.

27

SHRP SECTION B

0

200

400

600

800

1000

1200

1400

1600

Surface layer

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION B

0

5

10

15

20

25

30

Subgrade

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION B

0

20

40

60

80

100

120

140

160

180

200

Base layer

Bac

kcal

cula

ted

mod

uli,

Ksi

FIGURE 3.3 Comparison of backcalculated moduli for SHRP section B.

28

SHRP SECTION C

0

5

10

15

20

25

30

35

40

45

Subgrade

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION C

0

100

200

300

400

500

600

700

800

900

surface layer

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION C

0

200

400

600

800

1000

1200

Base layer

Bac

kcal

cula

ted

mod

uli,

Ksi

FIGURE 3.4 Comparison of backcalculated moduli for SHRP section C.

29

SHRP SECTION D

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Surface layer

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION D

0

500

1000

1500

2000

2500

3000

Base layer

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION D

0

5

10

15

20

25

Subgrade

Bac

kcal

cula

ted

mod

uli,

Ksi

FIGURE 3.5 Comparison of backcalculated moduli for SHRP section D.

30

FIGURE 3.6 Comparison of backcalculated moduli for SHRP section E.

SHRP SECTION E

0

10

20

30

40

50

60

70

80

90

Subgrade

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION E

0

20

40

60

80

100

120

140

160

180

200

Subbase layer

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION E

0

100

200

300

400

500

600

700

800

900

1000

Base layer

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION E

0

500

1000

1500

2000

2500

Surface layer

Bac

kcal

cula

ted

mod

uli,

Ksi

31

SHRP SECTION F

0

5

10

15

20

25

30

35

40

45

50

Subgrade

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION F

0

20

40

60

80

100

120

140

160

180

200

Base layer

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION F

0

200

400

600

800

1000

1200

1400

Surface layer

Bac

kcal

cula

ted

mod

uli,

Ksi

FIGURE 3.7 Comparison of backcalculated moduli for SHRP section F.

32

SHRP SECTION G

0

5

10

15

20

25

30

35

40

45

50

Subgrade

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION G

0

20

40

60

80

100

120

140

Subbase layer

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION G

0

2000

4000

6000

8000

10000

12000

Base layer

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION G

0

2000

4000

6000

8000

10000

12000

14000

Surface layer

Bac

kcal

cula

ted

mod

uli,

Ksi

FIGURE 3.8 Comparison of backcalculated moduli for SHRP section G.

33

SHRP SECTION H

0

5

10

15

20

25

30

35

40

Subgrade

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION H

0

2000

4000

6000

8000

10000

12000

14000

Surface layer

Bac

kcal

cula

ted

mod

uli,

Ksi

SHRP SECTION H

0

1000

2000

3000

4000

5000

6000

7000

Base layer

Bac

kcal

cula

ted

mod

uli,

Ksi

FIGURE 3.9 Comparison of backcalculated moduli for SHRP section H.

34

CHAPTER 4

COMPARISON OF BACKCALCULATION RESULTS

FOR SEVEN SELECTED SITES IN WEST VIRGINIA

FWD deflection data from seven different road sites in West Virginia were provided by

WVDOT for the backcalculation of layers moduli using three different backcalculation programs:

MODULUS5.0, EVERCALC4.0, and ELMOD4. The fourth program, MODCOMP3, was dropped

from the evaluation due to its high sensitivity to layer-deflection assignments, and its inability to

converge to a solution if a modulus of any layer, during the solution process, was found to be not

sensitive to a certain geophone deflection reading. Out of seven road sites, three were composite

pavements, two flexible, and two rigid. Pavement layer material types and layer thicknesses were

provided by WVDOT. Typical moduli ranges, as provided in Table 3.1, were used as seed moduli

values in the backcalculation programs.

In some cases, the backcalculation programs failed to produce a deflection basin that was

within the acceptable tolerance with the measured deflection basin. When this situation occurred, the

range of acceptable moduli was expanded in order to reach a convergence of the solution. The

assumptions used in backcalculations are provided in Table 4.1. When an infinite subgrade option

was used in the backcalculation analysis, most backcalculation programs over predicted the subgrade

moduli compared with the ones obtained through laboratory testing.

MODULUS5.0 and ELMOD4 programs calculate the depth to bedrock internally and use

this value in the backcalculation. Comparison of the backcalculated results obtained for different

pavement sections showed that when a section was assumed as infinitely thick, high values of the

subgrade moduli were frequently predicted. Inclusion of a finite depth to bedrock to the analysis led

to more realistic lower values for the subgrade moduli. EVERCALC4.0 calculates the depth to rigid

layer only if the subgrade modulus is provided. However, since the objective of backcalculation is

to obtain a subgrade modulus, the subgrade modulus is treated as an unknown. Therefore, it was not

35

possible to include the depth to bedrock in the analysis using EVERCALC4.0.

In practice, subgrades generally display an increase in the stiffness with depth due to

overburden pressure. However, laboratory tests are made for specimens of soil obtained immediately

after the base course. This resulted in a lower laboratory measured subgrade modulus. To account

for this, subgrade layers were divided into two layers and two different subgrade moduli were

evaluated for each section. In this case, the moduli of top subgrade layers were in closer agreement

with the laboratory measured moduli. This method did not work well with the ELMOD4 program

due to the limitation of the Transformed Section Method which is used as a forward calculation

algorithm. However, for the flexible pavement sections with granular bases, the ELMOD4 program

seems to produce reasonable subgrade moduli even with one layer subgrade system.

The following four step approach for evaluation of subgrade layer modulus was used in

backcalculation:

1. Run the program assuming that the subgrade layer is uniform and infinite and check the

subgrade modulus value. If the value is out of the expected moduli range for a given type of

subgrade material ( as given in Table 3.1) or the Root Mean Square (RMS) error for the

deflection basin fit is too high, proceed with the following steps.

2. Rerun the program using default depth to the subgrade layer calculated by the program and

check the moduli and RMS again.

3. If the resulting moduli in Step 2 are not acceptable, see if there will be any improvements by

increasing or deceasing the default depth value.

4. If subgrade modulus or RMS is not very sensitive to the changes in Step 3, subdivide the

subgrade layer into two sublayers with top subgrade sublayer height H not exceeding

36

H� (36" - Height of Pavement Structure above Subgrade)

Repeat the backcalculation process starting from Step 1.

The backcalculated moduli obtained for every pavement section using three different

backcalculation programs are given in Table 4.2. Table 4.3 shows which of the moduli were lower,

higher, or within the range of moduli acceptable for the section materials types. Table 4.4

summarizes the accuracy of the backcalculation results for different programs and pavement types.

From the section by section comparison of the performances of the three backcalculation

programs the following conclusions were drawn:

1. MODULUS5.0 performed well with all three types of pavement structures. This program

consistently produced subgrade moduli that were reasonably close to the laboratory evaluated

values and within the material range (below 25 psi), as shown in Figures 4.1 through 4.20.

During the backcalculation process, the first program run for each section was carried out

assuming an infinite subgrade layer. If the percent of error was greater than five, then the

finite depth to bedrock calculated during the first run was obtained and another run of the

program was carried out assuming bedrock at a finite depth. This procedure always resulted

in lowering the percentage of error.

2. ELMOD4 predictions were very poor for the composite pavement sections. Out of the three

different pavement types shown in Figures 4.1 through 4.20, the program worked best with

flexible pavements. For flexible pavements, all backcalculated moduli for the surface and base

layers were within the acceptable range of pavement moduli. In the case of composite

pavements, the program produced very high moduli for the surface and subgrade layers and

very low moduli for the base layer, as shown in Figures 4.2 through 4.9. It was concluded

that the program works only in cases where the layer moduli gradually decrease with depth.

The program performed a little better with the rigid sections; however, the ELMOD4

37

program over predicted subgrade moduli in three out of five rigid pavement cases.

3. EVERCALC4.0 worked fairly well with flexible and rigid pavements. However, in some

flexible and rigid cases, backcalculated moduli for the base layer were on the low margin of

acceptance. In three out of seven cases for the flexible pavement sections and in three out of

five cases for rigid pavements, the program backcalculated very low modulus values for the

base layers. For all composite pavement sections, high moduli values were predicted for the

subgrade. The resulting moduli for surface and base layers in the composite pavement

sections were either under predicted or over predicted compared to the acceptable range of

moduli, and no common trend was possible to track down.

38

TABLE 4.1 Assumptions Used in Different Backcalculation Algorithms.

BackcalculationProgram

Road/StationNumber

PavementType

Moduli Range , Ksi SubgradeDepth toBedrock (in.).

SurfaceLayer

Base Subgrade Second SubgradeModulus if it isSubdivided intoTwo Layers

MODULUS5.0 US52/16.250 flexible 300-3000 5-100 4-7 calculated internally 183.7

ELMOD4 US52/16.250 flexible n / a n / a n / a 0 max 300

EVERCALC4.0 US52/16.250 flexible 200-3000 5-100 2-6 2-60 infinity

MODULUS5.0 US52/18.360 composite 200-3000 1000-9000 4-10 calculated internally 227.2

ELMOD4 US52/18.360 composite n / a n / a n / a 0 max 300

EVERCALC4.0 US52/18.360 composite 200-2500 1000-10000 3-20 2-45 infinity




MODULUS5.0 US60/1.230 composite 200-3000 1000-7000 4-6 calculated internally 300









MODULUS5.0 WV2/4.926 composite 200-3000 1000-9000 4-10 calculated internally 202.3

ELMOD4 WV2/4.926 composite n / a n / a n / a 0 max 300

EVERCALC4.0 WV2/4.926 composite 120-3000 100-7000 2-60 4.35 infinity

MODULUS5.0 WV2/6.100 composite 200-3000 1000-9000 4-10 calculated internally 300


EVERCALC4.0 WV2/6.100 composite 120-3000 100-7000 2-60 4-35 infinity

MODULUS5.0 WV2/7.333 composite 200-3000 1000-9000 4-10 calculated internally 121.3


EVERCALC4.0 WV2/7.333 composite 120-3000 100-7000 2-60 4-35 infinity

MODULUS5.0 WV3/40.806 flexible 200-3000 5-160 4-18 calculated internally 183.7

ELMOD4 WV3/40.806 flexible n / a n / a n / a 0 max 300

EVERCALC4.0 WV3/40.806 flexible 120-3000 -5-160 2-60 2-60 infinity

39

BackcalculationProgram

Road/StationNumber

PavementType

Moduli Range , Ksi SubgradeDepth toBedrock (in.)

SurfaceLayer

Base Subgrade Second SubgradeModulus if it issubdivided intoTwo Layers



EVERCALC4.0 WV3/41.013 flexible 120-3000 5-160 2-60 2-60 infinity













MODULUS5.0 WV2/18.250 rigid 1000-10000 10-160 4-18 calculated internally 182.7

ELMOD4 WV2/18.250 rigid n / a n / a n / a 0 max 300

EVERCALC4.0 WV2/18.250 rigid 1000-1000 10-160 2-60 3-38 infinity

MODULUS5.0 WV2/19.028 rigid 1000-10000 10-160 5-7 calculated internally 279.2

ELMOD4 WV2/19.028 rigid n / a n / a n / a 0 max 300

EVERCALC4.0 WV2/19.028 rigid 1000-1000 10-160 4-10 3-38 infinity

MODULUS5.0 US19/20.856 rigid 1000-10000 10-160 5-7 calculated internally 300

ELMOD4 US19/20.856 rigid n / a n / a n / a 0 max 300

EVERCALC4.0 US19/20.856 rigid 1000-1000 5-160 4-10 3-38 infinity

MODULUS5.0 US19/21.563 rigid 1000-10000 10-160 5-7 calculated internally 300



MODULUS5.0 US19/21.839 rigid 1000-10000 10-160 5-8 calculated internally 202.6



40

TABLE 4.2a Backcalculated Layer Moduli (Ksi) for Flexible Pavement Sections.

Site/Station Program Surface Layer Base Layer Top Subgrade

Layer

Subgrade

US52_pre

Station

16.250

MODULUS5.0 594.0 42.6 7.0 17.1

ELMOD4 537.0 27.0 14.8 14.8

EVERCALC4.0 510.0 61.0 7.0 20.0

WV3_whit

Station

40.806

MODULUS5.0 321.0 14.8 7.3 18.9

ELMOD4 315.0 12.7 19.5 19.5

EVERCALC4.0 291.0 7.0 12.0 26.0

WV3_whit

Station

41.013

MODULUS5.0 366.0 43.6 11.0 11.8

ELMOD4 360.0 32.3 10.1 10.1

EVERCALC4.0 418.0 5.0 3.0 24.0

WV3_whit

Station

41.221

MODULUS5.0 454.0 66.7 15.8 9.3

ELMOD4 540.0 61.7 9.8 9.8

EVERCALC4.0 520.0 18.0 16.0 12.0

WV71_blu

Station 0.009

MODULUS5.0 643.0 17.1 4.9 30.4

ELMOD4 487.0 59.6 11.2 11.2

EVERCALC4.0 751.0 5.0 4.0 35.0

WV71_blu

Station 1.259

MODULUS5.0 508.0 6.3 12.5 6.7

ELMOD4 498.0 8.1 8.0 8.0

EVERCALC4.0 425.0 5.0 3.0 27.0

WV_whit

Station 2.740

MODULUS5.0 274.0 9.7 4.9 6.2

ELMOD4 247.0 9.9 8.0 8.0

EVERCALC4.0 264 5.0 4.0 50

41

TABLE 4.2b Backcalculated Layer Moduli (Ksi) for Composite Pavement Sections.

Site/Statiom Program Surface Layer Concrete

Slab

Base Layer Subgrade

US52_pre

Station

18.360

MODULUS5.0 561.0 6122.9 8.0 36.1

ELMOD4 621.0 1214.0 49.8 49.8

EVERCALC4.0 516.0 7026.0 25.0 45.0

US52_pre

Station

19.179

MODULUS5.0 422.0 1638.7 8.8 34.9

ELMOD4 654.0 606.0 35.3 35.3

EVERCALC4.0 445.0 1023.0 17.0 36.0

US60_smi

Stastion

1.230

MODULUS5.0 274.0 6196.0 5.2 16.6

ELMOD4 973.0 611.0 23.5 23.5

EVERCALC4.0 273.0 3920.0 7.0 24.0

US60_smi

Sration 2.267

MODULUS5.0 747.0 2267.2 4.9 17.7

ELMOD4 4255.0 84.1 19.3 19.3

EVERCALC4.0 3000.0 384.0 14.0 30.0

WV2_frie

Station 4.926

MODULUS5.0 1620.0 1823.7 5.3 16.2

ELMOD4 8884.0 30.2 20.0 20.0

EVERCALC4.0 3000.0 550.0 5.0 35.0

WV2_frie

Station 4.926

MODULUS5.0 203.0 1326.7 7.7 19.8

ELMOD4 264.0 434.0 26.7 26.7

EVERCALC4.0 192.0 1323.0 4.0 29.0

WV2_frie

Station 6.100

MODULUS5.0 200.0 1910.1 11.0 18.6

ELMOD4 240.0 722.0 22.8 22.8

EVERCALC4.0 137.0 2473.0 22.0 22.0

WV2_frie

Station 7.333

MODULUS5.0 222.0 600.0 4.0 20.9

ELMOD4 305.0 136.0 31.9 31.9

EVERCALC4.0 301.0 121.0 11.0 35.0

42

TABLE 4.2c Backcalculated Layer Moduli (Ksi) for Rigid Pavement Sections.

