Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296
Foreword

The elastic or resilient modulus of pavement materials is an important material property in any 

mechanistically based design/analysis procedure for flexible pavements. Repeated load resilient 

modulus tests are being performed on all unbound materials and soils of the Specific Pavement 

Studies (SPS) and General Pavement Studies (GPS) test sections that are in the Federal Highway 

Administration (FHWA) Long Term Pavement Performance (LTPP) program in accordance with 

LTPP test protocol P46. Previous studies have shown that the resilient modulus test results can 

be affected by sampling technique, testing procedure, and errors that can occur during the testing 

program. Thus, the FHWA sponsored a detailed review of the resilient modulus test results that 

have a Level E status in the LTPP database, i.e., they have passed all levels of the quality control 

(QC) checks. 

This report documents the first comprehensive review and evaluation of the resilient modulus 

test data measured on pavement materials and soils recovered from the LTPP test sections. The 

resilient modulus test data were found generally to be in excellent condition with less than 10 

percent of the tests exhibiting potential anomalies or discrepancies in the data. 

The resilient modulus data were further investigated to evaluate relationships between resilient 

modulus and the physical properties of the unbound materials and soils. The primary result from 

these studies is that the resilient modulus can be reasonably predicted from the physical 

properties included in the LTPP database, but there is a bias present in the calculated values. 

Thus, until additional test results become available to improve or confirm these relationships, it 

is recommended that at least some laboratory tests be performed to measure the resilient modulus 

for unbound pavement materials and soils. 

T. Paul Teng, P.E. 

Director 

Office of Infrastructure 

 Research and Development 

Notice

This document is disseminated under the sponsorship of the Department of Transportation in the 

interest of information exchange. The United States Government assumes no liability for its 

contents or use thereof. This report does not constitute a standard, specification, or regulation. 

The United States Government does not endorse products or manufacturers. Trade and 

manufacturers= names appear in this report only because they are considered essential to the 

object of the document. 
Technical Report Documentation Page

1. Report No.

FHWA-RD-02-051

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

5. Report Date

OCTOBER 2002

4. Title and Subtitle

Study of LTPP Laboratory Resilient Modulus Test Data and Response 

Characteristics

6. Performing Organization Code

7. Author(s)

Amber Yau and Harold L. Von Quintus

8. Performing Organization Report No.

3032.1

10. Work Unit No. (TRAIS)

C6B

9. Performing Organization Name and Address

Fugro-BRE, Inc.

8613 Cross Park Drive

Austin, TX 78754 11. Contractor Grant No.

DTFH61-95-C-00028

13. Type of Report and Period 

Covered

June 2000-October 2001 Final Report

12. Sponsoring Agency Name and Address

Office of Infrastructure Research and Development

Federal Highway Administration

6300 Georgetown Pike

McLean, Virginia 22101 14. Sponsoring Agency Code

HCP 30-C

15. Supplementary Notes

Contracting Officer’s Technical Representative (COTR): Cheryl Allen Richter, HRDI-13

16. Abstract

The resilient modulus of every unbound structural layer of the Long Term Pavement Performance (LTPP) Specific Pavement and 

General Pavement Studies Test Sections is being measured in the laboratory using LTPP test protocol P46. A total of 2,014 

resilient modulus tests have passed all quality control checks and are included in the LTPP database with a Level E data status. As 

of October 2000, there were 1,639 resilient modulus tests yet to be performed. In some cases, these missing tests may have been 

performed, but did not achieve a Level E status (did not pass all quality control checks) in the LTPP database. However, these test

results have not been evaluated in detail. This report documents the first comprehensive review and evaluation of the resilient 

modulus test data measured on pavement materials and soils recovered from the LTPP test sections.

The resilient modulus data were reviewed in detail to identify anomalies or potential errors in the database. From this review, a 

total of 185 resilient modulus tests were identified with possible problems or data entry errors. These tests were reported to 

FHWA for further review and/or retesting. The resilient modulus test data were found generally to be in excellent condition with 

less than 10 percent of the tests exhibiting potential anomalies or discrepancies in the data.

The resilient modulus test data were then studied for the effect of test variables, such as the test and sampling procedures, on the 

resulting resilient moduli. These data were analyzed by material code for the base and subbase aggregate layers and by soil type 

for the subgrade. Sampling technique (auger versus test pit) was found to have the most effect on the crushed stone aggregate and 

uncrushed gravel base materials. For the subgrade soils, sampling technique (Shelby tubes versus auger samples) had the most 

effect on the clay soils. Sampling technique was found to have little to no effect on the sand base/subbase materials and sand soils.

The resilient modulus data were further investigated to evaluate relationships between resilient modulus and the physical 

properties of the unbound materials and soils. Using nonlinear regression optimization techniques, equations for each base and 

soil type were developed to calculate the resilient modulus at a specific stress state from physical properties of the base materials 

and soils. The primary result from these studies is that the resilient modulus can be reasonably predicted from the physical 

properties included in the LTPP database, but there is a bias present in the calculated values. Thus, until additional test results 

become available to improve or confirm these relationships, it is recommended that at least some laboratory tests be performed to 

measure the resilient modulus for unbound pavement materials and soils.

17. Key Words

Resilient modulus, LTPP.

18. Distribution Statement

No restrictions. This document is available to the public through the 

National Technical Information Service, Springfield, Virginia 22161.

19. Security Classification (of this 

report) Unclassified

20. Security Classification (of this page)

Unclassified

21. No. of Pages

173

22. Price

Form DOT F1700.7 (8-72) Reproduction of completed page authorized
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AREA AREA 

in2 square inches 645.2 square millimeters mm2 mm2 square millimeters 0.0016 square ft2 square feet 0.093 square meters m2 m2 square meters 10.764 square yd2 square yard 0.836 square meters m2 m2 square meters 1.195 square ac acres 0.405 hectares ha ha hectares 2.47 acres mi2 square miles 2.59 square kilometers km2 km2 square kilometers 0.386 square 

VOLUME VOLUME 

fl oz fluid ounces 29.57 milliliters mL mL milliliters 0.034 fluid ougal gallons 3.785 liters L L liters 0.264 gallons ft3 cubic feet 0.028 cubic meters m3 m3 cubic meters 35.314 cubic feyd3 cubic yards 0.765 cubic meters m3 m3 cubic meters 1.307 cubic yNOTE: volumes greater than 1000 L shall be shown in m3

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oz ounces 28.35 grams g g grams 0.035 ounces lb pounds 0.454 kilograms kg kg kilograms 2.202 pounds T short tons (2000 lb) 0.907 megagrams 

(or "metric ton") 

Mg (or "t") 

Mg (or "t") 

megagrams (or "metric ton") 

1.103 short to

TEMPERATURE (exact degrees) TEMPERATURE (exact degrees) oF Fahrenheit 5 (F-32)/9 Celsius oC oC Celsius 1.8C+32 Fahren

 or (F-32)/1.8 

ILLUMINATION ILLUMINATION 

fc foot-candles 10.76 lux lx lx lux 0.0929 foot-cafl foot-Lamberts 3.426 candela/m2 cd/m2 cd/m2 candela/m2 0.2919 foot-La

FORCE and PRESSURE or STRESS FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N N newtons 0.225 poundflbf/in2 poundforce per 

square inch 

6.89 kilopascals kPa kPa kilopascals 0.145 poundfo

square 

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

ii 
 iii

TABLE OF CONTENTS 

Chapter Page

1. INTRODUCTION.....................................................................................................................1 

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

 STUDY OBJECTIVES......................................................................................................2 

 SCOPE OF REPORT.........................................................................................................2 

2. REVIEW OF RESILIENT MODULUS TEST DATA ............................................................3 

 IDENTIFICATION OF MISSING RESILIENT MODULUS TESTS .............................3 

 RESILIENT MODULUS CONSTITUTIVE EQUATION ...............................................4 

 IDENTIFICATION OF TEST DATA ANOMALIES ....................................................13 

3. EFFECT OF SAMPLING TECHNIQUE ON RESILIENT MODULUS .............................25 

 DATA GROUPS EVALUATED – SOURCES OF VARIABILITY..............................25 

 IDENTIFICATION OF OUTLIERS ...............................................................................26 

 COMPARISON OF RESILIENT MODULUS TEST RESULTS...................................27 

 Effect of Stress State ..................................................................................................27 

 Unbound Aggregate Layers – Test Pit Versus Auger Samples .................................28 

 Soils – Test Pit Versus Auger Samples......................................................................31 

 Soils – Shelby Tubes (Undisturbed) Versus Recompacted (Disturbed) Samples......31 

 SUMMARY .....................................................................................................................33

4. EFFECT OF PHYSICAL PROPERTIES ON RESILIENT MODULUS .............................37 

 PHYSICAL PROPERTIES USED IN STUDY...............................................................37 

 STATISTICAL PROCEDURE........................................................................................38 

 CORRELATION STUDY FOR MODEL DEVELOPMENT.........................................38 

 Effect of Material/Soil Type ......................................................................................41 

 Unbound Aggregate Base/Subbase Materials............................................................41 

 Subgrade Soils............................................................................................................48 

 SUMMARY .....................................................................................................................51

5. SUMMARY AND FUTURE RECOMMENDATIONS .......................................................55 

 FINDINGS AND OBSERVATIONS ..............................................................................55 

 RECOMMENDATIONS .................................................................................................57 
 iv

TABLE OF CONTENTS (continued) 

Chapter Page

APPENDIX A. SUMMARY OF k-COEFFICIENTS FOR THE LTPP RESILIENT 

 MODULUS TESTS .........................................................................................................59 

APPENDIX B. GEOGRAPHICAL EXAMPLES OF THE DIFFERENT TYPES OF 

 ANOMALIES IDENTIFIED IN THE RESILIENT MODULUS TEST DATA ...........97 

APPENDIX C. SUMMARY OF THE FLAGGED RESILIENT MODULUS TESTS BY 

 ANOMALY TYPE .......................................................................................................113 

APPENDIX D . PARAMETERS AND THEIR VALUES INCLUDED IN THE 

 NONLINEAR REGRESSION RELATING RESILIENT MODULUS TO 

 PHYSICAL PROPERTIES............................................................................................129 

APPENDIX E . RESULTS FROM NONLINEAR OPTIMIZATION REGRESSION 

 STUDY RELATING RESILENT MODULUS TO PHYSICAL PROPERTIES .........139 

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

LIST OF FIGURES 

Figure Page

1 Distribution of the k-coefficients of constitutive equation 3, assuming k6 =0,

 for the entire LTPP resilient modulus database .................................................................. 6 

2 Distribution of the k-coefficients of constitutive equation 3, assuming k6 =0,

 for the unbound aggregate base and subbase materials ...................................................... 7 

3 Distribution of the k-coefficients of constitutive equation 3, assuming k6 =0,

 for the coarse-grained subgrade soils.................................................................................. 8 

4 Distribution of the k-coefficients of constitutive equation 3, assuming k6 =0,

 for the fine-grained subgrade soils...................................................................................... 9 

