PAVIMENTOS COMPUESTOS BACKCALCULATION

7/27/2019 PAVIMENTOS COMPUESTOS BACKCALCULATION

1/504

TECHNICAL REPORT GL-90-15

BACKCALCULATION OF COMPOSITEPAVEMENT LAYER MODULIby

Mark AndersonU) Geotechnical Laboratory1"% DEPARTMENT OF THE ARMYN Waterways Experiment Station, Corps of Engineers< 3909 Halls Ferry Road, Vicksburg, Mississippi 39180-6199

OCTO0 990Ur~ $~

September 1990Final ReportApproved for Public Rpluas,(? Distr buton Unlimited

Prepared for DEPARTMENT OF THE ARMYLABORTORYUS Army Coro nf EngiineersLABORATQ~vWashington, DC 20314-1000


2/504

Destroy this report when no longer needed. Do not returnit to the originator.

The findings in this report are not to be construed as an officialDepartment of the Army position unless so designatedby other authorized documents.

The contents of this report are not to be used foradvertising, publication, o. promotional purposes.Citation of trade names does not constitute anofficial endorsement or approval of the use ofsuch commercial products.


3/504

UnclassifiedSECURITY CLASSIFICATION OF THIS PAGE Form Approved

REPORT DOCUMENTATION PAGE OMBNo. 0704-0Arla REPORT SECURITY CLASSIFICATION Io RESTRICTIVE MARKINGSUnclassified2a. SECURITY CLASSIFICATION AUTHORITY 3 DSTIBUTION/AVAILABILITY OF REPORTApproved for public release; distribution2b DECLASSIFICATIONI DOWNGRADING SC,4EOULE unlimited.4. PERFORMING ORGANIZATION REPORT NUMBER(S) S. ONITORING ORGANIZATION REPORT NUMBER(S)Technical Report GL-90-156a. NAME OF PERFORMING ORGANIZATIOIN 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATIONUSAEWES (if aplicable)Geotechnical Laboratory I6 ADDRESS (City, State, and ZIPCode) 7b. ADDRESS (City, State, and ZIP Code)

3909 Halls Ferry RoadVicksburg, MS 39180-6199Ps NAME Or FUNDING;SPuNSORiNG a8r. OFFCE S, 8OL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER

ORGANIZATION (if applicable)US Army Corps of Engineers

1C. ADDRESS (City. State, and ZIP Code) 10 SOURCE OF FUNDING NUMBERSPROGRAM PROJECT TASK WORK UNITWashington, DC 20314-1000 ELEMENT NO NO. NO. 1CCESSION NO.

11. TITLE (Include Security Classlfication)Backcalculation of Composite Pavement Layer Moduli

12. PERSONAL AUTHOR(S)Anderson, Mark13 . TYPE OF REFORT 13b. TIME COVERED 14 DATE OF REPORT (Year,Month, Day) 5.AGE COUNT

Final report FROM TO September 1990 50616. SUPPLEMENTARY NOTATION

Available from National Technical Information Service, 5285 Port Royal Road, Springfield, VA 22161.17. COSATI CODES I18 UBJECT TERMS (Continue on reverse if necessary and idnti'fyby block number)FIELD GROUP SUB-GROUP Backcalculation Falling Weight Nondestructive testingComposite pavement Deflectometer Pavement evaluation

Database Modulus Road RaterDynamic19. ABSTRACT (Continue on reverse if necessary and identify by block number)A backcalculation program called COMDEF has been written that utilizes a new database technique to speedprogram execution. Like most backcalculation algorithms, COMDEF compares measured deflections with theoreticalsolutions. However, the COMDEF approach is to apply interpolating functions to a database of precalculatedsolutions, so that the comparison basins are calculated quickly with reasonable accuracy. The state of the art ofnondestructive testing of pavements is reviewed and problems in evaluating composite pavements are discussed. Asensitivity study is presented which includes solutions using COMDEF and a general purpose backcalculationprogram. COMDEF consistently outperformed the general purpose program in both speed and accuracy. Agreementbetween laboratory modulus tests on field specimens and backcalculated moduli from COMDEF wa s reasonable. Aversion of COMDEF using a quasistatic response model is presented and the limitations of this method are discussed.Dynamic theory is presented as a more realistic way to predict structural responses. 1A version of COMDEF whichuses a dynamic response model is presented that clearly shows the importance of dynamic theory in the analysis ofnondestructive test data. -

20. DISTRIBUTION / AVAILABILITY OF ABSTRACT 21 'ABSTRACT SECURITY CLASSIFICATION[] UNCLASSIFIED/UNLIMITEO r-3 AME AS RPT []OTIC USERS Unclassified

22a. NAME OF RESPONSIBLE INDVIDUAL 22 b TELEPHONE (Include Area Code) 22c. OFFICE SYMBOL

D Form 1473, JUN 36 Previousedition$are obsolete. SECURITY CLASSIFICATION OF THIS PAGEUnclassified


4/504

PREFACE

This report was submitted as a doctoral dissertation to the Universityof Kentucky by the author, Dr. Mark Anderson, and is published herein indissertation format. The dissertation was directed by Dr. Vincent PaulDrnevich, of the Department of Civil Engineering, University of Kentucky.Dr. Anderson received his degree (Doctor of Philosophy in Civil Engineering)from the University of Kentucky on 16 December 1988.

The major funding source for th e research presented herein was theUS Army Corps of Engineers, who funded the author through an IntergovernmentalPersonnel Act (IPA) agreement with th e University of Kentucky from January1986 through December 1987. During this period, th e author developed computeralgorithms and collected data necessary fo r the completion of the project.This research was conducted at the US Army Engineer Waterways ExperimentStation (WES), Geotechnical Laboratory (GL), for the Office, Chief ofEngineers, US Army, under a project fo r the Facilities Investigation andStudies Program entitled "NDT Evaluation of Asphalt Concrete Overlays OverPortland Cement Concrete Base Pavement." During the period from January 1988through December 1988, the author completed additional research and preparedthis document, without additional funding.

Research completed at WES was conducted under the general supervision ofDr. W. F. Marcuson III, Chief, GL, Mr. H. H. Ulery, Jr., Chief, Pavement Systems Division(PSD), and Mr. J. W. Hall, Jr., Chief, Engineering Investigations, Testing, and ValidationGroup. Direct supervision of this research was provided by Dr. A. J. Bush Ill, PSD,who was the responsible Principal Investigator.

COL Larry B. Fulton, EN, is Commander and Director of WES. Dr. Robert W.Whalin is Technical Director. 7

Av o


5/504

ACKNOWLEDGMENTS

The author gratefully acknowledges Dr. Vincent P. Drnevich, aprofessional and personal role model both during graduate school and forlife. The advice, support, and encouragement of Dr. Drnevich wasinstrumental in the undertaking and in the completion of this research.

With sadness, the author acknowledges the contribution ofDr. Robert C. Deen, who served as a doctoral committee member until hisuntimely death. Special thanks to Dr. Jerry G. Rose, who replaced Dr.Deen on the committee. Grateful acknowledgment also is given for thegenerous assistance of committee members Dr. Bobby 0. Hardin, Dr. PaulM. Eakin, Dr. Ronald L. Street, and Dr. Ronald E. Phillips.

The author thanks the Office of the Chief of Engineers, US Army,the primary funding source for this research, and to all of the person-nel at the US Army Waterways Experiment Station (WES), who made the stayin Vicksburg, Mississippi, such a pleasure. The author thanks WaterwaysExperiment Station Technical Director Dr. Robert W. Whalin, GeotechnicalLaboratory Chief Dr. William F. Marcuson III, and Pavement SystemsDivision Chief Mr. Harry H. Ulery, Jr. for their support.

The author wishes special thanks to a number of Waterways Experi-ment Station employees who made exceptional contributions to thiseffort. Special thanks to the Chief of the Engineering Investigation,Testing, and Validation Group, Mr. Jim W. Hall, Jr., who was largelyresponsible for the Intergovernmental Personnel Act agreement which madethis research possible. Special thanks to Dr. Albert J. Bush, whoprovided routine supervision and a wealth of experience. Special thanksto Mr. Robert W. Grau, who helped the author gather validation data

ii


6/504

through hi s airfield evaluation program. Special thanks to Mr. Do n R.Alexander, who acted as a sounding board in numerous brainstorming ses-sions, often contributing his off-duty time. Special thanks toMr. Patrick S. McCaffrey, Jr., who provided exceptional support in thecollection of field data at the Waterways Experiment Station Bomb DamageRepair Site. Special thanks to Mr. Carlos Gonzalez, who provided assis-tance with graphic scanning. Special thanks to all of th e personnel inthe Prototype Testing an d Evaluation Unit who allowed the author use oftheir personal computers for data generation when they were on temporaryduty. Special thanks to all of the Waterways Experiment Station tech-nicians who contributed to this effort, including (but not limited to):Messrs. Thomas V. McEwen, Mitchell S. Jones, Harold T. Carr, Terry V.Jobe, S. Wallace Guy, Joseph C. Ables, and D. Dennis Mathews. Addition-ally, the author thanks fellow IPA researchers Dr. Dennis Hiltunen andDr. Soheil Nazarian for their assistance and support.

The author gratefully acknowledges Dr. Cornelius J. Higgins,Dr. Gerald P. D'Arcy, Mr. William C. Dass, and Mr. Floyd L. Mitchell ofApplied Research Associates, Inc., for their support and assistance.The author gratefully acknowledges Mr. Tommy Hopkins, Mr. Paul Heath,and Ms. Georgiana E. Anderson for their personal support at criticaltimes in th e doctoral process.

