Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Review of the Long-Term Pavement

Performance Backcalculation Results—

Final Report

PUBLICATION NO. HRT-05-150 FEBRUARY 2006
FOREWORD

This report is a comprehensive review and evaluation of the Long-Term Pavement Performance (LTPP) 

backcalculation data. In this study, a new approach, called forwardcalculation was developed to determine 

layered elastic moduli from in situ load-deflection data with procedures and results documented. The 

entire set of LTPP-computed parameters of backcalculation results was screened using forwardcalculated 

moduli. 

Although users cannot reject any backcalculated modulus value merely because it is outside a reasonable 

or acceptable range, the forwardcalculated values were, in most cases, more stable on a section-by-section 

basis than the backcalculated values in the LTPP database. The exception was the portion of the 

backcalculated database based on slab-on-dense-liquid and slab-on-elastic-solid theory, where the 

correspondence between the two rigid pavement analysis techniques was excellent and both the 

backcalculated and forwardcalculated moduli and k-values were very stable. 

It is recommended that the backcalculated database be retained as is, with the addition of the 

complementary forwardcalculated dataset and screening flags, so the database user can decide which 

method is more suitable to the application. 

This report will interest highway agency engineers involved in pavement analysis, design, construction, 

and deflection data collection, as well as researchers who use LTPP load-deflection data to improve 

design procedures and standards for constructing and rehabilitating pavements. 

 Gary L. Henderson 

 Office of Infrastructure 

 Research and Development 

Notice 

This document is disseminated under the sponsorship of the U.S. Department of Transportation in the 

interest of information exchange. The U.S. Government assumes no liability for the use of the information 

contained in this document. This report does not constitute a standard, specification, or regulation. 

The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers’ names 

appear in this report only because they are considered essential to the objective of the document. 

Quality Assurance Statement 

The Federal Highway Administration (FHWA) provides high-quality information to serve Government, 

industry, and the public in a manner that promotes public understanding. Standards and policies are used 

to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA 

periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality 

improvement. 
Technical Report Documentation Page 

1. Report No. 

FHWA-HRT-05-150

2. Government Accession 

No. 

3. Recipient's Catalog No. 

5. Report Date 

February 2006 

4. Title and Subtitle 

Review of the Long-Term Pavement Performance 

Backcalculation Results—Final Report 

6. Performing Organization Code 

7. Author(s) 

R.N. Stubstad, Y.J. Jiang, M.L. Clevenson, and E.O. 

Lukanen

8. Performing Organization Report No. 

9. Performing Organization Name and Address 10. Work Unit No. (TRAIS) 

Applied Research Associates, Inc. 

7184 Troy Hill Drive, Suite N 

Elkridge, Maryland 21075-7056 11. Contract or Grant No. 

DTFH61-02-D-00138

13. Type of Report and Period Covered 

Final Report 

12. Sponsoring Agency Name and Address 

Office of Infrastructure Research and Development 

Federal Highway Administration 

6300 Georgetown Pike 

McLean, Virginia 22101-2296 14. Sponsoring Agency Code 

15. Supplementary Notes 

Contracting Officer’s Technical Representative (COTR): Larry Wiser, HRDI 

LTPP Data Analysis Contract.

16. Abstract 

A new approach to determine layered elastic moduli from in situ load-deflection data was developed. This “forwardcalculation” 

approach differs from backcalculation in that modulus estimates come directly from the load and deflection data using closed-form 

formulae rather iteration. The forwardcalculation equations are used for the subgrade and the bound surface course for both flexible 

and rigid pavement falling weight deflectometer (FWD) data. Intermediate layer moduli are estimated through commonly used 

modular ratios between adjacent layers. 

The entire LTPP set of backcalculated parameters was screened using forwardcalculated moduli. Any assumed or fixed modulus 

value was left as is and not further screened (e.g., hard bottom). Further, any back- or forwardcalculated values outside a broad range 

of reasonable values were not further screened, but flagged as unreasonable. Finally, a set of broad range convergence flags (0 = 

acceptable, 1 = marginal, 2 = questionable, and 3 = unacceptable) were applied to the backcalculated dataset, depending on how 

closely the pairs of back- and forwardcalculated moduli matched. Since both techniques used identical FWD load-deflection data as 

input, the moduli derived from each approach should be reasonably close to each other (within a factor of 1.5 to qualify as acceptable, 

for example). 

Although backcalculated values cannot be rejected merely because they are outside a reasonable or acceptable range, the 

complementary forwardcalculated values were usually more stable on a section-by-section basis. The exception was the portion of the 

database based on slab-on-dense-liquid or slab-on-elastic-solid theory, where the correspondence between the two approaches was

excellent and very stable. Therefore, it is recommended that the backcalculated database be retained as is, with the addition of checks 

and flags so the database user can choose the best method, depending on the application.

17. Key Words 

Pavements, LTPP, FWD, deflection data, elastic 

modulus, backcalculation, forwardcalculation, 

screening.

18. Distribution Statement 

No restrictions. This document is available to the public through 

the National Technical Information Service, Springfield, VA 

22161.

19. Security Classification (of this 

report) 

Unclassified

20. Security Classification (of this 

page) 

Unclassified

21. No. of Pages 

97 

22. Price 

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized 
ii

SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol 

LENGTH 

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2 square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m2

yd2 square yard 0.836 square meters m2

ac acres 0.405 hectares ha

mi2 square miles 2.59 square kilometers km2

VOLUME 

fl oz fluid ounces 29.57 milliliters mL 

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m3 

yd3 cubic yards 0.765 cubic meters m3 

NOTE: volumes greater than 1000 L shall be shown in m3

MASS 

oz ounces 28.35 grams g

lb pounds 0.454 kilograms kg

T short tons (2000 lb) 0.907 megagrams (or "metric ton") Mg (or "t") 

TEMPERATURE (exact degrees) o

F Fahrenheit 5 (F-32)/9 Celsius oC 

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2 poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH

mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA mm2

 square millimeters 0.0016 square inches in2 

m2 square meters 10.764 square feet ft2 

m2 square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac

km2 square kilometers 0.386 square miles mi2 

VOLUME 

mL milliliters 0.034 fluid ounces fl oz 

L liters 0.264 gallons gal 

m3 cubic meters 35.314 cubic feet ft3 

m3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T 

TEMPERATURE (exact degrees) o

C Celsius 1.8C+32 Fahrenheit oF 

ILLUMINATION 

lx lux 0.0929 foot-candles fc 

cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2

*SI is the symbol for th International System of Units. Approp e riate rounding should be made to comply with Section 4 of ASTM E380. 

(Revised March 2003)
iii

TABLE OF CONTENTS 

CHAPTER 1. INTRODUCTION.................................................................................................1

BACKGROUND.......................................................................................................................................................1

STUDY OBJECTIVES AND SCOPE ......................................................................................................................1

LTPP DATA SOURCE .............................................................................................................................................1

REPORT ORGANIZATION.....................................................................................................................................2

CHAPTER 2. INTRODUCTION TO BACKCALCULATION AND 

FORWARDCALCULATION METHODS..............................................................................3

LITERATURE REVIEW ..........................................................................................................................................3

INTRODUCTION TO BACKCALCULATION ......................................................................................................3

INTRODUCTION TO FORWARDCALCULATION..............................................................................................4

CHAPTER 3. FORWARDCALCULATION METHODOLOGY............................................7

BACKGROUND AND PREVIOUS DEVELOPMENTS ........................................................................................7

CENTERLINE SUBGRADE MODULUS BASED ON THE HOGG MODEL.......................................................7

BOUND SURFACE COURSE MODULUS BASED ON THE AREA METHOD..................................................9

INTERMEDIATE LAYER MODULUS CALCULATIONS .................................................................................12

CHAPTER 4. INITIAL LTPP BACKCALCULATION DATA SCREENING 

RESULTS ..................................................................................................................................15

OVERVIEW............................................................................................................................................................15

ORGANIZATION OF DATA.................................................................................................................................15

CHECK FOR ERRORS OR ANOMALIES IN THE BACKCALCULATION PROCESS ...................................16

SUBGRADE SCREENING RESULTS ..................................................................................................................16

SURFACE COURSE SCREENING RESULTS.....................................................................................................19

INTERMEDIATE (BASE) COURSE SCREENING RESULTS............................................................................24

EXTRA LAYER RESULTS FROM BACKCALCULATION...............................................................................27

CHOICE OF SCREENING LIMITS AND CODES ...............................................................................................29

CHAPTER 5. LTPP BACKCALCULATION DATABASE SCREENING 

METHODOLOGY ...................................................................................................................31

LTPP DATA SOURCE USED IN THIS STUDY ..................................................................................................31

KEY STEPS FOR SCREENING THE LTPP BACKCALCULATION DATA .....................................................33

CHAPTER 6. LTPP BACKCALCULATION DATABASE SCREENING RESULTS .......43

LEVEL E AND OTHER LEVELS OF DATA QUALITY.....................................................................................43

SCREENING OF THE FLEXIBLE PAVEMENT BACKCALCULATION PARAMETERS—LINEAR 

ELASTIC MODEL.............................................................................................................................................44

SCREENING OF THE FLEXIBLE PAVEMENT BACKCALCULATION PARAMETERS—NONLINEAR 

ELASTIC MODEL.............................................................................................................................................47

ADAPTATION OF FORWARDCALCULATION TECHNIQUE FOR LTPP RIGID PAVEMENT SECTIONS50

SCREENING OF THE RIGID PAVEMENT BACKCALCULATION PARAMETERS—LINEAR ELASTIC 

MODEL..............................................................................................................................................................55

SCREENING OF THE RIGID PAVEMENT BACKCALCULATION PARAMETERS—SLAB-ON-ELASTICSOLID ANALYSIS............................................................................................................................................59

SCREENING OF THE RIGID PAVEMENT BACKCALCULATION PARAMETERS—SLAB-ON-DENSELIQUID ANALYSIS..........................................................................................................................................62

SCREENING OF THE SECTION AVERAGE BACKCALCULATED DATABASE..........................................66
iv

CHAPTER 7. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS....................71

SUMMARY ............................................................................................................................................................71

CONCLUSIONS .....................................................................................................................................................74

RECOMMENDATIONS.........................................................................................................................................76

APPENDIX A...............................................................................................................................79

REFERENCES.............................................................................................................................87
v

LIST OF FIGURES 

FIGURE 1. EQUATION. COMPOSITE SUBGRADE MODULUS AT AN OFFSET. .......................................................................7

FIGURE 2. EQUATION. HOGG SUBGRADE MODULUS........................................................................................................8

FIGURE 3. EQUATION. OFFSET DISTANCE WHERE DEFLECTION IS HALF OF CENTER DEFLECTION....................................8

FIGURE 4. EQUATION. CHARACTERISTIC LENGTH OF DEFLECTION BASIN. ......................................................................8

FIGURE 5. EQUATION. THEORETICAL POINT LOAD STIFFNESS/PAVEMENT STIFFNESS RATIO. ..........................................8

FIGURE 6. EQUATION. COMPOSITE MODULUS UNDER FWD LOAD PLATE. ....................................................................10

FIGURE 7. EQUATION. 914-MILLIMETER (MM) (36-INCH) AREA EQUATION FOR RIGID PAVEMENTS. ...........................10

FIGURE 8. EQUATION. 305-MM (12-INCH) AREA EQUATION FOR FLEXIBLE PAVEMENTS. ............................................10

FIGURE 9. EQUATION. AREA FACTOR FOR RIGID PAVEMENTS. ....................................................................................11

FIGURE 10. EQUATION. AREA FACTOR FOR FLEXIBLE PAVEMENTS. ............................................................................11

FIGURE 11. EQUATION. STIFFNESS OR MODULUS OF THE UPPER PCC LAYER. ..............................................................12

FIGURE 12. EQUATION. STIFFNESS OR MODULUS OF THE UPPER AC LAYER. ................................................................12

FIGURE 13. EQUATION. MODULUS OF THE UNBOUND BASE LAYER USING THE DORMAN AND 

METCALF RELATIONSHIP. ...................................................................................................................................12

FIGURE 14. GRAPH. BACK- VERSUS FORWARDCALCULATED SUBGRADE MODULI FOR 15 TRIAL LTPP

FLEXIBLE SECTIONS. ...........................................................................................................................................17

FIGURE 15. GRAPH. BACK- VERSUS FORWARDCALCULATED SUBGRADE MODULI FOR THREE TRIAL 

LTPP RIGID SECTIONS.........................................................................................................................................19

FIGURE 16. GRAPH. BACK- VERSUS FORWARDCALCULATED ASPHALT LAYER MODULI FOR 15 TRIAL 

LTPP FLEXIBLE SECTIONS. .................................................................................................................................20

FIGURE 17. GRAPH. BACK- VERSUS FORWARDCALCULATED CONCRETE LAYER MODULI FOR THREE 

TRIAL LTPP RIGID SECTIONS. .............................................................................................................................23

FIGURE 18. GRAPH. BACK- VERSUS FORWARD-BASED BASE LAYER MODULI FOR 15 FLEXIBLE LTPP

SECTIONS. ...........................................................................................................................................................25

FIGURE 19. GRAPH. BACK- VERSUS FORWARDCALCULATED ASPHALT LAYER MODULI FOR ONE TRIAL 

LTPP FLEXIBLE SECTION WITH TWO UPPER (BOUND) LAYERS.............................................................................27

FIGURE 20. GRAPH. BACK- VERSUS FORWARDCALCULATED SUBGRADE MODULI FOR FIVE TRIAL 

LTPP FLEXIBLE SECTIONS WITH TWO SUBGRADE (LOWER UNBOUND) LAYERS...................................................28

FIGURE 21. GRAPH. BACK- VERSUS FORWARDCALCULATED BASE COURSE MODULI FOR FOUR TRIAL 

LTPP FLEXIBLE SECTIONS WITH TWO INTERMEDIATE LAYERS............................................................................28

FIGURE 22. EQUATION. INTERQUARTILE RANGE...........................................................................................................39

FIGURE 23. CHARTS. SCREENING RESULTS OF THE ELASTIC MODULI OF THE SUBGRADE FOR ALL 

FLEXIBLE SECTIONS IN THE MON_DEFL_FLX_BAKCALC_POINT TABLE BASED ON THE 

LINEAR ELASTIC MODEL (THE LEVEL E RECORDS ONLY). ....................................................................................43
vi

FIGURE 24. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE SUBGRADE FOR ALL THE 

FLEXIBLE SECTIONS IN THE MON_DEFL_FLX_BAKCALC_POINT TABLE BASED ON THE 

LINEAR ELASTIC MODEL (CONTAINS BOTH LEVEL E AND NONLEVEL E RECORDS)...............................................44

FIGURE 25. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE ASPHALT CONCRETE LAYER 

FOR THE FLEXIBLE SECTIONS IN THE MON_DEFL_FLX_BAKCALC_POINT TABLE BASED 

ON THE LINEAR ELASTIC MODEL..........................................................................................................................45

FIGURE 26. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE SUBGRADE FOR THE FLEXIBLE 

SECTIONS IN THE MON_DEFL_FLX_BAKCALC_POINT TABLE BASED ON THE LINEAR 

ELASTIC MODEL. .................................................................................................................................................46

FIGURE 27. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE BASE LAYER FOR THE FLEXIBLE 

SECTIONS IN THE MON_DEFL_FLX_BAKCALC_POINT TABLE BASED ON THE LINEAR 

ELASTIC MODEL. .................................................................................................................................................47

FIGURE 28. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE ASPHALT CONCRETE LAYER FOR 

THE FLEXIBLE SECTIONS IN THE MON_DEFL_FLX_ NMODEL_POINT TABLE BASED ON THE 

NONLINEAR ELASTIC MODEL...............................................................................................................................48

FIGURE 29. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE BASE LAYER FOR THE FLEXIBLE 

SECTIONS IN THE MON_DEFL_FLX_ NMODEL_POINT TABLE BASED ON THE NONLINEAR 

ELASTIC MODEL. .................................................................................................................................................49

FIGURE 30. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE SUBGRADE FOR THE FLEXIBLE SECTIONS 

IN THE MON_DEFL_FLX_ NMODEL_POINT TABLE BASED ON THE NONLINEAR ELASTIC MODEL. ...............50

FIGURE 31. EQUATION. PCC SLAB MODULUS—100 PERCENT UNBONDED CASE...........................................................51

FIGURE 32. EQUATION. PCC SLAB MODULUS—100 PERCENT BONDED CASE. ..............................................................51

FIGURE 33. EQUATION. LAYER THICKNESS RELATIONSHIP—BOTH CASES....................................................................51

FIGURE 34. EQUATION. MODULAR RATIO β—BOTH CASES..........................................................................................51

FIGURE 35. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE INTERIOR CONCRETE SLAB FOR THE 

RIGID SECTIONS IN THE MON_DEFL_FLX_BAKCALC_POINT TABLE BASED ON THE LINEAR ELASTIC 

MODEL FOR BACKCALCULATION AND A BONDED CONDITION BETWEEN THE SLAB AND BASE FOR 

FORWARDCALCULATION. ....................................................................................................................................55

FIGURE 36. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE INTERIOR CONCRETE SLAB FOR THE 

RIGID SECTIONS IN THE MON_DEFL_FLX_BAKCALC_POINT TABLE BASED ON THE LINEAR 

ELASTIC MODEL FOR BACKCALCULATION AND AN UNBONDED CONDITION BETWEEN THE SLAB AND BASE 

FOR FORWARDCALCULATION. .............................................................................................................................56

FIGURE 37. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE BASE LAYER FOR THE RIGID SECTIONS 

IN THE MON_DEFL_FLX_BAKCALC_POINT TABLE BASED ON THE LINEAR ELASTIC MODEL FOR 

BACKCALCULATION AND A BONDED CONDITION BETWEEN THE CONCRETE SLAB AND BASE LAYER FOR 

FORWARDCALCULATION. ....................................................................................................................................57
vii

FIGURE 38. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE BASE LAYER FOR THE RIGID SECTIONS 

IN THE MON_DEFL_FLX_BAKCALC_POINT TABLE BASED ON THE LINEAR ELASTIC MODEL FOR 

BACKCALCULATION AND AN UNBONDED CONDITION BETWEEN THE CONCRETE SLAB AND BASE LAYER 

FOR FORWARDCALCULATION. .............................................................................................................................57

FIGURE 39. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE SUBGRADE FOR THE RIGID SECTIONS IN 

THE MON_DEFL_FLX_BAKCALC_POINT TABLE BASED ON THE LINEAR ELASTIC MODEL. .........................58

FIGURE 40. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE PCC SLAB FOR THE RIGID SECTIONS IN 

THE MON_DEFL_RGD_BAKCALC_POINT TABLE USING THE ELASTIC SOLID MODEL FOR 

BACKCALCULATION AND ASSUMING BONDED CONDITION BETWEEN THE SLAB AND THE BASE FOR BACKAND FORWARDCALCULATION. ............................................................................................................................59

FIGURE 41. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE PCC SLAB FOR THE RIGID SECTIONS 

IN THE MON_DEFL_RGD_BAKCALC_POINT TABLE USING THE ELASTIC SOLID MODEL FOR 

BACKCALCULATION AND ASSUMING UNBONDED CONDITION BETWEEN THE SLAB AND THE BASE FOR 

BACK- AND FORWARDCALCULATION. .................................................................................................................60

FIGURE 42. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE BASE LAYER FOR THE RIGID SECTIONS 

IN THE MON_DEFL_RGD_BAKCALC_POINT TABLE USING THE ELASTIC SOLID MODEL FOR 

BACKCALCULATION AND ASSUMING BONDED CONDITION BETWEEN THE SLAB AND THE BASE FOR 

BACK- AND FORWARDCALCULATION. .................................................................................................................60

FIGURE 43. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE BASE LAYER FOR THE RIGID SECTIONS 

IN THE MON_DEFL_RGD_BAKCALC_POINT TABLE USING THE ELASTIC SOLID MODEL FOR 

BACKCALCULATION AND ASSUMING UNBONDED CONDITION BETWEEN THE SLAB AND THE BASE FOR 

BACK- AND FORWARDCALCULATION. .................................................................................................................61

FIGURE 44. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE SUBGRADE FOR THE RIGID SECTIONS 

IN THE MON_DEFL_RGD_BAKCALC_POINT TABLE USING THE ELASTIC SOLID MODEL FOR 

BACKCALCULATION. ...........................................................................................................................................62

FIGURE 45. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE PCC SLAB FOR THE RIGID SECTIONS 

IN THE MON_DEFL_RGD_BAKCALC_POINT TABLE USING THE DENSE LIQUID MODEL FOR 

BACKCALCULATION AND ASSUMING BONDED CONDITION BETWEEN THE SLAB AND THE BASE FOR 

BACK- AND FORWARDCALCULATION. .................................................................................................................63

FIGURE 46. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE PCC SLAB FOR THE RIGID SECTIONS 

IN THE MON_DEFL_RGD_BAKCALC_POINT TABLE USING THE DENSE LIQUID MODEL FOR 

BACKCALCULATION AND ASSUMING UNBONDED CONDITION BETWEEN THE SLAB AND THE BASE FOR 

BACK- AND FORWARDCALCULATION. .................................................................................................................64

FIGURE 47. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE BASE LAYER FOR THE RIGID SECTIONS 

IN THE MON_DEFL_RGD_BAKCALC_POINT TABLE USING THE DENSE-LIQUID MODEL FOR 

BACKCALCULATION AND ASSUMING BONDED CONDITION BETWEEN THE SLAB AND THE BASE FOR 

BACK- AND FORWARDCALCULATION. .................................................................................................................64
viii