5 Comparison of measured and predicted resilient modulus (from regressed k-values 

 from measured MR data) for the crushed stone materials sampled from the test pit 

 locations ............................................................................................................................ 11 

6 Comparison of measured and predicted resilient modulus (from regressed k-values 

 from measured MR data) for the crushed stone materials sampled from the auger 

 locations ............................................................................................................................ 11 

7 Graphical comparison of the calculated MR (using the regressed k-coefficients from 

 the LTPP test results) to the measured MR for the gravel soils ......................................... 12 

8 Graphical comparison of the calculated MR (using the regressed k-coefficients from 

 the LTPP test results) to the measured MR for the clay soils ............................................ 12 

9 Repeated-load resilient modulus test results for section 014073, layer 3, at the 

 approach end ..................................................................................................................... 16 

10 Repeated-load resilient modulus test results for section 480802, layer 3, at the 

 leave end............................................................................................................................ 16 

11 Repeated-load resilient modulus test results for section 352007, layer 2, at the 

 approach end ..................................................................................................................... 17 

12 Repeated-load resilient modulus test results for section 390209, layer 2, at the 

 approach end ..................................................................................................................... 17 

13 Repeated-load resilient modulus test results for section 481093, layer 2, at the 

 approach end ..................................................................................................................... 18 

14 Sample from test section 010102, layer 1, at the leave end exhibits specimen 

 distortion or excess softening............................................................................................ 21 

15 Sample from test section 171003, layer 1, at the leave end shows significant effect 

 of confining pressure on resilient modulus ....................................................................... 21 

16 Sample from test section 014129, layer 1, at the leave end shows sudden drop and 

 then increase in resilient modulus..................................................................................... 22 

17 Sample from test section 055803, layer 1, at the approach end exhibiting localized 

 softening or disturbance of the specimen during the test or LVDT movement................ 22 

18 Sample from test section 473108, layer 1, at the leave end shows higher confining 

 pressures result in lower resilient modulus ....................................................................... 23 

19 Sample from test section 123811, layer 1, at the approach end shows that resilient 

 modulus is independent of confining pressure at the lowest vertical stress...................... 23 

20 Sample from test section 473104, layer 2, at the approach end shows possible data 

 entry error.......................................................................................................................... 24 
 vi

LIST OF FIGURES (continued) 

Figure Page

21 Graphical comparison of the predicted and measured resilient modulus for the 

 crushed stone base materials ............................................................................................. 43 

22 Graphical comparison of the predicted and measured resilient modulus for the 

 crushed gravel base materials............................................................................................ 43 

23 Graphical comparison of the predicted and measured resilient modulus for the 

 uncrushed gravel base materials........................................................................................ 45 

24 Graphical comparison of the predicted and measured resilient modulus for the 

 sand base materials............................................................................................................ 45 

25 Graphical comparison of the predicted and measured resilient modulus for the 

 coarse-grained soil-aggregate base materials.................................................................... 46 

26 Graphical comparison of the predicted and measured resilient modulus for the 

 fine-grained soil-aggregate base materials........................................................................ 46 

27 Graphical comparison of the predicted and measured resilient modulus for the 

 fine-grained soil base materials......................................................................................... 48 

28 Graphical comparison of the predicted and measured resilient modulus for the 

 coarse-grained gravel soils................................................................................................ 50 

29 Graphical comparison of the predicted and measured resilient modulus for the 

 coarse-grained sand soils................................................................................................... 50

30 Graphical comparison of the predicted and measured resilient modulus for the 

 fine-grained silt soils......................................................................................................... 52

31 Graphical comparison of the predicted and measured resilient modulus for the 

 fine-grained clay soils ....................................................................................................... 52 

32 Graphical comparison of the resilient modulus predicted from the data sets 

 for crushed stone materials sampled from the test pit and auger locations....................... 53 

33 Graphical comparison of the calculated MR using the regressed k-coefficients from 

 the physical properties of the sand soil group sampled from augers and test pits ............ 54 

34 Sample from test section 010111, layer 1, at the leave end exhibits specimen 

 distortion or excess softening............................................................................................ 98 

35 Sample from test section 063030, layer 1, at the approach end exhibits specimen 

 distortion or excess softening............................................................................................ 98 

36 Sample from test section 067455, layer 1, at the approach end exhibits specimen 

 distortion or excess softening............................................................................................ 99 

37 Sample from test section 370212, layer 1, at the approach end exhibits specimen 

 distortion or excess softening............................................................................................ 99 

38 Sample from test section 179327, layer 1, at the approach end shows significant 

 effect of confining pressure on resilient modulus........................................................... 100 

39 Sample from test section 295403, layer 1, at the approach end shows significant 

 effect of confining pressure on resilient modulus........................................................... 100 

40 Sample from test section 296067, layer 1, at the approach end shows significant 

 effect of confining pressure on resilient modulus........................................................... 101 

41 Sample from test section 289030, layer 1, at the leave end shows significant effect 

 of confining pressure on resilient modulus ..................................................................... 101 
 vii

LIST OF FIGURES (continued) 

Figure Page

42 Sample from test section 123811, layer 1, at the leave end shows sudden drop and 

 then increase in resilient modulus................................................................................... 102 

43 Sample from test section 280508, layer 1, at the leave end shows sudden drop and 

 then increase in resilient modulus................................................................................... 102 

44 Sample from test section 283089, layer 1, at the leave end shows sudden drop and 

 then increase in resilient modulus................................................................................... 103 

45 Sample from test section 483875, layer 1, at the leave end shows sudden drop and 

 then increase in resilient modulus................................................................................... 103 

46 Sample from test section 483589, layer 1, at the leave end exhibiting localized 

 softening or disturbance of the specimen during the test or LVDT movement.............. 104 

47 Sample from test section 483609, layer 1, at the leave end exhibiting localized 

 softening or disturbance of the specimen during the test or LVDT movement.............. 104 

48 Sample from test section 053048, layer 1, at the leave end exhibiting localized 

 softening or disturbance of the specimen during the test or LVDT movement.............. 105 

49 Sample from test section 541640, layer 1, at the leave end exhibiting localized 

 softening or disturbance of the specimen during the test or LVDT movement.............. 105 

50 Sample from test section 014125, layer 1, at the approach end shows higher 

 confining pressures result in lower resilient modulus..................................................... 106 

51 Sample from test section 014127, layer 1, at the leave end shows higher confining 

 pressures result in lower resilient modulus ..................................................................... 106 

52 Sample from test section 473109, layer 1, at the leave end shows higher confining 

 pressures result in lower resilient modulus ..................................................................... 107 

53 Sample from test section 481047, layer 1, at the leave end shows higher confining 

 pressures result in lower resilient modulus ..................................................................... 107 

54 Sample from test section 095001, layer 1, at the approach end shows that resilient 

 modulus is independent of confining pressure at the lowest vertical stress.................... 108 

55 Sample from test section 480801, layer 1, at the approach end shows that resilient 

 modulus is independent of confining pressure at the lowest vertical stress.................... 108 

56 Sample from test section 480802, layer 1, at the approach end shows that resilient 

 modulus is independent of confining pressure at the lowest vertical stress.................... 109 

57 Sample from test section 566031, layer 1, at the approach end shows that resilient 

 modulus is independent of confining pressure at the lowest vertical stress.................... 109 

58 Sample from test section 014073, layer 3, at the approach end shows possible 

 data entry error ................................................................................................................ 110 

59 Sample from test section 014084, layer 2, at the leave end shows possible data 

 entry error........................................................................................................................ 110 

60 Sample from test section 124106, layer 2, at the approach end shows possible data 

 entry error........................................................................................................................ 111 

61 Sample from test section 124106, layer 3, at the approach end shows possible data 

 entry error........................................................................................................................ 111 
 viii

LIST OF FIGURES (continued) 

Figure Page

62 Residuals, R, for the combined resilient modulus prediction equation for all base 

 and subbase materials...................................................................................................... 153

63 Residuals, R, for the uncrushed gravel (LTPP material code 302) resilient modulus 

 prediction equation.......................................................................................................... 153 

64 Residuals, R, for the crushed stone (LTPP material code 303) resilient modulus 

 prediction equation.......................................................................................................... 154 

65 Residuals, R, for the crushed gravel (LTPP material code 304) resilient modulus 

 prediction equation.......................................................................................................... 154 

66 Residuals, R, for the sand (LTPP material code 306) resilient modulus prediction 

 equation........................................................................................................................... 155 

67 Residuals, R, for the fine-grained soil-aggregate mixture (LTPP material code 307) 

 resilient modulus prediction equation ............................................................................. 155 

68 Residuals, R, for the coarse-grained soil-aggregate mixture (LTPP material 

 code 308) resilient modulus prediction equation ............................................................ 156 

69 Residuals, R, for the fine-grained soil (LTPP material code 309) resilient modulus 

 prediction equation.......................................................................................................... 156 

70 Residuals, R, for the resilient modulus prediction equation for all subgrade soils ......... 157 

71 Residuals, R, for the gravel soils resilient modulus prediction equation ........................ 157 

72 Residuals, R, for the sand soils resilient modulus prediction equation........................... 158 

73 Residuals, R, for the silt soils resilient modulus prediction equation ............................. 158 

74 Residuals, R, for the clay soils resilient modulus prediction equation............................ 159 
 ix

LIST OF TABLES 

Table Page

1 Summary of completed and missing resilient modulus tests as of the October 2000 

 LTPP data release................................................................................................................ 3 

2 Summary of the median and mean values for each coefficient of constitutive 

 equation 3, assuming k6 = 0, for each of the base and subbase pavement materials and 

subgrade soils .................................................................................................................... 10 

3 Example results of the statistical analyses of the repeated-load resilient modulus tests 

performed on unbound pavement materials and soils from the LTPP test sections ......... 15 

4 Summary of identified anomaly types .............................................................................. 18 

5 Data groups for the base/subbase and subgrade soils ....................................................... 26 

6 Results of ANOVA to determine if the resilient modulus ratio (auger versus 

 test pit test specimens) is a function of stress.................................................................... 27 

7 Summary of ANOVA to determine effect of sampling technique (auger versus 

 test pit) on resilient modulus ............................................................................................. 29 

8 Summary of the student t-test on the difference between augured and test pit samples 

 for the base/subbase materials and subgrade soils ............................................................ 30 

9 Comparison of results using k-values and resilient modulus values to determine 

 effect of sampling technique (auger versus test pits) on resilient modulus test data ........ 30 

10 Summary of ANOVA to determine effect of sampling technique (Shelby tube 

 versus auger) on resilient modulus.................................................................................... 32 

11 Summary of the student t-test on the difference between disturbed and undisturbed 

 samples for the subgrade soils........................................................................................... 32 

12 Comparison of results using k-values and resilient modulus values to determine 

 the effect of sampling technique of undisturbed (Shelby tubes) and disturbed 

 (auger) test specimens on resilient modulus test data ....................................................... 33 