The author gratefully acknowledges Ms. Suzanne Johnston for herediting assistance during the final document preparation.

The author gratefully acknowledges Dr. Eduardo Kausel for supply-ing the source code for his mainframe dynamic structural response model.

The author gratefully and everlastingly thanks his mother,Ms . Vera Kirkpatrick Anderson, who was always there when it counted.

iii


7/504

TABLE OF CONTENTS

CHAPTER TITLE PAGE

INTRODUCTION .................................................... 1TERMINOLOGY ..................................................1BACKGROUND ................................................... 2

Historical ................................................ 2Idealized Modeling ........................................5

OBJECTIVE .................................................... 7SCOPE ........................................................ 9

II CURRENT NONDESTRUCTIVE TESTING TECHNOLOGY ...................... 10LITERATURE REVIEW ........................................... 10NONDESTRUCTIVE TESTING DEVICES .............................. 11

Introduction .............. ..........................11Quasistatic Deflection Devices ........................... 11Vibratory Deflection Devices ............................. 16Impulsive Deflection Devices ............................. 19Wave Propagation Devices ................................. 24

PAVEMENT STRUCTURAL RESPONSE MODELS ......................... 27Introduction ............................................. 27Equivalent Thickness Models .............................. 27Plate Bending Models .....................................28Multilayer Linear Elastic Models ......................... 30Time-independent Continuum Models ........................ 32Time-dependent Models ....................................35

METHODS OF BACKCALCULATION .................................. 38Introduction .............................................38Simplified Methods .......................................39Gradient Relaxation Methods .............................. 40Direct Interpolation Method .............................. 44

III DEVELOPMENT OF THE COMDEF METHODOLOGY .......................... 45SELECTION OF A NONDESTRUCTIVE TESTING DEVICE ................ 45SELECTION OF A STRUCTURAL RESPONSE MODEL .................... 47STRUCTURAL RESPONSE BY MULTILAYER LINEAR ELASTIC THEORY .... 48BACKCALCULATION OF COMPOSITE PAVEMENT LAYER MODULI .......... 60EXECUTION TIME AS A CONTROLLING FACTOR ...................... 62EVOLUTION OF THE COMDEF METHOD .............................. 66THE COMDEF METHOD ...........................................70THE METHOD OF STEPWISE DIRECT OPTIMIZATION .................. 74BISDEF VERSUS COMDEF ........................................79

iv


8/504

TABLE OF CONTENTS (Continued)

CHAPTER TIILE PAGE

RELATIONSHIP OF CRACKING IN PC C LAYER TO BACKCALCULATEDPCC MODULI ............................................80TREATMENT OF HIGH VALUES OF BACKCALCULATED PCC MODULUS ...... 81

IV SENSITIVITY STUDIES ............................................82INTRODUCTION ................................................ 82COMDEF DEFLECTION APPROXIMATIONS ............................ 85BISDEF AND COMDEF SENSITIVITY STUDIES ....................... 90RANDOM ERRORS ............................................... 96

V VERIFICATION TESTING ...........................................98INTRODUCTION ................................................ 98VERIFICATION TESTS ......................................... 107NONDESTRUCTIVE TESTING ..................................... IIIDYNAMIC STIFFNESS MODULUS (DSM) TESTS ...................... 116PAVEMENT CONDITION INDEX (PCI) SURVEYS ..................... 119FALLING WEIGHT DEFLECTOMETER WAVE MEASUREMENTS ............. 121SMALL APERTURE TESTING ..................................... 123SOIL SAMPLING AND TESTING .................................. 125LABORATORY ASPHALTIC CONCRETE MODULUS TESTS ................ 128

Background .............................................. 128Testing ................................................. 130Results........................................... 132Development of the COMDEF Temperature Data Option ....... 143

LABORATORY PCC MODULUS TESTS ............................... 145VERIFICATION OF THE DEGREE OF CRACKING IN CC LAYERS ....... 149LABORATORY PCC SPLITTING TENSILE TESTS ..................... 162REPRESENTATIVE BASIN ....................................... 167

VI DYNAMIC VERSION OF COMDEF ..................................... 174BACKGROUND ................................................. 174DYNAMIC STRUCTURAL RESPONSE PREDICTIONS BY GREEN'S

FUNCTIONS ............................................ 176USE OF DYNAMIC THEORY TO PREDICT FALLING WEIGHTDEFLECTOMETER RESPONSES .............................. 188

USE OF ARRIVAL TIME TO DETERMINE MODULI VALUES ............. 191A TRUE DYNAMIC BACKCALCULATION ALGORITHM ................... 198

Background .............................................. 198Verification Data for Dynamic Analysis .................. 202

v


9/504

TABLE OF CONTENTS (Concluded)

CHAPTER TITLE PAGE

Backcalculation Schema .................................. 212Formulation of Database Files ........................... 214Depth to Bedrock as a Controlling Factor ................ 216Role of Material Damping Ratio in he Dynamic

Calculations ......................................217Results of the Dynamic Backcalculations ................. 225Interpretation of Dynamic Backcalculation Results ....... 228

VII CLOSURE ....................................................... 230SUMMARY .................................................... 230CONCLUSIONS ................................................ 235FUTURE RESEARCH ............................................ 237

REFERENCES .......................................................... 238BIBLIOGRAPHY ........................................................ 249VITA ................................................................ 283APPENDIX A: COMDEF USER'S GUIDE ..................................... AlAPPENDIX B: COMPLETE RESULTS FROM SENSITIVITY STUDIES ............... B1APPENDIX C: PROCEDURE FOR SOIL RESILIENT MODULUS TESTS .............. CIAPPENDIX D: DESIGN PLANS FOR ASPHALTIC CONCRETE RESILIENT MODULUS

APPARATUS .........................................D1APPENDIX E: SOURCE CODE FOR RESMA.BAS ............................... ElAPPENDIX F: SOURCE CODE FOR LONGMA.BAS .............................. F1APPENDIX G: A GUIDE FOR THE USE OF THE JAMES V-METER ................ GIAPPENDIX H: SOURCE CODE FOR GREEN-MA.FOR ............................H

vi


10/504

LIST OF TABLES

TABLE TITLE PAGE

1 Trial Value Combinations for Sensitivity Studies ............. 832 Variable Matrix for Asphalt Database Files ................... 873 Construction Histories for Verification Sites ............... 1034 Core Logs and Verification Testing Quick Reference .......... 1065 FWD Data an d Backcalculation Analysis for Verification

Sites ................................................. 112

6 Verification Site Documentation by Feature .................. 1177 AC Modulus as a Function of Temperature an d Frequency ....... 1348 Approximate PCC Moduli Values from Splitting Tensile Tests..1629 Use of Direct Arrival Survey Method for FWD Data ............ 197

10 Road Rater 2008 Raw Data .................................... 21011 Real Time (Dynamic) Deflection Basin ........................ 21012 Backcalculation Schema for Dynamic Study .................... 21213 Standard Road Rater 2008 Data from BDRS Site ................ 22314 Effects of Assumed Material Damping Ratio (DR) at 20 Hz .... 22415 Tabular Results of Dynamic Backcalculation .................. 225Al Variable Matrix for Asphalt Database Files ................... A4

BI-B15 Complete Tabular Results from Sensitivity Studies ............ B2

vii


11/504

LIST OF FIGURES

FIGURE TITLE PAGE

1 Idealized Modeling of Composite Pavement Systems .............. 62 Idealized Plate Bearing Test ................................. 123 Idealized Benkelman Beam Test ................................ 144 Idealized Curvature Meter Test ............................... 155 Idealized Vibratory Deflection Test .......................... 176 Idealized Impulsive Deflectior Test .......................... 207 Typical Falling Weight Deflectometer Load Cell Output ........ 238 Frequency Spectrum of Typical FWD Load Pulse ................. 239 The Falling Weight Deflectometer (FWD) ....................... 46

10 Typical Deflection Basins .................................... 6111 Forward Response Model Time Comparison (DELTA vs. BISAR) .... 6312 Comparison of Execution Times for COMDEF an d BISDEF .......... 6513 BRATIO Method Used in SEED Program ........................... 6814 Trial Value Estimation for Stepwise Direct Optimization ...... 7415 Deflection Errors Due to the COMDEF Approximation Method ..... 8916 Summary of Results from Sensitivity StuG--s .................. 9117 Comparison of the Range of Errors in Fitted Basins ........... 9318 Comparison of the Range of Errors in Backcalculated Moduli...9319 Effect of "Random" Deflection Errors on Backcalculation ..... 9720 Site Identification Map, Godman Army Airfield (GAAF) ......... 99

viii


12/504

LIST OF FIGURES (Continued)