FIGURE 48. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE BASE LAYER FOR THE RIGID SECTIONS 

IN THE MON_DEFL_RGD_BAKCALC_POINT TABLE USING THE DENSE-LIQUID MODEL FOR 

BACKCALCULATION AND ASSUMING UNBONDED CONDITION BETWEEN THE SLAB AND THE BASE FOR 

BACK- AND FORWARDCALCULATION. .................................................................................................................65

FIGURE 49. EQUATION. SUBGRADE K-VALUE. ..............................................................................................................65

FIGURE 50. CHARTS. SCREENING RESULTS OF THE SUBGRADE K-VALUES FOR THE RIGID SECTIONS IN THE 

MON_DEFL_RGD_BAKCALC_POINT TABLE USING THE DENSE-LIQUID MODEL FOR 

BACKCALCULATION. ...........................................................................................................................................66

FIGURE 51. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE POINT BASE LAYER FOR THE FLEXIBLE 

SECTIONS IN THE MON_DEFL_FLX_BAKCALC_POINT TABLE BASED ON THE LINEARELASTIC MODEL. .................................................................................................................................................67

FIGURE 52. CHARTS. SCREENING RESULTS OF ELASTIC MODULI OF THE SECTION BASE LAYER FOR THE 

FLEXIBLE SECTIONS IN THE MON_DEFL_FLX_BAKCALC_SECT TABLE BASED ON THE LINEARELASTIC MODEL. .................................................................................................................................................68

FIGURE 53. CHARTS. SCREENING RESULTS OF THE SUBGRADE POINT K-VALUE TABLE FOR THE RIGID SECTIONS 

IN THE MON_DEFL_RGD_BAKCALC_POINT TABLE USING THE DENSE-LIQUID MODEL FOR 

BACKCALCULATION. ...........................................................................................................................................68

FIGURE 54. CHARTS. SCREENING RESULTS OF THE SUBGRADE SECTION K-VALUE TABLE FOR THE RIGID 

SECTIONS IN THE MON_DEFL_RGD_BAKCALC_SECT TABLE USING THE DENSE-LIQUID MODEL 

FOR BACKCALCULATION. ....................................................................................................................................69

FIGURE 55. CHARTS. SCREENING RESULTS OF SECTION AVERAGE ELASTIC MODULI OF THE ASPHALT 

CONCRETE LAYER FOR THE FLEXIBLE SECTIONS IN THE MON_DEFL_FLX_BAKCALC_SECT TABLE 

BASED ON THE LINEAR ELASTIC MODEL. .............................................................................................................79

FIGURE 56. CHARTS. SCREENING RESULTS OF SECTION AVERAGE ELASTIC MODULI OF THE BASE LAYER 

FOR THE FLEXIBLE SECTIONS IN THE MON_DEFL_FLX_BAKCALC_SECT TABLE BASED ON THE 

LINEAR ELASTIC MODEL......................................................................................................................................80

FIGURE 57. CHARTS. SCREENING RESULTS OF SECTION AVERAGE ELASTIC MODULI OF THE SUBGRADE FOR 

THE FLEXIBLE SECTIONS IN THE MON_DEFL_FLX_BAKCALC_SECT TABLE BASED ON THE LINEAR 

ELASTIC MODEL. .................................................................................................................................................80

FIGURE 58. CHARTS. SCREENING RESULTS OF SECTION AVERAGE ELASTIC MODULI OF THE ASPHALT CONCRETE 

LAYER FOR THE FLEXIBLE SECTIONS IN THE MON_DEFL_FLX_BAKCALC_SECT TABLE BASED ON 

THE NONLINEAR ELASTIC MODEL. .......................................................................................................................81

FIGURE 59. CHARTS. SCREENING RESULTS OF THE SECTION AVERAGE ELASTIC MODULI OF THE BASE LAYER 

FOR THE FLEXIBLE SECTIONS IN THE MON_DEFL_FLX_BAKCALC_SECT TABLE BASED ON THE 

NONLINEAR ELASTIC MODEL...............................................................................................................................81
ix

FIGURE 60. CHARTS. SCREENING RESULTS OF THE SECTION AVERAGE ELASTIC MODULI OF THE SUBGRADE 

FOR THE FLEXIBLE SECTIONS IN THE MON_DEFL_FLX_BAKCALC_SECT TABLE BASED ON THE 

NONLINEAR ELASTIC MODEL...............................................................................................................................82

FIGURE 61. CHARTS. SCREENING RESULTS OF THE SECTION AVERAGE ELASTIC MODULI OF THE PCC SLAB 

FOR THE RIGID SECTIONS IN THE MON_DEFL_FLX_BAKCALC_SECT TABLE BASED ON THE LINEAR 

ELASTIC MODEL USING MODCOMP...................................................................................................................82

FIGURE 62. CHARTS. SCREENING RESULTS OF THE SECTION AVERAGE ELASTIC MODULI OF THE BASE LAYER 

FOR THE RIGID SECTIONS IN THE MON_DEFL_FLX_BAKCALC_SECT TABLE BASED ON THE LINEAR 

ELASTIC MODEL USING MODCOMP...................................................................................................................83

FIGURE 63. CHARTS. SCREENING RESULTS OF THE SECTION AVERAGE ELASTIC MODULI OF THE SUBGRADE 

FOR THE RIGID SECTIONS IN THE MON_DEFL_FLX_BAKCALC_SECT TABLE BASED ON THE LINEAR 

ELASTIC MODEL USING MODCOMP...................................................................................................................83

FIGURE 64. CHARTS. SCREENING RESULTS OF THE SECTION AVERAGE ELASTIC MODULI OF THE PCC SLAB FOR 

THE RIGID SECTIONS IN THE MON_DEFL_RGD_BAKCALC_SECT TABLE BASED ON THE SLAB-ONELASTIC-SOLID MODEL........................................................................................................................................84

FIGURE 65. CHARTS. SCREENING RESULTS OF THE SECTION AVERAGE ELASTIC MODULI OF THE PCC SLAB FOR 

THE RIGID SECTIONS IN THE MON_DEFL_RGD_BAKCALC_SECT TABLE BASED ON THE SLAB-ONDENSE-LIQUID MODEL.........................................................................................................................................84

FIGURE 66. CHARTS. SCREENING RESULTS OF THE SECTION AVERAGE ELASTIC MODULI OF THE BASE LAYER 

FOR THE RIGID SECTIONS IN THE MON_DEFL_RGD_BAKCALC_SECT TABLE BASED ON THE SLAB-ONELASTIC-SOLID MODEL........................................................................................................................................85

FIGURE 67. CHARTS. SCREENING RESULTS OF THE SECTION AVERAGE ELASTIC MODULI OF THE BASE LAYER 

FOR THE RIGID SECTIONS IN THE MON_DEFL_RGD_BAKCALC_SECT TABLE BASED ON THE SLAB-ONDENSE-LIQUID MODEL.........................................................................................................................................85

FIGURE 68. CHARTS. SCREENING RESULTS OF THE SECTION AVERAGE ELASTIC MODULI OF THE SUBGRADE 

FOR THE RIGID SECTIONS IN THE MON_DEFL_RGD_BAKCALC_SECT TABLE BASED ON THE SLAB-ONELASTIC-SOLID MODEL........................................................................................................................................86

FIGURE 69. CHARTS. SCREENING RESULTS OF THE SECTION AVERAGE K-VALUES OF THE SUBGRADE FOR THE 

RIGID SECTIONS IN THE MON_DEFL_RGD_BAKCALC_SECT TABLE BASED ON THE SLAB-ON-DENSELIQUID MODEL. ...................................................................................................................................................86
x

LIST OF TABLES 

TABLE 1. HOGG MODEL COEFFICIENTS. ..........................................................................................................................9

TABLE 2. MODULI USED FOR SCREENING OF LTPP DATABASE VALUES........................................................................13

TABLE 3. STATISTICS FOR BACK- AND FORWARDCALCULATED SUBGRADE MODULI FOR 15 TRIAL 

FLEXIBLE SECTIONS. ...........................................................................................................................................17

TABLE 4. BACK- AND FORWARDCALCULATED MODULI FOR TWO TRIAL FLORIDA SECTIONS........................................20

TABLE 5. BACK- AND FORWARDCALCULATED MODULI FOR TWO TRIAL NEBRASKA SECTIONS. ...................................21

TABLE 6. STATISTICS FOR BACK- AND FORWARDCALCULATED SURFACE COURSE MODULI FOR FLEXIBLE SECTIONS....22

TABLE 7. STATISTICS FOR BACK- AND FORWARDCALCULATED PCC MODULI FOR RIGID SECTIONS..............................24

TABLE 8. STATISTICS FOR BACKCALCULATED AND PSEUDOBACKCALCULATED BASE COURSE MODULI FOR 

FLEXIBLE SECTIONS. ...........................................................................................................................................25

TABLE 9. STATISTICS FOR BASE COURSE MODULI FROM BACKCALCULATION AND FROM FORWARDCALCULATION 

USING DORMAN AND METCALF’S EQUATION FOR NINE TRIAL FLEXIBLE SECTIONS.............................................26

TABLE 10. FLAGGING CODES SUGGESTED FOR SCREENING OF THE BACKCALCULATED LTPP DATABASE TABLES........29

TABLE 11. LTPP BACKCALCULATION TABLES AND NUMBER OF RECORDS SCREENED..................................................32

TABLE 12. ASSIGNMENT OF BACKCALCULATED LAYERS FOR FORWARDCALCULATION OF FLEXIBLE PAVEMENTS. ......35

TABLE 13. FWD- AND TIME-SPECIFIC SENSOR POSITIONING ANOMALIES IN THE LTPP DATABASE. .............................38

TABLE 14. REASONABLE RANGES FOR VARIOUS PAVEMENT LAYERS IN THE LTPP DATABASE.....................................40

TABLE 15. FLAGGING CODES USED TO SCREEN THE BACKCALCULATED LTPP DATABASE. ..........................................41

TABLE 16. BACK- AND FORWARDCALCULATED MODULUS RATIOS FOR EPCC /EBASE......................................................53

TABLE 17. REASONABLE RANGES FOR VARIOUS PAVEMENT LAYERS IN THE LTPP DATABASE (SAME AS TABLE 14). ..72
1

CHAPTER 1. INTRODUCTION 

BACKGROUND 

The Long-Term Pavement Performance Program (LTPP) has incorporated within its database a 

set of computed parameter tables. These tables include backcalculated moduli and other related 

pavement layer data from falling weight deflectometer (FWD) deflections taken before the 

summer of 1998. Backcalculated data, however, do not exist for all of the pre-1998 data. Some 

of these data were gathered at joints and other noncontinuous pavement features (where 

backcalculation is not used), while other data produced results that were already identified as 

unreliable or out of range. 

Deflection data, corresponding backcalculated moduli, or other deflection-based parameters 

strongly relate to pavement performance, and the premise of mechanistic-empirical design 

methods is to control stresses and strains as a response to traffic loads. In addition, although 

many of the available backcalculated moduli certainly appear reasonable, some do not, which 

has raised some concerns. Based on earlier work where these data have been used, it became 

desirable to review and screen the backcalculated moduli database to ascertain whether, and to 

what extent, unreasonable or unlikely values currently exist. 

This report documents the procedures and results of a comprehensive review of the LTPP 

backcalculation results. For this study, only the existing backcalculation data derived for the 

1998 or earlier FWD were evaluated. All work was completed under the LTPP Data Analysis 

Contract (Federal Highway Administration (FHWA) Contract No. DTFH61-02-D-00138). 

STUDY OBJECTIVES AND SCOPE 

The main objective of this project is to assess and improve the quality of the present and future 

backcalculated modulus data in the LTPP database. The following are the main activities carried 

out under this project to meet the primary objective: 

1. Provide an assessment of the validity of the LTPP backcalculated modulus parameters that 

have been derived through the backcalculation process. 

2. Develop additional procedures and criteria that can be applied to evaluate the results of 

backcalculation (whether for LTPP or for other purposes) to ensure that the backcalculated 

layer parameters are valid. 

An additional product from this study is a screening method to assist the analyst in assessing 

whether the backcalculated moduli obtained, using any backcalculation program, are reasonable. 

A separate report documents generic draft guidelines for review and evaluation of backcalculated 

pavement layer parameters. 

LTPP DATA SOURCE 

The complete LTPP backcalculation and supporting data were requested and received from the 

FHWA-LTPP customer support center at the beginning of this project. The research team used 

LTPP Data Release 16.0—July 2003 Upload throughout this project. These data included all 

available asphalt concrete (AC) and portland cement concrete (PCC) LTPP sections where 

backcalculation was carried out, including both level E data and nonlevel E data. 
2

REPORT ORGANIZATION 

This report is organized into seven chapters, including an introduction, background methods, 

development of the forwardcalculation methodology, initial evaluation with backcalculation 

screening results, backcalculation screening methods, summary of the LTPP backcalculation data 

screening results, and an overall summary with conclusions and recommendations. 

This chapter presents a background of the problem, study objectives, LTPP data source, and 

report organization. Chapter 2 gives a summary of the literature reviewed with an introduction of 

both the backcalculation and the forwardcalculation techniques. Chapter 3 documents the 

development of the forwardcalculation methodology that was used in this study, followed by the 

results of the initial phase I pilot screening results in chapter 4. Chapter 5 outlines the subsequent 

method for screening the entire LTPP database of the backcalculated computed parameter tables, 

followed by a summary of the screening results and recommendations for identifying 

backcalculated data anomalies in chapter 6. Finally, chapter 7 contains a summary, conclusions, 

and recommendations to complete the report. 

Microsoft® Excel spreadsheets have been prepared containing all formulae used in phase I of this 

study. All forwardcalculation input quantities are totally transparent to those who wish to use the 

methodology, whether for screening or in rehabilitation design. To this end, four spreadsheets are 

available—two for asphalt-bound surfaces (using SI and U.S. Customary units) and two for 

cement-bound surfaces (SI and U.S. Customary). These spreadsheets can be obtained by 

contacting LTPP Customer Support Services: by phone at 202–493–3035 or by e-mail at 

ltppinfo@fhwa.dot.gov. 
3

CHAPTER 2. INTRODUCTION TO BACKCALCULATION AND 

FORWARDCALCULATION METHODS 

LITERATURE REVIEW 

To review the approach through which backcalculation took place and the load-deflection data 

were used to create the computed parameter tables of the backcalculated database, two primary 

references were consulted: 

• FHWA, Backcalculation of Layer Parameters for Long-Term Pavement Performance 

(LTPP) Test Sections, Volume I: Slab on Elastic Solid and Slab on Dense-Liquid Foundation 

Analysis of Rigid Pavements, FHWA-RD-00-086, Washington, DC: FHWA, December 

2001.(1)

• FHWA, Backcalculation of Layer Parameters for LTPP Test Sections―Volume II: Layered 

Elastic Analysis for Flexible and Rigid Pavements, FHWA-RD-01-113, Washington, DC: 

FHWA, December 2001.(2)

These publications describe how backcalculation was calculated for rigid and flexible pavement 

sections, respectively. After review of these documents, the researchers determined that the 

described processes used to perform the backcalculation and prescreen the data for outliers were 

reasonable, though (at least in hindsight) perhaps somewhat imperfect. 

The processing of the rigid pavement data appeared to be somewhat more effective than for the 

flexible pavement data, mainly because rigid pavements were generally divided into only two 

unknown structural layers, while flexible pavements generally used three, four, and sometimes 

even five unknown structural layers. 

Additionally, the following documents were used, as needed: 

• National Cooperative Highway Research Program (NCHRP), LTPP Data Analysis: 

Feasibility of Using FWD Deflection Data to Characterize Pavement Construction Quality,

Project 20-50(09): NCHRP Web Document #52, Washington, DC: NCHRP, November 

2002. Web address: http://trb.org/news/blurb_detail.asp?id=942.

(3)

• FHWA, Study of LTPP Pavement Deflections, Project DTFH61-01-P-00144: Unpublished 

Final Report Submitted to FHWA in September 2001.(4)

These documents were helped to ensure the quality of the FWD load-deflection data and to 

verify the sensor positions used during FWD testing. 

INTRODUCTION TO BACKCALCULATION 

Most backcalculation programs, including those used to generate the backcalculated modulus 

data in the LTPP computed parameter tables, involve numerical integration subroutines that are 

capable of calculating FWD pavement deflections (and other parameters), given the stiffnesses 

(or moduli) of the various pavement layers and their thicknesses. If all assumptions are correct, 

(i.e., each layer is an elastic layer, isotropic and homogeneous, and all other boundary conditions 

are correct), then it is possible to iterate various combinations of moduli to reach a (virtually) 

perfect match between the measured and theoretical FWD deflections. In this manner, a solution 

to the problem of deriving moduli from deflections is obtained. 
4

A serious drawback to this approach is that one or more of the many input assumptions 

mentioned above may be incorrect and therefore may not apply to the actual pavement system. In 

spite of this potential drawback, many of the moduli in the database appear to be reasonable and 

rational, based on common engineering sense and a working knowledge of pavement materials. 

INTRODUCTION TO FORWARDCALCULATION 

Forwardcalculation techniques were developed and used for the pilot study to generate moduli 

that are independent of the backcalculated values so they can be used for comparison to screen 

the backcalculated moduli in the database. This approach is based on the premise that two 

substantially different approaches to calculated layered elastic parameters from the same 

deflection data should produce at least somewhat similar moduli given that either approach is 

credible. 

Forwardcalculation involves using certain portions of the FWD deflection basin to derive an 

apparent modulus or stiffness of the subgrade and/or the bound surface course, using closed-form 

as opposed to iterative solutions. The deflections measured at larger distances from the load 

mainly determine the subgrade modulus, while the surface course modulus is mainly a function 

of the near-load deflections and/or the radius of curvature of the deflection basin. Including the 

center deflection reading, which in effect is a reflection of the overall pavement system stiffness 

also enhances both of these forwardcalculation approaches. 

The advantages of forwardcalculation are as follows: 

1. Since the subgrade and bound surface course stiffnesses obtained are not dependent on the 

other moduli within the pavement system, as is the case with backcalculation, each problem 

provides a unique solution. 

2. Forwardcalculation is easy to understand and use, whereas backcalculation is presently more 

of an art than a science. Anyone can perform forwardcalculation, while backcalculation 

requires expert engineering judgment along with the art of running the iterative program of 

choice. For backcalculation, the art is in the evaluation of the reasonableness of the results 

and selection of the model and other input parameters. 

3. The forwardcalculation techniques developed for this project produce considerably less 

scatter in the data (for the same layer and test section) than do backcalculation techniques. 

Nothing in pavement analysis comes without its own unique drawbacks. As such, these 

drawbacks are not limited to backcalculation alone, for example: 

1. Since the subgrade and surface course stiffnesses are calculated independently, in 

combination the values obtained may or may not be reasonable with respect to the total 

center deflection. 

2. To obtain a third, intermediate layer stiffness (if present), such as a granular base, analysts 

could then assume that the surface and subgrade stiffnesses are correct and then fit the center 

deflection to the remaining unknown stiffness of, for example, a base course layer. This 

approach suffers from the same drawback as backcalculation—the layer’s modulus depends 

on another layer’s, or layers’, analysis results. 

3. It is also possible to use a ratio between the subgrade modulus calculated through 

forwardcalculation and apply the modular ratio relationship for unbound base materials. 

Certainly, there is no assurance that this method is correct; however, the test of 

reasonableness is best applied to the results. 
5

4. Since this method produces approximate values (particularly for the base or intermediate 

layer/s), these results should only be used as layer modulus estimates, for example, for 

screening or quality assurance/quality control (QA/QC) purposes. 

In the following sections, the method used in forwardcalculation is described, followed by a 

section with the screening results from phase I (modified during phase II) of this study that 

compares the backcalculated (computed) parameters in the database to the forwardcalculated 

values for the 18 trial sections evaluated in the pilot study. 

7

CHAPTER 3. FORWARDCALCULATION METHODOLOGY 

BACKGROUND AND PREVIOUS DEVELOPMENTS 

Closed-form solutions for determining select layered-elastic properties of pavement systems 

have been used extensively in the past. 

In 1884, Boussinesq developed a set of closed-form equations for a semi-infinite, linear elastic 

median half-space, including the modulus of elasticity of the median, based on a point load. 

Subsequent study has shown that the apparent or composite subgrade modulus derived from any 

FWD sensor at offset "r" can be calculated from the equation in Figure 1:(5)

Eo,r = (0.84 • a2 • σo) / (dr • r)

Figure 1. Equation. Composite subgrade modulus at an offset. 

 where: Eo,r = Surface or composite modulus of the subgrade beneath the sensor used 

 a = Radius of FWD loading plate 

 σo = (Peak) pressure of FWD impact load under loading plate 

 dr = (Peak) FWD deflection reading at offset distance r

 and r = Distance of deflection reading dr from center of loading plate 

The suggested constant of 0.84 assumes that Poisson’s ratio is 0.4 (from the calculation 1−μ

2

). If 

dr is a reasonably large distance from the edge of the loading plate, the load can be assumed a 

point load, so the plate pressure distribution does not matter. Furthermore, small changes in 

Poisson’s ratio have only a minimal impact on this equation. 

Subsequent developments have allowed the use of the shape of the deflection basin to estimate 

various layered elastic (or slab-on-dense-liquid) moduli from FWD deflection readings. 