13 Summary comparison of the resilient modulus test results for different sampling 

 techniques.......................................................................................................................... 35 

14 Summary of the MR physical property regression variables ............................................. 38 

15 Summary of the physical properties that were found to be important for predicting 

 resilient modulus for each material and soil type.............................................................. 40 

16 k-values determined from nonlinear regression analyses of LTPP resilient modulus 

 test of unbound materials .................................................................................................. 61 

17 Resilient modulus tests showing characteristics of exhibiting test specimen distortion 

 or excessive softening ..................................................................................................... 114

18 Resilient modulus tests showing significant effect of confining pressure ...................... 115 

19 Resilient modulus tests with a sudden drop and then an increase in resilient modulus.. 116 

20 Resilient modulus tests exhibiting localized softening or disturbance of the specimen 

 during the test or LVDT movement ................................................................................ 117 

21 Resilient modulus tests that result in lower resilient moduli for the higher confining 

pressures.......................................................................................................................... 125 

22 Resilient modulus tests showing resilient modulus is independent of confining 

 pressure at the lowest vertical stress ............................................................................... 126 

23 Resilient modulus tests with potential data entry error................................................... 128 
 x

LIST OF TABLES (continued) 

Table Page

24 Summary of the LTPP data used in the nonlinear regression study of resilient 

 modulus for all granular base and subbase material data set .......................................... 130 

25 Summary of the LTPP data used in the nonlinear regression study of resilient 

 modulus for LTPP base and subbase material code 302 data set – uncrushed gravel .... 130 

26 Summary of the LTPP data used in the nonlinear regression study of resilient 

 modulus for LTPP base and subbase material code 303 data set – crushed stone.......... 131 

27 Summary of the LTPP data used in the nonlinear regression study of resilient 

 modulus for LTPP base and subbase material code 304 data set – crushed gravel ........ 131 

28 Summary of the LTPP data used in the nonlinear regression study of resilient 

 modulus for LTPP base and subbase material code 306 data set – sand ........................ 132 

29 Summary of the LTPP data used in the nonlinear regression study of resilient 

 modulus for LTPP base and subbase material code 307 data set – fine-grained soil- 

 aggregate mixture............................................................................................................ 132 

30 Summary of the LTPP data used in the nonlinear regression study of resilient 

 modulus for LTPP base and subbase material code 308 data set – coarse-grained soil- 

 aggregate mixture............................................................................................................ 133 

31 Summary of the LTPP data used in the nonlinear regression study of resilient 

 modulus for LTPP base and subbase material code 309 data set – fine-grained soil ..... 133 

32 Summary of the LTPP data used in the nonlinear regression study of resilient 

 modulus for all subgrade soils data set............................................................................ 134 

33 Summary of the LTPP data used in the nonlinear regression study of resilient 

 modulus for the gravel subgrade soils data set................................................................ 135 

34 Summary of the LTPP data used in the nonlinear regression study of resilient 

 modulus for the sand subgrade soils data set .................................................................. 136 

35 Summary of the LTPP data used in the nonlinear regression study of resilient 

 modulus for the silt subgrade soils data set..................................................................... 137 

36 Summary of the LTPP data used in the nonlinear regression study of resilient 

 modulus for the clay subgrade soils data set................................................................... 138 

37 Results from the nonlinear optimization regression study for all base and subbase 

 material types combined.................................................................................................. 140 

38 Results from the nonlinear optimization regression study for the LTPP base and 

 subbase material code data set 302 – uncrushed gravel.................................................. 141 

39 Results from the nonlinear optimization regression study for the LTPP base and 

 subbase material code data set 303 – crushed stone........................................................ 142 

40 Results from the nonlinear optimization regression study for the LTPP base and 

 subbase material code data set 304 – crushed gravel...................................................... 143 

41 Results from the nonlinear optimization regression study for the LTPP base and 

 subbase material code data set 306 – sand ...................................................................... 144 

42 Results from the nonlinear optimization regression study for the LTPP base and 

 subbase material code data set 307 – fine-grained soil-aggregate mixture..................... 145 

43 Results from the nonlinear optimization regression study for the LTPP base and 

 subbase material code data set 308 – coarse-grained soil-aggregate mixture................. 146 
 xi

LIST OF TABLES (continued) 

Table Page

44 Results from the nonlinear optimization regression study for the LTPP base and 

 subbase material code data set 309 – fine-grained soil ................................................... 147 

45 Results from the nonlinear optimization regression study for the combined 

 subgrade soil data set....................................................................................................... 148 

46 Results from the nonlinear optimization regression study for the LTPP gravel 

 subgrade soil data set....................................................................................................... 149 

47 Results from the nonlinear optimization regression study for the LTPP sand 

 subgrade soil data set....................................................................................................... 150 

48 Results from the nonlinear optimization regression study for the LTPP silt 

 subgrade soil data set....................................................................................................... 151 

49 Results from the nonlinear optimization regression study for the LTPP clay 

 subgrade soil data set ...................................................................................................... 152 

 1

CHAPTER 1. INTRODUCTION 

BACKGROUND 

 

The elastic or resilient modulus of pavement materials is an important material property in any 

mechanistically based design/analysis procedure for flexible pavements. In fact, the resilient 

modulus (MR) is the material property required for the 1993 American Association of State 

Highway and Transportation Officials (AASHTO) Design Guide, which is an empirically based 

design procedure, and is the primary material input parameter for the 2002 Design Guide.(1) The 

2002 Design Guide is being developed based on mechanistically based principles under National 

Cooperative Highway Research Program (NCHRP) Project 1-37A, ìDevelopment of Design 

Procedure for New and Rehabilitated Pavements.î 

 

Repeated load resilient modulus tests are being performed on all unbound materials and soils of 

the Specific Pavement Studies (SPS) and General Pavement Studies (GPS) test sections that are 

in the Federal Highway Administration (FHWA) Long Term Pavement Performance (LTPP) 

program in accordance with LTPP test protocol P46.(2) The MR of unbound pavement materials 

and soils is a measure of the elastic modulus of the material at a given stress state. It is 

mathematically defined as the applied deviator stress divided by the ìrecoverableî strain that 

occurs when the applied load is removed from the test specimen. 

r

d MR

ε

σ

= (1) 

Where: 

σd = applied deviator stress in a repeated load triaxial test. 

εr = recoverable or resilient strain. 

 

The MR measured at different stress states have been included in the LTPP Information 

Management System (IMS), but the test results have not been evaluated for use in future research 

studies. 

Previous studies have shown that the resilient modulus test results can be affected by sampling 

technique, testing procedure, and errors that can occur during the testing program. Some of these 

errors include incorrect conditioning/stress sequence, leaks in the membrane, incorrect stress 

levels, unstable Linear Variable Differential Transducer (LVDT) clamps attached to the 

specimen, exceeding the LVDT linear range limits, and specimen disturbance at the higher stress 

states. Thus, FHWA authorized a detailed review of the resilient modulus test results that have a 

Level E status in the LTPP database, i.e., they have passed all levels of the quality control (QC) 

checks. This report summarizes the findings from the detailed review of the resilient modulus 

test data. 
 2

STUDY OBJECTIVES 

This study focused on determining anomalies in the unbound resilient modulus data in the 

database to ensure data quality and to identify any bias between different data sets. The MR data 

were extracted first from the April 2000 data release and updated with additional MR tests from 

the October 2000 release. The MR data were obtained from the TST_UG07_SS07_WKSHT_ 

SUM table in the IMS. The following tasks define the work performed to accomplish the goals 

of the study: 

Task 1: Identify any and all of the repeated load resilient modulus data for unbound 

pavement materials and soils that are not at Level E. 

Task 2: Review and evaluate the resilient modulus data to identify any anomalies in the 

database. 

MR tests with potential anomalies were flagged and a ìcleanedî data set was used to determine 

any bias in the data and identify other factors that influence the tests results. The cleaned data 

set also was used to perform correlation studies between the MR of the selected constitutive 

equation and the physical properties of the unbound materials and soils in support of NCHRP 

Project 1-37A. 

SCOPE OF REPORT 

This report summarizes the review of the resilient modulus test results that have a Level E status 

in the LTPP database. The report is divided into five chapters, including the introduction 

(chapter 1). Chapter 2 provides the process of identifying missing tests and anomalies in the 

Level E data. Chapter 3 discusses the effect of test variables on resilient modulus. A correlation 

between the MR determined from the selected constitutive equation and physical properties of the 

tests specimens is presented in chapter 4. Chapter 5 summarizes all of the findings and provides 

recommendations for future research. 
 3

CHAPTER 2. REVIEW OF RESILIENT MODULUS TEST DATA 

IDENTIFICATION OF MISSING RESILIENT MODULUS TESTS 

A total of 1,970 resilient modulus tests were extracted from the April 2000 LTPP database (most 

current at the time of data extraction) of unbound materials and soils. The October 2000 data 

release was cross-checked with the April release for additional tests to update the review and 

findings. A total of 44 additional resilient modulus tests were extracted from the October 

release, resulting in a total of 2,014 MR tests. 

The resilient modulus tests in the LTPP database were organized by State and layer type for each 

SPS project and by State, layer number, layer type, and section identification number for the 

GPS test sections. The data were cross-checked with the required number of resilient modulus 

tests per layer for each project to determine the number of missing tests. 

 

Table 1 summarizes the number of completed and missing resilient modulus tests by layer type 

as of the October 2000 data release. The numbers of completed and missing tests do not add up 

to the number of tests required because extra tests were performed. The resilient modulus tests 

in the database that are counted as complete are identified as Level E data. The number of 

missing tests includes those MR tests that have not been performed plus those that have been 

completed, but which have not passed all QC levels. 

Table 1. Summary of completed and missing resilient modulus tests 

as of the October 2000 LTPP data release. 

Layer Type Soil Type 

No. of Tests 

Required 

No. of Tests 

Completed 

No. of Tests 

Missing 

All 1886 1347 594 

Clay 652 513 168 

Gravel 262 123 140 

Rock 24 3 21 

Sand 765 580 208 

Silt 169 116 55 

Subgrade Soil 

Unknown 14 12 2 

Granular Subbase All 685 259 427 

Granular Base All 956 385 573 

Unknown Unknown -- 23 -- 

Total 3527 2014 1594 

The missing resilient modulus tests were categorized by LTPP region, State, experiment type, 

and layer type. Data feedback reports for the missing tests were summarized by region and 

submitted to LTPP. There are a total of 23 MR tests that cannot be summarized using the layer 

type due to missing layer structure information. The MR tests for the subgrade soils were further 

divided into soil type (i.e., clay, gravel, rock, sand, and silt) since more than half of the total 

required resilient modulus tests are for the subgrade. Some tests cannot be grouped by soil type 

due to missing soil classification information. 
 4

In summary, more than half of the required testing has been completed and the data have 

achieved a Level E status. The other half of the required tests either have not been completed or 

the tests have been performed, but the QC process is incomplete. It is expected that the number 

of completed MR tests with a Level E data status will significantly increase in future data 

releases. 