FIGURE TITLE PAGE

21 Site Identification Map, Sherman Army Airfield (SAAF) ....... 10122 Site Identification Map, WES Bomb Damage Repair

Site (BDRS) ........................................... 10223 Typical Sections, Godman Army Airfield (GAAF) ............... 10424 Typical Soctions, Sherman Army Airfield (SAAF) .............. 10525 Typical Section, WES Bomb Damage Repair Site (BDRS) ......... 105^6 Subsurface Exploration, Godman Army Airfield (GAAF) ......... 10927 Subsurface Exploration, Sherman Army Airfield (SAAF) ........ 11028 Mean DSM (WES 16-kip Vibrator) Versus Mean ISM (FWD) ........ 11829 Mean ISM (FWD) Versus Pavement Condition Index .............. 12030 In-place CBR Versus Backcalculated Subgrade Modulus ......... 12431 Soil Resilient Modulus Test, Feature GAAF T5E ............... 12632 Soil Resilient Modulus Test, Feature GAAF TIE ............... 12633 Soil Resilient Modulus, Feature GAAF AlE .................... 12734 Soil Resilient Modulus Test, Feature SAAF T2E ............... 12735 Apparatus for AC Resilient Modulus Test (ASTM D 4123) ....... 12936 TAI Curves for AC Modulus ................................... 13237 Published Curves for AC Modulus Versus Temperature .......... 13338 InsLantaneous AC Modulus by ASTM D 4123, Feature GAAF T5E...13639 Total AC Modulus by ASTM D 4123, Feature GAAF TE ........... 136

ix


13/504


FIGURE TITLE PAGE

40 Dynamic AC Modulus by ASTM D 3497, Feature GAAF T5E ......... 13741 Instantaneous AC Modulus by ASTM D 4123, Feature WES BDRS...13742 Total AC Modulus by ASTM D 4123, Feature WES BDRS ........... 13843 Dynamic AC Modulus by ASTM 0 349/, Feature WES BDRS ......... 13844 Laboratory AC Modulus Curves Overlaid on Published

Curves ................................................ 13945 AC Modulus Verification, Feature WES BDRS ................... 14146 AC Modulus Verification, Feature GAAF T5 E ................... 14147 Pavement Temperature Distribution ........................... 14248 Allowable AC Moduli Range in COMDEF Temperature Data

Option ................................................ 14449 Field Versus Laboratory PCC Modulus, Feature WES BDRS ....... 14750 Backcalculated PCC Modulus with Core Status, GAAF AlE ....... 15151 Backcalculated PCC Modulus with Core Status,

GAAF AIE & A2E ........................................ 15252 Backcalculated PCC Modulus with Core Status,

GAAF RIE & R5E ........................................ 15353 Backcalculated PCC Modulus with Core Status, GAAF TIE ....... 15454 Backcalculated PCC Modulus with Core Status,

GAAF T5E & T6E ........................................ 15555 Backcalculated PCC Modulus with Core Status, SAAF AIE ....... 15656 Backcalculated PCC Modulus with Core Status, SAAF A2E ....... 157

x


14/504


FIGURE TITLE PAGE

57 Backcalculated PCC Modulus with Core Status,SAAF RiE & R5E ........................................ 15858 Backcalculated PCC Modulus with Core Status,

SAAF TIE & T2E ........................................ 15959 Average Backcalculated PCC Modulus for Core Sites ........... 16 160 Correlation Between Splitting Tensile and Flexural

Strength .............................................. 16361 Correlation Between PCC Modulus and Flexural Strength ....... 16462 Backcalculated Modulus Versus Splitting Tension "Modulus"...16563 Mean Coefficient of Variation of Layer Moduli ............... 16 864 Mean Subgrade Modulus Versus Representative Basin ........... 16 965 Mean AC Modulus Versus Representative Basin ................. 170

66 Mean PCC Modulus Versus Representative Basin ................ 17067 Mean "Uncracked" PCC Modulus Versus Representative Basin ....7268 Mean "Cracked" PCC Modulus Versus Representative Basin ...... 17269 Summary of PCC Modulus Versus Representative Basin .......... 17370 Time Required to Compute Comparison Basins .................. 17571 Dynamic Time Histories Compared to Peak FWD Deflections ..... 19 072 Measured Velocity Time Histories from FWD Geophones ......... 19173 Measured Velocity Time Histories from Selected FWD

Geophones ............................................. 19 2

xi


15/504


FIGURE TITLE PAGE

74 Difference in Direct Arrival Time fo r FW D CompressionWave .................................................. 19375 Difference in Direct Arrival Time for FWD Shear Wave ........ 19376 Difference in Direct Arrival Time for FWD Rayleigh Wave.....19477 Road Rater Model 2008 .......................................20078 Schematic of the Road Rater Model 2008 ...................... 20179 Relative Phase Shift from Cross Spectrum Measurement ........ 20380 Time Domain of Reference Geophone Voltage ................... 20581 Time Domain of Comparison Geophone Voltage .................. 20582 Time Domain of Reference Geophone Velocity.................. 20683 Time Domain of Comparison Geophone Velocity ................. 206

84 Frequency Domain of Reference Geophone Velocity ............. 20785 Frequency Domain of Comparison Geophone Velocity ............ 20786 Frequency Domain of Reference Geophone Deflection ........... 20887 Frequency Domain of Comparison Geophone Deflection .......... 20888 Deflection Ratio Analogous to Transfer Function ............. 20989 "Real Time" Deflection Basins ............................... 21190 Effect of Material Damping Ratio on Phase Shift ............. 21891 Effect of Material Damping Ratio on Sensor I Deflection ..... 21992 Effect of Material Damping Ratio on Sensor 2 Deflection .... 219

xii


16/504


FIGURE TITLE PAGE

93 Effect of Material Damping Ratio on Sensor 3 Deflection ..... 22094 Effect of Material Damping Ratio on Sensor 4 Deflection .... 22095 Effect of Material Damping Ratio on Sensor 5 Deflection ..... 22196 Effect of Material Damping Ratio on Sensor 6 Deflection ..... 22197 Effect of Material Damping Ratio on Sensor 7 Deflection .... 22298 Backcalculated AC Modulus from Dynamic Analysis ............. 22699 Backcalculated PCC Modulus from Dynamic Analysis ............ 226

100 Backcalculated Subgrade Modulus from Dynamic Analysis ....... 227Al Data File "DUMMY.DTA" Used to Generate Constants Files ....... A5A2 Typical Data File "EXAMPLE.DTA" for COMDEF ................... A7A3 Interactive Screen Display During COMDEF Execution .......... AOA4 Typical Output File "EXAMPLE.OUT" .... ......................A21A5 The COMDEF Analysis System .................................. A25A6 Flowchart of the DELTA Subroutine ........................... A29A7 Flowchart of the INPUTF Subroutine .......................... A31A3 Allowable AC Moduli Range in COMDEF Temperature Data

Option ................................................ A32A9 AC Pavement Temperature Distribution ........................ A33

A1O Flowchart of the EACHL Subroutine ........................... A37Al l Flowchart of the ITERAT Subroutine .....................A39

xiii


17/504

LIST OF FIGURES (Concluded)

FIGURE TITLE PAGE

A12 Flowchart of the RANGES Subroutine ..........................A44A13 Trial Value Estimation for Stepwise Direct Optimization ..... A47A14 Flowchart of the Completion of the Method of Stepwise

Direct Optimization ................................... A49B1-B45 Complete Graphical Results from the Sensitivity Studies ..... B17D-D9 Complete Design Plans for Asphaltic Concrete Resilient

Modulus Apparatus ...................................... D2G1-G2 Views of the James V-Meter (Model C-4902) .................... G4G3-G4 Correction Factors for Steel in Travel Path .................. G7

G5 Influence of Poisson's Ratio on Modulus Equations ........... G15

xi v


18/504

CHAPTER IINTRODUCTION

TERMINOLOGY

Conventional pavements are three-layer systems which are composedof an underlying subgrade material, a base layer, an d a surface layer.The base layer is typically composed of a densely graded crushed rockmaterial. There are two general conventional pavement types, rigid andflexible, which use Portland cement concrete (PCC) and asphaltic con-crete (AC) as their surface layers, respectively. Full-depth pavementsare similar to conventional pavements, but with the surface layerfounded directly on the subgrade material.

Composite pavement is a term which has been used in various publi-cations to describe a variety of pavement types. A composite pavement,in general, is a pavement which is composed of layers and/or materialsnot commonly found in conventional pavements. Examples of compositepavements include pavements with stabilized subgrade or subbase layers,semi-rigid or rigid bases, and multiple surface layers. When usedwithout qualification within this document, the term composite pavementdescribes a full-depth Portland cement concrete pavement which has beenoverlain with asphaltic concrete.

When used without qualification in this document, the termnondestructive testing refers to load-deflection pavement evaluationtesting using either a vibratory deflection device or an impulsivedeflection device.


19/504

BACKGROUND

HistoricalThe use of nondestructive testing has been an increasingly cost

effective tool in the evaluation of both airfield and highway pavementsfor the determination of structural condition. Results from nondestruc-tive evaluations are used to estimate remaining life and allowableloads, as well as to provide data for design calculations. Evaluationmethods have been developed (Bush and Alexander 1985) which givereasonable results for both rigid an d flexible pavements. However, anincreasingly large number of rigid pavements have been overlain withasphaltic concrete. These pavements have posed particular problems forevaluation an d design.

Most design procedures for overlays of rigid airfield pavements,including the current Department of Defense (1986) procedure, use anequivalent thickness method. The typical method is to compute a designthickness of Portland cement concrete pavement and estimate an overlaythickness of asphaltic concrete which will provide equivalent support.The total overlay thickness depends not only on the existing rigid pave-ment layer thickness, but also on condition factors which are determinedfrom a visual inspection of the condition of the Portland cement con-crete slabs. This method was developed fo r the case of an initial over-lay design for an exposed rigid pavement layer, and the method ha sdeficiencies when used to design additional overlays. Overdesigns whichlead to increased costs can occur when a sound Portland cement concretelayer with a nonstructural overlay is assumed to be badly cracked.Underdesigns which lead to pavement failures can occur when a badly

2


20/504

cracked Portland cement concrete layer with a structural overlay isassumed to be of good quality. When a Portland cement concrete pavementha s already ha d an asphaltic concrete overlay, so that th e condition ofthe underlying rigid layer cannot be determined by visual inspection,there are three general evaluation alternatives for the determination ofdesign criteria. These alternatives are the use of historical data, theuse of destructive testing, or the us e of nondestructive testing.