CENTERLINE SUBGRADE MODULUS BASED ON THE HOGG MODEL 

One method to ascertain the approximate subgrade stiffness, or elastic modulus, directly under 

an imposed surface load is the Hogg model. The Hogg model is based on a hypothetical twolayer system consisting of a relatively thin plate on an elastic foundation. The method in effect 

simplifies the typical multilayered elastic system with an equivalent two-layer stiff-layer-onelastic foundation model. Depending on the choice of values along the deflection basin used to 

calculate subgrade stiffness, the tendency exists to either over- or underestimate the subgrade 

modulus. The Hogg model uses the deflection at the center of the load and one of the offset 

deflections. Hogg showed that the offset distance where the deflection is approximately one-half 

of that under the center of the load plate was effective at removing estimation bias. His 

calculations consider variations in pavement thickness and the ratio of pavement stiffness to 

subgrade stiffness, since the distance to where the deflection is one-half of the deflection under 

the load plate is controlled by these factors. 

The underlying model development for a finite subgrade was first published in 1944.(6) The 

implementation of the model used in this study was published in 1983.(7) The equations are as 

follows: 
8

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

Δ ⎟

⎟

⎠

⎞ ⎜

⎜

⎝

⎛

−

+ − = l

p

S

S E I

0

0

0

0 0

0 2(1 )

(1 )(3 4 )

μ

μ μ

Figure 2. Equation. Hogg subgrade modulus. 

B

B r r

r

− ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − Δ

Δ

− = β

β

α

α

1/

0

1/

50

1 1

(1/ )

Figure 3. Equation. Offset distance where deflection is half of center deflection. 

[( ) ]2

1

50

2

0 50

50

0 4

2 y r mar r l = y + −

if < 0.2

l

a , then 0 50 l = ( y − 0.2m)r

Figure 4. Equation. Characteristic length of deflection basin. 

⎟

⎠

⎞ ⎜

⎝

⎛ = − − ⎟

⎟

⎠

⎞ ⎜

⎜

⎝

⎛ 1 0.2 0

l

a

m

S

S

if < 0.2

l

a , then 1.0 0 =⎟

⎟

⎠

⎞ ⎜

⎜

⎝

⎛

S

S

Figure 5. Equation. Theoretical point load stiffness/pavement stiffness ratio. 

 where: 

E0 = Subgrade modulus 

μ0 = Poisson’s ratio for subgrade 

S0 = Theoretical point load stiffness 

S = Pavement stiffness = p/Δ0 (area loading) 

p = Applied load 

Δ0 = Deflection at center of load plate 

Δr = Deflection at offset distance r 

r = Distance from center of load plate 

r50 = Offset distance where Δr/Δ0 = 0.5 

l = Characteristic length 

h = Thickness of subgrade 

I = Influence factor—see Table 1 

α = Curve fitting coefficient—see Table 1 

β = Curve fitting coefficient—see Table 1 

Β = Curve fitting coefficient—see Table 1 

y0 = Characteristic length coefficient—see Table 1 

m = Characteristic length coefficient—see Table 1 

m = Stiffness ratio coefficient—see Table 1 

Wiseman (7) described the implementation of the Hogg model using three cases. One is for an 

infinite elastic foundation, and the other two cases are for a finite elastic layer with an effective 

thickness that is assumed to be approximately 10 times the characteristic length, l. The two finite 

thickness cases are for fixed Poisson’s ratios of 0.4 and 0.5, respectively. Figure 1 shows the 

various constants used for the three versions of the Hogg model. 
9

Table 1. Hogg model coefficients. 

Hogg model case I II III 

Depth to hard bottom h/l 10 10 Infinite 

Eqn. Poisson’s ratio μ0 0.50 0.40 All Values 

2 Influence factor I 0.1614 0.1689 0.1925 

Range ∆r/∆0 > 0.70 > 0.43 All Values 

α 0.4065 0.3804 0.3210 

β 1.6890 1.8246 1.7117 

r50=f(∆r/∆0) 

Β 0 0 0 

Range ∆r/∆0 < 0.70 < 0.43 

α 2.6947E-3 4.3795E-4

β 4.5663 4.9903 

3 

r50=f(∆r/∆0) 

Β 2 3 

4 l=f(r50,a) y0 0.642 0.603 0.527 

m 0.125 0.108 0.098 

5 (S/S0)=f(a/l) m 0.219 0.208 0.185 

Case II of the Hogg model, used for the past 15 years, has been found to be reasonably stable on 

a wide variety of pavement types and locations, tending toward high correlation with 

backcalculated subgrade moduli but with significantly lower (and more conservative) results 

than the corresponding backcalculated values. This difference is because of apparent or actual 

subgrade nonlinearity (effectively, stress-softening) and/or a finite depth of subgrade (as 

calculated by Case II) to a semirigid bottom layer of subgrade material. 

In addition, less variation is indicated between FWD test points when the Hogg model of 

forwardcalculation is used, as compared to virtually any backcalculation approach. This 

phenomenon is examined in the subgrade screening results in chapter 4. 

Both as a screening tool and to derive relatively accurate, in situ subgrade stiffnesses, the Hogg 

model is effective and very easy to use compared to others and thus Case II is the recommended 

method to calculate subgrade moduli in forwardcalculation. 

BOUND SURFACE COURSE MODULUS BASED ON THE AREA METHOD 

A viable method to determine the apparent surface course stiffness of the upper-most bound 

layer(s), under an imposed surface load is called the AREA (or quasi-radius of curvature) 

approach. 

This approach was first introduced in NCHRP Study 20-50(09), LTPP Data Analysis: Feasibility 

of Using FWD Deflection Data to Characterize Pavement Construction Quality.

(3) More 

recently, the equations originally suggested have been updated and calibrated for AC and PCC 

pavement surfaces. 

For both pavement types, the radius of curvature method is based on the AREA concept (a 

deflection basin curvature index) and the overall composite modulus of the entire pavement 

structure, Eo, as the equation in Figure 6 shows. 
10

Eo = (1.5 • a • σo) / do

Figure 6. Equation. Composite modulus under FWD load plate. 

 where: Eo= Composite modulus of the entire pavement system beneath the load plate 

 a = Radius of FWD load plate 

 σo= (Peak) pressure of FWD impact load under the load plate 

 and do= (Peak) center FWD deflection reading 

The equation in Figure 6 has been extensively used over the past three to four decades. A 1987 

textbook by P. Ullidtz(5) gives an excellent introduction to this approach. 

Figure 6 is the most commonly used version of this equation. In theory, it is based on an evenly 

distributed and uniform FWD load and a Poisson's ratio of 0.5. Generally, Poisson's ratio will be 

less than 0.5 (usually thought to be between 0.15 and 0.20 for PCC layers and between 0.3 and 

0.5 for most other pavement materials), while the distribution of the load under the FWD plate 

will not be exactly uniform (rather it will be somewhat nonuniform because of the rigidity of the 

loading plate). These two offsetting factors have resulted in the widely used and straightforward 

1.5 times composite modulus formula, which was therefore chosen to develop the 

forwardcalculation spreadsheets. 

AREA, used for rigid pavements in this study, and as reported by AASHTO in 1993, is 

calculated as:(8)

 

A36 = 6 ∗ [1 + 2(d12/d0) + 2(d24/d0) + (d36/d0)] 

Figure 7. Equation. 914-millimeter (mm) (36-inch) AREA equation for rigid pavements. 

 where: A36 = AREA beneath the first 914 mm (36 inches) of the deflection basin 

 d0 = FWD deflection measured at the center of the FWD load plate 

 d12 = FWD deflection measured 305 mm (12 inches) from the center of the plate 

 d24 = FWD deflection measured 610 mm (24 inches) from the center of the plate 

 and d36 = FWD deflection measured 914 mm (36 inches) from the center of the plate 

When calculating AREA36, the diameter of the loading plate must be between 300 mm (11.8 

inches) and 305 mm (12 inches). An AREA36 calculation of 36 is achieved if all four deflection 

readings, at the 0-, 305-, 610-, and 914-mm (0-, 12-, 24-, and 36-inch) offsets are identical, 

which is equivalent to an infinitely stiff upper layer. 

While the equation in Figure 7 has been found to be well suited for rigid pavements with a large 

radius of curvature, flexible pavements generally have a much smaller radius of curvature (i.e., a 

steeper deflection basin). Accordingly, for AC pavements a new version of the AREA concept 

based on FWD sensors placed at 0-, 203-, and 305-mm (0-, 8-, and 12-inch) offsets was derived: 

A12 = 2 ∗ [2 + 3(d8/d0) + (d12/d0)]

Figure 8. Equation. 305-mm (12-inch) AREA equation for flexible pavements. 

 where: A12 = AREA beneath the first 305 mm (12 inches) of the deflection basin 

 d0 = FWD deflection measured at the center of the FWD load plate 

 d8 = FWD deflection measured 203 mm (8 inches) from the center of the plate 

 and d12 = FWD deflection measured 305 mm (12 inches) from the center of the plate 
11

An AREA12 calculation of 12 is achieved if all three deflection readings, at the 0-, 203-, and 305-

mm (0-, 8-, and 12-inch) offsets, are identical, which is equivalent to an infinitely stiff upper 

layer (never very close to this value for flexible pavements, however). 

A series of calculations were made for AC and PCC pavement types to see what the AREA term 

becomes if all layers in a multilayered elastic system have identical stiffnesses or moduli (and 

Poisson’s ratios). This can be calculated using, for example, the CHEVRON, CHEVLAY2, 

ELSYM5, or BISAR multilayered elastic programs (CHEVLAY2 was used in this case). It turns 

out that, no matter which modulus value is selected, as long as all of the layers are assigned the 

same identical modulus of elasticity, the AREA36 term is always equal to 11.04 for rigid 

pavements (assuming no bedrock) and AREA12 is always equal to 6.85 if bedrock is assumed for 

flexible pavements. (Note: The AREA12 calculation for identical moduli with no bedrock = 6.91, 

close in value.) The reason that bedrock was assumed for AC and not PCC pavements is that 

FWD deflection readings generally reflect the presence of an underlying stiff layer for flexible 

pavements, but not for rigid pavements. Using either approach, however, the resulting 

calculations for upper layer pavement stiffness will be nearly the same, whether or not bedrock is 

assumed. 

The minimum AREA values of 11.04 and 6.85 for the 914-mm (36-inch) and 305-mm (12-inch) 

areas, respectively, are important in the following equations because they can now be used to 

ascertain whether the upper layer has a significantly higher stiffness than the underlying layer(s), 

and to what extent this increase affects the stiffness of the upper, bound pavement layers. For 

example, if the AREA36 term is much larger than 11.04, then the concrete layer is appreciably 

stiffer than the underlying (unbound) layer(s). The value 11.04 is therefore used in Figure 9, 

while Figure 10 can be considered as a radius of curvature stiffness index, based on the stiffness 

of the bound upper layer(s) compared to the composite stiffness of the underlying unbound 

layers. 

The calculation of Eo was previously explained in connection with the presentation of Figure 6, 

as a composite, effective stiffness of all the layers under the FWD loading plate. If these two 

terms are combined so that the boundary conditions are correct and the logic of the two AREA 

concepts are followed for PCC and AC pavements, the following equations result: 

AFPCC = [(k2 - 1) / {k2 - (AREA36 / k1)}] 1.79 

Figure 9. Equation. AREA factor for rigid pavements. 

where: AFPCC = AREA factor, i.e., the improvement in AREA from 11.04 to the 1.79 power 

 k1 = 11.04 (the AREA when the stiffness of the concrete layer is the same as the 

 lower layers) 

 k2 = 3.262 (maximum possible improvement in AREA = 36 / 11.037) 

AFAC = [(k2 - 1) / {k2 - (AREA12 / k1)}] 1.35

Figure 10. Equation. AREA factor for flexible pavements. 

where: AFAC = AREA factor, i.e., the improvement in AREA to the 1.35 power 

 k1 = 6.85 (the AREA when the stiffness of the asphalt layer is the same as the lower 

layers) 

 k2 = 1.752 (maximum possible improvement in AREA = 12 / 6.85) 
12

EPCC = [Eo ∗ AFPCC ∗ k3

(1/AFpcc)] / k32.38

Figure 11. Equation. Stiffness or modulus of the upper PCC layer. 

EAC = [Eo ∗ AFAC ∗ k3

(1/AFac)] / k32

Figure 12. Equation. Stiffness or modulus of the upper AC layer. 

 where: EPCC= Stiffness or modulus of the upper PCC (bound) layer(s) 

 EAC = Stiffness or modulus of the upper AC (bound) layer(s) 

 Eo = As defined by Figure 6 

 AF = As defined by Figure 9 for PCC or Figure 10 for AC 

 k3 = Thickness ratio of upper layer thickness / load plate diameter = h1 / (2∗a) 

 and a = Radius of the FWD load plate 

Both Figure 11 and Figure 12 have been calibrated using a large number of trial CHEVLAY2 

runs, and they work very well for typical pavement materials and moduli ratios. However, this 

approach is empirical rather than totally rigorous or scientific. Thus this method can be used 

effectively to approximate the relative stiffness of the upper (bound) layer(s) in a pavement cross 

section for QC, comparative, or routine testing and analysis. 

The advantage of using the equations in Figure 9 through Figure 12 or similar equations 

developed elsewhere is that forwardcalculation techniques, together with commonly used 

deflection-based quantities (such as AREA), can be combined. Only the composite modulus or 

stiffness of the pavement system, the AREA, and the pavement thickness normalized to the 

diameter of the loading plate are needed to calculate the relative stiffness of the bound upper 

layer(s) of pavement. 

INTERMEDIATE LAYER MODULUS CALCULATIONS 

Forwardcalculation techniques, as discussed in chapter 3, for the subgrade and bound surface 

courses, can in turn be used in a pseudobackcalculation manner to derive the approximate 

stiffness of the intermediate layer, or layers, situated between the subgrade and bound surface 

course. Alternatively, the modulus relationship developed by Dorman and Metcalf between two 

adjacent layers of unbound materials can be used.(9) This method computes the base modulus as 

shown by Figure 13: 

EBase = 0.2 • h2

0.45 • ESub

Figure 13. Equation. Modulus of the unbound base layer using 

the Dorman and Metcalf relationship. 

 where: EBase = Dorman and Metcalf base modulus, MPa 

 h2 = Thickness of the intermediate base layer, mm 

 and ESub = Subgrade modulus, MPa 

Some philosophical issues exist with this quasi-backcalculation approach. The most important is 

that the calculations of the surface course modulus and the centerline subgrade modulus, as 

outlined in chapter 3, are virtually independent of one another and usually use different 
13

deflection sensors (except the center deflection) to derive the appropriate forwardcalculated 

values. Thus, when the center deflection is once again used to close the multilayered system by 

matching up the total center deflection with the pair of surface course and subgrade modulus 

values, the base course modulus so derived will be the least reliable of the three. 

Accordingly, the trial data used in phase I for the 15 flexible sections chosen for the pilot study 

were a matrix of forward- and backcalculated values shown in Table 2. For PCC sections, only 

the surface course and the subgrade were forwardcalculated by the two-layer variable method 

used in the backcalculation process from the LTPP database. 

Table 2. Moduli used for screening of LTPP database values. 

Layer First Method Second Method 

Asphalt Layer(s) AREA12 modulus AREA12 modulus 

Base Layer(s) Pseudobackcalculated Dorman & Metcalf—from Hogg subgrade

Subgrade Layer Case II Hogg modulus Case II Hogg modulus 

In summary, using forwardcalculated modulus data is not intended to replace backcalculation or 

any other form of modulus of elasticity measurements. Forwardcalculation, like all other 

methods of determining apparent, in situ stiffnesses or moduli merely gives the engineer 

estimates of these values. The only question is: How realistic are such estimates for pavement 

evaluation or design? 

Accordingly, forwardcalculation is designed for routine FWD-based project use and for 

screening purposes for moduli derived using other methods, especially backcalculation. The 

present study attempts to determine which of the backcalculated modulus values in the LTPP 

database—which are also estimates—are reasonable, since two distinctly different methods of 

deriving stiffnesses or moduli from the same FWD load-deflection data should not produce 

vastly dissimilar results. 

15

CHAPTER 4. INITIAL LTPP BACKCALCULATION DATA SCREENING RESULTS 

OVERVIEW 

During the development phase of the project (phase I), the researchers selected 18 LTPP pilot 

sections to evaluate and verify the forwardcalculation methodology. Although only these pilot 

test sections (albeit with a wide variety of layer thicknesses and test locations) were screened for 

comparison purposes, this selection still resulted in a large number of data pairs and, 

accordingly, an adequate sampling of the large volume of data in the LTPP database. Many data 

points resulted because each individual FWD test point (each with up to four FWD drop heights 

using multiple drops) provided independently calculated values using both back- and 

forwardcalculation techniques. Thus, each of the fifteen 152.4-meter (m) (500-foot (ft)) -long 

flexible sections contains around 500 comparable pairs of moduli. In addition, each 152.4-m 

(500-ft) rigid section contains somewhat fewer moduli—around 80 comparable pairs of data for 

the 3 rigid sections screened. 

ORGANIZATION OF DATA 

For the phase I study, the researchers picked representative but diverse test sections from the 

appropriate data tables. In all, 15 flexible and 3 rigid sections were selected for review and the 

development of the screening techniques that were eventually used during phase II. The 18 

sections all contained backcalculated data for most or all of the FWD test points along each of 

the test sections, and they were selected based on diverse layer thicknesses, geographic location, 

and test dates. Both General Pavement Studies (GPS) and Specific Pavement Studies (SPS) 

sections were used to further ensure a wide range of input values. 

The data were imported from the appropriate LTPP data tables into various MicrosoftTM Excel 

spreadsheets for further processing. Parallel columns of data, both backcalculated and 

forwardcalculated (described below), were arranged for ease of postprocessing and comparisons 

of related stiffnesses, or moduli. 

The following LTPP sections and dates of FWD tests comprised the 18 trial datasets: 

• 04-0114 17 February 1994 (flexible SPS). 

• 04-0117 7 January 1998 (flexible SPS). 

• 04-0221 8 February 1994 (rigid SPS). 

• 04-1003 26 February 1992 (flexible GPS). 

• 05-3011 15 June 1993 (rigid GPS). 

• 12-1370 14 December 1989 (flexible GPS). 

• 12-9054 26 September 1989 (flexible GPS). 

• 13-4111 16 September 1992 (flexible GPS). 

• 16-1021 13 August 1991 (flexible GPS). 

• 20-1005 20 February 1992 (flexible GPS). 

• 23-1001 24 April 1995 (flexible GPS). 

• 31-0120 3 August 1995 (flexible SPS). 
16

• 31-0121 10 June 1997 (flexible SPS). 

• 32-1020 14 September 1994 (flexible GPS). 

• 35-1003 26 April 1995 (flexible GPS). 

• 35-1005 18 April 1994 (flexible GPS). 

• 36-1011 16 August 1993 (flexible GPS). 

• 48-4143 24 July 1990 (rigid GPS). 

For the phase I preliminary analyses, these data were processed and analyzed as described in the 

following sections. 

CHECK FOR ERRORS OR ANOMALIES IN THE BACKCALCULATION PROCESS 

At the outset of phase I, the scope of work assumed that the level E backcalculated values 

present in the database, for both rigid and flexible pavements, at a minimum, matched the 

measured deflection basin, i.e., within a reasonable root mean square (RMS) value. Accordingly, 

spot checks were made on a few of the deflection basins to see whether the same set of moduli 

could be obtained using the same backcalculation program (MODCOMP). Even if these results 

were not exactly the same, another approach was to determine whether the RMS values in the 

level E database were the same as those that could be derived by using the backcalculated values 

in the database to forwardcalculate a new RMS value. 

Although the RMS value comparisons were within reason, they were not identical. It was also 

not possible, in all cases, to obtain the same set of backcalculated values by rerunning the FWD 

data through MODCOMP. Nevertheless, the differences could well be attributed to how the 

backcalculation program was run (e.g., user-controlled inputs) or to rounding differences that 

cannot be precisely reproduced. 

Based on the LTPP sections checked and a general review of the results, the researchers 

determined that the data in the existing level E database are acceptable insofar as the 

backcalculated moduli can be used to recalculate a deflection basin and an RMS value that are 

within reason. Accordingly, the existing backcalculated database was screened as originally 

proposed in the original scope of work. 

SUBGRADE SCREENING RESULTS 

Figure 14 shows a log-log plot of all flexible test points analyzed using forwardcalculation 

techniques versus the backcalculated values for the same test points and drop heights. This graph 

shows that the two methods of analysis correlate well for most of the data. However, the overall 

correlation is not very good (the r-squared value = 0.39). A careful review of Figure 14 reveals 

that a number of outliers caused the low r-squared value and that these outliers are primarily 

caused by backcalculated values that do not follow the trend. (Using a log-log scale makes the 

graph look better than a linear plot and regression analysis would.) 
17

y = 1.4493x1.0355

R2 = 0.3905

10

100

1,000

10,000

10 100 1,000 10,000

Forwardcalculated Modulus (MPa)

Backcalculated Modulus (MPa)

Modulus Relationship

Power (Modulus Relationship)

Figure 14. Graph. Back- versus forwardcalculated subgrade moduli 

for 15 trial LTPP flexible sections. 

Another way to view the data is to examine the overall nationwide averages and the variability of 

each set of values. 