RESILIENT MODULUS CONSTITUTIVE EQUATION 

LTPP test protocol P46 is being used to measure the MR of unbound pavement materials and 

subgrade soils. This test is performed over a wide range of vertical stresses and confining 

pressures to measure the nonlinear (stress-sensitivity) elastic behavior of these materials and 

soils. Various types of relationships have been used to represent the repeated-load MR test 

results of coarse-grained and fine-grained soils. However, Von Quintus and Killingsworth found 

that the so-called ìuniversalî constitutive equation provided a very good fit to the LTPP MR test 

data.(3) The specific equation used is given below: 

2 3

1

K K

d

R a

a a

M KP

P P

   θ σ =      

 (2) 

As noted in chapter 1, the 2002 Design Guide uses MR as the primary material property for all 

unbound pavement layers and subgrade soils. The constitutive equation used for determining the 

MR of a material is given below and represents an expanded version of equation 2:(4)

2 3

1 3 6

1

k

a

oct

k

a

R a P P

k

M k P 



 



  +



 



 − = θ τ (3) 

where: Pa = atmospheric pressure. 

θ = bulk stress: 

 θ = . σ 1 +σ 2 +σ 3 (4) 

 σ1 = major principal stress. 

σ2 = intermediate principal stress = σ3 for MR test on cylindrical 

specimen. 

σ3 = minor principal stress/confining pressure. 

τoct = octahedral shear stress: 

 ( )( )( )2

2 3

2

1 3

2

1 2 3

1

τ oct = σ −σ + σ −σ + σ −σ (5) 

k1, k2, 

k3, k6 = regression constants. 

Observation: 2,014 MR tests of unbound pavement materials and soils have a Level E 

data status as of the October 200 LTPP data release, while 1,594 have not yet obtained a 

Level E status. 
 5

Coefficient k1 is proportional to Youngís modulus. Thus, the values for k1 should be positive 

since MR can never be negative. Increasing the volumetric stress (θ) should produce a stiffening 

or hardening of the material, which results in a higher MR. Therefore, the exponent (k2) of the 

bulk stress term for the above constitutive equation should also be positive. Coefficient k6 is 

intended to account for pore-water pressure or cohesion and is a measure of the materialís ability 

to resist tension. The values for k6 are expected to be negative or, when positive, less than or 

equal to a third of the bulk stress. Coefficient k3 is the exponent of the octahedral shear stress 

term. The values for k3 should be negative since increasing the shear stress will produce a 

softening of the material, i.e., a lower MR. 

The regression for the four k-coefficients in equation 3 was performed, restraining the regression 

constants to their physical limits using the LTPP April and October 2000 data releases. Only 

those resilient modulus tests with 12 or more data points were used, resulting in a total of 1,920 

tests. A total of 94 MR tests (approximately 4 percent of the total number of tests) had less than 

12 data points. It is important to note that all regressions were performed using units of MPa for 

MR and kPa for the stress and pressure parameters in equation 3. 

More than half of the k6 values were equal to zero, while the non-zero values were highly 

variable with a uniform distribution. Therefore, k6 was set to zero and the regression was 

repeated. No significant effect was observed on the regression statistics setting k6 equal to zero. 

Figure 1 presents the distributions of the final results for the k-coefficients. The values for the kcoefficients are presented in appendix A. 

Coefficient k1 ranged from 0 to 3. These values are actually factors of a thousand because the 

MR value used was in MPa instead of kPa. Coefficient k2 ranged from 0 to 1.5 and has a binormal population. The bi-normal population suggests two different groups of soils. Figures 2 

through 4 confirm that the coarse-grained soils are different from the fine-grained soils. 

Coefficient k3 ranged from 0 to -7 and has a skewed distribution. About 25 percent of the values 

were equal to zero. The majority of MR tests with a k3 coefficient equal to zero were for the 

unbound aggregate materials or coarse-grained soils. 

Figures 2 through 4 present the distributions of the k-coefficients for the unbound aggregate 

materials and coarse-grained and fine-grained soils, while table 2 summarizes a comparison of 

the median and mean values for the coefficients from each data group. As shown, coefficients k1

and k2 have a normal distribution, while k3 has a skewed distribution for the base/subbase 

materials (figure 2). However, the distributions for k1 and k2 become skewed as the material 

becomes finer, while the distribution for k3 becomes more normal (figures 3 and 4). 

Observation: Coefficient k6 in equation 3 was found to be zero for more than 50 percent 

of the MR tests. 
 6

Figure 1. Distribution of the k-coefficients of constitutive equation 3, assuming k6 = 0, for the 

entire LTPP resilient modulus database. 

K1

1

2

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 2.7055

 2.1431

 1.5692

 1.2637

 1.0150

 0.8036

 0.6391

 0.5174

 0.3913

 0.2629

 0.1583

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

 0.855

 0.313

 0.007

 0.869

 0.841

 1920.000

 1920.000

K2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1.3450

 0.9747

 0.8275

 0.7299

 0.6335

 0.4824

 0.2570

 0.1710

 0.0902

 0.0000

 0.0000

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

 0.457

 0.219

 0.005

 0.467

 0.447

 1920.000

 1920.000

K3

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 0.0000

 0.0000

 0.0000

 0.0000

-0.0948

-0.6536

-1.6649

-2.6841

-3.9364

-5.1932

-6.5304

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

 -1.033

 1.132

 0.026

 -0.983

 -1.084

 1920.000

 1920.000
 7

Figure 2. Distribution of the k-coefficients of constitutive equation 3, assuming k6 = 0, for the 

unbound aggregate base and subbase materials. 

K1:MRK12000STAT

1

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1.8474

 1.8002

 1.4835

 1.2097

 1.0498

 0.8527

 0.6778

 0.5267

 0.4105

 0.3013

 0.2809

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

 0.8732

 0.2726

 0.0133

 0.8993

 0.8472

 423.0000

 423.0000

K2:MRK12000STAT

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1.0622

 1.0211

 0.9025

 0.7712

 0.7000

 0.6280

 0.5646

 0.4867

 0.2738

 0.1880

 0.1741

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

 0.6261

 0.1330

 0.0065

 0.6388

 0.6134

 423.0000

 423.0000

K3:MRK12000STAT

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 0.0000

 0.0000

 0.0000

 0.0000

 0.0000

-0.1294

-0.2606

-0.4007

-0.6245

-0.8154

-2.8978

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

 -0.1696

 0.2148

 0.0104

 -0.1490

 -0.1901

 423.0000

 423.0000
 8

Figure 3. Distribution of the k-coefficients of constitutive equation 3, assuming k6 = 0, for the 

coarse-grained subgrade soils. 

K1:MRK12000STAT:k6eql0_property

1

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1.8894

 1.8408

 1.4490

 1.1558

 0.9294

 0.7635

 0.6094

 0.5050

 0.4284

 0.3736

 0.3727

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

 0.8019

 0.2661

 0.0166

 0.8345

 0.7692

 257.0000

 257.0000

K2:MRK12000STAT:k6eql0_property

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

0.89552

0.88562

0.79432

0.71210

0.62000

0.44597

0.28199

0.19680

0.14334

0.09506

0.08290

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

 0.4521

 0.1927

 0.0120

 0.4758

 0.4284

 257.0000

 257.0000

K3:MRK12000STAT:k6eql0_property

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 0.0000

 0.0000

 0.0000

-0.1401

-0.6423

-1.0518

-1.5820

-2.2226

-2.8804

-3.0199

-3.0230

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

 -1.1401

 0.7365

 0.0459

 -1.0496

 -1.2305

 257.0000

 257.0000
 9

Figure 4. Distribution of the k-coefficients of constitutive equation 3, assuming k6 = 0, for the 

fine-grained subgrade soils.

K1:MRK12000STAT:k6eql0_property

0.5

1.0

1.5

2.0

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 1.8391

 1.8391

 1.7168

 1.3225

 1.0925

 0.8037

 0.6565

 0.5867

 0.4459

 0.2750

 0.2750

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

 0.8962

 0.3133

 0.0306

 0.9568

 0.8356

 105.0000

 105.0000

K2:MRK12000STAT:k6eql0_property

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

0.85065

0.85065

0.66573

0.53715

0.34959

0.24320

0.17651

0.13522

0.05900

0.00034

0.00034

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

 0.2824

 0.1552

 0.0151

 0.3124

 0.2523

 105.0000

 105.0000

K3:MRK12000STAT:k6eql0_property

-5

-4

-3

-2

-1

0

Quantiles

maximum

quartile

median

quartile

minimum

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

 0.0000

 0.0000

 0.0000

-0.1749

-0.8130

-1.3993

-2.2409

-3.1481

-4.3063

-4.9793

-4.9793

Moments

Mean

Std Dev

Std Error Mean

Upper 95% Mean

Lower 95% Mean

N

Sum Weights

 -1.5764

 1.1014

 0.1075

 -1.3632

 -1.7895

 105.0000

 105.0000
 10

Table 2. Summary of the median and mean values for each coefficient of constitutive equation 

3, assuming k6 = 0, for each of the base and subbase pavement materials and subgrade soils. 

Material/Soil Group 

Coefficient Unbound BaseSubbase Materials Coarse-Grained Soils Fine-Grained Soils 

Median 0.853 0.764 0.804 

k1 Mean 0.873 0.802 0.896 

Standard Deviation 0.2726 0.2661 0.3133 

Median 0.628 0.446 0.243 

k2 Mean 0.626 0.452 0.282 

Standard Deviation 0.1330 0.1927 0.1552 

Median -0.129 -1.052 -1.399 

k3 Mean -0.170 -1.140 -1.576 

Standard Deviation 0.2148 0.7365 1.1014 

Number of Tests 423 257 105 

Table 2 shows that the median value for coefficient k2 increases as the amount of fines in the 

material/soil increases (fine-grained soils to unbound aggregate base material). Similarly, the 

median value for k3 becomes more negative as the material/soil becomes more fine-grained. The 

majority of the zero values for k3 were from the unbound base materials and coarse-grained soils, 

approximately 25 percent of the MR tests for the unbound aggregate base/subbase materials and 

10 percent of the tests for the coarse-grained subgrade soils. Thus, the regressed k-coefficients 

from the LTPP MR test results are consistent with previous experience. 

Figures 5 and 6 compare the calculated MR from the regressed k-coefficients of the constitutive 

equation to the measured MR for the test pit and augured samples, respectively. Figures 7 and 8 

compare the calculated MR from the regressed k-coefficients of the constitutive equation to the 

measured MR for the gravel and clay soil groups, respectively. As shown, the constitutive 

equation provides an excellent fit to the LTPP MR test data. The universal constitutive equation 

provides a similar good fit to the other base materials and subgrade soils. 

Observation: Equation 3 provides an excellent fit to the LTPP resilient modulus test 

data. 
 11

Figure 5. Comparison of measured and predicted resilient modulus (from regressed k values 

from measured MR data) for the crushed stone materials sampled from the test pit locations. 