The determination of pavement structural condition from historicaldata is ambiguous. Visual surveys have not been performed routinely onmost airfield pavements. In most cases, historical data is limited tovery general construction records. Use of construction data is compli-cated by the lack of knowledge about past overlays. A past overlay mayhave been designed for structural or nonstructural purposes, or both.Nonstructural overlays serve such purposes as improved skid resistanceor to match the elevation of an adjoining pavement section. Structuraloverlays may be used to return a damaged pavement to the original designcapability or to increase the structural capability when a change inmission has increased the design requirements. Long-term maintenanceplans or stage designs may include periodic overlays which fulfill bothstructural and nonstructural needs. Overlay designs are further compli-cated when runways are extended or built in sections. It is thereforepossible that an asphaltic concrete overlay over a rigid airfield pave-ment may be attributed to a combination of factors, some of which maynot be structurally related. Judging rigid layer condition by thethickness of overlay or other available historical data is a ques-tionable practice which usually involves the use of "rules-of-thumb" oris based on the experience of the design engineer.

3


21/504

Destructive testing for the determination of the structural condi-tion of an underlying rigid layer is preferred to the use of historicaldata, but has definite drawbacks. Small area tests, such as coring orsawing of rectangular prisms, may not be representative of the struc-tural capability of the entire underlying rigid layer. It is not pos-sible to accurately determine the condition of the underlying rigidlayer by destructive testing without gross disturbance of relativelylarge areas by pavement surface removal or pavement trenching. Thistype of testing is costly, time consuming, and can lead to confusingresults due to the sample disturbance which undoubtedly occurs duringthe removal process.

The preferred alternative for the determination of the conditionof an underlying rigid pavement layer would involve nondestructive test-ing. Past nondestructive evaluations of military airfields have typi-cally been accomplished by the dynamic stiffness modulus method (Greenand Hall 1975), which is a good indicator of the overall structuralcapability of pavements. However, the dynamic stiffness modulus methoddoes not give a clear indication of the relative structural behavior ofthe pavement layers. Recent developments in the nondestructive evalua-tion of pavements has led to the use of multilayer linear elastic model-ing (Bush and Alexander 1985). Analysis is accomplished by modeling thepavement system as an equivalent elastic layered system. Utilization ofthis technique to evaluate pavement systems makes it possible to distin-guish the relative behavior of the pavement layers. However, this dif-ferentiation is particularly difficult for rigid pavements with flexibleoverlays because both of the upper layers are relatively stiff comparedto the underlying material. To be effective, a nondestructive testing

4


22/504

procedure for these pavement types must be able to identify th e relativestructural behavior of the Portland cement concrete and asphaltic con-crete layers, so that an improved design method using multilayer linearelastic theory could be utilized.

Both evaluation an d design procedures can be improved by th e useof multilayer theories, and computer programs for this purpose have beendeveloped (Department of the Navy 1986). However, for these design pro-cedures to be effective, a fast and accurate method of determining layermoduli of elasticity must be available. The use of nondestructive test-ing for the estimation of layer moduli of elasticity is clearly the bestalternative. Analysis of nondestructive testing data using multilayerlinear elastic theory may be accomplished by existing methods fo r con-ventional pavement types, but an improved method is needed to separatethe relative behavior of adjacent layers of asphaltic concrete andPortland cement concrete.

Idealized ModelingAll common methods of nondestructive evaluation of pavement sys-

tems utilize an idealized mathematical model for comparison with thereal pavement system. Figure 1 illustrates some of the differencesbetween a typical idealized model and a real pavement system. Ingeneral, the properties of the real and idealized systems are not thesame. Use of nondestructive test data to backcalculate layer propertiesimplies that equivalent deflection responses are indicative of equiv-alent systems. In fact, this is not the case. Backcalculated moduliare effective moduli which apply only to the assumed idealized model.If layer properties from the idealized model are to be used in a

5


23/504

subsequent overlay design or remaining life prediction, it is essentialthat a consistent idealized modeling approach be used in the subsequentprocesses. As more sophisticated design procedures are developed andimplemented, consistent evaluation models are required. Use of adynamic structural response model can provide a more realistic model forcomparison and subsequent design. However, the use of a dynamic modeldoes not remove the need for consistency between evaluation and designprocedures because the layer moduli backcalculated with a dynamic modelare still effective moduli which apply only to the assumed dynamicidealized model.

REAL COMPOSITE IDEALIZED MODEL OFPAVEMENT COMPOSITE PAVEMENT

VfaterSubgrade Subgrade

/ Bedroc

ACTUAL BEHAVIOR ASSUMED BEHAVIOR1) Multiple layers 1) Few layers2) Layers have variable thickness 2) Layers are horizontal3) Properties vary with depth 3) Layers are homogeneous4) Interface friction varies 4) Interfaces are consistent5) Anisotropic and stress dependent 5) Isotropic and elastic6) Variable depth to rock 6) Constant depth to rock7)Pore pressures occur 7) Water table ignored

FIGURE 1. Idealized Modeling of Composite Pavement Systems

6


24/504

OBJECTIVE

The overall objective of this study was to develop an evaluationalgorithm for composite pavements which will utilize nondestructivetesting techniques to produce values of in-place modulus of elasticityof the principle layers. This objective was accomplished by:

1. Reviewing current methods for nondestructive testing,structural response modeling, and backcalculation oflayer moduli of elasticity.

2. Determining suitable nondestructive testing equipmentfor composite pavements for an implementation orientedmethod as well ,s a method utilizing a dynamic struc-tural response model.

3. Developing an algorithm for the backcalculation of layermoduli of composite pavements from nondestructive test-ing data. Validation of the algorithm was accomplishedby a sensitivity study which used theoretical data tocompare known theoretical modulus values to backcalcu-lated values. A User's Guide was prepared.

4. Verifying the evaluation method on field test sites.Nondestructive data were analyzed to produce backcalcu-lated moduli values. The backcalculated moduli valueswere compared with moduli values from both field andlaboratory testing.

5. Examining the acceptability of layer moduli values cal-culated using multilayer linear elastic (quasistatic)theory. The backcalculated moduli values were used in a

7


25/504

dynamic structural response model to predict dynamicdeflections which were compared with measured dynamicdeflections.

6. Developing a version of th e algorithm which uses dynamictheory. This version was used to demonstrate the adapt-ability of the COMDEF method and also to demonstrate theimportance of using dynamic theory in the analysis ofnondestructive testing data.

8


26/504

SCOPE

The scope of this study was restricted to the development of amethod for th e estimation of layer moduli of elasticity of three layerpavement systems composed of a full-depth Portland cement concrete pave-ment which has been overlain with asphaltic concrete and is supported bya uniform subgrade material. Emphasis was given to development of amethod which could be quickly implemented into routine evaluation proce-dures, but which provides a framework such that future improvements intheoretical modeling ca n be incorporated easily. The scope included ademonstration of th e adaptability of th e program by incorporation of adynamic model within the backcalculation algorithm.

9


27/504

CHAPTER IICURRENT NONDESTRUCTIVE TESTING TECHNOLOGY

LITERATURE REVIEW

Three separate computerized literature searches have been com-pleted by the author on the subject of nondestructive testing of pave-ments. All references reviewed are listed in the Bibliography. Currenttechnology is presented in three major sections. These are:(1) nondestructive testing devices, (2) pavement structural responsemodels, and (3) methods of backcalculation. Several summary reportswere utilized in the literature review portion of this study whichprovided information as well as identifying additional references forreview. These include summary reports by Hall and Alexander (1985),Bush (1980 a,b), Lytton, et al. (1986), an d Moore, et al. (1978).

10


28/504

NONDESTRUCTIVE TESTING DEVICES

IntroductionA number of nondestructive testing devices are available. These

may be grouped into four general areas: (1) quasistatic deflectiondevices, (2) vibratory deflection devices, (3) impulsive deflectiondevices, an d (4) ave propagation devices. Several summary reports wereutilized in the review of nondestructive testing devices which gave goodcomparative descriptions of their relative capabilities (Bush 1980a,Smith and Lytton 1985, and Hall 1987).

Quasistatic Deflection DevicesThe nondestructive test device which most nearly represents a

static loading condition is the plate bearing test. In pavements test-ing, the reaction for the plate bearing test is usually generated with ahydraulic jacking system applied against a large reaction mass. Thereaction mass is typically a large truck or other heavy constructionequipment. To reduce plate curvature under the heavy loadings required,a stacked series of decreasing diameter steel plates is used to transmitthe load from the hydraulic jack to the largest diameter plate at thepavement surface. The typical data from this test is a series ofmeasurements of the gross load an d deflection of the plate as measuredagainst a reference bar. An idealized illustration of the plate bearingtest is shown in Figure 2. Complete details about the equipment andtesting method may be found in various references (Lytton, et a7. 1975,The Asphalt Institute 1978, and ASTM D 1196-64). Although this test hasbeen used in various research and evaluation tests in the past, it is

11


29/504

not commonly used at the present time. The main reasons for the testfalling into disfavor include the time required to set up an d completethe testing, the difficulty in establishing a reference bar whichprovides a fixed datum, the limited amount of information which ca n bederived from gross load-deflection data, and the heavy equipmentrequired on site to provide the reaction mass.