Certainly, variability in subgrade moduli is to be expected. Examining at least 15 varying 

subgrade soils spread across several states and regions with obvious differences causes 

differences, while spatial variability also exists within any given 152.4-m (500-ft) test section. 

On the other hand, both the averages and the overall variability for each method should be 

similar, since they are all based on the same FWD test data, the same sections, and the same test 

points. Table 3 summarizes the basic statistics for the two analysis methods. 

Table 3. Statistics for back- and forwardcalculated subgrade moduli 

for 15 trial flexible sections.

Statistic 

Hogg 

Subgrade

Backcalculated 

Subgrade 

Median (MPa*) 129 236 

Average (MPa) 150 320 

Std. Dev. (MPa) 68 493 

COV (%) 46 154 *1 megapascal (MPa) = 145 pounds per square inch (psi) 

Based on the overall results shown in Table 3, it is apparent that the Hogg forwardcalculation 

model indicates a smaller variability in subgrade stiffness (coefficient of variation (COV) = 

46%) compared to the backcalculation method (COV = 154%). Some of the subgrade layers used 
18

during backcalculation (when more than one layer was classified as a subgrade material) were 

not included in this pilot analysis. The subgrade layers that were not included were the ones with 

the poorest relationship to forwardcalculation and with the highest variability (see also Figure 20 

in chapter 4). Also the median value is probably more indicative of a true average than the 

averages (arithmetic means), which are increased by the high and implausible modulus values in 

the backcalculated database. 

It appears that the nationwide variability of subgrade materials, expressed as COV, should be in 

the 40 to 60 percent range. The nationwide standard deviation for backcalculation was even 

larger than the average value found, which is not feasible and confirms again that some 

backcalculated values were implausibly high. 

By comparison, the average P46 laboratory moduli reported for LTPP’s fine-grained soils was 71 

MPa (around 55% of the forwardcalculated median). Meanwhile, the COV in moduli for the 

same nationwide soil samples was 45 percent—see, for example, LTPP Data Analysis: 

Variations in Pavement Design Inputs (10). This NCHRP research indicates that the distribution 

of forwardcalculated subgrade moduli is similar to the distribution of the LTPP P46 laboratory 

test moduli. 

The 45 percent COV for subgrade materials found through an independent means therefore adds 

credence to the Hogg model COV of 46 percent found during Phase I of this study. The 

difference between the forwardcalculated Hogg modulus and the laboratory-associated P46 

modulus is probably because the subgrade, when tested in situ by the FWD, is covered and wellconfined by a pavement system, while the laboratory P46 tests are conducted directly on 

elements of the subgrade, whether disturbed or not, with or without soil suction, etc. 

One level of identifying suspect backcalculated subgrade moduli using the forwardcalculated 

values could be to limit the divergence of the two approaches to a factor of two. Using this factor 

of two as an example, if the subgrade modulus from forwardcalculation = 80 MPa (11,600 psi), 

then the acceptable (unflagged) range of the backcalculated values would be 40–160 MPa 

(5,800–23,200 psi). Out of the 15 flexible section set of trial data, some 30% of the 

backcalculated values were not within this acceptable range. 

For the concrete sections, all 132 backcalculated subgrade moduli were within a factor of 1.5 

below or above the minimum and maximum of the forwardcalculated values. Figure 15 shows 

that the values were always above so for PCC sections, none of the phase I backcalculated 

subgrade moduli appear to be candidates for flagging. Figure 15 also shows that the Hogg model 

produces lower subgrade modulus values, probably because these values represent the apparent 

(estimated) subgrade modulus under the load, with an effective depth to a rigid layer, whereas 

the backcalculation approach did not use such an assumption. 

Since the spread in back- and forwardcalculated subgrade moduli under concrete pavements was 

smaller than in the case of the other values compared in the phase I pilot study, these values were 

plotted in arithmetic form in Figure 15—which still resulted in a surprisingly good r-squared 

value of 0.84. 
19

y = 1.7436x - 82.095

R2

 = 0.8401

100

200

300

400

100 200 300

Forwardcalculated Modulus (MPa)

Backcalculated Modulus (MPa)

Modulus Relationship

Linear (Modulus Relationship)

Figure 15. Graph. Back- versus forwardcalculated subgrade moduli 

for three trial LTPP rigid sections. 

SURFACE COURSE SCREENING RESULTS 

Figure 16 shows a log-log plot of all flexible layer test points analyzed using forwardcalculation 

techniques introduced in chapter 3 versus the backcalculated values for the same test points and 

drop heights. This graph shows that the overall values track quite well; the correlation is good, 

with an r-squared of 0.67 for the back- versus forwardcalculated moduli. 

Although there is a reasonable correlation between the back- versus forwardcalculated AC 

moduli, as shown in Figure 16, this graph (and others that follow) reveals two or more 

simultaneous trends. In this instance, out of the 15 asphaltic test sections, most of the points 

north of the best-fit regression line were from two Florida sites while most of the points south of 

the line were from two Nebraska sites. Table 4 (Florida) and Table 5 (Nebraska) show the 

average moduli (all layers) for these four sites using the two methods of analysis. 
20

y = 1.2382x0.9617

R2 = 0.6694

1,000

10,000

100,000

1,000 10,000 100,000 Forwardcalculated Modulus (MPa)

Backcalculated Modulus (MPa)

Modulus Relationship

Power (Modulus Relationship)

Figure 16. Graph. Back- versus forwardcalculated asphalt layer moduli 

for 15 trial LTPP flexible sections. 

Table 4. Back- and forwardcalculated moduli for two trial Florida sections. 
21

Table 5. Back- and forwardcalculated moduli for two trial Nebraska sections. 

Results in Table 4 and Table 5 above show two primary factors involved in these discrepancies. 

The first was that the two Florida sections shown in Table 4 had a very thin layer of asphalt 

concrete (64 mm (2.5 inches) or less), which is not well suited for backcalculation. In contrast, 

the forwardcalculation results for these two sections appear reasonable. 

The second and probably the most important overall factor that caused the relatively large 

discrepancies between back- and forwardcalculated values for these four sections was the socalled compensating layer effect that often results from an iterative backcalculation routine. 

The compensating layer effect is a result of backcalculating the modulus of successive layers 

from the subgrade up, which has a tendency to compensate for even relatively small errors in the 

layer or layers below by alternately over- and underestimating the modulus of each successive 

layer in the pavement system. The compensating layer effect is especially pronounced for Florida 

section 12-9054, where the subbase layer (actually a compacted fine-grained soil) results in an 

unrealistically high modulus (14,000 MPa (2,000,000 psi)), followed upwards by a base layer 

(well-compacted limerock) with an unrealistically low modulus of 80 MPa (11,600 psi). This 

layer, in turn, is followed by an unrealistically high modulus (at that test site) for the hot mixed 

asphalt surface course of some 12,500 MPa (1,800,000 psi). Meanwhile, forwardcalculation 

results in a subgrade modulus of approximately upper 3 m (10 ft) of material of 120 MPa (17,000 

psi), followed by a combined base and subbase layer of 300 MPa (42,000 psi). Finally, 

forwardcalculation indicates a modulus for the asphalt layer of around 6,000 MPa (880,000 psi), 

resulting in asphalt moduli points north of the best-fit line for all sections shown in Figure 16. 

The materials used in Florida section 12-1370 were identical (see modulus comparison in Table 

4, although the compensating layer effect is different, with too high a subgrade modulus for the 

upper 3 m (10 ft) of subgrade from backcalculation. 

The opposite effect in the asphaltic surface course is evident for the Nebraska sections shown in 

Table 5, although to a lesser degree, with seemingly reasonable backcalculated subgrade and 
22

subbase moduli, but very high base course moduli, especially for section 31-0121. Because of 

the compensating layer effect, lower surface course moduli result from backcalculation than 

from forwardcalculation (see values in Table 5). In both of these sections, the subbase was a 

crushed stone, the base was a permeable asphalt treated base, and the surface course was dense 

graded asphalt concrete. 

As was shown with the subgrade moduli screening results in chapter 4, another way to examine 

these data is to consider the overall nationwide averages and the variability associated with each 

set of values. With the asphalt layer, the averages and variability associated with the same set of 

test sections and the time of FWD test should be similar. 

Table 6 summarizes the basic statistics for both the backcalculated and forwardcalculated 

(AREA12) analysis methods. 

Table 6. Statistics for back- and forwardcalculated surface course moduli 

for flexible sections. 

Statistic 

AREA12

Asphalt Layer 

Backcalculated 

Asphalt Layer 

Median (MPa*) 7,164 5,730 

Average (MPa) 7,704 7,448 

Std. Dev. (MPa) 4,316 5,850 

COV (%) 56 79 

 *1 megapascal (MPa) = 145 pounds per square inch (psi) 

Based on the overall results shown in Table 6, both methods produce essentially the same 

average AC modulus, approximately 7,500 MPa (1,100,000 psi). While these modulus levels 

appear higher than normal for asphalt concrete, in fact these results are reasonable medians and 

averages, since the data included both high, medium, and low AC mat temperatures from FWD 

tests conducted at all seasons except when the subgrade was frozen. Furthermore, the coefficient 

of variation associated with each analysis procedure appears plausible (56 and 79 percent for 

forward- and backcalculation, respectively), although once again the forwardcalculation method 

appears somewhat more stable. The 15-section nationwide forwardcalculated COV is greater for 

AC than for subgrade materials, probably because of the temperature-sensitive, viscoelastic 

properties of asphalt-bound materials as opposed to unbound subgrade materials, which are 

generally not viscoelastic. 

One of the 15 flexible sections analyzed had two surface course layers that were used in 

backcalculation. The extra or second-layer plots are described in the extra layer results section. 

Since these were not indicative of the overall trend, they are not included in Figure 16 or the 

statistics shown above. 

In screening the backcalculated results, if a criterion of a factor of two (times or divided by) were 

used, then some 15 percent of the backcalculated asphalt concrete moduli would be flagged as 

out-of-range; if the factor is changed to 1.5, then 24 percent would be out-of-range, and so on. 

The use of several levels of flagging was eventually adopted and recommended for the LTPP 

backcalculated database (see chapter 5). 
23

Figure 17 shows a log-log plot of all rigid test points analyzed using the checking for errors or 

anomalies screening method versus the backcalculated values for the same test points and drop 

heights. Two backcalculated values are shown because two methods were used in the 

backcalculation process: slab-on-dense-liquid (DL) foundation and slab-on-elastic-solid (ES) 

foundation. In both cases, the r-squared values are somewhat poorer than with asphalt concrete 

(r-squared = 0.61 and 0.70 for the ES and DL cases, respectively). However, this result is to be 

expected, since the range of values encountered for AC is greater than for PCC because of the 

viscoelastic nature of asphalt-bound materials. 

Using screening criteria, for example, where the backcalculated values should be within a factor 

of 1.5 times, or divided by 1.5, the corresponding forwardcalculated values, only 18 out of 124 

PCC moduli (or 14.5 percent of the total) would be considered out-of-range (reduced to 8 out of 

124, or 6.5 percent, if a flagging factor of 2 is used). 

y = x

y = 1304.8x0.346

R2 = 0.6139

y = 390.26x0.4313

R2 = 0.6955

10,000

100,000

10,000 100,000 1,000,000

Forwardcalculated Modulus (MPa)

Backcalculated Modulus (MPa)

EPCC_DL (MPa)

EPCC_ES (MPa)

Linear (y=x)

Power (EPCC_DL (MPa))

Power (EPCC_ES (MPa))

Figure 17. Graph. Back- versus forwardcalculated concrete layer moduli 

for three trial LTPP rigid sections. 

Table 7 summarizes the basic statistics for both the backcalculated and forwardcalculated 

(AREA36) rigid pavement analysis methods. 
24

Table 7. Statistics for back- and forwardcalculated PCC moduli for rigid sections. 

Statistic 

Forwardcalculated PCC 

modulus 

Backcalculated 

EPCC_ES 

Backcalculated 

EPCC_DL 

Average (MPa*) 54218 42351 55973 

Std. Dev. (MPa) 24774 7849 8755 

COV (%) 46 19 16 

 *1 megapascal (MPa) = 145 pounds per square inch (psi) 

The averages are very similar between the forwardcalculated model and the backcalculated DL 

model, while the backcalculated ES model is somewhat lower. 

The coefficients of variation were 16, 19, and 46 percent for the backcalculated DL model, ES 

model, and forwardcalculated AREA36 model, respectively. The forwardcalculation model 

results in a COV that appears too high when compared to both backcalculation models in the 

LTPP computed parameter database. Yet it is still possible that the forwardcalculation model 

used in this study is better able to reveal significant differences between low- and high-strength 

concrete mixes than either backcalculation model. This trend was discovered during an NCHRP 

project.(3)

INTERMEDIATE (BASE) COURSE SCREENING RESULTS 

As stated in chapter 3, backcalculation of the intermediate layer, or layers, between a subgrade 

and a bound surface course is the most tenuous and uncertain of all. This situation is true whether 

the analyst starts with both of the upper and lower layers as through forwardcalculation or with 

the subgrade alone, as is generally done through backcalculation. To reiterate this point, any

errors in the process leading up to the base course calculation of stiffness or modulus, however 

slight they may be, will lead to much larger and offsetting errors in the base layer(s) if a closedloop solution is sought. (A closed-loop solution is one where the sum of the vertical strains under 

the FWD test load in all underlying pavement layers is equal to the load from the measured 

center deflection.) In backcalculation, this phenomenon is known as the compensating layer 

effect, which will influence the pseudobackcalculation routine developed for the intermediate 

layer after forwardcalculation of the upper and lower layers, even if to a lesser degree. If the 

Dorman and Metcalf equation is used, this drawback will not apply since the intermediate layer 

is simply calculated as a ratio of the subgrade modulus (as a function of the thickness of this 

layer). 

Figure 18 shows a log-log plot of all flexible test points analyzed using the pseudobackcalculation screening approach versus the backcalculated values for the same test points and 

drop heights. 
25

.

y = 2.0137x0.7852

R2 = 0.1503

1

10

100

1,000

10,000

100,000

1 10 100 1,000 10,000 100,000

Pseudo-Backcalculated Modulus Derived from 

Forwardcalculated Moduli (MPa)

Backcalculated Modulus (MPa)

Modulus Relationship

Power (Modulus Relationship)

Figure 18. Graph. Back- versus forward-based base layer moduli 

for 15 flexible LTPP sections. 

Figure 18 shows virtually no relationship between the two sets of values. The backcalculation 

routine chosen to create the computed parameter data tables has evidently fixed the minimum 

possible base course modulus at 5 or 6 MPa (~750 psi), while the pseudobackcalculation/ 

forwardcalculation-based approaches used a maximum possible base course modulus of some 

2,500 MPa (360,000 psi). Obviously, both of these values are outside of typical ranges for 

granular or unbound base courses. As Figure 18 shows, the correlation between the 

forwardcalculation-based method and backcalculation only yields an r-squared value of 0.15. 

Meanwhile, both approaches suffer from excessive variability, with the pseudobackcalculation 

approach having a COV of 66 percent and backcalculation having a COV of 272 percent (see 

Table 8). This anomaly presents a problem because COV levels should be similar to those found 

for unbound (and generally even more inconsistent) subgrade materials. 

Table 8. Statistics for backcalculated and pseudobackcalculated 

base course moduli for flexible sections. 

Statistic 

E(2) based on forwardcalculated 

surface course and subgrade moduli

E(2) from 

backcalculation database

Median (MPa*) 306 148 

Average (MPa) 361 565 

Std. Dev. (MPa) 238 1,538 

COV (%) 66 272 

 *1 megapascal (MPa) = 145 pounds per square inch (psi) 
26

As Table 8 shows, the average and median intermediate layer moduli derived through either 

approach appear reasonable, with the possible exception of the median backcalculated value 

(approximately 150 MPa (~20,000 psi)), which is too low. 

Of the 15 flexible sections analyzed, 4 had 2 base course layers that were used in 

backcalculation. The extra, or second-value, plots are discussed below. 

These high variability trends were indicative of the two methods throughout the entire FWD 

load-deflection database and the backcalculated tables. Therefore, the researchers felt it more 

realistic to use the ratio published by Dorman and Metcalf to estimate the intermediate layer 

modulus.(9) This approach assumes that a well-constructed unbound subbase or base course will 

realize an increase in modulus over and above that of the subgrade by a factor that is only 

dependent on the thickness of the intermediate layer or layers. This ratio is considered valid for 

intermediate layer thicknesses between 50 and 600 mm (2 and 24 inches), resulting in ratios from 

1.16 for a 50-mm (2-inch) layer and 3.56 for a 600-mm (24-inch) layer. 

Using the same 15 flexible section dataset, and considering the fact that 6 of these 15 sections 

had intermediate layers that were classified in the LTPP database basically as “improved 

subgrade,” Table 9 shows the remaining 9 section statistics. 

Table 9. Statistics for base course moduli from backcalculation and from 

forwardcalculation using Dorman and Metcalf’s equation 

for nine trial flexible sections. 

Statistic 

E(2) using Dorman and Metcalf 

ratio to forwardcalculated 

subgrade moduli 

E(2) from backcalculation 

database 

Median 

(MPa*) 313 247 

Average 

(MPa) 361 921 

Std. Dev. 

(MPa) 142 1,991 

COV (%) 39 216 

 *1 megapascal (MPa) = 145 pounds per square inch (psi) 

The researchers concluded that the median and average base or subbase moduli from Dorman 

and Metcalf’s relationship were far more realistic (310–360 MPa (45,000–50,000 psi)) as 

screening values, as was the reasonable nationwide COV of 39 percent (see Table 9). By 

contrast, the COV using the pseudobackcalculation procedure was 66 percent (see Table 8). The 

median base course modulus from backcalculation (250 MPa (35,000 psi)) also appears 

reasonable, but certainly not the backcalculated average of 921 MPa (135,000 psi) or the COV of 

216 percent gained using this method (see Table 9). 

Accordingly, the Dorman and Metcalf relationship was used for phase II to screen the entire 

database. For PCC sections, only two back- or forwardcalculated values were derived, one for 

the subgrade and one for the rigid upper layer or layers. 
27

EXTRA LAYER RESULTS FROM BACKCALCULATION 

This section shows the extra layers used in backcalculation for the phase I trial database, over 

and above the two or three layers calculated through forwardcalculation. These situations 

occurred when the MODCOMP backcalculation program used more than three layers (plus any 

assumed rigid bottom) when generating the computed parameter file of backcalculated values. 

 

y = 6E+07x-1.0511

R2 = 0.0932

1,000

10,000

100,000

1,000 10,000 100,000

Forwardcalculated Modulus (MPa)

Backcalculated Modulus (MPa)

Modulus Relationship

Power (Modulus Relationship)

y (the y axis—the backcalculated modulus) = 6 times 10 to the 7th power (6E+07) times x (the axis—the 

forwardcalculated modulus) raised to the -1.0511 power; R2

 (the coefficient of determination) = 0.0932 

Figure 19. Graph. Back- versus forwardcalculated asphalt layer moduli 

for one trial LTPP flexible section with two upper (bound) layers. 
28

y = 203.83x0.173

R2 = 0.0054

10

100

1000

10000

100000

10 100 1000 10000 100000

Forwardcalculated Modulus (MPa)

Backcalculated Modulus (MPa)

Modulus Relationship

Power (Modulus Relationship)

R2 = the coefficient of determination 

Figure 20. Graph. Back- versus forwardcalculated subgrade moduli for five trial 

LTPP flexible sections with two subgrade (lower unbound) layers. 

y = 2E+15x-5.1193

R2 = 0.294

10

100

1000

10000

100000

10 100 1000 10000 100000

Derived from Forwardcalculated Moduli (MPa)

Backcalculated Modulus (MPa)

Modulus Relationship

Power (Modulus Relationship)

y (the y axis—the backcalculated modulus) = 2 times 10 to the 15th power (2E+15) times x (the axis—the 

forwardcalculated modulus) raised to the -5.1193 power; R2

 (the coefficient of determination) = 0.294 

Figure 21. Graph. Back- versus forwardcalculated base course moduli 

for four trial LTPP flexible sections with two intermediate layers. 
29

In the three figures above, two of the three exhibit correlations that regress in the wrong 

direction. The r-squared values indicate an extremely poor fit, whatever the direction of the bestfit line. Accordingly, it would appear that backcalculation, or any other available method, is not 

very good at deriving stiffnesses or moduli for more than three unknown structural layers (plus a 

rigid layer at-depth, if any). 

CHOICE OF SCREENING LIMITS AND CODES 

Based on the analyses carried out during phase I, the following screening limits were developed. 

Table 10 shows these limits with a generic description of each. 

Table 10. Flagging codes suggested for screening of the 

backcalculated LTPP database tables. 

Generic description of the 

correspondence between backand forwardcalculated moduli 

Suggested 

correspondence 

codes (flags) 

Ratio between the 

forwardcalculated and 

backcalculated modulus values 

Acceptable 0 2/3 ≤ Ratio ≤ 1.5 

Marginal 1 1/2 ≤ Ratio ≤ 2 (and not code 0) 

Questionable 2 1/3 ≤ Ratio ≤ 3 (and not codes 0 or 1) 

Unacceptable 3 Ratio < 1/3 or Ratio > 3 

In the selection of a fairly broad range of values that are acceptable as far as the backcalculated 

LTPP computed parameter tables are concerned, researchers found that neither back- nor 

forwardcalculation offers any certain or unequivocal ground truth of in situ moduli. Both 

methods, using distinctly different assumptions and theory, arrive at approximations (at best) of 

in situ modulus values in a layered elastic system consisting of two or more layers. Therefore, it 

is certainly acceptable if these two different approaches produced moduli within a factor of 1.5 

times or divided by each other, for the same layer and test point. In such cases, it is impossible to 

claim that one is correct while the other is incorrect, because no known ground truth exists. The 

only valid conclusion is that each value, within an acceptable range of each other, is therefore 

reasonable or acceptable, provided as well that each lies within a reasonable range for the 

materials it represents (see also chapter 5 and Table 14). 