Figure 6. Comparison of measured and predicted resilient modulus (from regressed k values 

from measured MR data) for the crushed stone materials sampled from the auger locations. 

Resilient Modulus for Crushed Stone (matl code = 303) Test Pit Samples

0

50

100

150

200

250

300

350

400

450

500

0 50 100 150 200 250 300 350 400 450 500

Mr Measured

Mr Predicted (Mr = f (k)

Resilient Modulus for Crushed Stone (matl code = 303) Auger Samples

0

100

200

300

400

500

600

0 100 200 300 400 500 600

Mr Measured

Mr Predicted (Mr = f (k)
 12

Figure 7. Graphical comparison of the calculated MR (using the regressed k-coefficients from the 

LTPP test results) to the measured MR for the gravel soils. 

Figure 8. Graphical comparison of the calculated MR (using the regressed k-coefficients from the 

LTPP test results) to the measured MR for the clay soils. 

0

25

50

75

100

125

150

175

200

225

250

0 25 50 75 100 125 150 175 200 225 250

Mr Measured

Mr 

Ca

lcu

lat

ed Mr Calculated 

Resilient Modulus Comparison for Gravel Samples (Calculated Mr using regressed k-values 

vs. Measured Mr values)

0

25

50

75

100

125

150

175

200

225

250

0 25 50 75 100 125 150 175 200 225 250

Mr Measured

Mr Calculated 
 13

IDENTIFICATION OF TEST DATA ANOMALIES 

Approximately 10 percent of the regression results for the k-coefficients have se/sy values greater 

than 0.5, suggesting that the regressions are not good fits. The reason for the poor fit could be a 

result of errors that occurred during the test procedure or that the constitutive equation does not 

represent the actual behavior of selected unbound materials and soils. It is important to ensure 

that the data are of good quality and without errors prior to making an assessment on the 

applicability of equation 3. Some possible problems that can occur during the MR test are listed 

below: 

• Different conditioning sequences or different stress application sequences used in the test 

program. 

• Leaks occurring in the membrane during the test (i.e., an unconfined test). 

• Different stress states (applied stress and confining pressure) used in the test program than 

required by the test protocol. 

• Test specimens that begin to fail or exhibit disturbance at the higher stress states. 

• LVDT clamps that begin to move or move suddenly because of vibrations during the loading 

sequence. 

• LVDTs that begin to drift during the testing sequence or become restricted due to friction in 

the measurement system. 

• Measured deformations that begin to exceed the linear range of the LVDTs. 

The second objective of this study was to identify any possible anomalies that may exist in the 

resilient modulus database and to determine their possible cause. The process used to identify 

and flag the resilient modulus test data, with possible anomalies, is summarized below: 

Step 1. The resilient modulus test data were organized by material type or code for the 

review. 

 

Step 2. A regression analysis was conducted of the resilient modulus test data to define 

selected statistical parameters of the relationship between stress and resilient 

modulus. 

Step 3. A correlation matrix of the resilient modulus test data (resilient modulus correlation 

with bulk stress and octahedral shear stress) was determined. 

 

Step 4. A summary of the results from the regression (R2

, se/sy) and correlation matrix by 

material type was prepared. 

 
 14

Step 5. The resilient modulus tests, with possible anomalies, using the following criteria or 

threshold values, were identified and flagged: 

 *R2

<0.99 

 *se/sy>0.50 

 *Absolute Values of the Correlation Matrix <0.50 

Step 6. For those resilient modulus tests that were flagged, a graphical presentation of the 

data was prepared for a detailed review to confirm the test data anomaly, identify any 

similarities between these data sets or tests, and determine the probable cause of and 

recommend an action for the anomaly. If an anomaly could not be observed in the 

graphical presentation of the data, the MR test was de-flagged. 

Previous studies have found that equation 3 is a good simulation of the measured responses from 

repeated-load resilient modulus tests. The authors have also found that many anomalies that can 

and do occur in resilient modulus tests are difficult to identify after the testing has been 

completed. To ensure that all possible anomalies or discrepancies in the resilient modulus data 

were identified, fairly restrictive criteria or threshold values were used, as noted in Step 5. These 

threshold values were used to ensure that the test results were initially reviewed for which 

equation 3 is not an extremely close mimic of the test results. Simply flagging the test data does 

not mean that the test results have anomalies. Some of the tests were critically reviewed and 

were de-flagged because no anomaly could be identified, as noted in Step 6. 

Out of 1,920 MR tests, 212 were flagged using the criteria in Step 5 above. These tests (resilient 

modulus versus vertical stress) were plotted for the detailed review, as described in step 6. As an 

example, graphical presentations of the flagged and non-flagged resilient modulus test data 

summarized in table 3 are shown in figures 9 through 13 and explained briefly below. 

• Figures 9 and 10 for test sections 014073 and 480802, respectively, were flagged (see table 

3). The resilient modulus test from test section 014073 (figure 9) is characteristic of a coarsegrained soil. The MR increases with increasing confining pressure as expected. However, the 

incremental change in MR increases with repeated vertical stress for the lowest and highest 

confining pressures, while the incremental change in resilient modulus decreases with 

increasing repeated vertical stress for the mid-range confining pressure. This characteristic 

can be the result of binding (friction) in the LVDT core, which can restrict movement of the 

LVDTs at the lower or smaller repeated vertical loads for a specific confinement level. 

Figure 10, for test section 480802, shows that the MR increases with confining pressure 

between the lower and mid-range confinement, but significantly decreases for the highest 

confinement, implying a softening effect. In addition, the MR increases between the first two 

repeated vertical stresses applied to the test specimen, but then continues to decrease with 

increasing repeated vertical stresses. This characteristic can be caused by leaks developing in 

the membrane during the application of the series of vertical loads for the mid-range 

confinement. Both tests (figures 9 and 10) were identified as questionable. 

• The resilient modulus test on section 352007 initially was flagged (see table 3). Figure 11 

shows that the resilient modulus test from this test section is characteristic of fine-grained 

soils. Fine-grained soils typically soften (decreasing resilient modulus) with increasing 
 15

vertical pressures. However, no anomalies were observed in the test data. Since no anomaly 

was observed, this test was de-flagged. The statistical parameters from the regression for the 

k-coefficients for this test suggest that the constitutive equation may not describe the 

material/soil response characteristics accurately. 

• Figures 12 and 13 for test sections 390209 and 481093, respectively, were not flagged 

because they meet all of the above criteria. These graphs of non-flagged data are provided 

for comparative purposes. 

After step 6 was completed, 185 MR tests were flagged for potential anomalies (about 10 percent 

of the tests). These flagged MR tests were divided into seven groups of anomalies that are 

defined in table 4. Figures 14 through 20 are graphical examples for each potential anomaly. 

Table 3. Example results of the statistical analyses of the repeated-load resilient modulus tests 

performed on unbound pavement materials and soils from the LTPP test sections. 

Correlations with 

MR

STATE 

CODE

SHRP 

ID 

LAYER 

NO. 

TEST 

NO. 

LOC 

NO. 

SAMPLE 

NO. R2

 SE/SY

MATL 

CODE

N 

Cycles BULK 

STRESS 

BULK 

STRESS 

MR Test 

Initially 

Flagged 

1 4073 3 1 BA* BG** 0.8508 0.7095 308 0.2039 0.8829 2

35 2007 2 1 BA* BS** 0.9873 0.8197 309 15 0.6279 -0.3566 2

39 0209 2 1 B22 BG22 0.9996 0.0676 303 15 0.9959 0.7118 

48 0802 3 2 B4 BG01 0.9924 1 302 13 -0.4163 0.0445 2

48 1093 2 1 BA* BG** 0.9995 0.0469 303 15 0.9985 0.8394 

* - reference to LTPP database code list 

** - reference to LTPP database code list
 16

Figure 9. Repeated-load resilient modulus test results for section 014073, layer 3, 

at the approach end. 

Figure 10. Repeated-load resilient modulus test results for section 480802, layer 3, 

at the leave end. 

 

014073 Layer 3 Approach End 

Material Code = 308 

(Coarse Soil-Aggregate Mixture)

0

50

100

150

200

250

300

0 50 100 150 200

Repeated Vertical Pressure, kPa

Resilient Modulus, MPa

20.7

34.5

68.9

103.4

Confining 

Pressure, 

kPa

480802 Layer 3 Leave End 

Material Code = 302 

(Uncrushed Gravel)

0

20

40

60

80

100

0 20 40 60 80

Repeated Vertical Pressure, kPa

Resilient Modulus, MPa

13.8

27.6

41.3

Confining 

Pressure, 

kPa
 17

Figure 11. Repeated-load resilient modulus test results for section 352007, layer 2, 

at the approach end. 

Figure 12. Repeated-load resilient modulus test results for section 390209, layer 2, at the 

approach end. 

390209 Layer 2 Approach End 

Material Code = 303 

(Crushed Stone)

0

50

100

150

200

250

300

350

400

0 50 100 150 200

Repeated Vertical Pressure, kPa

Resilient Modulus, MPa

20.8

33.2

69.3

103.5

137.8

Confining 

Pressure, 

kPa

352007 Layer 2 Approach End 

Material Code = 309 

(Fine-Grained Soil)

0 

10 

20 

30 

40 

50 

60 

70 

80 

90 

100 

0 20 40 60 80

Repeated Vertical Pressure, kPa 

Resilient Modulus, MPa

13.8 27.6 41.4 

Confining Pressure, kPa 
 18

Figure 13. Repeated-load resilient modulus test results for section 481093, layer 2, 

at the approach end. 

Table 4. Summary of identified anomaly types. 

Type of Anomaly Definition of Anomaly Number of MR Tests 

Type 1 Potential disturbance or excessive softening of test specimen at 

the higher repeated vertical stresses. 17 

Type 2 Big gap between confining pressure for the lower repeated 

loads, which reduces or begins to merge for the higher loads. 15 

Type 3 A sudden drop in MR for a specific confinement, after which the 

MR continues to increase with higher vertical loads. 10 

Type 4 The different confinement curves cross – one confinement has 

a different stress sensitivity than the other confinement curve. 103 

Type 5 The curves for each of the confining pressures are completely 

out of order (e.g., highest confinement below mid-confinement). 11 

Type 6 All confinements show nearly the same MR for the lower 

repeated vertical loads. 20 

Type 7 Possible data entry error with both the MR and vertical stress at 

zero. 

9 

481093 Layer 2 Approach End

Material Code = 303

(Crushed Stone)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

Repeated Vertical Pressure, kPa

Resilient Modulus, MPa

20.7

34.5

68.9

103.4

137.9

Confining

Pressure,

kPa
 19

• Type 1 Anomaly Example – Figure 14. This test shows that the MR increases and then 

decreases with increasing repeated vertical loads for each confining pressure. These results 

are characteristic of specimen disturbance or excess softening at the higher repeated vertical 

loads. More examples of type 1 anomalies are presented in appendix B, figures 34 through 

37. 

