Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Long-Term Pavement Performance 

Program Determination of In-Place

Elastic Layer Modulus: Backcalculation 

Methodology and Procedures

PUBLICATION NO. FHWA-HRT-15-036 DECEMBER 2015
FOREWORD

The Long-Term Pavement Performance (LTPP) database includes deflection basins measured on 

thousands of test sections across the United States. These deflection data were used to 

backcalculate the elastic layer modulus of both flexible and rigid pavements. This report 

documents the tools, data analyses, backcalculation and forward calculation packages, and 

procedures used to calculate the in-place elastic layer modulus of the LTPP test sections. It

summarizes the backcalculated elastic layered modulus of both new and rehabilitated flexible 

and rigid pavements in the LTPP program and demonstrates their use in day-to-day practice for 

pavement design, rehabilitation, and management. Many agencies have used the LTPP deflection 

data for calibrating mechanistic-empirical distress transfer functions, including those in the 

Mechanistic-Empirical Pavement Design Guide.

(1)

An important outcome presented in this report is the documentation of methods and procedures 

for calculating in-place elastic layer modulus, including the pre- and post-processing tools so the 

results can be recreated by others to make the process less user-dependent. In addition, the elastic 

modulus computed parameter tables included in the LTPP database (Standard Data Release 27.0 

released in 2013) are defined and explained in this report so agencies can use these results in 

multiple areas.(2) This final report is intended for use by pavement researchers as well as by 

practicing engineers involved in rehabilitation design and management of agencies’ pavements.

Jorge E. Pagán-Ortiz

Director, 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-15-036

2. Government Accession No. 3. Recipient’s Catalog No.

4. Title and Subtitle

Long-Term Pavement Performance Program Determination of In-Place 

Elastic Layer Modulus: Backcalculation Methodology and Procedures

5. Report Date

December 2015

6. Performing Organization Code

7. Author(s)

Harold L. Von Quintus, P.E., Chetana Rao, and Lynne Irwin

8. Performing Organization Report No.

9. Performing Organization Name and Address

Applied Research Associates, Inc.

100 Trade Centre Drive, Suite #200

Champaign, IL 61820

10. Work Unit No. (TRAIS)

11. Contract or Grant No.

DTFH61-11-C-00051

12. Sponsoring Agency Name and Address

Office of Infrastructure Research and Development

Federal Highway Administration

6300 Georgetown Pike

McLean, VA 22101-2296

13. Type of Report and Period Covered

Draft Final Report

September 30, 2011–October 30, 2014

14. Sponsoring Agency Code

15. Supplementary Notes

The Contracting Officer’s Technical Representative (COTR) was Ms. Yan “Jane” Jiang.

16. Abstract

Deflection data have been measured at periodic intervals with a falling weight deflectometer on all rigid, flexible, semirigid, and rehabilitated pavement test sections included in the Long-Term Pavement Performance (LTPP) program. A 

common use of deflection data is to backcalculate in-place layered elastic modulus values. The Federal Highway 

Administration sponsored earlier studies to backcalculate elastic layer modulus values from deflection basins measured 

on all LTPP test sections and included those computed values in the LTPP database.(3–5) While the earlier studies focus 

on the use of nonlinear methods and were considered to have minimal success, Some of the methods used have 

advanced within the past decade. As such, there was a need to revisit the methods used to improve on the results. 

This report summarizes all activities completed to backcalculate the elastic layered modulus from deflection basins 

measured on all test sections included in the LTPP program. Specifically, the report documents the tools, data analyses, 

backcalculation and forward calculation packages, and procedures used to calculate, on a production basis, the in-place 

elastic layer modulus of the LTPP test sections. Multiple packages (including BAKFAA, EVERCALC©, 

MICHBACK©, MODULUS, MODCOMP©, and the area and best fit methods) were considered and evaluated for 

estimating layered elastic modulus values on a production basis. (See references 6–10.) The methods used in 

production for backcalculating elastic layer moduli include a combination of EVERCALC© and MODCOMP© for all 

types of pavements and the best fit method for rigid pavements. The methods and procedures, including the pre- and 

post-processing tools, have been automated so the results can be recreated by others not directly involved in 

development of the tools and procedures. The report also summarizes the results from the production runs to calculate 

the elastic layered modulus of flexible and rigid pavements (new construction and rehabilitation) as well as 

demonstrate the application and use of the results.

17. Key Words

Backcalculation, Deflection data, Elastic modulus, 

EVERCALC©, Falling weight deflectometer, Long-Term 

Pavement Performance, LTPP, MODCOMP©, 

MODTAG©, Modulus, Mechanistic-Empirical Pavement 

Design Guide, Pavement evaluation

18. Distribution Statement

No restrictions. This document is available to the public 

through the National Technical Information Service, 

Springfield, VA 22161.

http://www.ntis.gov

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

177

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 the International System of Units. Appropriate 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

PROJECT OBJECTIVE.........................................................................................................1

SCOPE OF REPORT AND ORGANIZATION...................................................................2

CHAPTER 2. BACKCALCULATION METHODOLOGY AND PACKAGES ....................3

TYPES OF BACKCALCULATION METHODS................................................................3

Iterative Search Methods .....................................................................................................3

Database Search Methods....................................................................................................3

Equivalent Thickness Methods............................................................................................4

Forward Calculation Methods or Closed-Form Solutions...................................................4

Other Methods .....................................................................................................................4

Summary..............................................................................................................................5

CANDIDATE BACKCALCULATION PROGRAMS ........................................................5

Comparison of Backcalculation Programs...........................................................................5

Ground Truth Regarding Backcalculated Modulus Values.................................................8

Factors Considered in Selecting Candidate Programs.......................................................11

STANDARDIZATION OF BACKCALCULATION PROCESS .....................................14

CHAPTER 3. CASE STUDIES ..................................................................................................15

LTPP TEST SECTIONS SELECTED FOR CASE STUDIES .........................................15

COMPARISON OF RESULTS FROM CANDIDATE BACKCALCULATION 

PROGRAMS ..........................................................................................................................16

Deflection Basin Matching—RMSE .................................................................................16

Distribution of Elastic Moduli ...........................................................................................17

Layer Stiffness Properties of Flexible Pavements.............................................................18

Layer Stiffness Properties of Rigid Pavements .................................................................22

Field-Derived and Laboratory-Measured Layer Stiffness Properties................................25

CASE STUDY SUMMARY..................................................................................................33

CHAPTER 4. BACKCALCULATION PROCESS..................................................................35

OVERVIEW OF PROCESS.................................................................................................35

Backcalculation Programs .................................................................................................38

LTPP Data..........................................................................................................................40

Presence of Bedrock Layer................................................................................................42

Presence of Ground Water or Wet Layer...........................................................................42

Pre-Processing and Computational Tools..........................................................................42

Pre-Processing Deflection Data .........................................................................................44

PAVEMENT SIMULATION RULES.................................................................................45

DEFINING ACCEPTABLE ELASTIC LAYER MODULUS VALUES.........................48

Error Between Predicted and Measured Deflection Basins...............................................48

Range of Calculated Modulus Values................................................................................49

Normality Test Using Jarque-Bera Test Statistic...............................................................50

CHAPTER 5. BACKCALCULATION RESULTS ..................................................................53

LTPP DATA SOURCE .........................................................................................................53
iv

BASIC FACTS ABOUT THE BACKCALCULATION PROCESS.................................53

Number of GPS and SPS Test Sections.............................................................................53

Hardware Used in Backcalculation Processing .................................................................61

EVALUATING THE SUCCESS OF BACKCALCULATION.........................................61

Manual Review of Results.................................................................................................64

Post-Processing Evaluation Factors...................................................................................65

CPTS .......................................................................................................................................68

CHAPTER 6. APPLICATION AND USE OF BACKCALCULATION RESULTS ............71

SETTING DEFAULTS FOR MATERIAL TYPES ...........................................................71

STRESS SENSITIVITY OF NONLINEAR MATERIALS AND SOILS ........................72

MEPDG HMA DAMAGE CONCEPT: FACT OR FICTION?........................................77

Time-Dependent Damage Values......................................................................................78

Modulus Differences Between Wheel Paths and Non-Wheel Paths .................................80

DIFFERENCES BETWEEN FIELD-DERIVED AND LABORATORYMEASURED MODULI.........................................................................................................82

HMA Layers ......................................................................................................................82

PCC Layers........................................................................................................................83

Unbound Aggregate Base and Soils Layers.......................................................................84

TIME AND SEASONAL EFFECTS....................................................................................84

Seasonal Temperature Effects on HMA ............................................................................84

Seasonal Moisture Effects for Unbound Aggregate Base Layers......................................86

Seasonal Moisture Effects for the Weathered Soil Layers ................................................88

Seasonal Moisture Effects for the SS Layers.....................................................................90

MIXTURE TIME-DEPENDENT MODULI.......................................................................91

HMA Aging .......................................................................................................................91

PCC Modulus-Gain Relationship ......................................................................................92

MODULUS OF FRACTURED PCC LAYERS..................................................................93

RECLAIMED ASPHALT PAVEMENT (RAP) AND VIRGIN MIXTURES.................97

CHAPTER 7. CONCLUSIONS................................................................................................103

FINDINGS............................................................................................................................103

RECOMMENDATIONS.....................................................................................................105

APPENDIX A: BEST FIT METHOD—CALCULATING PCC ELASTIC LAYER 

MODULI.....................................................................................................................................107

APPENDIX B: LTPP TEST SECTIONS WITH A MODERATE AND HIGH 

PERCENTAGE OF ERRORS..................................................................................................119

APPENDIX C: DEVELOPMENT OF THE SIMULATED LAYER STRUCTURE 

FOR THE BACKCALCULATION PROCESS USING EVERCALC© AND 

MODCOMP©..............................................................................................................................131

REFERENCES...........................................................................................................................161
v

LIST OF FIGURES

Figure 1. Photo. Core recovered from an LTPP test section used to equate laboratorymeasured modulus values to backcalculated elastic modulus values (Texas SPS-5 section)........10

Figure 2. Photo. Cross-section of the pavement layers exposed during a forensic 

investigation to measure the rutting within individual pavement layers (Arizona 

SPS-1 section)................................................................................................................................11

Figure 3. Graph. Comparison of RMSE values between backcalculation programs for 

flexible pavement sections comparing MODULUS, MODTAG©, and EVERCALC©.................16

Figure 4. Graph. Comparison of RMSE values between backcalculation programs for 

rigid pavement sections comparing best fit method and EVERCALC©........................................17

Figure 5. Graph. Normal distribution of calculated elastic modulus for a crushed stone 

base aggregate................................................................................................................................18

Figure 6. Graph. Bimodal distribution of calculated elastic modulus for the weathered 

soil layer.........................................................................................................................................18

Figure 7. Graph. Comparison of backcalculated moduli from the candidate programs for 

the HMA layer ...............................................................................................................................19

Figure 8. Graph. Comparison of backcalculated moduli from the candidate programs for 

the asphalt stabilized base layer.....................................................................................................19

Figure 9. Graph. Comparison of backcalculated moduli from the candidate programs for 

the weathered soil layer modulus values .......................................................................................20

Figure 10. Graph. Comparison of backcalculated moduli from the candidate programs for 

the natural subgrade modulus values.............................................................................................20

Figure 11. Graph. Comparison of backcalculated moduli from the candidate programs for 

aggregate base layers .....................................................................................................................21

Figure 12. Graph. Backcalculated layer PCC modulus from EVERCALC© compared to 

the elastic modulus calculated with the area and best fit methods ................................................23

Figure 13. Graph. Comparison of forward and backcalculated moduli from the candidate 

programs for the subgrade layer ....................................................................................................23

Figure 14. Graph. Comparison of forward and backcalculated moduli from the candidate 

programs for the aggregate base layer ...........................................................................................24

Figure 15. Graph. Comparison of forward and backcalculated moduli from the candidate 

programs for the PCC layer ...........................................................................................................24

Figure 16. Graph. Comparison of backcalculated and laboratory-measured PCC moduli............26

Figure 17. Graph. Comparison of backcalculated HMA surface and binder layer moduli 

and laboratory-measured moduli from the Iowa SPS-1 project.....................................................27

Figure 18. Graph. Comparison of backcalculated HMA base layer moduli and laboratorymeasured moduli from the Iowa SPS-1 project .............................................................................27

Figure 19. Graph. Comparison of backcalculated HMA surface and binder layer moduli 

and laboratory-measured moduli from the Wisconsin SPS-1 project............................................28

Figure 20. Graph. Comparison of backcalculated HMA base layer moduli and laboratorymeasured moduli from the Wisconsin SPS-1 project ....................................................................28

Figure 21. Graph. Comparison of backcalculated HMA overlay moduli and laboratorymeasured moduli from the Mississippi SPS-5 project...................................................................29
vi

Figure 22. Graph. Comparison of backcalculated HMA surface layer moduli of the 

existing pavement after overlay placement and laboratory-measured moduli from the 

Mississippi SPS-5 project ..............................................................................................................29

Figure 23. Graph. Comparison of backcalculated HMA surface layer moduli of the 

existing pavement prior to overlay placement and laboratory-measured moduli from the 

Mississippi SPS-5 project ..............................................................................................................30

Figure 24. Graph. Comparison of backcalculated HMA base layer moduli of the existing 

pavement prior to overlay placement and laboratory-measured moduli from the Mississippi 

SPS-5 project .................................................................................................................................30

Figure 25. Graph. Comparison of backcalculated HMA moduli and laboratory-estimated 

dynamic modulus for the Oklahoma SPS-6 project.......................................................................31

Figure 26. Graph. Comparison of backcalculated HMA moduli and laboratory-estimated 

dynamic modulus for the Georgia SMP project ............................................................................31

Figure 27. Graph. Comparison of backcalculated elastic moduli of unbound layers using 

EVERCALC© and laboratory-derived resilient modulus..............................................................32

Figure 28. Graph. Comparison of backcalculated elastic moduli of unbound layers using 

MODULUS and laboratory-derived resilient modulus..................................................................33

Figure 29. Graph. Comparison of backcalculated elastic moduli of unbound layers using 

MODTAG© and laboratory-derived resilient modulus..................................................................33

Figure 30. Flowchart. Major steps and decisions in linear elastic backcalculation process..........36

Figure 31. Equation. Skewness factor............................................................................................50

Figure 32. Equation. Kurtosis factor..............................................................................................51

Figure 33. Equation. Jarque-Bera statistic used for verifying normality in data ...........................51

Figure 34. Photo. Cores recovered where moisture damage occurred, decreasing the 

in-place modulus of the layer/mixture (Texas SPS-5 project).......................................................67

Figure 35. Graph. Backcalculated elastic moduli for all aggregate base layers for the 

Georgia (GA(13)) LTPP test sections classified as an AASHTO A-1-a material.........................71

Figure 36. Graph. Backcalculated elastic moduli for all aggregate base layers for the 

Minnesota (MN(27)) LTPP test sections classified as an AASHTO A-1-a material ....................72

Figure 37. Graph. Comparison of backcalculated elastic moduli for the aggregate base 

layer from the Texas SPS-8 project 48-0801.................................................................................73

Figure 38. Graph. Comparison of backcalculated elastic moduli for the weathered finegrained soil layer from the Texas SPS-8 project 48-0801 .............................................................74

Figure 39. Graph. Comparison of backcalculated elastic moduli for the fine-grained 

subgrade from the Texas SPS-8 project 48-0801 ..........................................................................74

Figure 40. Graph. Comparison of backcalculated elastic moduli for the aggregate base 

layer from the Utah SPS-8 project 49-0803...................................................................................75

Figure 41. Graph. Comparison of backcalculated elastic moduli for the weathered 

coarse-grained layer from the Utah SPS-8 project 49-0803 ..........................................................75

Figure 42. Graph. Comparison of backcalculated elastic moduli for the coarse-grained 

subgrade from the Utah SPS-8 project 49-0803 ............................................................................76

Figure 43. Graph. Comparison of backcalculated elastic moduli for the aggregate base 

layer from New York SPS-8 project 36-0802................................................................................76

Figure 44. Graph. Comparison of backcalculated elastic moduli for the weathered 

coarse-grained layer from the New York SPS-8 project 36-0802 .................................................77
vii

Figure 45. Graph. Comparison of backcalculated elastic moduli for the coarse-grained 

subgrade from the New York SPS-8 project 36-0802 ...................................................................77

Figure 46. Graph. Decreasing elastic moduli of the asphalt layer over time for use in 

rehabilitation design for Minnesota GPS section 27-6251 ............................................................78

Figure 47. Graph. Decreasing elastic moduli of the asphalt layer over time for use in 

rehabilitation design for Minnesota GPS section 27-1018 ............................................................79

Figure 48. Graph. Decreasing elastic moduli of the asphalt layer between 60 and 66 oF 

over time for use in rehabilitation design for Minnesota GPS section 27-1016............................80

Figure 49. Graph. Decreasing elastic moduli of the asphalt layer between 60 and 66 oF 

over time for use in rehabilitation design for Minnesota GPS section 27-6251............................80

Figure 50. Graph. Elastic moduli of the asphalt layer between the wheel path and 

non-wheel path lanes for Minnesota GPS section 27-6251...........................................................81

Figure 51. Graph. Elastic moduli of the asphalt layer between the wheel path and 

non-wheel path lanes for Minnesota GPS section 27-1018...........................................................82

Figure 52. Graph. Comparison of the dynamic moduli computed from the Witczak 

regression equation and the backcalculated elastic moduli for four SPS-1 projects .....................83

Figure 53. Graph. Comparison of HMA backcalculated elastic layer moduli for Idaho 

SMP section 16-1010.....................................................................................................................84

Figure 54. Graph. Comparison of HMA backcalculated elastic layer moduli for New Mexico

SMP section 35-1112.....................................................................................................................85

Figure 55. Graph. Comparison of HMA backcalculated elastic layer moduli for Minnesota 

SMP section 27-1018.....................................................................................................................85

Figure 56. Graph. Comparison of HMA backcalculated elastic layer moduli for Texas 

SMP section 48-1077.....................................................................................................................86

Figure 57. Graph. Comparison of aggregate base backcalculated elastic layer moduli 

for Idaho SMP section 16-1010 .....................................................................................................86

Figure 58. Graph. Comparison of aggregate base backcalculated elastic layer moduli 

for New Mexico SMP section 35-1112 .........................................................................................87

Figure 59. Graph. Comparison of aggregate base backcalculated elastic layer moduli 

for Minnesota SMP section 27-1018 .............................................................................................87

Figure 60. Graph. Comparison of aggregate base backcalculated elastic layer moduli 

for Texas SMP section 48-1077.....................................................................................................88

Figure 61. Graph. Comparison of weathered soil backcalculated elastic layer moduli 

for Idaho SMP section 16-1010 .....................................................................................................88

Figure 62. Graph. Comparison of weathered soil backcalculated elastic layer moduli 

for Minnesota SMP section 27-1018 .............................................................................................89

Figure 63. Graph. Comparison of weathered soil backcalculated elastic layer moduli 

for Texas SMP section 48-1077.....................................................................................................89

Figure 64. Graph. Comparison of SS backcalculated elastic layer moduli for Idaho SMP 

section 16-1010..............................................................................................................................90

Figure 65. Graph. Comparison of SS backcalculated elastic layer moduli for New Mexico 

SMP section 35-1112.....................................................................................................................90

Figure 66. Graph. Comparison of SS backcalculated elastic layer moduli for Minnesota 

SMP section 27-1018.....................................................................................................................91

Figure 67. Graph. Comparison of SS backcalculated elastic layer moduli for Texas SMP 

section 48-1077..............................................................................................................................91
viii

Figure 68. Graph. Backcalculated PCC elastic moduli over time from EVERCALC©

for selected SPS-2 test sections......................................................................................................92

Figure 69. Graph. Backcalculated PCC elastic moduli over time from the best fit 

unbonded method for selected SPS-2 test sections........................................................................93

Figure 70. Graph. Comparison of backcalculated PCC elastic moduli from EVERCALC©

and the best fit unbonded method for selected SPS-2 test sections...............................................93

Figure 71. Graph. Backcalculated elastic moduli for the Oklahoma SPS-6 rubblized test 

sections...........................................................................................................................................95

Figure 72. Graph. Backcalculated elastic moduli for the Indiana SPS-6 crack and seat 

test sections....................................................................................................................................95

Figure 73. Graph. Backcalculated elastic moduli comparing the PCC intact, crack and 

seat, and rubblized test sections for the Arizona SPS-6 test sections............................................96

Figure 74. Graph. Backcalculated elastic moduli comparing the PCC intact, crack and 

seat, and rubblized test sections for the Michigan SPS-6 test sections..........................................96

Figure 75. Graph. Backcalculated elastic moduli comparing the PCC intact, crack and 

seat, and rubblized test sections for the Pennsylvania SPS-6 test sections....................................97

Figure 76. Graph. Comparison of RAP and virgin backcalculated elastic HMA moduli 

from the Minnesota SPS-5 project.................................................................................................98

Figure 77. Graph. Comparison of RAP and virgin mix backcalculated elastic HMA 

moduli from the Arizona SPS-5 project.........................................................................................99

Figure 78. Graph. Comparison of RAP and virgin mix backcalculated elastic HMA 

moduli from the Mississippi SPS-5 project ...................................................................................99

Figure 79. Graph. Comparison of RAP and virgin mix backcalculated elastic HMA 

moduli from the Oklahoma SPS-5 project...................................................................................100

Figure 80. Graph. Comparison of RAP and virgin mix backcalculated elastic HMA 

moduli from the Maine SPS-5 project .........................................................................................100

Figure 81. Illustration. Transformation of design structure to effective structure used 

by the neural networks to compute mechanistic responses .........................................................108

Figure 82. Equation. Error function definition for best fit procedure..........................................109

Figure 83. Equation. Calculated deflection..................................................................................109

Figure 84. Equation. Radius of relative stiffness.........................................................................110

Figure 85. Equation. Error function in alternate form .................................................................110

Figure 86. Equation. Partial derivative of F with respect to k .....................................................110

Figure 87. Equation. Partial derivative of F with respect to l......................................................110

Figure 88. Equation. k-value........................................................................................................110

Figure 89. Equation. Radius of relative stiffness.........................................................................110

Figure 90. Equation. Modular ratio..............................................................................................111

Figure 91. Equation. Flexural stiffness........................................................................................113

Figure 92. Equation. Slab modulus from effective modulus for unbonded condition.................114

Figure 93. Equation. Base modulus from effective modulus for unbonded condition................114

Figure 94. Equation. Sab modulus from effective modulus for bonded condition......................114

Figure 95. Equation. Base modulus for bonded condition...........................................................114

Figure 96. Equation. Depth of the parallel axis from the surface ................................................114

Figure 97. Equation. Equivalent beta when multiple layers are combined into the base ............116

Figure 98. Equation. Equivalent thickness ..................................................................................116

Figure 99. Equation. Expr1..........................................................................................................116
ix

Figure 100. Equation. Expr2........................................................................................................117

Figure 101. Equation. Depth of parallel axis from the surface when multiple layers are 

combined into the base.................................................................................................................117

Figure 102. Equation. Expr3........................................................................................................117

Figure 103. Equation. Expr4........................................................................................................117
x

LIST OF TABLES

Table 1. Backcalculation software packages used in the case studies...........................................13

Table 2. LTPP test sections used for the case studies....................................................................15

Table 3. Comparison of datasets from selected LTPP flexible test sections.................................22

Table 4. Comparison of datasets from selected LTPP rigid test sections......................................25

Table 5. Tables from the LTPP database for evaluating data for the backcalculation process .....41

Table 6. Typical range of modulus for different paving materials and soils.................................49

Table 7. Statistical parameters calculated for normality check .....................................................50

Table 8. Critical chi-squared value for different degrees of freedom and levels of 

significance ....................................................................................................................................51

Table 9. Summary of LTPP data used in the backcalculation analyses by experiment.................54

Table 10. Summary of LTPP deflection basin data .......................................................................55

Table 11. Number of deflection basins analyzed and percentage of those deflection basins 

considered acceptable ....................................................................................................................57

Table 12. Deflection basins analyzed and percentage classified as acceptable drops using 

EVERCALC© and MODCOMP© for all pavements.....................................................................58

Table 13. Deflection basins analyzed and percentage classified as acceptable drops using 

the best fit method for PCC-surfaced pavements ..........................................................................60

Table 14. LTPP test sections identified as errors and eliminated from determining the 

test section statistics.......................................................................................................................62

Table 15. Error flags used in the CPTs..........................................................................................63

Table 16. Backcalculation results for the Oklahoma SPS-6 project—intact and rubblized 

test sections....................................................................................................................................94

Table 17. Modular ratio to estimate the relative stiffness between PCC slab and base in 

the best fit procedure (for both bonded and unbonded conditions) .............................................112

Table 18. Effect of layer structure on base layer—number of layers underneath the 

PCC slab included in the effective base layer..............................................................................115

Table 19. LTPP test sections with a moderate percentage of errors............................................120

Table 20. LTPP test sections with a high percentage of errors....................................................127

Table 21. AC surface with two layers between AC and subgrade...............................................132

Table 22. PCC surface with two layers between PCC and subgrade...........................................135

Table 23. AC surface with three layers between AC and subgrade.............................................137

Table 24. PCC surface with three layers between PCC and subgrade.........................................139

Table 25. AC surface with four layers between AC and subgrade..............................................141

Table 26. PCC surface with four layers between PCC and subgrade..........................................142

Table 27. AC surface with five layers between AC and subgrade ..............................................143

Table 28. PCC surface with six layers between PCC and subgrade............................................143

Table 29. AC surface with seven layers between AC and subgrade ...........................................144

Table 30. PCC surface with seven layers between PCC and subgrade .......................................144

Table 31. AC surface with one layer between AC and subgrade ................................................145

Table 32. PCC surface with one layer between PCC and subgrade ............................................146

Table 33. AC surface with two layers between AC and subgrade...............................................147

Table 34. PCC surface with two layers between PCC and subgrade...........................................149

Table 35. AC surface with three layers between AC and subgrade.............................................151

Table 36. PCC surface with three layers between PCC and subgrade.........................................154
xi

Table 37. AC surface with four layers between AC and subgrade..............................................156

Table 38. PCC surface with four layers between PCC and subgrade..........................................157

Table 39. AC surface with five layers between AC and subgrade ..............................................158

Table 40. PCC surface with six layers between PCC and subgrade............................................158

Table 41. AC surface with seven layers between AC and subgrade ...........................................159

Table 42. PCC surface with seven layers between PCC and subgrade .......................................159
xii

LIST OF ACRONYMS AND SYMBOLS

AASHTO American Association of State Highway and Transportation Officials

AC asphalt concrete

ANN artificial neural network

ATB asphalt-treated base

CPT computed parameter table

CRCP continuously reinforced concrete pavement

FHWA Federal Highway Administration

FWD falling weight deflectometer

GB granular base

GPR ground-penetrating radar

GPS General Pavement Studies

GS granular subbase

HMA hot mix asphalt

JPCP jointed plain concrete pavement

JRCP jointed reinforced concrete pavement

LTE load transfer efficiency

LTPP Long-Term Pavement Performance

MEPDG Mechanistic-Empirical Pavement Design Guide

PCC portland cement concrete

RAP reclaimed asphalt pavement

RMSE root mean squared error

SDR Standard Data Release

SHRP Strategic Highway Research Program

SLIC Sensor Location Independent Check

SMP Seasonal Monitoring Program

SPS Specific Pavement Studies

SS subgrade soil

TB treated base

TS treated subgrade
1

CHAPTER 1. INTRODUCTION

BACKGROUND

Deflection data have been measured at periodic intervals with a falling weight deflectometer 

(FWD) on all rigid, flexible, and composite pavement test sections included in the Long-Term 

Pavement Performance (LTPP) program. These data or deflection basins have been measured to 

determine the load-response properties of the pavement structure and subgrade. Currently, there 

are 16,364 FWD testing days and more than 2,400 test sections in the LTPP database. 

Deflections are measured approximately every 2 years for sections included in Specific 

Pavement Studies (SPS) experiments and every 5 years for sections included in General 

Pavement Studies (GPS) experiments. There are 64 test sections included in the LTPP Seasonal 

Monitoring Program (SMP), and deflection data were measured every month for 1 to 2 years 

for these sites. The SMP sites were used to determine the change in structural properties 

throughout the year and how changes in moisture and temperature affect the in-place

structural response properties.

A common use of deflection data is to backcalculate in-place layered elastic modulus values. 

Layered elastic modulus values and how the values change over time are used as inputs for 

estimating remaining life and deciding on an appropriate rehabilitation and design strategy. In 

addition, many agencies have used the LTPP deflection data for use in calibrating mechanisticempirical distress transfer functions, including those in the Mechanistic-Empirical Pavement 

Design Guide (MEPDG).(1)

The Federal Highway Administration (FHWA) sponsored earlier studies to backcalculate elastic 

layer modulus values from deflection basins and included these computed values in the LTPP 

database. (See references 3, 4, 11, and 12.) Some of the methods used in the earlier studies, 

however, have been advanced within the past decade. In addition, the amount of deflection data 

in the LTPP database has increased substantially, especially for the SPS sites. As such, FHWA 

sponsored a follow-up project to revisit the methods used in the first round of backcalculation

and to calculate the elastic layered modulus values for the deflection data that did not exist 

during the first round of backcalculation.

1

PROJECT OBJECTIVE

The objective of this study was to select one or more methods to determine the in-place elastic 

layered modulus from deflection basin measurements for the LTPP test sections and execute 

those methods for all flexible, rigid, and composite pavement sections included in the LTPP 

program. These backcalculated elastic layer modulus values, simulated pavement structures for 

each LTPP test section, and related parameters were integrated into the computed parameter 

tables (CPTs) of the LTPP database. The project was divided into the following two phases:

 1

In this report, “backcalculation packages” refers to both forward calculation and backcalculation software programs for estimating the in-place 

layered elastic modulus values from deflection basin data.
2

• Phase I: Phase I included selecting methods and demonstrating those methods and 

associated pre- and post-processing tools for estimating in-place elastic layered modulus 

values.2 As part of phase I, the recommended procedures to be used in the next phase

were demonstrated through a series of case studies.3

• Phase II: Phase II included executing the methods selected from phase I and 

backcalculating the elastic layered modulus from deflection basin data stored in the LTPP 

data for the simulated flexible, rigid, composite, and rehabilitated pavement structures.

This phase also included uploading the calculated values and associated parameters into a 

set of CPTs in the LTPP database.

SCOPE OF REPORT AND ORGANIZATION

This report is divided into seven chapters, including this introductory chapter, as follows:

• Chapter 2 describes the process used to select candidate backcalculation methodologies 

and programs. It summarizes the work completed under phase I of this project.

• Chapter 3 summarizes the case studies that were used to select the backcalculation 

methods and develop the pre- and post-processing utility tools as well as the 

automated procedure.

• Chapter 4 provides an overview of the backcalculation process. This includes the rules of 

simulation, deflection data evaluation to identify problem basins, and acceptance criteria 

used to judge and interpret the results of the backcalculation process. 

• Chapter 5 summarizes the results from the backcalculation process and the data included 

in the computed parameter database. It also identifies the evaluation factors used to judge 

the results of test sections that had moderate to high errors and were excluded from the 

statistical summaries in the CPTs.

• Chapter 6 includes examples to demonstrate application of the backcalculated elastic 

layered modulus results.

• Chapter 7 summaries the findings and recommendations from this project.

This report also contains three appendices that provide detailed information on the computed 

parameter database, the tools and macros written to facilitate the entry of required data, and the 

backcalculation process so that similar results can be obtained by others not directly involved in 

this project.

 2

The project team reviewed multiple methods to determine the in-place elastic layered modulus values, and the results were reported to FHWA 

in an unpublished technical memorandum, the contents of which are summarized in this report.

 3

The project team reported the phase I results to FHWA in an unpublished interim report. The contents of the interim report are summarized in 

this report.
3

CHAPTER 2. BACKCALCULATION METHODOLOGY AND PACKAGES

This chapter summarizes the activities completed in phase I of this project.(13) It describes how 

specific backcalculation packages were selected as candidates to determine the elastic layer 

modulus values for all test sections included in the LTPP program.

TYPES OF BACKCALCULATION METHODS

There are many programs and methods that can be used to estimate the in-place elastic modulus 

values of pavement structural layers from deflection basins. Hou developed one of the first 

solutions for backcalculation of elastic layer modulus values of more than two layers.

(13) Hou’s 

approach is to search for the set of layer modulus values that minimize the sum of the squared 

differences between the calculated and measured deflections. Many backcalculation software 

programs use this general approach, matching measured deflections to deflections calculated 

with multilayer elastic theory.

The types of backcalculation methods can be grouped into five generalized categories, which are 

summarized in the following sections.

Iterative Search Methods

The iterative search method is based on the backcalculation program making repeated calls to an 

elastic layer subroutine to match the measured to calculated deflections for program-selected or 

derived layer moduli. The iteration process stops when the measured and calculated deflections 

are within a tolerance level or when the maximum number of iterations is reached. The user sets 

the tolerance and maximum number of iterations.

Lytton and Anderson provided a detailed description of two algorithms included in this category

of programs.

(15,16) The iterative search method involves selecting an initial set of layer modulus 

values. These modulus values are used to compute surface deflections, which are compared to 

the measured deflections. The assumed modulus values are adjusted, and the process is repeated 

until the calculated deflections match the measured deflections within a specified tolerance.

Many backcalculation packages use this method, especially those that are used for production 

and research purposes.

EVERCALC© and MODCOMP© are two programs that fall within this category.(7,9) The 

MODCOMP© software package was used in the first round of backcalculation for all 

pavements.

(4) Both EVERCALC© and MODCOMP© were selected for this study to 

backcalculate the elastic layer modulus for all of the LTPP sections.

Database Search Methods

Backcalculation by database search involves searching a database of calculated deflection basins 

generated for varying modulus values for specific pavement structure to find the calculated 

deflection basin that best matches the measured deflection basin. Database backcalculation 

programs work by generating a database of deflection basins for a matrix of elastic layer 
4

modulus values and either fixed layer thicknesses or a matrix of thicknesses and then searching 

the database for the deflection basin that most closely matches the measured basin.

The database search-based programs include MODULUS, COMDEF, and DBCONPAS, which

were all developed about the same time. (See references 16–21 and 8.)

Equivalent Thickness Methods

Odemark presented an equivalent thickness method for analyzing deflections.(22) The equivalent 

thickness approach reduces a multilayer elastic system to an equivalent system with fewer layers

(generally three or less) for which a solution is easily obtainable. Equivalent thickness-based 

methods use either the iterative or database search methods in finding a calculated deflection 

basin for a set of layer moduli that best match the measured basin.

Examples of equivalent thickness-based backcalculation programs include those developed by 

Ullidtz and by Lytton and Michalak.

(23–25) Ullidtz’s program, Evaluation of Layer Moduli and 

Overlay Design (ELMOD©), is widely used since it is distributed by Dynatest® as part of a

software package offered to purchasers of the Dynatest FWDs. ELMOD© is a proprietary 

software package.