The same logic was used to arrive at the generic terms marginal, questionable, and unacceptable, 

as outlined in Table 10. For example, it was unacceptable if records occurred from the two 

dissimilar methods of analysis, although using exactly the same FWD input data, resulted in a 

layer modulus more than a factor of three times or divided by each other. In such cases, either 

one of the two values is reasonable or both are unreasonable. The key screening steps in chapter 

5 discuss in more detail how these and the other cases of back- versus forwardcalculation 

discrepancies delineated in Table 10 were handled. 

31

CHAPTER 5. LTPP BACKCALCULATION DATABASE SCREENING 

METHODOLOGY 

LTPP DATA SOURCE USED IN THIS STUDY 

The complete computed parameter tables of backcalculated pavement layer data plus the 

supporting tables (Release 16.0—July 2003 Upload) were used and screened in this study. 

LTPP Data Tables Used 

The following tables from the LTPP database were used in either computing the 

forwardcalculated moduli or screening the backcalculation values: 

• EXPERIMENT_SECTION—Stores current experiment information that is driven by 

maintenance and rehabilitation (M and R) activities. 

• TST_L05B—Table containing section representative layer thickness and descriptions for all 

constructions. 

• MON_DEFL_FLX_BAKCAL_BASIN—Deflection basin parameters used for the pavement 

backcalculation computations using MODCOMP v4.2 computer program. 

• MON_DEFL_FLX_BAKCAL_LAYER—Layer structure and material inputs for the 

pavement backcalculation computations using MODCOMP v4.2 computer program. 

• MON_DEFL_FLX_BAKCAL_POINT—Interpreted results of backcalculated elastic layer 

moduli from FWD measurements for flexible and rigid pavement structures using 

MODCOMP v4.2 computer program. 

• MON_DEFL_FLX_BAKCAL_SECT—Summary of results presented in 

MON_DEFL_FLX_BAKCAL_POINT by section and test date. Results in 

MON_DEFL_FLX_BAKCAL_POINT with greater than 2 percent ERROR_RMSE were 

excluded from summary statistics. 

• MON_DEFL_FLX_NMODEL_POINT—Interpreted results of nonlinear backcalculated 

from FWD measurements for flexible and rigid pavement structures using MODCOMP v4.2 

computer program. 

• MON_DEFL_FLX_NMODEL_SECT—Summary of results presented in 

MON_DEFL_FLX_NMODEL_POINT by section and test date. Results in 

MON_DEFL_FLX_NMODEL_POINT with greater than 2 percent ERROR_RMSE were 

excluded from summary statistics. 

• MON_DEFL_FWDCHECK_CMNTS—Comments generated during use of FWDCHECK 

for basic analysis of the deflection data (not part of the backcalculation process, but listed 

here as a possible information source even though it is only partially populated). 
32

• MON_DEFL_LOC_INFO—Test point specific condition data for Dynatest FWD. 

• MON_DEFL_MASTER—FWD data collection general site measurement information. 

• MON_DEFL_RGD_BAKCAL_BASIN—Deflection basin parameters used in 

backcalculation of rigid pavement structures. 

• MON_DEFL_RGD_BAKCAL_LAYER—Pavement structure input parameters used in the 

backcalculation of elastic layer moduli and pavement structural material properties. 

• MON_DEFL_RGD_BAKCAL_POINT—Interpreted elastic layer moduli and pavement 

structural material properties from backcalculation and direct computations of FWD 

measurements of rigid pavement structures using version 2.2 of ERESBACK. 

• MON_DEFL_RGD_BAKCAL_SECT—Test section statistics for interpreted elastic layer 

moduli and pavement structural material properties from backcalculation and direct 

computations of FWD measurements for rigid pavement structures for each measurement 

pass. 

LTPP Backcalculation Tables Screened 

All the LTPP tables containing backcalculated moduli were screened using the forwardcalculated 

values. Table 11 gives a list of these tables, as well as the number of records contained and 

screened in each computed parameter table in the LTPP database. 

Table 11. LTPP backcalculation tables and number of records screened. 

Name of Backcalculation Table for 

Screening 

Number of 

Data 

Records 

Number of 

Records 

Screened 

% Records 

Screened 

MON_DEFL_FLX_BAKCAL_POINT 1,645,615 1,088,679 66.2% 

MON_DEFL_FLX_BAKCAL_SECT 44,544 25,564 57.4% 

MON_DEFL_FLX_NMODEL_POINT 181,051 130,805 72.2% 

MON_DEFL_FLX_NMODEL_SECT 3,852 2,754 71.5% 

MON_DEFL_RGD_BAKCAL_POINT 37,246 36,989 99.3% 

MON_DEFL_RGD_BAKCAL_SECT 1,189 1,183 99.5% 

The first four lines of Table 11 are the MODCOMP data records, while the last two lines are the 

two-layer rigid pavement data using the dense liquid and elastic solid methodology. Almost all 

of the unscreened data from Table 11 resulted from the use of a rigid or stiff layer at some depth 

in the flexible section data tables (for both the flexible and some of the rigid section data) created 

by MODCOMP or an assumed layer modulus for any other structural layer when MODCOMP 

was used. These moduli were assumed, or fixed, and were therefore not screened. 

In addition, with data migration and other issues, the records in tables *_BAKCAL_LAYER, 

*_BAKCAL_BASIN, and *_BAKCAL_POINT are no longer directly connectable with one 
33

another. Since data from these tables (plus TST_L05B and others) were used in the screening 

process, a very limited number (for example, <1 percent of the total number of records in the 

rigid backcalculated data tables from the last two lines of Table 11) of records that could not be 

connected were left unscreened. 

Since the completion of the backcalculation project (in 1999), the LTPP program underwent a 

major change in the way the CONSTRUCTION_NO field is assigned. As a result, the 

CONSTRUCTION_NO values in the backcalculation tables do not directly correlate with the 

CONSTRUCTION_NO values in other key LTPP tables such as the EXPERIMENT_SECTION 

and TST_L05B tables. For this study, the forwardcalculation method used the deflection basins 

in the MON_DEFL_FLX_BAKCAL_BASIN table and the 

MON_DEFL_RGD_BAKCAL_BASIN table (which use the former CONSTRUCTION_NO 

assignments) while using the pavement structure data (material type and layer thicknesses) from 

the TST_L05B table (which uses the current CONSTRUCTION_NO assignments). To ensure 

the proper connection of the corresponding records, the following fields were compared to 

ensure the proper assignment of the CONSTRUCTION_NO values: 

EXPERIMENT_SECTION.CN_ASSIGN_DATE, 

MON_DEFL_FLX_BAKCAL_LAYER.CN_REF_DATE, and MON_DEFL_RGD_BAKCAL 

_LAYER.CN_REF_DATE. This process was successful in almost all cases, as indicated above. 

KEY STEPS FOR SCREENING THE LTPP BACKCALCULATION DATA 

The following steps were taken to screen backcalculated moduli: 

1. Obtain the FWD deflection basin data. 

2. Determine the forwardcalculation layer structures. 

3. Conduct forwardcalculation for each basin with layer structure identified. 

4. Compute section level summary statistics of forwardcalculation parameters. 

5. Correspond (connect) the forwardcalculated moduli with the backcalculated moduli. 

6. Screen the backcalculated moduli using the corresponding forwardcalculated moduli. 

Each step is discussed in detail below. 

Step 1. Obtain the FWD Deflection Basins for Forwardcalculation 

The objective of this study was to screen the backcalculated moduli in the LTPP database and 

use the same deflection basins that were used to derive these backcalculated moduli. As a result, 

the deflection basins from the tables MON_DEFL_FLX_BAKCAL_BASIN and 

MON_DEFL_RGD _BAKCAL_BASIN were extracted and subsequently used in the 

forwardcalculation computations. 

Step 2. Determine the Pavement Layer Structures for Forwardcalculation 

As presented in chapter 4, elastic moduli for up to three layers are forwardcalculated for each 

deflection basin. Then the pavement systems were divided or combined into a two- or three-layer 

structure, as follows: 

1. Surface (bound) layer (AC or PCC). 

2. Base layer (unbound or granular). 

3. Subgrade; depth to apparent stiff layer calculated from the deflection basin. 
34

For rigid pavements, the uppermost base layer below the PCC slab was considered the base 

layer. 

For flexible pavements, the layer system is more complex, and more than three layers were used 

in backcalculation for many flexible pavement sections. The researchers applied engineering 

judgment to assign each of the backcalculation layers to correspond to a forwardcalculation 

layer, according to the scheme shown in Table 12. 

Step 3. Conduct Forwardcalculation 

Forwardcalculation is carried out using the method discussed in chapter 3 for each of the two or 

three forwardcalculation layers (i.e., the bound surface course, base if present, and subgrade). 

A small percentage of the FWD load-deflection data has been associated with nonstandard 

sensor positions. These nonstandard positions were adjusted to their actual positions before 

applying the forwardcalculation procedures. 

Table 13 gives an outline of the deflection data where nonstandard sensor positions were 

considered, provided there were any backcalculated data in the database associated with these 

data (seldom the case). 
35

Table 12. Assignment of backcalculated layers for forwardcalculation 

of flexible pavements. 

Layer Structure Information from the TST_L05B or 

Backcalculation Tables 

Layer Description Layer 

Type 

LTPP 

Code Material Type 

Assigned 

Forwardcalculated 

Layer 

Overlay AC 1

Hot mixed, hot laid AC, 

dense graded 

Asphalt concrete 

layer 

Overlay AC 13

Recycled AC, hot laid, 

central plant mix 

Asphalt concrete 

layer 

Overlay AC 16

Recycled AC, heater 

scarification/recompaction 

Asphalt concrete 

layer 

Seal Coat AC 20 Other 

Asphalt concrete 

layer 

Seal Coat AC 71 Chip seal 

Asphalt concrete 

layer 

Seal Coat AC 72 Slurry seal 

Asphalt concrete 

layer 

Seal Coat AC 73 Fog seal 

Asphalt concrete 

layer 

Seal Coat AC 82 Sand seal 

Asphalt concrete 

layer 

AC Layer Below 

Surface (Binder 

Course) AC 1

Hot mixed, hot laid AC, 

dense graded 

Asphalt concrete 

layer 

AC Layer Below 

Surface (Binder 

Course) AC 13

Recycled AC, hot laid, 

central plant mix 

Asphalt concrete 

layer 

Base Layer AC 319 HMAC 

Asphalt concrete 

layer 

Base Layer AC 321 Asphalt treated mixture 

Asphalt concrete 

layer 

Interlayer AC 71 Chip seal 

Asphalt concrete 

layer 

Interlayer AC 75 Nonwoven geotextile 

Asphalt concrete 

layer 

Interlayer AC 77

Stress absorbing membrane 

interlayer 

Asphalt concrete 

layer 

Interlayer AC 78

Dense graded asphalt 

concrete interlayer 

Asphalt concrete 

layer 

Friction Course AC 2

Hot mixed, hot laid AC, 

open graded 

Asphalt concrete 

layer 
Table 12. Assignment of backcalculated layers for forwardcalculation 

of flexible pavements—Continued

36

Friction Course AC 71 Chip seal 

Asphalt concrete 

layer 

Surface Treatment AC 9

Plant mix (emulsified 

asphalt) material, cold laid 

Asphalt concrete 

layer 

Surface Treatment AC 11 Single surface treatment 

Asphalt concrete 

layer 

Surface Treatment AC 71 Chip seal 

Asphalt concrete 

layer 

Surface Treatment AC 82 Sand seal 

Asphalt concrete 

layer 

Interlayer EF 74 Woven geotextile Subgrade 

Interlayer EF 75 Nonwoven geotextile Subgrade 

Base Layer GB 302 Gravel (uncrushed) Granular base layer 

Base Layer GB 303 Crushed stone Granular base layer 

Base Layer GB 304 Crushed gravel Granular base layer 

Base Layer GB 306 Sand Granular base layer 

Base Layer GB 309 Fine-grained soils Granular base layer 

Base Layer GB 310 Other (specify if possible) Granular base layer 

Base Layer GB 337 Limerock, caliche Granular base layer 

Base Layer GB 307

Soil-aggregate mixture 

(predominantly finegrained) Subgrade 

Base Layer GB 308

Soil-aggregate mixture 

(predominantly coarsegrained) Subgrade 

Subbase Layer GB 308

Soil-aggregate mixture 

(predominantly coarsegrained) Subgrade 

Subbase Layer GS 302 Gravel (uncrushed) Granular base layer 

Subbase Layer GS 303 Crushed stone Granular base layer 

Subbase Layer GS 304 Crushed gravel Granular base layer 

Base Layer GS 308

Soil-aggregate mixture 

(predominantly coarsegrained) Subgrade 

Subbase Layer GS 306 Sand Subgrade 

Subbase Layer GS 307

Soil-aggregate mixture 

(predominantly finegrained) Subgrade 

Subbase Layer GS 308

Soil-aggregate mixture 

(predominantly coarsegrained) Subgrade 

Subbase Layer GS 309 Fine-grained soils Subgrade 

Subbase Layer GS 310 Other (specify if possible) Subgrade 

Subbase Layer GS 338 Lime-treated soil Subgrade 
Table 12. Assignment of backcalculated layers for forwardcalculation 

of flexible pavements—Continued

37

Embankment Layer GS 102

Fine-grained soils: lean 

inorganic clay Subgrade 

Embankment Layer GS 131 Fine-grained soils: silty clay Subgrade 

Base Layer TB 319 HMAC 

Asphalt concrete 

layer 

Base Layer TB 320 Sand asphalt 

Asphalt concrete 

layer 

Base Layer TB 321 Asphalt treated mixture 

Asphalt concrete 

layer 

Base Layer TB 324

Dense graded, cold laid, 

mixed in place 

Asphalt concrete 

layer 

Base Layer TB 328

Recycled asphalt concrete, 

plant mix, hot laid 

Asphalt concrete 

layer 

Base Layer TB 334 Lean concrete 

Asphalt concrete 

layer 

Base Layer TB 325

Open graded, hot laid, 

central plant mix Granular base layer 

Base Layer TB 327

Open graded, cold laid, 

mixed in place Granular base layer 

Base Layer TB 331 Cement aggregate mixture Granular base layer 

Base Layer TB 350 Other Granular base layer 

Base Layer TB 333 Cement-treated soil Subgrade 

Base Layer TB 339 Soil cement Subgrade 

Base Layer TB 340

Pozzolanic-aggregate 

mixture Subgrade 

AC Layer Below 

Surface (Binder 

Course) TS 1

Hot mixed, hot laid AC, 

dense graded 

Asphalt concrete 

layer 

Subbase Layer TS 320 Sand asphalt 

Asphalt concrete 

layer 

Subbase Layer TS 325

Open graded, hot laid, 

central plant mix Granular base layer 

Subbase Layer TS 331 Cement aggregate mixture Granular base layer 

Subbase Layer TS 338 Lime-treated soil Subgrade 

Subbase Layer TS 339 Soil cement Subgrade 
38

Table 13. FWD- and time-specific sensor positioning anomalies in the LTPP database. 

Region & 

FWD S/N

Dates Affected 

(inclusive) 

Actual Sensor Positions 

(inches) 

Approx. 

# of Test 

Dates 

Reg. 1–s/n129 3 Nov ’95→14 Apr ’96 0, 8, 12, 18, 24, 36 & 48 21 

Reg. 1–s/n129 15 Apr ’97→21 May ’97 0, 8, 12, 18, 24, 36 & 48 12 

Reg. 2–s/n061* 4 Aug ’89→10 Aug ’89 0, 8, 12, 24, 30.5, 48 & 72 4 

Reg. 2–s/n130 25 Aug ’94→7 Sep ’94 0, 8, 12, 18, 36, 48 & 60 16 

Reg. 3–s/n075 17 Jan ’90→22 Jan ’90 0, 8, 12, 18, 30, 42 & 66 4 

Reg. 3–s/n132 29 Jul ’96→25 Oct ’96 0, 8, 12, 18, 24, 36 & 48 29 

Reg. 4–s/n061* <26 Feb ’89→8 Sep ’89 0, 8, 12, 24, 30.5, 48 & 72 97 

Reg. 4–s/n061 17 Jul ’95→31 Oct ’95 0, 8, 12, 18, 24, 36 & 48 65 

Reg. 4–s/n131 <24 May ’ 94→30 Apr ’96 0, 8, 12, 18, 24, 36 & 48 191 

Reg.4–s/n13110 16 Dec ’97→20 Jan ’98 0, 8, 18, 24, 36, 48 & 60 ≥ 8 

 * Same FWD and overlapping dates—LTPP field tests conducted in two different LTPP Regions. 

Step 4. Compute Section Level Summary Statistics of Forwardcalculated Parameters 

For the section level data, to identify and remove outliers for a given section (and test date), the 

researchers used the so-called interquartile range (IQR) as outlined below. 

Pavement engineers typically use two standard deviations as criteria for identifying outliers. The 

shortcoming of this approach is that neither the population mean nor the population standard 

deviation is available when evaluating the data for outliers. Instead, the sample mean and sample 

standard deviation are generally used, without consideration of the actual distribution. This 

technique introduces a bias in identifying the outliers when using the two standard deviation 

approach because outliers are (incorrectly) included in the computation of the sample mean and 

the sample standard deviation. In addition, the section standard deviation on an arithmetic basis 

is often large enough to compute negative values on the low end of the section level modulus 

range. This calculation results in elimination of few (if any) of the unreasonably low values and 

only eliminates the unreasonably high values. The nonnormal and asymmetric distribution of the 

modulus data usually causes this problem. In fact, the distribution of moduli generally is closer 

to a log-normal distribution than an arithmetic normal distribution. 

To overcome these difficulties, the IQR method has been used to identify and remove outliers in 

the computed point-by-point moduli for each section (and date of test).(11) The following 

provides specifics of this method: 
39

IQR = Q3 - Q1

Figure 22. Equation. Interquartile range. 

 where: Q1 = 25th quartile of the logs of the moduli 

 and Q3 = 75th quartile of the logs of the moduli 

Outliers are defined as values that are outside the range: (Q1 - 1.5 * IQR, Q3 + 1.5 * IQR). 

Data points that were outside of the above range were identified as outliers and not used to 

calculate the section means from forwardcalculation. 

Step 5. Correspond the Forwardcalculated Moduli with the Backcalculated Moduli 

After all forwardcalculation is completed, the forwardcalculated moduli were paired with the 

backcalculated moduli using their section IDs, according to table 12. 

Step 6. Screen the Backcalculated Moduli Using the Corresponding Forwardcalculated 

Moduli 

The LTPP database of backcalculated moduli was screened. This screening took place using the 

following sequential steps: 

1. The modulus values in the backcalculation tables that were assumed or held constant were 

not screened—Since these values are presumably a good educated guess at the actual in situ 

stiffness, they were not screened and accordingly were left as is in the database with an 

appropriate flag. 

2. Reasonableness screening—Various pavement materials are commonly associated with 

typical or reasonable moduli, depending on the material type and other factors. Assuming the 

backcalculated value was not fixed, a wide range of feasible modulus values was assigned to 

the various material types, and any value outside of these rather liberal ranges could then be 

called into question, whether the method of determining the modulus is back- or 

forwardcalculation. Table 14 lists these values. During screening of the database, also 

including the newly created forwardcalculated values, these limits were applied before

applying the remaining criteria. In other words, if a given modulus calculation was outside of 

the broad ranges indicated in Table 14, then it was either flagged in the case of the existing 

tables or noted in the case of forwardcalculated values, and then not used in further screening 

routines. 

3. Correspondence screening using forwardcalculated values – Provided the data did not 

become flagged during Steps 1 or 2 of the screening process, each backcalculated value was 

then compared to the corresponding forwardcalculated value. If the backcalculated modulus 

was within a factor of 1.5 of the forwardcalculated value, then it was assumed to be 

“acceptable” and not recommended for flagging (except through the use of a “0,” see Table 

15) in the database. If it was outside of this reasonable range (1.5 times the forwardcalculated 

value or the forwardcalculated value divided by 1.5), then the flags shown in 
40

Table 15 were used to indicate that the existing value in the database was “suspect.” These 

flagging codes were used for both the “point” data tables and the “section” data tables. 

Table 14. Reasonable ranges for various pavement layers in the LTPP database. 