• Type 2 Anomaly Example – Figure 15. This test shows large gaps between different 

confining pressures for the lower repeated loads (i.e., significant effect of confining 

pressure), which decreases to almost no effect of confining pressure at the higher repeated 

loads. In other words, the MR for the different confining pressures merge with increasing 

repeated vertical loads. More examples of type 2 anomalies are presented in appendix B, 

figures 38 through 41. 

• Type 3 Anomaly Example – Figure 16. This test shows a sudden drop and then increase in 

the MR for the highest confining pressure, while the MR slightly decreases with increasing 

repeated vertical loads for the two lower confining pressures. This anomaly can be 

characteristic of re-zeroing the LVDTs in the middle of the test or an unstable LVDT clamp 

as the specimen deforms under load. More examples of type 3 anomalies are presented in 

appendix B, figures 42 through 45. 

• Type 4 Anomaly Example – Figure 17. The change in MR with increasing repeated vertical 

loads do not follow the same trend or have the same stress sensitivity for the different 

confining pressures. In other words, one confining pressure exhibits stress-hardening 

characteristics, while another exhibits stress-softening characteristics. This characteristic 

can be the result of restrictions in LVDT movement or unstable LVDT clamps. A majority 

of the flagged tests fall into this category (see table 4). More examples of type 4 anomalies 

are presented in appendix B, figures 46 through 49. 

• Type 5 Anomaly Example – Figure 18. The curves of resilient moduli for the different 

confining pressures are out of order. The highest confining pressure results in lower resilient 

modulus. This anomaly can be characteristic of leaks that develop in the membrane during 

the test. Additional examples of type 5 anomalies are presented in appendix B, figures 50 

through 53. 

• Type 6 Anomaly Example – Figure 19. All confining pressures show nearly the same 

resilient modulus at the lower repeated vertical loads. In other words, the resilient modulus 

is independent of confining pressure for the lower repeated vertical loads, but dependent on 

confinement for the higher loads, in direct opposition to a type 2 anomaly. Additional 

examples of type 6 anomalies are presented in appendix B, figures 54 through 57. 

• Type 7 Anomaly Example – Figure 20. There appears to be a data entry error with both the 

resilient modulus and the vertical stress at zero. More examples of type 7 anomalies are 

presented in appendix B, figures 58 through 61. 
 20

All anomalous data (measured responses and computations) should be checked to confirm that 

the data are correct. If correct, the data should be removed, a comment should be added to the 

test result (i.e., ìpossible anomalous dataî), or the material from the specific layer and location 

should be retested. It is suggested that the flagged samples be retested, because none of the test 

sections had the same layer or material flagged from both ends of the same section. 

For tests where more than one anomaly type is present, the type that best describes the data 

anomaly was selected. Anomaly types 3, 4, and 5 are usually a result of laboratory test 

problems. Anomaly types 1, 2, and 6 could be representative of the inability of the selected 

constitutive equation to describe the soilís response characteristics. Twenty-seven flagged MR

tests were de-flagged after step 6, resulting in 185 tests that were identified as having potential 

anomalies. This represents just over 8 percent of the MR tests for which the constitutive equation 

does not accurately describe the material/soil response characteristics. 

Feedback reports were prepared to identify and document those tests with possible anomalies by 

the seven groups and the reports were submitted to FHWA. [Tables 17 through 23 in appendix C 

summarize the anomaly types 1 through 7, respectively, along with the anomalyís initial 

description for each flagged test.] 

Observation: Almost 92 percent of the LTPP MR tests have response characteristics that 

are accurately simulated by the ìuniversalî constitutive equation selected for the 2002 

Design Guide. 
 21

Figure 14. Sample from test section 010102, layer 1, at the leave end exhibits specimen 

distortion or excess softening. 

Figure 15. Sample from test section 171003, layer 1, at the leave end shows significant effect of 

confining pressure on resilient modulus. 

010102 Layer 1 Leave En d 

Material Code = 131 

(Silty C lay)

0

10

20

30

40

50

60

70

80

90

0 20 40 60 80

Repeated Vertical Pressure, kPa

Resilient Modulus, MPa

13.8

27.6

41.3

Confining

Pressure, 

kPa

171003 Layer 1 Leave End 

Material Code = 102 

(Lean Clay)

0

5

10

15

20

25

30

35

40

0 20 40 60 80

Repeated Vertical Pressure, kPa 

Resilient Modulus, MPa 

13.8

27.7

41.5

Confining 

Pressure, 

kPa

 
 22

Figure 16. Sample from test section 014129, layer 1, at the leave end shows sudden drop and 

then increase in resilient modulus. 

Figure 17. Sample from test section 055803, layer 1, at the approach end exhibiting localized 

softening or disturbance of the specimen during the test or LVDT movement. 

014129 Layer 1 Leave End 

Material Code = 215 

(Silty Sand with Gravel)

0

20

40

60

80

100

120

0 20 40 60 80

Repeated Vertical Pressure, kPa

Resilient Modulus, MPa 

13.8

27.6

41.4

Confining 

Pressure, 

kPa

 

055803 Layer 1 Approach End 

Material Code = 217 

(Clayey Sand with Gravel)

0

10

20

30

40

50

60

70

80

0 20 40 60 80

Repeated Vertical Pressure, kPa

Resilient Modulus, MPa

13.8

27.6

41.4

Confining 

Pressure, 

kPa

 
 23

Figure 18. Sample from test section 473108, layer 1, at the leave end shows higher confining 

pressures result in lower resilient modulus. 

Figure 19. Sample from test section 123811, layer 1, at the approach end shows that resilient 

modulus is independent of confining pressure at the lowest vertical stress. 

473108 Layer 1 Leave End 

Material Code = 114

(Sandy Lean Clay)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70

Repeated Vertical Pressure, kPa

Resilient Modulus, MPa

13.8

27.6

41.4

Confining 

Pressure, 

kPa

 

123811 Layer 1 Approach End 

Material Code = 216 

(Silty Sand with Gravel)

0

20

40

60

80

100

120

140

160

0 20 40 60 80

Repeated Vertical Pressure, kPa

Resilient Modulus, MPa

13.8

27.6

41.4

Confining 

Pressure, 

kPa

 
 24

Figure 20. Sample from test section 473104, layer 2, at the approach end shows possible data 

entry error. 

473104 Layer 2 Approach End 

Material Code = 303

(Crushed Stone)

0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300

Repeated Vertical Pressure, kPa

Resilient Modulus, MPa

20.7

34.5

68.9

103.4

137.9

Confining 

Pressure, 

kPa
 25

CHAPTER 3. EFFECT OF SAMPLING TECHNIQUE ON RESILIENT MODULUS 

As mentioned in chapter 1, previous studies have shown that the MR can be affected by sampling 

technique and errors that may occur during the testing program. Chapter 2 focused on 

identifying anomalies in the resilient modulus test data, while this chapter focuses on the effect 

of sampling technique. 

The materials used for the resilient modulus tests were obtained from one of three sampling 

techniques: (1) pavement materials and soils sampled from the augers, (2) pavement materials 

and soils removed from test pits, and (3) soils extracted from Shelby tubes. The difference 

between auger-test pit samples and auger-Shelby tube samples was evaluated using the cleaned 

data set (i.e., excluding the anomalies). 

There are three other factors, however, that can cause variability and possible bias in the resilient 

modulus test data. These factors include: (1) the use of different testing contractors and/or 

operators, (2) test specimen preparation technique, and (3) material variation along a project. 

Each of these potential sources of variation in resilient modulus test data was considered in 

evaluating the effect of sampling technique on resilient modulus, with the exception of testing 

contractor and/or operator. 

DATA GROUPS EVALUATED – SOURCES OF VARIABILITY 

The laboratory test procedure used for coarse-grained soils (base/subbase materials) is different 

from that used for fine-grained soils. To eliminate the testing procedure effect, the base/subbase 

materials were evaluated separately from the subgrade soils. Typical testing errors that can 

occur during repeated load resilient modulus testing were assumed to be random within a 

specific material/soil group. Random errors should have no bias on the effect of sampling 

technique on the resilient modulus test results. 

In coarse-grained materials, the sampling technique used can change the gradation of the 

material. The base/subbase materials were grouped by material codes as defined using LTPP 

terminology. For each base/subbase group, resilient modulus test results for the auger samples 

were compared to the test pit samples for each site. The auger versus test pit samples analysis 

was repeated for the subgrade soils since coarse-grained soils also are present in the subgrade. 

The resilient modulus for both data groups (test pit and auger samples) was measured on test 

specimens recompacted to the moisture content and density of the in-place materials. 

Differences caused by the compaction process or moisture content and density differences 

between the in-place material and test specimens were assumed to be random within a specific 

materials/soil group. 

The subgrade soils were grouped by soil type (i.e., clay, gravel, sand, and silt). The difference 

between auger and Shelby tube samples was evaluated because the undisturbed samples in thinwalled Shelby tubes were retained for nearly 2 years prior to removal and testing for some of the 

test sections. As noted above, moisture content and density differences exist between the 
 26

undisturbed (Shelby tube sample) test specimens and those recompacted in the laboratory 

(augured or test pit samples). However, these differences were assumed to be random within 

each soil group and have no bias on the effect of sampling technique on the resilient modulus test 

results. 

Materials and soils recovered from the test pits were always taken from the leave end of the test 

section, while the augured materials and soils were taken from the approach end. Although this 

represents a systematic difference due to sample location, there is no reason these materials and 

soils would be consistently different between the ends of the test section. The location of the 

GPS test sections was selected at random along a project. The differences between the ends of a 

test section due to sample location were assumed to be random. 

Table 5 lists the data groups evaluated for both the base/subbase materials and subgrade soils. 

The test results that were compared included the MR at specific stress states and the regressed kcoefficients of the constitutive equation (equation 3). The first comparison was completed on the 

MR measured at each stress state. This comparison was then followed by a comparison of the 

regressed k-values from equation 3. Comparisons of the k-values were completed to determine 

if there is an effect due to sampling differences on a specific part of the constitutive equation that 

is not detected by the individual MR. 

Table 5. Data groups for the base/subbase and subgrade soils. 

Number of Tests by Sampling 

Pavement Layer Technique 

Type Material Code/Type* 

Auger Test Pit Shelby 

Tube 

Total 

Number 

of Tests 

All 405 212 NA 617 

302, Uncrushed Gravel 48 33 NA 81 

303, Crushed Stone 63 46 NA 109 

304, Crushed Gravel 32 17 NA 49 

306, Sand 47 19 NA 66 

307, Fine-Grained Soil-Aggregate Mixture 22 10 NA 32 

308, Coarse-Grained Soil-Aggregate Mixture 127 60 NA 187 

Base/Subbase 

309, Fine-Grained Soil 65 27 NA 92 

All 476 319 456 1,251 

Gravel 78 32 12 122 

Sand 223 150 136 509 

Silt 42 34 32 108 

Subgrade Soil 

Clay 133 103 276 512 

Total Number of Tests 881 531 456 1,868 

Those material codes not listed above had too few MR tests to be included in the test of significance for the effect of 

sampling technique. 