Forward Calculation Methods or Closed-Form Solutions

Some methods use specific points of the measured deflection basin to directly calculate the 

modulus of limited layers. These methods are referred to as “forward” calculation methods and 

provide a unique solution for each deflection basin. The forward calculation method or closedform solution was used during the first round of modulus determination for LTPP.(3)

Most of the closed-form solution methods are limited to three or fewer layers (including the 

subgrade or foundation)—a major disadvantage of these methods. This limitation makes 

individual layers with anomalies or defects difficult to identify because it requires use of the 

equivalent stiffness concept. More importantly, the error can be large between the measured and 

calculated deflections for the sensors excluded from the calculation process.

The Hogg model is an example of closed-form solutions for flexible pavements.

(26) The area and 

best fit methods are a deviation from the elastic layer theory approach commonly used for 

flexible pavements. The area-based procedure for backcalculating the k-value from deflections 

for rigid pavement analyses was developed in the 1980s and enhanced in the 1990s. (See 

references 27–32.) The best fit method was used in the first round of backcalculation for rigid 

pavement structures and was also selected for use for this study.

Other Methods

Other methods that have been recently developed include the use of artificial neural networks

(ANNs), genetic algorithms, and dynamic backcalculation methods.
5

ANNs

DIPLOBACK is an example of one backcalculation package that uses ANN.

(33) Software 

packages that use ANNs to complete the backcalculation in terms of pattern recognition similar 

to the procedure established by Lytton and Michalak through the SEARCH program.(25) Some 

researchers have developed neural network models using a large synthetic database generated 

from routine finite element analysis software programs, such as ILLI-SLAB for rigid pavements 

and ILLI-PAVE for flexible pavements. (See references 34–40.) Most ANN methods are 

confined to a small infra-space of pavements, and site features and are not used routinely 

by practitioners.

Genetic Algorithms

Multiple programs have been developed based on genetic algorithms. Zhang et al. developed a 

modified genetic algorithm called MGABPLM in 1998, which is based on the Homotopy 

method.

(41) This category of backcalculation has been used very infrequently and only for 

research purposes.

Dynamic Analysis Methods

Dynamic analysis methods require the use of FWD deflection-time histories using frequency and 

time-domain solutions. DYNABACK-F is a program based on dynamic analyses.(42) This 

category of backcalculation packages is complex, requires a lot of data, and as such, is only used 

by a small group within the industry for research purposes.

Summary

Practitioners commonly use iterative and database search backcalculation packages for research, 

pavement evaluation, and rehabilitation design. Unfortunately, none of the programs that fall in 

these categories result in a unique set of modulus values for a specific pavement structure. 

Multiple combinations of elastic layer modulus values with similar errors can exist. This nonuniqueness of solutions is the major reason for debate on which method is the better one and 

which set of layer modulus values is the correct one. The closed form solution package 

ELMOD© is widely used, but it is a proprietary program. Moreover, a closed form solution 

(unique set of layer modulus values) does not necessarily imply a correct or accurate solution.

CANDIDATE BACKCALCULATION PROGRAMS

Many published documents have included a literature review and comparison of backcalculation 

methods. This section includes a brief review of the findings from other studies related to the 

selection and use of candidate backcalculation programs. It also identifies factors that can have a 

significant impact on the results and how those items can be handled as part of executing large 

batch files for production backcalculation.

Comparison of Backcalculation Programs

Rada et al. published a comparison of the features of several computer programs for 

backcalculation.(43) More recently, a European study tabulated the features of 20 different 
6

computer programs used for backcalculation.

(44) Most backcalculation programs rely on 

an elastic layer program to calculate surface deflections and use the iterative or database 

search methods.

Von Quintus and Killingsworth used multiple software packages to backcalculate layer modulus 

from the same deflection basin data for selected LTPP test sections.

(45–47) The following

programs were included in this study: 

• MODULUS 4.2.

(8)

• MODCOMP3© and MODCOMP3.6©.

• WESDEF.

• WESNET.

• MICHBACK 1.0©.

(10)

• FWD-DYN.

These programs were evaluated on the basis of technical merit, functionality, and data processing 

compatibility using 18 test sections located in the LTPP southern region. Von Quintus and 

Killingsworth concluded that one software package should be used because of the large 

differences found between many of the programs. 

Von Quintus and Simpson followed up with a similar study for selecting a package to 

backcalculate elastic layer modulus values for the deflection basins measured on the approach 

and leave ends of each LTPP test section.(4) The approach and leave ends were used because 

many cores were extracted from these locations for layer thickness determination after the first 

round of deflection basin measurements. Von Quintus and Simpson compared multiple packages 

using the following five evaluation factors:

• Accuracy of the program.

• Operational characteristics.

• Ease of use of the program.

• Stability of the program.

• Probability of success.

They recommended the use of MODCOMP4.0© for backcalculating elastic layer moduli.
7

Generally, nearly all previous studies recommended one method over others, recommended 

multiple methods, or determined that all methods compared produced similar results.

The following list summarizes the results from a few other projects that compared 

backcalculation programs:

• Gergis conducted a comparison of ELMOD©, MODULUS, EVERCALC©, 

MODCOMP©, and WESDEF and recommended EVERCALC© for routine 

research use.

(48)

• Al-Suhaibani et al. compared six backcalculation programs (CHEVDEF, ELSDEF, 

FDEDD1, WESDEF, SEARCH, and BISDEF©) and reported that CHEVDEF and 

ELSDEF produced more reliable results than the others.(49)

• Zhou et al. compared EVERCALC©, WESDEF, and MODULUS and reported that the 

results from all three packages were basically the same.

(49) This finding was in direct 

contrast to the finding by Von Quintus and Killingsworth.

(45)

The first backcalculation study sponsored by FHWA for flexible pavements used the software 

package MODCOMP4.0© for consistency of results between linear and nonlinear solutions.

(4)

MODCOMP4.0© was also used for rigid pavements along with a forward calculation procedure

developed by Khazanovich.

(3) MODCOMP4.0© was selected over EVERCALC©, MODULUS, 

and other programs because of its capability and versatility to consider different constitutive 

equations for unbound layers and soils. This same finding was reached in backcalculating layer 

elastic modulus values for multiple local calibration and commercial projects.

(51)

Many agencies have backcalculated layer modulus values for the LTPP test sections located 

within their agency. States in which layer modulus values have been backcalculated from LTPP 

FWD deflection data include Arizona, Colorado, Michigan, Mississippi, Missouri, Montana, 

Ohio, Texas, Utah, Washington, Wisconsin, and Wyoming. EVERCALC©, MODULUS, and 

ELMOD© have been used most extensively for backcalculating in-place elastic layer modulus 

values used in the local calibration studies. However, MODCOMP© and MICHBACK© have 

also been used by selected agencies.(10) The MODCOMP© program was used to generate in-place 

layer modulus values for the global calibration effort of the MEPDG.

(52)

FHWA sponsored two more recent studies related to the use of FWD deflection data and 

backcalculation of layer modulus data (Smith et al. and Rada et al.).(53,5) These two studies and 

reports are referred to throughout this report as the Smith and Rada studies.

(53,5) Both studies 

include a review of FWD deflection data and backcalculation software packages for estimating 

in-place modulus values. The Smith study includes a more extensive review of backcalculation 

methods for both rigid and flexible pavements, while the Rada study was prepared using a 

complete set of deflection data from the LTPP SPS-1 experiment. These literature reviews also 

documented the programs that are being used by different agencies for rehabilitation, evaluation,

and forensic investigations. Knowing the programs that agencies are using is important so that 

the results will be readily useable to as many agencies as possible. 

While both the Smith and Rada studies provide a comparison of backcalculation programs, 

the Smith study includes a more detailed comparison of selected backcalculation packages.(53,5)
8

Both of these studies used case studies from the LTPP program to evaluate and compare the 

results from different software packages. The summaries included in the Smith study and the 

earlier backcalculation projects provide an excellent comparison of the different software 

packages. The Rada study uses the MODULUS and MODCOMP© software packages and found 

that the MODULUS program resulted in many more acceptable solutions.(5) The Smith study 

documented the use of the MODCMOP, MICHBACK©, and EVERCALC© programs and 

found varying results.(53) The EVERCALC© program, however, consistently resulted in lower 

error terms. 

Results from the two literature reviews confirmed the summary of available backcalculation 

programs that have already been summarized in the existing literature. Hall also completed a

similar unpublished literature review of deflection data and backcalculation methods. Hall’s

review included international projects and software packages that are available from outside the 

United States. These summaries and others list and compare the following:

• The maximum number of sensors considered by the software package.

• The maximum number of layers that can be backcalculated depending on the number 

of sensors.

• Nonlinear and linear capabilities and the type of constitutive equations considered by the 

software package.

• Convergence scheme.

• Advantages and disadvantages of the program in relation to its application with the 

MEPDG software.

• Support services for the software.

• Operational properties and physical features of the software.

In summary, many of the backcalculation procedures are similar, but the results can be different 

due to assumptions, iteration technique, backcalculation, or forward calculation schemes used 

within the programs. Some of these methods, such as MODCOMP© and EVERCALC©, also 

have the capability to estimate the elastic layer modulus values and coefficients of nonlinear 

constitutive relationships (stress-sensitivity properties). Specifically, these methods can be 

grouped in those with different constitutive models for describing the behavior between load and 

deflection or stress and strain: linear, quasi-nonlinear, and nonlinear backcalculated modulus 

values. Regardless, results from the backcalculation packages have been debated and questioned 

since their development in the mid-1970s. There is no consensus on the best procedure or the 

one providing the most reliable and accurate results. 

Ground Truth Regarding Backcalculated Modulus Values

The deflection-based elastic moduli represent composite values and do not result in a unique set 

of elastic layer moduli. It is challenging to determine which set of elastic layer moduli represents 
9

the real values and which backcalculation package consistently results in those values. The 

following list contains some points that must be considered in explaining any discrepancy

between the modulus values determined through different techniques and in defining an 

acceptable set of elastic layer moduli:

• The field-derived elastic modulus is an equivalent value for multiple layers of similar 

materials that can have substantial differences in how a material responds to load (see 

figure 1 and figure 2), while the laboratory-measured dynamic or resilient modulus is a 

specific value for one mixture or material. The five arrows included in figure 1 designate 

the individual layers or lifts included in the asphalt concrete core.

• The field-derived elastic modulus is an equivalent value that includes the effects of any 

cracking or fatigue damage in the bound layers, while the laboratory-measured value is 

an intact specimen, either cored from the pavement or compacted in the laboratory.

• Multiple combinations of field-derived elastic modulus values can result from a 

deflection basin, as there is no unique combination of layer modulus values, while a 

unique modulus value is obtained in the laboratory for each test specimen based on the 

specific testing conditions.

• The resulting backcalculated elastic modulus value is dependent on the allowable error 

between the computed and measured deflection basins, while the resulting laboratorymeasured dynamic or resilient modulus value is dependent on the precision and bias of 

the test procedure.

• The resulting backcalculated elastic modulus value is subject to compensating errors 

(increasing and decreasing modulus values of adjacent layers), boundary conditions, and 

stress conditions, while there is no compensating error effect in the laboratory-measured 

dynamic or resilient modulus values.

As an example, five asphalt concrete layers or lifts are shown in figure 1. These five individual 

layers result in different dynamic moduli. The upper three layers are less than 2 inches each,

which are too thin for backcalculating the elastic moduli from deflection basins. The 

backcalculation process would combine all layers into one hot mix asphalt (HMA) layer for 

which an equivalent or composite elastic modulus would be determined from the deflection 

basins. One main issue is that these structures, which are typical, increase the variance between 

the laboratory measured and backcalculated modulus values. Some procedures combine the 

laboratory measured values into an equivalent modulus using the equivalent modulus concept.

It is difficult, if not impossible, to determine the ground truth values because of the simplifying 

assumptions used in all backcalculation programs. More importantly, there is significant debate 

within the pavement engineering community of what constitutes ground truth. Thus, the software 

packages that result in values consistent with the perceived realistic values and results between 

multiple programs were used in selecting the candidate packages to be used in the case studies as 

well as for the production runs.
10

Figure 1. Photo. Core recovered from an LTPP test section used to equate laboratorymeasured modulus values to backcalculated elastic modulus values (Texas SPS-5 section).
11

Figure 2. Photo. Cross-section of the pavement layers exposed during a forensic 

investigation to measure the rutting within individual pavement layers 

(Arizona SPS-1 section).

Factors Considered in Selecting Candidate Programs

The following factors were considered in selecting candidate programs for use in the 

case studies:

• Probability of success in matching measured to calculated deflection basins: This 

was a difficult factor to consider between software programs because the real in-place 

modulus values were unknown, and the lowest error or difference between the measured 

and calculated deflection basins did not necessarily mean the layer modulus values were 

more correct than another set with a slightly higher error. Different error terms are used 

by different backcalculation programs which represent different values. The root mean 

squared error (RMSE) term was used in comparing the candidate programs. It was 

assumed that a “good” match between the calculated and measured deflection basins (low 

RMSE) is a reasonable estimate of the in-place values. 
12

• Applicability to diverse pavement structures and layer conditions: If possible, the 

same program should be applicable and used for all pavement types included in the LTPP 

database. These include thin and thick HMA pavements; HMA overlays of flexible, rigid, 

rubblized, and recycled layered pavements; jointed plain concrete pavement (JPCP), 

jointed reinforced concrete pavement (JRCP), continuously reinforced concrete pavement 

(CRCP), and portland cement concrete (PCC) overlays of rigid pavements. It is a 

possibility that the same package might not be applicable for all pavement types. Results 

from the case studies included in the demonstration did result in the use of a primary and 

a secondary package.

• Capability to execute large batch files: From a production standpoint, this was an 

important requirement. Any package without the capability to execute large batch files 

was excluded from further consideration for making the production runs.

• Maximum number of layers for which the layer modulus values can be determined 

from the deflection basins: The maximum number of five layers was used in the 

backcalculation process, including a bedrock layer when present. A backcalculation study 

sponsored by FWHA in 1997 included determining the modulus of HMA layers with 

stripping, foundation layers below and above the water table depth, and selected 

stabilized layers.

(46)

• Software package is available in the public domain: This factor takes into account the 

ease with which other agencies may procure the same software. It is important for future 

use to backcalculate layer moduli as more deflection basins are added to the LTPP 

database so it can be used by other agencies to backcalculate modulus values for their 

own roadway segments to be consistent with LTPP, if desired.

• Soundness of the technical approach used in the backcalculation algorithm and its 

relevance to the MEPDG procedures: Results from the backcalculation process need to 

be applicable for use in the MEPDG because many agencies are using or are planning to 

use the MEPDG for pavement design.(1)

• Speed of convergence: Speed of convergence of the software package to determine the 

set of layer modulus values is important for large production runs. In addition, the 

iteration process for convergence can be a consideration for the production runs. Speed of 

convergence is a preferred feature in a program but is not considered a critical factor. 

Accuracy and lack of bias are more salient features.

Six programs were selected for use in the case studies for calculating layer stiffness properties 

from deflection basins on a production basis. The selection of these six programs was based on 

the results and recommendations from published documents and, to a minor degree, on the 

experience of the authors. Table 1 summarizes the features of the six packages selected for use in 

the case studies.
13

Table 1. Backcalculation software packages used in the case studies.

Feature of Packagea

Backcalculation Software Packages/Methods

BAKFAA(6) EVERCALC©(7) MICHBACK©(10) MODCOMP©(9) MODULUS(8)

Area 

Methodb

Backcalculation 

method

Iterative Iterative 

(optimization)

Raphson-Newton Iterative Database 

(optimization)

Closed form 

solution

Convergence scheme Sum of squares 

of absolute error

Sum of absolute 

error

Least squares Relative deflection 

error at sensors

Sum of relative 

squared error

N/A

Non-linear analysis 

capability

No Yes, limited No Yes No No

Visual image of 

basin convergence

Yes Yes No No No N/A

Pavement type 

specific

Rigid and 

flexible

Rigid, flexible, 

and composite

Flexible and

composite

Rigid, flexible, and

composite

Flexible Rigid and

composite

Forward response 

calculation method

Multilayer 

elastic theory

Multilayer elastic 

theory

Multilayer elastic 

theory

Multilayer elastic 

theory

Multilayer 

elastic theory

Closed form 

solution

Ability to fix 

modulus

Yes Yes Yes Yes Yes No

Maximum number of 

Layers

5 5 3 5 4 2

Layer interface 

analysisc

Variable Fixed Fixed Fixed Fixed Fixed

N/A = Not applicable. a

Forward calculation methods used to determine seed values for the backcalculation procedures are not listed in this table. b

The best fit method was evaluated simultaneously, and the differences in the computed values as well as the feasibility to automate the procedure were evaluated. 

In addition, the forward calculation spreadsheets prepared using the Hogg model were used.

(26)

c

The layer interface condition was selected to be consistent with the field distress development.
14

STANDARDIZATION OF BACKCALCULATION PROCESS

The first version of ASTMD 5858-96(2015), Standard Guide for Calculating In Situ Equivalent 

Elastic Moduli of Pavement Materials Using Layered Elastic Theory, was published in 1996 and 

last updated in 2008.

(54) This guide presents the concepts for backcalculating pavement layer 

elastic modulus values from measured deflections using elastic layer theory. The guide does not 

address adjustments for load level, frequency, temperature, or seasonal variation. Since the 

backcalculation guidance provided in ASTM D5858-96 is based on elastic layer theory, it is 

applicable to flexible pavements and only to a limited extent to rigid pavements (i.e., interior 

loading and slab size/stiffness ratios less than 8). Neither ASTM International nor the American 

Association of State Highway and Transportation Officials (AASHTO) has approved further 

standards or guidance. As such, ASTM D5858-96 was followed in backcalculating elastic 

layer moduli.
15

CHAPTER 3. CASE STUDIES

The purpose of the case studies conducted in phase I of this project were twofold: (1) select 

the forward and/or backcalculation methods from the candidates identified in chapter 2 and 

(2) provide direction for automating the backcalculation process by establishing the 

decisionmaking criteria in evaluating the results. In addition, results from the case studies 

were used to confirm the rules of simulation in establishing the pavement structure on an 

automated basis.

LTPP TEST SECTIONS SELECTED FOR CASE STUDIES

Test sections from the LTPP SPS and SMP experiments were selected because deflection basins 

for these experiments were measured at shorter time intervals than for the GPS experiments. 

Six case studies were used to compare and evaluate the candidate backcalculation and forward 

calculation programs and to demonstrate the different pre- and post-processing tools to be used 

for the production runs. The LTPP projects selected for the case studies are listed in table 2. The 

reasons for selecting these sites are as follows:

• Two of the case studies are LTPP SMP sites. The reason for selecting these seasonal sites 

was to estimate the variation in elastic modulus values over temperature and other 

seasonal changes as determined from deflection basins. One of the seasonal sites included 

in the demonstration is a rigid pavement (Utah 49-3011), and the other is a flexible 

pavement (Georgia 13-1005).

• Three case studies represent newly constructed pavements—two new construction 

flexible pavements from the SPS-1 experiment (Iowa and Wisconsin) and one new 

construction rigid pavement from the SPS-2 experiment (North Carolina). These projects 

were selected to include a wide range of layer thicknesses and materials for both 

pavement types.

• Two case studies represent rehabilitated or overlaid pavements—one from the SPS-5 

experiment (rehabilitated flexible pavements) and one from the SPS-6 experiment 

(rehabilitated rigid pavements). The sections selected are from the Mississippi SPS-5 

project to include varying HMA overlay mixtures (virgin and recycled asphalt pavement 

mixes) and layer thicknesses, while sections were selected from the Oklahoma SPS-6 

project to include varying types of treatments to the existing PCC slabs. 

Table 2. LTPP test sections used for the case studies.

Pavement 

Type New Construction Sites Rehabilitation Sites SMP Sites

Rigid North Carolina SPS-2: all 

sections

Oklahoma SPS-6 intact 

and rubblized sections

49-3011 

(Utah)

Flexible Wisconsin SPS-1 sections 

0113, 0116, and 0119; Iowa 

SPS-1 sections 0101, 0106, 

and 0109

Mississippi SPS-5

control, virgin, and 

recycled asphalt 

pavement sections

13-1005 

(Georgia)
16

COMPARISON OF RESULTS FROM CANDIDATE BACKCALCULATION 

PROGRAMS

This section provides a brief comparison of the results between the candidate backcalculation 

software packages in terms of the evaluation factors set forth in chapter 2. The BAKFAA and 

MICHBACK© programs were dropped from further consideration because of issues encountered 

in executing large batch files for the first few case study sites.(10) For the other four programs, 

three criteria were used in judging the acceptability of the results from the candidate forward and

backcalculation methods: RMSE values, magnitude of the moduli, and comparison to laboratorymeasured modulus values.

Deflection Basin Matching—RMSE

Figure 3 summarizes and compares the average RMSE values resulting from the backcalculation 

of layer moduli at each test section and day of testing. As shown, MODTAG© consistently had 

lower RMSE values, while MODULUS consistently had higher RMSEs.1(55) Many of the 

MODTAG© RMSE values were less than 1 percent. EVERCALC© and MODTAG© also had a

higher percentage of stations with less than 2 percent RMSE. Based on the RMSE values, 

MODTAG© and EVERCALC© consistently resulted in a closer match between the measured and 

calculated deflection basins. The MODULUS program exhibited higher RMSE values in almost 

all cases for the two conditions: assuming the presence and absence of an apparent rigid layer

or bedrock.

Figure 3. Graph. Comparison of RMSE values between backcalculation programs for 

flexible pavement sections comparing MODULUS, MODTAG©, and EVERCALC©.

Figure 4 summarizes and compares the average RMSEs from the best fit forward calculation 

method and EVERCALC©. As shown, the RMSEs from the best fit method were significantly 

higher than from the EVERCALC© program. This observation is in line with the authors’ 

experience from other projects with using the forward calculation equations based on the Hogg

 1

MODTAG© includes various data subroutines for evaluating the deflection basin data and uses MODCOMP© for the backcalculation process. 

MODTAG© was used in the comparison of the programs within the first phase of the project. However, MODCOMP6© was used for the 

production or batch runs under the second phase of the project.
17

model for flexible pavements—the forward calculation program resulted in sets of layer moduli 

with significantly higher RMSE values than the backcalculation program.(26)

Figure 4. Graph. Comparison of RMSE values between backcalculation programs for rigid 

pavement sections comparing best fit method and EVERCALC©.

Distribution of Elastic Moduli

The range of default elastic modulus values included in the MEPDG was used to define the

initial acceptable range of elastic modulus values for comparing the results between different 

programs for different materials and soils.

(1) The percentage of values within the acceptable 

range of moduli with RMSE less than 2 percent is summarized in the interim report for this 

project.(13) EVERCALC© exhibited a higher percentage of stations for which moduli were 

calculated within the typical range for the specific material in question. Backcalculated layer 

moduli for individual stations were outside the acceptable range of values, but the averages and 

majority of stations were within the range of typical values.

The distribution of resulting layer moduli for each layer during a day’s testing can be used to 

investigate the reasonableness of the results. Figure 5 shows the distribution of results for the 

crushed stone base material at the Georgia 13-1005 site, which exhibits a normal distribution. 

This type of distribution is typical of many pavement materials. In fact, many of the layers 

(bound and unbound) exhibit this type of distribution.
18

Figure 5. Graph. Normal distribution of calculated elastic modulus for a crushed stone 

base aggregate.

Conversely, figure 6 shows a bimodal distribution of results for the weathered soil layer at the 

Georgia 13-1005 site. A bimodal distribution can reflect a change in the results caused by 

changing material properties or thickness deviations along the section, compensating errors 

between two layers, and/or hitting a boundary condition or limit at multiple stations. Based on a 

review of previous backcalculated layer modulus values in the LTPP database, the results can 

also exhibit a uniform distribution.

(4,46) However, none of the test sections included in the case 

studies exhibited this type of distribution.

Figure 6. Graph. Bimodal distribution of calculated elastic modulus for the weathered soil 

layer.

Layer Stiffness Properties of Flexible Pavements

Figure 7 through figure 11 provide a comparison of the results from the candidate 

backcalculation methods in terms of elastic layer moduli for different layer or material types.
19

Figure 7. Graph. Comparison of backcalculated moduli from the candidate programs for 

the HMA layer.

Figure 8. Graph. Comparison of backcalculated moduli from the candidate programs for 

the asphalt stabilized base layer.
20

Figure 9. Graph. Comparison of backcalculated moduli from the candidate programs for 

the weathered soil layer modulus values.

Figure 10. Graph. Comparison of backcalculated moduli from the candidate programs for 

the natural subgrade modulus values.
21

Figure 11. Graph. Comparison of backcalculated moduli from the candidate programs for 

aggregate base layers.

The following list summarizes the results related to selection of the backcalculation programs for 

flexible pavements:

• All three programs (EVERCALC©, MODCOMP©, and MODULUS) resulted in similar 

values with a lot less difference between the elastic layer moduli calculated by different 

procedures for the surface layer (figure 7) and subgrade (figure 10), regardless of the type 

of deflection basins.

• All three programs resulted in the same elastic layer moduli for the conditions when the 

deflection basins would be categorized as typical as defined by Von Quintus and 

Simpson and Von Quintus and Killingsworth.(4,46) For the type II deflection basins, as 

defined by Von Quintus et al., the three programs resulted in different elastic layer 

moduli for the intermediate layers (i.e., the weathered soil layer and thinner aggregate 

base layers) (see figure 9 through figure 11).(46)

• All three programs correctly identified some form of damage that was observed through 

forensic investigations or surface distress recorded in the LTPP database. Stripping, 

moisture damage, and debonding were identified as issues by all three programs.

• The MODULUS program consistently generated sets of layer moduli that exhibit much 

higher RMSE values than for EVERCALC© and MODCOMP©, while MODCOMP©

consistently resulted in slightly lower RMSEs than EVERCALC© (see figure 3 and 

figure 4).

A t-test was used to determine if the average test day results from the two candidate programs 

with the lower RMSE values (EVERCALC© and MODCOMP©) were statistically indifferent.

Table 3 provides a summary for a few of the test sections from three of the case studies. Both 

EVERCALC© and MODCOMP© resulted in indifferent elastic moduli for many of the test 

sections. About a fourth of the layers, however, resulted in statistically different datasets. The 
22

majority of the test sections with statistically different moduli were those for which the majority 

of the deflection basins are classified as type II. 

Table 3. Comparison of datasets from selected LTPP flexible test sections.

Test 

Section

Number 

of Test 

Days

Layer 

Designation

EVERCALC©

Results

MODCOMP©

Results

Comments

Average

Elastic 

Modulus

Standard 

Deviation

of Elastic 

Modulus

Average

Elastic 

Modulus

Standard 

Deviation

of Elastic 

Modulus

Georgia

13-1005 29

Aggregate 

base

16.38 3.23 23.72 11.91 Statistically 

different 

Subgrade 62.16 2.84 60.25 3.61 datasets

Iowa

19-1001 7

Aggregate 

base

13.98 5.84 13.43 11.84 Statistically 

indifferent 

Subgrade 20.37 1.67 20.41 3.70 datasets

Mississippi

28-0501 7

Asphalttreated base

(ATB)

790.4 291.6 918.6 268.8 Statistically 

indifferent 

datasets Subgrade 54.43 15.65 55.35 14.18

Layer Stiffness Properties of Rigid Pavements

The primary material properties needed for completing a rigid pavement rehabilitation design or 

evaluation in accordance with the MEPDG are the k-value of the lower pavement layers and 

subgrade, the static elastic modulus for the PCC, and the resilient modulus of aggregate base 

layers.(1) The area and best fit closed form solution methods were used to estimate the elastic 

modulus of the PCC and aggregate base layers and the k-value for the combined lower pavement 

layers and subgrade. 

Figure 12 includes a comparison of the elastic modulus calculated with EVERCALC© and the 

moduli calculated using the area and best fit methods. As shown, the resulting elastic layer 

moduli from the EVERCALC© program and the area method are variable but have minimal bias 

between the two. In addition, the unbonded condition of the best fit method has less bias than its 

bonded condition to EVERCALC©. The bonded condition simply means the two layers are tied 

together, while the unbonded condition means the two layers are not tied together, and there is no 

shear transfer between the two layers. This brings up an issue of which method should be used in 

computing the elastic modulus of the PCC layer, the area or best fit method, as well as which 

condition should be simulated, bonded, or unbonded.
23

Figure 12. Graph. Backcalculated layer PCC modulus from EVERCALC© compared to the 

elastic modulus calculated with the area and best fit methods.

The best fit method (unbonded condition) was selected for rigid pavements because it was used 

for global calibration for the MEPDG under NCHRP Project 1-37A.

(52)

Figure 13 and figure 14 show a comparison of results for the subgrade and aggregate base layers

between EVERCALC© and the best fit unbonded condition, while figure 15 shows a comparison 

of results for PCC layers. The best fit method resulted in significantly different or lower elastic 

layer moduli than EVERCALC© for PCC (figure 12 and figure 15), while the bias was much less 

between the computed elastic layer moduli of the base layer between the best fit method and 

EVERCALC© (figure 14).

Figure 13. Graph. Comparison of forward and backcalculated moduli from the candidate 

programs for the subgrade layer.
24

Figure 14. Graph. Comparison of forward and backcalculated moduli from the candidate 

programs for the aggregate base layer.

Figure 15. Graph. Comparison of forward and backcalculated moduli from the candidate

programs for the PCC layer.

The t-test was used to determine if the average test day results from the forward and 

backcalculation programs were statistically indifferent. Table 4 provides a summary for a few of 

the test sections from three of the case studies for rigid pavements. As shown, the forward and 

backcalculation methods (best fit method and EVERCALC©) resulted in significantly different 

PCC elastic moduli for most of the test sections, while about half of the test sections resulted in 

significantly indifferent elastic moduli for the base layer. This large bias between EVERCALC©

and the best fit method can have a critical impact in determining the PCC elastic modulus for 

input into the MEPDG.(1) This issue of bias is discussed further in the next section.
25

Table 4. Comparison of datasets from selected LTPP rigid test sections.

Test 

Section

Number 

of Test 

Days

Layer 

Designation

EVERCALC© Results MODCOMP© Results

Comments

Average

Elastic 

Modulus

Standard 

Deviation

of Elastic 

Modulus

Average

Elastic 

Modulus

Standard 

Deviation

of Elastic 

Modulus

North 

Carolina

37-0201

48

PCC 5,795.5 601.3 3,125.5 1,601.8 Statistically 

different 

datasets

Aggregate 

base

46.8 27.4 20.8 10.7

Utah

49-3011 37

PCC 6,584.7 1,167.0 2021.2 570.6 Statistically 

different 

datasets

Stabilized

base

665.6 718.9 570.6 114.1 Statistically 

indifferent 

datasets

Oklahoma

40-0601 7

PCC 4,749.9 418.2 2,461.5 1,099.3 Statistically 

different 

datasets

Aggregate 

base

12.5 4.9 16.4 7.3 Statistically 

indifferent 

datasets

Field-Derived and Laboratory-Measured Layer Stiffness Properties

PCC Materials

Static elastic moduli for the PCC layers were extracted from the LTPP database. Figure 16

compares the laboratory-measured elastic moduli and backcalculated values for the PCC layers. 

As shown, the results from EVERCALC© and the best fit method are highly variable in 

comparison to the measured PCC static modulus. The average elastic modulus ratio (i.e., E-ratio 

between the laboratory-measured and field-derived elastic moduli) for the PCC layer are

as follows:

• EVERCALC©: Mean E-ratio = 0.77; standard deviation = 0.176.

• Best fit method bonded: Mean E-ratio = 1.92; standard deviation = 1.254.

• Best fit method unbonded: Mean E-ratio = 1.00; standard deviation = 0.436.

Results from the EVERCALC© program exhibited a coefficient of variation of 23 percent for the 

averages, which is much lower than the best fit method, which had a coefficient of variation of 

65 percent for the bonded condition and 44 percent for the unbonded condition.
26

Figure 16. Graph. Comparison of backcalculated and laboratory-measured PCC moduli.

2

The best fit bonded condition significantly underpredicted the measured values, while 

EVERCALC© overpredicted the measured values. On average, the best fit unbonded condition 

resulted in no bias.

In summary, there is a significant difference between the resulting PCC elastic moduli from 

EVERCALC© and the best fit method. The best fit unbonded condition resulted in an unbiased 

prediction of the laboratory-measured values. Assuming laboratory elastic moduli are used in the 

global or local calibration effort, an adjustment needs to be made to the EVERCALC© dataset for 

use with the MEPDG software, similar to using the c-factor for unbound layers.

(45,46,1)

HMA and Bituminous Stabilized Materials

Backcalculated elastic layered moduli from deflection basins are used in the MEPDG for the 

rehabilitation and evaluation of flexible pavements.(1) Dynamic modulus values are estimated 

using the Witczak regression equation included in the MEPDG to represent the undamaged 

condition of HMA mixtures. These same values were calculated using the dynamic modulus 

regression equation from the MEPDG and included in the LTPP databases for the HMA and 

other bituminous layers.(1)

Dynamic moduli for the HMA layers were extracted from the LTPP database. Figure 17 through

figure 26 compare the laboratory estimated dynamic moduli and backcalculated values for the 

HMA layers. As shown, most of the backcalculation programs underpredict the laboratorymeasured values for the loading frequency typically used for the FWD (25 Hz). All 

three backcalculation programs resulted in similar average values on a day of testing basis 

for many of the test sections, but not all. 

 2

Some of the PCC elastic modulus values from the best fit unbonded condition exceeded 10 million psi, and these are not shown in the figure. 

These high elastic moduli resulted in a much higher standard deviation than for the EVERCALC© method. 
27

Figure 17. Graph. Comparison of backcalculated HMA surface and binder layer moduli 

and laboratory-measured moduli from the Iowa SPS-1 project.

Figure 18. Graph. Comparison of backcalculated HMA base layer moduli and laboratorymeasured moduli from the Iowa SPS-1 project.
28

Figure 19. Graph. Comparison of backcalculated HMA surface and binder layer moduli

and laboratory-measured moduli from the Wisconsin SPS-1 project.

Figure 20. Graph. Comparison of backcalculated HMA base layer moduli and laboratorymeasured moduli from the Wisconsin SPS-1 project.
29

Figure 21. Graph. Comparison of backcalculated HMA overlay moduli and laboratorymeasured moduli from the Mississippi SPS-5 project.

Figure 22. Graph. Comparison of backcalculated HMA surface layer moduli of the existing 

pavement after overlay placement and laboratory-measured moduli from the Mississippi 

SPS-5 project.
30

Figure 23. Graph. Comparison of backcalculated HMA surface layer moduli of the existing 

pavement prior to overlay placement and laboratory-measured moduli from the 

Mississippi SPS-5 project.

Figure 24. Graph. Comparison of backcalculated HMA base layer moduli of the existing 

pavement prior to overlay placement and laboratory-measured moduli from the 

Mississippi SPS-5 project.
31

Figure 25. Graph. Comparison of backcalculated HMA moduli and laboratory-estimated 

dynamic modulus for the Oklahoma SPS-6 project.

Figure 26. Graph. Comparison of backcalculated HMA moduli and laboratory-estimated 

dynamic modulus for the Georgia SMP project.

In summary, there is an insignificant difference between the resulting HMA elastic moduli from 

EVERCALC©, MODULUS, and MODCOMP©, but none of the programs resulted in unbiased 

predictions of the laboratory-measured values. This observation is important because it supports 

the MEPDG methodology for using FWD testing and backcalculated layer moduli of HMA 

layers for estimating the damage in those layers.(1) The sites that exhibited greater dispersion 

between the laboratory-estimated (undamaged dynamic moduli) and field-derived (damaged 

elastic moduli) moduli were found to have stripping or moisture damage and/or extensive 

cracking reported in the LTPP database. 