 Reasonable Range 

 MPa psi LTPP 

Code 

min max min Max 

Base Materials

Asphalt-Treated Mixture, not Permeable 

Asphalt-Treated Base (PATB) 321 700 25,000 101,500 3,625,000

Gravel, Uncrushed 302 50 750 7,250 108,750

Crushed Stone 303 100 1,500 14,500 217,500

Crushed Gravel 304 75 1,000 10,875 145,000

Sand 306 40 500 5,800 72,500

Soil-Aggregate Mixture 

(predominantly fine-grained) 307 50 700 7,250 101,500

Soil-Aggregate Mixture 

(predominantly coarse-grained) 308 60 800 8,700 116,000

Fine Grained Soil or Base 309 35 450 5,100 65,000

Hot-Mixed AC 319 700 25,000 101,500 3,625,000

Sand Asphalt 320 700 25,000 101,500 3,625,000

Dense-Graded, Cold-Laid, Central Plant 

Mix AC 323 700 25,000 101,500 3,625,000

Open-Graded, Hot Laid, Central Plant Mix AC 325 350 3,500 50,750 507,500

Cement Aggregate Mixture 331 2,000 20,000 290,000 2,900,000

Econocrete 332 3,500 35,000 507,500 5,075,000

Lean Concrete 334 4,500 45,000 652,500 6,525,000

Soil Cement 339 1,000 7,000 145,000 1,015,000

Open-Graded, Cold Laid, In-Place Mix AC 327 200 3,000 29,000 435,000

Limerock; Caliche 337 150 1,500 21,750 217,500

Other—Treated Base (TB) 350 400 8,000 58,000 1,160,000

Bound Surface Courses 

Concrete Surface (uncracked) 10,000 70,000 1,450,000 10,150,000

AC Surface (>0 OC–<45 OC, not alligatored) 700 25,000 101,500 3,625,000

Unbound Subgrades 

Any unbound type 15 650 2,175 94,250
41

Table 15. Flagging codes used to screen the backcalculated LTPP database. 

Description of the 

correspondence between the 

forwardcalculated and the 

backcalculated modulus values 

Correspondence 

code values 

(flags) 

Ratio between the 

forwardcalculated and 

backcalculated modulus values 

Acceptable 0 2/3 ≤ Ratio ≤ 1.5 

Marginal 1 1/2 ≤ Ratio ≤ 2 (& not code 0) 

Questionable 2 1/3 ≤ Ratio ≤ 3 (& not codes 0 or 1) 

Unacceptable 3 Ratio < 1/3 or Ratio > 3 

Incorporation of the Screening Results into the LTPP Database 

All applicable flags associated with the backcalculated moduli in the LTPP computed parameter 

database will be submitted to FHWA, including all records where the backcalculated values were 

assumed (fixed) or not reasonable. All remaining data will be submitted with an appropriate 

correspondence flag (i.e., 0, 1, 2, or 3—see Table 15) to be incorporated into the existing 

backcalculation data tables, as outlined above. 

In addition, tables of all forwardcalculated moduli, both at the point and section levels, will be 

given to FHWA as candidates for incorporation into the LTPP database as computed parameters. 

These data will also include the “reasonableness flag” where applicable. 

43

CHAPTER 6. LTPP BACKCALCULATION DATABASE SCREENING RESULTS 

This chapter gives a summary and discussion of the screening results of the LTPP 

backcalculation database. Backcalculation data at all LTPP record levels (A to E) were screened. 

Level E data versus other levels’ (A to D) backcalculation data are compared first. Screening 

results of the flexible pavement systems are then provided, followed by the screening results of 

the rigid pavement systems using various backcalculation procedures or models. Finally, 

screening results of the section average values are presented. 

LEVEL E AND OTHER LEVELS OF DATA QUALITY 

In the past, LTPP generally released only those data that had passed to level E in the database. In 

the case of FWD data, the status of level E was principally assigned when the LTPP data tables 

were complete in other regards, the quality or correctness of the FWD data notwithstanding. 

Figure 23 is an example of a level E data analysis for the subgrade layer(s) using a linear-elastic 

model from MODCOMP compared to the forwardcalculation approach using the Hogg model as 

delineated in the previous sections. Figure 24, meanwhile, is the same set of subgrade charts, but 

for all levels of subgrade data in the flexible pavement system database. 

For all pie chart figures in this chapter, the slices are shown in clockwise order, starting with the 

“not assumed”/“acceptable”/“reasonable” slice, which always faces right. 

145518; 

39%

91965; 

25%

88007; 

24%

42407; 

12%

Acceptable

Marginal

Questionable

Unacceptable

367897; 

86%

417; 0%

259; 0%

59870; 

14%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

13938; 

3%

428026; 

97%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 23. Charts. Screening results of the elastic moduli of the subgrade for all flexible 

sections in the MON_DEFL_FLX_BAKCALC_POINT table based on 

the linear elastic model (the level E records only). 
44

115197; 

25%

110941; 

24%

57807; 

13%

175162; 

38%

Acceptable

Marginal

Questionable

Unacceptable

459107; 

83%

946; 0%

96242; 

17%

1233; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

22494; 

4% 557528; 

96%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 24. Charts. Screening results of elastic moduli of the subgrade for all the flexible 

sections in the MON_DEFL_FLX_BAKCALC_POINT table based on the 

linear elastic model (contains both level E and nonlevel E records). 

Comparing the pie charts in Figure 23 and Figure 24 shows no appreciable difference in the 

results. The level E data consist of about 442,000 records, of which 3 percent were assumed, or 

fixed. Of the remaining 97 percent, 86 percent of these were reasonable, meaning they were 

within the broad limits shown in Table 14 for subgrade materials (15–650 MPa (2,000–95,000 

psi). By contrast, the entire data set consisted of some 580,000 records, with 96 percent not 

assumed, and 83 percent of these were reasonable—not much different from the level E data. 

Finally, in the case of the level E data, 39 percent will not be assigned any outlier flag, or a flag 

of “0.” For the entire data set, the corresponding percentage for a flag of “0” is 38 percent. (A 

flag of “0” means that the backcalculated modulus is within a factor of 1.5 times or divided by 

the forwardcalculated subgrade modulus value.) 

In almost all other instances, the differences between level E data and all the data were 

negligible. Therefore, in the following sections, results of screening the entire database will be 

reported without breaking out the level E data as a separate subcategory of these data. 

SCREENING OF THE FLEXIBLE PAVEMENT BACKCALCULATION 

PARAMETERS—LINEAR ELASTIC MODEL 

This section deals with the portion of the database that comprises asphalt (flexible) pavements 

where the MODCOMP backcalculation program was used to populate the current LTPP 

computed parameter data table, using a linear elastic model.(2)

The entire set of backcalculated asphalt surface course moduli consists of more than 200,000 

records. Only 1 percent used an assumed value for backcalculation purposes (see Figure 25, left 

pie chart). 
45

25543; 

14%

14930; 

8%

11803; 

7%

127164; 

71%

Acceptable

Marginal

Questionable

Unacceptable

179440; 

88%

8558; 4%

12981; 6%

4479; 2%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

205458 ; 

99%

1352 ; 

1%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 25. Charts. Screening results of elastic moduli of the asphalt concrete layer for the 

flexible sections in the MON_DEFL_FLX_BAKCALC_POINT table based 

on the linear elastic model. 

Of the 99 percent of moduli that were not assumed, both backcalculated and forwardcalculated 

values were reasonable in 88 percent of the remaining records, meaning the estimated moduli 

were within a very broad range for asphalt-bound surface layers of 700–25,000 MPa (100,000–

3,600,000 psi) in these records. The reason for such a broad range is that asphalt concrete 

surfaces are viscoelastic and influenced by seasonal temperatures, which in the case of LTPP 

ranged from well below freezing to over 50 °C (122 °F). Both values were outside of this broad 

range in only 2 percent of all nonassumed records (see Figure 25, middle pie chart). 

Of the above 88 percent, the right-hand pie chart in Figure 25 shows that 71 percent were 

acceptable, again meaning that the forwardcalculated values were within a factor of 1.5 times or 

2/3 of the backcalculated value (see Table 15). In addition, 14 percent of the backcalculated 

values were marginal, 8 percent were questionable, and 7 percent were unacceptable. Table 15 

explains these terms in detail. 

Figure 26 shows the subgrade charts for the flexible pavement, linear elastic set of data. 
46

115197; 

25%

110941; 

24%

57807; 

13%

175162; 

38%

Acceptable

Marginal

Questionable

Unacceptable

459107; 

83%

946; 0%

96242; 

17%

1233; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

22494; 

4% 557528; 

96%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 26. Charts. Screening results of elastic moduli of the subgrade for the flexible 

sections in the MON_DEFL_FLX_BAKCALC_POINT table based 

on the linear elastic model. 

In this case, the number of records is about 2.5 times greater than for the surface course layer, 

because the MODCOMP program generally divides the subgrade into two or more layers. In 

addition, many records have a subgrade modulus listed but not a bound layer modulus, probably 

because of problems in the backcalculation process, which starts with the determination of the 

subgrade modulus based on one of the outermost sensors. 

The Hogg model handles the subgrade as a single effective layer, under the load and to a finite 

depth (to hard bottom or the appearance of a hard bottom). 

Because the Hogg forwardcalculation model, on average, calculates a subgrade modulus around 

half that of the linear elastic backcalculation model, the percentage of acceptable moduli is much 

lower than that associated with the asphalt surface course (38 percent versus 71 percent). This 

phenomenon is mainly because the backcalculation model uses the outer sensor deflections to 

calculate the subgrade response characteristics, while the Hogg model uses the center deflection 

and the shape of the entire deflection basin to arrive at an effective subgrade modulus under the 

load. For pavement performance and design applications, the Hogg model is the more 

conservative and realistic. This difference is one reason why the older AASHTO design guides 

recommend dividing the subgrade modulus by three for a more conservative pavement design. 
47

Figure 27 shows plots of the intermediate or unbound base course moduli (linear model). 

38373; 

32%

29659; 

25%

29678; 

25%

22037; 

18%

Acceptable

Marginal

Questionable

Unacceptable

119747; 

66%

6011; 3%

47109; 

26%

8189; 5%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

6255; 

3%

181056; 

97%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 27. Charts. Screening results of elastic moduli of the base layer for the flexible 

sections in the MON_DEFL_FLX_BAKCALC_POINT table based 

on the linear elastic model. 

The middle chart in Figure 27 indicates that only about 70 percent of the backcalculated base 

course moduli were within the rather broad limits set forth in Table 14. Furthermore, of the 66 

percent of records where both values were reasonable, only 32 percent of the records involved 

were acceptable by Table 15 definitions. Also, 18 percent of the backcalculated intermediate 

layer data were unacceptable (i.e., different by more than a factor of 3). Clearly, the base course 

is the most difficult to backcalculate with any consistency. 

SCREENING OF THE FLEXIBLE PAVEMENT BACKCALCULATION 

PARAMETERS—NONLINEAR ELASTIC MODEL 

This section deals with the portion of the database that comprises asphalt (flexible) pavements 

and where the MODCOMP backcalculation program was used to populate the current LTPPcomputed parameter data table using a nonlinear elastic model. 

While the linear elastic dataset of backcalculated asphalt surface course moduli consists of some 

200,000 records, the nonlinear elastic dataset only contains 37,000 records, covering essentially 

the same data for the same structural layer. Evidently, the nonlinear feature of the MODCOMP 

program was only used when beneficial to do so (see Figure 25 and Figure 28, left pie charts). 
48

18429; 

57%

5955; 

18%

4085; 

13%

3787; 

12%

Acceptable

Marginal

Questionable

Unacceptable

32256; 

86%

1252; 3%

3254; 9%

789; 2%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

86; 0%

37551; 

100%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 28. Charts. Screening results of elastic moduli of the asphalt concrete layer for the 

flexible sections in the MON_DEFL_FLX_ NMODEL_POINT table based 

on the nonlinear elastic model. 

There was not a great deal of difference between the linear elastic and nonlinear elastic model 

results. If anything, the correspondence between forwardcalculation and backcalculation is 

slightly poorer with the nonlinear model. For example, 57 percent of the AC modulus values 

were acceptable (see right pie chart in Figure 28), whereas 71 percent were acceptable using the 

linear elastic model (see Figure 25). 

These counterintuitive results are not necessarily because the materials were truly linear elastic, 

but rather because the use of any backcalculation program is highly user-dependent, requiring 

engineering skill and knowledge to model the pavement to get reasonable results. Such results 

were not possible with the LTPP data because it was processed in batch mode, so attention to 

each individual test point (record) was not feasible. 
49

Figure 29 shows plots of the intermediate (unbound) base course moduli using the nonlinear 

model. 

4970; 

37%

3128; 

24%

3025; 

23%

2142; 

16%

Acceptable

Marginal

Questionable

Unacceptable

13265; 

67%

526; 3%

5540; 

28%

308; 2%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

232; 

1%

19639; 

99%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 29. Charts. Screening results of elastic moduli of the base layer for the flexible 

sections in the MON_DEFL_FLX_ NMODEL_POINT table based 

on the nonlinear elastic model. 

The three plots in Figure 29 once again don’t show a great deal of difference in their comparison 

to forwardcalculated values, between the base moduli derived though linear (Figure 27) and 

nonlinear (Figure 29) backcalculation. In spite of an attempt to improve the large variability 

associated with backcalculated base course moduli, the batch mode of nonlinear backcalculation 

did not help a great deal. 
50

Figure 30 shows the subgrade charts for the nonlinear elastic flexible pavement set of data. 

23329; 

38%

15543; 

25%

14097; 

23%

8430; 

14%

Acceptable

Marginal

Questionable

Unacceptable

61399; 

87%

7; 0%

9293; 

13%

43; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

2427; 

3% 70742; 

97%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 30. Charts. Screening results of elastic moduli of the subgrade for the flexible 

sections in the MON_DEFL_FLX_ NMODEL_POINT table based 

on the nonlinear elastic model. 

In the case of the subgrade, for all practical purposes, no difference exists between the linear and 

nonlinear elastic analysis methods (see Figure 26 and Figure 30). Evidently, in spite of using the 

nonlinear model on about 15 percent of available FWD load-deflection records, backcalculation 

still results in subgrade moduli that are much higher than the Hogg model calculations (or 

ELMOD, for example), because of the differences in how nonlinearity is handled by the three 

methods. 

It is possible to use the MODCOMP program and model the nonlinearity of the subgrade (or the 

upper portion of the subgrade) in another manner, which can result in lower subgrade moduli in 

many cases. Once again, however, this technique was not possible because of the need for 

careful attention on a case-by-case basis to material properties, nonlinear models, and material 

coefficients in the various LTPP test sections. 

ADAPTATION OF FORWARDCALCULATION TECHNIQUE FOR LTPP RIGID 

PAVEMENT SECTIONS 

This section deals with the criteria used to adapt the forwardcalculation routines to the 

backcalculation database. 
51

Since forwardcalculation is designed to calculate only two modulus values directly (the bound 

surface course and the subgrade), it is necessary to use relationships between one of these layers 

and the base course, whether bound or unbound. Additionally, since one of the methods used to 

generate the backcalculated tables in the LTPP database involved a choice between a 100 percent 

bonded and a 100 percent unbonded condition between the PCC slab and the base course, it was 

also necessary to develop a method for forwardcalculation that would consider these two 

different input assumptions. 

As discussed previously, only the PCC surface course and the subgrade moduli are 

forwardcalculated, essentially ignoring the effect of the base layer. Therefore, the computed EPCC

actually reflects the effect of both the upper PCC layer and the underlying base layer. In other 

words, EPCC is an apparent modulus of these two upper layers, and needs to be divided into two 

parts, especially when a bound base layer is involved: the actual modulus of the PCC layer and 

the calculated modulus of the base. In these cases, EPCC is called Epcc,app., which is the apparent 

modulus of the PCC layer alone as influenced by the base. 

The method used to divide the calculated Epcc,app.-value is adopted from Khazanovich, et al.(1)

The upper PCC surface layer and the base layer may be bonded or unbonded and are assumed to 

act as plates. Thus, no through-the-thickness compression is assumed. The details of this method 

are given below for an unbonded and bonded condition between the PCC slab and the base, 

respectively. 

For the unbonded case, the PCC slab modulus is computed from the equation in Figure 31. 

Epcc app h h

h E 3 ,

2

3

1

3

1

1

+ β =

Figure 31. Equation. PCC slab modulus—100 percent unbonded case. 

For the bonded case, the PCC slab modulus is computed from the equation in Figure 32. 

E h

h h hx h hh x h

1 Ee 1

3

1

3

2

3

1

1

2

2 1

2

2

12

2

12

2

=

++ − ⎛

⎝

⎜ ⎞

⎠

⎟ + −+ ⎛

⎝

⎜ ⎞

⎠ β β ⎟

Figure 32. Equation. PCC slab modulus—100 percent bonded case. 

 where: 

x

h h h h

h h =

+ + ⎛

⎝

⎜ ⎞

⎠

⎟

+

1

2

2 1

2

1 2

2 2 β

β

Figure 33. Equation. Layer thickness relationship—both cases. 

 and: 

β = E

E

2

1

Figure 34. Equation. Modular ratio β—both cases. 
52

 and: 

Epcc,app. = Apparent modulus of the PCC layer, assuming no base course effect 

E1 = Modulus of upper plate, i.e., the PCC layer 

E2 = Modulus of lower plate, i.e., the base layer 

h1 = Thickness of upper plate, i.e., the PCC slab 

h2 = Thickness of lower plate, i.e., the base layer 

The procedures presented above require the modular ratio as an input parameter. Engineering 

judgment should determine this ratio. It is assumed that if the ratio is assigned within reasonable 

limits, the PCC modulus results (= E1) are insensitive to the ratio. Table 16 presents the 

recommended modular ratios (β) of the calculated PCC and base moduli for each type of base 

layer. It should be noted that β from Figure 34 is defined as a ratio of base to PCC moduli. This 

equation creates stability for the case of a weak base (i.e., when β approaches 0). Therefore, the 

ratios from Table 16 should be inverted before using them in the procedure described above. 

Given the values for β and for the actual plate thicknesses, h1 and h2, the equations in Figure 31 

and Figure 32 may be used with the forwardcalculated Epcc,app.-value to yield E1 and E2 for the 

two upper layers. 

Identify Interface Condition Between the PCC Slab and the Base Layer(s) 

For the point-by-point forwardcalculated moduli, modulus values were calculated for both the 

unbonded and the bonded cases. These values can be used to screen the corresponding unbonded 

and bonded values in the backcalculation tables. 

For the section mean modulus, the bond condition between the PCC slab and the base is given in 

the backcalculation table as a bond index, as estimated by Khazanovich, et al.(1) The same bond 

index was adopted for the forwardcalculation moduli to select either the unbonded or the bonded 

values for the section database. 
53

Table 16. Back- and forwardcalculated modulus ratios for EPCC /EBase. 

LTPP 

Code Base Type 

Ratio 

β*=1/β

1 Hot-mixed, hot-laid AC, dense graded 10 

2 Hot-mixed, hot-laid AC, open graded 15 

3 Sand asphalt 50 

4 Jointed plain concrete pavement (JPCP) 1 

5 Jointed reinforced concrete pavement (JRCP) 1 

6 Continuously reinforced concrete pavement (CRCP) 1 

7 PCC (prestressed) 1 

8 PCC (fiber reinforced) 1 

9 Plant mix (emulsified asphalt) material, cold laid 20 

10 Plant mix (cutback asphalt) material, cold laid 20 

13 Recycled AC, hot laid, central plant mix 10 

14 Recycled AC, cold laid, central plant mix 15 

15 Recycled AC, cold laid, mixed in place 15 

16 Recycled AC, heater scarification/recompaction 15 

17 Recycled JPCP 100 

18 Recycled JRCP 100 

19 Recycled CRCP 100 

181 Fine-grained soils: lime-treated soil 100 

182 Fine-grained soils: cement-treated soil 50 

183 Bituminous-treated subgrade soil 100 

292 Crushed rock 150 

302 Gravel, uncrushed 200 

303 Crushed stone 150 

304 Crushed gravel 175 

305 Crushed slag 175 

306 Sand 250 

307 Soil-aggregate mixture (predominantly fine grained) 400 
Table 16. Back- and forwardcalculated modulus ratios for EPCC /EBase—Continued

54

308 Soil-aggregate mixture (predominantly coarse grained) 250 

319 Hot-mixed AC 15 

320 Sand asphalt 50 

321 Asphalt-treated mixture 50 

322 Dense-graded, hot-laid, central plant mix AC 10 

323 Dense-graded, cold-laid, central plant mix AC 15 

324 Dense-graded, cold-laid, mixed-in-place AC 15 

325 Open-graded, hot-laid, central plant mix AC 15 

326 Open-graded, cold-laid, central plant mix AC 15 

327 Open-graded, cold-laid, mixed-in-place AC 15 

328 Recycled AC, plant mix, hot laid 10 

329 Recycled AC, plant mix, cold laid 15 

330 Recycled AC, mixed in place 15 

331 Cement aggregate mixture 5 

332 Econocrete 4 

333 Cement-treated soil 50 

334 Lean concrete 2 

335 Recycled PCC 100 

338 Lime-treated soil 100 

339 Soil cement 10 

340 Pozzolanic-aggregate mixture 100 

341 Cracked and seated PCC layer 25 

351 Treatment: lime, all classes of quick lime and hydrated lime 100 

352 Treatment: lime fly ash 150 

353 Treatment: lime and cement fly ash 150 

354 Treated: PCC 50 

355 Treatment: bitumen (includes all classes of bitumen and asphalt 

treatments) 

100 

700 AC 15 

730 PCC 1 
55

SCREENING OF THE RIGID PAVEMENT BACKCALCULATION PARAMETERS—

LINEAR ELASTIC MODEL 

The same linear elastic backcalculation program (MODCOMP) used to populate the 

backcalculated flexible pavement system data was also used to backcalculate interior slab 

layered elastic moduli. 

Since the forwardcalculation routines developed to screen the LTPP backcalculated database 

were designed to operate in two modes—one with and one without bond between the PCC and 

base layers—the summary charts shown in this section are divided into two parts. One of these 

compares the forwardcalculated values assuming 100 percent bond between layers and the other, 

assuming 100 percent slip between the concrete surface layer and the base. 