Reaction ForceDATUM-AU ------ --- ----- ---------- ------------ -

-=Initialo Poti o A Loadedo Position

------------------- mtRIGID PLATE.................

FIGURE 2. Idealized Plate Bearing Test

A second nondestructive testing device for the measurement ofquasistatic deflection of pavements is the Benkelman Beam. While somemodified beams have been used for this test, the standard Benkelman Beamis 12 feet (3.65 m) long, with a pivot at one of the third points. Thelonger, 8 feet (2.44 m), levered end rests on the pavement and deflectsdownward as the pavement deflects downward. The shorter, 4 feet(1.22 m), levered end deflects upward as the pavement deflects downward,and this movement is measured by a dial indicator at the end of the

12


30/504

beam. The standard load is applied by a truck which has an 18 kip(80 kN) load distributed on the dual wheels of a single axle. There aretwo standard test methods for the Benkelman Beam Test, th e AASHTO method(AASHTO T 256-77) and The Asphalt Institute method (The Asphalt Insti-tute 1983), which is also known as the Canadian Good Roads Associationmethod. Both of the methods use a truck with the standard 18 kip(80 kN) axle load, but each method uses a different standard truck tire.Both methods are rebound tests, with the initial reading taken while thepavement is loaded with the standard load and the final reading takenafter removal of the load. An idealized illustration of the BenkelmanBeam test is shown in Figure 3. The Benkelman Beam test has been usedextensively in the past for research and evaluation testing. Thereasons for past acceptance of this test include the relatively lowexpense for obtaining, maintaining, an d transporting the equipment, thecapability to apply realistic wheel loads during the testing process,and a relatively large base of historical data. The Benkelman Beam testis not commonly used at the present time. One problem with the Benkel-man Beam test is that it is a relatively slow test compared with manynewer methods. However, the major reason for the test falling into dis-favor is the relative difficulty in the interpretation of the data. Thelack of an independent datum makes interpretation difficult, par-ticularly for cases which involve pavements which are at leastmoderately stiff. In these cases, the pivot point of the beam may bewithin the deflected area influenced. If there is displacement of thepivot point by the load, the measured deflection will be less than theactual total deflection due to the loading. In addition, the overall

13


31/504

deflected shape is difficult to determine with this test. Often, theresults (as with the plate bearing test) are restricted to gross load-deflection data.

DIALINDICATORRELEASEDPOSITION

LOAD

PIVOT

DEFLECTEDPOSITIONFIGURE 3. Idealized Benkelman Beam Test

A third nondestructive testing device for the measurement ofquasistatic response of pavements is the Curvature Meter. This deviceis used to predict the curvature of the deflected pavement surface undera typical axle load. The device consists of a reference bar supportedat each end and a spring dial gauge at the center. The test predictsthe curvature of the pavement under the tire load based on the knownchord length (length of reference bar) an d the middle ordinate (measureddeflection) and is described in several references (Idaho Department ofTransportation 1965, Guozheng 1982). An idealized illustration of theCurvature Meter test is shown in Figure 4. The Curvature Meter has

14


32/504

never been a commonly used test, even though it is inexpensive and easyto perform, due to the difficulty in interpreting the data. A standardtest method has not been accepted, and reference bars of differinglengths give confusing results (Guozheng 1982). In addition, the pave-ment curvature measured in this test appears to be more indicative ofthe capability of the near surface layers and has not been shown to be auseful indicator of the relative structural capability of pavementlayers.

CHORD LENGTH$ S! LOAD

; [ " MIDDLE

"ORDINATE

FIGURE 4. Idealized Curvature Meter Test

A number of automated tests are available which use beam-deflection principles similar to the Benkelman Beam test. These includethe LaCroix Deflectograph (Kennedy 1978), the British Pavement Deflec-tion Data Logging Machine (Kennedy, et al. 1978), the California Travel-in g Deflectometer (Roberts 1977), and the CEBTP Curviameter (Paquet1978). All of these tests provide automated testing using a beam-deflection principle and displacement transducers, except the CEBTP Cur-viameter which uses geophones to measure the displacement by electronicintegration of velocity output. None of these testing devices have ever

15


33/504

achieved widespread acceptance. While automation of the beam-deflectionprinciple ha s made the time per test comparable with newer nondestruc-tive test methods, the problems with data interpretation remain. Aswith the standard Benkelman Beam test, the beam support may beinfluenced by the wheel load and it is difficult to define the overalldeflected shape of the pavement under the load.

Vibratory Deflection DevicesVibratory deflection devices have gained a great deal of accept-

ance in pavement research and evaluation. Most common vibratory deflec-tion devices have the same basis. A static preload is applied to thepavement, a haversine loading is superimposed on the static preload, andthe peak deflections caused by the dynamic loading is measured atvarious radial distances away from the load by the electronic integra-tion of the velocity outputs of geophones. The static preload is neces-sary to provide stability during the test, i.e. to hold down the testingdevice during the unloading portion of the sine loading. The magnitudeof the preload is typically near the half-amplitude of the sinusoidalloading. A major advantage of vibratory deflection testing as comparedto quasistatic deflection testing is the use of geophones to measure thepavement deflection. By electronically integrating the geophonevelocity outputs, the need for a fixed datum as reference is eliminated.An inertial reference is utilized, so that the measured peak deflectionsare the deflections which can be attributed to th e dynamic loading. Anillustration of an idealized vibratory deflection test is shown inFigure 5.

16


34/504

P(t) A sin (ct)GEOPHONE

LOADPLATE d(t) = D sin (wt)

FIGURE 5. Idealized Vibratory Deflection Test

The first vibratory deflection device to gain widespread accept-ance, and the most commonly used, is the Dynaflect (Uddin, et al. 1983).The Dynaflect, manufactured by Geo-Log, Inc., of Granbury, Texas, gener-ates its dynamic loading with a dual rotating mass system. This systemuses two eccentric flywheels which rotate in opposite directions an d arebalanced so that their horizontal components cancel. The vertical com-ponents of the two rotating masses combine to produce a very smoothsteady-state sinusoidal loading with a peak-to-peak amplitude of 1.0 kip(4.4 kN) at a frequency of 8 Hz. With a typical static preload of about2 kips (8.9 kN), the typical total load varies from 1.5 kips (6.7 kN) to2.5 kips (11.2 kN), and is applied to the pavement surface through apair of 4 inch (0.1 m) wide, 16 inch (0.4 m) diameter wheels. Deflec-tions are measured by the electronic integration of the outputs fromfive geophones (210 ohm, 2. 4 Hz , shunted). The geophones are suspendedfrom an automated placing bar and are typically spaced at 1 foot (0.3 m)

17


35/504

intervals, beginning at the center point between th e loading wheels. Amajor advantage of the Dynaflect over common hydraulic vibratory deflec-tion devices is its transportability, due to the relatively light weightof the loading trailer. Another advantage is the smooth loading func-tion produced by the rotating mass loading system. The main disad-vantage of the Dynaflect is the relatively small magnitude of dynamicload, which is not variable. For stiff pavements, the peak-to-peakdynamic load of 1 kip (4.4 kN) produces deflections with such low mag-nitudes that small errors in the measurement of the deflections maycreate significant errors in subsequent data analysis. Another disad-vantage is the fixed frequency of the Dynaflect loading (8 z).

The most widely accepted hydraulic vibratory deflection device isthe Road Rater (Sharpe 1978), which is manufactured by FoundationMechanics, Inc., of El Segundo, California. The available modelsinclude the 400A, 400B, 2000, and 2008. The model 400A has the uniquefeature of a bumper mounted loading device. All of the other Road Ratermodels are trailer mounted. Series 400 Road Raters use two rectangularload plates of 4 inches (0.1 m) by 7 inches (0.2 m), spaced at 10 inches(0.3 m) center to center. Series 2000 Road Raters use a circular loadplate of 18 inches (0.5 m) diameter. Static load for the model 400A isvehicle dependent. Static loads for the models 400B, 2000, and 2008 ar e2.4 kip (11 kN), 3.8 kip (17 kN), and 5.8 kip (2 6 kN), respectively.Dynamic load ranges are 0.5 kip to 1.0 kip (2 N to 4 kN) for the model400A, 0.5 kip to 3.0 kip (2 kN to 13 kN) for the model 400B, I kip to5 kip (4 kN to 24 kN) for the model 2000, and 1.2 ki p to 8 ki p (5 kN to36 kN) for the model 2008. Deflections are determined by the electronicintegration of the velocity outputs from four geophones (590 ohm,

18


36/504

4.5 Hz, shunted), typically spaced on 1 foot (0.3 m) centers from thecenter of th e loading plate(s). An advantage of the Road Rater is thatthe dynamic load magnitude and frequency ca n be varied by the operator.Disadvantages include the limited dynamic load capabilities of theseries 400 models and th e high static loading of the series 2000 models.

A few other vibratory deflection devices have been used for pave-ment analysis, bu t these ar e typically custom designed and manufactured.Examples of custom devices include th e Waterways Experiment Station "WES16-kip Vibrator" (Hall 1973) and the Federal Highway Administration"FHWA Thumper" (May 1981). These devices have similarities to the othervibratory deflection devices, but have th e obvious disadvantage of notbeing generally available to th e engineering community.