Unbound Materials

Figure 27 through figure 29 compare the backcalculated elastic moduli from EVERCALC©,

MODULUS, and MODCOMP©, respectively, and the laboratory-derived resilient moduli for 

each site for the weathered soil and subgrade layers. As shown, there is a lot of dispersion 
32

between the results, but the results are somewhat consistent with some of the earlier studies.(45,46)

The average c-factors calculated for the subgrade layers using the three candidate programs are 

as follows:

• EVERCALC©: Average c-factor = 0.35; standard deviation = 0.136.

• MODCOMP©: Average c-factor = 0.36; standard deviation = 0.146.

• MODULUS: Average c-factor = 0.41; standard deviation = 0.266.

Results from EVERCALC© exhibited a coefficient of variation of 39 percent for the averages, 

which were about equal to the results from MODCOMP© with a coefficient of 40 percent but 

much lower than the results from MODULUS, which had a coefficient of variation of 65 percent.

Figure 27. Graph. Comparison of backcalculated elastic moduli of unbound layers using 

EVERCALC© and laboratory-derived resilient modulus.
33

Figure 28. Graph. Comparison of backcalculated elastic moduli of unbound layers using 

MODULUS and laboratory-derived resilient modulus.

Figure 29. Graph. Comparison of backcalculated elastic moduli of unbound layers using 

MODTAG© and laboratory-derived resilient modulus.

CASE STUDY SUMMARY

Candidate programs were used to estimate elastic layer modulus values for the same deflection 

basins. Observations from the case studies were the same as those documented in the Smith 

study.

(53) EVERCALC© consistently resulted in lower error terms and a higher number of 

successful modulus determination when considering all deflection basins. When only 

considering those deflection basins that ran successfully, the MODCOMP© program resulted in 

the lower RMSE values.

The results from the case studies suggest the use of multiple software packages for various 

pavement types. Thus, two software packages and one method were selected for use in the 

production runs for flexible and rigid pavements: EVERCALC© and MODCOMP© for flexible 
34

pavements and those two plus the best fit method for rigid pavements. EVERCALC© was 

selected as the primary package, while MODCOMP© was used to confirm discrepancies or 

anomalies identified by EVERCALC©. Another reason for selecting MODCOMP© is that

EVERCALC© is restricted to five layers, including a rigid layer if present, while MODCOMP©

can simulate up to seven layers.
35

CHAPTER 4. BACKCALCULATION PROCESS

One of the difficulties in backcalculation is that no unique solution or set of elastic layer moduli 

for a specific set of measured deflection basins is determined. More importantly, the quality of 

the results is heavily dependent on the knowledge and expertise of the user in setting up the 

problem. In other words, different users can obtain different results for the same set of deflection 

basins. This non-uniqueness of solutions has been a major deterrent for some agencies to take

full advantage of backcalculation methods for routine rehabilitation design. Many agencies limit 

use of the deflection data to determine the subgrade elastic modulus. Thus, a key goal of this 

project was to automate the process and make it less dependent on the user so that others not 

directly involved in the development of the tools and procedures can recreate the results.

This chapter provides a general overview of the backcalculation process. In addition, it discusses

the steps and decisions that were automated in setting up the problem and describes the tools 

written to simplify the backcalculation process while taking full advantage of the entire 

deflection basin data for rehabilitation design in accordance with the MEPDG.

(1) The criteria 

used for determining whether the results are acceptable are also included in this chapter. The

automated process is specific to LTPP and the data structure/tables included in the LTPP 

database. However, the steps and activities presented here can be used to improve the

backcalculation of elastic layer moduli for individual rehabilitation projects.

Backcalculation Procedures and User Guide for Software Programs and Utility Tools includes a 

user’s guide for the automated backcalculation process as well as executing the utility and 

software tools for organizing the results included in the CPTs in the LTPP database.

(56) This 

chapter summarizes the decisions for the pre-processing part as well as the generation the inputs 

for the backcalculation programs and a review of the results for acceptability.

OVERVIEW OF PROCESS

Figure 30 shows a simplified flowchart of the major steps and decisions used in the 

backcalculation process.
36

Figure 30. Flowchart. Major steps and decisions in linear elastic backcalculation process.

(4)

• Load-Response Classification

• Deflection Basin Classification

• Section Uniformity Classification

1. Data Extraction

2. Classify Test Section

Establish Analysis Sections 

from Deflection Data.

Average deflections for a specific drop 

height at each test point location.

Select random test points for trial 

l i

Are most of 

the results 

reasonable?

3. Determine Input to 

Software Package. Revise one or more 

inputs (combine 

different layers, 

apparent rigid layer, 

etc.).

Select initial layer-sensor 

assignment, if applicable.

5. Mass Backcalculation of 

deflection basin data.

Decide on number of 

subgrade layers.

No

Yes

Are the other results reasonable (RMS 

error & E-values)?

Are there 

insensitive layers?

Yes No

6. Store results in 

summary tables.

4. Trial Computations.

Determine cross-section 

(layer type & thickness); 

combine “like” layers.

Determine Poisson’s ratio for 

each layer.

Determine depth to apparent 

rigid layer.

Execute software for specific test points 

& deflection basin data.

Assume E-value for 

insensitive layer & revise 

layer-sensor assignment.

Yes

No

NOTE: 

Averaging of the

deflection basins 

applies to the site 

& deflection basin 

characterization.
37

The following list explains the major steps and activities for each step:

1. Extract the following data needed for the backcalculation and interpretation of results:

• Deflection basin data and associated information (dates and times of testing, 

temperatures, etc.).

• Sensor location or offset distance.

• Pavement cross section (layer types and thicknesses).

• Maintenance and rehabilitation activities. The maintenance and rehabilitation history of 

the selected sections were used for establishing the layering of each section with time.

• Shoulder or boring information from the deeper samples. A macro was written to identify 

selected words on the boring logs to determine the depth to refusal or some hard layer as 

well as the depth to a saturated or wet layer.

• Information on the types and magnitudes of distress along the test section.

• Distress data measured over time, specifically, the distresses that affect the load-response 

behavior (cracking and distortion (rutting and faulting)).

2. Categorize test section and deflection basin data to identify anomalies and determine if there 

is an issue with the deflection basins. The important point of this step is to determine if the 

categories changed during different testing dates. If there appears to be a problem with the 

deflection basins within a specific date that is different from the others, these are marked 

and coded. Steps include the following:

• Execute the deflection basin and load-deflection response classification. All deflection 

basins were characterized by the same four categories established by Von Quintus and 

Simpson: type 1, type 2, type 3, and typical.(4) The decision criteria for the categories are 

included in a flow chart in Backcalculation Procedures and User Guide for Software 

Programs and Utility Tools.

(56)

• Execute the Sensor Location Independent Check (SLIC) program within MODTAG© to 

confirm or check any anomaly identified.

3. Determine structure or layering assumptions to be used as follows:

• Identify insensitive layers; assume the modulus of an insensitive layer or combine it with 

an adjacent layer.

• Combine similar and adjacent layers but separate significantly different and thick soil 

strata as well as thick aggregate layers.

• Identify layer anomalies and potential problem layers, such as sandwich sections, stiff 

soils above weaker or saturated soils, etc.
38

• Estimate depth to apparent rigid layer.

• Estimate depth to the water table.

4. Format deflection basin data into the requirements of the software package and set up 

preliminary trial runs. Most of the inputs are the same between the different programs, but 

the format for the deflection basin data is different. Steps are as follows:

• Execute trial computations.

• Compare the results with the allowable RMSE and acceptable modulus values for the 

layers and materials in question.

• Review adjacent layer modulus ratios between unbound layers to identify unrealistic or 

improbable conditions.

• Make any necessary adjustments to the layering assumptions.

5. Execute mass or batch backcalculation of deflection basin data for a specific site.

6. Extract and store results in summary tables from the backcalculation package (discussed

further in chapter 5).

Backcalculation Programs

As discussed in chapter 3, two backcalculation programs and one method were used in step 5 and 

are described as follows:

• EVERCALC© was the primary program used for the analyses and was used for all data

and all pavement types in LTPP. The pre- and post-processing utility tools for the

EVERCALC© analyses were fully automated. The automation process included the 

generation of input files based on pavement simulation rules, the execution of 

EVERCALC©, and post-processing the results.

• MODCOMP6.0© was used as the auxiliary program to backcalculate results for those 

LTPP sections that did not yield acceptable results with EVERCALC©. The 

MODCOMP© analyses were semi-automated as an iterative approach, and the simulated

backcalculation structure was selected on a case-by-case basis until the results converged

within the selected criteria. A few test sections or portions of test sections did not

converge to produce satisfactory results even after multiple efforts using EVERCALC©

and MODCOMP©. Chapter 5 provides more information on the feedback reports and 

error flags to identify these sections as part of the post-processing process.

• The best fit method was used to analyze LTPP sections with a PCC surface to obtain the 

subgrade k-value and the elastic moduli of the PCC and base layers. The PCC and base 

modulus values were determined for two interface conditions—bonded and unbonded.
39

Prior to the execution of the backcalculation programs, the project team established the criteria 

for establishing a quantitative measure for categorizing the validity of the backcalculated 

modulus values. This was based on two parameters: the generated RMSE and the magnitude of 

the backcalculated modulus value for each layer depending on the layer type and layer category.

The RMSE criterion was set at 3 percent (i.e., for the results to be valid, the RMSE needed to be 

at or below 3 percent). Also, the backcalculated modulus value for each layer had to fall within 

the acceptable or atypical range for each material type (see Backcalculation Procedures and 

User Guide for Software Programs and Utility Tools).

(56) It was envisioned that all results would 

ultimately be categorized as follows and defined by the assigned ERROR_STATUS, which is a 

term used to identify the RMSE magnitude in a column within the LTPP backcalculated elastic 

layer moduli computed parameter table database:(57)

• Accept: This includes basins for which the RMSE values were less than or equal to 

3 percent, and the backcalculated modulus results were within the specified acceptable 

range for each layer. The range specified for each layer depended on the layer type and 

layer category, which are discussed in Backcalculation Procedures and User Guide for 

Software Programs and Utility Tools.

(56)

• Atypical: This includes basins for which the RMSE values were less than 3 percent and

the backcalculated modulus values exceeded the acceptable range but were within the 

atypical range as defined in Backcalculation Procedures and User Guide for Software 

Programs and Utility Tools.

(56)

• Error: This includes basins for which the RMSE values exceeded 3 percent and/or the 

backcalculated modulus values exceeded the atypical range defined in Backcalculation 

Procedures and User Guide for Software Programs and Utility Tools.

(56)

The error status for the best fit results was based on the modulus values of the PCC and the base 

layers for the bonded condition. Additionally, the RMSE4 value, which is the RMSE value 

determined from the measured and computed deflections for the four sensors used in the best fit

analysis, was the basis for assigning the error status for the best fit method. 

All programs were executed in a batch mode process on a state-by-state basis to handle the large 

volume of deflection basins in the LTPP database. Most of this chapter focuses on the decisions 

made in automating the process to determine inputs to the EVERCALC© and MODCOMP©

programs. The best fit method provides unique solutions for PCC-surfaced pavement using a 

three-layered structure. Appendix A provides more detailed information on the computations and 

equations used to calculate the unique solutions from selected sensors within the deflection 

basin. Some revisions were made to the method that was originally developed during the first 

round of backcalculation sponsored by FHWA.

(3) Thus, appendix A focuses on describing the 

mathematics used to calculate the elastic modulus and k-value of the PCC-surfaced test sections.

The EVERCALC© and MODCOMP© analyses were performed in four main analysis phases.

Each phase progressively identified and filtered out those cases with poor quality results and 

made appropriate adjustments to the analysis parameters to improve the convergence in the 

subsequent phase. The first phase included all LTPP data, while the second used a subset from 
40

the first phase. The third and fourth analysis phases, if required, used a subset from the second 

phase. The four phases include the following:

1. The first analysis phase included EVERCALC© analysis for all LTPP sections using material 

parameters selected to represent typical ranges of inputs values for each material/layer type.

Results from the first phase analyses were examined to classify them into the accept, 

atypical, or error categories described previously.

2. The second analysis phase included an expanded modulus range for the analyses of the LTPP 

test sections or test days with more than 25 percent atypical (i.e., invalid) results in the first 

phase analysis (converged to one of the boundary limits with RMSE values less than 

3 percent) and RMSE values for the other stations being less than 5 percent. If the majority of 

the results converged to one of the boundary modulus values and resulted in high RMSE 

values (greater than 5 percent) defined as errors, the results and pavement simulation 

structure were manually reviewed based on compensating error effects (two layers resulted in 

hitting upper and lower modulus boundary limits) and the potential for layer anomalies.

3. The third analysis phase included test days with erroneous results at the end of the second 

phase and was performed using MODCOMP©. Results from the second phase were evaluated 

between multiple test days for inconsistency in results. The focus of the third phase was 

performing a manual review of the results and making appropriate revisions of the simulated 

structure to obtain acceptable results. The pavement structure simulation was revised based 

on whether the second phase results showed an invalid layer modulus, whether there were 

compensating errors (defined in chapter 5), whether extensive distresses were present, and 

whether the potential for layer anomalies could exist.

4. In some cases, a fourth analysis phase analysis was performed using MODCOMP© and a 

revised pavement simulation structure based on the results from the second and third analysis 

phases. If unacceptable results were obtained after the fourth phase, no additional analyses 

were completed.

LTPP Data

The deflection data were extracted from LTPP Standard Data Release (SDR) 27.0 (released in 

2013) and included specific data from all LTPP test sections for all days of deflection basin 

testing. The data needed for the backcalculation of layer modulus values were grouped into 

two categories: direct and indirect. Table 5 lists the LTPP data tables from which the direct and 

indirect data were extracted for the pre-processing tools to establish the inputs and the postprocessing tools to evaluate the final results.

The direct data were from tables that needed to establish the inputs for the backcalculation and

forward calculation of layer moduli, and the indirect data were from tables that needed to 

evaluate the results from the backcalculation process. The direct data elements were extracted 

from the LTPP database for all test sections on an experiment basis. The indirect data elements 

were extracted for those test sections that had an appreciable number of results that were 

considered unacceptable in order to identify potential reasons for the unacceptable or 

poor results.
41

Table 5. Tables from the LTPP database for evaluating data for the backcalculation 

process.

Data 

Category Data Table Name Purpose of Data Use

Direct use 

of data 

elements

EXPERIMENT_SECTION Identifies the specific experiment and pavement 

type.

MON_DEFL_LOC_INFO FWD deflection basin data and location information 

measured along each section. MON_DEFL_MASTER

MON_DEFL_DROP_DATA

MON_DEFL_TEMP_DEPTHS Pavement and air temperatures measured during 

MON_DEFL_TEMP_VALUES FWD testing.

MON_DEFL_DEV_SENSORS Location of each sensor from loading plate.

MON_DEFL_FLX_BACKCAL_BASIN Backcalculated layer modulus values for flexible 

pavements from first round study; available in 

SDR 20.0. Structure listed in SDR 20.0 was used to 

set the initial cross section.(2)

MON_DEFL_FLX_BACKCAL_LAYER

MON_DEFL_FLX_BACKCAL_POINT

MON_DEFL_FLX_BACKCAL_SECT

MON_DEFL_FLX_NMODEL_POINT Backcalculated nonlinear values; these were not 

MON_DEFL_FLX_NMODEL_SECT used in current study.

MON_DEFL_RGD_BACKCAL_BASIN Backcalculated layer modulus values for rigid 

pavements; available in SDR 20.0. Structure listed 

in SDR 20.0 was used to set the initial cross section.

MON_DEFL_RGD_BACKCAL_LAYER

MON_DEFL_RGD_BACKCAL_POINT

MON_DEFL_RGD_BACKCAL_SECT

SECTION_LAYER_STRUCTURE Layer type and thickness information for simulating 

pavement structure; both the layer thickness on each 

end of the project will be extracted as well as the 

representative thickness.

TST_L05A

TST_ L05B

GPR_MASTER Ground-penetrating radar (GPR) data for estimating 

thickness along the test section. GPR_THICK_POINT

GPR_THICK_SECT

GPR_LINK_LAYER Layer identification for GPR data.

TST_HOLE_LOG Boring log information and data to determine or 

confirm depth to rigid layer and depth of water table 

of saturated materials.

TST_SAMPLE_LOG

Indirect 

Use of 

Data 

Elements

INV_GENERAL Lane width, type of shoulder, and other information.

TST_ESTAR_MASTER Dynamic modulus for HMA mixtures. Other tables 

TST_ESTAR_MODULUS are included for the volumetric data.

TST_ACO2 and TST_ACO3 Data needed to determine the air voids of each 

HMA.

TST_AG04 and INV_GRADATION Data needed to determine the gradation of the 

HMA.

TST_MR Resilient modulus data for unbound materials.

TST_ISD_MOIST Moisture content data to confirm high or low values.

MON_DIS_AC_REV Flexible and rigid pavement distress data to confirm 

MON_DIS_JPCC_REV low elastic modulus values.

Note: Other data elements were extracted and used indirectly from the LTPP database. The ones listed in this table are more 

commonly used.
42

Presence of Bedrock Layer

In the first and second phases of the analyses, all sections were analyzed using the following

two assumptions:

• Without a rigid layer: All cases were analyzed using the EVERCALC© program 

interface. The execution of EVERCALC© using this assumption was automated, thereby 

eliminating the need for manual intervention to complete the analyses.

• With a rigid layer: All these cases were analyzed by running EVERCALC© using the 

backcalculation.exe application from the MS-DOS prompt. In many cases, the depth to a 

rigid layer was calculated, but the RMSE was high, exceeding its upper limit.

The automation process compared the RMSE and range of backcalculated elastic moduli 

resulting from the pavement simulation with and without a rigid layer. Whichever simulation 

resulted in the lower RMSE was used for further analyses. In many cases, the RMSEs were 

significantly different.

The presence of a rigid layer was also verified independently in the second and third analysis 

phases. The depth to a hard layer was included in the automation process by identifying selected 

words on the deeper borings or shoulder probes. Some of the words included in the search were 

refusal, hard layer, hard pan, rock, and limestone.

The best fit procedure did not require a different treatment of the data for sections with or 

without a stiff layer. The k-value was assumed to reflect, or at least account for, the presence of a 

bedrock layer in the backcalculation structure.

Presence of Ground Water or Wet Layer

It has been the authors’ experience that separating dry and wet or saturated layers improves the 

accuracy of the solution. Thus, the same tool to determine the depth to a hard layer was used to 

search the shoulder probes for wet layers. The words used in the search were “water,” “wet,”

“soft,” and “saturated.” This depth was used to initially separate the weathered subgrade layer 

from the natural subgrade.

Pre-Processing and Computational Tools

The analyses were performed in a systematic manner, as documented in Backcalculation 

Procedures and User Guide for Software Programs and Utility Tools.

(56) In keeping with the 

requirements outlined by LTPP, the analyses were automated to minimize manual errors and to 

enable an independent user the ability to reproduce the results. In addition, the automation 

process was designed to enable users to generate results for additional data collected by LTPP in

the future. The analyses utilized raw data in Microsoft Access® format from the LTPP database 

as the starting point to generate the backcalculation results. The results were merged back into 

Microsoft Access® tables with common reference fields with the original deflection tables, as 

explained in the description of the data schema provided in Schema for the Computed 

Parameters Table.

(57) Therefore, Microsoft Access®-based macros, Microsoft Windows®-based 

utilities, and user interfaces were developed to do the following:
43

• Perform general data validity checks.

• Use the original LTPP tables to merge deflection, sensor spacing, and temperature data.

• Establish data flags to filter out problem basins (i.e., those with non-decreasing 

deflections, missing deflection data, or missing sensor spacing data). Missing temperature 

data were flagged but not discarded for backcalculation.

• Process pavement layer information from raw data in LTPP tables to develop 

backcalculation structure suitable for use in the EVERCALC© program. This involved 

combining pavement layers so as to reduce the pavement structure to an equivalent 

backcalculation layer structure meeting EVERCALC© requirements.

• Assign reasonable seed modulus values and range of modulus values for use in the 

backcalculation process.

• Generate the input files in the format necessary for use in the EVERCALC© program.

• Generate input files in the format necessary for use in the MODCOMP© analyses.

Because the MODCOMP© analyses followed EVERCALC©, the input files for 

MODCOMP© were created by modifying the EVERCALC© input files.

• Generate the input files in the format necessary for the best fit analyses program. These 

files were created directly from the Microsoft Access® data tables and were independent 

of the EVERCALC© or MODCOMP© analyses.

• Execute the EVERCALC© analyses in a batch mode.

• Execute the MODCOMP© analyses in a batch mode.

• Execute the best fit analyses in a batch mode.

• Calculate the load transfer efficiency (LTE) across the transverse and longitudinal joints 

in JPCP sections and across transverse cracks in CRCP sections.

• Read output data files, merge results, and compute summary tables for inclusion in LTPP 

results database.

The macros were developed in Microsoft Access® primarily because the raw data resided in 

Microsoft Access® tables. The macros were used to perform the preliminary data checks and to 

create supplementary data tables. Supplementary data are all data other than the raw FWD 

deflection data that are necessary to perform the backcalculation analyses, including sensor 

spacing, temperature data, backcalculation layer structure and layer thicknesses, layer material 

information including specified ranges for EVERCALC© analysis, and beta factors for the best 

fit analysis methods.
44

A standalone software program, Back Calculator, was developed for this current study for bulk 

processing and filtering the deflection data, for executing the EVERCALC© program and the

best fit method, and for processing the backcalculation results. Back Calculator is discussed in 

Backcalculation Procedures and User Guide for Software Programs and Utility Tools.

(56)

MODCOMP© analyses were not included in this program because only a limited number of 

sections were analyzed using MODCOMP©. MODCOMP© analyses were performed in a batch 

mode by executing the application file from an MS-DOS prompt.

Pre-Processing Deflection Data

The pre-processing tools for the deflection data were used to convert deflection basin data from 

the format in which they were collected to the format required for input to the backcalculation 

program as well as to identify deflection data anomalies that cause the program to generate 

unrealistic solutions and establish the pavement layering simulation.

Two parameters were checked in terms of pre-processing the deflection basin data: the type of 

deflection basins (typical and types I, II, or III) and type of structure (deflection softening, 

elastic, or deflection hardening). Von Quintus and Simpson and Von Quintus and Killingsworth 

defined and used these parameters during the first round of backcalculation of layer moduli as 

well as in other local calibration studies.

(4,45) Deflection basins identified along a test section 

inconsistent with elastic layer theory were flagged. 

The deflection basin and load-response behavior categories can also be used to guide the initial 

pavement layering simulation. For example, sites with a high percentage of type II deflection 

basins usually indicate some stiff layer close to the surface but not at the surface or some 

discontinuity at the surface varying from cracks to debonding. Different pre-processing activities

related to the deflection data include the following:

• Pre-processing of deflection data was performed to determine the deflection basin and 

load-response categories, as well as identify sensor data issues using SLIC (part of the

MODTAG© program for evaluating the deflection basin data). The decision criteria for 

categorizing each test section and deflection basin are documented in the Von Quintus 

and Simpson report.

(4)

• An apparent rigid or stiff layer was estimated along each test section in accordance 

with the procedure identified by EVERCALC© and MODCOMP©. The depth to an 

apparent rigid layer can be highly variable along a test section as well as between 

test days.

• Deflection basin data were reviewed to identify changes in the categories over time,

which could indicate a seasonal water table depth, increased damage, and/or occurrence 

of distress (cracking and distortion) or debonding between adjacent layers.

The representative thickness of the structural layers of an LTPP test section was determined to be 

the average thickness of that layer. For most of the LTPP test sections, layer thicknesses were 

only measured at the beginning and end of the section. In a few cases, the layer thickness and 
45

material types varied from one end of the section to the other. Thickness variations along a site 

can have a detrimental effect on trying to determine acceptable layer modulus values for that site.

The measured deflections were used to subdivide the sections into two parts when the layer 

thickness from the approach and leave ends of the section varied significantly. There were sites 

with an abrupt change in the measured deflections from one end to the other, and other sites 

where the measured deflections continually decreased or increased from one end to the other. 

LTPP sponsored a study using GPR data to estimate the variation of layer thickness throughout 

some of the test sections. These GPR data, when available, were used to make a decision on 

subdividing an individual section.

The process compared the layer thickness measured on the leave and approach ends of each test 

section. The initial criteria used for comparison was 0.5 inch for PCC and HMA layers and 

1 inch for the unbound base and treated subgrade (TS) layers. If no significant difference in layer 

thickness was measured, LTPP materials data table TST_L05B within the LTPP materials 

database was used to determine the representative layer type and thickness at the site. For those 

sites with large deviations in layer thickness, the layer thicknesses determined from the GPR data 

were used to determine if the test section should be subdivided. If GPR data were unavailable, 

the deflection data were used to decide whether the test section should be subdivided into 

multiple test sections for backcalculating elastic modulus values.

PAVEMENT SIMULATION RULES

The number of layers and individual layer thickness are critical parameters for backcalculating 

the elastic modulus of structural layers (i.e., layers that have a significant impact on the 

deflection basin with reasonable changes or variation in modulus). Getting a reasonable starting 

pavement simulation for the measured deflection basin is probably the most important activity in 

the backcalculation process, and as such, was included as an automated feature in the preprocessing tools to remove subjectivity.

Most backcalculation software packages limit the number of layers that can be backcalculated 

to a maximum of three and five, but that number depends on the number of sensors and their 

spacing. The first and second phases of the backcalculation process were limited to five layers to 

accommodate the features of the selected backcalculation program. The third and fourth analysis 

phases explored the option of using up to seven layers, including any known layer modulus or 

insensitive layer. However, the results that were acceptable included no more than five layers.

Therefore, under this project no more than five layers were backcalculated.

The rules of simulation reported in the MEPDG were used to set up the pavement structure for 

each LTPP test section.(1) Setting up the initial pavement layering simulation is straightforward, 

but there are factors that complicate the process. For example, layer thicknesses are not known 

at every deflection point, and some subsurface layer conditions can be overlooked or not 

adequately identified throughout the test section. The following lists provide some general rules 

of simulation for creating the pavement structure used in backcalculating elastic layered modulus 

for each of the structural layers. Many of these rules are discussed in other areas of the report, 

but they are repeated here for the convenience of the reader.
46

General notes include the following:

• It is optimal to start with the fewest number of layers possible and estimate the depth to 

an apparent rigid or stiff layer for each drop height along the test section prior to 

program execution.

• Thin non-structural layers should be combined with adjacent like layers. Thin is defined 

as less than 2 inches or less than half the thickness of the layer above the layer in 

question. As an example, an HMA open-graded friction course should be combined with 

the supporting HMA layer. In many cases, thin layers are defined as insensitive layers.

• The moduli for the insensitive layers were assumed using typical values included and 

reported in the MEPDG, or the layer was combined with an adjacent “like” layer.(1) As 

noted above, an insensitive layer is defined as one that has little to no impact on the 

measured deflection basin.

• GPR data were used to estimate the change in thickness and subsurface conditions along 

the test section. Where available, GPR data were reviewed to estimate significant changes 

along the test section from what is recorded in the L05B table (layer thickness, 

subsurface feature, etc.). If the GPR data suggested variable layer thickness between 

the ends of the section, a decision was made on whether to subdivide the section into 

two parts. If a substantial difference in surface layer thickness was found between the 

leave and approach ends and GPR data were unavailable, deflection data were used to 

determine the location of the transition. If an abrupt change was identified via the 

deflection basin, the section was subdivided into two subsections.

• Similar or like materials of adjacent layers should be combined into one layer. Like is 

defined as materials or layers with the same AASHTO classification exhibiting similar 

laboratory-measured modulus values and the same stress-sensitivity and physical 

properties. Like layers were combined in setting up the structure at a particular site. This 

is one of the reasons for extracting the layer material properties for use in this study.

• The lower layers should be combined first, and the upper pavement layers should be 

treated in more detail, if possible. The discussion and guidance that follows, however, 

starts with the foundation layers and proceeds up to the surface layers.

Subgrade layer notes include the following

• Boring logs and shoulder probes should be reviewed to determine the foundation soils 

and the vertical strata and their condition.

• At the beginning, the subgrade or foundation soils should be divided into two layers, 

especially when bedrock and other hard soils are not encountered. The lower layer 

represents the natural soil, while the upper layer represents the compacted soils just 

beneath the pavement materials. This layer is considered to be the weathered soil layer.
47

• Bedrock and other hard soils (such as hard pan, shale, sandstone, etc.) believed to be 

more than about 20 ft below the surface usually have an insignificant effect on the 

calculated pavement responses for predicting various distresses. In some cases, however, 

better results were obtained if that hard layer was simulated within 600 inches to 

the surface.

• Depth to a water table or wet layer is important for both structural evaluation and 

backcalculation of layer modulus. It is optimal to stratify the subgrade at the depth of the 

water table because of the different layer response to load. The water table can vary by 

season, so the layering at a site can be different within different seasons.

• Geo-synthetic fabrics and other materials are not simulated by themselves in the 

structural response program. However, these types of reinforcing fabrics can result in a 

higher modulus of the layer in which they are placed. Filter fabrics used for drainage 

purposes between a fine-grained soil and aggregate base material are not simulated 

in the pavement structure and usually have no impact on the structural response of 

the pavement.

Unbound aggregate material notes include the following:

• In most cases, the number of unbound granular base (GB) and subbase layers should not 

exceed two, especially when one of those layers is thick (more than 18 inches in 

thickness). Sand and other soil-aggregate materials should be simulated separately from 

crushed stone or crushed aggregate base materials.

• If thick, unbound aggregate or select materials (i.e., exceeding 18 inches) are used, this 

layer can be treated as the upper subgrade layer. Thick granular layers are typically used 

in northern climates as non-frost susceptible materials. When these layers are treated as 

the upper subgrade, then only one subgrade layer is needed.

• If a thin aggregate base layer is used between two thick unbound materials, the thin layer 

should be combined with the weaker or lower layer. For example, a 6-inch sand subbase 

layer placed between an A-1-b AASHTO classified subgrade soil (SS) and crushed stone 

base can be combined with the upper subgrade layer.

• When similar aggregate base and subbase materials are used, those materials can be 

combined into one layer.

Treated and stabilized material notes include the following:

• ATB layers, sometimes referred to as “blackbase,” should be treated as separate layers

and not combined with dense-graded HMA base mixtures. Typically, these are crushed 

stone base materials that have a small amount of asphalt and/or emulsion that can be 

produced at a plant or mixed in place. However, ATB materials that are designed using 

the gyratory compactor or other compaction device and produced through a production 

facility can be treated as an HMA base material and combined with other dense-graded 

HMA layers.
48

• Cement-treated and other pozzolanic stabilized materials that are used as a base layer for 

structural support should be treated as a separate layer. In some cases, a small portion of 

cement, lime, or fly ash may be added to GB materials to improve the strength or lower 

the plasticity index of those materials for constructability issues. These materials should 

still be considered as a separate layer.

• Lime and lime-fly ash stabilized SSs should be treated as a separate layer, if possible. In 

some cases, a small amount of lime or lime-fly ash is added to soils in the upper subgrade 

to lower the plasticity index and from a constructability standpoint. For these cases, the 

lime or lime-fly ash stabilized soil should be combined with the upper subgrade layer.

Drainage layers/material notes indicate that permeable ATB drainage layers should be treated as 

separate layers and not combined with dense-graded HMA layers or ATB layers, if possible. 

HMA mixture notes include the following:

• Similar HMA materials should be combined into one layer. For example, an HMA 

wearing surface or mix and an HMA binder layer can be combined into one layer without 

affecting the accuracy of the predictions.

• Thin HMA layers can be combined with an adjacent HMA layer. As noted earlier, thin is 

defined as less than 2 inches in thickness. Thin HMA leveling courses, or for the 

condition when the thickness of the leveling course is highly variable along the roadway, 

can be combined with the other HMA layers or ignored without affecting the overall 

accuracy of the results.

• The number of HMA layers should not exceed two, if at all possible. All layers that are 

dense-graded HMA mixtures should initially be combined.

DEFINING ACCEPTABLE ELASTIC LAYER MODULUS VALUES

Two parameters were used to judge the acceptability of the backcalculated values: (1) the error 

or RMSE between the measured and calculated deflection basins and (2) a comparison of the 

backcalculated values to the range of typical material specific values. A third factor was used 

(normality test for the results for a day’s test) but only for evaluating the acceptability of

the results.

Error Between Predicted and Measured Deflection Basins

All of the measurement points that have excessive error terms were flagged and not used in 

determining the statistics (means and standard deviation) for the test section and day of testing.

Excessive is defined as an RMSE value greater than 3 percent. Deflection basins with RMSE

values greater than 3 percent were included in the point-by-point CPTs (see Schema for the 

Computed Parameters Table) but excluded from the CPTs in determining the average of the inplace elastic moduli for each test section and test date.(57) Chapter 5 provides a summary of the 

CPTs for the backcalculation of elastic layer moduli.
49

Range of Calculated Modulus Values

The other criterion used in judging the acceptance of the results is the range of typical modulus 

values. The range of modulus values for typical materials and soils was determined to be 

consistent with values reported in the MEPDG.

(1) Table 6 provides the range of typical modulus 

values included in the MEPDG.(1) The table also includes the range of values used for judging 

the reasonableness of the backcalculated layered elastic modulus values. Note that the table does 

not list all materials that are included in the LTPP program. It is a partial list to show examples 

of the typical range in material moduli.

Table 6. Typical range of modulus for different paving materials and soils.

Material Type

MEPDG Range 

(ksi)

Range for Backcalculation 

(ksia)

Lower Value Upper Value Lower Value Upper Value

PCC, intact 1,000 7,000 1,000 10,000

Fractured PCC 200 5,000 30 2,000

HMA, uncracked Temperature dependent 100 4,000

HMA, cracked Temperature dependent 50 2,000

Cement-treated base 50 4,000 100 4,000

ATB Same as HMA Same as HMA 100 2,000

Stripped HMA N/A N/A 50 500

Cold in-place recycled 10 30 20 200

Crushed stone 20 45 10 80

Crushed gravel 20 30 10 60

Soil-cement 50 4,000 50 1,000

Lime-stabilized soil 50 4,000 20 100

AASHTO 

standard soil 

classes 

A-1-a 16 42 10 60 A-1-b 16 40

A-2-4 14 37.5

A-3 14 35.5 5 40

A-4 13 29

A-5 6 25.5

A-6 12 24 5 40

A-7-6 5 13.5

N/A = Not applicable. a

The range of values for the backcalculation process are preliminary and depend on the physical properties and 

condition of the layers documented in the LTPP database or extracted from other reports and construction records.

During the first round of backcalculation values, some of the results were believed to be 

unacceptable because the backcalculated values fell outside the range of typical values. Although 

this factor was used to judge the results, the results are not necessarily unacceptable simply 

because the values fall outside a perceived range of values. Some of the results that were 

believed to be unacceptable from the first round have been found to be reasonable as a result of 

forensic and other investigations completed at specific LTPP test sections.

For example, some of the elastic modulus values for unbound aggregate base layers in Arizona 

were found to be greater than 100 ksi, which is extremely high. It was later found, however, that 
50

these unbound aggregate base layers had very low water content, and the fines were binding the 

base particles together so the aggregate layers were responding as bound layers. Some of the 

crushed limestone aggregates used in central Texas exhibited the same behavior when dry.