Site/Station Program Surface Layer Base Layer Top Subgrade

Layer

Subgrade

US2_moun

Station

18.250

MODULUS5.0 5280.0 21.9 6.2 22.4

ELMOD4 4840.4 5.2 37.4 37.43

EVERCALC4.0 4308.0 17.0 4.0 38.0

US2_moun

Station

19.028

MODULUS5.0 6567.0 34.6 5.5 14.8

ELMOD4 6157.0 1.5 32.6 32.6

EVERCALC4.0 5679.0 10.0 4.0 23.0

US19_hic

Station

20.856

MODULUS5.0 8152.0 25.1 5.6 14.2

ELMOD4 6706.0 24.5 15.1 15.1

EVERCALC4.0 5948.0 5.0 3.0 18.0

US_hic

Station

21.653

MODULUS5.0 5094.0 20.1 6.4 7.0

ELMOD4 4117.0 16.0 10.6 10.6

EVERCALC4.0 3869.0 5.0 3.0 12.0

US_hic

Station

21.839

MODULUS5.0 7160.0 39.5 5.3 14.7

ELMOD4 4565.0 39.3 26.0 26.0

EVERCALC4.0 4716.0 5.0 3.0 34.0

43

TABLE 4.3 Comparison of Pavement Moduli Backcalculated by Different Programs.

Backcalculationprogram

Road/StationNumber

Pavement Type SurfaceLayer

Base Top Subgrade

MODULUS5.0 US52/16.250 flexible acceptable acceptable acceptable

ELMOD4 US52/16.250 flexible acceptable acceptable acceptable

EVERCALC4.0 US52/16.250 flexible acceptable acceptable acceptable

MODULUS5.0 US52/18.360 composite acceptable acceptable high

ELMOD4 US52/18.360 composite acceptable acceptable high

EVERCALC4.0 US52/18.360 composite acceptable acceptable high

MODULUS5.0 US52/19.179 composite acceptable acceptable high

ELMOD4 US52/19.179 composite acceptable low high

EVERCALC4.0 US52/19.179 composite acceptable acceptable high

MODULUS5.0 US60/1.230 composite acceptable acceptable acceptable

ELMOD4 US60/1.230 composite acceptable low high

EVERCALC4.0 US60/1.230 composite acceptable high high

MODULUS5.0 US60/2.267 composite acceptable high acceptable

ELMOD4 US60/2.267 composite very high very low high

EVERCALC4.0 US60/2.267 composite high very low high

MODULUS5.0 US60/3.393 composite acceptable acceptable acceptable

ELMOD4 US60/3.393 composite acceptable very low high

EVERCALC4.0 US60/3.393 composite acceptable low high

MODULUS5.0 WV2/4.926 composite acceptable acceptable acceptable

ELMOD4 WV2/4.926 composite acceptable low high

EVERCALC4.0 WV2/4.926 composite acceptable acceptable high

MODULUS5.0 WV2/6.100 composite acceptable acceptable acceptable


EVERCALC4.0 WV2/6.100 composite low acceptable high

MODULUS5.0 WV2/7.333 composite acceptable acceptable high


EVERCALC4.0 WV2/7.333 composite acceptable low high

MODULUS5.0 WV3/40.806 flexible acceptable acceptable high

ELMOD4 WV3/40.806 flexible acceptable acceptable high

EVERCALC4.0 WV3/40.806 flexible acceptable acceptable high

44

Backcalculation program Road/StationNumber

Pavement Type SurfaceLayer

Base Top Subgrade

MODULUS5.0 WV3/41.013 flexible acceptable acceptable acceptable

ELMOD4 WV3/41.013 flexible acceptable acceptable acceptable

EVERCALC4.0 WV3/41.013 flexible acceptable acceptable high



EVERCALC4.0 WV3/41.221 flexible acceptable acceptable acceptable



EVERCALC4.0 WV71/0.009 flexible acceptable low high







MODULUS5.0 WV2/18.250 rigid acceptable acceptable high

ELMOD4 WV2/18.250 rigid acceptable acceptable high

EVERCALC4.0 WV2/18.250 rigid acceptable acceptable high

MODULUS5.0 WV2/19.028 rigid acceptable acceptable acceptable

ELMOD4 WV2/19.028 rigid acceptable acceptable high

EVERCALC4.0 WV2/19.028 rigid acceptable low high


ELMOD4 WV19/20.856 rigid acceptable acceptable acceptable

EVERCALC4.0 WV19/20.856 rigid acceptable low acceptable


ELMOD4 US19/21.563 rigid acceptable acceptable acceptable

EVERCALC4.0 US19/21.563 rigid acceptable low acceptable

MODULUS5.0 US19/21.839 rigid acceptable acceptable high

ELMOD4 US19/21.839 rigid acceptable acceptable high

EVERCALC4.0 US19/21.839 rigid acceptable acceptable high

45

TABLE 4.4 Number of Backcalculated Out of Range Moduli.

Backcalculation

Program

Flexible Pavement

Sections

Composite Pavement

Sections

Rigid Pavement Sections

Surface

layer

Base Subgrade Surface

layer

Base Subgrade Surface

layer

Base Subgrade

MODULUS5.0 0 0 3/7 0 1/8 3/8 0 0 2/5

ELMOD4 0 0 1/7 2/9 7/8 8/8 0 0 3/5

EVERCALC4.0 0 3/7 5/7 3/9 4/8 8/8 0 3/5 3/5

46

460

480

500

520

540

560

580

600

620

Surface Layer

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4EVERCALC4.0

0

10

20

30

40

50

60

70

Base Layer

Mod

ulus

(K

si)


0

2

4

6

8

10

12

14

16

Top SubgradeM

odul

us (

Ksi

)


0

5

10

15

20

25

Subgrade

Mod

ulus

(K

si)


FIGURE 4.1 Backcalculated layer moduli (Ksi) for flexible pavement section US52_pre station 16.250.

47

0

100

200

300

400

500

600

700

Surface Layer

Mod

ulus

(K

si)


0

1000

2000

3000

4000

5000

6000

7000

8000

PCC Slab

Mod

ulus

(K

si)


0

10

20

30

40

50

60

Base LayerM

odul

us (

Ksi

)


0

10

20

30

40

50

60

Subgrade

Mod

ulus

(K

si)


FIGURE 4.2 Backcalculated layer moduli (Ksi) for composite pavement section US52_pre station 18.360.

48

0

100

200

300

400

500

600

700

Surface Layer

Mod

ulus

(K

si)


0

200

400

600

800

1000

1200

1400

1600

1800

PCC Slab

Mod

ulus

(K

si)


0

5

10

15

20

25

30

35

40

Base LayerM

odul

us (

Ksi

)


34.2

34.4

34.6

34.8

35

35.2

35.4

35.6

35.8

36

36.2

Subgrade

Mod

ulus

(K

si)


FIGURE 4.3 Backcalculated layer moduli (Ksi) for composite pavement section US52_pre station 19.179.

49

0

200

400

600

800

1000

1200

Surface Layer

Mod

ulus

(K

si)


0

1000

2000

3000

4000

5000

6000

7000

PCC Slab

Mod

ulus

(K

si)


0

5

10

15

20

25

Base LayerM

odul

us (

Ksi

)


0

5

10

15

20

25

30

Subgrade

Mod

ulus

(K

si)


FIGURE 4.4 Backcalculated layer moduli (Ksi) for composite pavement section US60_smi station 1.230.

50

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Surface Layer

Mod

ulus

(K

si)


0

500

1000

1500

2000

2500

PCC Slab

Mod

ulus

(K

si)


0

5

10

15

20

25

Base LayerM

odul

us (

Ksi

)


0

5

10

15

20

25

30

35

Subgrade

Mod

ulus

(K

si)



51

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Surface Layer

Mod

ulus

(K

si)


0

200

400

600

800

1000

1200

1400

1600

1800

2000

PCC Slab

Mod

ulus

(K

si)


0

5

10

15

20

25

Base LayerM

odul

us (

Ksi

)


0

5

10

15

20

25

30

35

40

Subgrade

Mod

ulus

(K

si)



52

0

200

400

600

800

1000

1200

1400

PCC Slab

Mod

ulus

(K

si)


0

5

10

15

20

25

30

Base LayerM

odul

us (

Ksi

)


0

5

10

15

20

25

30

35

Subgrade

Mod

ulus

(K

si)


0

50

100

150

200

250

300

Surface Layer

Mod

ulus

(K

si)


FIGURE 4.7 Backcalculated layer moduli (Ksi) for composite pavement section WV2_frie station 4.926.

53

0

50

100

150

200

250

300

Surface Layer

Mod

ulus

(K

si)


0

500

1000

1500

2000

2500

3000

PCC Slab

Mod

ulus

(K

si)


0

5

10

15

20

25

Base LayerM

odul

us (

Ksi

)


0

5

10

15

20

25

Subgrade

Mod

ulus

(K

si)



54

0

50

100

150

200

250

300

350

Surface Layer

Mod

ulus

(K

si)


0

100

200

300

400

500

600

700

PCC Slab

Mod

ulus

(K

si)


0

5

10

15

20

25

30

35

40

Base LayerM

odul

us (

Ksi

)


0

5

10

15

20

25

30

35

40

Subgrade

Mod

ulus

(K

si)



55

275

280

285

290

295

300

305

310

315

320

325

Surface Layer

Mod

ulus

(K

si)


0

2

4

6

8

10

12

14

16

Base Layer

Mod

ulus

(K

si)


0

5

10

15

20

25

Top SubgradeM

odul

us (

Ksi

)


0

5

10

15

20

25

30

Subgrade

Mod

ulus

(K

si)


FIGURE 4.10 Backcalculated layer moduli (Ksi) for flexible pavement section WV3_whit station 40.806.

56

330

340

350

360

370

380

390

400

410

420

430

Surface Layer

Mod

ulus

(K

si)


0

5

10

15

20

25

30

35

40

45

50

Base Layer

Mod

ulus

(K

si)


0

2

4

6

8

10

12

Top Subgrade

Mod

ulus

(K

si)


0

5

10

15

20

25

30

Subgrade

Mod

ulus

(K

si)



57

400

420

440

460

480

500

520

540

560

Surface Layer

Mod

ulus

(K

si)


0

10

20

30

40

50

60

70

80

Base Layer

Mod

ulus

(K

si)


0

2

4

6

8

10

12

14

16

18

Top SubgradeM

odul

us (

Ksi

)


0

2

4

6

8

10

12

14

Subgrade

Mod

ulus

(K

si)



58

0

100

200

300

400

500

600

700

800

Surface Layer

Mod

ulus

(K

si)


0

10

20

30

40

50

60

70

Base Layer

Mod

ulus

(K

si)


0

2

4

6

8

10

12

Top SubgradeM

odul

us (

Ksi

)


0

5

10

15

20

25

30

35

40

Subgrade

Mod

ulus

(K

si)


FIGURE 4.13 Backcalculated layer moduli (Ksi) for flexible pavement section WV71_blu station 0.009.

59

380

400

420

440

460

480

500

520

Surface Layer

Mod

ulus

(K

si)


0

1

2

3

4

5

6

7

8

9

Base Layer

Mod

ulus

(K

si)


0

2

4

6

8

10

12

14

Top SubgradeM

odul

us (

Ksi

)


0

5

10

15

20

25

30

Subgrade

Mod

ulus

(K

si)



60

0

1000

2000

3000

4000

5000

6000

PCC Slab

Mod

ulus

(K

si)


0

5

10

15

20

25

Base Layer

Mod

ulus

(K

si)


0

5

10

15

20

25

30

35

40

Subgrade

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

5

10

15

20

25

30

35

40

Top SubgradeM

odul

us (

Ksi

)

MODULUS5.0 ELMOD4

EVERCALC4.0


61

0

1000

2000

3000

4000

5000

6000

Surface Layer

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

5

10

15

20

25

Base Layer

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

5

10

15

20

25

30

35

40

Top SubgradeM

odul

us (

Ksi

)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

5

10

15

20

25

30

35

40

Subgrade

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

FIGURE 4.16 Backcalculated layer moduli (Ksi) for rigid pavement section US2_moun station 18.250.

62

5200

5400

5600

5800

6000

6200

6400

6600

6800

Surface Layer

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

5

10

15

20

25

30

35

40

Base Layer

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

5

10

15

20

25

30

35

Top SubgradeM

odul

us (

Ksi

)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

5

10

15

20

25

30

35

Subgrade

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

FIGURE 4.17 Backcalculated layer moduli (Ksi) for rigid pavement section US2_moun station 19.028.

63

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

Surface Layer

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

2

4

6

8

10

12

14

16

Top SubgradeM

odul

us (

Ksi

)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

5

10

15

20

25

30

Base Layer

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

2

4

6

8

10

12

14

16

18

20

Subgrade

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

FIGURE 4.18 Backcalcualted layer moduli (Ksi) for rigid pavement section US19_hic station 20.856.

64

0

1000

2000

3000

4000

5000

6000

Surface Layer

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

5

10

15

20

25

Base Layer

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

2

4

6

8

10

12

14

16

Top SubgradeM

odul

us (

Ksi

)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

2

4

6

8

10

12

14

Subgrade

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

FIGURE 4.19 Backcalculated layer moduli (Ksi) for rigid pavement section US19_hic station 21.563.

65

0

1000

2000

3000

4000

5000

6000

7000

8000

Surface Layer

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

5

10

15

20

25

30

35

40

45

Base Layer

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

5

10

15

20

25

30

Top SubgradeM

odul

us (

Ksi

)

MODULUS5.0 ELMOD4

EVERCALC4.0

0

5

10

15

20

25

30

35

40

Subgrade

Mod

ulus

(K

si)

MODULUS5.0 ELMOD4

EVERCALC4.0

FIGURE 4.20 Backcalculated layer moduli (Ksi) for rigid pavement section US19_hic station 21.839.

66

CHAPTER 5

FIELD TESTING

5.1 PAVEMENT SITES

Field tests were performed at three different sites located in Morgantown, West Virginia. The

selected sites were chosen to be representative of the three types of pavement structures: rigid,

flexible, and composite (rigid pavement overlaid by asphalt layer). In each tested site, the pavement

surface was checked so that it was free from visible signs of distress such as transverse or longitudinal

cracks.

1. Flexible Pavement Site

This site was the traffic lane of a divided four-lane road on Route 857, opposite Mountaineer

Mall. The lane width is 12 ft. and the asphalt concrete layer is 9 in. thick constructed over a 7 in. base

of crushed stone. The subgrade soil is a clay material. Figure 5.1 illustrates the different layers in this

section.

2. Rigid Pavement Site

This site was located on Route 857. The traffic lane of a divided four-lane jointed Portland

cement concrete pavement with untied shoulder. The spacing between the transverse joints in this

site varied between 20 and 45 ft. The lane is 12 ft. wide and the slab is 9 in. thick. The slabs are

supported by an 8 in. thick granular base of crushed stone. The subgrade soil in this site was silty clay.

Figure 5.2 provides a section of this site showing the different layers.