Figure 35 summarizes the screening results for forwardcalculated PCC moduli based on 100 

percent bond between the concrete slab and the base, while Figure 36 is based on 

forwardcalculated values based on 100 percent slip between the two upper layers. 

6155; 

61%

2044; 

21%

1379; 

14%

377; 4%

Acceptable

Marginal

Questionable

Unacceptable

9955; 

86%

442; 4%

848; 7%

310; 3%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

45; 0% 11555; 

100%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 35. Charts. Screening results of elastic moduli of the interior concrete slab for 

the rigid sections in the MON_DEFL_FLX_BAKCALC_POINT table based on 

the linear elastic model for backcalculation and a bonded condition 

between the slab and base for forwardcalculation. 
56

8339; 

83% 1536; 

15%

176; 2%

21; 0%

Acceptable

Marginal

Questionable

Unacceptable

10072; 

325; 3% 87%

617; 5%

541; 5%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

11555; 

100%

45; 0%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 36. Charts. Screening results of elastic moduli of the interior concrete slab for 

the rigid sections in the MON_DEFL_FLX_BAKCALC_POINT table based on 

the linear elastic model for backcalculation and an unbonded condition 

between the slab and base for forwardcalculation. 

Similarly, Figure 37 depicts the screening results for forwardcalculated base course moduli based 

on 100 percent bond between the concrete surface and the base, while Figure 38 reflects the 

forwardcalculated moduli based on 100 percent slip between the two upper layers. 
57

747; 

35%

398; 

18%

461; 

21%

565; 

26%

Acceptable

Marginal

Questionable

Unacceptable

2171; 32%

861; 13%

547; 38%

1183; 17%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

6762; 

7933; 46%

54%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 37. Charts. Screening results of elastic moduli of the base layer for the rigid sections 

in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model 

for backcalculation and a bonded condition between the concrete slab 

and base layer for forwardcalculation. 

661; 

31%

392; 

18%

525; 

25%

555; 

26%

Acceptable

Marginal

Questionable

Unacceptable

2133; 

32%

899; 13%

2587; 

38%

1143; 

17%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

6762; 

46%

7933; 

54%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 38. Charts. Screening results of elastic moduli of the base layer for the rigid sections 

in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model 

for backcalculation and an unbonded condition between the concrete slab 

and base layer for forwardcalculation. 
58

The four preceding figures do not show a great deal of difference in the charts comparing the 

forwardcalculated values with slip between the concrete and the base and the cases with no slip 

to backcalculated moduli. These values are not because there isn’t any difference in the two; 

rather, the acceptance and flagging criteria for the backcalculated tables is rather broad, as for 

example having to be more than a factor of 1.5 different before any flag (1, 2, or 3) is applied. 

In the case of the backcalculated PCC modulus, the 100 percent slip criterion used in 

forwardcalculation resulted in a somewhat better comparison: 83 percent versus 61 percent of the 

remaining values (see right pie charts in Figure 36 and Figure 35, respectively). Conversely, in 

the case of the base course moduli, the use of the 100 percent bonded criterion results in a 

slightly better comparison: 35 percent versus 31 percent—see Figure 37 and Figure 38, 

respectively. 

Figure 39 shows the comparison of the screening results for forwardcalculated subgrade moduli 

based on the Hogg model versus backcalculated subgrade moduli using MODCOMP. Since the 

Hogg model uses a direct (closed form) solution that is not dependent on the moduli of the 

overlying layers, no difference occurs whether there is 100 percent slip or 100 percent bond 

between the surface and the base course. 

4440; 50%

1184; 13%

1172; 13%

2174; 24%

Acceptable

Marginal

Questionable

Unacceptable

8970; 88%

0; 0%

1249; 12%

1; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

1380; 

12%

10220; 

88%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 39. Charts. Screening results of elastic moduli of the subgrade for the rigid sections 

in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model. 

There is some improvement in the backcalculated table of subgrade moduli for rigid sections 

compared to the table for flexible sections. For the rigid sections, 50 percent of the sections were 

within a factor of 1.5 of the forwardcalculated subgrade moduli, while in the flexible case only 

31 percent of the values were within the same factor of 1.5. 
59

SCREENING OF THE RIGID PAVEMENT BACKCALCULATION PARAMETERS—

SLAB-ON-ELASTIC-SOLID ANALYSIS 

Another method used to populate the table of backcalculated moduli in the LTPP database was 

the theory of a concrete slab on an elastic solid foundation. The method used was developed 

specifically for the LTPP FWD database and the rigid pavements within that database.(1) Using 

this approach, two different backcalculation methods can be employed: bonded and unbonded 

condition between the concrete slab and the base. 

Figure 40 and Figure 41 show the screening results for this portion of the database, for the 

concrete layer with a bonded and unbound condition between the slab and the base. Figure 42 

and Figure 43 show the corresponding base course charts for the elastic solid model set of data. 

32761; 

97%

936; 3%

80; 0%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

33777; 

98%

855; 2%

14; 0%

106; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 40. Charts. Screening results of elastic moduli of the PCC slab for the rigid sections 

in the MON_DEFL_RGD_BAKCALC_POINT table using the elastic solid model 

for backcalculation and assuming bonded condition between the slab 

and the base for back- and forwardcalculation. 
60

32278; 

99%

210; 1%

23; 0%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

975; 3%

137; 0%

433; 1%

32511; 

96%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 41. Charts. Screening results of elastic moduli of the PCC slab for the rigid sections 

in the MON_DEFL_RGD_BAKCALC_POINT table using the elastic solid model 

for backcalculation and assuming unbonded condition between the slab 

and the base for back- and forwardcalculation. 

29544; 

96% 737; 2%

100; 0%

574; 2%

Acceptable

Marginal

Questionable

Unacceptable

129; 0%

1991; 6%

777; 2%

30955; 

92%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 42. Charts. Screening results of elastic moduli of the base layer for the rigid sections 

in the MON_DEFL_RGD_BAKCALC_POINT table using the elastic solid model 

for backcalculation and assuming bonded condition between the slab 

and the base for back- and forwardcalculation. 
61

29677; 

95%

356; 1%

332; 1%

834; 3%

Acceptable

Marginal

Questionable

Unacceptable

31199; 

1019; 3% 94%

736; 2%

202; 1%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 43. Charts. Screening results of elastic moduli of the base layer for the rigid sections 

in the MON_DEFL_RGD_BAKCALC_POINT table using the elastic solid model 

for backcalculation and assuming unbonded condition between the slab 

and the base for back- and forwardcalculation. 

As Figure 40 and Figure 41 show, the correspondence between the reasonable range 

forwardcalculated and backcalculated concrete modulus is excellent, both for the bonded and 

unbonded cases (97 and 99 percent, respectively). This correlation is mainly because the 

backcalculation method used, which was essentially a two-layer system with fixed ratios 

between the concrete surface and base courses, was also used in forwardcalculation of rigid 

pavement systems. In the forwardcalculation procedure, the same ratios, as a function of the base 

course type, were used to calculate the base course modulus. It is believed that this approach to 

both back- and forwardcalculation is much more tenable—and realistic. 

Accordingly, the base course moduli comparison between back- and forwardcalculation was also 

very good. Of all reasonable values, at least 95 percent were within a factor 67 to 150 percent of 

the forwardcalculated modulus (see Figure 42 and Figure 43). 
62

Figure 44 shows the subgrade modulus charts for the elastic solid backcalculation method. 

35529; 

99%

346; 1%

3; 0%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

35878; 

100%

0; 0%

6; 0%

0; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 44. Charts. Screening results of elastic moduli of the subgrade for 

the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT 

table using the elastic solid model for backcalculation. 

Once again, the correspondence between back- and forwardcalculation of the subgrade was 

excellent (see Figure 44). In fact, the subgrade modulus relationship is the best of all, with close 

to 100 percent of the values in the backcalculated database (i.e., the elastic solid model) being in 

the reasonable range and 99 percent of these being within a factor of 1.5 of the forwardcalculated 

moduli from the Hogg model. 

SCREENING OF THE RIGID PAVEMENT BACKCALCULATION PARAMETERS—

SLAB-ON-DENSE-LIQUID ANALYSIS 

The last approach used for backcalculating the moduli of rigid pavement layers is based on the 

theory of a slab on dense liquid, which also was originally developed by Westergaard. This 

approach is explained in full in the same reference as the slab-on-dense-liquid model.(1) Similar 

to the elastic solid model, two different backcalculation methods were used, a bonded and an 

unbonded condition between the concrete slab and the base layer. 

Figure 45 and Figure 46 show the screening results for this portion of the database, for the 

concrete layer, for a bonded and unbonded condition between the slab and the base. Figure 47 

and Figure 48 show the corresponding base course charts for the dense-liquid model set of data. 

These four figures show that the correspondence between back- and forwardcalculation is also 

excellent for the dense liquid model of backcalculation, compared to forwardcalculation. 

Nevertheless, the percentages that were within of 67 to 150 percent (2/3 to 3/2) of the 
63

forwardcalculated values were lower than for the elastic solid model. Most of these values were 

around 90 percent with no flag identified, for both a bonded and an unbonded condition between 

the concrete slab and the base course. 

The slightly better results associated with the elastic solid model are not surprising, since the 

forwardcalculation formulae for a concrete layer were developed using elastic layer theory, not 

Westergaard’s equations. 

32094; 

92%

1; 0%

2632; 

8%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

34727; 

96%

573; 2%

389; 1%

188; 1%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 45. Charts. Screening results of elastic moduli of the PCC slab for the rigid sections 

in the MON_DEFL_RGD_BAKCALC_POINT table using the dense liquid model 

for backcalculation and assuming bonded condition between the slab and 

the base for back- and forwardcalculation. 
64

27790; 

3465; 89%

11%

1; 0%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

31256; 

96%

168; 1%

965; 3%

101; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 46. Charts. Screening results of elastic moduli of the PCC slab for the rigid sections 

in the MON_DEFL_RGD_BAKCALC_POINT table using the dense liquid model 

for backcalculation and assuming unbonded condition between the slab 

and the base for back- and forwardcalculation. 

29221; 

2358; 7% 90%

464; 1%

669; 2%

Acceptable

Marginal

Questionable

Unacceptable

767; 2%

1135; 3%

348; 1%

32712; 

94%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 47. Charts. Screening results of elastic moduli of the base layer for the rigid sections 

in the MON_DEFL_RGD_BAKCALC_POINT table using the dense-liquid model 

for backcalculation and assuming bonded condition between the slab 

and the base for back- and forwardcalculation. 
65

25245; 85% 3244; 11%

1041; 3%

283; 1%

Acceptable

Marginal

Questionable

Unacceptable

29813; 94%

719; 2%

817; 3%

227; 1%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 48. Charts. Screening results of elastic moduli of the base layer for the rigid sections 

in the MON_DEFL_RGD_BAKCALC_POINT table using the dense-liquid model 

for backcalculation and assuming unbonded condition between the slab 

and the base for back- and forwardcalculation. 

When the dense-liquid model is used, the subgrade is not characterized by a modulus of 

elasticity, but rather by a k-value. Accordingly, the k-value in the case of forwardcalculation was 

derived using the same relationship developed when the dense-liquid and elastic-solid models 

were developed. Since this relationship is empirical and has inconsistent units, the E-value must 

be in MPa while the k-value is in kPa/mm. 

k-value = 0.296 x Esubgrade [R2 = 0.87] 

Figure 49. Equation. Subgrade k-value. 

 and: 

 k-value. = Subgrade modulus of reaction, k-value, kPa/mm 

Esubgrade = Subgrade modulus of elasticity, MPa 

Figure 50 shows the subgrade k-value charts for the dense-liquid backcalculation method. 
66

32830; 

92%

3010; 8%

36; 0%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

35876; 

97%

1111; 3%

0; 0%

0; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 50. Charts. Screening results of the subgrade k-values for the rigid sections 

in the MON_DEFL_RGD_BAKCALC_POINT table using 

the dense-liquid model for backcalculation. 

Again, the correspondence between the two methods of calculating the k-value of the subgrade 

under a concrete slab is very good, although somewhat poorer than with the elastic solid model 

versus forwardcalculation. In this case, 92 percent of all reasonable values were within 67 to 150 

percent of the forwardcalculated k-value. 

SCREENING OF THE SECTION AVERAGE BACKCALCULATED DATABASE 

In addition to the point tables, the LTPP database also consists of section backcalculated data 

tables, designed to represent LTPP pavement section average moduli rather than point-by-point 

moduli as were screened in the preceding subsections. Each LTPP section was typically 152 m 

(500 ft) in length. 

The existing section average data in the LTPP database were derived by first calculating the 

arithmetic average and standard deviation of the moduli for a given layer for each pavement 

section. Next, all data lying outside of two standard deviations were eliminated, and a new 

average was calculated based on the remaining moduli after elimination of outliers. One of the 

problems with this approach is that the data typically are not normally distributed on an 

arithmetic scale, but rather much closer to a log normal distribution. Accordingly, more often 

than not—especially when more than two unknown structural layers were backcalculated—the 

two standard deviation approach did not eliminate the very low modulus values, since two 

standard deviations downwards on an arithmetic scale often resulted in negative moduli. 

Accordingly, many higher-than-reasonable values were (correctly) eliminated while the lowerthan-reasonable values were (incorrectly) retained from the section average. Accordingly, this 

procedure often introduces a bias (on the low side) into the section averages. 
67

To rectify this discrepancy, the forwardcalculated values were treated as follows: The logarithms 

of all point data from a given section and structural layer were tabulated. Next, the IQR was 

calculated on these data, as Moore and McCabe describe in chapter 5.(11) Outliers then were 

identified as those values outside the range of (Q1 - 1.5 * IQR, Q3 + 1.5 * IQR). Finally, the 

average of the remaining (unexcluded) moduli was calculated, which is the section average 

modulus for a given layer. 

Figure 51 and Figure 52 show examples of a section data table from back- and 

forwardcalculation as compared to the equivalent example from the point data table. Figure 51 

represents the results for screening of the base course layer(s) in the point data table from 

MODCOMP (linear elastic model) for the flexible pavement database. (This figure is the same as 

Figure 27.) Figure 52 shows the corresponding section data, screened using the same criteria as 

for the point data according to the above-outlined procedure. There is little percentage difference 

between the two figures, although a small improvement occurs from the point to the section level 

in the backcalculated tables. 

Figure 53 and Figure 54 show another example of the difference between the point and section 

data tables for the subgrade k-value in the rigid section LTPP database, based on the dense-liquid 

model of backcalculation. In this example, a small improvement occurs in the correspondence 

between back- and forwardcalculation from the point level to the section level. This pattern was, 

in general, the case for other layers and backcalculation methods. 

All charts associated with the section database are presented in appendix A. 

38373; 

32%

29659; 

25%

29678; 

25%

22037; 

18%

Acceptable

Marginal

Questionable

Unacceptable

119747; 

66%

6011; 3%

47109; 

26%

8189; 5%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

6255; 

3%

181056; 

97%

Backcalculated Values Not

Assumed 

Backcalculated Values Assumed

Figure 51. Charts. Screening results of elastic moduli of the point base layer for 

the flexible sections in the MON_DEFL_FLX_BAKCALC_POINT 

table based on the linear-elastic model. 
68

840; 

34%

601; 

24%

636; 

25%

428; 

17%

Acceptable

Marginal

Questionable

Unacceptable

2505; 

74%

171; 5%

616; 18%

118; 3%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 52. Charts. Screening results of elastic moduli of the section base layer for 

the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT 

table based on the linear-elastic model. 

32830; 

92%

3010; 8%

36; 0%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

35876; 

97%

1111; 3%

0; 0%

0; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 53. Charts. Screening results of the subgrade point k-value table for 

the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT 

table using the dense-liquid model for backcalculation. 
69

1061; 

96%

48; 4%

1; 0%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

1110; 

98%

0; 0%

18; 2%

0; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 54. Charts. Screening results of the subgrade section k-value table for 

the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT 

table using the dense-liquid model for backcalculation.

71

CHAPTER 7. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS 

SUMMARY 

This report presents the results of a study that uses forwardcalculation techniques to screen the 

backcalculated computed parameter files in the LTPP database. The two different 

forwardcalculation techniques developed appear to produce reasonable results, both for 

screening and for estimates of moduli—one for the subgrade and one for the bound surface 

course layer. In addition, for flexible pavements a relationship developed by Dorman and 

Metcalf was used for estimates of the modulus of the unbound base course(s). For rigid 

pavements, a set of ratios relating the modulus of the concrete layer to the base layer was used, 

very similar to the method in part of the LTPP database covering backcalculation of rigid 

pavement systems. 

The entire set of computed parameter tables of backcalculated pavement layer data was screened 

with appropriate forwardcalculated moduli. These data cover all available AC and PCC sections 

where backcalculation was carried out, including both level E and nonlevel E (Release 16.0—All 

QC Levels, July 2003 Upload). These computations were divided into two parts: a layeredelastic backcalculation approach using the MODCOMP computer program and a backcalculation 

approach developed specifically for rigid pavement systems using slab-on-dense-liquid and slabon-elastic solid theory. 

Some percentage of the backcalculated flexible pavement layered elastic moduli in the LTPP 

database derived from MODCOMP were assumed, or fixed, based on engineering judgment and 

to facilitate the backcalculation process. These values were not screened, but rather left 

unchanged as they exist in the existing tables with an associated “Y” flag. An even larger 

percentage of the backcalculated (and some of the forwardcalculated) data were considered to be 

not within a reasonable range according to the values presented in Table 14. For easy reference, 

this table is reproduced in this section as Table 17. Records containing moduli outside of the 

ranges shown in Table 17 were not further screened. Instead, they were flagged (using an “N” 

data cell, as appropriate) as not reasonable. All remaining records were then screened using the 

corresponding forwardcalculated moduli. Four different correspondence flags associated with 

each screened data record have been designated (see Table 15): 

0 = Acceptable: The backcalculated value is within a factor of 1.5 of the forwardcalculated 

value. 

1 = Marginal: The backcalculated value is within a factor of 2.0 of the forwardcalculated 

value (not 0). 

2 = Questionable: The backcalculated value is within a factor of 3.0 of the forwardcalculated 

value (not 0 or 1). 

3 = Unacceptable: The backcalculated value is greater than 3 times or less than 1⁄3 times the 

forwardcalculated value. 
72

Table 17. Reasonable ranges for various pavement layers 

in the LTPP database (same as Table 14). 

 Reasonable Range 

 MPa psi LTPP 

Code 

min max min Max 

Base Materials

Asphalt-Treated Mixture, not Permeable 

Asphalt-Treated Base (PATB) 321 700 25,000 101,500 3,625,000

Gravel, Uncrushed 302 50 750 7,250 108,750

Crushed Stone 303 100 1,500 14,500 217,500

Crushed Gravel 304 75 1,000 10,875 145,000

Sand 306 40 500 5,800 72,500

Soil-Aggregate Mixture 

(predominantly fine grained) 307 50 700 7,250 101,500

Soil-Aggregate Mixture 

(predominantly coarse grained) 308 60 800 8,700 116,000

Fine Grained Soil or Base 309 35 450 5,100 65,000

Hot-Mixed AC 319 700 25,000 101,500 3,625,000

Sand Asphalt 320 700 25,000 101,500 3,625,000

Dense-Graded, Cold-Laid, Central 

Plant Mix AC 323 700 25,000 101,500 3,625,000

Open-Graded, Hot-Laid, Central 

Plant Mix AC 325 350 3,500 50,750 507,500

Cement-Aggregate Mixture 331 2,000 20,000 290,000 2,900,000

Econocrete 332 3,500 35,000 507,500 5,075,000

Lean Concrete 334 4,500 45,000 652,500 6,525,000

Soil Cement 339 1,000 7,000 145,000 1,015,000

Open-Graded, Cold-Laid, In-Place Mix AC 327 200 3,000 29,000 435,000

Limerock; Caliche 337 150 1,500 21,750 217,500

Other—Treated Base (TB) 350 400 8,000 58,000 1,160,000

Bound Surface Courses 

Concrete Surface (uncracked) 10,000 70,000 1,450,000 10,150,000

AC Surface (>0 OC–<45 OC, not alligatored) 700 25,000 101,500 3,625,000

Unbound Subgrades 

Any unbound type 15 650 2,175 94,250

Evaluation of the Rigid Pavement Backcalculated Data Derived from Slab-on-DenseLiquid and Slab-on-Elastic-Solid Foundation Models 

By and large, the screening process produced a set of excellent relationships for the rigid 

pavement data, essentially based on two-layer slab-on-elastic-solid and slab-on-dense-liquid 

models, modified as mentioned above for the base layer by using appropriate ratio-based 
73

formulas. For all structural layers, nearly 95 percent of all records screened were labeled with a 

flag of “0,” or acceptable, while most of the few remaining nonzero flags were “1,” or marginal. 

Evaluation of the Backcalculated Data Derived from Layered Elastic Analysis 

For the flexible pavement data and for the rigid pavement data using layered elastic theory (all 

generated through the MODCOMP backcalculation program), the screening process produced 

some data tables with fairly good agreement between the two analysis methods and many tables 

with relatively poor agreement between the back- and forwardcalculated moduli. 