Normality Test Using Jarque-Bera Test Statistic

Another factor included in the automated process for evaluating the acceptability of the results 

was to determine if the calculated elastic layer moduli are characteristic of a normal distribution.

Just about all volumetric and structural properties exhibit a normal distribution unless there 

is some type of bias that is created during construction or a boundary condition. Thus, 

results from a single test day were evaluated to determine if those results exhibited a 

normal distribution.

The verification for normal distribution was performed using the Jarque-Bera test statistic. For 

given data, x1, x2, ..., xn, the statistical terms shown in table 7 are calculated based on the 

normality test class.

Table 7. Statistical parameters calculated for normality check.

Statistic terms Statistic Symbol Functions from Code

Sample mean Mean

Second central moment (variance) Variance

Third central moment (skewness) S Skewness

Fourth central moment (kurtosis) K Kurtosis

Jarque-Bera test statistic JB JarqueBeraTestStatistic

Figure 31 shows the formula for the skewness factor, figure 32 shows the equation for kurtosis

factor, and figure 33 shows the equation for the Jarque-Bera statistic.

Figure 31. Equation. Skewness factor.

Where:

S = Skewness factor.

n = Number of data points in the sample.

i = Individual data point within the sample.

xi = Data value within the sample.

= Sample mean.

x�

σ�

2

2

3

1

2

1

2

( ) 1

) 1





 



 −

−

=

∑

∑

=

=

n

i

i

n

i

i

x x

n

(x x

n S

x�
51

Figure 32. Equation. Kurtosis factor.

Where K = Kurtosis factor.

Figure 33. Equation. Jarque-Bera statistic used for verifying normality in data.

Where JB = Jarque-Bera statistic.

For a dataset that is normally distributed, it is expected that S and K both equal zero.

JB asymptotically has a chi-squared distribution with 2 degrees of freedom. The critical value is 

determined using table 8. Hence, at a significance level of 5 percent and 2 degrees of freedom, 

the critical value is 5.99 (shown in bold in the table). Therefore, if JB is greater than 5.99, S and 

excess K tend to deviate from zero, which does not imply a normal distribution. JB values less 

than 5.99 indicate a normal distribution.

Table 8. Critical chi-squared value for different degrees of freedom and levels of 

significance.

Degrees of 

Freedom Chi-Squared Value

1 0.004 0.02 0.06 0.15 0.46 1.07 1.64 2.71 3.84 6.64 10.83

2 0.1 0.21 0.45 0.71 1.39 2.41 3.22 4.60 5.99 9.21 13.82

3 0.35 0.58 1.01 1.42 2.37 3.66 4.64 6.25 7.82 11.34 16.27

4 0.71 1.06 1.65 2.20 3.36 4.88 5.99 7.78 9.49 13.28 18.47

5 1.14 1.61 2.34 3.00 4.35 6.06 7.29 9.24 11.07 15.09 20.52

6 1.63 2.20 3.07 3.83 5.35 7.23 8.56 10.64 12.59 16.81 22.46

7 2.17 2.83 3.82 4.67 6.35 8.38 9.80 12.02 14.07 18.48 24.32

8 2.73 3.49 4.59 5.53 7.34 9.52 11.03 13.36 15.51 20.09 26.12

9 3.32 4.17 5.38 6.39 8.34 10.66 12.24 14.68 16.92 21.67 27.88

10 3.94 4.86 6.18 7.27 9.34 11.78 13.44 15.99 18.31 23.21 29.59

p-value 

(probability)

0.95 0.90 0.80 0.70 0.50 0.30 0.20 0.10 0.05 0.01 0.001

Typically Non-Significant Values Significant Values

Note: Bolding indicates the critical value.

2

1

2

1

4

( ) 1

( ) 1





 



 −

−

=

∑

∑

=

=

n

i

i

n

i

i

x x

n

x x

n K

( ) 



 



 = + − 2 2 3

4

1

6

S K n JB

53

CHAPTER 5. BACKCALCULATION RESULTS

This chapter provides a review of the procedures for post-processing the results and determining 

their accuracy as well as the CPTs used to store the backcalculated elastic layer moduli and 

other data.

LTPP DATA SOURCE

As stated in chapter 4, the deflection data were obtained from SDR 27.0 and included data from 

all LTPP test sections and all days of deflection testing. The dataset contained both GPS and SPS 

experimental sections and represented all pavement design alternatives included in the 

LTPP database.

BASIC FACTS ABOUT THE BACKCALCULATION PROCESS

There were a total of 7,771 test days, of which 4,534 sections had an HMA surface, and 

2,237 sections had a PCC surface. All LTPP sections were grouped by State code, Strategic 

Highway Research Program (SHRP) ID, and construction number to facilitate the pre-processing 

described in chapter 4.

Number of GPS and SPS Test Sections

The number of sections by each LTPP experiment included 1,744 sections with an HMA surface 

and 1,008 sections with a PCC surface. The surface type changed in 381 of the test sections. For 

example, a JPCP with a PCC surface that was eventually overlaid with HMA was counted in 

two categories or experiments. Therefore, there were a total of 3,133 unique sections in all States 

combined, as listed in table 9. Table 10 lists the total number of deflection basins and those 

basins falling within each of the four categories. As shown, the LTPP quality control processes 

have resulted in nearly 97 percent of the basins falling within the typical and type 2 categories, 

which the authors consider excellent. As such, 5,847,770 deflection basins (typical and type 2) 

were used in the backcalculation process. 

The number of deflection basins analyzed and included in the backcalculation process are listed 

in table 11. The table also lists the percentage of deflection basins that were found to be 

acceptable after the initial evaluation with EVERCALC© using an expanded range of the upper 

and lower modulus limits and for the final results. As shown, about 75 percent of all deflection 

basins were considered acceptable after the second phase analysis and defined as accept or 

atypical, while about 85 percent of the deflection basins resulted in acceptable values from 

EVERCALC© and MODCOMP©.

Table 12 lists the percentage of deflection basins defined as acceptable on a State-by-State basis.

The percentage of acceptable deflection basins increased to about 85 percent after the fourth

phase analysis using MODCOMP© for those basins considered unacceptable from the second 

and third phase analyses. Table 13 summarizes the percentage of deflection basins defined as 

acceptable on a State-by-State basis for the PCC-surfaced pavements from the best fit method.
54

Table 9. Summary of LTPP data used in the backcalculation analyses by experiment.

HMA Surface PCC Surface

LTPP Experiment Number of Sections LTPP Experiment Number of Sections

GPS 1 233 GPS 3 133

GPS 2 145 GPS 4 69

GPS 6A 63 GPS 5 85

GPS 6B 131 GPS 9 26

GPS 6C 31 SPS 1 1

GPS 6D 24 SPS 2 205

GPS 6S 162 SPS 4 220

GPS 7A 35 SPS 6 170

GPS 7B 56 SPS 7 39

GPS 7C 18 SPS 8 16

GPS 7D 3 SPS 9C 7

GPS 7F 3 SPS 9J 37

GPS 7S 27

SPS 1 245

SPS 2 2

SPS 3 445

SPS 5 204

SPS 6 123

SPS 7 1

SPS 8 37

SPS 9C 7

SPS 9J 38

SPS 9N 50

SPS 9O 42

Total GPS sections 931 Total GPS sections 313

Total SPS sections 1,194 Total SPS sections 695

Grand Total 2,125 Grand Total 1,008

Note: Blank cells indicate no additional LTPP experiment within the pavement type.
55

Table 10. Summary of LTPP deflection basin data.

State/

Canadian 

Province/ 

Territory

Number of Drops Percentage of Total Drops

Percentage 

of Typical 

Type 1 Type 2 Type 3 Typical Total Type 1 Type 2 Type 3 Typical and Type 2

AL 593 56,826 3,326 150,435 211,180 0.28 26.91 1.57 71.24 98.14

AK 8 6703 20 17,856 24,587 0.03 27.26 0.08 72.62 99.89

AZ 982 117,565 5,720 253,549 377,816 0.26 31.12 1.51 67.11 98.23

AR 1,221 33,772 6,271 44,550 85,814 1.42 39.35 7.31 51.91 91.27

CA 2,566 72,207 5,384 129,688 209,845 1.22 34.41 2.57 61.80 96.21

CO 590 40,960 1,671 89,608 132,829 0.44 30.84 1.26 67.46 98.30

CT 87 13,727 1,350 43,544 58,708 0.15 23.38 2.30 74.17 97.55

DE 231 23,371 1,437 41,918 66,957 0.34 34.90 2.15 62.60 97.51

DC 0 311 2 711 1,024 0.00 30.37 0.20 69.43 99.80

FL 319 33,062 6,038 102,937 142,356 0.22 23.22 4.24 72.31 95.53

GA 813 53,464 7,195 99,894 161,366 0.50 33.13 4.46 61.91 95.04

HI 1 4,768 58 11,328 16,155 0.01 29.51 0.36 70.12 99.63

ID 2,104 35,038 1,321 45,974 84,437 2.49 41.50 1.56 54.45 95.94

IL 1,804 42,460 7,052 43,692 95,008 1.90 44.69 7.42 45.99 90.68

IN 1,384 56,244 13,013 54,283 124,924 1.11 45.02 10.42 43.45 88.48

IA 2,117 43,359 6,820 52,852 105,148 2.01 41.24 6.49 50.26 91.50

KS 2,122 47,191 3,343 80,159 132,815 1.60 35.53 2.52 60.35 95.89

KY 150 8,066 685 16,291 25,192 0.60 32.02 2.72 64.67 96.69

LA 242 7,165 1,241 10,932 19,580 1.24 36.59 6.34 55.83 92.43

ME 584 17,903 2,770 63,596 84,853 0.69 21.10 3.26 74.95 96.05

MD 300 44,640 2,009 61,514 108,463 0.28 41.16 1.85 56.71 97.87

MA 55 6,993 247 40,637 47,932 0.11 14.59 0.52 84.78 99.37

MI 775 27,481 3,224 66,084 97,564 0.79 28.17 3.30 67.73 95.90

MN 1,502 67,018 6,828 198,733 274,081 0.55 24.45 2.49 72.51 96.96

MS 615 42,521 1,112 101,452 145,700 0.42 29.18 0.76 69.63 98.81

MO 1,467 49,275 3,194 76,189 130,125 1.13 37.87 2.45 58.55 96.42

MT 455 38,957 2,782 139,478 181,672 0.25 21.44 1.53 76.77 98.22
56

NE1,317 25,4031,562 73,746 102,028 1.29 24.90 1.53 72.28 97.18

NV1,403 27,078 894 75,115 104,490 1.34 25.91 0.86 71.89 97.80

NH 316,642 257 29,166 36,096 0.09 18.40 0.71 80.80 99.20

NJ 129 29,857 692 82,542 113,220 0.11 26.37 0.61 72.90 99.27

NM 39 17,194 551 90,288 108,072 0.04 15.91 0.51 83.54 99.45

NY 133 10,847 359 77,420 88,759 0.15 12.22 0.40 87.22 99.45

NC1,067 40,4612,584 91,811 135,923 0.79 29.77 1.90 67.55 97.31

ND 4628,184 3228,015 16,983 2.72 48.19 1.90 47.19 95.38

OH2,072 40,9844,895 62,117 110,068 1.88 37.24 4.45 56.44 93.67

OK 661 40,7621,114 97,209 139,746 0.47 29.17 0.80 69.56 98.73

OR1,257 10,3492,5059,067 23,178 5.42 44.65 10.81 39.12 83.77

PA1,446 37,1365,584 49,688 93,854 1.54 39.57 5.95 52.94 92.51

RI14,035 2951,7016,032 0.02 66.89 4.89 28.20 95.09

SC 218,906 5226,623 16,072 0.13 55.41 3.25 41.21 96.62

SD 704 33,4002,553 100,325 136,982 0.51 24.38 1.86 73.24 97.62

TN 78 26,4021,137 54,864 82,481 0.09 32.01 1.38 66.52 98.53

TX1,381 113,1268,176 425,696 548,379 0.25 20.63 1.49 77.63 98.26

UT 599 22,078 725 64,515 87,917 0.68 25.11 0.82 73.38 98.49

VT 310 13,3921,314 53,877 68,893 0.45 19.44 1.91 78.20 97.64

VA 156 26,417 923 126,862 154,358 0.10 17.11 0.60 82.19 99.30

WA 635 22,2071,348 60,124 84,314 0.75 26.34 1.60 71.31 97.65

WV 1447,307 4106,347 14,208 1.01 51.43 2.89 44.67 96.10

WI1,237 37,3486,628 46,604 91,817 1.35 40.68 7.22 50.76 91.43

WY 295 35,151 772 54,942 91,160 0.32 38.56 0.85 60.27 98.83

PR 312,384 104,9427,367 0.42 32.36 0.14 67.08 99.44

AB18,119 51 44,672 52,843 0.00 15.36 0.10 84.54 99.90

BC01,2282 16,096 17,326 0.00 7.09 0.01 92.90 99.99

MB 504 27,9988,294 98,541 135,337 0.37 20.69 6.13 72.81 93.50

NB02,771 154 10,640 13,565 0.00 20.43 1.14 78.44 98.86

NF0 697 348,0108,741 0.00 7.97 0.39 91.64 99.61

NS0 10913,7613,871 0.00 2.82 0.03 97.16 99.97

ON 1759,4151,184 56,362 67,136 0.26 14.02 1.76 83.95 97.98
57

PE 0 1,235 0 9,597 10,832 0.00 11.40 0.00 88.60 100.00

QB 265 10,933 508 34,926 46,632 0.57 23.45 1.09 74.90 98.34

SA 125 17,359 5,470 55,714 78,668 0.16 22.07 6.95 70.82 92.89

Total 39,766 1,717,961 155,943 4,129,809 6,043,479 0.66 28.43 2.58 68.33 96.76

PR = Puerto Rico; AB = Alberta; BC = British Columbia; MB = Manitoba; NB = New Brunswick; NF = Newfoundland; NS = Nova Scotia; ON = Ontario; 

PE = Prince Edward Island; QB = Quebec; and SA = Saskatchewan.

Table 11. Number of deflection basins analyzed and percentage of those deflection basins considered acceptable.

EVERCALC© Analysis

Total 

Drops 

Analyzeda

Accept 

Results

Atypical 

Results

Atypical 

and 

Accept 

Results

Error 

Drops

Percentage 

Atypical 

and Accept

Results

Run 1 using typical material-specific ranges for 

each layer

5,694,207 2,573,025 1,327,896a 3,900,921 1,793,286 68.5

Run 2 using wider range for cases where more 

than 25 percent of the run 1 results hit the limits

5,611,563 1,853,484 2,377,648b 4,390,049 1,380,431 75.4

Final Results (EVERCALC© and MODCOMP©) 5,662,494 1,817,186 2,494,628 4,311,814 1,350,680 76.1

Note: Different values are reported for the total number of basins analyzed because the total number accounts for basins that may have been dropped or added 

for the individual runs for basins that were borderline between typical and type 2 versus types 1 and 3.

a

The atypical results in run 1 represent basins with backcalculated moduli that converge to the lower or upper limits of the specified typical range. These may 

include sections that may produce results outside the atypical range if the range is expanded. Therefore, these basins may include basins that can be categorized 

as errors if the range is expanded. b

The atypical results in run 2 represent basins with backcalculated moduli that converge within the lower or upper limits of the specified atypical range (i.e.,

these basins may not be categorized as errors).
58

Table 12. Deflection basins analyzed and percentage classified as acceptable drops using 

EVERCALC© and MODCOMP© for all pavements.

STATE_

CODE

TOTAL_

DROPS

ERROR_

DROPS

ATYPICAL_

DROPS

ACCEPT_

DROPS

Percent 

Acceptable

1 199,465 28,341 99,850 71,274 85.8

2 24,559 6,188 6,018 12,353 74.8

4 367,159 116,309 162,913 87,937 68.3

5 77,904 14,206 30,161 33,537 81.8

6 193,500 60,991 75,684 56,825 68.5

8 130,421 49,733 47,512 33,176 61.9

9 57,271 6,129 17,565 33,577 89.3

10 65,289 9,282 36,820 19,187 85.8

11 1,022 160 319 543 84.3

12 135,999 50,662 48,522 36,815 62.7

13 153,065 16,886 69,767 66,412 89.0

15 16,096 3,727 6,307 6,062 76.8

16 80,804 28,423 33,432 18,949 64.8

17 86,152 22,671 34,200 29,281 73.7

18 93,376 24,438 39,795 29,143 73.8

19 95,867 28,030 40,923 26,914 70.8

20 126,318 38,013 46,290 42,015 69.9

21 24,357 8,725 9,355 6,277 64.2

22 18,097 1,324 4,621 12,152 92.7

23 81,499 6,151 33,610 41,738 92.5

24 106,138 27,664 49,703 28,771 73.9

25 44,976 4,671 21,745 18,560 89.6

26 93,392 15,832 34,056 43,504 83.0

27 264,185 54,432 112,931 96,822 79.4

28 143,797 31,183 72,221 40,393 78.3

29 117,624 44,556 51,913 21,155 62.1

30 178,393 39,040 91,324 48,029 78.1

31 98,629 18,671 40,554 39,404 81.1

32 101,504 17,931 56,182 27,391 82.3

33 35,808 2,775 12,998 20,035 92.3

34 112,399 12,285 65,259 34,855 89.1

35 107,482 20,493 45,650 41,339 80.9

36 88,267 8,243 58,641 21,383 90.7

37 132,159 32,663 56,570 42,926 75.3

38 16,199 4,218 6,972 5,009 74.0

39 103,092 24,359 37,449 41,284 76.4

40 136,754 25,706 56,493 54,555 81.2

41 19,416 5,817 8,703 4,896 70.0

42 86,759 28,033 47,666 11,060 67.7

44 5,736 1,488 3,825 423 74.1

45 15,529 7,544 5,710 2,275 51.4
59

46 130,246 21,574 48,238 60,434 83.4

47 81,234 31,811 32,462 16,961 60.8

48 534,862 134,664 219,904 180,294 74.8

49 86,480 29,619 48,924 7,937 65.8

50 67,199 4,830 34,503 27,866 92.8

51 153,279 32,257 89,569 31,453 79.0

53 81,825 23,132 37,514 21,179 71.7

54 12,316 6,630 3,970 1,716 46.2

55 82,468 20,558 40,304 21,606 75.1

56 90,093 29,562 42,538 17,993 67.2

72 7,326 4,178 2,912 236 43.0

81 52,791 21,534 26,103 5,154 59.2

82 17,324 1,682 4,952 10,690 90.3

83 126,539 21,726 44,798 60,015 82.8

84 13,411 4,480 8,562 369 66.6

85 8,164 1,871 2,147 4,146 77.1

86 3,870 180 1,176 2,514 95.3

87 65,777 7,945 20,217 37,615 87.9

88 10,832 4,454 5,606 772 58.9

89 45,250 13,087 19,373 12,790 71.1

90 73,073 27,001 32,359 13,713 63.0

Note: Not all agencies are included within this table because of missing data that were needed for the 

backcalculation process for the LTPP sections, or there were no LTPP test sections within that agency.
60

Table 13. Deflection basins analyzed and percentage classified as acceptable drops using 

the best fit method for PCC-surfaced pavements.

STATE_

CODE

TOTAL_

DROPS

ERROR_

DROPS

ATYPICAL_

DROPS

ACCEPT_

DROPS

Percent 

Acceptable

1 7,246 1,076 580 5,590 85.2

4 23,495 1,950 1,913 19,632 91.7

5 20,167 2,242 1,976 15,949 88.9

6 22,712 3,455 5,539 13,718 84.8

8 15,798 733 4,040 11,025 95.4

9 960 4 44 912 99.6

10 11,698 449 1,248 10,001 96.2

12 6,793 1,707 777 4,309 74.9

13 14,018 1,985 6,400 5,633 85.8

16 6,103 256 1,357 4,490 95.8

17 8,646 438 211 7,997 94.9

18 11,663 406 6,296 4,961 96.5

19 16,935 482 4,399 12,054 97.2

20 24,563 1,942 3,348 19,273 92.1

21 1,788 229 89 1,470 87.2

22 655 12 174 469 98.2

23 1,603 8 822 773 99.5

26 15,148 955 2,388 11,805 93.7

27 19,250 1,110 4,494 13,646 94.2

28 4,922 892 2,210 1,820 81.9

29 20,662 2,192 1,818 16,652 89.4

31 11,970 576 6,561 4,833 95.2

32 8,772 2,101 2,946 3,725 76.0

34 337 0 0 337 100.0

35 953 131 89 733 86.3

36 5,265 330 426 4,509 93.7

37 17,420 1,202 4,440 11,778 93.1

38 13,673 241 1,200 12,232 98.2

39 21,524 991 4,701 15,832 95.4

40 8,077 565 4,508 3,004 93.0

42 16,876 4,409 1,865 10,602 73.9

45 1,161 12 0 1,149 99.0

46 12,766 771 3,272 8,723 94.0

47 4,146 59 579 3,508 98.6

48 18,083 2,384 11,062 4,637 86.8

49 12,253 1,173 5,004 6,076 90.4

50 433 24 0 409 94.5

51 156 47 8 101 69.9

53 21,151 1,937 5,909 13,305 90.8

54 1,489 312 61 1,116 79.0

55 22,021 2,701 5,139 14,181 87.7
61

56 1,110 1 331 778 99.9

72 1,892 1,126 154 612 40.5

83 4,096 485 34 3,577 88.2

84 564 1 21 542 99.8

89 8,103 361 681 7,061 95.5

Note: Not all agencies are included within this table because some of the agencies did not have any LTPP rigid 

pavement test sections.

Hardware Used in Backcalculation Processing

The following subsection provides a summary of the hardware used to backcalculate the results

as well as an estimate of the length or amount of computational time to execute the first phase

analysis using EVERCALC©.

The first and second phase analyses were performed in two modes using the interface for the 

cases with a bedrock layer and by running the executable from an MS-DOS prompt for the cases 

without a bedrock layer. The runs were executed in a batch mode for both cases.

For cases with the bedrock layer, three virtual machines were used, each with 2 GB of random

access memory, and running the Windows XP® operating system. These machines had 2.4 Ghz 

dual core processors. The runs took about 2 weeks of computational time (336 h), with the

programmer or user having to monitor the progress of the software’s status. In some cases, the 

program had to be restarted twice each day.

For cases without the bedrock layer, three virtual machines were used, and they had the same 

specifications as those described. The analyses took about 1 week of computational time (168 h).

These analyses were more stable, but the programmer still had to monitor the program’s status

when processing data for States with large data sets (e.g., Arizona, Colorado, and Texas).

EVALUATING THE SUCCESS OF BACKCALCULATION

The two parameters used to determine whether the results were acceptable were also used as a 

measure to judge the success of the backcalculation process: (1) the average error or difference 

between the measured and calculated deflection basin and (2) the percentage of points with 

acceptable modulus values for all layers. The criteria for determining acceptable and 

unacceptable backcalculated layer modulus values were discussed earlier. The following list 

provides a generic definition of success:

• Definition for and measurement of success in terms of backcalculated modulus 

values: The difference between the calculated and measured deflection basins or RMSE 

was determined for each test date or test point from the backcalculation process. The 

points with less than 3 percent RMSE were considered acceptable solutions, while the 

solutions with RMSE values greater than 5 percent were considered poor or

unacceptable. Solutions with RMSE values between 3 and 5 percent were considered 

questionable. A similar definition was used in the first backcalculation project sponsored 

by FHWA.

(4) Only the deflection basins with an RMSE less than 3 percent were used to 

determine the average and standard deviation elastic layer moduli on a test section and 

test day basis.
62

• Definition for and measurement of success in terms of number of sites with

acceptable values: The percentage of test dates with backcalculated modulus values that 

meet the definition of a good or acceptable solution from the deflection basin for an 

appreciable number of points along the LTPP test section. Appreciable is defined as more 

than 75 percent of the points having RMSE values less than 3 percent with modulus 

values within the expected range of values. 

For sites with anomalies or high RMSE, the resulting elastic layer moduli were identified as 

such. MODCOMP© was used to determine a probable reason for the results. These sites or days 

of testing were flagged for investigation, if still available. If forensics have not been completed 

and a site has been taken out of service, these were simply identified along with some potential 

causes for the differences encountered.

Table 14 lists the LTPP test sections and the areas within the test section for which the results 

were eliminated from the CPT because most of the results were found to be outside one or both 

of the acceptance criteria. Table 15 lists the error flags and their description used in the CPTs and 

included in the feedback reports.

Table 14. LTPP test sections identified as errors and eliminated from determining the test 

section statistics.

Test 

Section

Area Excluded 

Station Type of Structure

01-4127 110+ Conventional flexible pavement structure

01-4129 -40 Conventional flexible pavement structure with a thin surface

04-1006 140+ Conventional flexible pavement structure

02-9035 80+ Conventional flexible pavement structure with a thin overlay

04-1022 -50 Conventional flexible pavement structure

04-1015 120+ Conventional flexible pavement structure with overlay

06-8534 130+ Conventional flexible pavement structure with a thin surface

30-7088 70+ Conventional flexible pavement structure with overlay

37-2824 -60 Semi-rigid pavement

38-2001 80+ Semi-rigid pavement

40-4088 50+ Semi-rigid pavement

42-1618 -35 Conventional flexible pavement structure with overlay

48-9005 -50 Conventional flexible pavement structure with overlay

53-1002 -40 Conventional flexible pavement structure
63

Table 15. Error flags used in the CPTs.

Report 

No. Flag Subject Situation

Recommended 

Action

1 MISSING_DEFL Missing 

deflection data

Deflection data is missing in the 

MON_DEFL_DROP_

DATA for this STATE_

CODE, SHRP_ID, TEST_

DATE, TEST_TIME, POINT_

LOC, and DROP_NO.

None. The basin 

was not used in 

backcalculation 

analysis.

2 LAYER_THK_

UNAVAILABLE

Missing 

thickness data

Layer thickness data is missing 

in the TST_L05B table for this 

STATE_CODE, SHRP_ID, 

TEST_DATE, and 

CONSTRUCTION_NO

None. The basin 

was not used in 

backcalculation 

analysis.

3 BLACKLISTED_

BASINTYPE

Nondecreasing 

deflection 

basin

Invalid deflection data for the 

basin in the MON_DEFL_

DROP_DATA table. The test 

location has a non-decreasing 

deflection basin and was 

characterized as either a type I or 

a type III basin.

None. The basin 

was not used in 

backcalculation 

analysis.

4 MISSING_TEMP Missing 

temperature 

data and depth 

of temperature 

measurement

Temperature measurement and 

depth of measurement is missing 

in the MON_DEFL_TEMP_

DEPTHS and MON_DEFL_

TEMP_VALUES for this 

SHRP_ID, test_date, and 

Point_LOC.

None. The basin 

was used in 

backcalculation 

analysis.

5 MISSING_DEPTH_

THKCOR

Missing depth 

of temperature 

measurement

Missing layer depth Information 

in the MON_DEFL_TEMP_

DEPTHS table LAYER_TEMP_

DEPTH from the Supplementary 

Temperature Table).

None. The basin 

was used in 

backcalculation 

analysis.

6 TEMPERATURE_

DEPTH_MISMATCH

Temperature 

depth 

mismatch

The data for the layer 

thicknesses from TST_L05B and 

depth of temperature 

measurements do not align

None. The basin 

was used in 

backcalculation 

analysis.

7 MISSING TEMP_

DEPTH

Missing 

temperature 

within the 

surface layer

For the STATE_CODE, 

SHRP_ID, and TEST_DATE,

the temperature within surface 

layer could not be determined 

using the temperature depth and 

temperature values reported in 

MON_DEFL_TEMP_DEPTHS 

and MON_DEFL_TEMP_

VALUES tables.

None. The basin 

was used in 

backcalculation 

analysis.
64

8 INVALID_LTE Invalid LTE Deflection measurement was 

considered invalid because of 

missing deflection or sensor 

spacing.

None. The LTE 

was not reported 

in the summary 

tables.

9 LTE_NON_DEC LTE non 

decreasing

Invalid deflection data for the 

basin in the MON_DEFL_

DROP_DATA table. The test 

location has a non-decreasing 

deflection basin.

None. The LTE 

was not reported 

in the summary 

tables.

10 F_OUTPUT_IDD_

MISMATCH

Failure to 

obtain results 

for all basins 

for an

identification 

descriptor 

designation

Results were generated for a 

subset of the drops for the IDD. 

The results are written to the 

drops starting from the first 

drop; however a mismatch might 

exist.

None. The 

results are 

reported for the 

IDD.

11 F_NO_IDD_MATCH No results 

were obtained 

for this IDD 

No output data are found for an 

IDD (i.e., POINT_LOC, 

TEST_DATE, TEST_TIME, 

SHRP_ID, and STATE (likely 

that the input data were not fully 

processed by EVERCALC©).

No results 

reported for 

IDD.

12 EXCLUDED_FROM_

SUMMARY

Subsection 

excluded from 

results 

summary

Subsection of the SHRP_ID 

showed high variability in 

calculated modulus values 

relative to the majority of the 

section. Subsection had higher 

error rate.

Results 

excluded from 

summary.

Note: “Report No.” refers to an integer that defines a specific error flag.

The individual test sections with error numbers 1 through 9 in table 15 were included in

unpublished data feedback reports and were submitted to FHWA because these pertain to the 

data themselves. Error numbers 10–12 were excluded from the unpublished data feedback 

reports, which were prepared and submitted to LTPP to document and report errors or anomalies 

found in the database, because these errors only pertain to the results from the backcalculation 

programs. In addition, error numbers 1–3 were excluded in the datasets for the individual results 

because of missing critical data such that the backcalculation process could not be performed. 

Manual Review of Results

The first level review of results was the post-processing of the backcalculated results. The postprocessor groups and determines the number of deflection basins that are found to be acceptable 

and unacceptable based on the two parameters previously discussed. If the majority of the results 

were found to be acceptable, that test section and test date were accepted, and the averages, 

standard deviation, and other information were determined in the post-processing of the data. If a 

significant amount of the results are unacceptable, the test section and test date went through a 

second and possibly third level review. 
65

The second level review was a more exhaustive review to identify possible causes for the 

unacceptable results. This included an indepth review of the post-evaluation factors and other 

LTPP data and layer properties to try to identify the reasons for the high error term or modulus 

values that fell outside the range of typical values. If the results were still considered 

unacceptable after the second level review, the test section and test date moved to a 

third level review.

The third level review included making additional runs with MODCOMP© based on all available 

information. If this third level did not result in acceptance, a feedback report was prepared for the 

test section and test dates. As part of this review level, a decision was made regarding the 

probable cause for the unaccepted results and the results flagged. The probable cause and 

recommended resolution were included in the feedback reports. Appendix B lists the test sections 

that exhibited a high percentage of moderate to high RMSE values and did not meet all of the

acceptance criteria.

Post-Processing Evaluation Factors

Many factors can lead to erroneous results in the backcalculation process because they impact 

the measured deflection basin. Some evaluation factors include the following:

• Cracks in the pavement can cause the deflection data to depart drastically from the 

assumed conditions.

• Layer thicknesses are not uniform nor are materials in the layers completely 

homogeneous. For example, variations in layer thickness and material properties along 

the roadway affect the stiffness of the pavement layer, which in term affects the 

deflection basin.

• Some pavement layers are too thin to be backcalculated in the pavement model, and these 

are usually assumed or combined with an adjacent layer. The technique used to estimate 

the fixed modulus for these layers is important.

• Moisture content and the depth to a hard bottom layer can vary widely along the road, 

causing the results to be highly variable in the unbound layers.

• Temperature gradients in the pavement can lead to modulus variation in HMA layers and 

warping in PCC layers.

• Most unbound pavement materials are stress-dependent, and most backcalculation 

programs do not have the capability to handle this issue.

Another evaluation criterion was to compare the backcalculated elastic modulus values with 

those values measured in the laboratory for PCC, HMA, and unbound materials and soils. LTPP 

sponsored other projects to determine the dynamic and resilient modulus values that are 

consistent with the MEPDG methodology and inputs.(1) Dynamic moduli were calculated for the 

different HMA mixtures from volumetric and component properties and are included in the 

LTPP database, which represent an undamaged and unaged condition. The backcalculated 
66

modulus values, however, represented an in-place composite elastic modulus and were not 

discrete values, as measured in the laboratory. In addition, the backcalculated modulus values 

represented any in-place damage and aged conditions. As such, one-to-one correspondence was 

not expected between the backcalculated elastic modulus values and those calculated from 

volumetric properties (laboratory-derived dynamic modulus values). 

The layer- or mixture-specific dynamic modulus values were combined to determine a composite 

modulus value using the equivalent modulus concept and compared to the backcalculated 

composite values. The equivalent modulus concept was used in the FHWA-sponsored study to 

compare backcalculated values to laboratory-derived values.

(45) Use of the equivalent modulus 

concept to determine the composite laboratory-derived dynamic modulus was found to be of 

little value in explaining the difference between the laboratory-derived and field-derived values.

Compensating Layer Effects

Identifying compensating layer effects is an important step in the backcalculation process. 

Compensating layer effects occurs when one layer consistently increases in stiffness while an 

adjacent layer decreases in stiffness. Compensating layer effects can result in layer modulus 

values that are inappropriate for the pavement structure, even when the error between the 

measured and predicted deflection basins is considered acceptable. Characterizing the deflection 

basins can assist in identifying LTPP test sections that are prone to compensating layer effects. 

The deflection basins were categorized in the first backcalculation study to identify the sites 

where this characteristic is likely to occur.(4) The same process was used in this project to reduce 

the possibility for compensating layer effects on the calculated elastic modulus values. When 

compensating errors identified for a specific test section, MODOMP was used or the pavement 

structure was revised.

Discontinuities

Discontinuities in the pavement structure (i.e., cracks, joints, segregation, etc.) have an impact on 

selected deflection basins, especially if the discontinuity is supporting a sensor platform or 

located between two sensors near the loading plate. The sensor bar and loading plate are usually 

located in intact areas, but that is not always possible or the condition noted by the operator. The 

shape of the deflection basin can distinguish some of these conditions.

As part of the backcalculation process, the distress data were extracted for each site for review 

when selected areas along the LTPP site continually do not meet the acceptance criteria to 

explain the high RMSE or surface layer modulus values that deviate significantly from typical 

laboratory-derived values. These results were flagged as having extensive cracking or distress 

along the section as part of the post-processing of results.

HMA Stripping and Other Material Defects

Stripping can have a softening effect on HMA mixtures. Some of the forensic investigations that 

have been completed on the SPS-1 and SPS-2 supplemental sites have identified HMA mixtures 

that exhibit stripping in selected layers. This softening effect can result in low elastic modulus 

values backcalculated for that structure. The first LTPP backcalculation study recognized this 

behavior, and all layers that were found to exhibit stripping were simulated as a separate layer. 
67

The error term using this approach was lower in comparison to combining all HMA layers into a 

composite layer. 