Impulsive Deflection DevicesImpulse deflection testing is typically accomplished by a device

known as the Falling Weight Deflectometer (FWD). The basis of th e fall-ing weight test is to lift a weight to a height above th e pavement anddrop it on a spring system which transfers th e impulse to a load plate,and subsequently measuring the impulse force transmitted to the loadplate and the peak deflections at various radial distances from theimpact point. The test imparts a very small static preload to the pave-ment prior to the impulse. A rubber buffer system and a rubber padunder the load plate help to spread the loading function over a durationof about 30 milliseconds, approximating the passing of a moving wheelload. An idealized impulsive deflection (Falling Weight Deflectometer)test is illustrated in Figure 6. Numerous authors have noted the advan-tages of the Falling Weight Deflectometer. For example, the Falling

19


37/504

Weight Deflectometer provides the most realistic loading function of anynondestructive testing device compared to actual moving wheel loads(Hoffman 1983), is the fastest and most versatile nondestructive testingdevice (Bentsen, et al. 1988), and has been rated as the best overallpavement testing device (Lytton, et al. 1986).

Falling IWeight T I inch 1000 mils = 25.4 mmDrop HeightI

S"g I'$

RADIAL DISTANCE, inchesP 12 24 36 48 60 72

20

FIGURE 6. Idealized Impulsive Deflection Test

In the United States, the most widely used impulsive deflectiondevice is the Dynatest 8000 Falling Weight Deflectometer System (Ullidtzand Stubstad 1985), available through Dynatest Consulting of Ojai,California. Based on Bretonniere's (1963) early work, the Technical

20


38/504

University of Denmark, the National Danish Road Laboratory, and theDynatest Group have gradually developed and employed the Falling WeightDeflectometer for use in the nondestructive testing of highway and air-field pavements. The Dynatest 7800 Falling Weight Deflectometer wasintroduced in 1977. This equipment showed promise but needed moreautomation to work well in a production testing situation. The Dynatest8000 Falling Weight Deflectometer Test System was introduced in 1981.This system consisted of three parts, the Dynatest 8002 Falling WeightDeflectometer, the Dynatest 8600 System Processor, and the Hewlett-Packard HP-85 Portable Computer. The Dynatest 8000 Falling WeightDeflectometer System can produce a dynamic peak load of 25 kips (111 kN)and allows the simultaneous measurement of peak load an d seven peakdeflections. Deflections ar e calculated by the electronic integrationof the outputs from seven geophones, typically spaced at I foot (0.3 m)intervals from the load. The load is produced by dropping a weight on aloading plate of approximately 1 foot (300 mm) diameter. The loading istransient and of short duration (about 30 milliseconds). The load isadjustable both by varying the amount of weight dropped an d by varyingthe height of drop. For testing of composite airfield pavements, themaximum dynamic load of 25 kips (111 kN) is normally used for non-destructive evaluation. This loading level simulates the load durationand stress levels produced by the passing of one wheel of a heavilyloaded aircraft. Use of the highest load level also increases the mag-nitude of deflections. High deflection magnitudes decrease measurementround-off errors and improve measurement signal-to-noise ratios. Inweakened areas, excessive deflections can occur when the maximum load isused. Deflections greater than the allowable value of 79 mils (2 mm)

21


39/504

cannot be measured accurately by the Falling Weight Deflectometergeophones. The Falling Weight Deflectometer is equipped with an errormessage to 'ndicate that a deflection ha s exceeded th e allowable value.When this occurs, the load is reduced by adjusting the height of drop.

Dynatest has also developed a prototype device called the HeavyWeight Deflectometer (HWD) which is capable of providing impulsive loadsof very high magnitudes. The Heavy Weight Deflectometer is intended forevaluating very stiff pavement systems such as rigid airfield pavementsdesigned for higher magnitude traffic loadings (Bentsen, et al. 1988).The Heavy Weight Deflectometer has a maximum impulse load of 56 kips(250 kN). Other impulsive deflection devices available in this countryinclude the PaveTech Falling Weight Deflectometer (Smith and Lytton1983), the Phonix Falling Weight Deflectometer (Smith an d Lytton 1983),and the KUAB Falling Weight Deflectometer (Bentsen, et al. 1988). Noneof these devices are as fast or versatile as the Dynatest 8000 FallingWeight Deflectometer System (Bentsen, et al. 1988), but all share

similar advantages and disadvantages. The advantages of the FallingWeight Deflectometer are its speed of testing, transportability, lowstatic preload, and its close approximation of the passing of a wheelload. A disadvantage of the Falling Weight Deflectometer is the com-plexity of the transient test dynamics. A typical Falling WeightDeflectometer load pulse is shown in Figure 7. The distorted shape istypical of the test, due to the complex load buffering system. Figure 8shows the load magnitude spectrum in the frequency domain as obtained bya Fast Fourier Transform for the load pulse shown in Figure 7.

22


40/504

26z 24' 20&$18" 16

14 1 kip 4.448 kNo 1210S8

S6S4

o 2

0 10 20 3'0 40 5'0 6'0 7'0 80TIME, milliseconds

FIGURE 7. Typical Falling Weight Deflectometer Load Cell Output

0.9n 0.8

-t 0.70.60.5 I kip 4.448 kN

0 0.4S0.3S0.2

0.10*0 100 200 300 400 500

FREQUENCY, HzFIGURE 8. Frequency Spectrum of Typical FWD Load Pulse

23


41/504

By inspection of Figure 8, there are large magnitudes at all frequenciesup to about 60 Hz and significant energy at all frequencies up to about250 Hz for the Falling Weight Deflectometer test. In addition, the rub-ber buffer system and rubber pad beneath the load plate are difficult tomodel properly.

Wave Propagation DevicesThere are a number of wave propagation devices and techniques cur-

rently under study and development. None of these techniques have beendeveloped sufficiently to be useful for routine pavement evaluation, butare worthy of mention due to the potential of these tests for futureevaluation procedures. Typical wave propagation techniques for pavementevaluations use the principle of dispersion of Rayleigh waves. Disper-sion is a change in wave velocity with frequency, or equivalently withwavelength. In a homogeneous, elastic half-space, the velocity ofpropagat~on of Rayleigh waves is independent of frequency. However,there is dispersion of Rayleigh waves in a layered medium. Rayleighwaves with longer wavelengths tend to propagate at deeper depths, sothat the dispersion of the Rayleigh waves in a layered system is indica-tive of the relative material properties of the component layers. Thereare three common methods of generating Rayleigh waves for pavementevaluations. These are drop weight devices which provide very shortrise times, vibratory devices, and strike hammers. An example of a dropweight device is the Texas Drop Hammer (Heisey 1981). An example of avibratory device is the Air Force Nondestructive Pavement Testing Van(Steedman 1979). A variety of strike hammers have been used in a ne wtechnique termed the spectral analysis of surface waves (SASW) method,

24


42/504

with progressively larger hammers being used to generate longerwavelengths (Nazarian, et al. 1983). The majority of recent research onpavement evaluation by wave propagation has centered on the spectralanalysis of surface waves technique. Measurement of dispersion isaccomplished by monitoring the outputs of two transducers separated by aknown distance. Spectral analysis is used to determine phase shift as afunction of frequency. A dispersion curve of surface wave phasevelocity as a function of frequency may be determined by the correctapplication of the Haskell-Thomson formulation for Rayleigh wavepropagation in a multilayered medium (Haskell 1953, Thomson 1950).Recent advances in data reduction techniques have greatly improved thequality of the dispersion curves determined by the spectral analysis ofsurface waves method (Drnevich an d Sayyedsadr 1987). Determination oflayer properties requires inversion of the dispersion curve to obtain arelationship of wave velocity as a function of depth. This very dif-ficult process is typically performed by making assumptions about thedepth of propagation as a function of wavelength (Heisey 1981) or byapplying a trial and error iteration to determine the inverted relation-ship (Nazarian, et al. 1983). Successful application of either of thesemethods requires a great deal of experience and judgment. Widespreadacceptance of wave propagation techniques for pavement evaluation willrequire more sophisticated methods for the inversion process. The dif-ficulty in obtaining a valid relationship for wave velocity as a func-tion of depth is the biggest disadvantage of the spectral analysis ofsurface waves method. Another disadvantage is the time required to col-lect enough data to provide a well defined dispersion curve. The big-gest advantage of this method, when sufficiently developed, is th e

25


43/504

ability to determine layer properties when the layer thicknesses areunknown. Proper application of this method will allow layer thicknessesto bc determined from the dispersion data by modeling the pavement sys-tem as a large number of thin layers and comparing the materialproperties of adjacent thin layers.

26


44/504

PAVEMENT STRUCTURAL RESPONSE MODELS

IntroductionStructural response models are used to predict the response of

pavements to external loadings. A good structural response model shouldbe able to predict the responses for a nondestructive test device andalso be able to predict actual responses to service traffic. This com-bination allows a design engineer to predict design responses from apavement evaluation within the same framework. This section provides ageneral discussion of currently available structural response models,which may be grouped into five general categories: (1) equivalentthickness models, (2) late bending models, (3) ultilayer linear elas-tic models, (4) time-independent continuum models, and (5) time-dependent models.