3. Composite Pavement Site

This site was located on Interstate I-68, station 2.644. The test was performed on the traffic

lane of the eastbound side. The pavement section consists of a 9.5 in. concrete slab overlaid by a 5

in. asphalt concrete layer. The concrete slab is supported by a 3 in. base of crushed stone. The

67

subgrade soil is clay material. Figure 5.3 illustrates the different layers of this pavement section.

Each site was fitted with a set of sensors to measure the temperature gradient and

displacements of the layers due to the application of FWD load. Two boreholes were drilled in each

site for the placement of these gauges. The two boreholes were placed at a distance of 6 ft from each

other as shown in Figure 5.4. Each borehole was drilled to a depth of 32 in. and core samples were

taken for laboratory testing by WVDOH. All boreholes were placed at a distance of 1 ft from the

shoulder edge of the traffic lane. During borehole sampling the correct thickness of each pavement

structure was identified and recorded. After placing the sensors in each borehole, it was filled with

fine sand and covered on top with a concrete mix. All lead cables of geophones and thermocouples

from each borehole were routed into a 0.75 in. deep groove sawn in the surface layer leading to the

end of the shoulder and then covered with concrete grouting. Each trench terminates with a small

hole to keep the ends of the cables accessible for measurements.

5.2 MEASUREMENTS

Temperature gradient through the depth of pavement structure was measured using

thermocouples. The thermocouples were placed such that one was at the interface between the base

and subgrade, and another at the interface between the surface layer and the base. For the composite

pavement site, an additional thermocouple was placed at the interface between the asphaltic layer and

the concrete. The connecting cables of each thermocouple were covered with Teflon. Additionally,

the cables were environmentally shielded using a 0.25 in. diameter polyethylene tube that extended

the full length of the cable. The connections of the tube with the thermocouple-sensing element were

sealed using a heat shrink water-proof tube. Each thermocouple was placed in position inside a 3 in.

diameter borehole that was drilled adjacent to the shoulder edge of the pavement site. Each

thermocouple had a sensitivity of 0.1(F. The temperature readings were acquired using a hand held

digital readout unit, type HH-21 produced by the OMEGA company. At the time of the Falling

Weight Deflectometer test, acquired temperature measurements were as follows:

68

Rigid Pavement Site

On top of the concrete slab T = 47.0 Foo

At the concrete-base interface T = 49.5 F1o

At the base-subgrade interface T = 51.5 F2o

Flexible Pavement Site

On top of the asphaltic layer T = 38.5 Foo

At the asphalt-base interface T = 41.0 F1o


Composite Pavement Site

On the top the of asphaltic layer T = 38.3 Foo

At the asphalt-concrete interface T = 40.3 F1o

At the concrete-base interface T = 41.4 F2o


None of the temperature measurements showed a significant temperature gradient, due to the

fact that the measurements were carried out during the months of March and April from 10:00 am

to 2:00 pm. The absence of a significant thermal gradient was considered advantageous from the

point of view of finite element modeling.

It was the intention in this study to measure the displacement of every pavement layer in order

to observe the possibility of separation between layers and to provide additional confirmation of the

accuracy of the finite element models. For this reason, a set of twelve geophones were acquired with

the following specifications:

Geophone type: PE-8-SM 6UB

Manufacturer: SENSOR, Netherlands.

Measuring direction: Vertical

69

Resistance: 375 Ohm

Resonant frequency: 4.5 Hz

Each geophone was placed in an environmentally isolated casing to protect the sensing

element from being damaged by underground water or humidity. During the installation of geophones

in each borehole, care was taken to ensure that they were vertically aligned inside each hole. The

displacement data measured from the geophones contained significantly high levels of noise, which

hindered any reliable readings. Considering the effort of arranging for traffic control and because of

the time span of the project, no attempts were made to replace the geophones with more sophisticated

sensors. Thus, additional geophone measurements were omitted on the basis that verification of the

FE models could be achieved through an additional comparison of the deflection-time histories with

those measured using FWD geophones.

5.3 DEFLECTION TESTING

The Falling Weight Deflectometer (FWD) test was performed using WVDOH equipment.

The equipment is manufactured by DYNATEST and operated by WVDOH Materials Division

personnel. The FWD was calibrated in accordance with SHRP procedures in May 1997. The

calibration results demonstrated that both the FWD load cell and sensors were in excellent condition,

and that their readings fell within the tolerance range set by the manufacturer. During each FWD test,

surface deflections were measured using nine geophone sensors located at distances of 0, 8, 12, 18,

24, 36, 48, 60, and 72 in. away from the center of the 11.8 in. diameter steel loading plate. The

sensors’ positions remained unchanged for all three pavement sites.

For every pavement site, the FWD deflection data were collected at three drop heights. At

each height two drops were made in accordance with ASTM-Standard D 4694 - 87, article 9.4.

Since the temperature measurements did not show appreciable thermal gradient, no temperature

corrections were considered necessary during the backcalculation of layers moduli. Table 5.1

70

contains a list of the load and deflection data measured using FWD for the three tested sites.

Additionally, the data were acquired in graphical format and the loading curves were digitized for use

with the finite element models, as will be discussed in the next chapter.

5.4 EVALUATION OF BACKCALCULATED MODULI

FWD deflection data obtained from testing the three sites were analyzed using three different

backcalculation programs: MODULUS5.0, EVERCALC4.0, and MODCOMP3. The information

required for the evaluation of layers moduli for each site includes the deflection data and the

pavement profile. The pavement profile consists of layer thicknesses and material types. The

material types were determined from visual examination of the layers material extracted during

borehole drilling. All backcalculation programs require the user to supply seed values for the moduli

of each layer. Those values were selected by referring to the ranges listed in Table 3.1. In some

circumstances, the backcalculation program failed to produce a deflection basin that fits the measured

one within the specified tolerance. In this case, the moduli ranges were expanded to reach a

convergence of the solution. As discussed in Chapter 4, the subgrade layers were divided into two

layers to take into account the change of the value of subgrade modulus with depth. Consequently,

two different subgrade moduli were evaluated for each section.

The results of backcalculated moduli obtained for each pavement section are given in Table

5.2. For every pavement site, an average modulus was estimated for each layer. This average was

obtained by taking the mean of the three moduli produced for the same layer by the three

backcalculation programs. Next, the average was used to estimate the Percent Deviation From

Average (PDFA) in modulus produced by each program (shown in Table 5.2 as percent error).

5.5 CONCLUSIONS

Based on the results listed in Table 5.2, the following conclusions were reached:

71

1. MODULUS5.0 program performed well with all types of pavement structures and resulted

in moduli values that seemed reasonable and close to the average.

2. EVERCALC4.0 program overestimated the values of subgrade moduli for the three types of

pavements compared to the other two programs. For the composite pavement structure, the

program overestimated the modulus of the asphalt layer.

3. MODCOMP3 program resulted in moduli values which seemed to be reasonable and within

the material range. However, the resulting modulus value of the concrete layer in the rigid

pavement section seemed to be high compared with those resulting from the other two

programs. This program requires more engineering judgement and experience from the user

in introducing the values of seed moduli for different layers to obtain reasonable results. The

high sensitivity of the program to the deflection reading assignments may cause the

termination of the program if the values of seed moduli are not compatible with the deflection

readings.

4. Comparison of the backcalculated moduli for the pavement layers reveals that for each

pavement type the results obtained using MODULUS5.0 were always close to the average

obtained from all three programs. The values of the layers moduli obtained for all pavement

structures using MODULUS5.0 seemed reasonable and the mean percent difference did not

exceed eleven percent.

5. None of the three programs tested in this study produced extremely unreasonable values.

This is reflected in the fact that the error relative to the average calculated modulus never

exceeded 100 percent for any layer.

6. It should be remembered that all three programs evaluated in this study are designed primarily

to handle flexible pavements. The capability of predicting layers moduli for rigid and

composite pavements is an added advantage.

72

TABLE 5.1 Deflection Data Collected from Field Tests.

Applied load Radial offset from center of loading plate (in.)

lbf psi 0.00 8.00 12.00 18.00 24.00 36.00 48.00 60.00 72.00

RIGID PAVEMENT SITE:

10124 92.6 3.46 3.23 3.04 2.74 2.43 1.90 1.40 0.98 0.69

10135 92.7 3.46 3.19 3.02 2.74 2.43 1.89 1.40 0.96 0.69

13110 119.9 4.63 4.30 4.05 3.66 3.25 2.52 1.87 1.35 0.98

13186 120.6 4.66 4.26 4.03 3.66 3.26 2.52 1.87 1.35 0.98

17877 163.5 6.37 5.89 5.56 5.04 4.47 3.47 2.59 1.89 1.38

17899 163.7 3.36 5.85 5.54 5.03 4.46 3.47 2.59 1.89 1.38

FLEXIBLE PAVEMENT SITE:

10037 91.8 10.11 8.82 7.97 6.78 5.70 3.88 2.45 1.49 1.02

10048 91.9 10.13 8.84 7.99 6.79 5.72 3.91 2.46 1.46 1.02

12793 117.0 13.33 11.73 10.63 9.10 7.67 5.21 3.40 2.15 1.29

12815 117.2 13.40 11.79 10.69 9.17 7.72 5.25 3.42 2.15 1.30

17853 164.2 18.23 16.07 14.60 12.58 10.62 7.41 4.81 2.97 1.96

17998 164.6 18.08 15.96 14.50 12.47 10.53 7.35 4.77 2.95 1.95

COMPOSITE PAVEMENT SITE:

9873 90.3 2.96 2.45 2.31 2.17 2.03 1.66 1.32 1.03 0.77

9873 90.3 2.97 2.46 2.31 2.19 2.03 1.68 1.32 1.03 0.79

12596 115.2 3.99 3.32 3.14 2.96 2.75 2.28 1.84 1.41 1.10

12617 115.4 4.00 3.35 3.15 2.97 2.76 2.29 1.83 1.41 1.09

17330 158.0 5.51 4.63 4.37 4.14 3.83 3.19 2.54 1.99 1.54

17384 159.0 5.50 4.62 4.36 4.13 3.82 3.19 2.55 1.98 1.54

73

Table 5.2 BACKCALCULATED LAYERS MODULI (Ksi).

PROGRAM Surface PDFA* Base PDFA Subgrade PDFA Subgrade PDFATop** Bottom

FLEXIBLE MODULUS 837 20.5% 34.9 -32.1% 10.7 18.9% 9.3 -50.0%

EVERCALC 338 -51.3% 100 94.4% 4.7 -48.1% 34.5 85.5%

MODCOMP 909 30.9% 19.4 -62.3% 11.6 28.8% 12 -35.5%

LAYERAVERAGE

694.6 51.4 9.00 18.6

RIGID

MODULUS 3278 -0.7% 162 11.2% 13.4 10.9% 14.5 -44.2%

EVERCALC 2997 -20.2% 52 -64.3% 20 65.6% 50 92.3%

MODCOMP 4540 20.9% 223 53.1% 2.8 -76.5% 13.5 -48.1%

LAYERAVERAGE

3755 145.7 12.1 26.0

COMPOSITE

MODULUS 805 -33.6% 5880 9.7% 156 39.3% 13.7 -33.0%

EVERCALC 2000 65.0% 5000 -6.7% 100 -10.7% 30 46.8%

MODCOMP 832 -31.4% 5200 -3.0% 80 -28.6% 17.6 -13.9%

LAYERAVERAGE

1212.3 5360 112 20.4

* PDFA= Percent Deviation from Average.** The subgrade was divided into two layers for the purpose of backcalculation.

75

FIGURE 5.4 Instrumentation layout.

76

CHAPTER 6

EVALUATION OF BACKCALCULATION ALGORITHMS

THROUGH FINITE ELEMENT MODELING OF FWD TEST

6.1 INTRODUCTION

In this chapter, a new approach for the evaluation of the performance of backcalculation

algorithms is developed using Finite Element (FE) analysis. Currently, the only means of assessing

the performance of a backcalculation algorithm is to compare the layers’ moduli results with

laboratory measurements of core samples. The wide discrepancies between the backcalculated and

measured moduli are often attributed to the difficulty in obtaining undisturbed soil samples. The end

result is that backcalculated moduli for the same pavement structure may differ widely, depending on

the backcalculation algorithm used and the assumptions made by the program operator. In this

Chapter, Three Dimensional Finite Element (3D-FE) approach is used to simulate the response of the

three sections, tested in Chapter 5, to FWD load. For each pavement structure, the deflection basin

obtained from the finite element model is compared with the one experimentally measured. The

elastic moduli used in the model are changed until a satisfactory agreement between the Finite

Element-Calculated and the experimental basins is reached. Next, the layers moduli are evaluated

from the FE-generated deflection basin using the three backcalculation programs MODULUS5.0,

EVERCALC4.0 and MODCOMP3, and the results are compared with the layers moduli used in the

finite element model. Correction factors for backcalculated moduli were developed and found to be

in close agreement with the values recommended by SHRP Pavement Design Guide.

6.2 REVIEW OF FINITE ELEMENT MODELING OF PAVEMENTS

A number of 2D finite element programs such as ILLI-PAVE and MICH-PAVE were

developed to analyze flexible pavements. In these programs, the 3D pavement structure is idealized

77

using 2D axially symmetric elements. To account for material nonlinearity, the unbounded nature of

granular soils, and “locked-in” lateral stresses produced by compaction, stress-dependant resilient

moduli were incorporated for granular and cohesive soils (4,19). In MICH-PAVE, a flexible boundary

was utilized at the bottom of the FE model to reduce computer memory and processing time (19).

Limitations of the axi-symmetric assumptions used in these programs include: inability to simulate

asymmetrical loading condition, assumption of full contact with the base layer, inability to simulate

cracks and rutting conditions, and the use of static loading. Other 2D finite element programs for rigid

pavements include ILLI-SLAB, JSLAB, KENSLABS, WESLIQUID, FEACONS III, KENSLABS,

and WESLAYER (20-25). In these programs the concrete slab was treated as a 2D medium-thick

plate. To accommodate the presence of the base layer, the slab and base are transformed into one

equivalent layer. Although the programs are specifically designed for rigid pavement analysis, the

actual behavior of concrete pavements is more complex than the 2D model idealization . The

capability of handling a moving load was introduced to ILLI-SLAB by Chatti et al. (26, 27); recently,

Roesler et al. (28) modified the program to allow for partial-depth crack analysis (ILSL97). The

major limitation of the 2D FE modeling approach is its inability to handle the geometrical features

near dowel bars without a significant degree of approximation. The need for developing a deep

understanding of pavement behavior motivated researchers to use the 3D FE approach.

None of the available 3D finite element codes is specifically designed for pavement analysis.

Ioannides et al. (29) studied stress-dependant foundation using the GEOSYS program which is

primarily designed for geotechnical problems. Starting the late 1980's, general purpose finite element

codes such as ABAQUS, DYNA3D, and NIKE3D were introduced in pavement engineering research

(30-38). Zagloul and White studied the dynamic response of flexible pavements to FWD loading and

moving loads using ABAQUS. The modeling results were found to be in close agreement with the

field measurements (39,41). Seaman et al. (34) examined the response of airport runways using

NIKE3D. This work was later extended by Kennedy et al. (35-38) who developed a user interface

to DYNA3D and NIKE3D specially designed for pavement structural analysis.