Figure 34 illustrates this point for an LTPP site where deflection testing was done prior to any 

forensic investigation. The pavement structure was an HMA overlay of an existing HMA 

pavement. The backcalculated modulus reported for the in-place dense-graded base mixture 

beneath the HMA overlay was similar to that of a good quality aggregate base material. That 

modulus value was believed to be incorrect and rejected. After coring operations, the low 

modulus value was found to be representative of moisture-induced damage or stripping. Similar 

examples are applicable for the unbound layers (e.g., high water content resulting in very low 

modulus values to base layers with an excessive amount of fines or low water content (a dry 

condition) resulting in very high modulus values representative of a bound layer).

Figure 34. Photo. Cores recovered where moisture damage occurred, decreasing the 

in-place modulus of the layer/mixture (Texas SPS-5 project).

Loss of Bond between Layers

Most backcalculation studies and software packages assume adjacent layers are fully bonded. 

However, forensic investigations have shown that there were SPS-1 and -5 test sections where 

bond was lost with time. Some of these sections have been reconstructed or taken out of the 

LTPP monitoring cycle because the distress increased significantly. 

HMA Dense-Graded Base Mixture that Exhibits Moisture 

Damage and Disintegrated During Wet Coring Operations.
68

The bond between adjacent bound layers can affect the deflection basin, but the effect is usually 

considered minor. Based purely on the deflection basins, it is difficult to determine if bonded or 

full slip between layers should be assumed. If adjacent layers become debonded, the distresses 

usually increase at a significant rate. Simulating this condition becomes difficult because of the 

limit on the number of layers that can be backcalculated, and most of the commonly used 

programs have the bond between layers fixed to full bond. If this condition is expected from 

the results of the backcalculation process through low modulus values, the results are flagged 

as such. 

Variable or Perched Water Table Depth

The water content of unbound materials has a significant effect on the elastic properties of that 

layer. This was recognized during the first backcalculation study, so boring logs and water 

content were used to determine if this condition was exhibited at each LTPP site. Where this 

condition was found, two runs were made—one where the subgrade was combined as one layer 

and another where the subgrade was divided into two layers where the water table or nearly 

saturated conditions existed. The error between the measured and calculated deflection basins 

was almost always lower by simulating the depth of saturation. In most cases, the backcalculated 

elastic modulus values were also higher for the layer above the water table depth than the values 

below the water table depth. In some cases, these depths were seasonal.

Variable Depth of an Apparent Rigid Layer

The depth to bedrock can be determined from the shoulder borings that were drilled at all (or 

nearly all) of the LTPP test sections. However, a saturated or soft (weak) layer overlying a dry, 

overconsolidated clay layer can behave as a very stiff layer; all of the energy is being absorbed in 

the soft, weak layer. Similar to the comments relative to saturated layers, the boring logs and 

physical properties were used to identify these conditions. Where these conditions were found, 

two runs were made, one with and one without a rigid layer at the interface between the wet and 

dry layers. In most cases, the error between the measured and calculated deflection basins was

less by simulating a rigid or stiff layer at that location or dividing the subgrade into two layers at 

that depth. 

Warping and Curling of PCC Slabs

Curling of JPCP slabs can occur over a day’s test program and significantly impact the measured 

deflection basin. It this condition is not recognized, it will result in lower PCC elastic modulus 

values not representative of the in-place material.

CPTS

The CPTs were designed to store the results from the backcalculation process and assist in 

interpreting the results. One set of tables stores the EVERCALC© and MODCOMP© results, 

while a second set of tables stores the best fit results. The data in these sets of tables include

the following:

• Non-backcalculated values table: This table includes general information on each test 

section analyzed through the backcalculation programs and compares the pavement 
69

structure included in the LTPP database to the structure simulated in the backcalculation 

process. It also includes the number of basins analyzed, number of basins and stations 

with acceptable moduli, whether the LTPP section has been subdivided into two sections, 

whether a rigid layer is present, etc.

• Backcalculated values from individual deflection basins: This table includes all results 

for individual deflection basins along a specific test section for all dates that deflection 

basins were measured. The calculated layer moduli, even those identified as errors, are 

included in this table. Test time and pavement temperatures are also included, as well as 

other factors that can be used to determine how the results are influenced from the 

different factors included in the backcalculation process. This information can be used 

to evaluate the stress sensitivity, temperature sensitivity, and seasonal sensitivity of 

the results.

• Summary of results or processed data: These are the representative values for each test 

section that are layer dependent, test lane dependent, drop height dependent, season 

dependent, temperature dependent, etc. This table includes the average and standard 

deviation of elastic layer moduli along the test section on a test day basis. The averages 

and standard deviations were determined using the individual deflection basins not 

identified as an error.

The data included in the CPTs are similar to those designed and prepared from the first round of 

backcalculation results in 2002 and include, as a minimum, the following:

(4)

• Representative layer structure (material type and layer thickness) used in the 

backcalculation process. Some of the structure simulations varied from season to season 

because of fluctuations in water content and damage that occurred over time for some of 

the bound layers. In addition, the depth to bedrock was included in the structure and 

summary tables. In a few cases, including or excluding bedrock varied between test days.

• Deflection basin characterization and load-response category were included for the

individual deflection basins.

• All deflection basins that do not meet the acceptance criteria were flagged and removed 

from the summary database. The individual deflection basins with error flags, however, 

were included in the tables for the individual deflection basins.

• Layer modulus and the error term from the results for each deflection basin as well as the 

average and standard deviation along the test lane on a test day basis of a test section

were included in the tables.

• The spatial variability was included in the CPTs so that future users understand the mean 

and the amount of variation from those mean values.

A user’s manual and source code, Backcalculation Procedures and User Guide for Software 

Programs and Utility Tools, was prepared for all software packages and tools that were 

modified, revised, or developed as a part of this study.

(56) In addition, source codes were 
70

prepared for each of the pre- and post-processing utility tools used in this round of 

backcalculation. Source codes were not prepared for any program that was already available in 

the public domain and was not changed in any manner.
71

CHAPTER 6. APPLICATION AND USE OF BACKCALCULATION RESULTS

This chapter illustrates the use of the backcalculated elastic layer modulus values for a range of 

topics related to day-to-day design applications as well as for research purposes. These examples 

demonstrate the application of the backcalculated elastic moduli and not a detailed or complete 

analysis related to any one topic. 

SETTING DEFAULTS FOR MATERIAL TYPES

Histograms can be prepared to determine the spread and mean for a particular material or

pavement layer. Figure 5 and figure 6 in chapter 3 are examples of a test section basis for one of 

the case studies. These histograms can be used for judging the reasonableness of the results, 

identifying outliers, and comparing the mean value to the default value included in the MEPDG 

for that material.(1) Additionally, figure 35 and figure 36 show a histogram of the GB layers or 

aggregate bases classified as an AASHTO A-1-a material from all LTPP test sections in Georgia 

and Minnesota. The overall distribution has a positive skew for both sets of data with a mean of

about 28 ksi for the Georgia sections and 23 ksi for the Minnesota sections. 

Figure 35. Graph. Backcalculated elastic moduli for all aggregate base layers for the

Georgia (GA(13)) LTPP test sections classified as an AASHTO A-1-a material.
72

Figure 36. Graph. Backcalculated elastic moduli for all aggregate base layers for the 

Minnesota (MN(27)) LTPP test sections classified as an AASHTO A-1-a material.

The default resilient modulus included in the MEPDG is 40 ksi for an AASHTO A-1-a base, 

30 ksi for crushed stone, and 25 psi for crushed gravel.(1) The values included in the MEPDG are 

for optimum conditions, and it is expected that optimum conditions do not exist in the field over 

time. The mean value from the distribution shown in figure 35 and figure 36 is probably more 

similar to the representative value that can be entered in the MEPDG—an average weighted 

value throughout the year.

There are outliers in the Georgia and Minnesota datasets of around 100 and 200 ksi; however, 

these values are believed to represent a frozen or partially frozen base layer. In addition, a fairly 

large number of elastic modulus values were computed around 5 ksi, which was the lower limit 

set during the backcalculation process. Although these values were previously eliminated during 

the first round of backcalculation from the LTPP database as being too low, they are believed to 

be representative of saturated or wet conditions, when the frozen layer thaws or water enters the 

aggregate base layer through lateral flow of water or cracks in the pavement surface. Similarly, 

the high values were also eliminated from the first round of backcalculation but may be accurate

in the case where the base layer is very dry.

STRESS SENSITIVITY OF NONLINEAR MATERIALS AND SOILS

Most unbound aggregate base materials and soils are sensitive to changes in the applied stress, 

and the resilient modulus is dependent on the stress state or level. Coarse-grained aggregate base 

materials and coarse-grained soils generally exhibit a stress hardening pattern where the resilient 

modulus increases with increasing stress level, while most fine-grained soils exhibit a stress 

softening pattern where the resilient modulus decreases with increasing stress level. Some sands 

or soils at the transition between fine and coarse-grained soils exhibit no stress sensitivity in the 

practical range of applied stresses.
73

Deflection basins were measured over four drop heights on all LTPP test sections to determine 

the nonlinearity behavior of the unbound layers. Backcalculating the nonlinearity behavior or 

properties of the unbound layers was an objective during the first round of backcalculation. 

Determining the nonlinearity of the unbound layers was found to be problematic and resulted in 

a poor success rate. This round of backcalculation focused on using linear elastic methods to

calculate the elastic moduli for each drop height. The layer moduli from each drop height could 

then be used to determine the nonlinearity coefficients of the selected constitutive equation. 

Three SPS-8 projects (New York, Texas, and Utah) were used to demonstrate the variation in 

backcalculated elastic moduli for the four drop heights used in the LTPP deflection basin testing 

program. The SPS-8 projects were used in this demonstration because these sections generally 

have very low truck traffic and thin HMA layers—conditions that should exhibit a layer’s 

nonlinearity response, if present. In other words, the differences in the in-place stresses from 

drop heights 1 to 4 should be the greatest because the HMA is thin for these sections.

Figure 37 through figure 45 show the change in elastic layer moduli between drop heights 1 to 4 

for the aggregate base, weathered soil, and subgrade at the SPS-8 project sites. The average 

backcalculated elastic moduli were determined for 3 to 4 test days at each site. As shown, most 

of the layers did not exhibit a constant change in elastic moduli with increasing drop height or 

stress level, with the exception of the aggregate base at the Texas site and the coarse-grained SS

at the New York site. Most of the unbound layers at these three sites exhibited no stress 

sensitivity or the moduli increased and then decreased, making the determination of the nonlinear 

coefficients of a constitutive equation difficult. In specific, the change in modulus between the 

drop heights was considered insignificant relative to the variation or standard deviation of 

moduli along the test section (not illustrated in the figures) as well as with time.

Figure 37. Graph. Comparison of backcalculated elastic moduli for the aggregate base

layer from the Texas SPS-8 project 48-0801.
74

Figure 38. Graph. Comparison of backcalculated elastic moduli for the weathered finegrained soil layer from the Texas SPS-8 project 48-0801.

Figure 39. Graph. Comparison of backcalculated elastic moduli for the fine-grained 

subgrade from the Texas SPS-8 project 48-0801.
75

Figure 40. Graph. Comparison of backcalculated elastic moduli for the aggregate base

layer from the Utah SPS-8 project 49-0803.

Figure 41. Graph. Comparison of backcalculated elastic moduli for the weathered coarsegrained layer from the Utah SPS-8 project 49-0803.
76

Figure 42. Graph. Comparison of backcalculated elastic moduli for the coarse-grained 

subgrade from the Utah SPS-8 project 49-0803.

Figure 43. Graph. Comparison of backcalculated elastic moduli for the aggregate base

layer from New York SPS-8 project 36-0802.
77

Figure 44. Graph. Comparison of backcalculated elastic moduli for the weathered coarsegrained layer from the New York SPS-8 project 36-0802.

Figure 45. Graph. Comparison of backcalculated elastic moduli for the coarse-grained 

subgrade from the New York SPS-8 project 36-0802.

MEPDG HMA DAMAGE CONCEPT: FACT OR FICTION?

One of the unique components of the MEPDG methodology for rehabilitation design is the 

characterization of the in-place asphalt layers in terms of damage.(1) The MEPDG method uses 

backcalculated elastic layer moduli of the HMA or bituminous layer to determine the amount of 

damage in the existing asphalt layers by comparing the in-place backcalculated elastic layer 

modulus to that of an intact undamaged modulus measured in the laboratory. The damage is 

defined as the ratio of the backcalculated elastic layer modulus to the laboratory-measured 

dynamic modulus. The greater the damage or the lower the ratio, the greater the structural 

thickness required for an overlay. If this concept is correct, the backcalculated moduli should 

decrease over time as damage starts to accumulate.
78

Time-Dependent Damage Values

Figure 46 illustrates the change in modulus over time for LTPP GPS site 27-6251. As shown, the 

elastic layer moduli are about the same between 1990 and 1993, while there is a significant 

decrease in elastic moduli for 2003 when the pavement is about 10 years older. This decrease or 

softening in the moduli is defined as damage by the MEPDG.(1) Conversely, figure 47 illustrates 

no change in moduli and no damage or softening between 1990 and 1997 for LTPP GPS 

site 27-1018. In other words, this section did not exhibit any damage between 1990 and 1997.

Thus, the LTPP backcalculated elastic layer moduli can be used to confirm or reject this damage 

concept determination and its use for pavement evaluation and rehabilitation design.

Figure 46. Graph. Decreasing elastic moduli of the asphalt layer over time for use in 

rehabilitation design for Minnesota GPS section 27-6251.
79

Figure 47. Graph. Decreasing elastic moduli of the asphalt layer over time for use in 

rehabilitation design for Minnesota GPS section 27-1018.

It can be seen that the backcalculated elastic layer modulus values were about the same at colder 

temperatures during the winter months and approached each other at the higher temperatures 

during the summer months. The difference in moduli over time is exhibited within the 

intermediate temperature range. Figure 48 and figure 49 illustrate the change in modulus within a 

narrow temperature range of 60 to 66 oF for Minnesota section 27-1016 and section 27-6251, 

respectively. As shown, there is a continuous decrease in the elastic modulus from the deflection 

basin tests conducted between these temperatures. Thus, the time of year for measuring the 

amount of in place damage is probably important. If this observation holds true for many other 

LTPP test sections, the mathematical relationship used in the MEPDG for calculating damage 

may need to be revised to be temperature dependent.(1)
80

Figure 48. Graph. Decreasing elastic moduli of the asphalt layer between 60 and 66 oF over 

time for use in rehabilitation design for Minnesota GPS section 27-1016.

Figure 49. Graph. Decreasing elastic moduli of the asphalt layer between 60 and 66 oF over 

time for use in rehabilitation design for Minnesota GPS section 27-6251.

Modulus Differences Between Wheel Paths and Non-Wheel Paths

Minnesota section 27-6251 exhibited significant damage as defined by the MEPDG, while 

Minnesota section 27-1018 did not exhibit any damage.(1) Deflection basins in LTPP were 

measured in the wheel paths (lane F3) as well as out of the wheel paths (lane F1) to determine if 

the load-response properties were different between the two areas. If the damage concept is 

correct, then the measurements within the wheel path should be statistically different than the 

non-wheel path measurements for the test section exhibiting damage, and there should be no 

difference between the two lines for the section not exhibiting damage.
81

Figure 50 and figure 51 include a comparison of the backcalculated elastic layer moduli for the 

wheel path and non-wheel path areas for these two LTPP sections in Minnesota. As shown, a 

significant difference was observed for GPS section 27-6251, and no difference was observed for 

GPS section 27-1018. This observation provides support for the damage concept incorporated 

within the MEPDG.(1) If this concept holds true for many more LTPP sections, this will make it 

easier for agencies to determine whether there is a difference in the loaded and non-loaded areas 

of the pavement by simply testing along two lanes, reducing the number of cores that are now 

required to determine the in-place damage for rehabilitation design and managing an agency’s 

roadway network for planning future rehabilitation projects.

This observation by itself should be of significant value to agencies for improving their 

management prediction and planning capabilities. Simply measuring the deflection basins in the 

wheel path versus outside the wheel path provides a comparison of elastic moduli and whether 

damage is starting to occur. As extensive surface cracking starts to occur and spread beyond the 

wheel paths, however, any difference between measurements made in and outside the wheel 

paths is expected to decrease.

Figure 50. Graph. Elastic moduli of the asphalt layer between the wheel path and nonwheel path lanes for Minnesota GPS section 27-6251.
82

Figure 51. Graph. Elastic moduli of the asphalt layer between the wheel path and nonwheel path lanes for Minnesota GPS section 27-1018.

DIFFERENCES BETWEEN FIELD-DERIVED AND LABORATORY-MEASURED 

MODULI

The MEPDG software requires the entry of laboratory-measured moduli.(1) This section 

compares the backcalculated elastic layer moduli to laboratory-measured moduli.

HMA Layers

Elastic moduli were calculated and are in the CPTs in the LTPP database for all HMA-surfaced

test sections. The projects included in the SPS-1 experiment were used to compare the 

laboratory-derived dynamic moduli and field-derived elastic moduli of the HMA layers for 

four test sections in Florida, Montana, New Mexico, and Wisconsin. The deflection basin test 

days used in this analysis were the first three recorded for each project because it is expected that 

no damage should have occurred shortly after the mixtures were placed. In addition, the 

backcalculated elastic moduli were derived from the deflection basins measured outside the 

wheel path to further reduce any possibility of damage skewing the comparison.

Figure 52 compares the laboratory-computed dynamic moduli using the Witczak regression 

equation to the backcalculated elastic moduli. A loading frequency of 20 Hz was used in the 

comparison. In addition, the mid-depth temperature for the layer in question was used to estimate 

the laboratory-derived value. As shown, there is a slight bias in the backcalculated moduli—

slightly lower moduli were computed from the deflection basins in comparison to the laboratoryderived values computed with the dynamic modulus regression equation. This bias could be 

related to the assumed loading frequency and/or temperature used to estimate the laboratoryderived values. It could also be related to the thickness of the HMA layer used in the 

backcalculation process.
83

Figure 52. Graph. Comparison of the dynamic moduli computed from the Witczak 

regression equation and the backcalculated elastic moduli for four SPS-1 projects.

It is the authors’ opinion that temperature is not the controlling factor causing the bias, but load 

frequency and thickness could be contributing factors. It is suggested that the LTPP 

backcalculated elastic moduli can be compared to the dynamic moduli calculated using 

Witczak’s or another regression equation for making a recommendation on the loading frequency 

to be used and determine whether it is thickness dependent. By defining the equivalent load

frequency and whether it is dependent on some other factor, no adjustments need to be made to 

the backcalculated elastic layer moduli for the HMA or bituminous layers.

PCC Layers

Static elastic moduli were measured in the laboratory for most of the PCC mixtures placed on the 

SPS-2 projects. The projects included in the SPS-2 experiment were investigated to compare the 

laboratory equivalent and field-derived elastic moduli of the PCC layers for four test sections. 

The deflection basin test days used in this analysis were the first ones recorded for each project 

after construction because it was expected that no damage occurred shortly after the mixtures 

were placed. The first deflection basin measurements for many of the SPS-2 projects, however, 

were taken more than 1 year after placement. As such, the elastic moduli measured on the GPS 

test sections were compared to the backcalculated moduli because both represent long-term 

properties. As was shown in figure 16, there was extensive variation in the backcalculated 

moduli, but the bias was minimal. One observation from the comparison is that the 

backcalculated elastic PCC moduli from EVERCALC© and MODCOMP© need to be adjusted to 

remove the bias for estimating laboratory-measured static elastic moduli and results from the 

best fit unbonded condition method. It is suggested that more sites be included in the comparison 

to confirm or reject the hypothesis.
84

Unbound Aggregate Base and Soils Layers

The case study sites were used to compare the laboratory-derived resilient modulus of the 

unbound layers at equivalent stress states under FWD testing to the average backcalculated 

elastic moduli. The resulting c-factors were found to be similar to the values reported in the 

literature as well as the default c-factors recommended for use in the MEPDG.(1) No further 

analyses comparing laboratory-derived resilient moduli to field-derived elastic moduli were 

completed under this study to determine if the c-factor was dependent on other factors.

TIME AND SEASONAL EFFECTS

The backcalculated elastic layer moduli for each pavement layer were reviewed from selected 

sites in the SMP experiment to evaluate the change in values over time or by month. Four SMP 

sites were used: two from a cold environment (Idaho (16-1010) and Minnesota (27-1018)) and 

two from a warm environment (New Mexico (35-1112) and Texas (48-1077)).

Seasonal Temperature Effects on HMA

Figure 53 through figure 56 show the backcalculated elastic layer moduli for the HMA layers 

from the four SMP sites. The backcalculated elastic moduli for the two SMP sites located in a 

warm climate had significantly lower elastic moduli during the winter months in comparison to 

the SMP sites located in a cold climate. The elastic moduli calculated for the winter months in 

the cold climates exceeded values that were considered too large in comparison to typical values 

measured in the laboratory. This represents a significant difference between the laboratoryderived and field-derived moduli during the winter months that should be investigated. It was 

expected that a partially frozen layer directly beneath the HMA had an effect on the HMA 

field-derived moduli.

Figure 53. Graph. Comparison of HMA backcalculated elastic layer moduli for Idaho SMP 

section 16-1010.
85

Figure 54. Graph. Comparison of HMA backcalculated elastic layer moduli for New 

Mexico SMP section 35-1112.

Figure 55. Graph. Comparison of HMA backcalculated elastic layer moduli for Minnesota 

SMP section 27-1018.
86

Figure 56. Graph. Comparison of HMA backcalculated elastic layer moduli for Texas SMP 

section 48-1077.

Seasonal Moisture Effects for Unbound Aggregate Base Layers

Figure 57 through figure 60 show the backcalculated elastic layer moduli for the unbound 

aggregate base from the four SMP sites. The two SMP sites located in a cold climate had very 

high elastic moduli during the winter months that were representative of a frozen or partially 

frozen layer (Idaho section 16-1010 and Minnesota section 27-1018). For the two SMP sites 

located in a hot climate, the elastic modulus was significantly higher during the summer months 

in comparison to the winter months (New Mexico section 35-1112 and Texas section 48-1077). 

The water content of the aggregate base layers in the summer months in a hot dry climate can be 

lower in comparison to the winter months and result in higher modulus values.

Figure 57. Graph. Comparison of aggregate base backcalculated elastic layer moduli for 

Idaho SMP section 16-1010.
87

Figure 58. Graph. Comparison of aggregate base backcalculated elastic layer moduli for 

New Mexico SMP section 35-1112.

Figure 59. Graph. Comparison of aggregate base backcalculated elastic layer moduli for 

Minnesota SMP section 27-1018.
88

Figure 60. Graph. Comparison of aggregate base backcalculated elastic layer moduli for 

Texas SMP section 48-1077.

Seasonal Moisture Effects for the Weathered Soil Layers

Figure 61 through figure 63 show the backcalculated elastic layer moduli for the weathered soil 

layers at three of the SMP sites (Idaho, Minnesota, and Texas). A weathered layer was not 

included in the New Mexico SMP site because a bedrock or very stiff layer existed at this site. 

The two SMP sites located in a cold climate had very high elastic moduli during the winter 

months that were representative of a frozen or partially frozen layer (Idaho section 16-1010 and 

Minnesota section 27-1018). For the SMP site located in a hot climate with a weathered soil 

layer, the elastic modulus was significantly higher during the summer months in comparison to 

the winter months (Texas section 48-1077). The water content of the weathered soil in the 

summer months in a hot dry climate can be lower in comparison to the winter months and result 

in higher modulus values.

Figure 61. Graph. Comparison of weathered soil backcalculated elastic layer moduli for 

Idaho SMP section 16-1010.
89

Figure 62. Graph. Comparison of weathered soil backcalculated elastic layer moduli for 

Minnesota SMP section 27-1018.

Figure 63. Graph. Comparison of weathered soil backcalculated elastic layer moduli for 

Texas SMP section 48-1077.

The Idaho SMP site included a thick rock fill. The elastic modulus of this layer steadily 

increased over time to a value of about 150 ksi. The authors completed deflection testing and 

backcalculation of elastic layer moduli using EVERCALC© on other commercial-type projects

that included rock fills located in central Texas and Wyoming. Similar results were obtained

from unpublished design reports, with the in-place elastic moduli varying from about 80 to over 

150 ksi. However, time-dependent results from these other projects were unavailable. Rock fills 

have been placed at other LTPP test section locations and should be investigated to determine if 

they exhibit this same time-dependent characteristic and magnitude of in-place elastic moduli.
90

Seasonal Moisture Effects for the SS Layers

Figure 64 through figure 67 show the backcalculated elastic layer moduli for the SS at the four 

SMP sites. The two SMP sites located in a cold climate had higher elastic moduli during the 

winter months that would be representative of a partially frozen layer. For the two SMP sites 

located in a hot climate, the elastic modulus was about the same between the summer and winter 

months. Significant variations in water content of the deeper SSs do not usually occur unless 

there is an external factor causing the change in the water content, such as the lateral flow of 

water or seasonal perched water tables.

Figure 64. Graph. Comparison of SS backcalculated elastic layer moduli for Idaho SMP 

section 16-1010.

Figure 65. Graph. Comparison of SS backcalculated elastic layer moduli for New Mexico

SMP section 35-1112.
91

Figure 66. Graph. Comparison of SS backcalculated elastic layer moduli for Minnesota 

SMP section 27-1018.

Figure 67. Graph. Comparison of SS backcalculated elastic layer moduli for Texas SMP 

section 48-1077.

MIXTURE TIME-DEPENDENT MODULI

HMA Aging

The SPS-1 and -5 test sections were investigated to determine the increase in elastic moduli over 

time and if the values could be used to estimate the hardening that occurs with time.

Figure 52 shows a comparison of the laboratory-derived dynamic moduli to the field-derived 

elastic moduli for the first 3 test days when the majority of the hardening occurred after HMA 

placement. The HMA layers were combined for most of the SPS-1 test sections and represent 

weighted or composite values for all of the HMA lifts or layers. Even for the SPS-5 test sections 

where the overlay was represented as a separate layer, there was no clear increase in the fieldderived elastic moduli over time. More importantly, the HMA elastic layer moduli were heavily 
92

influenced by temperature, so the increase in HMA elastic modulus through hardening could not 

be determined because of the variability in the computed results.

PCC Modulus-Gain Relationship

The PCC backcalculated elastic layer moduli from selected SPS-2 test sections were used to 

determine if these values could be used to confirm the modulus-time or strength gain relationship 

included in the MEPDG software.

(1) Figure 68 and figure 69 show the backcalculated elastic 

layer moduli from the EVERCALC© program and best fit method, respectively, for multiple 

SPS-2 test sections. As shown, there was too much variation in the backcalculated moduli values 

over time to estimate the strength or stiffness versus time relationship. Figure 70 provides a 

comparison between the PCC elastic modulus from the best fit unbonded method to the elastic 

moduli backcalculated with EVERCALC©. The PCC elastic moduli from the unbonded best fit

method are consistently higher than from the moduli backcalculated with EVERCALC©.

Figure 68. Graph. Backcalculated PCC elastic moduli over time from EVERCALC© for 

selected SPS-2 test sections.
93

Figure 69. Graph. Backcalculated PCC elastic moduli over time from the best fit unbonded 

method for selected SPS-2 test sections.

Figure 70. Graph. Comparison of backcalculated PCC elastic moduli from EVERCALC©

and the best fit unbonded method for selected SPS-2 test sections.

MODULUS OF FRACTURED PCC LAYERS

The MEPDG provides recommended default elastic moduli for fractured PCC slabs, but 

two questions have been raised regarding the elastic moduli that are representative of the 

fractured PCC layer: (1) what is the representative elastic modulus after construction, and 

(2) does this value change over time? The LTPP backcalculated elastic layer moduli from SPS-6 

test sections were used to determine if those two questions can be answered. Test sections from 

Arizona, Indiana, Michigan, Oklahoma, and Pennsylvania were used to compare the 

backcalculated elastic layer moduli between the fractured and intact PCC slabs. The Arizona, 
94

Michigan, and Pennsylvania projects included both crack and seat and rubblized test sections, 

but the Indiana and Oklahoma projects did not. The Indiana project only included the crack and 

seat method, while the Oklahoma project only included the rubblization method.

The Oklahoma SPS-6 project was used as one of the case studies because the existing pavement 

consisted of a JRCP that was rehabilitated using multiple techniques. The first layering 

simulation included the JRCP as one continuous layer for both the rubblization method as well as 

for the intact slabs. Table 16 lists the backcalculated layer moduli before and after rehabilitation 

for the last testing day at this project site. A second run was made for the rubblized section but 

with a different layering simulation: JRCP was divided into two layers above and below the 

reinforcement. The table also includes the values resulting from that condition for the last testing 

day included in the LTPP database.

Table 16. Backcalculation results for the Oklahoma SPS-6 project—intact and rubblized 

test sections.

Item or Element

Section 0606 Major Restoration Section 0608 Rubblization

Intact Slabsa Crack & Seat

Intact 

Slabsa One Layer Two Layers

PCC modulus 4,799 3,615 5,082 301 284

2,013

Aggregate base 

modulus

11.4 16.3 10.2 56.4 N/A

Weathered soil 

layer modulus

67.5 13.6 10.1 45.5 27.5

Subgrade natural 

modulus

33.6 32.5 37.8 34.5 35.0

HMA overlay 

modulus

N/A 617 N/A 848 880

Average RMSE 1.4 1.6 1.1 1.2 1.1

N/A = Layer not applicable or used in backcalculation process.

a

Backcalculated elastic modulus values include those prior to major restoration and rubblization; there was no HMA 

overlay because deflection basins were measured prior to restoration or rubblization.

The simulation of two PCC layers resulted in about the same RMSE value as for the single layer 

simulation. The modulus of the upper PCC layer, however, was significantly lower than that of 

the lower PCC layer. More importantly, the elastic modulus of the upper layer was found to be 

only slightly lower than that of the single JRCP layer. Thus, it was decided the structure would 

initially be simulated as one PCC fractured layer. If high RMSE values resulted, then the PCC 

fractured layer was divided into two layers in an effort to reduce the RMSE.

Figure 71 shows the backcalculated elastic modulus of the rubblized PCC at the Oklahoma 

SPS-6 site. The elastic modulus of the rubblized PCC was less than 100 ksi after construction,

but it steadily increased over time. The PCC moduli for intact slabs of the control section 

(without an HMA overlay) and the section with maximum restoration activities are also shown 

in figure 71. The elastic moduli varied from 3 to 6 million psi at this site.
95

Figure 71. Graph. Backcalculated elastic moduli for the Oklahoma SPS-6 rubblized test 

sections.

Figure 72 shows the backcalculated elastic layer modulus for the PCC modulus for the Indiana 

crack and seat sections. As shown, the elastic modulus for the PCC crack and seat was about 

one-third the modulus of the intact slabs and then increased over time. 

Figure 72. Graph. Backcalculated elastic moduli for the Indiana SPS-6 crack and seat test 

sections.

Figure 73 through figure 75 compare the backcalculated elastic moduli for the intact, crack and 

seat, and rubblized test sections from the Arizona, Michigan, and Pennsylvania SPS-6 projects. 

As shown, the Arizona crack and seat section was the only one where the elastic moduli 

decreased over time. All other SPS-6 sections stayed about the same or increased over time.

10

100

1000

10000

0 5 10 15

Backcalculated PCC Elastic Modulus, ksi

Overlay Age, years

Section 40-0601 - No

Overlay

Section 40-0605 -

Max Restoration

Section 40-0607 -

Rubblized

Section 40-0608 -

Rubblized

0

1000

2000

3000

4000

5000

6000

7000

0 5 10 15 20

Backcalculated PCC Elastic Modulus, ksi

Overlay Age, years

Section 18-0602 - AC

Overlay, No Crack

and Seat

Section 18-0607 -

Crack and Seat

Section 18-0608 -

Crack and Seat

Section 18-0662 -

Crack and Seat
96

Figure 73. Graph. Backcalculated elastic moduli comparing the PCC intact, crack and seat, 

and rubblized test sections for the Arizona SPS-6 test sections.

Figure 74. Graph. Backcalculated elastic moduli comparing the PCC intact, crack and seat, 

and rubblized test sections for the Michigan SPS-6 test sections.
97

Figure 75. Graph. Backcalculated elastic moduli comparing the PCC intact, crack and seat, 

and rubblized test sections for the Pennsylvania SPS-6 test sections.

The default values included in the MEPDG for the crack and seat method are 150,000 to 

2 million psi, and for the rubblization method the default values are 50,000 to 1 million psi.(1) 

Both represent a wide range of moduli. The following list summarizes some observations from 

these SPS-6 projects relative to the range of values included in the MEPDG:

(1)

• With the exception of the Indiana project, the backcalculated elastic moduli for the crack 

and seat method increased over time to a value of about one-half to one-third of the 

elastic modulus of the intact slabs.

• For the rubblized sections, the backcalculated elastic moduli were greater than 50 ksi but 

less than 1,000 ksi for all test sections. The backcalculated elastic modulus stayed about 

the same after construction except at the Oklahoma project.

• The backcalculated elastic modulus values for the intact slabs without an HMA overlay 

were found to be greater than 5 million psi at the Michigan, Oklahoma, and Indiana 

projects but not the Arizona and Pennsylvania projects. The backcalculated elastic 

modulus of the intact slabs from the Arizona and Pennsylvania sections without an 

overlay were representative of cracked PCC for the test sections included in this 

preliminary evaluation.

Based on these observations, a detailed evaluation of the backcalculated elastic moduli for the 

fractured PCC slabs should be conducted for recommending a narrower range of default values 

included in the MEPDG.(1)

RECLAIMED ASPHALT PAVEMENT (RAP) AND VIRGIN MIXTURES

Many agencies have limits on the amount of RAP included in HMA base mixtures as well as for 

wearing surfaces. The asphalt industry has been pushing the use of higher percentages of RAP in 
98

asphalt mixtures in all layers of the pavement. The LTPP SPS-5 experiment was designed to 

provide data to evaluate the difference between mixtures with about 30 percent RAP and those 

without RAP. The backcalculated layer elastic modulus was used to evaluate whether there was a 

difference between the structural responses of the sections with and without RAP. Figure 76

provides a comparison of the RAP and virgin mixture backcalculated elastic layer moduli for the 

SPS-5 Minnesota project. As shown, there was no significant difference in the structural 

responses of the asphalt mixtures with and without RAP.

Another important observation from figure 76 is that the backcalculated elastic modulus for the 

existing asphalt mixture (the control section which was not overlaid) had a significantly higher

in-place modulus value than the virgin and RAP mixtures of the overlay. This observation was 

expected because the existing HMA was much older than the two overlay mixtures, 

demonstrating the difference that can be caused by long-term aging.

Figure 76. Graph. Comparison of RAP and virgin backcalculated elastic HMA moduli 

from the Minnesota SPS-5 project.

The backcalculated moduli from four additional SPS-5 projects were used to investigate the 

difference between the RAP and virgin mixtures in relation to the existing HMA layers. 

Figure 77 through figure 80 show a comparison of the backcalculated elastic moduli for the 

different mixtures at four of the SPS-5 projects.
99

Figure 77. Graph. Comparison of RAP and virgin mix backcalculated elastic HMA moduli 

from the Arizona SPS-5 project.

Figure 78. Graph. Comparison of RAP and virgin mix backcalculated elastic HMA moduli 

from the Mississippi SPS-5 project.
100

Figure 79. Graph. Comparison of RAP and virgin mix backcalculated elastic HMA moduli 

from the Oklahoma SPS-5 project.