NA – Not applicable 

IDENTIFICATION OF OUTLIERS 

The student t-test was used to test any difference in the k-coefficients of samples obtained by 

different techniques. The student t-test assumes that the data have a normal distribution. 

Therefore, each data group listed in table 5 was checked initially for normality using the ShapiroWilk W Test.(5) The data for some of the groups were not distributed normally. These data then 
 27

were checked for outliers using the Mahalanobis outlier distance plot. The identified outliers 

were removed before the student t-test was performed. For those data sets that were not 

distributed normally even after removing the outliers, the Welch analysis of variance (ANOVA) 

test was used to determine if the different data groups were from the same population of data. 

COMPARISON OF RESILIENT MODULUS TEST RESULTS 

Effect of Stress State 

An ANOVA was completed on the MR measured at the different stress states included in the test 

procedure to determine if sampling technique has an effect on the test results. The data were first 

checked for outliers and normality, as noted above. A model of one variable (sampling 

technique) was used in the ANOVA. The one variable has two choices or discrete values related 

to sampling the materials ñ test pits or augers and augers or Shelby tubes. 

Results from the one-way ANOVA are summarized in table 6. Table 6 identifies those materials 

and soils for which the MR ratio was found to be independent or dependent on stress state. The 

MR ratio is defined in table 6. The MR ratio was found to be independent of stress state for most 

base/subbase materials and all soils. For the materials and soils for which the MR ratio is 

independent of stress state, the MR ratios determined at each stress state can be combined in the 

analysis to determine if sampling technique has a significant effect on the test results. Material 

codes 306 (sand) and 308 (coarse-grained soil-aggregate mixture) were the only materials and 

soils for which the MR ratio was dependent on stress state. 

Table 6. Results of ANOVA to determine if the resilient modulus ratio (auger versus test pit test 

specimens) is a function of stress. 

Material/Soil Type ANOVA, Prob.>F

MR Ratio is a Function 

of Stress(1)

All 0.0238 Yes ñ Vertical Loads 

302, Uncrushed Gravel 0.3769 No 

303, Crushed Stone 0.2874 No 

304, Crushed Gravel 0.4809 No 

306, Sand 0.0123 Yes ñ Confinement 

307, Fine-Grained Soil-Aggregate Mixture 0.9112 No 

308, Coarse-Grained Soil-Aggregate Mixture 0.0022 Yes ñ Vertical Loads 

Base/Subbase 

Materials 

309, Fine-Grained Soil 0.1057 No 

All 0.1598 No 

Gravel 0.4932 No 

Sand 0.6691 No 

Silt 0.8497 No 

Subgrade Soils 

Clay 0.3552 No 

(1) MR Ratio = Resilient modulus of test specimens prepared from materials recovered from auger samples divided 

by the resilient modulus of test specimens prepared from materials recovered from test pits; MR(Auger)/MR(Test 

Pit). 
 28

Unbound Aggregate Layers – Test Pit Versus Auger Samples 

The samples for the base/subbase resilient modulus test were either obtained from the augering 

process or from cutting a test pit and removing bulk samples of the material. The augering 

process can degrade the larger diameter aggregates. Therefore, the resilient modulus test results 

for the augured samples were compared to the test results for the test pit samples. 

The data were first checked for outliers and normality, as noted above. Assuming that the 

sample variance is equal to the population variance, a student t-test was then performed with a 

95-percent confidence level using the following null and alternative hypotheses in comparing the 

two data sets: 

Ho: = 1

tp

a

k

k

 or = 1

Rtp

Ra

M

M

HA: ≠ 1

tp

a

k

k

 or ≠ 1

Rtp

Ra

M

M

Table 7 provides a summary of the results from the ANOVA to determine if the sampling 

technique auger versus test pits has an effect on resilient modulus. In summary, sampling 

technique does appear to have a significant effect on the resilient modulus ratio for uncrushed 

gravel, crushed stone, fine-grained soil-aggregate mixture, and fine-grained soil base material 

groups. The crushed gravel base material is considered borderline as to the effect of sampling 

technique on the resilient modulus because the probability value is slightly greater than 0.05 

(refer to table 7). Sand and coarse-grained soil-aggregate base materials are the only data groups 

for which the sampling technique of the base materials appears to have no effect on the MR ratio. 

Table 8 summarizes the probability from the student t-test that the k-coefficients and exponents 

for the auger and test pit samples are equal. With a 95-percent confidence level, a probability 

value less than 0.05 rejects the null hypothesis. The shaded cells show the data groups that are 

indifferent. 

No difference was observed when all the base/subbase materials were tested together. However, 

when the materials are grouped by material codes, k1a and k1tp were different from each other for 

the uncrushed gravel. For the crushed stone material, both k1 and k3 were found to be different 

between augured and test pit samples. Although not all the k-coefficients for the uncrushed 

gravel and the crushed stone were different, it is reasonable to conclude that the sampling 

technique has an effect on the MR test results since k1 is directly proportional to MR. 

Table 9 provides a summary of the results from the different analyses for comparing the 

differences between two populations of data that are defined by different sampling techniques 

using the k-values and resilient modulus. As tabulated, the results are similar for the base and 

subbase materials, except for the soil-aggregate mixtures. 
 29

Table 7. Summary of ANOVA to determine effect of sampling technique (auger versus test pit) 

on resilient modulus. 

Material/Soil Type Stress 

State(1)

Median 

MR Ratio 

Mean MR

Ratio 

Standard 

Deviation 

ANOVA, 

Prob.>[t] 

Null 

Hypothesis, 

MR Ratio = 

1(2)

Low 0.9706 0.9763 0.1875 0.2022 Accept 

All Medium 1.0000 1.0092 0.1264 0.4308 Accept 

High 1.0000 1.0111 0.1183 0.3146 Accept 

302, Uncrushed 

Gravel 

All Values 1.0253 1.0438 0.1712 <0.0001 REJECT 

303, Crushed 

Stone 

All Values 0.9527 0.9391 0.1621 <0.0001 REJECT 

304, Crushed 

Gravel 

All Values 1.0444 1.0323 0.1841 0.0670 Accept 

Low 0.9706 1.0540 0.1882 0.4143 Accept 

306, Sand Medium 1.0000 0.9971 0.0539 0.8759 Accept 

High 0.9563 0.9735 0.0664 0.2652 Accept 

307, FineGrained SoilAggregate 

Mixture 

All Values 1.0041 1.0494 0.1660 0.0145 REJECT 

Low 0.9592 0.9321 0.2097 0.0720 Accept 

Medium 1.0000 1.0124 0.1307 0.5631 Accept 

308, CoarseGrained SoilAggregate 

Mixture 

High 1.0327 1.0253 0.1666 0.3303 Accept 

Base/ 

Subbase 

Materials 

309, FineGrained Soil All Values 1.0092 1.0331 0.1264 <0.0001 REJECT 

All All Values 1.0476 1.0600 0.2810 <0.0001 REJECT 

Gravel All Values 1.2226 1.2437 0.2690 <0.0001 REJECT 

Sand All Values 1.0099 0.9990 0.2016 0.8980 Accept 

Silt All Values 1.1061 1.0886 0.3112 0.0010 REJECT 

Subgrade 

Soils 

Clay All Values 1.2803 1.1606 0.3283 <0.0001 REJECT 

(1) Low: Confinement = 20.7 kPa, Cyclic Load = 18.6 kPa; Medium: Confinement = 68.9 kPa, Cyclic Load = 124.1 

kPa; High: Confinement = 137.9 kPa, Cyclic Load = 248.2 kPa. 

(2) Null Hypothesis: MR(Auger)/MR(Test Pit) = 1. 
 30

Table 8. Summary of the student t-test on the difference between augered and test pit 

samples for the base/subbase materials and subgrade soils. 

Student t-Test Probability (Prob > |t|) 

Material/Soil Type k1 k2 k3

All 0.2378 0.5846 0.5070 

302, Uncrushed Gravel 0.0260 0.0850 0.3919 

303, Crushed Stone 0.0350 0.1868 0.0025 

304, Crushed Gravel 0.5228 0.7903 0.5193 

306, Sand 0.3149 0.1512 0.7767* 

307, Fine-Grained Soil-Aggregate Mixture 0.4134 0.3213 0.8316 

308, Coarse-Grained Soil-Aggregate Mixture 0.3731 0.4863 0.0192* 

Base/Subbase 

Materials 

309, Fine-Grained Soil 0.3931 0.6256 0.4354 

All 0.0328 0.0013 0.6553 

Gravel 0.0710 0.9120 0.0169 

Sand 0.8287 0.0050 0.3052 

Silt 0.1059 0.1569 0.2512 

Subgrade Soils 

Clay 0.1153 0.1594 0.9407 

*Student t-test not valid because sample population not normally distributed. 

Table 9. Comparison of results using k-values and resilient modulus values to determine effect 

of sampling technique (auger versus test pits) on resilient modulus test data. 

k-Values; Hypothesis, ka/ktp = 1 

Material/Soil Type 

k1 k2 k3

MR Values; 

Hypothesis, 

MRa/MRtp = 1 

All Accept Accept Accept Accept 

302 REJECT Accept Accept REJECT 

303 REJECT Accept REJECT REJECT 

304 Accept Accept Accept Accept 

306 Accept Accept Accept Accept 

307 Accept Accept Accept REJECT 

308 Accept Accept REJECT Accept 

Base/Subbase 

Materials 

309 Accept Accept Accept REJECT 

All REJECT REJECT Accept REJECT 

Gravel Accept Accept REJECT REJECT 

Sand Accept REJECT Accept Accept 

Silt Accept Accept Accept REJECT 

Subgrade Soil 

Clay Accept Accept Accept REJECT 

Observation: Sampling technique of base materials (auger versus test pit samples) has 

an effect on the MR test results for the uncrushed gravels and crushed stone materials. 
 31

Soils – Test Pit Versus Auger Samples 

Table 7 summarizes the difference between the resilient modulus measured on test specimens 

prepared from soils recovered from test pit samples and those from augured samples. As 

tabulated, the resilient modulus values are different for all subgrade soil groups with the 

exception of sand. This observation is consistent with previous experience. 

The difference between the k-coefficients regressed from MR tests performed on test specimens 

compacted from auger and test pit samples was evaluated for the subgrade soils. Table 8 

summarizes the findings of the analysis and comparisons. The shaded cells show the data groups 

that are the same, i.e., student t-test probability greater than 0.05. 

Differences were observed for k1 and k2 of the overall subgrade data group, k3 of the gravel 

group, and k2 of the sand group. Note that some differences in the exponents were found for the 

coarse-grained soils, but no differences were found for the fine-grained soils. This observation is 

consistent with the base/subbase materials, with the exception of the crushed gravels (material 

code 304) and sands (material code 306). 