The earlier finite element codes developed for the purpose of modeling FWD test were based

78

on static interpretation of FWD load (41-43). Many studies were conducted to compare deflection

basins resulting from dynamic analysis and those from static analysis. Mamlouk and Davies

developed a multi-degree of freedom model based on the principle of elasto-dynamics; it accounted

for the three-dimensional response properties and the inertia effects. Transient loading was

represented by a series of steady-state harmonic loadings with different frequencies and magnitudes

(44, 45). Sebaaly modified the program to include the calculation of stresses and strains in pavements

caused by harmonic and impulsive loading (46). The results showed that the surface deflections

obtained using elasto-dynamic analysis of FWD tests were within 3 to 15 percent from field

measurements. Static representation of FWD load was found to produce surface deflections that

are up to 40 percent larger than field measurements (46, 47). Mallela et al. (48) developed a three-

dimensional response model for a rigid pavement structure subjected to FWD load. Linear elastic

materials were used to characterize all pavement layers. This assumption was based on the argument

that the stresses induced in each layer under standard 18 Kip equivalent single axle load are not likely

to produce stresses which exceed the elastic limits of each layer. The deflection basin resulting from

dynamic FEM showed a good agreement with the measured one while the deflection basin resulting

from the static FEM was 80 percent larger than that measured experimentally. Nazarian et al. (49)

conducted an investigation to assess the significance of layer stiffnesses, thicknesses, and the depth

to bedrock on the measured and backcalculated deflections. They found that the dynamic nature of

the FWD load significantly affects the deflections measured away from the load. The depth to

bedrock and load duration interacted to produce significantly different static and dynamic deflections.

Uddin et al. (50, 51) reported an increase of 22 percent in maximum deflections due to the presence

of multiple cracks. The role of pavement layers interfaces in transmitting FWD load was examined

by Shoukry et al. (52, 53) who reported stiffer FWD response due to the lack of adequate interface

representation.

6.3 GUIDELINES FOR 3D FEM OF PAVEMENT STRUCTURES

From the above review, it can be seen that 3D FE modeling of pavements has reached a

degree of maturity which permits its use in pavement structural evaluation problems. In building a

Fringe plots are colored visualization of the deformations and stresses in the finite element model. Each color1

represents a certain region of stress or the deformation. For example, see Figures 6.6 and 6.9.

79

finite element structural model, there are guidelines which help produce theoretical results close to

the experimentally measured ones. These guidelines can be summarized as follows:

1. Finite element model loading should have the same dynamic characteristics and time duration

as that applied in practice. This means that traffic and/or impact loads should be dynamically

applied in the model with the same duration or speed encountered in practice.

2. Structural interfaces between different parts should be represented in the model. Allowing

separation of the interfaces under inertia and/or thermal effects is a primary factor which

influences the deflections and stresses obtained from the model. Approximate values of

coefficients of friction at the interface help produce more realistic results.

3. For short time duration studies and transient analysis, it seems practical to assume that all

pavement layers behave elastically. The need for using nonlinear material models should be

assessed carefully by the engineer. In most cases, nonlinear material models require the use

of constants that may not be available and must be assumed. The benefits gained from using

nonlinear material models may be lost due to incorrect assumptions of material constants.

In most cases which do not involve repeated application of loads in the model, the use of

nonlinear material models for base and/or subgrade may not be necessary. On the other

hand, studies of rutting development in flexible pavements would certainly require the use of

inelastic material models.

4. The continuity of the stresses and deformation in the model should be checked using fringe

plots . The changes in fringe intensity from one element to another should be smooth and1

continuous. If this is not the case, the finite element mesh should be refined until smooth

patterns of fringes are obtained. This provides a confirmation of the adequacy of the FE mesh

80

but does not guarantee that the values are correct. The values of the stresses and deflection

throughout the model are primarily dependent on the material constants used and accuracy

in representing different geometrical features.

5. In Explicit Finite Element analysis, the model deformation should be displayed using a large

scale factor to ensure that zero energy modes did not develop anywhere in the model and that

none of the interfaces penetrate each other.

6. Finite element model results should be verified experimentally. One simple experimental

proof of the correct operation of pavement structural models can be obtained from comparing

deflection basins produced by FWD loading with those obtained from the model.

7. Finite element solutions are numerical solutions of sets of partial differential equations which

combine materials constitutive laws with the geometry of the structure. The equations are

based on the same fundamental stress-strain relations used in developing any closed form

solution. However, while closed form solutions are limited to geometrically simple structures,

finite element analysis can handle any geometry. Thus FE solutions are dependent to a great

extent on the accuracy of modeling the structural geometry. Thus, if the true structure

contains a crack, finite element modeling cannot produce deflection results that mimic the

experimentally measured ones unless the crack is accounted for in the model. Engineering

judgement should be exercised in deciding the level of structural details that should be

included in the model in order to produce reliable results.

8. Use should be made of computer visualization and animation capabilities to display model

results. The selection of a powerful post processor is a key factor in understanding the model

results and drawing conclusions.

81

6.4 FINITE ELEMENT MODELS OF EXPERIMENTAL TEST SITES

6.4.1 Flexible Pavement Model

Flexible pavements are continuous in the direction of traffic and jointless in the transverse

direction. Due to the softness of the asphaltic material, it is expected that the response of pavement

to the FWD load will be localized. For this reason, the pavement structure was modeled as a

multilayered system consisting of asphaltic concrete layer, base, and subgrade as shown in Figure 6.1.

The model width was chosen to be the full lane width of 12.0 ft. The flexible pavement section has

a shoulder made from the same material as the surface layer. This allows for the assumption of a

continuity of the propagation of in-plane stress waves generated by impact load. To simulate this

continuity, non-reflective boundaries were modeled along the pavement sides. The model length in

the traffic direction is 20.0 ft. The center of the loading plate was located at a distance 5.0 ft from

the lane edge adjacent to the shoulder. Due to the geometrical symmetry around a vertical plane

passing through the center of the loading plate perpendicular to traffic direction, only one half of the

pavement was meshed as shown in Figure 6.1. A tied interface between base and subgrade was

assumed while a sliding interface with a coefficient of friction of 0.9 was assumed between the

asphaltic layer and the base.

6.4.2 Rigid Pavement Model

The pavement structure was modeled as a multilayered system consisting of a Portland

Cement concrete slab, base, and subgrade as shown in Figure 6.2. The model width was chosen to

be the full lane width of 12.0 ft. The center of the loading plate was located at the center of the

concrete slab. Due to the geometrical symmetry around the transverse plane passing through the

center of the loading plate, only one half of the pavement was meshed as shown in Figure 6.2. The

influence of dowel bars on the deflection basin was assumed to be negligible due to two reasons: (1)

large distance of the transverse joint from the center of FWD load application, and (2) the relatively

82

small magnitude of FWD load. Therefore, dowel bars at the transverse joint were not included in the

model. Figure 6.2 also illustrates the boundary conditions used in the model. A sliding interface with

a coefficient of friction of 0.9 was assumed between the concrete layer and subgrade while a fully tied

interface was assumed between the subgrade and base.

6.4.3 Composite Pavement Model

The pavement structure was modeled as a multilayered linear elastic system consisting of a

Portland Cement concrete slab overlaid by an asphaltic concrete layer, a base, and a subgrade as

shown in Figure 6.3 . The model width is 12.0 ft and its length in the traffic direction was chosen to

be a full slab length of 27.0 ft. The center of the loading plate was located at the center of the model.

As a result of loading and geometrical symmetry around the transverse plane passing through the

center of the loading plate, only one half of the pavement was meshed as shown in Figure 6.3. A

tied interface was assumed between the asphalt and concrete layers. A sliding interface with a

coefficient of friction of 0.9 was assumed between the concrete and subgrade while the base/subgrade

interface was assumed to be fully tied.

In all models, bedrock was assumed to lie at a depth which will not introduce reflections

within the loading time duration under investigation (30 ms). This was achieved by applying

nonreflective boundaries which simulate the semi-infinite extent of the subgrade at the bottom of each

model. All models were meshed using 8-node brick element with 24 degrees of freedom per element.

The mesh sizes varied through each model to assure the accuracy of the results within the regions of

interest. Thus, a refined mesh was necessary in regions of high stress intensity such as concrete slabs.

A coarser mesh was used for the base and subgrade. A one in. thick and 12 in. diameter steel loading

plate (modulus of elasticity = 30,000 Ksi, unit weight = 0.2831 lb/in. ) was added to each pavement3

model for more accurate simulation of the FWD setup.

The impact loads used in this investigation were obtained from the measured FWD loads

83

applied during tests. The impact loading-time relations recorded by the FWD load cell were digitized

over one millisecond time intervals and the pressure-time history was calculated by dividing the load

by the area of the loading plate. Figure 6.4 illustrates the digitized pressure-time curves used for

modeling the three types of pavements.

6.5 STRUCTURAL MATERIAL MODELING

The surface deflections measured at various FWD sensor locations can be useful in

determining if the pavement structure displays a significant degree of nonlinearity due to the

application of the FWD load. FWD tests were carried out at three different loading levels, as listed

in Table 5.1. The deflections versus FWD load recorded at each sensor location are shown in Figure

6.5. The plots reveal that the deflections measured at all sensor locations are directly proportional

to the applied load. In the case of the flexible pavement, a negligible nonlinearity can be observed

for sensors located at 0 in. and 8 in. from the center of load application. For all other sensor

locations, the experimentally measured deflections fell close to a straight line obtained through least

squares fitting. This linearity indicates that the structural materials of all three pavements behaved

elastically under the loading levels applied in each case. Since in the present analysis FWD load will

be limited to 10,000 lb, it is safe to assume that all materials used in the three models can be

represented using linear elastic models. That is, each layer material is characterized by its modulus

of elasticity, density, and Poisson’s Ratio. This choice of material model has been further confirmed

from studying the amount of stresses induced in different layers due to the application of the FWD

load. Figure 6.6 illustrates by fringes the distribution of vertical stresses for different pavements.

Furthermore, the vertical stress along the vertical line passing through the center of the loading plate

was plotted versus depth in each pavement structure as shown in Figure 6.7. It can be noticed that

the stresses induced in base and subgrade layers are very small which validate the assumption of linear

elastic material models.

84

6.6 LAYERS MODULI EVALUATION FROM FE MODEL RESULTS

Since the purpose of this study is to evaluate the structural capacity of the three pavement

structures, the elastic moduli of the pavement materials are all unknown. An iterative procedure

similar to that commonly used in backcalculation algorithms was employed to determine those

moduli. Iterative procedure steps are as follows:

1. FWD test is conducted and the experimental deflection basin is obtained.

2. The experimental basin is used with any backcalculation program to evaluate a set of layers

moduli.

3. The layers moduli obtained from backcalculation are used in the finite element model and a

theoretical deflection basin is obtained.

4. The FE generated deflection basin is compared with the experimental basin. If the two basins

are in good match, the moduli used in the finite element program are taken to be the correct

moduli.

5. If the basins are different from each other, the layers moduli are adjusted and inserted in the

finite element program to produce a new deflection basin.

The above procedures are repeated until the condition in step number 4 is satisfied. This

method of determining layers moduli was considered to be superior to backcalculation for the

following reasons:

1. FE does not contain assumptions about pavement geometry as traditional backcalculation

algorithms do. The model accounts for the layers interfaces and the inertial properties of the

85

materials.

2. The load used in the finite element programs is the experimentally measured load-time history

applied by FWD. This permits comparing the experimental and theoretical deflection time

histories at all sensor locations. All existing backcalculation programs reach convergence

based only on the maximum deflection measured at each sensor location.

6.7 VERIFICATION OF FINITE ELEMENT MODELS

6.7.1 Deflection Basins

The initial seed moduli used in the FE models produced highly stiff responses in all cases.

Therefore the moduli of different layers were reduced. After several cycles of adjusting the values

of layer moduli used in each model, a satisfactory match between the FE-generated and the FWD-

measured basins was reached for every pavement structure. The final basins are plotted together with

those experimentally measured in Figure 6.8. In all cases, the FE deflection basins fell close to those

measured experimentally. Figure 6.8 (c) for the composite pavement shows deviation between the

experimental and theoretical basins near the center of FWD load application. This deviation may be

attributed to one or both of the following reasons:

1. Existence of unrepaired cracks in the concrete slab.

2. The center of FWD loading plate fell near a transverse joint in the overlaid slab.

Additionally, the asphalt material under the loading plate, being confined between the loading

plate and the underlying concrete, has suffered local excessive deformation that was recorded by the

FWD sensor located at zero offset. At the locations of other sensors, the surface of the asphalt layer

is free to follow the deformation of underlying layers. As indicated in Figure 6.8 (c) the FE model

successfully simulated this behavior, however lack of representation of a cracked concrete layer

resulted in the small deviation between the FE-generated and the FWD-measured deflections up to

86

24 in. offset from the center of load application.

Figure 6.9 illustrates the fringes of vertical deformation at the time of maximum FWD load

through two sections; one is perpendicular to the traffic direction and the other passes through the

FWD sensors line. The patterns of vertical displacement fringes illustrate the uniformity of

displacements through different layers.

6.7.2 Displacement-Time History

The FE-generated and experimentally measured deflection-time histories are compared in Figure 6.10

for three different sensor positions. The plots reveal that as the FWD load is applied, both the

theoretical and experimental deflections increase at almost the same rate. After peak deflections are

reached, the FWD measured deflection curves rebound much faster than the FE-generated

deflections. This behavior could be attributed to one of two reasons:

1. The top layer separates from the base. If this is the case, then the FWD sensors should have

recorded different values of positive deflections at different sensor positions. As seen from

Figure 6.10 (a), this cannot be true since the sensor located at 48 in. recorded almost the same

positive deflections as the sensor located at the center of load application. Furthermore,

Figure 6.10 (b) shows that the magnitude of rebound at the center of FWD load application

exceeds that recorded by the sensor located at 12 or 48 in. offsets, which excludes layer

separation as a reason.

2. Either all the sensors, or the FWD structure (which supports all sensors) rebounded following

the application of FWD load. It is unlikely that all sensors rebound as the FWD manufacturer

makes sure that the magnitude of spring loading is large enough to keep the sensors in

intimate contact with the pavement surface. The rebound of the whole FWD structure is

more plausible and is observed during the FWD test. When the sensor supporting-structure

87

rebounds, the spring loaded sensors are lifted slightly up and the deflection recovery portion

of each deflection-time history takes place at a faster rate than reality. This explains the

positive deflections shown in Figure 6.8.

According to the above discussion only the Downward Portion (DP) of the experimental

deflection-time history is suitable for comparison with 3D-FEM results. Of all sensors, the DP of the

deflection-time history recorded at the center of FWD load application is the least affected by possible

rigid body rebounding of the FWD structure. Figures 6.10 (a), (b), and (c) reveal that the FWD-

recorded deflection-time history at zero sensor position coincides with the FE-generated deflection-

time history. Additionally, the major features of the experimentally measured response are also seen

in the FEM response. These features are a time delay of displacements measured at different offsets,

and a time delay between maximum loading and maximum displacement response (recorded at the

center of FWD load application) of around three to five milliseconds in both the theoretical and

experimental data.