Figure 80. Graph. Comparison of RAP and virgin mix backcalculated elastic HMA moduli

from the Maine SPS-5 project.

No significant and consistent difference was observed between the RAP and virgin mixtures 

used for the overlay. The Maine SPS-5 project exhibited the least difference between 

the mixtures, while the Arizona SPS-5 project exhibited the least difference across all pavement 

test temperatures.

The elastic moduli for the existing HMA layer for the Oklahoma project were very high across 

the entire temperature regime. These results are believed to be reasonable because the binder 

tests conducted on the extracted asphalt from the existing HMA layer suggest a severely aged 

material. Conversely, the elastic moduli of the existing HMA layer at the Maine project were 

only slightly greater than for the overlay mixtures during the summer months. The binder 

tests conducted on the extracted asphalt for the Maine project did not suggest a severely 

aged material.
101

The Mississippi project exhibited a lot of variation for all mixtures. This project experienced 

high rutting and was taken out of service because of stripping. As noted in chapter 3, it also 

exhibited high damage in the field-derived moduli.

103

CHAPTER 7. CONCLUSIONS 

The automated backcalculation procedure and tools reported in this report were used to 

determine the elastic layer properties (or Young’s modulus) from deflection basin measurements 

for all LTPP test sections. This report summarizes the reasons why EVERCALC© and 

MODCOMP© were selected for the computations and analyses of the deflection data, provides a 

summary of the results using the linear elastic modulus for selected test sections, and identifies

those factors that can have a significant effect on the results. This chapter includes some of the 

highlights and findings from this study and recommendations for future activities in support of 

accomplishing the overall LTPP objectives.

FINDINGS

Backcalculation of elastic properties is not an exact science and requires user interaction in some 

cases. However, the process was automated through a series of utility functions and tools to 

reduce the impact of user interaction, bias, and/or inexperience. Results from this automated

procedure provide elastic layer load response properties that are consistent with previous 

experience and laboratory material studies related to the effect of temperature, stress state, and 

seasonal effects on the material load-response behavior. The following list highlights some of the 

important findings from this study:

• In 1997, Von Quintus and Killingsworth recommended one software package to be used 

because of large differences between multiple programs.(46) Similarly, one package was 

used in the first backcalculation project, MODCOMP4.0©. The present study used three 

programs: EVERCALC© and MODCOMP© were used to calculate the elastic layer 

moduli of all pavement sections in the LTPP database, and the best fit method was used 

for all PCC-surfaced test sections. EVERCALC© and MODCOMP© are available in the 

public domain, and they provide non-unique solutions. The best fit method is a forward 

calculation procedure that provides unique solutions.

• EVERCALC© and MODCOMP© resulted in statistically indifferent results for deflection 

basins classified as typical or in conformance with elastic layer theory as defined by Von 

Quintus and Simpson and Von Quintus and Killingsworth.

(4,46) For type 2 deflection 

basins, the EVERCALC© and MODCOMP© programs resulted in statistically different 

elastic moduli for the intermediate layers (the weathered soil layer and thinner aggregate 

base layers, which accounted for about 25 percent of the deflection basins analyzed). As 

reported in the first backcalculation study, the pavements exhibiting deflection-softening 

behavior with type 2 deflection basins were the most difficult to analyze and were 

generally found to have higher RMSEs.(4) Some of these deflection basin analyses 

resulted in no reasonable solution, or the solution provided unrealistic layer moduli for 

the type of material defined in the LTPP database.

• The PCC elastic moduli calculated with EVERCALC© resulted in significantly greater 

values in comparison to the moduli calculated with the best fit unbonded method. Thus, 

results from the two methods should not be combined, or a factor needs to be used to 
104

adjust the EVERCALC©-generated PCC moduli to the best fit unbonded condition 

method or laboratory-measured elastic moduli.

• Over 90 percent of the deflection basins analyzed with EVERCALC© and MODCOMP©

resulted in layer moduli with an RMSE less than 3 percent and are considered acceptable.

• In the authors’ opinion, there is still no consensus on the best backcalculation package 

that provides the most reliable and accurate results. However, the case study findings 

were very similar to the findings documented in the Smith study.

(53) Specifically, 

EVERCALC© consistently resulted in lower error terms and a higher number of 

successful modulus determinations when considering all deflection basins. When only 

considering those deflection basins that ran successfully, however, the MODCOMP©

program resulted in lower RMSE values.

• Historically, a constant modulus for the PCC rubblized slabs has been used for 

rehabilitation design projects. The elastic modulus of the rubblized PCC slabs, however, 

was found to steadily increase over time for some of the LTPP SPS-6 test sections.

• No difference was found in the load-response properties (stiffness) between the RAP and 

virgin mixtures of the SPS-5 experiment.

• Similar c-factor values were found in this project to the values included in the MEPDG.(1)

More importantly, no significant difference or bias was found between the laboratoryderived dynamic modulus and the field-derived values for the HMA layers.

• The use of drop heights 1 to 4 in the LTPP deflection testing program did not result in 

significantly different elastic moduli for the unbound layers. As such, it was difficult to 

determine the coefficients of a constitutive equation to estimate the stress sensitivity of an 

unbound layer because of the variation in moduli over time and along a specific test 

section. The stress levels resulting from the four drop heights used in the LTPP deflection 

testing program are too narrow.

• Damage was determined in accordance with the MEPDG procedure for multiple LTPP 

test sections to demonstrate its use in rehabilitation design.(1) The results were found to be 

positive and used to support the MEDPG procedure. The damage concept as applied to 

interpreting the backcalculated moduli can be very useful in explaining low moduli. In 

addition, the Florida Department of Transportation was one of the first agencies to 

monitor changes in the deflection basin (similar to this damage concept) over time in 

planning rehabilitation projects from a pavement management standpoint. From the case 

study sites and examples of data use, the damage concept can be used to evaluate the 

condition of the existing pavement and plan future rehabilitation projects.

• The use of four layers generally resulted in lower RMSEs than the use of three layers. In 

many cases, breaking or separating the subgrade into at least two layers improved the 

match between the measured and calculated deflection basins.
105

RECOMMENDATIONS

The results from this study have shown that elastic layer moduli (or load-response properties)

can be computed from deflection basins and provide pavement engineers with useful information 

about the pavement structure and subgrade condition. However, this study only touched on the 

different ways the backcalculated elastic layer modulus database can be used for improving 

pavement design and rehabilitation strategies. More detailed analysis can be completed to 

demonstrate the usefulness of the deflection data and resulting elastic moduli. The following list

highlights some specific topics that can be investigated in the future:

• Compare the field-derived elastic moduli of HMA layers to the laboratory-derived 

dynamic moduli for determining the equivalent load frequency of the FWD for matching 

the two moduli.

• Compare the PCC laboratory-measured static elastic moduli to the field-derived values to 

determine the adjustment factor for the EVERCALC©/MODCOMP© backcalculated

elastic modulus of PCC layer to be used in the MEPDG.

(1)

• Use the LTPP database for preparing a set of guidelines for estimating damage through 

deflection basin testing and backcalculated elastic moduli between within and outside the 

wheel paths. Agencies can use this information for planning rehabilitation projects.

• Confirm or revise the default PCC elastic layer moduli of rubblized and crack and seat 

slabs, as well as define how those values change with time.

• Use the backcalculated results to confirm the default moduli included in the MEPDG or 

recommend revisions to those default values and determine whether these values depend 

on season or climate.

(1)

107

APPENDIX A: BEST FIT METHOD—CALCULATING PCC ELASTIC LAYER 

MODULI

The best fit method proposed previously for the backcalculation of LTPP rigid pavement 

deflection data was adopted in this project.(3) All concrete-surfaced LTPP sections were analyzed 

using the best fit procedure, which involves the backcalculation of a two-layered (PCC and base) 

slab-on-grade.

(28,58,59) The procedure was recommended after the completion of the case studies 

evaluation for the following reasons: 

• The procedure is founded on sound mechanistic concepts. It is based on Westergaard’s 

solution for an interior loading condition of a plate resting on a dense-liquid foundation.

The plate is assumed to behave as a linear elastic, homogeneous, and isotropic material.

• The results were found to be reasonable and generally producing reasonable RMSE 

values for sections included in the case studies to demonstrate and compare the use of the 

candidate programs.

• The procedure can be used for any sensor configuration and provides the best fit between 

the measured deflection and the calculated deflections.

• The procedure is consistent with the MEPDG rigid pavement analysis in aspects relating 

to the reduction of the pavement layer structure to a two-layered PCC slab-base 

structure.(1) Within the framework of the MEPDG analysis, the two-layered structure is 

subsequently simulated as an effective slab-on-grade problem, with the slab assigned an 

effective structural capacity determined by the thicknesses of the slab and base and the 

contact friction between them (see figure 81). The best fit method analyzes the structure 

as a slab-on-grade problem to determine the composite modulus of the effective slab.

Further, depending on the slab-base bond condition assumption, appropriate methods are 

used to apportion the stiffness of the effective slab between the individual slab and base.

• The results are generated rapidly, making it suitable for processing the large datasets used 

in this project. Each deflection basin is analyzed in a fraction of a second.

The best fit approach may be considered as one that determines the stiffness of a fictitious 

effective slab which deforms in a manner identical to the actual pavement under the applied 

FWD loads. Therefore, the procedure attempts to match the deflection of the simulated effective 

slab with the measured deflection from the FWD testing. The simulation uses the same level of 

load as the FWD test and positions the load in the slab interior comparable to the J1 point 

location in the LTPP database.
108

EPCC = Elastic modulus of the PCC layer.

Ebase = Elastic modulus of the base layer.

hPCC = Thickness of the PCC layer.

Hbase = Thickness of the base layer.

Heff = Effective thickness of the pavement.

Figure 81. Illustration. Transformation of design structure to effective structure used by 

the neural networks to compute mechanistic responses.

In the figure, the effective thickness parameter derived from section transformation in step 2 

changes with the interface bond condition (i.e., heff) is smaller for the unbond condition. 

Additionally, the JPCP faulting model uses an unbonded interface for the calculation of corner 

deflections, while CRCP is always modeled as an unbonded section.

Independent of 

friction

Effective k-value from 

backcalculation

Structure 1: Original 

Pavement Structure

Step 1. E to k 

transformation for 

each month

Structure 2: Original 

Pavement Structure

Concrete slab

(JPCP, CRCP)

Base course

(Cement, Asphalt, Unbound)

Subbase 

(Stabilized, Unbound)

Compacted subgrade

Natural subgrade

Bedrock

Epcc

Ebase

hpcc

hbase

Interface friction

Epcc

Ebase

Concrete slab

(JPCP, CRCP)

Base course

(Cement, Asphalt, Unbound)

hpcc

hbase

Interface friction

Step 2. Effective slab 

on grade section each 

month

Structure 3: Slab on 

grade structure used 

in neural network

Concrete slab

(JPCP, CRCP)

Epcc

heff

Friction 

dependent

INPUTS

Epcc, Ebase, hpcc, hbase, 

interface condition 

(bonded/unbonded) 

Effective k-value
109

The optimization procedure solves for the specific combination of the coefficient of subgrade 

reaction and the radius of relative stiffness, which result in slab deflections closest to the 

measured deflections at each sensor. The procedure allows for the use of weighting factors for 

the error at each sensor, and the convergence criterion is the minimization of the sum of the 

mean squared errors from each sensor, with the error weighted by a pre-defined factor for each 

sensor. Therefore, the solution is determined by the minimization of the error function expressed 

as follows:

Figure 82. Equation. Error function definition for best fit procedure.

Where:

F = Error function dependent on the elastic modulus and coefficient of subgrade reaction.

E = Elastic modulus.

k = Coefficient of subgrade reaction.

n = Number of increments.

α i = Weighting factor.

w(ri) = Calculated deflection.

Wi = Measured deflection.

The deflection at any point at a radial distance measured from the center of a circular load plate 

distributing uniform pressure may be expressed as a function of r as follows:

Figure 83. Equation. Calculated deflection.

Where:

r = Radial distance.

p = Pressure.

f = Function.

l = Relative stiffness.

Where f(r) is a function of two dimensionless parameters, the radius of the load plate normalized 

to the radius of relative stiffness, and the radial distance of the sensor normalized to the radius of 

relative stiffness. The pressure p is the uniform pressure under the applied load P, calculated as 

P/ a2

, where a is the loaded area under the loading plate.

The radius of relative stiffness and the subgrade k-value define the flexural rigidity of the 

effective slab. Most commonly, the radius of relative stiffness is expressed as a function of the 

effective plate thickness, h, elastic modulus of the effective plate, E, Poisson’s ratio, , and the 

k-value as follows:

2

0

( , ) ( ( ) ) i i

n

i

F E k = ∑ i w r −W =

α

( ) f (r,l) k

p w r =

π

μ
110

Figure 84. Equation. Radius of relative stiffness.

Where D = Stiffness of the PCC slab.

The error function in figure 82 can be rewritten using figure 83 as follows:

2

0

( , ) ( , ) ( ) 



 



 = = ∑ − =

i i

n

i

i f l W

k

p F E k F l k α

Figure 85. Equation. Error function in alternate form.

The best fit procedure satisfies the two conditions shown in figure 86 and figure 87

as follows:

Figure 86. Equation. Partial derivative of F with respect to k.

Figure 87. Equation. Partial derivative of F with respect to l.

The substitution of the error function in figure 85 in the conditions represented by figure 86 and 

figure 87 yields the equations to solve for k and l, as shown in figure 88 and figure 89.

Figure 88. Equation. k-value.

Figure 89. Equation. Radius of relative stiffness.

The computational effort involved in solving the equation in figure 89 forms the major 

component of the best fit procedure. The k and l values determined from the equations in figure 

88 and figure 89 are substituted into the equation in figure 84 to determine the modulus of the 

plate or the effective slab.

1/ 4

2

3 1/ 4

12(1 ) 















−  = 

 



 = k

Eh

k

D l

μ

= 0

∂

∂

k

F

= 0

∂

∂

l

F

[ ]

( )

( )

0

2

0

i i k

n

i

i

i k

n

i

i

W f l

f l

k p

∑

∑

=

= =

α

α

[ ] [ ( )]

' ( )

( )

( ) ' ( )

0

0

2

0

0

i i k

n

i

i

i i k

n

i

i

i k

n

i

i

i k i k

n

i

i

W f l

W f l

f l

f l f l

∑

∑

∑

∑

=

=

=

= =

α

α

α

α
111

ESTIMATION OF BASE LAYER MODULUS IN BEST FIT PROCEDURE

The modulus backcalculated for the effective slab using the best fit procedure is subdivided 

between the slab and the base, which are assumed to provide a composite section in the 

calculated deflections. The effective contribution of the base layer in the overall stiffness of the 

composite section depends on two factors: the relative stiffness of the materials itself and the 

bond condition at the slab base interface.

To estimate the relative stiffness of the slab and the base materials, an additional parameter is 

introduced to quantify the modular ratio of the slab and base. The modular ratio, , is defined as 

follows (where the asterisk represents an adjustment to the modular ratio):

Figure 90. Equation. Modular ratio.

Where: 

EBase = Base modulus.

EPCC = PCC modulus.

The * values used in the analyses were based on the LTPP material codes for the base layer and 

were borrowed from Khazanovich et al. (see table 17).

(3) Some material codes were assigned *

values under the current study and have been identified in the table. The selected values are 

based on * values previously assigned for similar materials. In addition, for PCC layers overlaid 

using an unbonded PCC overlay, assuming the layer has undergone a fair level of damage, the 

stiffness was considered to be lower than a concrete slab in good condition ( * = 1) but higher 

than an AC layer ( * = 10). Therefore, a * value of 5 was assigned for PCC layers that have an 

unbonded overlay according to the TST_L05B layer structure. Also, a material code of 1000 was 

assigned within the best fit software code to identify PCC layers with unbonded overlay.

β

EBase EPCC β* = /

β

β

β

β

β β
112

Table 17. Modular ratio to estimate the relative stiffness between PCC slab and base in the 

best fit procedure (for both bonded and unbonded conditions).

LTPP 

Code * = 1/ Base Type

1 10 HMA, dense graded 

2 15 HMA, open graded

3 50 Sand asphalt

4 1 JPCP

5 1 JRCP

6 1 CRCP

7 1 PCC (prestressed)

8 1 PCC (fiber-reinforced)

9 20 Plant mix (emulsified asphalt) material, cold laid

10 20 Plant mix (cutback asphalt) material, cold laid

13 10 Recycled asphalt concrete (AC), hot laid, central plant mix

14 15 Recycled AC, cold-laid, central plant mix

15 15 Recycled AC, cold-laid, mixed-in-place

16 15 Recycled AC, heater scarification/recompaction

17 100 Recycled JPCP

18 100 Recycled JRCP

19 100 Recycled CRCP

78* 10 Dense-graded AC interlayer

80* 20 Open-graded AC interlayer

181 100 Fine-grained soils: lime-treated soil

182 50 Fine-grained soils: cement-treated soil

183 100 Bituminous-treated SS

292 150 Crushed rock

302 200 Gravel, uncrushed

303 150 Crushed stone

304 175 Crushed gravel

305 175 Crushed slag

306 250 Sand

307 400 Soil-aggregate mixture (predominantly fine-grained)

308 250 Soil-aggregate mixture (predominantly coarse-grained) 

309* 250 Fine-grained soils

310* 250 Other (specify, if possible)

319 15 HMA

320 50 Sand asphalt

321 50 Asphalt-treated mixture 

322 10 Dense-graded, hot-laid, central plant mix AC

323 15 Dense-graded, cold-laid, central plant mix AC 

324 15 Dense-graded, cold-laid, mixed-in-place HMA 

325 15 Open-graded, hot-laid, central plant mix HMA 

326 15 Open-graded, cold-laid, central plant mix HMA

327 15 Open-graded, cold-laid, mixed-in-place HMA

β β
113

328 10 Recycled HMA, plant mix, hot laid

329 15 Recycled HMA, plant mix, cold laid

330 15 Recycled HMA, mixed-in-place

331 5 Cement aggregate mixture 

332 4 Econocrete 

333 50 Cement-treated soil 

334 2 Lean concrete 

335 100 Recycled PCC

337* 150 Limerock, caliche

338 100 Lime-treated soil

339 10 Soil cement 

340 100 Pozzolanic-aggregate mixture 

341 25 Cracked and seated PCC layer 

351 100 Treatment: lime, all classes of quick lime and hydrated lime

352 150 Treatment: lime-flyash 

353 150 Treatment: lime and cement flyash 

354 50 Treated: PCC

355 100 Treatment: bitumen (includes all classes of bitumen and asphalt 

treatments)

700 15 HMA 

730 1 PCC

999 10000 No base (fictitious base)

1000*# 5 Existing PCC underneath unbonded overlay assumed damaged 

with lower modulus

*Represents material codes for which the modular ratios were established under this study. #

Represents a material code assigned in the software program for all PCC layers that have an unbonded overlay.

The best fit procedure considers two distinct cases for the bond condition at the interface 

between the upper (PCC) and lower (base) slabs: unbonded slab-base interface and fully bonded 

slab-base interface. Intermediate levels of interface bond are not analyzed.

In the case of unbonded PCC-base condition, flexural stiffness of the effective slab can be 

presented as follows:

Figure 91. Equation. Flexural stiffness.

Where:

De = Flexural stiffness of the effective slab.

DPCC = Flexural stiffness of the PCC.

DBase = Flexural stiffness of the base.

De = DPCC + DBase
114

For the unbonded conditions, PCC and base moduli are defined as follows: 

Figure 92. Equation. Slab modulus from effective modulus for unbonded condition.

Where:

EPCC =Elastic modulus of the PCC slab.

hPCC = PCC thickness.

hBase = Base thickness.

Ee = Effective modulus from best fit backcalculation.

Figure 93. Equation. Base modulus from effective modulus for unbonded condition.

For the case of the bonded base condition, the flexural stiffness of the effective slabs is derived 

using the parallel axis theorem. The PCC and base moduli are defined as follows, where x is the 

depth of the parallel axis from the surface as defined in figure 96 :

Figure 94. Equation. Sab modulus from effective modulus for bonded condition.

Figure 95. Equation. Base modulus for bonded condition.

Figure 96. Equation. Depth of the parallel axis from the surface.

DEFINING THE BASE LAYER IN THE PAVEMENT STRUCTURE

The project team developed procedures to identify layers in the pavement structure that could be 

treated as the base layer in the best fit analysis. Table 18 lists the layers below the PCC slab that 

were included in the base layer for different layer structures. The selection of the base layer was 

based on the following general rules:

• If the layer immediately beneath the PCC layer was an unbound GB layer with all layers 

below the GB layer of lower stiffness based on material type, the GB layer beneath the 

PCC layer was considered as the base layer.

e

PCC Base

PCC

PCC E

h h

h

E 3 3

3

+ β =

e

PCC Base

PCC

Base E

h h

h

E 3 3

3

β

β

+ =

e

PCC Base PCC PCC Base PCC Base

PCC

PCC E

h h h x h h h x h

h

E 3 3 2 2

3

+ +12 ( − 0.5 ) +12 ( − − 0.5 ) = β β

EBase = βEPCC

PCC Base

PCC Base PCC Base

h h

h h h h

x

β

β

+

+ + = 0.5 ( 0.5 ) 2
115

• If the layer immediately beneath the PCC layer was a stabilized base layer with all layers 

below the stabilized base layer of lower stiffness based on material type, the stabilized 

base layer beneath the PCC layer was considered as the base layer.

• If the layer structure presented a stiffer layer below the layer immediately underneath the 

PCC slab, appropriate layers were combined to represent the base layer based on 

engineering judgment and as shown in table 18.

• If a TS layer was present, it was not combined into the base layer. Rather, the effect of 

the TS layer was apparent in the computed k-value of the subgrade.

• For unbonded overlay sections, the layers between the overlay up to and including the 

existing slab were included in the base layer.

• For bonded overlays, the existing slab and the overlay were combined into the surface 

layer. The layer immediately underneath the existing slab was used as the base layer.

Table 18. Effect of layer structure on base layer—number of layers underneath the PCC 

slab included in the effective base layer.

Number of Layers 

Between PCC

Surface Layer and 

Subgrade

Layer Types in the Layer Structure 

Included in TST_L05B Table

Number of layers 

beneath the PCC

layer included in the 

effective base layer

1 PCC, GB, SS 1

1 PCC, GS, SS 1

1 PCC, TB, SS 1

2 PCC, AC, PC, SS 2

2 PCC, AC, TB, SS 2

2 PCC, GB, GS, SS 1

2 PCC, GB, TS, SS 1

2 PCC, TB, GB, SS 1

2 PCC, TB, GS, SS 1

2 PCC, TB, TS, SS 1

3 PCC, AC, AC, GB, SS 2

3 PCC, AC, AC, PC, SS 3

3 PCC, AC, PC, GB, SS 2

3 PCC, AC, PC, TB, SS 3

3 PCC, AC, TB, GS, SS 2

3 PCC, AC, TB, TS, SS 2

3 PCC, GB, GB, GS, SS 2

3 PCC, GB, GS, GS, SS 1

3 PCC, GB, GS, TS, SS 1

3 PCC, TB, AC, GS, SS 2

3 PCC, TB, AC, TS, SS 2

3 PCC, TB, GB, GS, SS 1

3 PCC, TB, GB, TS, SS 1
116

3 PCC, TB, GS, GS, SS 1

3 PCC, TB, GS, TS, SS 1

3 PCC, TB, TS, GS, SS 2

3 PCC, TB, TS, TS, SS 1

4 PCC, AC, AC, PC, GB, SS 3

4 PCC, AC, PC, GB, GS, SS 2

4 PCC, AC, PC, GB, TS, SS 2

4 PCC, AC, PC, TB, GS, SS 3

4 PCC, GB, GS, GS, GS, SS 1

4 PCC, TB, GB, GB, GS, SS 1

4 PCC, TB, GB, GS, GS, SS 1

4 PCC, TB, GB, GS, TS, SS 1

4 PCC, TB, GS, GS, GS, SS 1

6 PCC, AC, AC, AC, PC, GB, GS, SS 4

6 PCC, AC, AC, AC, PC, GB, GS, SS 4

7 PCC, AC, AC, AC, AC, PC, TB, TS, SS 6

GS = granular subbase.

TB = Treated base.

In the case of more than one layer between the PCC and subgrade, all base layers were combined 

into one layer. Using parallel axis theorem and defining the equivalent base thickness, heq, as 

the sum of the base layers thicknesses, it was possible to calculate the equivalent base modular 

ratio, eq. eq calculations for a structure with up to five layers combined into the base layer is 

further described.

If hi is the thickness of the i

th base layers and i is the modular ratio of the ith layer (from 

table 17), then for the case of five base layers, the equivalent base modular ratio can be 

calculated as follows:

Figure 97. Equation. Equivalent beta when multiple layers are combined into the base.

Where:

Expri = A model parameter defined in figure 99 and figure 100.

The variables in figure 97 are defined as shown in figure 98 through figure 103.

Figure 98. Equation. Equivalent thickness.

Figure 99. Equation. Expr1.

β β

β

3 1

1 12 2 β β

eq

eq h

Expr + Expr =

∑=

=

5

i 1

eq i h h

3

51 5

3

41 4

3

31 3

3

21 2

3

1 Expr1 = h + β h + β h + β h + β h
117

Figure 100. Equation. Expr2.

Figure 101. Equation. Depth of parallel axis from the surface when multiple layers are 

combined into the base.

Figure 102. Equation. Expr3.

Figure 103. Equation. Expr4.

Note that in these equations, the values are the inverse of the * listed in table 17. The eq

value calculated in figure 97 provides the combined effective multilayer β value used in 

figure 89 to calculate the modulus of the effective base layer. 

2

) 3 0.5 1 2 ( 3 31

2

) 2 0.5 1 ( 2 21

2

) 1 (0.5 1 Expr2 = h h − x + h β h + h − x + h β h + h + h − x

2

) 5 0.5 1 2 3 4 ( 5 51

2

) 4 0.5 1 2 3 ( 4 41 + h β h + h + h + h − x + h β h + h + h + h + h − x

4

3

Expr

Expr x =

) 3 0.5 1 2 ( 31 3 ) 2 0.5 1 ( 21 2

2

1 Expr3 = 0.5h + β h h + h + β h h + h + h

) 5 0.5 1 2 3 4 ( 51 ) 4 0.5 1 2 3 ( 41 4 + β h h + h + h + h + β h + h + h + h + h

1 21 2 31 3 41 4 51 5 Expr4 = h + β h + β h + β h + β h

β β β

119

APPENDIX B: LTPP TEST SECTIONS WITH A MODERATE AND HIGH 

PERCENTAGE OF ERRORS

This appendix lists the LTPP test sections with a moderate and high percentage of errors from 

the backcalculation process. Table 19 includes the sections with a moderate percentage of error 

terms of the total number of deflection basins, while table 20 includes the sections with a high 

percentage of error terms. The deflection basins classified as errors for the test sections included 

in these tables represent only 9.6 percent of the total number of deflection basins.
120

Table 19. LTPP test sections with a moderate percentage of errors.

State 

Code

SHRP 

ID

Total 

Drops

Error 

Drops

Atypical 

Drops

Accept 

Drops

Percent 

Error

1 663 1,714 649 0 1,065 37.9

1 607 1,832 610 0 1,222 33.3

1 B330 720 208 51 461 28.9

1 508 3,697 993 326 2,378 26.9

1 C320 1,043 268 32 743 25.7

2 1008 2,680 1,151 238 1,291 42.9

2 6010 2,344 705 157 1,482 30.1

2 1002 5,686 1,508 494 3,684 26.5

4 1036 4,103 1,910 8 2,185 46.6

4 163 1,965 852 98 1,015 43.4

4 A310 789 341 1 447 43.2

4 217 961 408 39 514 42.5

4 A320 837 345 4 488 41.2

4 1015 3,381 1,363 114 1,904 40.3

4 C340 792 318 1 473 40.2

4 B320 528 199 2 327 37.7

4 1001 2,018 739 133 1,146 36.6

4 1037 2,688 962 8 1,718 35.8

4 1034 4,028 1,391 1 2,636 34.5

4 1025 4,192 1,404 374 2,414 33.5

4 503 3,462 1,139 20 2,303 32.9

4 1018 4,928 1,519 5 3,404 30.8

4 C330 936 286 10 640 30.6

4 A903 2,103 601 88 1,414 28.6

4 666 1,718 466 1 1,251 27.1

4 1016 6,208 1,653 148 4,407 26.6

4 1017 7,388 1,957 69 5,362 26.5

4 903 2,112 554 96 1,462 26.2

5 A350 1,077 501 30 546 46.5

5 A320 1,109 500 43 566 45.1

5 218 555 143 0 412 25.8

6 3021 1,164 490 251 423 42.1

6 9048 974 392 0 582 40.2

6 A361 915 350 11 554 38.3

6 605 565 214 15 336 37.9

6 662 809 290 64 455 35.8

6 A363 845 300 43 502 35.5

6 A340 1,189 419 59 711 35.2

6 3005 636 220 0 416 34.6

6 663 723 245 0 478 33.9

6 661 2,348 780 277 1291 33.2

6 A351 1,027 315 103 609 30.7
121

6 A362 789 241 44 504 30.5 6 501 2,579 780 248 1,551 30.2 6 1253 4,777 1,444 220 3,113 30.2 6 603 2,148 640 47 1,461 29.8 6 A350 1,209 353 50 806 29.2 6 A320 1,196 338 68 790 28.3 6 A310 1,187 333 72 782 28.1 6 A352 829 232 73 524 28.0 6 502 2,956 817 220 1,919 27.6 6 A321 1,055 272 67 716 25.8 8 9020 802 396 0 406 49.4 8 9019 647 303 0 344 46.8 8 7781 4,719 2,165 0 2,554 45.9 8 6013 3,392 1,493 0 1,899 44.0 8 501 2,312 893 17 1,402 38.6 8 560 2,112 755 52 1,305 35.7 8 508 2,252 778 174 1,300 34.5 8 B310 648 216 0 432 33.3 8 507 2,295 754 101 1,440 32.9 8 3032 1,520 496 3 1,021 32.6 8 7036 982 320 186 476 32.6 8 1029 4,711 1,481 216 3,014 31.4 8 6002 4,672 1,407 337 2,928 30.1 8 214 819 240 111 468 29.3

12 C330 951 469 18 464 49.3

12 41072,047 883 191,145 43.1

12 41373,3641,227 132,124 36.5

12 41363,3441,165 162,163 34.8

12 C320 942 318 16 608 33.8

12 41091,082 3259 748 30.0

12 C350 758 221 34 503 29.2

12 90542,176 588 271,561 27.0

12 C310 956 249 43 664 26.0

13 40933,3561,047 4231,886 31.2

16 B350 936 382 113 441 40.8

16 10213,7231,430 5601,733 38.4

16 B310 936 330 179 427 35.3

16 10092,364 673 5111,180 28.5

16 C330 504 133 88 283 26.4

16 90343,387 849 6071,931 25.1

17 52171,275 500 35 740 39.2

17 93272,182 554 2321,396 25.4

18 60125,2941,796 4843,014 33.9

18 1028 50231,343 3443,336 26.7

19 102 24611,080 610 771 43.9
122

19 1052,475 694 2781,503 28.0

19 709 216 60 76 80 27.8

20 A330 874 411 120 343 47.0

20 A320 926 423 130 373 45.7

20 1053,1401,141 1951,804 36.3

20 102 720 250 32 438 34.7

20 B3201,337 414 38 885 31.0

20 4063 888 2550 633 28.7

20 1082,956 847 3601,749 28.7

20 1093,330 920 1712,239 27.6

20 3060 884 235 59 590 26.6

20 1113,128 792 3332,003 25.3

21 B3201,059 4713 585 44.5

21 B3101,096 4330 663 39.5

24 28055,3602,16813,191 40.4

24 9611,230 4120 818 33.5

24 9601,350 4480 902 33.2

24 9011,261 4060 855 32.2

24 9031,363 3870 976 28.4

26 60161,406 607 674 125 43.2

26 1163,429 9801,596 853 28.6

26 1182,400 638 6951,067 26.6

27 B330 960 417 214 329 43.4

27 10042,8781,22411,653 42.5

27 502 692 242 78 372 35.0

27 A3301,088 363 230 495 33.4

27 D340 910 291 281 338 32.0

27 10202,653 755 7831,115 28.5

27 5083,515 914 7071,894 26.0

27 C340 927 238 23 666 25.7

27 5613,550 897 2952,358 25.3

28 30833,9981,745 4531,800 43.6

28 5032,800 722 3171,761 25.8

28 5042,326 583 3411,402 25.1

29 5071,038 509 169 360 49.0

29 501 687 290 146 251 42.2

29 5021,056 411 169 476 38.9

29 5031,040 393 143 504 37.8

29 54732,578 94761,625 36.7

29 707 742 269 13 460 36.3

29 A3511,310 435 282 593 33.2

29 607 429 1400 289 32.6

29 70542,678 82961,843 31.0

29 10023,6381,021 3682,249 28.1

29 A3401,438 399 147 892 27.7
123

29 5041,392 367 358 667 26.4

29 60671,351 350 98 903 25.9

30 60043,3721,204 2101,958 35.7

30 10013,5201,175 702,275 33.4

30 70752,700 901 2321,567 33.4

30 A320 864 224 44 596 25.9

30 A310 864 223 35 606 25.8

31 6701 654 2930 361 44.8

31 70401,927 825 416 686 42.8

31 67021,961 78891,164 40.2

31 A352 752 2270 525 30.2

31 A310 877 2233 651 25.4

31 A350 956 243 33 680 25.4

31 A320 972 244 49 679 25.1

32 A352 408 196 30 182 48.0

32 70002,047 89201,155 43.6

32 10212,3881,024 261,338 42.9

32 20272,064 714 2731,077 34.6

32 3013 693 2201 472 31.7

32 A3201,032 3125 715 30.2

32 A3301,020 283 49 688 27.7

32 10302,704 730 5671,407 27.0

32 B320 648 172 36 440 26.5

35 1111,752 771 534 447 44.0

35 901 944 359 77 508 38.0

35 9591,072 370 43 659 34.5

35 9021,072 357 115 600 33.3

35 9031,072 357 81 634 33.3

35 5011,408 4504 954 32.0

35 60334,0481,154 1112,783 28.5

35 10022,704 737 641,903 27.3

35 5022,107 534 1981,375 25.3

35 8021,752 442 531,257 25.2

37 9011,055 467 212 376 44.3

37 18176,0132,51203,501 41.8

37 9601,056 371 166 519 35.1

37 9621,056 367 38 651 34.8

37 9641,048 344 281 423 32.8

37 9611,067 3442 721 32.2

37 9021,050 314 70 666 29.9

37 9631,056 274 138 644 25.9

39 1051,517 584 255 678 38.5

40 1182,1171,039 103 975 49.1

40 5032,1431,038 601,045 48.4

40 5602,112 99821,112 47.3
124

40 5062,112 977 891,046 46.3

40 5022,112 961 461,105 45.5

40 1172,112 955 172 985 45.2

40 B350 768 3440 424 44.8

40 40881,952 80911,142 41.4

40 1142,030 775 1551,100 38.2

40 C3101,152 4370 715 37.9

40 B310 752 2650 487 35.2

40 1212,108 72501,383 34.4

40 41642,704 896 906 902 33.1

40 B330 768 2390 529 31.1

40 C3201,152 3390 813 29.4

40 C3301,147 3290 818 28.7

40 1202,112 586 4421,084 27.7

40 70242,655 6661,106 883 25.1

40 5042,112 528 301,554 25.0

42 15994,6082,108 1642,336 45.7

42 B3401,269 396 132 741 31.2

42 16271,186 313 85 788 26.4

45 10112,048 746 1051,197 36.4

46 859 458 2148 236 46.7

47 31042,143 882 1051,156 41.2

47 31083,9451,62102,324 41.1

47 60152,720 99901,721 36.7

48 A330 576 267 15 294 46.4

48 35791,744 7791 964 44.7

48 10873,3911,490 681,833 43.9

48 K310 960 419 59 482 43.6

48 1122 47,1801,9345 427 27,408 41.0

4811,325 542 174 609 40.9

48 F340 656 263 24 369 40.1

48 9011,407 563 43 801 40.0

48 10693,7681,478 7661,524 39.2

48 A340 576 213 55 308 37.0

48 E340 768 2820 486 36.7

48 F350 768 2770 491 36.1

48 J351 764 262 49 453 34.3

48 1602,430 827 4631,140 34.0

48 A320 576 187 10 379 32.5

48 F320 768 241 46 481 31.4

48 5035 865 2710 594 31.3

48 1232,549 780 6061,163 30.6

48 1061 704 215 127 362 30.5

48 1622,463 748 3691,346 30.4

48 1241,969 565 1611,243 28.7
125

48 L320 960 275 63 622 28.6

48 38653,5551,006 922,457 28.3

48 1612,419 679 1311,609 28.1

48 1212,451 683 778 990 27.9

48 A807 742 1890 553 25.5

48 36791,344 340 252 752 25.3

49 B330 786 3800 406 48.3

49 B390 648 3000 348 46.3

49 1001 38,092 17,628 993 19,471 46.3

49 B320 360 141 88 131 39.2

49 B350 792 2871 504 36.2

49 70821,206 4130 793 34.2

49 10082,351 755 1231,473 32.1

49 B331 432 1351 296 31.3

49 7083 997 3075 685 30.8

49 70851,195 3504 841 29.3

49 C350 790 225 150 415 28.5

49 C361 648 1802 466 27.8

49 8042,094 577 2991,218 27.6

49 3010 800 215 33 552 26.9

49 10044,1311,067 1672,897 25.8

51 1213,8301,353 2462,231 35.3

51 A350 859 2984 557 34.7

51 A320 845 261 171 413 30.9

51 A321 847 220 152 475 26.0

53 10022,5971,019 971,481 39.2

53 10053,9651,163 5552,247 29.3

53 18013,501 937 3932,171 26.8

54 40042,9831,140 1151,728 38.2

55 1131,158 471 101 586 40.7

55 1151,394 529 274 591 37.9

55 1201,408 491 398 519 34.9

55 1211,408 461 406 541 32.7

55 1171,403 414 234 755 29.5

55 B9031,951 571 1461,234 29.3

55 B9081,785 448 801,257 25.1

56 60312,8421,24201,600 43.7

56 60293,3921,205 1562,031 35.5

56 1007 41,739 10,5681,724 29,447 25.3

72 4121 966 4490 517 46.5

72 10032,7171,102 991,516 40.6

81 5082,8301,367 101,453 48.3

81 5022,6561,060 191,577 39.9

81 18044,7201,439 9092,372 30.5

81 18034,0471,064 562,927 26.3
126

82 9017 2,048 551 264 1,233 26.9

89 903 2,346 700 243 1,403 29.8

90 A340 1,079 468 1 610 43.4

90 A310 762 254 17 491 33.3

90 A320 1,031 310 6 715 30.1

90 A351 1,048 311 9 728 29.7

90 A330 853 216 7 630 25.3

Total number of 

drops

638,739 221,144 42,268 375,327 30
127

Table 20. LTPP test sections with a high percentage of errors.