By way of background, for backcalculation involving more than two unknown layers, in most 

backcalculation programs, the modulus values are effectively derived from the bottom up. This 

factor is also true for the MODCOMP program. As a result, when a small error occurs in the 

lowest unknown layer—the subgrade—the compensating layer effect will inevitably occur, by 

alternately under- and over-estimating the moduli of the succeeding (overlying) layers. In these 

cases, by the time the fourth or fifth layer from the bottom is adjusted through the iteration 

process—the bound surface course—the necessary compensation for an incorrect subgrade 

modulus has taken place and a reasonable result has generally been obtained in spite of 

alternating too-high and too-low results in the intermediate layers beneath the surface course. 

The compensating layer effect appears to be mainly associated with distressed pavements that 

usually do not follow the rules and assumptions made of linear or even nonlinear layered elastic 

theory. On the other hand, with homogeneous, undistressed, and well-defined pavement 

structures, backcalculation often appears to work quite well. This observation is especially true 

for interior slab concrete tests—although only when a two-unknown layer system is used (plus a 

hard layer at some depth, if present). 

Accordingly, the backcalculated asphalt and concrete surface course moduli using MODCOMP 

resulted in the best correspondence to the forwardcalculated moduli of all layers analyzed. For 

the asphalt moduli, better than 70 percent of the correspondence screened values (for both the 

point- and the section-data) were acceptable (flag = 0). For the concrete moduli at the point data 

level using MODCOMP, better than 60 percent of the screened data using a bonded condition in 

forwardcalculation were acceptable (flag = 0), while more than 80 percent of these data were 

acceptable assuming an unbonded condition between the PCC surface and the base course, when 

compared to the forwardcalculated values for rigid pavements. At the section level for the 

concrete modulus derived from MODCOMP, better than 90 percent of the backcalculated 

screened data were acceptable, with a correspondence flag of “0.” 

For the subgrade layer, the correspondence between back- and forwardcalculated moduli using 

MODCOMP (both linear and nonlinear) was somewhat poorer than with the asphalt layer. 

However, these results are principally from the methodology, not the correctness (or lack 

thereof) of each method. Forwardcalculation uses the center deflection and the shape of the 

deflection bowl to characterize the subgrade stiffness under the load plate to a finite depth, as 

defined by the shape of the deflection bowl. Backcalculation uses one or more of the outer 

geophones to characterize the subgrade stiffness at that particular distance from the load, 

assuming it will also have the same stiffness under the load plate. Often this does not appear to 

be the case—hence, the compensating layer effect. In other instances, in particular with concrete 

or a very stiff AC pavements, a horizontally constant subgrade modulus appears to be a more 

reasonable assumption. 
74

Consequently, only about 40 percent of the correspondence screened records for flexible 

pavement subgrades were classified as acceptable (flag = 0). The results of screening the 

subgrade section tables as well as the nonlinear version of MODCOMP were similar. On the 

other hand, most of the bias between the two methods was in the same direction—the 

backcalculated subgrade moduli from MODCOMP were generally higher than those from 

forwardcalculation. For the concrete sections, the correspondence between the two approaches 

was somewhat better, with about 50 percent of these being classified as acceptable, with a 

correspondence flag = 0. In all unacceptable cases, MODCOMP versus forwardcalculation 

produced divergent results that were about equally divided between marginal, questionable, and 

unacceptable (flag = 1, 2, or 3, respectively). 

For the base layer using the MODCOMP backcalculation program, many of the backcalculated 

moduli (and some of the forwardcalculated moduli from the use of the Dorman and Metcalf 

relationship) were not reasonable according to the broad ranges given in Table 17. Of the 

remaining values that were screened using the correspondence flags, only between 30 and 40 

percent of the data resulted in an acceptable flag of “0,” with the remainder once again divided 

more or less evenly among marginal, questionable, and unacceptable (corresponding flags = 1, 2, 

or 3, respectively). 

The Microsoft® Excel spreadsheets containing all formulae used in phase I of this study have 

been provided to FHWA, so all forwardcalculation input quantities are totally transparent to 

those who wish to use the methodology, whether for screening or in rehabilitation design. To this 

end, four spreadsheets are available—two for asphalt-bound surfaces (using SI and U.S. 

Customary units) and two for cement-bound surfaces (SI and U.S. Customary). These 

spreadsheets can be obtained by contacting LTPP Customer Support Services: by phone at 

202– 493–3035 or by e-mail at ltppinfo@fhwa.dot.gov. A publication entitled Guidelines for 

Review and Evaluation of Backcalculation Results (FHWA-HRT-05-152) is also available from 

FHWA for those wishing to use these spreadsheets. 

CONCLUSIONS 

This report presents the results of a study that used forwardcalculation techniques to screen the 

entire set of backcalculated computed parameter results in the LTPP database. Two parallel 

computed parameter data sets now exist: one existing set resulting from backcalculation and one 

newly created set resulting from forwardcalculation, for the same LTPP sections and using the 

same FWD input data. This choice does not mean that one method or the other is strictly right or 

wrong. They are, however, in many instances different. 

As this report shows, backcalculation is more of an art than a science, although it is certainly 

rigorous and scientific in the sense that it can use the entire deflection basin to fairly accurately 

match up the theoretical and actual measured deflections with backcalculated modulus values. 

The user, however, must be aware of its limitations and assumptions, such as linear-elasticity, 

homogeneity, isotropic behavior, in addition to the assumption of being horizontally identical in 

stiffness for each structural layer beneath the width of the deflection basin, especially if a linearelastic model is chosen for backcalculation. A skilled backcalculation analyst can deal with these 

potential shortfalls quite well by skillfully modeling the pavement system and by dealing with 

apparent or actual nonlinearity in a variety of ways. 
75

For example, the analyst can assign a semirigid layer at some depth where the deflection basin 

suggests a possible stiff layer or bedrock, similar to how the Hogg model in forwardcalculation 

defines a depth to an apparent stiff layer, whether there actually is a very stiff layer or bedrock or 

not at that depth. Adjacent structural layers may also be combined to backcalculate an unknown 

layer modulus that would otherwise not influence the deflection basin enough to enable the 

derivation of a modulus value for a relatively thin structural layer. In other cases, a single, 

relatively thick pavement layer can be separated into two layers in the input file to characterize 

the apparent difference in material response as a function of depth within the pavement. 

What would be most satisfying and give considerably more credibility to both backcalculated 

and forwardcalculated results is if they are both reasonable and correspond to one another 

(within reason) with a flag of “0” (i.e., within a factor of 1.5 of one another). For in situ layeredelastic properties of pavement systems, this level of correspondence can be considered 

reasonable and generally satisfactory for engineering purposes. When this correlation occurs, it 

can be maintained that the input assumptions for either approach were essentially correct and that 

either set of moduli may be used with confidence,. 

But what should be done when the correspondence flags between back- and forwardcalculation 

are 1, 2, or 3 (i.e., greater than a factor of 1.5 different from one another)? This situation means 

that both values are within a reasonable range according to Table 17 and are neither fixed nor 

assumed. It probably also means that the theoretical assumptions of one or the other, or both, 

methods are incorrect—or the method of choice is not being used wisely or correctly. Although 

forwardcalculation produced more stable results, globally, than the three- or more-layer 

backcalculation approach (using MODCOMP), backcalculated values cannot be categorically 

rejected, because they do offer a theoretically correct solution to a specific FWD deflection 

basin, however implausible they may appear. Accordingly, some of these cases may well be 

implausible, but there is still a possibility—however remote—that the values are in fact more or 

less correct, given the nature of in situ pavement materials and the often bizarre behavior of these 

materials under a load and under the influence of ever-changing environmental and other sitespecific factors. 

Now, however, the LTPP database user can be forewarned by the various flags and data quality 

checks as outlined in this report and assess whether to accept the values present in the existing 

backcalculated database (or the forwardcalculated parallel database), depending on the intended 

evaluation purpose. 

In conclusion, the slab-on-elastic-solid or slab-on-dense-liquid models for backcalculation offer 

excellent correspondence with the rigid pavement forwardcalculation techniques, with very few 

values being labeled unreasonable. Accordingly, in the vast majority of cases, either (or both) 

may be used with a good degree of confidence. 
76

RECOMMENDATIONS 

Existing LTPP Backcalculation Data—Flagging and Addition of Forwardcalculation Data

As a remedial measure, it is recommended that the current LTPP backcalculated tables be 

retained as is, although with the various checks and flags added as outlined in this report. It is 

also recommended that the forwardcalculated values be appended to the computed parameter 

data tables, so that an LTPP database user can compare the two sets of values obtained from the 

same deflection basin. When these pairs of values pass both the reasonableness test and the 

acceptable (correspondence flag) test, then either (or both) may then be used with a greater 

degree of confidence than one or the other as a stand-alone value. 

Future Analysis of the LTPP FWD Deflection Data—Conduct both Back- and 

Forwardcalculation 

To date, only a limited percentage of the total volume of FWD load-deflection data have been 

processed through either back- or forwardcalculation. As this report documents, no single truth 

exists to determine or quantify actual in situ layered elastic moduli. The results obtained through 

backcalculation depend at least as much on how the program of choice is used than on the actual 

mechanics of how the program functions. Although forwardcalculation produces a unique set of 

values, these values are approximations, not cast-in-stone truth or baseline values. However, 

these approximations can certainly be used to guide the backcalculation program user to see if 

he/she is in the ballpark with answers obtained through any chosen method of load-deflection 

data analysis. 

As a QA measure, it is further recommended that the entire FWD load-deflection database, 

where back- or forwardcalculation can be carried out, be reanalyzed in the case of the previously 

analyzed MODCOMP data along with the unanalyzed post-1998 data. Furthermore, since LTPP 

is a research project, it is not recommended that only one solution be offered as new or improved 

LTPP computed parameters, but rather two or more different solutions be provided to the LTPP 

database user. Forward- and backcalculation programs with different theoretical assumptions (for 

example, by comparing MODCOMP and forwardcalculation results) should be employed so that 

the LTPP database user can compare the values obtained for the same layer, test point, and test 

section. 

Especially in the case of layered elastic backcalculation of three or more unknown layers, it is 

very important that each test section be handled on an individual basis by an experienced and 

savvy user of the selected backcalculation program. Even for an experienced analyst, this process 

will take some time, since each LTPP section should be carefully reviewed for discrepancies 

between the program’s input assumptions and actual deflection behavior. If MODCOMP (or any 

other backcalculation program) is selected for a second round of LTPP deflection data analysis, 

much more time will be necessary than for a typical batch processing of load-deflection data. For 

any layered elastic analysis using backcalculation, forwardcalculation as outlined herein may be 

used as a comparison and, if desired, to seed the backcalculation routine selected, as long as the 

forwardcalculated values are well within the reasonable ranges in Table 17. This table may be 

changed and updated as appropriate, for example by narrowing the range of reasonable asphalt 

layer moduli as a function of pavement temperature (if available), if new in situ modulus 

information is forthcoming about any of the materials listed in the table. Seeding with 
77

forwardcalculated values may well positively affect the backcalculated solutions, providing a 

more reasonable starting point for a good deflection basin fit and a more believable set of moduli 

in the output. 

It will not be necessary to reanalyze or rescreen the back- or forwardcalculated values in the 

slab-on-elastic-solid or slab-on-dense-liquid database, since these two different approaches 

produced very similar results. It is recommended that experienced analysts carry out the same 

two approaches on the remaining rigid pavement data measured at interior slab locations using 

slab-on-dense-liquid and slab-on-elastic-solid theory for backcalculation. 

Selection of Future LTPP FWD Data Analysis Tools—Backcalculation and 

Forwardcalculation 

It is recommended that a second round of LTPP FWD deflection data analysis consist of the 

following steps: 

• Forwardcalculation of all LTPP sections—Use the methods as outlined in this report. 

• Backcalculation of the LTPP rigid pavement sections—Use slab-on-elastic-solid or slabon-dense-liquid foundation analysis, as developed under the previous LTPP backcalculation 

project (FHWA-RD-01-113). 

• Backcalculation of the LTPP flexible pavement sections—Use a sound and user-friendly 

layered elastic backcalculation analysis program and seed values from forwardcalculation 

(provided these values are within reasonable ranges). 

Recommended Actions to Improve Future Backcalculation Results 

In the future, the forwardcalculated values can be used in the following ways to improve the 

backcalculation results: 

• The forwardcalculated values (if they are within a reasonable range) should be used to "seed" 

most backcalculation routines to assist in arriving at more reasonable and accurate 

backcalculated modulus values. 

• When a "flag" arises for any reason (reasonable ranges, large discrepancies with 

forwardcalculation, etc.), at the discretion of the analyst backcalculation can be modified and 

repeated to minimize these differences and/or mitigate the compensating layer effect, thereby 

improving the backcalculated database while leaving the forwardcalculated results in the 

database as well. 

Notes on a Viable Alternative to Classic Multilayered Elastic Backcalculation 

This section is based primarily on the knowledge and experience of the investigators of this task 

order, not an evaluation outcome of the project. 

As an alternative to classic, multilayered backcalculation (e.g., MODCOMP, MODULUS, 

EVERCALC, etc.), some LTPP database processing time could be saved by using the proprietary 

ELMOD program, which is easier for a hands-off batch mode. This technique would still provide 

LTPP database users with the results of two different approaches using two methods 

(backcalculation with ELMOD and forwardcalculation as developed for this project) that are 

similar in some respects and dissimilar in others. The current version of ELMOD offers the user 
78

two internal processing engines—one using a deflection basin matching routine similar to 

traditional backcalculation and the other using the radius of curvature method, which is similar to 

the forwardcalculation routine for bound surface layers presented in this report. Based on our 

experience with ELMOD, the latter is more stable, and therefore more believable, because in 

many cases, layered elastic pavement systems (especially distressed pavement sections) 

generally do not follow the classical laws of homogeneity, isotropic properties, and horizontally 

constant moduli. Accordingly, both ELMOD approaches should be batch-processed so as to 

provide the LTPP database user with three comparable solutions—two from ELMOD and one 

from forwardcalculation. Traditional backcalculation (for example, using MODCOMP again) 

could also be added as a fourth set of values, as long as they are carried out more carefully and 

thoroughly than before, as mentioned previously. 

The suggestion to consider the use of ELMOD, above, does not necessarily mean that ELMOD 

is better or more accurate than MODCOMP, EVERCALC, or MODULUS, etc. All of these 

traditional programs—as well as ELMOD and the forwardcalculation techniques presented in 

this report—produce approximations of in situ modulus values, at best. When using elastic 

layered theory on the vast quantity of LTPP data, ELMOD as a backcalculation engine would be 

both less costly and more efficient than most other backcalculation approaches known to the 

research team. 

There may well be a public domain or other alternative to ELMOD, but the research team is not 

familiar with such an alternative. As far as is known, ELMOD is the only program that will both 

run deflection basin matching and radius of curvature or a similar method in one package. 
79

APPENDIX A 

This appendix consists of charts showing the screening results of the section average 

backcalculation data. 

3564; 

72%

644; 

13%

376; 

8%

341; 

7%

Acceptable

Marginal

Questionable

Unacceptable

4925; 

86%

220; 4%

400; 7%

155; 3%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 55. Charts. Screening results of section average elastic moduli of the asphalt 

concrete layer for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT 

table based on the linear elastic model. 
80

840;

34%

601; 

24%

636; 

25%

428; 

17%

Acceptable

Marginal

Questionable

Unacceptable

2505; 

74%

171; 5%

616; 

18%

118; 3%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

 

Figure 56. Charts. Screening results of section average elastic moduli of the base layer 

for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT 

table based on the linear elastic model. 

3651; 

37%

2693; 

27%

2420; 

24%

1149; 

12%

Acceptable

Marginal

Questionable

Unacceptable

9913; 

82%

8; 0%

2253; 

18%

12; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

 

Figure 57. Charts. Screening results of section average elastic moduli of the subgrade 

for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT 

table based on the linear elastic model. 
81

438; 

63%

144; 

21%

59; 9%

49; 7%

Acceptable

Marginal

Questionable

Unacceptable

690; 87%

40; 5%

59; 7%

11; 1%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 58. Charts. Screening results of section average elastic moduli of the asphalt 

concrete layer for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT 

table based on the nonlinear elastic model. 

149; 

40%

106; 

28%

65; 17%

57; 15%

Acceptable

Marginal

Questionable

Unacceptable

377; 78%

18; 4%

74; 16%

8; 2%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 59. Charts. Screening results of the section average elastic moduli of the base 

layer for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT 

table based on the nonlinear elastic model. 
82

444; 

35%

352; 

28%

299; 

24%

163; 

13%

Acceptable

Marginal

Questionable

Unacceptable

1258; 

85%

0; 0%

219; 15%

0; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 60. Charts. Screening results of the section average elastic moduli of the 

subgrade for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT 

table based on the nonlinear elastic model. 

1148; 

92%

95; 8%

5; 0%

2; 0%

Acceptable

Marginal

Questionable

Unacceptable

1250; 

93% 4; 0%

86; 6%

13; 1%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 61. Charts. Screening results of the section average elastic moduli of the PCC slab 

for the rigid sections in the MON_DEFL_FLX_BAKCALC_SECT table based on 

the linear elastic model using MODCOMP. 
83

388; 

44%

149; 

17%

165; 

19%

173; 

20%

Acceptable

Marginal

Questionable

Unacceptable

875; 51%

153; 9%

551; 32%

129; 8%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 62. Charts. Screening results of the section average elastic moduli of the base layer 

for the rigid sections in the MON_DEFL_FLX_BAKCALC_SECT table 

based on the linear elastic model using MODCOMP. 

655; 

53%

158; 

13%

194; 

16%

228; 

18%

Acceptable

Marginal

Questionable

Unacceptable

1235; 

0; 0% 91%

118; 9%

0; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 63. Charts. Screening results of the section average elastic moduli of the subgrade 

for the rigid sections in the MON_DEFL_FLX_BAKCALC_SECT table 

based on the linear elastic model using MODCOMP. 
84

1133; 

99%

17; 1%

0; 0%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

1150; 

99%

11; 1%

0; 0%

0; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 64. Charts. Screening results of the section average elastic moduli of the PCC slab 

for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT table 

based on the slab-on-elastic-solid model. 

1077; 

97% 39; 3%

1; 0%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

1117; 

99%

8; 1%

0; 0%

0; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 65. Charts. Screening results of the section average elastic moduli of the PCC slab 

for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT table 

based on the slab-on-dense-liquid model. 
85

993; 

98%

14; 1%

14; 1%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

1021; 

92%

3; 0%

61; 6%

21; 2%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 66. Charts. Screening results of the section average elastic moduli of the base layer 

for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT table 

based on the slab-on-elastic-solid model. 

966; 

94%

36; 3%

31; 3%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

1033; 

96%

19; 2%

18; 2%

4; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 67. Charts. Screening results of the section average elastic moduli of the base layer 

for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT table 

based on the slab-on-dense-liquid model. 
86

1158; 

99%

7; 1%

0; 0%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

1165; 

100%

0; 0%

0; 0%

0; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 68. Charts. Screening results of the section average elastic moduli of the subgrade 

for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT table 

based on the slab-on-elastic-solid model. 

1061; 

96%

48; 4%

1; 0%

0; 0%

Acceptable

Marginal

Questionable

Unacceptable

1110; 

98%

0; 0%

18; 2%

0; 0%

Both Values Reasonable

Only Backcalculated Value Reasonable

Only Forwardcalculated Value Reasonable

Both Values Unreasonable

Figure 69. Charts. Screening results of the section average k-values of the subgrade 

for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECTtable 

based on the slab-on-dense-liquid model. 
87

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Long-Term Pavement Performance (LTPP) Test Sections, Volume I: Slab on Elastic Solid 

and Slab on Dense-Liquid Foundation Analysis of Rigid Pavements, FHWA-RD-00-086, 

Washington, DC, Federal Highway Administration, December 2001. 

2. Von Quintus, H.L., and A.L. Simpson, Backcalculation of Layer Parameters for LTPP Test 

Sections―Volume II: Layered Elastic Analysis for Flexible and Rigid Pavements, FHWARD-01-113, Washington, DC, Federal Highway Administration, October 2002. 

3. National Cooperative Highway Research Program, LTPP Data Analysis: Feasibility of Using 

FWD Deflection Data to Characterize Pavement Construction Quality, Project 20-50(09): 

NCHRP Web Document #52 (http://trb.org/news/blurb_detail.asp?id=942), Washington, DC, 

National Cooperative Highway Research Program, November 2002. 

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Philosophical Magazine, volume 35 (243), 1944, pp. 265–276. 

7. Wiseman, G., and J. Greenstein, “Comparison of Methods of Determining Pavement 

Parameters from Deflection Bowl Measurements,” Proceedings of the 7th Asian Regional 

Conference on Soil Mechanics and Foundation Engineering, 1983, pp. 158–165. 

8. American Association of State Highway and Transportation Officials, AASHTO Guide for 

Design of Pavement Structures, Washington, DC: AASHTO, 1993. 

9. Dorman, G.M., and C.T. Metcalf, “Design Curves for Flexible Pavements Based on Layered 

System Theory,” Highway Research Record No. 1188, Washington, DC, National Academy 

Press, 1965, pp. 69–84. 

10. National Cooperative Highway Research Program, LTPP Data Analysis: Variations in 

Pavement Design Inputs, NCHRP Web Document #48 

(http://trb.org/news/blurb_detail.asp?id=742), Washington, DC, National Cooperative 

Highway Research Program, July 2002. 

11. Moore, D.S., and McCabe, G.P., Introduction to the Practice of Statistics, 5th Edition, W.H. 

Freeman, New York, 2005.