6.8 EVALUATION OF BACKCALCULATION PROGRAMS

Backcalculation programs terminate as soon as either the deflection basin fit precision

tolerance or the moduli convergence is satisfied. Although all the theoretical deflection basins from

different backcalculation programs match the FWD measured ones, this doesn’t mean that the layers

moduli profiles reached by these programs are correct. Backcalculation programs interpret the

measured deflection basin as being produced by an applied static load. The short load duration of

FWD load does not allow the structural materials to deflect fully in response to the maximum load

magnitude. This means that if the same FWD load is statically applied for a longer time duration, the

deflection basin measured would be larger. Previous studies(45-48) reported that experimentally

measured deflection basins produced by the application of static load (whose magnitude is equal to

FWD load) are up to 80 percent larger than those measured during FWD tests. Thus backcalculation

programs that are based on static interpretation of FWD load may overestimate the layers moduli.

88

The 3D-FEM approach accounts for both the inertia properties of the structural materials and the

dynamic nature of FWD load. When the backcalculated moduli were used as seed moduli in the FE

models they resulted in highly stiff basins. As the values of layers moduli were reduced, the FE

deflection basins converged to those experimentally measured. The measured, backcalculated, and

FE-generated deflection basins are compared in Figure 6.11. All deflection basins are very close to

each other. However, deviations were found between the backcalculated moduli using different

programs and those obtained using 3D-FEM as shown in Figure 6.12.

Using the FE-backcalculated subgrade modulus, a set of correction factors were computed

for the subgrade modulus value obtained from each program when used for different types of

pavements and the results are given in Table 6.1. The correction factor is computed by dividing the

FE-backcalculated subgrade modulus by the value obtained from the specific backcalculation

program. From the values listed in Table 6.1, the following remarks could be drawn:

1. MODULUS has the best consistency among the three programs. The correction factors

obtained for this program fell very close to the values recommended by the American

Association of State and Transportation Officials (AASHTO) Pavement Design Guide (5).

2. MODCOMP behaved similar to MODULUS with flexible pavements, however it

underestimated the value of the subgrade modulus of the rigid pavement.

3. EVERCALC produced a subgrade modulus for the flexible pavement that is very close to the

FE-backcalculated value. For rigid and composite pavements it under estimated the subgrade

modulus. The correction factors found for rigid pavements for this program fell within the

0.25 recommended for rigid pavements by AASHTO Pavement Design Guide (5).

4. The FE-backcalculated modulus for the three pavements tested in this study did not

significantly change. This may be due to the fact that the three pavement sections were

located in Morgantown, West Virginia within a circle of radius less than seven miles.

89

The AASHTO Pavement Design Guide recommends (based on experimental observations)

that a correction factor less than 0.33 is used with backcalculated subgrade modulus of flexible

pavements. For concrete pavements the recommended factor is less than 0.25. It can be seen from

table 6.1 that the mechanistic 3D-FEM approach in backcalculating layers moduli produced almost

the same result. That is, the FE-evaluated moduli don’t require correction and therefore can be used

as a reference for assessing the performance of backcalculation algorithms.

90

TABLE 6.1 Correction Factors for Backcalculated Subgrade Modulus.

PAVEMENT FE-Backcalculated MODCOMP MODULUS EVERCALC AVERAGE

TYPE Modulus (kPa)

Flexible 0.85*27.56 0.34 0.37 0.35

Rigid 26.18 1.34* 0.28 0.19 0.24

Composite 27.56 0.23 0.29 0.13 0.22* Value excluded for the calculation of average

91

Concrete

Base 8 in.

Subgrade

144 in.120 in.

FWD loading plate

Non-reflective bottom

Non-reflective boundariesfor all layers

Symmetry plane

9 in.

72 in.60 in.

Non-reflective endsof all layers

Non-reflective edgeof all layers

FIGURE 6.1 Finite element mesh of the flexible pavement model.

92

PCC slab9 in.

Base 8 in.

Subgrade72 in.

144 in.

162 in.

FWD loading plate

Non-reflectivebase & subgrade

Non-reflectiveends of layers


72 in.

Symmetry plane Reflective side of concrete slab

Non-reflective edgeends of layers

FIGURE 6.2 Finite element mesh of the rigid pavement model.

93

Asphalt 5 in.

PCC slab 9.5 in.Base 3 in.

Subgrade 72 in.

72 in.

162 in.

FWD loading plate

144 in.

Non-reflective base & subgrade

Reflective side ofconcrete slab

Non-reflective endsof all layers


FIGURE 6.3 Finite element mesh of the composite pavement model.

94

a. Flexible Pavement b. Rigid Pavement

c. Composite Pavement

FIGURE 6.4 Impact loading curves used in different finite element models.

95



FIGURE 6.5 Load-Deflection relation for different types of pavements.

96

-6.000E+01>-5.500E+01>-5.000E+01>-4.500E+01>-4.000E+01>

-3.500E+01>-3.000E+01>

-2.500E+01>-2.000E+01>

-1.500E+01>

-1.000E+01>-5.000E+00>0.000E+00>

-7.000E+01>-6.417E+01>-5.833E+01>

-5.250E+01>-4.667E+01>

-4.083E+01>-3.500E+01>-2.917E+01>

-2.333E+01>

-1.750E+01>-1.167E+01>

-5.833E+00>0.00E+00>



-1.500E+02>-1.375E+02>

-1.250E+02>

-1.000E+02>

-8.750E+01>-7.500E+01>

-6.250E+01>

-5.000E+01>

-3.750E+01>-2.500E+01>-1.250E+01>0.000E+00>

-1.125E+02>

Figure 6.6 Fringes of vertical stresses at time of maximum FWD load.

Asphalt LayerBase Layer

Subgrade

Vertical Stress, psi

0

20

60

40

80

10075604530150 90

ConcreteBase Layer

Subgrade


AsphaltConcrete

Subgrade

Base Layer


a. Flexible Pavement. b. Rigid Pavement

c. Composite Pavement.

0

20

60

40

80

100

0

20

60

40

80

10075604530150 90

75604530150 90

97

FIGURE 6.7 Vertical stresses in different types of pavement due to FWD load.

98



FIGURE 6.8 Comparison between experimental and FE deflection basins for different pavements models.

99

FIGURE 6.9 Fringes of vertical displacement at time of maximum FWD load. (Display scale factor 2500)

100

FIGURE 6.10 Deflection-time histories for different pavement models.

101



FIGURE 6.11 Comparison between backcalculated deflection basins and measured basins.

102

Surface layer (Ksi)

0

200

400

600

800

1000M

odul

us, K

si

Subgrade (Ksi)

0

2

4

6

8

10

12

14

Mod

ulus

, Ksi

Base layer (Ksi)

0

20

40

60

80

100

120

Mod

ulus

, Ksi

Subgrade (Ksi)

0

5

10

15

20

25

Mod

ulus

, Ksi

Base Layer (Ksi)

0

20

40

60

80

100

120

Mod

ulus

, Ksi

Surface Layer (Ksi)

0

1000

2000

3000

4000

5000

Mod

ulus

, Ksi

Subgrade (Ksi)

0

5

10

15

20

25

30

35

Mod

ulus

, Ksi

Base Layer (Ksi)

0

50

100

150

200

Mod

ulus

, Ksi

Surface Layer (Ksi)

0

500

1000

1500

2000

2500

Mod

ulus

, Ksi

PCC Layer (Ksi)

0

1000

2000

3000

4000

5000

6000

7000

Mod

ulus

, Ksi

a. Backcalculated layer moduli for flexible pavement

b. Backcalculated layer moduli for rigid pavement

c. Backcalculated layer moduli for composite pavement

FIGURE 6.12 Comparison of backcalculated layer moduli for the three types of pavements.

103

CHAPTER 7

SOME FACTORS INFLUENCE BACKCALCULATIONS

OF RIGID PAVEMENTS

7.1 INTRODUCTION

This chapter focuses on examining the behavior of rigid pavement layers during the Falling

Weight Deflectometer (FWD) test; factors affecting the design of a concrete slab, such as whether

the joints are doweled or undoweled and the spacing between transverse joints were considered.

Explicit finite element analysis was employed to investigate the response of pavement layers to the

action of FWD impulse load. The accuracy of the finite element models developed in this investigation

was verified by comparing the finite element-generated deflection basin with that experimentally

measured during an actual test. The results showed that the measured deflection basin can be

reproduced through finite element modeling of the pavement structure. The resulting deflection basins

from different models which simulate different pavement design features were processed using several

backcalculation programs. The results reveal the effect of different pavement design features on the

backcalculated moduli profile. It was found that ignoring the dynamic nature of the FWD load may

lead to crude results, especially during backcalculation procedures.

7.2 FINITE ELEMENT STRUCTURAL MODEL

A rigid pavement (SHRP section No. 285823) located in Mississippi was selected for this

study. The pavement structure was modeled as a multilayered linear elastic system consisting of a

Portland Cement Concrete (PCC) slab, base, and subgrade as shown in Figure 1. The model

dimensions were chosen to be the full lane width, that is 12 ft and extended in the longitudinal

direction from both sides to include two quarter parts of the adjacent slabs. The slab length was taken

to be 20 ft . To study the effect of the slab length on the performance of a rigid pavement under the

104

effect of FWD load, four other models were developed using slabs of lengths 16 ft, 15 ft , 12 ft, and

10 ft. The slab width was kept constant, 12 ft for all models. The center of the loading plate was

located at the center of the middle slab for all models. Due to the geometrical symmetry around the

longitudinal plane passing through the center of the loading plate, only one half of the pavement was

meshed. In absence of data about the depth to bedrock, it was assumed to be typical of what can be

found in West Virginia, i.e. from 5-15 ft under the bottom of the base layer. In this study, it was taken

as 6 ft measured from the bottom of the base layer. Additionally, nonreflective boundaries were

applied at the bottom of the subgrade to eliminate reflection of the stress wave from affecting the

surface displacements. To account for the effect of model size, nonreflective boundaries which

simulate a semi-infinite extension of layers were applied at all sides of base and subgrade as well as

the transverse ends of the two half slabs as shown in Figure 7.1. A sliding interface was assumed

between the concrete slab and the base layer, and a fully bonded interface was assumed between the

base layer and the subgrade. All layers were meshed using 8-node brick elements having 24 degrees

of freedom per element. The mesh sizes varied through the model to assure the accuracy of the results

within the regions of interest. Thus a refined mesh was necessary in regions of high stress intensity

such as concrete slabs especially at transverse joints. A coarser mesh was used for the base and

subgrade.

The steel dowel bars (modulus of elasticity=30, 000 psi, unit weight= 488.81 pcf) in the

transverse joints were modeled using brick elements. The main function of dowel bars is to transfer

the load across the joint while allowing the slabs to move longitudinally relative to each other in order

to relieve the tensile or thermal stresses due to slab contraction. Therefore the dowel bar may be

bonded to one concrete slab while its other end is free to slide in the adjacent slab. Consequently, one

end of the dowel bar was modeled with a tied interface with the concrete slab, while the other end

was modeled with a sliding interface with the adjacent concrete slab as illustrated is Figure 7.2.

105

7.2.1 Model Loading and Material Model

The FWD impact load was applied to the model through a 12 in. diameter steel loading plate.

The impact load used in this investigation was obtained from the experimental results of SHRP

section No. 285803 reported by J. Mallela, et al. (48). The impact pressure on the loading plate

surface was assumed to be uniformly distributed due to the semi-rigid behavior of the plate. The

pressure-time relation, Figure 7.3, was digitized over time increments of 0.25 milliseconds and the

values were used in the finite element program . The different load magnitudes employed in the FWD

tests are designed so that all pavement layers behave within their elastic limits. Thus the assumption

of linear elastic behavior of all layers is realized for this study. This assumption is further confirmed

by research studies (48,49) which indicate that the stresses induced in different pavement layers under

a maximum impact pressure of 92.8 psi (used in this study) are likely to be within the elastic range.

Therefore linear elastic materials models were used for all layers and the material parameters are

given in Table 1.

TABLE 7.1 Properties of Pavement Materials.

Material Property Values published in Ref. (48)

Concrete Slab, Modulus (Ksi) 4650thickness= 8 in. Poisson’s Ratio 0.18

Unit Weight (pcf) 149.8

Base Layer, Modulus (Ksi) 1700thickness= 6 in. Poisson’s Ratio 0.40


Subgrade, Modulus (Ksi) 11.87thickness =72 in. Poisson’s Ratio 0.30


106

7.2.2 Model Verification

Figure 7.4 (a) illustrates a comparison between the experimental deflection basin obtained

from SHRP data base for section No. 285803 and the corresponding deflection basin obtained from

the 3D-FEM model. Initially, the value of 11.87 ksi for the subgrade modulus, backcalculated by

Mallela (48), was used in the model. The FEM model produced a deflection basin which was on

average 16% less then the experimentally measured one. However, both the theoretical and

experimental basins showed a remarkable agreement in their slopes, this agreement indicated that the

FEM model is slightly stiffer than the actual pavement. The higher stiffness of the model may be

reduced by decreasing the layers moduli values used in the model. When the modulus of the subgrade

was reduced to 8.0 ksi, while keeping the moduli of the surface and base layers as listed in Table 7.1,

a remarkable agreement between the theoretical and experimental results was realized as illustrated

in Figure 7.4 (a). Since the original modulus value of 11.87 ksi was evaluated using backcalculation

(Mallela (48)), a 32% reduction in the modulus value will be within the expected error associated

with most backcalculation algorithms. In fact, it is not uncommon for the error in evaluating

subgrade modulus to exceed 100% (see Reference13). Even in well controlled laboratory testing of

subgrade modulus, errors more than 50% are expected.

The most important thing to consider is the ability of the model to simulate the relative

displacement of any point to another one on the structure. The success of this model is demonstrated

in the good agreement between the slopes of the deflection basins as we move away from the point

of load application. Only at a distance of 48 in. did the slopes of the experimental and theoretical

basins start to show some deviation. One reason for this divergence may be the approximate values

adopted for the moduli of the base and subgrade layers which were evaluated using backcalculation,

the value of subgrade modulus is the only one adjusted in this study. Another reason may be due to

unreported dowel bar looseness or loss of aggregate interlock. The third reason may be simply the

experimental error encountered in measuring very small displacements away from the center of the

loading plate. In order to illustrate the effect of dowel bars on the deflection basin, another FEM

model was constructed without dowels at the joints and its deflection basin was compared with the

107

experimentally measured one in Figure 7.4 (b).

7.3 PERFORMANCE ASSESSMENT OF BACKCALCULATION PROGRAMS

In this study, finite element modeling was used for the evaluation of conventional

backcalculation programs. Since a FWD measured deflection basin could be reproduced through

finite element modeling of the pavement structure, the FEM generated deflection basin can be used

to backcalculate the layers moduli. To evaluate the performance of different backcalculation

algorithms the following procedures were followed:

1.The rigid pavement structural model results were verified by comparing the FEM-generated

deflection basin with the FWD measured one as shown in Figure 7.4.

2. The theoretical deflection basin obtained from the finite element model was used together

with different backcalculation programs to evaluate the moduli of different layers, using

different backcalculation programs.

3. The backcalculated layers moduli were compared with the moduli used in the finite

element model as shown in Figure 7.5.

Figure 7.5 (a) illustrates the measured deflection basin together with those resulting from

using different backcalculation programs. It can be noticed that a remarkable agreement was achieved

between all the backcalculated basins and the measured one. However, the backcalculated layers’

moduli obtained from each program were found to be different from those used in the finite element

model as shown in Figure 7.5 (b). This is primarily due to the dynamic nature of the FWD which was

accounted for in FE analysis while the backcalculation programs are based on static analysis. Figure

7.5 (b) also indicates that all programs have produced top layer moduli close to that used in the FE

model. The values of the base modulus evaluated using conventional backcalculation programs are

108

significantly less than those used in the FE model. The subgrade layer modulus produced by all three

backcalculation programs was significantly larger than that used in the finite element model.