State 

Code

SHRP 

ID Total Drops

Error 

Drops

Atypical 

Drops

Accept 

Drops

Percent 

Error

4 504 3,355 3,318 0 37 98.9

4 507 3,087 2,918 0 169 94.5

4 502 3,857 2,912 46 899 75.5

4 501 1,553 1,035 8 510 66.6

4 508 3,353 2,102 96 1,155 62.7

4 6060 2,059 1,281 29 749 62.2

4 560 3,496 2,149 12 1,335 61.5

4 6054 1,869 1,134 0 735 60.7

4 506 3,878 2,347 27 1,504 60.5

4 A350 619 349 4 266 56.4

4 509 3,895 2,195 43 1,657 56.4

4 505 3,968 2,209 57 1,702 55.7

4 A330 792 428 3 361 54.0

4 1002 2,662 1,421 62 1,179 53.4

4 6055 2,720 1,446 4 1,270 53.2

4 6053 1,376 715 7 654 52.0

4 122 479 246 119 114 51.4

6 A353 719 603 4 112 83.9

6 8156 3,709 2,806 21 882 75.7

6 602 593 427 3 163 72.0

6 7454 3,309 1,991 63 1,255 60.2

6 569 1,882 1,044 9 829 55.5

8 2008 2,894 2,842 0 52 98.2

8 B330 295 222 0 73 75.3

8 B320 640 479 0 161 74.8

8 503 2,256 1,625 1 630 72.0

8 B350 360 254 40 66 70.6

8 509 2,252 1,496 1 755 66.4

8 506 2,281 1,451 2 828 63.6

8 502 2,292 1,418 0 874 61.9

8 505 2,256 1,214 34 1,008 53.8

8 1057 1,392 701 143 548 50.4

12 102 1,751 1,751 0 0 100.0

12 103 1,907 1,907 0 0 100.0

12 105 1,802 1,802 0 0 100.0

12 107 1,881 1,881 0 0 100.0

12 108 1,704 1,704 0 0 100.0

12 161 1,500 1,500 0 0 100.0

12 4103 1,864 1,860 0 4 99.8

12 109 1,792 1,785 0 7 99.6

12 106 1,893 1,881 0 12 99.4

12 110 1,800 1,748 1 51 97.1
128

12 1112,0161,9402 74 96.2

12 1041,7491,6407 102 93.8

12 1011,7961,636 1573 91.1

12 1121,8731,4262 445 76.1

12 10602,0321,3237 702 65.1

12 41353,3161,977 671,272 59.6

12 41542,4741,442 122 910 58.3

13 41181,126 6490 477 57.6

16 1005 273 27300 100.0

16 60271,375 776 41 558 56.4

16 10013,2481,74831,497 53.8

19 60491,5601,481 66 13 94.9

19 10443,6682,166 613 889 59.1

20 1071,0561,012 34 10 95.8

20 10062,0731,6470 426 79.5

20 1033,1232,297 355 471 73.6

20 60265,2393,760 1291,350 71.8

20 1063,1501,819 546 785 57.7

20 1043,0641,638 524 902 53.5

21 B3501,045 8922 151 85.4

21 A320 928 7110 217 76.6

21 10344,9402,51102,429 50.8

24 9621,201 7820 419 65.1

24 9021,353 7430 610 54.9

26 10103,0552,6010 454 85.1

27 60643,3763,316 591 98.2

27 20232,6561,555 389 712 58.5

28 30853,3631,895 381,430 56.3

29 8021,4011,39902 99.9

29 B3301,4541,3744 76 94.5

29 B3511,4701,3083 159 89.0

29 5061,3921,046 101 245 75.1

29 5081,052 6421 409 61.0

29 10101,7901,090 118 582 60.9

29 706 770 4480 322 58.2

29 10053,6871,916 2651,506 52.0

30 70764,7202,49902,221 52.9

31 67002,5161,5744 938 62.6

32 206 136 680 68 50.0

35 1051,7481,5330 215 87.7

35 8011,7581,179 35 544 67.1

37 13522,6792,665 140 99.5

37 10244,1823,15961,017 75.5

39 159 605 60500 100.0

39 A804 643 431 61 151 67.0
129

39 A803 455 2522 201 55.4

39 1032,0321,042 406 584 51.3

40 5092,1281,6846 438 79.1

40 10171,376 9010 475 65.5

40 B360 192 1210 71 63.0

40 60102,7121,604 201,088 59.1

40 5052,1121,1661 945 55.2

40 1162,0021,032 116 854 51.5

41 70191,9031,137 156 610 59.7

42 A310 864 8440 20 97.7

42 B3501,2961,2600 36 97.2

42 15976,6365,869 26 741 88.4

42 16182,7012,1900 511 81.1

42 A351 863 5651 297 65.5

45 10243,6843,132 13 539 85.0

45 10081,314 899 37 378 68.4

47 90253,9543,95400 100.0

47 90243,9953,99104 99.9

47 C350 764 7220 42 94.5

47 C330 768 7210 47 93.9

47 C311 576 5200 56 90.3

47 C310 767 6620 105 86.3

47 C320 766 6580 108 85.9

47 10235,0694,2240 845 83.3

47 31093,9793,294 62 623 82.8

47 10284,0393,135 76 828 77.6

47 A320 806 5086 292 63.0

47 31015,1182,739 3612,018 53.5

48 K340 944 94400 100.0

48 11232,0202,01307 99.7

48 K330 835 82609 98.9

48 11683,2663,198 18 50 97.9

48 K351 748 7150 33 95.6

48 K350 960 8400 120 87.5

48 A310 576 5001 75 86.8

48 9021,3011,1111 189 85.4

48 93551,232 962 196 74 78.1

48 K320 960 7273 230 75.7

48 52781,141 8552 284 74.9

48 38553,2992,446 93 760 74.1

48 90055,0193,700 301,289 73.7

48 H351 384 2380 146 62.0

48 10942,7181,656 501,012 60.9

48 9031,396 7613 632 54.5

48 J3101,136 5840 552 51.4
130

48 3689 3,288 1,678 3 1,607 51.0

49 B352 134 122 5 7 91.0

49 1007 1,360 943 1 416 69.3

49 1005 1,376 722 9 645 52.5

51 1419 4,731 3,937 1 793 83.2

51 1417 5,904 3,375 37 2,492 57.2

53 7322 4,064 2,296 264 1,504 56.5

54 1640 4,640 2,787 517 1,336 60.1

55 114 1,759 1,379 108 272 78.4

55 116 1,405 1,010 156 239 71.9

56 6032 2,478 1,946 64 468 78.5

72 4122 2,717 1,978 1 738 72.8

81 504 2,844 2,070 3 771 72.8

81 503 2,862 1,770 2 1,090 61.8

81 509 2,735 1,643 54 1,038 60.1

85 1801 3,342 2,723 0 619 81.5

88 1646 3,376 1,813 18 1,545 53.7

89 902 1,626 1,494 3 129 91.9

89 901 351 317 18 16 90.3

89 A902 2,332 1,729 0 603 74.1

Total number of 

drops

330,303 239,823 7,564 82,916 72.6
131

APPENDIX C: DEVELOPMENT OF THE SIMULATED LAYER STRUCTURE FOR 

THE BACKCALCULATION PROCESS USING EVERCALC© AND MODCOMP©

This appendix includes the tables used for developing the simulated pavement structure for the 

first segment analysis using EVERCALC©. Chapter 4 provided the rules of simulation used to 

create or combine different layers in the pavement structure for the initial two phases of analysis, 

while this appendix presents the layering information. The appendix is divided into two parts: the 

first part shows results for the simulated structure with a bedrock or apparent rigid layer (table 21

to table 29), and the second part shows the results for the condition or simulation without a 

bedrock layer (table 30 to table 42). Each section includes a series of generic tables for specific 

layer combination. 
132

BACKCALCULATION STRUCTURE FOR CASES USING BEDROCK IN THE BACKCALCULATION STRUCTURE

Table 21. AC surface with two layers between AC and subgrade.

LAYER_AFTER_

AC_1

LAYER_AFTER_

AC_2 SS_TYPE

BC_LAYER_2_

DESIG

BC_LAYER_3_

DESIG

BC_LAYER_SS_

DESIG

BEDROCK_

LAYER_NO

GB_COARSE GS_COARSE SS_COARSE 2 2 3 4

GB_COARSE GS_FINE SS_COARSE 2 2 3 4

GB_COARSE GS_SAND SS_COARSE 2 2 3 4

GB_COARSE GS_TYP SS_COARSE 2 2 3 4

GB_COARSE TS_LIME SS_COARSE 2 3 4 5

GB_COARSE TS_STAB SS_COARSE 2 3 4 5

GB_FINE GS_SAND SS_COARSE 2 2 3 4

GB_SAND GS_SAND SS_COARSE 2 2 3 4

GB_TYP GS_COARSE SS_COARSE 2 2 3 4

GB_TYP GS_FINE SS_COARSE 2 2 3 4

GB_TYP GS_SAND SS_COARSE 2 2 3 4

GB_TYP GS_TYP SS_COARSE 2 2 3 4

GB_TYP TB_AC SS_COARSE 2 3 4 5

GB_TYP TS_AC SS_COARSE 2 3 4 5

GB_TYP TS_LIME SS_COARSE 2 3 4 5

GB_TYP TS_STAB SS_COARSE 2 3 4 5

PC GB_COARSE SS_COARSE 2 3 4 5

PC GB_SAND SS_COARSE 2 3 4 5

PC GB_TYP SS_COARSE 2 3 4 5

PC TB_AC SS_COARSE 2 3 4 5

PC TB_LCB SS_COARSE 2 3 4 5

PC TB_STAB SS_COARSE 2 3 4 5

PC_RUBBLIZED GB_TYP SS_COARSE 2 3 4 5

PCC_CRACKED GB_COARSE SS_COARSE 2 3 4 5

PCC_CRACKED GB_TYP SS_COARSE 2 3 4 5

PCC_CRACKED GS_COARSE SS_COARSE 2 3 4 5

PCC_CRACKED TB_STAB SS_COARSE 2 3 4 5

TB_AC GB_TYP SS_COARSE 2 3 4 5

TB_AC GS_COARSE SS_COARSE 2 3 4 5

TB_AC GS_FINE SS_COARSE 2 3 4 5

TB_AC GS_SAND SS_COARSE 2 3 4 5

TB_AC GS_TYP SS_COARSE 2 3 4 5

TB_AC TB_AC SS_COARSE 2 2 3 4

TB_AC TS_LIME SS_COARSE 2 3 4 5
133

TB_AC TS_STAB SS_COARSE2345

TB_LCB GS_COARSE SS_COARSE2345

TB_LCB GS_TYP SS_COARSE2345

TB_STAB GS_COARSE SS_COARSE2345

TB_STAB GS_FINE SS_COARSE2345

TB_STAB GS_TYP SS_COARSE2345

TB_STAB TS_LIME SS_COARSE2345

GB_COARSE GS_COARSE SS_FINE2234

GB_COARSE GS_FINE SS_FINE2234

GB_COARSE TS_LIME SS_FINE2345

GB_COARSE TS_STAB SS_FINE2345

GB_FINE TS_LIME SS_FINE2345

GB_SAND GS_SAND SS_FINE2234

GB_TYP GS_COARSE SS_FINE2234

GB_TYP GS_FINE SS_FINE2234

GB_TYP GS_LIME SS_FINE2234

GB_TYP GS_SAND SS_FINE2234

GB_TYP GS_TYP SS_FINE2234

GB_TYP TS_LIME SS_FINE2345

GB_TYP TS_STAB SS_FINE2345

PC GB_FINE SS_FINE2345

PC GB_SAND SS_FINE2345

PC GB_TYP SS_FINE2345

PC TB_AC SS_FINE2345

PC TB_CEMENT SS_FINE2345

PC TB_LCB SS_FINE2345

PC TB_LIME SS_FINE2345

PC TB_STAB SS_FINE2345

PC_RUBBLIZED GB_TYP SS_FINE2345

PCC_CRACKED GB_FINE SS_FINE2345

PCC_CRACKED GB_TYP SS_FINE2345

PCC_CRACKED TB_AC SS_FINE2345

PCC_CRACKED TB_CEMENT SS_FINE2345

PCC_CRACKED TB_STAB SS_FINE2345

TB_AC GB_TYP SS_FINE2345

TB_AC GS_COARSE SS_FINE2345

TB_AC GS_FINE SS_FINE2345

TB_AC GS_TYP SS_FINE2345

TB_AC TB_AC SS_FINE2234
134

TB_AC TS_LIME SS_FINE 2 3 4 5

TB_AC TS_STAB SS_FINE 2 3 4 5

TB_CEMENT TS_LIME SS_FINE 2 3 4 5

TB_LCB GS_COARSE SS_FINE 2 3 4 5

TB_LCB GS_FINE SS_FINE 2 3 4 5

TB_LCB GS_TYP SS_FINE 2 3 4 5

TB_STAB GS_COARSE SS_FINE 2 3 4 5

TB_STAB GS_FINE SS_FINE 2 3 4 5

TB_STAB GS_TYP SS_FINE 2 3 4 5

TB_STAB TS_LIME SS_FINE 2 3 4 5

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.
135

Table 22. PCC surface with two layers between PCC and subgrade.

LAYER_

AFTER_PC_1

LAYER_

AFTER_PC_2 SS_TYPE

BC_LAYER_

2_DESIG

BC_LAYER_

3_DESIG

BC_LAYER_

SS_DESIG

BEDROCK_

LAYER_NO

AC TB_CEMENT SS_COARSE 2 3 4 5

AC TB_STAB SS_COARSE 2 3 4 5

GB_COARSE GS_COARSE SS_COARSE 2 2 3 4

GB_COARSE GS_FINE SS_COARSE 2 3 4 5

GB_COARSE GS_SAND SS_COARSE 2 3 4 5

GB_TYP GS_COARSE SS_COARSE 2 3 4 5

GB_TYP GS_FINE SS_COARSE 2 3 4 5

GB_TYP GS_SAND SS_COARSE 2 3 4 5

GB_TYP GS_TYP SS_COARSE 2 2 3 4

TB_AC GB_COARSE SS_COARSE 2 3 4 5

TB_AC GB_TYP SS_COARSE 2 3 4 5

TB_AC GS_COARSE SS_COARSE 2 3 4 5

TB_AC GS_FINE SS_COARSE 2 3 4 5

TB_AC GS_SAND SS_COARSE 2 3 4 5

TB_AC GS_TYP SS_COARSE 2 3 4 5

TB_AC TS_AC SS_COARSE 2 2 3 4

TB_AC TS_LIME SS_COARSE 2 3 4 5

TB_AC TS_STAB SS_COARSE 2 3 4 5

TB_CEMENT GS_FINE SS_COARSE 2 3 4 5

TB_LCB GB_TYP SS_COARSE 2 3 4 5

TB_LCB GS_COARSE SS_COARSE 2 3 4 5

TB_LCB GS_TYP SS_COARSE 2 3 4 5

TB_STAB GS_COARSE SS_COARSE 2 3 4 5

TB_STAB GS_FINE SS_COARSE 2 3 4 5

TB_STAB GS_SAND SS_COARSE 2 3 4 5

TB_STAB GS_TYP SS_COARSE 2 3 4 5

AC PC SS_FINE 2 3 4 5

AC TB_STAB SS_FINE 2 3 4 5

GB_COARSE GS_COARSE SS_FINE 2 2 3 4

GB_FINE GS_COARSE SS_FINE 2 2 3 4

GB_FINE GS_SAND SS_FINE 2 3 4 5

GB_TYP GS_COARSE SS_FINE 2 2 3 4

GB_TYP GS_FINE SS_FINE 2 3 4 5

GB_TYP GS_SAND SS_FINE 2 3 4 5

GB_TYP GS_TYP SS_FINE 2 2 3 4

GB_TYP TS_LIME SS_FINE 2 3 4 5
136

GB_TYP TS_STAB SS_FINE 2 3 4 5

TB_AC GB_TYP SS_FINE 2 3 4 5

TB_AC GS_COARSE SS_FINE 2 3 4 5

TB_AC GS_FINE SS_FINE 2 3 4 5

TB_AC GS_TYP SS_FINE 2 3 4 5

TB_AC TS_LIME SS_FINE 2 3 4 5

TB_CEMENT GS_FINE SS_FINE 2 3 4 5

TB_CEMENT TS_LIME SS_FINE 2 3 4 5

TB_LCB GS_COARSE SS_FINE 2 3 4 5

TB_LCB GS_FINE SS_FINE 2 3 4 5

TB_LCB GS_SAND SS_FINE 2 3 4 5

TB_LCB TS_LIME SS_FINE 2 3 4 5

TB_LCB TS_STAB SS_FINE 2 3 4 5

TB_STAB GB_TYP SS_FINE 2 3 4 5

TB_STAB GS_COARSE SS_FINE 2 3 4 5

TB_STAB GS_FINE SS_FINE 2 3 4 5

TB_STAB TS_LIME SS_FINE 2 3 4 5

TB_STAB TS_STAB SS_FINE 2 3 4 5

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.
137

Table 23. AC surface with three layers between AC and subgrade.

LAYER_

AFTER_AC_1

LAYER_

AFTER_AC_2

LAYER_

AFTER_AC_3 SS_TYPE

BC_LAYER_

2_DESIG

BC_LAYER_

3_DESIG

BC_LAYER_

4_DESIG

BC_LAYER_

SS_DESIG

BEDROCK_

LAYER_NO

GB_COARSE GS_COARSE TS_AC SS_COARSE 2 2 3 4 5

GB_COARSE GS_SAND TS_AC SS_COARSE 2 2 3 4 5

GB_TYP AC GS_TYP SS_COARSE 2 2 2 3 4

GB_TYP GB_TYP TS_LIME SS_COARSE 2 2 3 4 5

GB_TYP GS_COARSE GS_COARSE SS_COARSE 2 3 3 4 5

GB_TYP GS_COARSE TS_LIME SS_COARSE 2 2 3 4 5

GB_TYP GS_TYP GS_COARSE SS_COARSE 2 2 3 4 5

GB_TYP GS_TYP GS_SAND SS_COARSE 2 2 3 4 5

GB_TYP GS_TYP GS_TYP SS_COARSE 2 2 3 4 5

PC GB_TYP GS_COARSE SS_COARSE 2 3 3 4 5

PC GB_TYP GS_FINE SS_COARSE 2 3 3 4 5

PC GB_TYP GS_SAND SS_COARSE 2 3 3 4 5

PC GB_TYP GS_TYP SS_COARSE 2 3 3 4 5

PC TB_AC GS_COARSE SS_COARSE 2 3 3 4 5

PC TB_AC GS_FINE SS_COARSE 2 3 3 4 5

PC TB_AC GS_TYP SS_COARSE 2 3 3 4 5

PC TB_AC TS_LIME SS_COARSE 2 3 3 4 5

PC TB_LCB GS_TYP SS_COARSE 2 2 3 4 5

PC TB_STAB GS_COARSE SS_COARSE 2 3 3 4 5

PC TB_STAB GS_SAND SS_COARSE 2 3 3 4 5

PC TB_STAB GS_TYP SS_COARSE 2 3 3 4 5

PC_RUBBLIZED TB_STAB GS_TYP SS_COARSE 2 2 3 4 5

PCC_CRACKED TB_STAB GS_COARSE SS_COARSE 2 2 3 4 5

PCC_CRACKED TB_STAB GS_TYP SS_COARSE 2 2 3 4 5

TB_AC GB_TYP GS_COARSE SS_COARSE 2 3 3 4 5

TB_AC GB_TYP GS_FINE SS_COARSE 2 3 3 4 5

TB_AC GB_TYP GS_TYP SS_COARSE 2 3 3 4 5

TB_AC GB_TYP TS_LIME SS_COARSE 2 3 3 4 5

TB_AC GB_TYP TS_STAB SS_COARSE 2 3 3 4 5

TB_AC GS_COARSE GS_COARSE SS_COARSE 2 3 3 4 5

TB_AC GS_COARSE GS_SAND SS_COARSE 2 3 3 4 5

TB_AC GS_COARSE TS_LIME SS_COARSE 2 3 3 4 5

TB_AC GS_TYP GS_COARSE SS_COARSE 2 3 3 4 5

TB_AC GS_TYP GS_TYP SS_COARSE 2 3 3 4 5

TB_AC GS_TYP TS_STAB SS_COARSE 2 3 3 4 5

TB_AC TB_AC GS_COARSE SS_COARSE 2 2 3 4 5
138

TB_AC TB_AC GS_TYP SS_COARSE 2 2 3 4 5

TB_AC TB_AC TS_LIME SS_COARSE 2 2 3 4 5

TB_AC TB_AC TS_STAB SS_COARSE 2 2 3 4 5

TB_AC TB_STAB GS_COARSE SS_COARSE 2 3 3 4 5

TB_AC TS_AC GS_COARSE SS_COARSE 2 2 3 4 5

TB_STAB GS_FINE GS_COARSE SS_COARSE 2 3 3 4 5

GB_SAND GS_TYP GS_TYP SS_FINE 2 3 3 4 5

GB_TYP GS_COARSE GS_FINE SS_FINE 2 2 3 4 5

GB_TYP GS_COARSE TS_STAB SS_FINE 2 2 3 4 5

GB_TYP GS_SAND GS_FINE SS_FINE 2 3 3 4 5

GB_TYP GS_TYP GS_TYP SS_FINE 2 2 3 4 5

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.
139

Table 24. PCC surface with three layers between PCC and subgrade.

LAYER_AFT

ER_PC_1

LAYER_AFT

ER_PC_2

LAYER_AFT

ER_PC_3 SS_TYPE

BC_LAYER_

2_DESIG

BC_LAYER_

3_DESIG

BC_LAYER_

4_DESIG

BC_LAYER_

SS_DESIG

BEDRCK_

LAYER_NO

AC AC GB_TYP SS_COARSE 2 2 3 4 5

AC AC PC SS_COARSE 2 2 3 4 5

AC PC GB_TYP SS_COARSE 2 2 3 4 5

AC TB_STAB GS_COARSE SS_COARSE 2 2 3 4 5

GB_TYP GB_TYP GS_COARSE SS_COARSE 2 2 3 4 5

GB_TYP GS_COARSE GS_COARSE SS_COARSE 2 3 3 4 5

GB_TYP GS_COARSE GS_FINE SS_COARSE 2 2 3 4 5

GB_TYP GS_COARSE TS_LIME SS_COARSE 2 2 3 4 5

GB_TYP GS_FINE GS_FINE SS_COARSE 2 3 3 4 5

TB_AC GB_TYP GS_COARSE SS_COARSE 2 3 3 4 5

TB_AC GS_COARSE GS_COARSE SS_COARSE 2 3 3 4 5

TB_AC GS_COARSE TS_LIME SS_COARSE 2 3 3 4 5

TB_AC GS_TYP GS_TYP SS_COARSE 2 3 3 4 5

TB_AC TS_STAB GS_COARSE SS_COARSE 2 3 3 4 5

TB_CEMENT GS_FINE TS_LIME SS_COARSE 2 3 3 4 5

TB_LCB GB_TYP GS_COARSE SS_COARSE 2 3 3 4 5

TB_LCB GS_COARSE TS_LIME SS_COARSE 2 3 3 4 5

TB_LCB GS_TYP GS_COARSE SS_COARSE 2 3 3 4 5

TB_STAB GB_TYP GS_COARSE SS_COARSE 2 3 3 4 5

TB_STAB GS_FINE TS_LIME SS_COARSE 2 3 3 4 5

TB_STAB GS_TYP GS_COARSE SS_COARSE 2 3 3 4 5

TB_STAB GS_TYP GS_FINE SS_COARSE 2 3 3 4 5

TB_STAB GS_TYP GS_TYP SS_COARSE 2 3 3 4 5

TB_STAB TS_STAB GS_COARSE SS_COARSE 2 2 3 4 5

AC AC PC SS_FINE 2 2 3 4 5

AC PC GB_FINE SS_FINE 2 2 3 4 5

AC PC GB_SAND SS_FINE 2 2 3 4 5

AC PC GB_TYP SS_FINE 2 2 3 4 5

AC PC TB_CEMENT SS_FINE 2 2 3 4 5

AC PC TB_STAB SS_FINE 2 2 3 4 5

AC TB_STAB TS_LIME SS_FINE 2 3 3 4 5

GB_TYP GS_COARSE TS_LIME SS_FINE 2 3 3 4 5

GB_TYP GS_FINE GS_TYP SS_FINE 2 3 3 4 5

TB_AC AC GS_COARSE SS_FINE 2 2 3 4 5

TB_AC AC GS_SAND SS_FINE 2 2 3 4 5

TB_AC AC TS_LIME SS_FINE 2 2 3 4 5
140

TB_AC GB_TYP GS_FINE SS_FINE 2 3 3 4 5

TB_AC GB_TYP TS_LIME SS_FINE 2 3 3 4 5

TB_AC GB_TYP TS_STAB SS_FINE 2 3 3 4 5

TB_AC TS_AC TS_LIME SS_FINE 2 2 3 4 5

TB_AC TS_LIME GS_FINE SS_FINE 2 2 3 4 5

TB_CEMENT GS_SAND TS_LIME SS_FINE 2 3 3 4 5

TB_LCB GS_COARSE TS_LIME SS_FINE 2 3 3 4 5

TB_LCB GS_FINE GS_TYP SS_FINE 2 3 3 4 5

TB_STAB GS_COARSE TS_LIME SS_FINE 2 3 3 4 5

TB_STAB GS_TYP GS_COARSE SS_FINE 2 3 3 4 5

TB_STAB GS_TYP GS_FINE SS_FINE 2 3 3 4 5

TB_STAB TS_STAB GS_COARSE SS_FINE 2 3 3 4 5

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.
141

Table 25. AC surface with four layers between AC and subgrade.

LAYER_

AFTER_

AC_1

LAYER_

AFTER_

AC_2

LAYER_

AFTER_

AC_3

LAYER_

AFTER_

AC_4 SS_TYPE

BC_

LAYER_

2_DESIG

BC_

LAYER_

3_DESIG

BC_

LAYER_

4_DESIG

BC_

LAYER_

5_DESIG

BC_

LAYER_

SS_DESIG

BEDROCK_

LAYER_NO

PC AC PC GB_TYP SS_COARSE 2 2 2 3 4 5

PC GB_TYP GS_FINE GS_FINE SS_COARSE 2 3 3 3 4 5

PC TB_AC TS_STAB GS_COARSE SS_COARSE 2 3 3 3 4 5

PC TB_CEMENT GS_FINE TS_LIME SS_COARSE 2 3 3 3 4 5

PC TB_STAB GS_FINE TS_LIME SS_COARSE 2 3 3 3 4 5

PC TB_STAB TS_STAB GS_COARSE SS_COARSE 2 3 3 3 4 5

PCC_

CRACKED

TB_STAB GS_TYP GS_FINE SS_COARSE 2 3 3 3 4 5

TB_AC GB_TYP GB_TYP GS_COARSE SS_COARSE 2 3 3 3 4 5

TB_AC GB_TYP GS_COARSE TS_LIME SS_COARSE 2 3 3 3 4 5

TB_AC GB_TYP TS_STAB GS_COARSE SS_COARSE 2 3 3 3 4 5

TB_AC GS_TYP GS_COARSE GS_COARSE SS_COARSE 2 3 3 3 4 5

TB_AC TB_AC GB_TYP GS_COARSE SS_COARSE 2 2 3 3 4 5

TB_AC TB_AC GS_COARSE TS_LIME SS_COARSE 2 2 3 3 4 5

GB_TYP TS_AC GS_TYP GS_TYP SS_FINE 2 2 3 3 4 5

PC TB_CEMENT GS_COARSE TS_LIME SS_FINE 2 2 3 3 4 5

PC TB_CEMENT GS_SAND TS_LIME SS_FINE 2 3 3 3 4 5

PC TB_STAB GS_COARSE TS_LIME SS_FINE 2 3 3 3 4 5

PC TB_STAB GS_TYP GS_COARSE SS_FINE 2 3 3 3 4 5

PC TB_STAB TS_STAB GS_COARSE SS_FINE 2 3 3 3 4 5

PCC_

CRACKED

TB_STAB GS_TYP GS_FINE SS_FINE 2 3 3 3 4 5

TB_AC GB_TYP TS_STAB GS_COARSE SS_FINE 2 3 3 3 4 5

TB_AC GB_TYP TS_STAB GS_FINE SS_FINE 2 3 3 3 4 5

TB_AC TB_AC GB_TYP TS_STAB SS_FINE 2 2 3 3 4 5

TB_AC TB_AC TS_STAB GS_FINE SS_FINE 2 2 3 3 4 5

TB_AC TS_AC GS_TYP GS_FINE SS_FINE 2 2 3 3 4 5

TB_LCB TB_STAB TS_STAB TS_STAB SS_FINE 2 3 3 3 4 5

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.
142

Table 26. PCC surface with four layers between PCC and subgrade.

LAYER_

AFTER_

PC_1

LAYER_

AFTER_

PC_2

LAYER_

AFTER_

PC_3

LAYER_

AFTER_

PC_4 SS_TYPE

BC_

LAYER_

2_DESIG

BC_

LAYER_

3_DESI

G

BC_

LAYER_

4_DESIG

BC_

LAYER_

5_DESIG

BC_

LAYER_

SS_DESIG

BEDROCK

_LAYER_

NO

AC AC PC GB_TYP SS_COARSE 2 2 2 3 4 5

AC PC GB_TYP GS_COARSE SS_COARSE 2 2 3 3 4 5

AC PC GB_TYP GS_SAND SS_COARSE 2 2 3 3 4 5

AC PC TB_STAB GS_COARSE SS_COARSE 2 2 3 3 4 5

AC PCC_

CRACKED

TB_STAB GS_TYP SS_COARSE

2 2 2 3 4 5

GB_

COARSE

GS_COARSE GS_FINE GS_FINE SS_COARSE

2 2 3 3 4 5

TB_AC GB_TYP GB_TYP GS_COARSE SS_COARSE 2 3 3 3 4 5

TB_LCB GS_COARSE GS_COARSE GS_TYP SS_COARSE 2 3 3 3 4 5

AC AC PC GB_TYP SS_FINE 2 2 2 3 4 5

AC PC GB_COARSE TS_LIME SS_FINE 2 2 3 3 4 5

AC PC GB_TYP GS_COARSE SS_FINE 2 2 3 3 4 5

AC PC GB_TYP GS_SAND SS_FINE 2 2 3 3 4 5

TB_AC GB_TYP GS_COARSE TS_LIME SS_FINE 2 3 3 3 4 5

TB_AC GB_TYP GS_FINE GS_TYP SS_FINE 2 3 3 3 4 5

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.
143

Table 27. AC surface with five layers between AC and subgrade.

LAYER_AFTER_AC_1LAYER_AFTER_AC_2LAYER_AFTER_AC_3LAYER_AFTER_AC_4LAYER_AFTER_AC_5SS_TYPEBC_LAYER_2_DESIGBC_LAYER_3_DESIGBC_LAYER_4_DESIGBC_LAYER_5_DESIGBC_LAYER_6_DESIGBC_LAYER_SS_DESIGBEDROCK_LAYER_NO

PC GB_COARSE GS_COARSE GS_FINE GS_FINE SS_COARSE 2 3 3 3 3 4 5

TB_AC AC AC AC TS_STAB SS_COARSE 1 1 1 1 2 3 4

GB_TYP TS_AC GS_TYP GS_TYP GS_TYP SS_FINE 2 2 3 3 3 4 5

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.

Table 28. PCC surface with six layers between PCC and subgrade.