Equivalent Thickness ModelsThe concept of equivalent thickness (Odemark 1949) allows a multi-

layered pavement to be represented by a single layer of known elasticmodulus. The formula used to calculate the equivalent thickness is:

nTeq= cTi(Eu/Eeq)1/3 (1)i=1where

Teq = the equivalent pavement thicknessT. = actual thickness of the ith pavement layer, i=1,...,nE = actual modulus of the ith pavement layer, i=l,...,nEeq = the assumed modulus of th e equivalent pavementc = Odemark's constant = 0.8 to 0.9

27


45/504

The equivalent system is assumed to have the same responses as theactual pavement system, so that response predictions can be made quicklywith classical Boussinesq theory (Boussinesq 1885).

Ullidtz (1973) developed a more advanced approach which allowedthe use of a nonlinear (stress softening) elastic subgrade model byutilizing a set of deflection ratio curves. While this method is betterthan the traditional equivalent thickness method, it is still a rela-tively simple approach which can lead to significant errors in responsepredictions (Kuo 1979, Hung, et al. 1982).

The advantage of the methods which use equivalent thickness con-cepts is in the speed of calculation. Since the relationships areempirical and are represented by very simple equations, a solution canbe found extremely quickly. However, the simplification of the problemmakes these methods unreliable.

Plate Bending Models

The classical differential equation for bending of a medium thick-ness plate (Timoshenko and Woinowsky-Krieger 1959) has been used toprovide simple solutions for structural response of rigid pavements.This differential equation is:

Eh3 a4w(x,y) a4w(x,y) a4w(x,y)I + 2 + = p(x,y)-q(x,y) (2)12(1-A 2) ax Ox2 ay, aywhere

E = modulus of elasticity of the concrete slabI&= Poisson's ratio of the concrete slab

28


46/504

h = thickness of the concrete slabw(x,y) = deflection of the slab at point (x,y)p(x,y) = externally applied loadq(x,y) = reaction of the idealized subgrade

Use of the differential equation for plate bending has been implementedin two different simple models. The first case is Westergaard's (1926)formulation for maximum stresses an d deflections in a slab of infinitesize on a Winkler foundation. The second case was formulated by Hogg(1938) and by Holl (1938) for the case of a slab of infinite size placedon a semi-infinite elastic subgrade.

The assumption of th e Winkler foundation is a series of springs,each of which deflects in direct proportion to the load applied at thatpoint. Westergaard formulated equations for maximum stress and dis-placement for three different loading conditions. These are the inte-rior loading condition, edge loading condition, and corner loadingcondition. Influence charts (Pickett and Ray 1951) may be used toextend Westergaard's theory for the case of multiple loads. The mathe-matics of a plate on an elastic solid is more complicated than for theWinkler foundation and the solution for the maximum stress and displace-ment has been formulated (Hogg 1938, Holl 1938) only for the case of asingle load at the interior of an infinite slab. Use of classical platetheory has been used in various algorithms and methods, including thePortland Cement Association (Packard 1973) design method for portlandcement concrete pavements. As with equivalent thickness methods, themajor advantage of simple models based on plate theory is in the speed

29


47/504

of calculation. However, these methods cannot model multilayer pave-ments without equivalent thickness techniques, and even then predictonly the maximum stresses an d displacements.

Multilayer Linear Elastic ModelsRecent developments in nondestructive evaluation of pavements has

led to the use of layered elastic modeling (Bush and Alexander 1985).Analysis is accomplished by modeling the pavement system as an equiv-alent elastic layered system. Utilization of this technique makes itpossible to model the behavior of multiple distinct pavement layers.The solution to a multilayered system was first formulated by Burmister(1943), an d was limited to a two or three layer case. Burmister's workwas extended into an n-layer case by Mehta and Veletsos (1959). Th egeneral method of solution is to assume axial symmetry an d find a stressfunction which satisfies the governing differential equation for each ofthe layers. Numerical techniques are used to solve for a set ofintegration constants for the stress function which can be used to cal-culate predicted values of stress and displacement. The first commonlyavailable multilayer program for structural response modeling of pave-ments was the program LAYER, developed by the Chevron Oil Company(Michelow 1963). LAYER ha d severe limitations, particularly that only asingle load could be used, and that slip at the interface between layerswas not allowed. LAYER was improved and has become commonly known asCHEVRON. CHEVRON allowed multiple loads, but still allowed no slipbetween layers. ELSYM5 was developed by Ahlborn (1972) an d is based onthe LAYER program. ELSYM5 included significant improvements, includinga choice between full friction (continuity in displacement) or full slip

30


48/504

(continuity in stress) at the interface between layers. BISAR,developed by the Shell Oil Company (1978), further extended the state-of-the-art by allowing a range of slip conditions.

Multilayer elastic theory predicts the elastic response to staticor quasistatic loads. However, use of an equivalent elastic system canbe useful when analyzing dynamic loads and deflections. While thequasistatic analysis approach is certainly an empirical correlation whenapplied to dynamic nondestructive testing, a wealth of literature hasindicated that the empirical predictions based on linear elastic modelsare useful for evaluation and design calculations. For response pre-dictions of nondestructive testing loads, the typical method is o modelthe peak dynamic load as an equivalent quasistatic load and to assumethat the calculated equivalent elastic deflection basin is a goodapproximation of the envelope of measured peak deflections. Research byBodare and Orrje (1985) indicated that the theoretical dynamic modulusfrom a falling weight test approaches the theoretical static modulus fora homogeneous half-space when the time to peak load is relatively long.Although th e time length which would be considered long is a function ofvarious factors, including material properties an d load radius, Bodareand Orrje (1985) presented an example using typical system propertieswhich indicated that the needed time to peak was about 10 milliseconds,which is less than the time to peak of the Falling Weight Deflectometer.The multilayer linear elastic model tends to give larger deflectionsthan measured dynamic peak values when the bottom layer is assumed to besemi-infinite. Past research (Bush 1980) has indicated that agreementbetween predicted elastic deflections and measured dynamic deflectionsis improved if a rigid layer is placed in the equivalent elastic system

31


49/504

at a depth of 20 feet. Although this assumption is an empirical cor-relation, other researchers (Roesset and Shao 1985, Mamlouk 1985) havesupported the use of this assumption.

Time-independent Continuum ModelsNumerical application of continuum mechanics to pavement struc-

tural response modeling can allow more generalized descriptions to beincluded in the structural description. Continuum methods for makingstructural response predictions of pavements include the discrete ele-ment method, the finite element method, and the finite differencemethod.

Early development of continuum codes for rigid pavement analysiscentered around the discrete element method. Newmark (1949) developedthe use of discrete elements for plate analysis, and Hudson and Matlock(1966) extended the method to include rigid pavement models. The dis-crete element formulation for rigid pavement analysis implemented byHudson and Matlock is a lumped parameter model which idealizes the rigidslab as a collection of rigid bars, torsional bars, and elastic joints,which is supported by vertical springs. The equilibrium equation forthis lumped parameter system may be expressed in matrix form as:

[K] (w) (F) (3)where

[K] = the stiffness matrix{w) = the displacement vector(F) the load vector

32


50/504

Use of the discrete element method offers a significant improvement overthe simple plate models discussed previously, by allowing a moregeneralized description of th e slab system. Historically, this methodhas the advantage of requiring much less computer capability than isrequired by many newer finite element codes. However, with the com-puters which are available at the current time, this advantage hasbecome a smaller consideration.

The more popular method of time-independent continuum analysis ofpavements systems has become the finite element method. Although therewere other programs which pioneered the field of finite element analysisof pavements, such as KENTUCKY (Huang and Wang 1973), the use of thefinite element method for structural response modeling of pavements waspopularized by two codes developed at the University of Illinois atUrbana-Champaign. These time-independent continuum codes are calledILLI-SLAB (Tabatabaie-Raissi 1977) and ILLI-PAVE (Thompson 1982), andare used to make structural response predictions for rigid an d flexiblepavements, respectively. The finite element method breaks the pavementinto a set of discrete bodies, or "finite elements." Each element hasan element stiffness matrix, [k], which relates the element forces, (p),to the element displacements, (6). That is, for each element:

[k] (6) = (p) (4)A global stiffness matrix, [K], is formulated by superposition of theeleme... stiffness matrices, so that the generalized forces for th e sys-tem, (P), may be related to the generalized displacements, (A). Thatis, for the system:

[K] (A) (P) (5)

33


51/504

Both ILLI-SLAB and ILLI-PAVE simulate a three-dimensional pavementsystem with a two-dimensional finite element algorithm. A reasonabledegree of accuracy is achieved by the use of simplifying assumptions,such as axisymmetry, so that the three-dimensional behavior isapproximated numerically by a set of elements, each of which isrestricted to two-dimensional behavior. Three-dimensional codes providea more realistic formulation, since each finite element can behave in atrue three-dimensional sense. An example of a true three-dimensionalfinite element code which has been used for pavement structural responsemodeling is the SAP (Wilson 1969) program, which was used byTabatabaie-Raissi (1977) in the development of ILLI-SLAB. While it istrue that the three-dimensional finite element model is the moreaccurate from a theoretical viewpoint, the difference in complexity issignificant. While programs such as ILLI-SLAB and ILLI-PAVE have hadsufficient development so that they are reasonably fast an d easy to use,current three-dimensional codes require a high degree of sophistication,not only in terms of the computer equipment required, but also sophis-tication of the user/operator. Errors in solutions can arise due toviolation of computer memory requirements, as well as errors inmesh/element formulations or data manipulations. The additionalaccuracy of the three-dimensional method does not translate into a truebenefit for routine evaluation, when the difficulty of use and increasedpotential for operator errors is considered. Three-dimensional finiteelement modeling is a method which has promise for the future, bu t whoseuse will be limited until there is more development which will make theprograms easier to use by a typical design engineer on a variety of com-puter systems.