However, if we apply a correction factor of 0.28 (as recommended in Chapter 6 for MODULUS

program), in average, on the backcalculated subgrade modulus, the results become almost identical

to the modulus used in the finite element model. This further confirms the validity of the correction

factors reached in Chapter 6.

7.4 EFFECT OF SLAB LENGTH AND DOWEL BARS

The FE-generated deflection basins, for the models provided with dowel bars, are plotted for

different slab lengths in Figure 7.6 (a). The deflection basins are congruent indicating that, in the

presence of dowel bars, the slab length doesn’t affect the surface deflection values resulting from

FWD impact. This can be explained by the fact that the dowel bars transfer the load to the adjacent

slabs. Comparison of the deflection basins of the doweled models in Figure 7.6 (a) with those of

undoweled ones in Figure 7.6 (b) shows that dowel bars affect the value of the maximum deflection

measured at the center of FWD loading plate. Away from the center of load application, dowel bars

have the effect of introducing continuity of deformation at the transverse joint. Therefore no effect

of slab length on the measured deflection basin can be observed in Figure 7.6 (a) for doweled

pavement structures. In absence of dowel bars, Figure 7.6 (b), the slab length becomes an important

factor which affects the FWD deflection basin.

The plots in Figure 7.6 (b) for undoweled pavements indicate that as the slab length increases,

the surface deflection increases then begins to decrease at a slab length 15 ft. This is further illustrated

in Figure 7.7 which shows the change of the deflection under the center of FWD loading plate versus

slab length. Referring to Figure 7.6 (b), the difference between the deflections recorded at the

locations of the first and last sensors increases as the slab length increases. This causes

backcalculation programs to produce values of layers’ moduli which are slab length dependent for

undoweled pavement sections.

109

The deflection basins plotted in Figure 7.6-b were processed using MODULUS5.0 program

to study the effect of slab length on the backcalculated layers’ moduli. The resulting layers’ moduli

for each slab length together with the estimated depth to bedrock are plotted together with the value

used in FEM as shown in Figure 7.8. The plots show a significant change in the backcalculated

moduli values obtained for both the surface and the base layers from those used in FEM. However,

the values for subgrade modulus are found to be close to each other but still significantly larger than

that used in FEM. Therefore it seems that any change in the surface deflection affects the moduli of

the top layers more than they do the subgrade. This makes the use of a correction factor of 0.28 for

the subgrade modulus satisfactory for all slab lengths.

7.5 CONCLUSIONS

The 3D FEM approach used in this study provides a powerful tool for evaluating the

performance of existing backcalculation programs with rigid pavements under different situations

encountered in the field. Based on the presented results, the following conclusions can be drawn:

1. When testing an aged rigid pavement section in which cracks have developed, the FWD

testing engineer should check that the length of the tested slab part is not less than 10 ft to

assure that this part can produce a reliable deflection basin.

2. The correction factor of 0.28 reached in Chapter 6 is suitable for adjusting the backcalculated

subgrade modulus in all cases of doweled and undoweled joints. This value was found to be

in close agreement with the AASHTO experience-based correction factors.

110

60 in.

60 in.

8 in.

Subgrade72 in.

Loading Plate, 12 in. Diameter

144 in.Non-reflective sideof base & subgrade


Non-reflective sidesof concrete, base and

Reflective slab sides

240 in.

Concrete Slab,

Base, 6 in.

Nonreflective sides

Symmetry plane

Quarter slab

subgrade layers

Figure 7.1 Finite element mesh for a rigid pavement.

Figure 7.2 Cross section in a doweled joint.

0 0.01 0.02 0.03

30

60

90

0

Time, sec

111

Figure 7.3 Impact load curve used in finite element model (Ref. (48)).

112

Figure 7.4 Model verification. (Slab length=20 ft)

113

Figure 7.5 Comparison between the results of backcalculation programs.

Measured

FEM, E sub =8.00 ksi

MODULUS5.

EVERCALC4.0MODCOMP3

1.6

2.4

3.2

4.0

0 16 32 48 64

Distance from loading plate center, in.

Published, Ref. (48) FEM MODULUS

5EVERCALC MODCOMP 3

Subgrade

0

50

100

150

200

250

300 M

odu

lus,

MP

a

Base Layer

0

2000

4000

6000

8000

10000

12000

14000

Mod

ulus

, M

Pa

Concrete Slab

0 5000

10000 15000 20000 25000 30000 35000 40000 45000 50000

Mod

ulu

s, M

Pa

a. Deflection Basins.

b. Layers Moduli.

114

Figure 7.6 Effect of slab length on deflection basin.

0

1

2

3

4

5

10 12 14 16 18 20 22

115

FIGURE 7.7 Change of maximum deflection with slab length for undoweled pavement.

116

1.0 MPa=0.14504 ksi)

Figure 7.8 Effect of slab length on the backcalculation results ( Using MODULUS).

Base Layer

0 2000 4000 6000 8000

10000 12000 14000 16000

Mou

lus,

MP

a FE

Subgrade

0 20 40 60 80

100 120 140 160

Mod

ulus

, M

Pa

FE

Depth to Bedrock

0

2

4

6

8

10

De

pth

to b

edro

ck,

m.

Surface Layer

0

10000

20000

30000

40000

50000

60000

Mod

ulus

, M

Pa

FE

117

CHAPTER 8

EFFECT OF 3D FEM MODEL DEPTH ON BACKCALCULATIONS

OF FLEXIBLE PAVEMENTS

8.1 INTRODUCTION

Many researchers (Uddin et al.(54) , Yang et al. (55), Briggs et al. (56), Rhode et al. (57), and

Uzan (58)) reported that mechanistic analysis of pavement response to FWD impact load shows a

dependancy on the thickness of subgrade layer. Such a conclusion was reached under the assumption

that pavement response to a static load is equivalent to its response to a FWD impact load of the

same amplitude. Thus the elastic layer theory can be used to backcalculate the layers moduli.

However, Mamlouk (45), Seebaly (46), and Mallela (48) reported that the deflections produced under

impact loads may be from 40 to 80 percent less than those observed if the load was static. Under

the assumption of a statically applied load, each pavement layer, including the full subgrade depth,

has enough time to fully deflect, which is not the case if the applied load is a short duration impact.

On the other hand, the use of elastic layer theory and a static loading assumption required a

knowledge or estimate of the thickness of subgrade layer that can be used in backcalculation

programs in order to produce the same deflection measured from FWD test. The theoretical

dependancy of FWD surface deflections (predicted from the elastic layer theory) on the assumed

thickness of the subgrade layer is not supported in the literature by any known experimental

measurements where sites that have the same layers moduli profile but different depths to bedrock

are tested using FWD. Such measurements would be extremely difficult because of the variation of

subgrade conditions from one location to another. On the other hand, if FWD testing is to achieve

its objective, a means of nondestructive testing has to be developed to predict the appropriate depth

of subgrade layer that should be used in backcalculation algorithms.

Chang et al. (59) attempted to establish an analytical correlation between the results obtained

using Dynaflect (harmonic load) and those using FWD (impact load) to predict a depth to bedrock.

118

His results indicate that only the free vibration part of the FWD displacement-time history may be

correlated to the depth to bedrock; none of his results show that the FWD deflection basin is

influenced by the depth to the stiff layer. Bush (61) suggested using an arbitrary subgrade thickness

such as 20 ft in elastic layer-based backcalculations. Uddin (54) recommended that the actual

subgrade thickness should be used. Seng et al. (61) found that the depth to bedrock could be related

to the frequency of the free vibration portion of FWD sensors and the shear wave velocity in the

subgrade layer. For flexible pavements:

DB = T V / (6.33 -5.04 �) (1)d s1.08 1.13

and for rigid pavements:

DB = T V / (6.21 - 3.88 �) (2)d s1.11 1.14

Where:

T = the period of the free vibration portion of the FWD sensors, seconds.d

V = the shear wave velocity in the subgrade layer, ft/s.s

� = Poisson’s ratio of the subgrade material.

The major shortcoming in Seng’s approach is that the free vibration amplitudes from FWD

sensors are extremely small, which makes accurate measurement of the free vibration period difficult

if not impossible for many sites. If the layers’ interfaces are not fully bonded, the free vibration part

of surface displacements may not be related to the depth to bedrock.

Ullidtz (62) used Boussinesq’s equation to establish the concept of surface modulus and

compute the depth to bedrock. The surface modulus is defined (63) as the stiffness modulus of an

equivalent half space pertaining to a specific spacing from the load center that produces a deflection

identical to the deflection actually measured on the layered structure at the same spacing. The surface

modulus at a specific radius “r” from the center of FWD load application is given by:

E (r) = 2 (1-� ) P/(% r d ) (3)sm r2

119

where:

E (r) = Surface modulus at distance r from load center.sm

� = Poisson’s ratio.

P = Applied load.

d = Deflection at distance r.r

Ullidtz pointed out that if a stiff layer is found at a certain depth, it will have a consequence

that no surface deflection will occur beyond the offset at which the stress zone intercepts the stiff

layer. Thus the depth to bedrock can be obtained from the radial distance from the center of FWD

loading plate at which the surface deflection reduces to zero.

Rohde et al. (57) used Boussinesque’s analysis and the subsequent development by Ullidtz

to develop a set of regression expressions which accounted to the overall shape of the deflection basin

in the estimation of the apparent depth to bedrock. For flexible pavement sites having an AC layer

thickness greater than six inches and tested using 9000 lb FWD load, the apparent depth to bedrock

“B” is obtained from:

1/B= 0.0409 + 0.5669 r + 3.0137 r +0.0033 BDI - 0.0665 log (BCI) (4) o o2

where:

r = 1/r intercept by extrapolating the steepest part of the inverse radial distance (1/r) versuso

deflection curve, 1/ft.

BDI= Base Damage Index defined as the difference in surface deflection measured at radial

distances of 12 in. and 24 in., mils.

BCI= Base Curvature Index defined as the difference in surface deflection measured at radial

distances of 24 in. and 36 in., mils.

Other relations similar to Equation (4) were developed for different thicknesses of asphalt

layers and were subsequently implemented in MODULUS (16) backcalculation program.

120

Zaghloul et al. (41) examined the dependency of FWD deflection basin on the depth to

bedrock using 3D Finite Element Modeling (3D FEM). The FWD load was applied to the model as

an impact load of the same duration as measured from FWD load cell. The surface deflections were

computed and compared with those experimentally measured. He went on to change the depth of

the subgrade layer in the model from 95 in. to 140 in. while keeping the layers moduli and the applied

load the same. He reported that the variation of the depth to bedrock in the 3D FEM model had no

effect on the deflection basin, a conclusion that contradicts the findings in references 54-58.

Analysis of pavement structural response using 3D FEM analysis offers many advantages not

normally available using any other analytical approach. Perhaps one of the most important

advantages offered by 3D FEM is the ability to accurately simulate the nature and distribution of the

applied load. Other major advantages are:

1. accurate modeling of the pavement geometry including discontinuity at joints and modeling

of the surface layer with finite width bounded by shoulders,

2. the friction and separation at pavement layers’ interfaces are accounted for in the analysis,

and

3. any form of material behavior could be easily included in the model.

Realizing these advantages, Shoukry et al. (64) developed a new backcalculation algorithm

using 3D FEM. The method was shown to produce excellent results when tested on Flexible, Rigid,

and Composite pavement sites. The backcalculated moduli using 3D FEM were compared, for

several sites, with those obtained using three backcalculation programs: MODCOMP, MODULUS,

and EVERCALC. The 3D FEM results were considered to be more accurate than traditional

backcalculation algorithms. Correction factors were developed to adjust the values of layers moduli

evaluated using the MODULUS backcalculation program to the corresponding moduli values

obtained using 3D FEM. The mechanistically evaluated correction factors were found to be in close

agreement with the experience-based values recommended in the American Association of State

Highway Officials and Transportation (AASHTO) Pavement Design Guide.

1 The participants at this round-robin test were:1. F. Emanuel, University of Texas A& M. 6. J. Mahoney, University of Washington.2. D. Alexander, Waterways Experimental Station. 7. Y. R. Kim, North Carolina State University.3. G. M. Rowe and M. J Sharrock, England. 8. W. Uddin, University of Mississippi.4. L. Irwin, Cornell University. 9. S. Shoukry& G. William, West Virginia University.5. P. Ullidtz, Technical University of Denmark. 10. J. Uzzan, Technion, Israel.

121

The work presented in this chapter was initiated as a result of a round-robin test administered

by the Transportation Research Board (TRB) A2B05 subcommittee on Backcalculations of layers’

moduli. In this test, ten different research groups and individuals were requested to predict the1

depth to bedrock from the FWD measurements for two of four flexible pavement sites located in

Texas, USA. Texas DOT who provided the FWD data provided also the thicknesses of the surface

and subgrade layers of every site and the temperature of top, middle, and bottom of the asphalt layer

for every site. They also provided the measured depth to bedrock for sites No. 2 and 4. The author

participated in the test as it provided a good opportunity to evaluate the reliability of the 3D FEM

based backcalculation algorithm that was developed in Chapter 6 and to achieve the following

objectives:

1. Develop procedure for the evaluation of the apparent depth to bedrock from 3D FEM

pavement structural models which simulate FWD testing.

2. Investigate the effect of finite element model depth and the reflection from the model

bottom on the calculated deflection basin.

8.2 FINITE ELEMENT STRUCTURAL MODELS

The 3D FE models used for the backcalculation of the four Texas sites were identical to the

flexible pavement model that was used to calculate the flexible pavement site of West Virginia,

described in Chapter 6 and shown in Figure 8.1. The same input file that was used to generate the

flexible pavement model of chapter 6 was modified to be a parametric one. The advantage of using

a parametric input file is that it allows the user to change only layer thicknesses, applied load, and

122

material properties of different layers while the number of nodes, number of elements, model

boundaries, layers interface properties, conditions at model boundaries, and the subgrade layer depth

remained unchanged from those reported in Chapter 6. The parametric input file is listed in Appendix

A. In each model, the thicknesses of pavement layers were set to those of Texas sites listed in Table

8.1. The model was loaded using the measured FWD load provided by Texas DOT and shown in

Figure 8.2. In absence of any prior knowledge of the expected depth to bedrock , the thickness of

the subgrade layer in the model was left at 72 in.

8.3 EVALUATION OF LAYER MODULI

The iterative procedures described in Chapter 6 were used to backcalculate the moduli profile

of every site. The final FEM-computed deflection basins were plotted together with those

experimentally measured in Figure 8.3. For site 1, Figure 8.3 (a) shows a deviation between the

experimental and theoretical deflection basins at the position of the second FWD sensor. The reason

for this deviation is the presence of a large thermal gradient (16.6 C) in the asphalt layer, and theo

simplifying assumption (used in 3D FEM calculation) of an average elastic modulus for the asphalt

layer. Although the use of viscoelasto-plastic material model for the asphalt layer may improve the

convergence between the theoretical and experimental deflection basins shown in Figure 8.3 (a), this

would result in longer execution time. Thus for practical purposes, it was decided to use an average

elastic modulus for the asphalt layer and perform a temperature correction on the backcalculated

modulus similar to the practice used in elastic backcalculation programs.