LAYER_AFTER_PC_1LAYER_AFTER_PC_2LAYER_AFTER_PC_3LAYER_AFTER_PC_4LAYER_AFTER_PC_5LAYER_AFTER_PC_6SS_TYPEBC_LAYER_2_DESIGBC_LAYER_3_DESIGBC_LAYER_4_DESIGBC_LAYER_5_DESIGBC_LAYER_6_DESIGBC_LAYER_7_DESIGBC_LAYER_SS_DESIGBC_LAYER_NO

AC AC AC PC GB_COARSE GS_TYP SS_FINE 2 2 2 2 3 3 4 5

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the 

LTPP database.
144

Table 29. AC surface with seven layers between AC and subgrade.

LAYER_AFTER_AC_1LAYER_AFTER_AC_2LAYER_AFTER_AC_3LAYER_AFTER_AC_4LAYER_AFTER_AC_5LAYER_AFTER_AC_6LAYER_AFTER_AC_7SS_TYPEBC_LAYER_2_DESIGBC_LAYER_3_DESIGBC_LAYER_4_DESIGBC_LAYER_5_DESIGBC_LAYER_6_DESIGBC_LAYER_7_DESIGBC_LAYER_8_DESIGBC_LAYER_SS_DESIGBEDROCK_LAYER_NO

GB_TYP GS_TYP GS_TYP TS_AC GS_TYP GS_TYP GS_TYP SS_FINE 2 3 3 3 3 3 3 4 5

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.

Table 30. PCC surface with seven layers between PCC and subgrade.

LAYER_AFTER_PC_1LAYER_AFTER_PC_2LAYER_AFTER_PC_3LAYER_AFTER_PC_4LAYER_AFTER_PC_5LAYER_AFTER_PC_6LAYER_AFTER_PC_7SS_TYPEBC_LAYER_2_DESIGBC_LAYER_3_DESIGBC_LAYER_4_DESIGBC_LAYER_5_DESIGBC_LAYER_6_DESIGBC_LAYER_7_DESIGBC_LAYER_8_DESIGBC_LAYER_SS_DESIGBEDROCK_LAYER_NO

AC AC AC AC PC TB_CEMENT TS_LIME SS_FINE 2 2 2 2 2 3 3 4 5

AC AC AC AC PC TB_STAB TS_LIME SS_FINE 2 2 2 2 2 3 3 4 5

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the 

LTPP database.
145

BACKCALCULATION STRUCTURE FOR CASES WITHOUT BEDROCK IN THE BACKCALCULATION STRUCTURE

Table 31. AC surface with one layer between AC and subgrade.

LAYER_AFTER_

AC_1 SS_TYPE

BC_LAYER_2_

DESIG

BC_LAYER_SS_

DESIG

BC_LAYER_

NO

SS_sub_

24

GB_COARSE SS_COARSE 2 2 3 1

GB_FINE SS_COARSE 2 3 4 0

GB_SAND SS_COARSE 2 3 4 0

GB_TYP SS_COARSE 2 3 4 0

GS_COARSE SS_COARSE 2 2 3 1

PC SS_COARSE 2 3 4 0

TB_AC SS_COARSE 2 3 4 0

TB_CEMENT SS_COARSE 2 3 4 0

TB_STAB SS_COARSE 2 3 4 0

GB_COARSE SS_FINE 2 3 4 0

GB_FINE SS_FINE 2 2 3 1

GB_SAND SS_FINE 2 3 4 0

GB_TYP SS_FINE 2 3 4 0

PC SS_FINE 2 3 4 0

TB_AC SS_FINE 2 3 4 0

TB_CEMENT SS_FINE 2 3 4 0

TB_LCB SS_FINE 2 3 4 0

TB_LIME SS_FINE 2 3 4 0

TB_STAB SS_FINE 2 3 4 0

TS_AC SS_FINE 2 3 4 0

TS_LIME SS_FINE 2 3 4 0

TS_STAB SS_FINE 2 3 4 0

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined 

in the LTPP database.
146

Table 32. PCC surface with one layer between PCC and subgrade.

LAYER_AFTER_

PC_1 SS_TYPE

BC_LAYER_

2_DESIG

BC_LAYER_

SS_DESIG

BC_LAYER_

NO

SS_sub_

24

GB_COARSE SS_COARSE 2 2 3 1

GB_FINE SS_COARSE 2 3 4 0

GB_SAND SS_COARSE 2 3 4 0

GB_TYP SS_COARSE 2 3 4 0

GS_COARSE SS_COARSE 2 2 3 1

TB_AC SS_COARSE 2 3 4 0

TB_CEMENT SS_COARSE 2 3 4 0

TB_LCB SS_COARSE 2 3 4 0

TB_STAB SS_COARSE 2 3 4 0

GB_COARSE SS_FINE 2 3 4 0

GB_FINE SS_FINE 2 2 3 1

GB_SAND SS_FINE 2 3 4 0

GB_TYP SS_FINE 2 3 4 0

TB_AC SS_FINE 2 3 4 0

TB_CEMENT SS_FINE 2 3 4 0

TB_LCB SS_FINE 2 3 4 0

TB_STAB SS_FINE 2 3 4 0

TB_STAB SS_FINE 2 3 4 0

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined 

in the LTPP database.
147

Table 33. AC surface with two layers between AC and subgrade.

LAYER_AFTER_

AC_1

LAYER_

AFTER_AC_2 SS_TYPE

BC_LAYER_

2_DESIG

BC_LAYER_

3_DESIG

BC_LAYER_

SS_DESIG

BC_LAYER_

NO

SS_sub_

24

PC TB_AC SS_COARSE 2 3 4 5 0

PC TB_LCB SS_COARSE 2 3 4 5 0

PC TB_STAB SS_COARSE 2 3 4 5 0

PC_RUBBLIZED GB_TYP SS_COARSE 2 3 4 5 0

PCC_CRACKED GB_COARSE SS_COARSE 2 3 3 4 1

PCC_CRACKED GB_TYP SS_COARSE 2 3 4 5 0

PCC_CRACKED GS_COARSE SS_COARSE 2 3 3 4 1

PCC_CRACKED TB_STAB SS_COARSE 2 3 4 5 0

TB_AC GB_TYP SS_COARSE 2 3 4 5 0

TB_AC GS_COARSE SS_COARSE 2 3 3 4 1

TB_AC GS_FINE SS_COARSE 2 3 4 5 0

TB_AC GS_SAND SS_COARSE 2 3 4 5 0

TB_AC GS_TYP SS_COARSE 2 3 4 5 0

TB_AC TB_AC SS_COARSE 2 2 3 4 0

TB_AC TS_LIME SS_COARSE 2 3 3 4 0

TB_AC TS_STAB SS_COARSE 2 3 4 5 0

TB_LCB GS_COARSE SS_COARSE 2 3 3 4 1

TB_LCB GS_TYP SS_COARSE 2 3 4 5 0

TB_STAB GS_COARSE SS_COARSE 2 3 3 4 1

TB_STAB GS_FINE SS_COARSE 2 3 4 5 0

TB_STAB GS_TYP SS_COARSE 2 3 4 5 0

TB_STAB TS_LIME SS_COARSE 2 3 3 4 0

GB_COARSE GS_COARSE SS_FINE 2 2 3 4 0

GB_COARSE GS_FINE SS_FINE 2 3 3 4 1

GB_COARSE TS_LIME SS_FINE 2 3 3 4 0

GB_COARSE TS_STAB SS_FINE 2 3 4 5 0

GB_FINE TS_LIME SS_FINE 2 3 3 4 0

GB_SAND GS_SAND SS_FINE 2 2 3 4 0

GB_TYP GS_COARSE SS_FINE 2 3 4 5 0

GB_TYP GS_FINE SS_FINE 2 3 3 4 1

GB_TYP GS_LIME SS_FINE 2 3 3 4 0

GB_TYP GS_SAND SS_FINE 2 3 4 5 0

GB_TYP GS_TYP SS_FINE 2 2 3 4 0

GB_TYP TS_LIME SS_FINE 2 3 3 4 0

GB_TYP TS_STAB SS_FINE 2 3 4 5 0

PC GB_FINE SS_FINE 2 3 3 4 1
148

PC GB_SAND SS_FINE23450

PC GB_TYP SS_FINE23450

PC TB_AC SS_FINE23450

PC TB_CEMENT SS_FINE23450

PC TB_LCB SS_FINE23450

PC TB_LIME SS_FINE23340

PC TB_STAB SS_FINE23450

PC_RUBBLIZED GB_TYP SS_FINE23450

PCC_CRACKED GB_FINE SS_FINE23341

PCC_CRACKED GB_TYP SS_FINE23450

PCC_CRACKED TB_AC SS_FINE23450

PCC_CRACKED TB_CEMENT SS_FINE23450

PCC_CRACKED TB_STAB SS_FINE23450

TB_AC GB_TYP SS_FINE23450

TB_AC GS_COARSE SS_FINE23450

TB_AC GS_FINE SS_FINE23341

TB_AC GS_TYP SS_FINE23450

TB_AC TB_AC SS_FINE22340

TB_AC TS_LIME SS_FINE23340

TB_AC TS_STAB SS_FINE23450

TB_CEMENT TS_LIME SS_FINE23340

TB_LCB GS_COARSE SS_FINE23450

TB_LCB GS_FINE SS_FINE23341

TB_LCB GS_TYP SS_FINE23450

TB_STAB GS_COARSE SS_FINE23450

TB_STAB GS_FINE SS_FINE23341

TB_STAB GS_TYP SS_FINE23450

TB_STAB TS_LIME SS_FINE23340

GB_COARSE GS_COARSE SS_COARSE23341

GB_COARSE GS_FINE SS_COARSE23450

GB_COARSE GS_SAND SS_COARSE23450

GB_COARSE GS_TYP SS_COARSE23450

GB_COARSE TS_LIME SS_COARSE23340

GB_COARSE TS_STAB SS_COARSE23450

GB_FINE GS_SAND SS_COARSE23450

GB_SAND GS_SAND SS_COARSE22340

GB_TYP GS_COARSE SS_COARSE23341

GB_TYP GS_FINE SS_COARSE23450

GB_TYP GS_SAND SS_COARSE23450
149

GB_TYP GS_TYP SS_COARSE 2 2 3 4 0

GB_TYP TB_AC SS_COARSE 2 3 4 5 0

GB_TYP TS_AC SS_COARSE 2 3 4 5 0

GB_TYP TS_LIME SS_COARSE 2 3 3 4 0

GB_TYP TS_STAB SS_COARSE 2 3 4 5 0

PC GB_COARSE SS_COARSE 2 3 3 4 1

PC GB_SAND SS_COARSE 2 3 4 5 0

PC GB_TYP SS_COARSE 2 3 4 5 0

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.

Table 34. PCC surface with two layers between PCC and subgrade.

LAYER_

AFTER_PC_1

LAYER_

AFTER_PC_2 SS_TYPE

BC_LAYER_

2_DESIG

BC_LAYER_

3_DESIG

BC_LAYER_

SS_DESIG

BC_LAYER_

NO

SS_sub_

24

AC TB_CEMENT SS_COARSE 2 3 4 5 0

AC TB_STAB SS_COARSE 2 3 4 5 0

GB_COARSE GS_COARSE SS_COARSE 2 3 3 4 1

GB_COARSE GS_FINE SS_COARSE 2 3 4 5 0

GB_COARSE GS_SAND SS_COARSE 2 3 4 5 0

GB_TYP GS_COARSE SS_COARSE 2 3 3 4 1

GB_TYP GS_FINE SS_COARSE 2 3 4 5 0

GB_TYP GS_SAND SS_COARSE 2 3 4 5 0

GB_TYP GS_TYP SS_COARSE 2 2 3 4 0

TB_AC GB_COARSE SS_COARSE 2 3 3 4 1

TB_AC GB_TYP SS_COARSE 2 3 4 5 0

TB_AC GS_COARSE SS_COARSE 2 3 3 4 1

TB_AC GS_FINE SS_COARSE 2 3 4 5 0

TB_AC GS_SAND SS_COARSE 2 3 4 5 0

TB_AC GS_TYP SS_COARSE 2 3 4 5 0

TB_AC TS_AC SS_COARSE 2 2 3 4 0

TB_AC TS_LIME SS_COARSE 2 3 3 4 0

TB_AC TS_STAB SS_COARSE 2 3 4 5 0

TB_CEMENT GS_FINE SS_COARSE 2 3 4 5 0

TB_LCB GB_TYP SS_COARSE 2 3 4 5 0

TB_LCB GS_COARSE SS_COARSE 2 3 3 4 1

TB_LCB GS_TYP SS_COARSE 2 3 4 5 0

TB_STAB GS_COARSE SS_COARSE 2 3 3 4 1

TB_STAB GS_FINE SS_COARSE 2 3 4 5 0

TB_STAB GS_SAND SS_COARSE 2 3 4 5 0

TB_STAB GS_TYP SS_COARSE 2 3 4 5 0
150

AC PC SS_FINE 2 3 4 5 0

AC TB_STAB SS_FINE 2 3 4 5 0

GB_COARSE GS_COARSE SS_FINE 2 2 3 4 0

GB_FINE GS_COARSE SS_FINE 2 3 4 5 0

GB_FINE GS_SAND SS_FINE 2 3 4 5 0

GB_TYP GS_COARSE SS_FINE 2 3 4 5 0

GB_TYP GS_FINE SS_FINE 2 3 3 4 1

GB_TYP GS_SAND SS_FINE 2 3 4 5 0

GB_TYP GS_TYP SS_FINE 2 2 3 4 0

GB_TYP TS_LIME SS_FINE 2 3 3 4 0

GB_TYP TS_STAB SS_FINE 2 3 4 5 0

TB_AC GB_TYP SS_FINE 2 3 4 5 0

TB_AC GS_COARSE SS_FINE 2 3 4 5 0

TB_AC GS_FINE SS_FINE 2 3 3 4 1

TB_AC GS_TYP SS_FINE 2 3 4 5 0

TB_AC TS_LIME SS_FINE 2 3 3 4 0

TB_CEMENT GS_FINE SS_FINE 2 3 3 4 1

TB_CEMENT TS_LIME SS_FINE 2 3 3 4 0

TB_LCB GS_COARSE SS_FINE 2 3 4 5 0

TB_LCB GS_FINE SS_FINE 2 3 3 4 1

TB_LCB GS_SAND SS_FINE 2 3 4 5 0

TB_LCB TS_LIME SS_FINE 2 3 3 4 0

TB_LCB TS_STAB SS_FINE 2 3 4 5 0

TB_STAB GB_TYP SS_FINE 2 3 4 5 0

TB_STAB GS_COARSE SS_FINE 2 3 4 5 0

TB_STAB GS_FINE SS_FINE 2 3 3 4 1

TB_STAB TS_LIME SS_FINE 2 3 3 4 0

TB_STAB TS_STAB SS_FINE 2 3 4 5 0

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.
151

Table 35. AC surface with three layers between AC and subgrade.

LAYER_AFTE

R_AC_1

LAYER_

AFTER_AC_2

LAYER_

AFTER_AC_3 SS_TYPE

BC_

LAYER_

2_DESIG

BC_

LAYER_

3_DESIG

BC_LAYER

_4_DESIG

BC_

LAYER_

SS_DESIG

BC_

LAYER_

NO

SS_sub

_24

PC TB_LCB GS_TYP SS_COARSE 2 3 4 4 5 0

PC TB_STAB GS_COARSE SS_COARSE 2 3 4 4 5 1

PC TB_STAB GS_SAND SS_COARSE 2 3 4 4 5 0

PC TB_STAB GS_TYP SS_COARSE 2 3 4 4 5 0

PC_RUBBLIZED TB_STAB GS_TYP SS_COARSE 2 3 4 4 5 0

PCC_CRACKED TB_STAB GS_COARSE SS_COARSE 2 3 4 4 5 1

PCC_CRACKED TB_STAB GS_TYP SS_COARSE 2 3 4 4 5 0

TB_AC GB_TYP GS_COARSE SS_COARSE 2 3 4 4 5 1

TB_AC GB_TYP GS_FINE SS_COARSE 2 3 4 4 5 0

TB_AC GB_TYP GS_TYP SS_COARSE 2 3 3 4 5 0

TB_AC GB_TYP TS_LIME SS_COARSE 2 3 4 4 5 0

TB_AC GB_TYP TS_STAB SS_COARSE 2 3 4 4 5 0

TB_AC GS_COARSE GS_COARSE SS_COARSE 2 3 3 4 4 1

TB_AC GS_COARSE GS_SAND SS_COARSE 2 3 4 4 5 0

TB_AC GS_COARSE TS_LIME SS_COARSE 2 3 4 4 5 0

TB_AC GS_TYP GS_COARSE SS_COARSE 2 3 4 4 5 1

TB_AC GS_TYP GS_TYP SS_COARSE 2 3 3 4 5 0

TB_AC GS_TYP TS_STAB SS_COARSE 2 3 4 4 5 0

TB_AC TB_AC GS_COARSE SS_COARSE 2 2 3 3 4 1

TB_AC TB_AC GS_TYP SS_COARSE 2 2 3 4 5 0

TB_AC TB_AC TS_LIME SS_COARSE 2 2 3 3 4 0

TB_AC TB_AC TS_STAB SS_COARSE 2 2 3 4 5 0

TB_AC TB_STAB GS_COARSE SS_COARSE 2 3 4 4 5 1

TB_AC TS_AC GS_COARSE SS_COARSE 2 2 3 3 4 1

TB_STAB GS_FINE GS_COARSE SS_COARSE 2 3 4 4 5 1

GB_SAND GS_TYP GS_TYP SS_FINE 2 3 3 4 5 0

GB_TYP GS_COARSE GS_FINE SS_FINE 2 3 4 4 5 1

GB_TYP GS_COARSE TS_STAB SS_FINE 2 2 3 4 5 0

GB_TYP GS_SAND GS_FINE SS_FINE 2 3 4 4 5 1

GB_TYP GS_TYP GS_TYP SS_FINE 2 3 3 4 5 0

GB_TYP TS_STAB GS_COARSE SS_FINE 2 3 4 4 5 0

GB_TYP TS_STAB GS_FINE SS_FINE 2 3 4 4 5 1

GB_TYP TS_STAB TS_LIME SS_FINE 2 3 4 4 5 0

PC GB_COARSE GS_COARSE SS_FINE 2 3 3 4 5 0

PC GB_COARSE GS_TYP SS_FINE 2 3 3 4 5 0
152

PC GB_SAND GS_SAND SS_FINE233450

PC GB_TYP GS_COARSE SS_FINE233450

PC GB_TYP GS_FINE SS_FINE234451

PC GB_TYP GS_SAND SS_FINE234450

PC GB_TYP TB_LIME SS_FINE234450

PC GB_TYP TS_LIME SS_FINE234450

PC TB_AC GS_COARSE SS_FINE234450

PC TB_AC GS_TYP SS_FINE234450

PC TB_AC TS_LIME SS_FINE234450

PC TB_CEMENT GS_FINE SS_FINE234451

PC TB_LCB TS_LIME SS_FINE234450

PC TB_STAB GS_FINE SS_FINE234451

PC TB_STAB TS_LIME SS_FINE234450

PC_RUBBLIZED GB_TYP GS_SAND SS_FINE234450

PCC_CRACKED GB_TYP GS_COARSE SS_FINE233450

PCC_CRACKED GB_TYP GS_SAND SS_FINE234450

PCC_CRACKED TB_LCB GS_COARSE SS_FINE234450

TB_AC GB_TYP GS_COARSE SS_FINE234450

TB_AC GB_TYP GS_FINE SS_FINE234451

TB_AC GB_TYP GS_SAND SS_FINE234450

TB_AC GB_TYP TS_LIME SS_FINE234450

TB_AC GB_TYP TS_STAB SS_FINE234450

TB_AC GS_COARSE GS_COARSE SS_FINE234450

TB_AC GS_TYP GS_COARSE SS_FINE234450

TB_AC GS_TYP GS_SAND SS_FINE234450

TB_AC TB_AC GB_TYP SS_FINE223450

TB_AC TB_AC GS_FINE SS_FINE223341

TB_AC TB_AC GS_TYP SS_FINE223450

TB_AC TB_AC TS_FINE SS_FINE223450

TB_AC TB_AC TS_LIME SS_FINE223340

TB_AC TB_AC TS_STAB SS_FINE223450

TB_AC TS_AC GS_TYP SS_FINE223450

TB_AC TS_STAB GS_FINE SS_FINE234451

TB_CEMENT GS_COARSE GS_FINE SS_FINE234451

TB_STAB GS_COARSE GS_FINE SS_FINE234451

TB_STAB GS_COARSE TS_LIME SS_FINE234450

TB_STAB GS_TYP TS_STAB SS_FINE234450

TB_STAB TS_LIME GS_FINE SS_FINE234451

GB_COARSE GS_COARSE TS_AC SS_COARSE223450
153

GB_COARSE GS_SAND TS_AC SS_COARSE 2 2 3 4 5 0

GB_TYP AC GS_TYP SS_COARSE 2 3 4 4 5 0

GB_TYP GB_TYP TS_LIME SS_COARSE 2 2 3 3 4 0

GB_TYP GS_COARSE GS_COARSE SS_COARSE 2 3 3 4 4 0

GB_TYP GS_COARSE TS_LIME SS_COARSE 2 3 4 4 5 0

GB_TYP GS_TYP GS_COARSE SS_COARSE 2 2 3 3 4 1

GB_TYP GS_TYP GS_SAND SS_COARSE 2 2 3 4 5 0

GB_TYP GS_TYP GS_TYP SS_COARSE 2 3 3 4 5 0

PC GB_TYP GS_COARSE SS_COARSE 2 3 4 4 5 1

PC GB_TYP GS_FINE SS_COARSE 2 3 3 4 5 0

PC GB_TYP GS_SAND SS_COARSE 2 3 4 4 5 0

PC GB_TYP GS_TYP SS_COARSE 2 3 3 4 5 0

PC TB_AC GS_COARSE SS_COARSE 2 3 4 4 5 1

PC TB_AC GS_FINE SS_COARSE 2 3 4 4 5 0

PC TB_AC GS_TYP SS_COARSE 2 3 4 4 5 0

PC TB_AC TS_LIME SS_COARSE 2 3 4 4 5 0

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.
154

Table 36. PCC surface with three layers between PCC and subgrade.

LAYER_

AFTER_PC_1

LAYER_

AFTER_PC_2

LAYER_

AFTER_PC_3 SS_TYPE

BC_

LAYER_

2_DESIG

BC_

LAYER_

3_DESIG

BC_

LAYER_

4_DESIG

BC_

LAYER_

SS_DESIG

BC_

LAYER_

NO

SS_sub_

24

TB_AC TS_STAB GS_COARSE SS_COARSE 2 3 4 4 5 1

TB_CEMENT GS_FINE TS_LIME SS_COARSE 2 3 4 4 5 0

TB_LCB GB_TYP GS_COARSE SS_COARSE 2 3 4 4 5 1

TB_LCB GS_COARSE TS_LIME SS_COARSE 2 3 4 4 5 0

TB_LCB GS_TYP GS_COARSE SS_COARSE 2 3 4 4 5 1

TB_STAB GB_TYP GS_COARSE SS_COARSE 2 3 4 4 5 1

TB_STAB GS_FINE TS_LIME SS_COARSE 2 3 4 4 5 0

TB_STAB GS_TYP GS_COARSE SS_COARSE 2 3 4 4 5 1

TB_STAB GS_TYP GS_FINE SS_COARSE 2 3 3 4 5 0

TB_STAB GS_TYP GS_TYP SS_COARSE 2 3 3 4 5 0

TB_STAB TS_STAB GS_COARSE SS_COARSE 2 2 3 3 4 1

AC AC PC SS_FINE 2 2 3 4 5 0

AC PC GB_FINE SS_FINE 2 2 3 3 4 1

AC PC GB_SAND SS_FINE 2 2 3 4 5 0

AC PC GB_TYP SS_FINE 2 2 3 4 5 0

AC PC TB_CEMENT SS_FINE 2 2 3 4 5 0

AC PC TB_STAB SS_FINE 2 2 3 4 5 0

AC TB_STAB TS_LIME SS_FINE 2 3 4 4 5 0

GB_TYP GS_COARSE TS_LIME SS_FINE 2 3 4 4 5 0

GB_TYP GS_FINE GS_TYP SS_FINE 2 3 3 4 5 0

TB_AC AC GS_COARSE SS_FINE 2 2 3 4 5 0

TB_AC AC GS_SAND SS_FINE 2 2 3 4 5 0

TB_AC AC TS_LIME SS_FINE 2 2 3 3 4 0

TB_AC GB_TYP GS_FINE SS_FINE 2 3 4 4 5 1

TB_AC GB_TYP TS_LIME SS_FINE 2 3 4 4 5 0

TB_AC GB_TYP TS_STAB SS_FINE 2 3 3 4 5 0

TB_AC TS_AC TS_LIME SS_FINE 2 2 3 3 4 0

TB_AC TS_LIME GS_FINE SS_FINE 2 2 3 3 4 1

TB_CEMENT GS_SAND TS_LIME SS_FINE 2 3 4 4 5 0

TB_LCB GS_COARSE TS_LIME SS_FINE 2 3 4 4 5 0

TB_LCB GS_FINE GS_TYP SS_FINE 2 3 3 4 5 0

TB_STAB GS_COARSE TS_LIME SS_FINE 2 3 4 4 5 0

TB_STAB GS_TYP GS_COARSE SS_FINE 2 3 3 4 5 0

TB_STAB GS_TYP GS_FINE SS_FINE 2 3 4 4 5 1

TB_STAB TS_STAB GS_COARSE SS_FINE 2 3 3 4 5 0
155

AC AC GB_TYP SS_COARSE 2 2 3 4 5 0

AC AC PC SS_COARSE 2 2 3 4 5 0

AC PC GB_TYP SS_COARSE 2 2 3 4 5 0

AC TB_STAB GS_COARSE SS_COARSE 2 2 3 3 4 1

GB_TYP GB_TYP GS_COARSE SS_COARSE 2 2 3 3 4 1

GB_TYP GS_COARSE GS_COARSE SS_COARSE 2 3 3 4 5 1

GB_TYP GS_COARSE GS_FINE SS_COARSE 2 2 3 4 5 0

GB_TYP GS_COARSE TS_LIME SS_COARSE 2 2 3 3 4 0

GB_TYP GS_FINE GS_FINE SS_COARSE 2 3 3 4 5 0

TB_AC GB_TYP GS_COARSE SS_COARSE 2 3 4 4 5 1

TB_AC GS_COARSE GS_COARSE SS_COARSE 2 3 3 3 4 1

TB_AC GS_COARSE TS_LIME SS_COARSE 2 3 4 4 5 0

TB_AC GS_TYP GS_TYP SS_COARSE 2 3 3 4 5 0

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.
156

Table 37. AC surface with four layers between AC and subgrade.

LAYER_

AFTER_

AC_1

LAYER_

AFTER_

AC_2

LAYER_

AFTER_

AC_3

LAYER_

AFTER_

AC_4 SS_TYPE

BC_

LAYER

_2_

DESIG

BC_

LAYER_

3_

DESIG

BC_

LAYER

_4_

DESIG

BC_

LAYER

_5_

DESIG

BC_

LAYER

_SS_

DESIG

BC_

LAYER

_NO

SS_

sub_

24

TB_AC GB_TYP TS_STAB GS_COARSE SS_COARSE 2 3 3 4 4 5 1

TB_AC GS_TYP GS_COARSE GS_COARSE SS_COARSE 2 3 4 4 4 5 1

TB_AC TB_AC GB_TYP GS_COARSE SS_COARSE 2 2 3 4 4 5 1

TB_AC TB_AC GS_COARSE TS_LIME SS_COARSE 2 2 3 4 4 5 0

GB_TYP TS_AC GS_TYP GS_TYP SS_FINE 2 2 3 3 4 5 0

PC TB_CEMENT GS_COARSE TS_LIME SS_FINE 2 2 3 4 4 5 0

PC TB_CEMENT GS_SAND TS_LIME SS_FINE 2 3 3 4 4 5 0

PC TB_STAB GS_COARSE TS_LIME SS_FINE 2 3 3 4 4 5 0

PC TB_STAB GS_TYP GS_COARSE SS_FINE 2 3 4 4 4 5 0

PC TB_STAB TS_STAB GS_COARSE SS_FINE 2 3 3 4 4 5 0

PCC_

CRACKED

TB_STAB GS_TYP GS_FINE SS_FINE 2 3 4 4 4 5 1

TB_AC GB_TYP TS_STAB GS_COARSE SS_FINE 2 3 3 3 4 5 0

TB_AC GB_TYP TS_STAB GS_FINE SS_FINE 2 3 4 4 4 5 1

TB_AC TB_AC GB_TYP TS_STAB SS_FINE 2 2 3 3 4 5 0

TB_AC TB_AC TS_STAB GS_FINE SS_FINE 2 2 3 4 4 5 1

TB_AC TS_AC GS_TYP GS_FINE SS_FINE 2 2 3 4 4 5 1

TB_LCB TB_STAB TS_STAB TS_STAB SS_FINE 2 3 3 3 4 5 0

PC AC PC GB_TYP SS_COARSE 2 2 2 3 4 5 0

PC GB_TYP GS_FINE GS_FINE SS_COARSE 2 3 3 3 4 5 0

PC TB_AC TS_STAB GS_COARSE SS_COARSE 2 3 3 4 4 5 1

PC TB_CEMENT GS_FINE TS_LIME SS_COARSE 2 3 4 4 4 5 0

PC TB_STAB GS_FINE TS_LIME SS_COARSE 2 3 4 4 4 5 0

PC TB_STAB TS_STAB GS_COARSE SS_COARSE 2 3 3 4 4 5 1

PCC_

CRACKED

TB_STAB GS_TYP GS_FINE SS_COARSE 2 3 4 4 4 5 0

TB_AC GB_TYP GB_TYP GS_COARSE SS_COARSE 2 3 3 4 4 5 1

TB_AC GB_TYP GS_COARSE TS_LIME SS_COARSE 2 3 4 4 4 5 0

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.
157

Table 38. PCC surface with four layers between PCC and subgrade.

LAYER_

AFTER_

PC_1

LAYER_

AFTER_

PC_2

LAYER_

AFTER_

PC_3

LAYER_

AFTER_

PC_4 SS_TYPE

BC_

LAYER

_2_

DESIG

BC_

LAYER

_3_

DESIG

BC_

LAYER

_4_

DESIG

BC_

LAYER

_5_

DESIG

BC_

LAYER

_SS_

DESIG

BC_

LAYER_

NO

SS_

sub_

24

AC AC PC GB_TYP SS_COARSE 2 2 2 3 4 5 0

AC PC GB_TYP GS_COARSE SS_COARSE 2 2 3 4 4 5 1

AC PC GB_TYP GS_SAND SS_COARSE 2 2 3 4 4 5 0

AC PC TB_STAB GS_COARSE SS_COARSE 2 2 3 4 4 5 1

AC PCC_

CRACKED

TB_STAB GS_TYP SS_COARSE 2 2 3 4 4 5 0

GB_

COARSE

GS_

COARSE

GS_FINE GS_FINE SS_COARSE 2 2 3 3 4 5 0

TB_AC GB_TYP GB_TYP GS_COARSE SS_COARSE 2 3 3 4 4 5 1

TB_LCB GS_

COARSE

GS_

COARSE

GS_TYP SS_COARSE 2 3 3 4 4 5 0

AC AC PC GB_TYP SS_FINE 2 2 2 3 4 5 0

AC PC GB_

COARSE

TS_LIME SS_FINE 2 2 3 4 4 5 0

AC PC GB_TYP GS_COARSE SS_FINE 2 2 3 4 4 5 0

AC PC GB_TYP GS_SAND SS_FINE 2 2 3 4 4 5 0

TB_AC GB_TYP GS_

COARSE

TS_LIME SS_FINE 2 3 3 4 4 5 0

TB_AC GB_TYP GS_FINE GS_TYP SS_FINE 2 3 3 4 4 5 0

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.
158

Table 39. AC surface with five layers between AC and subgrade.

LAYER_AFTER_AC_1LAYER_AFTER_AC_2LAYER_AFTER_AC_3LAYER_AFTER_AC_4LAYER_AFTER_AC_5SS_TYPEBC_LAYER_2_DESIGBC_LAYER_3_DESIGBC_LAYER_4_DESIGBC_LAYER_5_DESIGBC_LAYER_6_DESIGBC_LAYER_SS_DESIGBC_LAYER_NOSS_sub_24

PC GB_COARSE GS_COARSE GS_FINE GS_FINE SS_COARSE 2 3 3 4 4 4 5 0

TB_AC AC AC AC TS_STAB SS_COARSE 2 3 3 3 4 4 5 0

GB_TYP TS_AC GS_TYP GS_TYP GS_TYP SS_FINE 2 3 4 4 4 4 5 0

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.

Table 40. PCC surface with six layers between PCC and subgrade.

LAYER_AFTER_PC_1LAYER_AFTER_PC_2LAYER_AFTER_PC_3LAYER_AFTER_PC_4LAYER_AFTER_PC_5LAYER_AFTER_PC_6SS_TYPEBC_LAYER_2_DESIGBC_LAYER_3_DESIGBC_LAYER_4_DESIGBC_LAYER_5_DESIGBC_LAYER_6_DESIGBC_LAYER_7_DESIGBC_LAYER_SS_DESIGBC_LAYER_NOSS_sub_24

AC AC AC PC GB_COARSE GS_TYP SS_FINE 2 2 2 3 4 4 4 5 1

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the 

LTPP database.
159

Table 41. AC surface with seven layers between AC and subgrade.

LAYER_AFTER_AC_1LAYER_AFTER_AC_2LAYER_AFTER_AC_3LAYER_AFTER_AC_4LAYER_AFTER_AC_5LAYER_AFTER_AC_6LAYER_AFTER_AC_7SS_TYPEBC_LAYER_2_DESIGBC_LAYER_3_DESIGBC_LAYER_4_DESIGBC_LAYER_5_DESIGBC_LAYER_6_DESIGBC_LAYER_7_DESIGBC_LAYER_8_DESIGBC_LAYER_SS_DESIGBC_LAYER_NOSS_sub_24

GB_TYP GS_TYP GS_TYP TS_AC GS_TYP GS_TYP GS_TYP SS_FINE 2 2 2 3 3 3 3 3 4 0

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.

Table 42. PCC surface with seven layers between PCC and subgrade.

LAYER_AFTER_PC_1LAYER_AFTER_PC_2LAYER_AFTER_PC_3LAYER_AFTER_PC_4LAYER_AFTER_PC_5LAYER_AFTER_PC_6LAYER_AFTER_PC_7SS_TYPEBC_LAYER_2_DESIGBC_LAYER_3_DESIGBC_LAYER_4_DESIGBC_LAYER_5_DESIGBC_LAYER_6_DESIGBC_LAYER_7_DESIGBC_LAYER_8_DESIGBC_LAYER_SS_DESIGBC_LAYER_NOSS_sub_24

AC AC AC AC PC TB_CEMENT TS_LIME SS_FINE 2 2 2 2 3 4 4 4 5 1

AC AC AC AC PC TB_STAB TS_LIME SS_FINE 2 2 2 2 3 4 4 4 5 1

Note: Abbreviations found in the table are standard notations included in the LTPP data tables and are defined in the LTPP database.

161

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