34


52/504

lime-dependent ModelsResponses of a pavement to a nondestructive test loading is a

dynamic (time-dependent) problem. To provide th e most accurate predict-ions of structural responses, th e time-dependence must be considered. Anumber of methods which attempt to make true dynamic predictions ofstructural response are available.

Viscoelastic structural response models, such as the computerprogram VESYS (Kenis 1980), predict long-term responses to time-independent loadings. The viscous response predicted by the program isrelated to performance models such as pavement rutting. The model usedin VESYS is a multilayer viscoelastic model which is analogous to alinear elastic system. Although VESYS is often presented as a "dynamic"program, it is actually a special case of the multilayer linear elasticsystem. The responses are not true dynamic responses, but are indica-tive only of material creep properties.

One method which would provide a tcue dynamic model withreasonable accuracy would be a time-dependent finite element model.However, even a two-dimensional finite element model with true time-dependence becomes complex enough to preclude routine use. A three-dimensional finite element model with time-dependence, such as DYNA(Hallquist 1976), typically requires a super-computer, such as a Cray,and a very experienced user/operator.

Another method for time-dependent analysis of pavement structuralbehavior is a time-dependent finite difference code. The finite dif-ference method is a numerical application of continuum mechanics whichutilizes many of the advantages of both the discrete element method andthe finite element method. In the finite difference method, the

35


53/504

material is broken into a system of elements, each of which canexperience complex behaviors, but the behavior of a given element iscontrolled by the elements in the vicinity of that element. A generalpurpose time-dependent finite difference program which has been used inlimited study of pavement structural responses is the STEALTH (Hofmann1981) program. Use of STEALTH is complicated, but requires much lesscomputer capability and operator experience than comparable finite ele-ment codes, and can include more complicated behaviors than the lumpedparameter models used in the discrete element method.

A method developed by Kausel (1981) utilizes Green's functions topredict the dynamic response of multilayered systems to single frequencyharmonic vibrations. This method will be discussed at length in a latersection. Roesset and Shao (1985) made dynamic predictions for pavementbehavior when loaded by the Falling Weight Deflectometer based on thismethod. Roesset's method required a large number of solutions fordynamic responses at single frequencies and predicted the response tothe Falling Weight Deflectometer loading by the use of an Inverse FastFourier Transform to create deflection time histories. Due to the com-plexity of the solution, Roesset limited his work to a very small numberof demonstration cases. As shown in Figure 7, the Falling WeightDeflectometer creates complex waveforms. The process used by Roessetrequires a Fast Fourier Transform of the load spectrum, application ofthat load spectrum to a unit load spectrum of single frequency deflec-tions, and an Inverse Fast Fourier Transform with suitable boundary con-ditions applied to obtain a transient deflection time history. Smallerrors in one part of the analysis may cause large errors in the overallprediction. The disadvantage of Roesset's method for predictions o.

36


54/504

Falling Weight Deflectometer response is that solution does not justifythe complexity. Use of a continuum method which will allow a load timehistory to be input would be no more difficult than the method used byRoesset, and should give more accurate answers. The potential forKausel's method in pavement structural response predictions is morelikely in the area of vibratory deflection devices, as used in thisstudy.

37


55/504

METHODS OF BACKCALCULATION

IntroductionA large number of computer programs for backcalculation of moduli

from nondestructive testing data have been reported. However, closeexamination of the available literature indicated that all common exist-ing algorithms could be grouped into three general methods. These are:(1) simplified methods, (2) radient relaxation methods, and (3) directinterpolation methods. The method used in most common backcalculationalgorithms is:

1. An ideal pavement system is assumed which corresponds tothe pavement which was tested with the nondestructivetesting device. It is typical to assume values of thelayer thicknesses. The assumed values of layer thick-ness are based on construction records and/or on othertests, such as coring. It is also typical to assume alllayer properties not related to stiffress (e.g.,Poisson's Ratio, density).

2. A set of layer stiffness values are assumed. The stiff-ness values which must be assumed depend on the forwardmodel which will be used. Typically, these values areeither elastic or resilient modulus values.

3. A set of theoretical deflections are calculated with theforward model fo r structural response. The deflectionsare calculated so that the deflection locations and theload intensity match the sensor locations and th e load-ing from the nondestructive test.

38


56/504

4. The calculated values of deflection are compared to thedeflections measured by the nondestructive testingdevice. If the values agree within a reasonabletolerance, the values of layer stiffness assumed in theforward model are accepted as the actual pavement layerstiffness values.

5. If the calculated deflections do not agree with measureddeflections within a reasonable tolerance, the valuesassumed for layer stiffness are adjusted so that animproved solution is determined. This process isreferred to as the backward model.

6. Successive applications, or iterations, of the forwardmodel (Step 3 above) and the backward model (Step 5above) continue until a reasonable tolerance betweencalculated deflections and measured deflections isreached (Step 4 above) or until some other limiting fac-tor is reached. Examples of limiting factors include alimit on the number of iterations or a limit on theoverall execution time.

Simplified MethodsA number of simplified approaches for the prediction of layer

properties from load-deflection data have been developed. Examples ofsimplified methods include equivalent thickness methods an d deflectionbasin geometry methods. An example of an equivalent thickness method isthe computer program ELMOD, developed by Ullidtz (1973). An example ofa deflectior basin geometry method is the method of surface curvature

39


57/504

index (SCI) reported by Van der Lo o (1982). These methods have as theirmajor advantage the speed of calculation, but their usefulness islimited (Ullidtz 1973, Kuo 1979, Van der Lo o 1982).

Gradient Relaxation MethodsA number of very similar programs exist which use a gradient

relaxation method pioneered by Michelow (1963) and developed at theWaterways Experiment Station (Bush and Alexander 1985) which wasoriginally used in a program called CHEVDEF (Bush 1980), and has beenused in a host of backcalculation programs with various names. Ingeneral, the backward models are the same for each of the backcalcula-tion programs, with the only difference being the structural responsemodel used as the forward model. For example, the forward models forthe programs BISDEF, ELSDEF, and CHEVDEF are the structural responsemodels BISAR, ELSYM5, and CHEVRON, respectively. The method searchesfor the best solution of layer moduli using iterative gradient relaxa-tion. The solution is achieved by forming gradient matrices and solvingfor solutions which minimize the errors in the fitted basin. Thismethod has the advantage of convergence in most cases with a small num-ber of iterations. The specific method of solution is escribed below.

It is assumed that a relationship exists between deflection andlayer moduli. The predicted deflection at a given sensor location j,Aj, is assumed to be a function of the unknown layer moduli, that is:

Aj f(E1,E2,E3,...,E) (6)where

n = number of unknown layer moduli of elasticity

40


58/504

so that the deviation at sensor location j, Si, between the measureddeflection, Dj, and the predicted deflection, Aj, is given by:

6j = D. - Aj = D. f(E,,E2,E3,...,En) (7)The sum of the squares of the deviations for all of the sensor locationsmay be written as:

62 = X [ j - f(E 1 ,E2 ,E3 ,...,E,) ]2 (8)j=1 j=2where

m = number of deflection measurementsTo minimize the error with respect to the unknown values of moduli, thepartial derivatives of the error function are taken with respect to theunknown moduli values. This gives a solution matrix of n equationsinvolving the unknown moduli values. The solution is calculated numeri-cally by forming gradient equations which approximate the partialderivative relationships. The gradient equations are formed by the fol-lowing method. A initial set of modulus values, E, is assumed and cor-responding deflections AO are computed. A second set of moduli values,EI, are assumed. A new set of deflections is calculated for each of thecombinations of moduli variations. That is, combinations where all butone of the moduli have values as in E an d one of the moduli is variedto a new value El. The deflection at a given sensor location j may thenbe given as a function of the gradient equation an d the unknown modulusof layer i. The general equation is:

Aj = Aji + Sjiloglo(Ei) (9)

41


59/504

whereAj = th e predicted deflection at sensor location jEi = the unknown layer moduli of layer i

AO - AlSji = ilogloE - log0 El

Aj ji 1E? = first assumed value of modulus for layer iEl = modulus fo r layer i after the variation'&= predicted deflection at sensor location j for EAl = predicted deflection at sensor location j fo r El

An expression can be written for the deflection at sensor location j,Aj, as a function of all the unknown moduli values, Ei. The equationmust relate the following:

A3 = AO + (AO change due to moduli variations) (10)The general equation is:

A A0. + S logoEi - loglor' " (11)1=1The value of A0 can be expressed in terms of one of the unknown moduli3(e.g., layer 3) as:

A' = A3 + S3 log,0 EO (12)Therefore the expression for A. an be written as:nAi= A33 + S3 Ilog EO + Si logoE - logloEO (13)=2

42


60/504

The expression for th e summation of the squared deviations may be writ-ten as:

j D A -S 3 10oE Si [og 10EilogoEJJ (14)j=1 j i j3 j = Ii

The squared errors in deviation are minimized by taking the par-tial derivatives of the error expression with respect to each of theunknown moduli values. By setting the partial derivatives equal tozero, the following matrix equation may be obtained:

[B] (E) = (C) (15)where, for i and

PAVIMENTOS COMPUESTOS BACKCALCULATION

Documents

Transcript of PAVIMENTOS COMPUESTOS BACKCALCULATION