Referring to the temperature measurements listed in Table 8.1, the backcalculated moduli

values of the asphalt layer should be adjusted to the standard temperature of 20 C (68 F). Theo o

following relation (65 ) used by the Japanese Highway agencies was used:

E = E * 10 (5)standard as -0.0184 (20-T )

123

where: E = Modulus at temperature 20 C (68(F).standardo

E = 3D FE-based backcalculated modulus at field temperature.as

T = The mean temperature of asphalt ( C).o

The 3D FEM-backcalculated layers’ moduli for each site are listed in Table 8.2 together with

three other sets of results that were independently computed by Ullidtz (66-68) who participated in

the TRB-A2B05 round robin test. Ullidtz used three different backcalculation algorithms:

1. A two dimensional (axially symmetric) finite element (2D FE) backcalculation program

with non-linear material models.

2. Waterways Experiment Station (WES) backcalculation program that is based on the elastic

layer theory.

3. A backcalculation program based on the Method of Equivalent Thickness (MET) with a

non-linear subgrade material model.

Examination of values listed in Table 8.2 reveal that the 3D FEM approach developed in this

Thesis independently produced layer moduli values that were close to the values provided by Ullidtz

for all sites. This indicates that the use of elastic material models in 3D FEM approach has no effect

on the backcalculated moduli specially for the subgrade layer. Examination of the subgrade layer

moduli backcalculated using different approaches reveals that the use of a nonlinear material model

for subgrade in the MET method resulted in subgrade moduli values which are close to those

obtained using the 3D FEM method and elastic material model. It should be remembered that the

correction factors computed in Chapter 6 are specific to MODULUS backcalculation program and

don’t apply to any of the three backcalculation algorithms used by Ullidtz.

8.4 EVALUATION OF DEPTH TO BEDROCK

Examination of the profile of displacement decay with depth at the location of the central

124

FWD sensor position shown in Figure 8.4 reveals that such a decay relation may be used to define

an apparent depth to bedrock. Thus, the same 3D finite element model used to backcalculate the

layers moduli can also be used to evaluate the depth to bedrock. The maximum vertical displacement

that propagates along the vertical line passing through the center of the FWD loading plate can be

obtained from the finite element model. From Figure 8.4, it seems plausible to assume that the

maximum vertical displacement measured at the center of the FWD loading plate decays exponentially

with depth. This assumption can be verified by plotting the natural logarithm of the deflection versus

depth as shown in Figure 8.5. The relation is a straight line over a significant portion of the curve.

Deviation from straight line relation is due to the effect of the fixed boundary at the model bottom.

The exponential decay of the maximum displacement in the subgrade layer with increasing subgrade

depth is assumed to be:

= e (6)z %%

��z

where: = Deflection at Depth zz

= FE calculated deflection at the top of subgrade.%%

Z = the depth of subgrade measured from top of subgrade to the point under consideration.

The displacement decay constant �� is determined in this analysis from the plots of Figure 8.5.

From Equation (6), the decay constant �� can be calculated as

��=1/Z . ln( / ) (7)z o

In order to minimize the error in calculation of the constant ��, it was calculated for all the

points which fall on the straight line portion of ln ( ) versus depth graph and the average value was

used to calculate the depth to bedrock.

The values of the decay constant �� obtained from Equation (7) for the four sites are listed

in Table 8.3. The apparent depth to bedrock is defined as the subgrade depth at which the vertical

125

displacement becomes very small. The definition of a small displacement can be related to the decay

of stress in subgrade layer. As it is common in the calculation of instantaneous settlement of a

foundation resting on a deep layer, the soil depth beneath the foundation should not be less than the

depth at which the maximum vertical stress decays to 10 percent of its value at the foundation level

(66). This depth can be identified by plotting the ratio between the vertical stress induced at any depth

in the subgrade to its value at the subgrade top as shown in Figure 8.6. The apparent depth to

bedrock can be predicted using the stress decay relation. However, the use of displacement decay

seems to be more convenient since the accuracy of calculating the displacement in FEM is higher than

that of stress calculation since the latter is dependent on the differentiation of nodal displacement with

respect to nodal position, so it is mesh dependant.

The plots in Figure 8.5 reveal that as the stress decayes to 10 percent of its value at the top

of subgrade, there is an 80 to 85 percent decay in subgrade displacement. Thus the deflection ratio

/ found at 10 percent decay of vertical stress is substituted in Equation (7) to calculate theo

apparent depth to bedrock, that is:

Apparent depth to bedrock =[ ln( / ) at 10% stress decay]/�� (8)o

The final values obtained after adjusting the computed depths to bedrock, so that their values are

measured from the top of the surface layer of each site, are listed in Table 8.3.

8.5 EFFECT OF 3D FE MODEL DEPTH ON 3D FEM RESULTS

Modeling of pavement structure in 3D-FEM requires adopting a pre-assumed depth of the

subgrade. The effect of this assumed depth on the model results should be examined. After evaluation

of pavement layers’ moduli and the depth to bedrock for each site using a model depth of 95 in.

(subgrade thickness= 72 in.), each 3D FE model was modified by changing the subgrade thickness

first to 40 in. and then to 144 inch. After each modification, the model for each site was loaded with

126

the corresponding FWD load and the deflection basin was obtained.

8.5.1 Effect of Model Depth on Deflection Basin

The 3D FEM-calculated deflection basins for different model depths are shown in Figure 8.7.

In each case, the subgrade depth was changed while keeping the layers’ moduli and the applied load

the same. As the depth to bedrock increases, the deflection values also slightly increase. However,

the amount of increase in deflection diminishes with the increase of the model depth. This means that

after a certain model depth, the deflection basin will remain the same and the subgrade below that

depth will not contribute to the surface deflection. This depth is the apparent depth to bedrock. The

differences observed between the deflection basins resulting from different model depths are very

small. Such differences are not expected to affect the accuracy of the backcalculated moduli. This

agrees with Zaghloul et al. (41) who found that the variation of depth to bedrock doesn’t affect the

peak surface deflections predicted by 3D-FEM.

8.5.2 Effect of Stress Wave Reflection from Model Bottom on Deflection Basin

To examine the effect of stress wave reflection from the model bottom on the 3D FEM-

generated deflection basin, reflective boundaries were applied to the bottom of the shallowest model

of each site (i.e. model with 40 inch subgrade layer thickness). Figure 8-8 illustrates that the wave

reflection causes a slight increase in the surface deflection measured at the center of the FWD loading

plate and decreases the deflections at sensor positions away from the center. The small deviations

observed in Figure 8-8 are not expected to have any significant effect on the backcalculated moduli.

8.5.3 Effect of Model Depth on the 3D FEM-Calculated Depth to Bedrock

The maximum vertical displacement in the subgrade at the position of the FWD loading plate

127

for each pavement site is plotted on a horizontal logarithmic scale versus depth in Figure 8.9. The

plots reveal that the change of the model depth slightly affects the maximum vertical displacement

observed on the top of subgrade ( ). The upper portions of the plots for model depths 95 in. ando

167 in. are almost congruent to each other. On the other hand, the vertical displacements of the

shallow models differ significantly from those obtained for the other two deeper models which

indicate that their results are influenced by the boundary conditions set on their subgrade bottoms.

The depth to bedrock was calculated for each model depth for every sites and the results are

listed in Table 8.5. The results indicate that the predicted values for the depth to bedrock resulted

from the models of depths 95 in. and 167 in. are very close to each other. The values obtained from

the shallow model are up to 25% less than those of the deeper models because of the effect of the

fixed boundary at the model bottom.

8.5.4 Effect of Model Depth on Stresses Induced in Subgrade

The above investigation of the effect of model depth is expanded to include the effect on the

stress level induced in the subgrade layer. For this reason, the vertical stress distribution is plotted for

the three different model depths as shown in Figure 8.10. The Figure shows the plots only for site 3

as an example and the other sites are similar. The plots show that at the upper one foot of the

subgrade, the vertical stresses obtained from different models are congruent to each other. For the

models of depths 95 in. and 167 in., the stress plots remain congruent up to depth of 2 ft from the

subgrade top, after which the boundary condition at the model bottom influence the stress profile in

the remaining subgrade depth.

From the above discussion, the use of subgrade layer thickness of 72 in. seems to be suitable

for use in finite element modeling of flexible pavements. A good degree of accuracy can be realized

since an increase in the model depth will not result in a significant change in the model results.

Limiting the subgrade thickness to 72 in. from the surface can significantly reduce the model size

128

which decreases the required computer memory and the computational time.

8.6 EFFECT OF LOAD DURATION ON THE DEFLECTION BASIN

To illustrate the influence of FWD loading time duration on the deflection basin, the flexible

pavement model used in site 3 was processed after modifying the load-time history so that the peak

of the load acts for a duration of 40 millisecond as shown in Figure 8.11 (a). The FEM-generated

deflection basin was plotted together with the one obtained using the shorter duration FWD load (as

measured) as shown in Figure 8.11 (b). The results in Figure 8.11 (b) illustrate that the surface

deflection under the center of the FWD loading plate increased by 150 percent. The increase in the

surface deflection decreases with the increase of radial distance from the center of load application.

The increase in the maximum deflection due to the increase of maximum load-time duration confirms

the findings of references (45-48) which reported that the deflection basins produced by an impact

load are 40 to 80 percent less than those produced by a static load of the same magnitude.

The most interesting point in Figure 8.11 (b) is that the two deflection basins intersect at an

offset of 48 in. from the center of the FWD load. This agrees with the experience-based choice of

this distance by some researchers (18,54) to calculate the subgrade modulus. The results indicate

that the deflection value at this sensor location is not affected by the assumption that FWD is acting

as a static load.

8.7 CONCLUSION

Based on the work presented in this chapter, a new mechanistic approach for evaluating the

apparent depth to bedrock has been suggested. This method can be applied for all types of pavements.

The method was verified by comparison with field measurements, as well as with the results of other

existing methods.

129

The effect of the pre-assumed FE model depth on the finite element results has been studied.

From this study, the following conclusions can be made:

1. The FE-generated deflection basin is insignificantly affected by the assumed model depth.

2. The FE-generated deflection basin is not sensitive to stress wave reflections at the bedrock.

3. The apparent depth to bedrock is the depth under which the subgrade will not deflect due

to the application of the FWD load. This indicates that the zone influenced by the FWD load

is in the load vicinity, which makes any prior knowledge about the depth to bedrock

unnecessary in backcalculation using 3D FEM.

4. For research purposes, modeling a flexible pavement structure with a subgrade thickness

of 6 ft seems to be suitable for producing satisfactory results for both displacements and

stresses at the top of the subgrade.

130

TABLE 8.1 Layer Thicknesses and Temperature Measurements.

Site 1 Site 2 Site 3 Site 4

Asphalt layer thickness, in.Base layer thickness, in.

8.00 8.00 7.25 7.2515 15 15 15

Temperature Measurements:½ in. from asphalt top ( C) 57.2 30.6 24.2 22.8o

Mid depth ( C) 50.5 28.7 24.3 21.1o

½ in. from asphalt bottom ( C) 40.6 27.5 24.4 19.4o

131

TABLE 8.2 Backcalculated Pavement Layers’ Moduli, Ksi.

A. Surface Layer

Method Computed by Site 1 Site 2 Site 3 Site 4

3D FEM This study 135 56 160 170

2D FE Ullidtz 160 140 790 669

WES Ullidtz 165 144 852 703

MET Ullidtz 154 123 669 560

B. Base Layer


3D FEM This study 450 90 120 47

2D FE Ullidtz 33.5 28.6 32.8 24.5

WES Ullidtz 31.5 27.8 23.8 19.5

MET Ullidtz 32.5 38.1 35 30.6

C. Subgrade


3D FEM This study 18 10 12 8.5

2D FE Ullidtz 36.8 10.5 18.2 11

WES Ullidtz 32.1 11.2 18.8 12.3

MET Ullidtz 20.0 8.5 11.9 8.5

132

TABLE 8.3 Comparison Between Measured and Calculated Depth to Bedrock.


Decay Constant (��), Model Depth= 95 in.

-0.03059682 -0.03478123 -0.03488303 -0.03333101

( / ) at 10% stress decayo 0.1903 0.1443 0.1446 0.1617

Calculated depth to bedrock, in. 76 78.65 77.69 76.91

Measured depth to bedrock, in.(By Texas DOT)

30.5 76 63 103

133

TABLE 8.4 Effect of Assumed Model Depth on the Calculated Depth to Bedrock.


Decay Constant (��)

Model depth= 63 in. -0.04471782 -0.046714987 -0.045303345 -0.034748846Model depth= 95 in. -0.03059682 -0.034781234 -0.034883027 -0.033331011Model depth= 167 in. -0.03007312 -0.034196126 -0.033572694 -0.032929402

Calculated Depth to Bedrock, in.

Model depth= 63 in. 60.10 64.44 64.94 74.68Model depth= 95 in. 77.22 78.65 77.69 76.91Model depth= 167 in. 78.17 79.61 79.85 77.58

134

- Sliding interface between the asphalt layer and the base (Coefficient of friction=0.90).- Fully tied interface between the base and the subgrade.

FIGURE 8.1 Finite element model.

135

0 0.020.01 0.03 0.060.050.04

120

100

80

60

40

20

0

-20

Time, sec.

0 0.020.01 0.03 0.060.050.04

120

100

80

60

40

20

0

-20

Time, sec.

0 0.020.01 0.03 0.060.050.040 0.020.01 0.03 0.060.050.04

120

100

80

60

40

20

0

-20

120

100

80

60

40

20

0

-20

140

Time, sec. Time, sec.

a. Site 1 b. Site 2

c. Site 3 d. Site 4

FIGURE 8.2 Measured FWD impact load curves used in finite element models.

-20

-15

-10

-5

0

0 20 40 60 80

Exp

FE

-25

-20

-15

-10

-5

0

0 20 40 60 80

Exp

FE

-12

-10

-8

-6

-4

-2

0

0 20 40 60 80

Exp

FE

-16

-14

-12

-10

-8

-6

-4

-2

0

0 20 40 60 80

Exp

FE

136

FIGURE 8.3 Measured and FE-calculated deflection basins.

137

FIGURE 8.4 Subgrade vertical displacement versus depth.

138

FIGURE 8.5 Subgrade vertical displacement on a logarithmic scale versus depth.

0 20 40 60 80 100 0 20 40 60 80 100

0 20 40 60 80 1000 20 40 60 80 100

40

80

120

160

Percentage of reductionPercentage of reduction

Percentage of reduction Percentage of reduction

a. Site 1 b. Site 2

c. Site 3 d. Site 4

Stress decay

Displacement decay

Stress decay

Displacement decay

Stress decay

Displacement decay

Stress decay

Displacement decay

40

80

120

160

40

80

120

160

40

80

120

160

139

FIGURE 8.6 Decay of vertical stress and displacement in subgrade.

-20

-15

-10

-5

0

0 20 40 60 80

Measured

Depth=63 in.

Depth= 95 in.

Depth=167 in.-25

-20

-15

-10

-5

0

0 20 40 60 80

Measured

Depth=63 in.

Depth= 95 in.

Depth=167 in.

-14

-12

-10

-8

-6

-4

-2

0

0 20 40 60 80

Measured

Depth=63 in.

Depth= 95 in.

Depth=167 in.

-16

-14

-12

-10

-8

-6

-4

-2

0

0 20 40 60 80

Measured

Depth=63 in.

Depth= 95 in.

Depth=167 in.

140

FIGURE 8.7 Effect of the depth to bedrock on the deflection basin.

-16

-14

-12

-10

-8

-6

-4

-2

0

0 20 40 60 80

Non-Reflective

Reflective

-14

-12

-10

-8

-6

-4

-2

0

0 20 40 60 80

Non-Reflective

Reflective

-20

-15

-10

-5

0

0 20 40 60 80

Non-Reflective

Reflective

-25

-20

-15

-10

-5

0

0 20 40 60 80

Non-Reflective

Reflective

141

FIGURE 8.8 Effect of reflective subgrade bottom on deflection basin.

142

Depth 63 in.

Depth 95 in.

Depth 167 in.

0.0001 0.001 0.01Vertical displacement, in.

20

40

60

80

100

120

140

0

Depth 63 in.

Depth 95 in.

Depth 167 in.

Vertical displacement, in.

20

40

60

80

100

120

140

0

Depth 63 in.

Depth 95 in.

Depth 167 in.

0.0001 0.001 0.01


20

40

60

80

100

120

140

0

Depth 63 in.

Depth 95 in.

Depth 167 in.

0.0001 0.001 0.01


20

40

60

80

100

120

140

0

0.0001 0.001 0.01

a. Site 1 b. Site 2

c. Site 3 d. Site 4

FIGURE 8.9 Subgrade vertical displacement for different model depths.

143

FIGURE 8.10 Effect of model depth on vertical stress distribution for site 3.

120

100

80

60

40

20

0

-200 0.01 0.030.02 0.050.04 0.070.06 0.08

Time, sec.

a. Impact load curves.

-30

-25

-20

-15

-10

-5

0

0 10 20 30 40 50 60 70 80

80 msec

40 msec

Distance, inch.

b. Deflection basins.

144

FIGURE 8.11 Effect of load duration on the deflection basin.

145

CHAPTER 9

CONCLUSIONS AND SUGGESTED RESEARCH

The importance of considering the dynamic nature of the FWD load in the deflection analysis

has been emphasized in this work. In this study, different pavement sections were evaluated with

different backcalculation programs that are currently in use. 3D Explicit Finite Element Analysis was

used to evaluate the moduli profile of different pavement structures and the resulting moduli were

compared with those obtained using three existing backcalculation programs: MODULUS5.0,

MODCOMP3, and EVERCALC4.0. The following conclusions can be made:

1. Comparison of the results obtained from the three backcalculation programs: MODULUS5.0,

EVERCALC4.0, and MODCOMP3 reveals that MODULUS5.0 has a consistent

performance for all types of pavement structures. EVERCALC4.0 and MODCOMP3

programs produce acceptable results; however, the moduli values may be overestimated

especially for the subgrade layer. The performance of the three programs decreases when

evaluating composite pavements.

2. The change of the seed moduli or the moduli range used as input for the backcalculation

programs may significantly alter the resulting moduli profile. In this case, the deflection fit

precision criterion used in backcalculation is not sufficient to judge the solution accuracy.

Thus the experience in analysis, with materials and with deflections, is essential to check that

the backcalculation process yields acceptable results.

3. A new mechanistic method for backcalculation of pavement layer moduli and estimating the

apparent depth to bedrock using 3D Explicit Finite Element approach was developed. The

method was used successfully to backcalculate pavement layer moduli for all types of

pavements: flexible, rigid, and composite. Backcalculation using 3D FEM offers the following

advantages:

146

a. The dynamic nature of the FWD load and the effects of inertia and material damping were

accounted for.

b. Layer interfaces and the 3D geometry of the pavement structure were taken into account.

4. The finite element approach enabled backcalculating the modulus of base layer in a composite

pavement structure which is extremely difficult, if not impossible, using traditional algorithms.

5. The method of evaluating the depth to bedrock is not specific for a particular type of

pavement. Therefore it may be used for rigid and composite pavements for which no method

is currently available.

6. The backcalculated modulus of subgrade using the threeconventional backcalculation

programs: MODULUS5.0, EVERCALC4.0, and MODCOMP3 requires multiplication by a

correction factor. Correction factors of 0.35, 0.24, and 0.22 were calculated using 3D FEM

for flexible, rigid, and composite pavement structures respectively.

7. The values of the correction factors obtained using 3D FEM are in good agreement with

those found by experience and recommended in the AASHTO Pavement Design Guide. This

suggests that 3D FEM backcalculation may be used as a reference for assessing the accuracy

of conventional backcalculation algorithms.

8. For doweled rigid pavements, the spacing between the transverse joints has no effect on the

deflection basin.

9. For undoweled rigid pavements, the slab length is an important factor which influences the

results of backcalculation programs.

10. For aged pavement sections in which transverse cracks developed, the FWD test should not

147

be carried out on a part of the slab that is less than 10 ft to assure that this part can produce

a reliable deflection basin provided that the slab width is 12 ft.

11. Provided that a subgrade layer thickness greater than 6 ft is used in modeling flexible

pavement structure using 3D FEM, any further increase in the subgrade layer thickness has

insignificant effect on the 3D FE-generated deflection basin.

12. Similarly, reflection of stress waves from the FE model bottom has little influence on the

FE-generated deflection basin provided that the subgrade layer thickness is greater than 4 ft.

13. When studying a flexible pavement structure using 3D FEM, limiting the subgrade thickness

to 6 ft was found to produce satisfactory results for both the stresses and displacements on

the top of subgrade layer.

14. Due to the dynamic nature of the FWD load, the pavement surface response depends on the

magnitude the FWD load pulse, shape, and duration. The assumption of static loading in

backcalculation programs may produce unrealistic results.

148

SUGGESTED FUTURE RESEARCH

The work presented in this study is one step towards a better understanding of the dynamic

response of pavement to FWD impact load. Future research studies should aim at:

1. Automation of the 3D FEM backcalculation procedures.

2. Utilization of the 3D FEM models developed for backcalculation in overlay design or in

pavement design.

3. Testing the reliability of the models developed in this thesis on a large number of pavement

sites under different environmental conditions.

149

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159

APPENDIX A

PARAMETRIC INPUT FILE TO GENERATE FLEXIBLE PAVEMENT MODEL

title FLEXIBLE PAVEMENT MODEL SUBJECTED TO FWD LOAD .

c Global Control Commands.dyna3d

lsdyopts hgen 2;endtim 0.040;glstat 0.001 matsum 0.001;d3plot dtcycl 0.001;qh 0.11;

parametersc Enter the surface Layer thickness (t1) with a negative sign, in.t1 -7.25c Enter the thickness of the Base Layer (t2) with a negative sign, in.t2 -15;

c Sliding Interface with friction Between the Surface Layer & Base.sid 1 fric 0.9 lsdsi 3;C Sliding Interface with Friction Between the Loading Plate & the Surface Layer..sid 2 fric 0.8 lsdsi 3;

plane 10.0 0.0 0.0 -1 0 0 0.001 symm;c Enter the Material Properties for Pavement Layers.dynamats 1 1 rho 2.240e-4 e 12e+4 pr 0.35;dynamats 2 1 rho 2.200e-4 e 120e+3 pr 0.30;dynamats 3 1 rho 1.950e-4 e 12.0e+3 pr 0.40;dynamats 4 1 rho 7.324e-4 e 29.0e+6 pr 0.30;

c Enter the measured Load Curve.lcd 10 0.0 2e-4 0.0 0.4e-3 0 0.6e-3 0

160

0.8e-3 0 1.0e-3 0 1.2e-3 0 1.4e-3 0 1.6e-3 0 1.8e-3 0 2.0e-3 1 2.2e-3 2 2.4e-3 4 2.6e-3 6 2.8e-3 10 3e-3 14 3.2e-3 19 3.4e-3 23 3.6e-3 30 3.8e-3 37 4e-3 47 4.2e-3 58 4.4e-3 72 4.6e-3 88 4.8e-3 107 5e-3 129 5.2e-3 152 5.4e-3 177 5.6e-3 203 5.8e-3 230 6e-3 257 6.2e-3 282 6.4e-3 306 6.6e-3 331 6.8e-3 354 7e-3 374 7.2e-3 392 7.4e-3 408 7.6e-3 422 7.8e-3 436 8e-3 449 8.2e-3 461 8.4e-3 473 8.6e-3 483 8.8e-3 493 9e-3 503 9.2e-3 514

161

9.4e-3 525 9.6e-3 536 9.8e-3 546 10e-3 558 10.2e-3 568 10.4e-3 579 10.6e-3 590 10.8e-3 600 11e-3 610 11.2e-3 620 11.4e-3 629 11.6e-3 638 11.8e-3 647 12e-3 656 12.2e-3 664 12.4e-3 673 12.6e-3 682 12.8e-3 691 13e-3 699 13.2e-3 708 13.4e-3 718 13.6e-3 726 13.8e-3 734 14e-3 742 14.2e-3 748 14.4e-3 753 14.6e-3 757 14.8e-3 759 15e-3 761 15.2e-3 760 15.4e-3 759 15.6e-3 755 15.8e-3 753 16e-3 746 16.2e-3 737 16.4e-3 729 16.6e-3 719 16.8e-3 708 17e-3 695 17.2e-3 682 17.4e-3 669 17.6e-3 657 17.8e-3 643

162

18e-3 630 18.2e-3 61518.4e-3 60318.6e-3 58918.8e-3 57519e-3 56119.2e-3 54819.4e-3 53419.6e-3 52019.8e-3 50520e-3 49120.2e-3 47820.4e-3 46520.6e-3 45120.8e-3 43921e-3 42621.2e-3 41321.4e-3 40221.6e-3 39021.8e-3 37822e-3 36822.2e-3 35622.4e-3 34422.6e-3 33322.8e-3 32223e-3 31023.2e-3 29823.4e-3 28523.6e-3 27323.8e-3 26124e-3 24924.2e-3 23724.4e-3 22624.6e-3 21324.8e-3 20125e-3 18925.2e-3 17925.4e-3 16725.6e-3 15725.8e-3 14626e-3 13726.2e-3 12826.4e-3 119

163

26.6e-3 11026.8e-3 10227e-3 9527.2e-3 8827.4e-3 8227.6e-3 7527.8e-3 6928e-3 6328.2e-3 5828.4e-3 5228.6e-3 4728.8e-3 4329e-3 3829.2e-3 3229.4e-3 2829.6e-3 2529.8e-3 2130e-3 1730.2e-3 1430.4e-3 1030.6e-3 730.8e-3 531e-3 231.2e-3 031.4e-3 031.6e-3 031.8e-3 032e-3 0;

c Define Asphalt-Concrete Layer.block1 3 31;1 16 19 22 37;1 4;

0.0 8.0 120.0;-72.0 -6 0 6 72.0;0.0 [%t1];

sii 1 2 ;2 4;1 1;2 s;

sii 1 3;1 5;2 2;1 s;

164

nr 1 1 1 3 1 2nr 1 1 1 1 5 2nr 3 1 1 3 5 2b 1 1 1 3 1 2 dy 1 rx 1;b 1 1 1 1 5 2 dx 1 ry 1;b 1 5 1 3 5 2 dy 1;b 3 1 1 3 5 2 dx 1 dy 1;

mate 1endpart

c Define Base Layer and subgrade .block1 41;1 25;1 5 15;

0.0 120;-72 72;[%t1] [%t1+%t2] [%t1+%t2-40];

mt 1 1 1 2 2 2 2mt 1 1 2 2 2 3 3

sii 1 2;1 2;1 1;1 m;

nr 1 1 1 1 2 3nr 2 1 1 2 2 3nr 1 2 1 2 2 3 nr 1 1 1 2 1 3c nr 1 1 3 2 2 3c Boundary Conditionsb 1 1 1 1 2 3 dx 1 dy 1 ry 1;b 2 1 1 2 2 3 dx 1 dy 1;b 1 2 1 2 2 3 dx 1 dy 1;b 1 1 1 2 1 3 dx 1 dy 1;b 1 1 3 2 2 3 dx 1 dy 1 dz 1 rx 1 ry 1 rz 1;

endpart

c Define Loading Plate (R=6 in).block

165

1 6 11 16 21;1 6 11 16 21;1 3;

-3. -3. 0. 3. 3.;-3. -3. 0. 3. 3.;0. 1.;

de 1 1 1 2 2 2de 4 1 1 5 2 2de 1 4 1 2 5 2de 4 4 1 5 5 2de 1 0 0 3 0 0

sf 2 1 1 4 1 2cy 0. 0. 0. 0. 0. 1. 6sf 1 2 1 1 4 2cy 0. 0. 0. 0. 0. 1. 6sf 2 5 1 4 5 2cy 0. 0. 0. 0. 0. 1. 6sf 5 2 1 5 4 2 cy 0. 0. 0. 0. 0. 1. 6

sii ; ; 1 1; 2 m;

c Ddfine applied pressure region.orpt - 0.0 0.0 -1000000 pr 1 1 2 5 5 2 1 0.145624;

mate 4endpart

merge stp 0.01

166

VITA

Gergis W. William was born in Alexandria, Egypt, on August 1, 1973. He received a Bachelor of

Science in Civil Engineering with honors from Alexandria University, Egypt. After his graduation

in June 1995, he joined the Consultative Bureau for Civil Constructions, Alexandria, as a structural

design engineer. During his employment, he took charge of several design projects which included

design of different types of hydraulic structures (Barrages, Syphons, Aqueducts, and pipelines),

bridges (over 20 bridges), roads (over 20 rural roads), three high-rise buildings, and Three steel

structures. In January 1998, he joined West Virginia University as a graduate research assistant in

the Department of Civil and Environmental Engineering, where he pursued a Master Degree in Civil

Engineering.

Publications:

1. Shoukry, S. N., G. W. William. “Performance Evaluation of Backcalculation Algorithms

Through 3D Finite Element Modeling of Pavement Structures”. Paper No. 991277, Accepted

for presentation and publication at the 78th Annual Transportation Research Board Meeting,

Washington, D.C., January, 1999.

2. Shoukry, S.N., and G. W. William. “Dynamic Backcalculation of Pavement Layer Moduli”.

Proceedings: ASNT Spring Conference and 8th Annual Research Symposium, American

Society of Nondestructive Testings, Florida, March 1999.

3. Shoukry, S.N., Gergis W. William, and D. R. Martinelli. “Assessment of the Performance of

Rigid Pavement Backcalculation Through Finite Element Modeling”. Proceedings of the

SPIE conference on Nondestructive Evaluation of Bridges and Highways III, California,

March, 1999, pp. 146-156.

4. Shoukry, S. N., and G. William. “3D FEM Analysis of Load Transfer Efficiency”.

Proceedings of the First National Symposium on 3D Finite Element Modeling for Pavement

Analysis & Design. Charleston, West Virginia, November, 1998, pp. 40-50.

5. Shoukry, S.N., D.R. Martinelli, G.W. William, and M. R. Fahmy. Applications of LS-DYNA

in Pavement Analysis and Design”. Proceedings: Fifth International LS-DYNA User’s

Conference, Detroit, Michigan, 1998.

Backcalculation of Pavement Layers Moduli Using 3D Nonlinear Explicit FEM

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