Based on the results summarized in table 9, the sampling effect on the MR ratio is dependent on 

the type of analysis. Since only one k-coefficient was found to be different for the gravel and 

sand soil groups, the effect of sampling technique (auger versus test pit) is believed to be small. 

However, comparison of the MR ratio suggests that there is a difference caused by sampling 

technique for all soils, but sand. 

Soils – Shelby Tubes (Undisturbed) Versus Recompacted (Disturbed) Samples

The undisturbed samples recovered from thin-walled Shelby tubes were retained in the tubes in 

some cases for nearly 2 years prior to removal and testing. The effect of storage time in the 

Shelby tubes on resilient modulus is unknown. However, the MR of some high-plasticity clays is 

known to be sensitive to sample preparation (disturbed versus undisturbed test specimens). 

Therefore, the MR test results in the LTPP database were evaluated to determine if there are 

significant differences in the regressed k-coefficients between the Shelby tubes (undisturbed) and 

recompacted (disturbed) samples. The effect of time retained in the Shelby tubes was not studied 

because there were too few MR tests within each of the subgroups at different times. 

For each of the data groups listed in table 5, the data were first tested for outliers, normality, and 

equal sample variances. Student t-tests were then performed with a 95-percent confidence level 

and the following null and alternative hypotheses: 

Ho: a ST k = k or MRa = MRST

HA: a ST k ≠ k or MRa ≠ MRST
 32

Table 10 summarizes the effects of sampling technique on the measured resilient modulus 

between undisturbed and disturbed subgrade soil samples. As shown, the resilient modulus is 

affected by sampling technique for all soil groups, with the exception of sand. This finding is 

consistent with the previous experience of the authors. 

Table 10. Summary of ANOVA to determine effect of sampling technique (Shelby tube versus 

auger) on resilient modulus. 

Soil Variances 

Type Prob.>F Equal 

Variances? 

Welch ANOVA 

Testing of 

Means With 

Unequal 

Variances, 

Prob.>F

ANOVA Testing 

of Means With 

Equal Variances, 

Prob.>F or 

Prob.>[t] 

Absolute 

Difference 

― LSD 

Null Hypothesis; 

MR(Shelby Tube), 

Undisturbed = 

MR(Auger), Disturbed 

All <0.0001 No <0.0001 --- 6.034 REJECT 

Gravel 0.0045 No <0.0001 --- 11.653 REJECT 

Sand <0.0001 No 0.2725 --- -0.514 Accept 

Silt 0.5582 Yes --- <0.0001 9.964 REJECT 

Clay 0.9484 Yes --- <0.0001 10.582 REJECT 

Table 11 summarizes the probability from the student t-test that the k-coefficient and exponents 

for the undisturbed and disturbed samples are equal. With a 95-percent confidence level, a 

probability value less than 0.05 rejects the null hypothesis. The shaded cells show the data 

groups that are indifferent. Five of the data groups failed the equal variance test. For these five 

groups, the Welch ANOVA test was used instead, as noted above. 

Table 11. Summary of the student t-test on the difference between disturbed and undisturbed 

samples for the subgrade soils. 

Student t-Test Probability (Prob > |t|) Material Type k1 k2 k3

All 0.7475 <0.0001* <0.0001* 

Clay 0.0314 0.8948* 0.0002 

Gravel 0.5080 0.2379 0.0001 

Sand 0.8865 0.0122 0.7961* 

Silt 0.9978* 0.1687 <0.0001 

* Welch ANOVA testing equal means, allowing unequal variance. 

The shaded cells show the data groups that are the same within a 95-percent confidence level 

(student t-test probability greater than 0.05). As shown, at least one of the k-coefficients for all 

groups tested was different. The coefficients from the undisturbed (Shelby tube) and disturbed 

(auger and test pit) data sets were found to be different for k1 of the clay soils, k2 of the overall 

and sand soil groups, and k3 of all soil groups, except for sand. Separating the subgrade into soil 

types reduced the sampling effect except for the clay soils. It is recommended that the MR results 

for the clay soils be considered different between the disturbed and undisturbed test specimens. 

Since only one k-coefficient was different for the other soil types, any sampling effect is 

considered small for these soil types, especially since k3 was zero for several MR tests. 
 33

Table 12 summarizes the results from the different analyses for comparing the differences 

between two populations of resilient modulus data that are defined by different sampling 

techniques using the k-values and resilient modulus. As shown, the results are similar for the 

subgrade soils. 

Table 12. Comparison of results using k-values and resilient modulus values to determine the 

effect of sampling technique of undisturbed (Shelby tubes) and disturbed (auger) test specimens 

on resilient modulus test data. 

Soil Type k-Value; Hypothesis, ka = kst

k1 k2 k3

MR Values; Hypothesis, 

MRa = MRst

All Accept REJECT REJECT REJECT 

Gravel Accept Accept REJECT REJECT 

Sand Accept REJECT Accept Accept 

Silt Accept Accept REJECT REJECT 

Clay REJECT Accept REJECT REJECT 

SUMMARY 

The data groups listed in table 5 were analyzed for the effects of sampling techniques. All 

materials were tested for differences between auger and test pit samples. The subgrade soils 

were also tested for differences between disturbed (auger and test pits) and undisturbed (Shelby 

tube) samples. 

Tables 9 and 12 summarize the results from the different analyses for comparing the differences 

between two populations of resilient modulus data that are defined by different sampling 

techniques using the k-values and resilient modulus values. Table 9 shows that the auger and 

test pit samples are different for some of the material groups. The difference was considered 

significant for the uncrushed gravel, crushed stone, and the overall subgrade data group. 

However, the difference was insignificant when the soils were divided into the four major soil 

types (i.e., clay, gravel, sand, and silt). Table 12 shows that the disturbed and undisturbed test 

specimens are different for the overall subgrade and clay data groups. The difference is only 

considered significant for the clay soils when the subgrade is divided into the four soil types. 

Observation: Sampling technique of subgrade soils (undisturbed versus disturbed test 

specimens) has an effect on the MR test results for the clay soils. 

Observation: Sampling technique of base and subgrade soils has no effect on the MR test 

results for sand base materials and soils. 
 34

It is interesting to note that the null hypothesis from the ANOVA was rejected when the resilient 

modulus ratio was found to be independent of the stress states and was accepted for those 

materials when the resilient modulus ratio was dependent on stress state in all cases, with the 

exception of base material code 304 (crushed gravel) and sand subgrades (refer to tables 6 and 

7). Another interesting observation is that the coarse-grained soils were found to have equal 

variances between the resilient modulus values measured on undisturbed (Shelby tubes) test 

specimens and disturbed (auger) test specimens. The significance of these observations is 

unknown. 

Table 13 provides an overall summary comparison of the different statistical methodologies 

used. Most of the results from these comparisons are consistent with previous experience. The 

following summarizes the recommendations for further data analyses for each material and soil 

type: 

• All sand base materials can be combined into one group, independent of sampling technique. 

In addition, all sand subgrades can also be combined into a single group for analysis 

purposes. 

• The resilient modulus of the crushed stone and uncrushed gravel base materials are 

dependent on the type of sampling technique used to recover samples for testing. These data 

groups should be kept separate for further data analyses. 

• The resilient modulus of the clay soils is dependent on whether the sample is undisturbed 

(recovered by Shelby tubes) or disturbed (sampled from augers or recovered from test pits 

and recompacted). These data groups should be kept separate for further data analyses. 

• The effect of sampling technique on the remaining data groups is dependent on the type of 

analysis used. Thus, it is suggested that the different data groups be combined for simplicity, 

but caution be taken in analyzing and using these data. 

These observations are considered important regarding the future use of the repeated load 

resilient modulus test data in the LTPP database to accomplish the objectives stated in the 

introduction chapter to this report and some of the overall LTPP objectives. For example, any 

differences caused by sampling technique must be clearly defined to determine the relationship 

between laboratory-measured resilient modulus and backcalculated elastic layer modulus. 
 35

Table 13. Summary comparison of the resilient modulus test results for different sampling 

techniques. 

Sampling Technique 

Consistently Different 

Results or Different 

Populations of Data 

Borderline ñ 

Dependent on Type of 

Data Used 

Consistently Indifferent 

Results or Populations of 

Data are the Same 

304, Crushed gravel 

302, Uncrushed gravel 306, Sand 

307, Fine-grained soilaggregate mixture 

Base and 

Subbase 

303, Crushed stone 309, Fine-grained soil 

308, Coarse-grained soilaggregate mixture 

Gravel 

Silt 

Auger Versus Test 

Pit 

Subgrade 

Soils 

None 

Clay 

Sand 

Undisturbed (Shelby Gravel 

Tubes) Versus 

Disturbed (Auger) 

Subgrade 

Soil Clay Silt Sand 

 37

CHAPTER 4. EFFECT OF PHYSICAL PROPERTIES ON RESILIENT MODULUS

As stated in chapter 1, the MR is the material property required for all unbound materials and 

soils for the 1986 and 1993 AASHTO Design Guide.(1) In 1995, Darter, et al., found that about 

75 percent of the State Highway Agencies (SHAs) in the United States use either the 1986 or 

1993 versions of the AASHTO Design Guide.(6) However, most of these agencies do not 

routinely measure the MR in the laboratory. The design MR is estimated from experience or from 

other material or soil properties (for example, CBR, R-value, or physical properties). 

A potential benefit of estimating the MR from physical properties is that seasonal variations in 

resilient modulus can be estimated from seasonal changes in the materialsí physical properties. 

Seasonal variations are critical for determining the design MR for a particular project. The 

concept being used in development of the 2002 Design Guide under NCHRP Project 1-37A is to 

apply the Enhanced Integrated Climatic Model (EICM) to predict changes in the physical 

properties of unbound pavement materials and soils and to estimate the effect those changes have 

on the resilient modulus. 

Some SHAs have developed relationships between the physical and/or strength properties of the 

soil and MR. Determining the MR from physical properties of unbound materials can capture the 

effect of the seasonal variations of the MR as a result of seasonal changes in the materialís 

physical properties, but it does not capture the effect of stress sensitivity. To capture the effects 

of stress sensitivity, the coefficients of the selected constitutive equation have been regressed for 

relationships to the soils physical properties. Von Quintus and Killingsworth and Santha, among 

others, have developed these types of relationships for use in design to capture the effect of stress 

sensitivity in determining the design MR.

(3,7) 

Previous studies have developed relationships between the soil properties and the regressed 

k-coefficients and exponents of the constitutive model. Those relationships that have good 

statistics were generally confined to specific soil types.(7) Other studies that have used a wide 

range of soil types and conditions have generally resulted in poor correlations.(3) The focus of 

this chapter is to use the cleaned database and determine those physical properties that have an 

effect on the MR test results and to determine the accuracy of developing relationships between 

physical properties and MR with the LTPP database. 

PHYSICAL PROPERTIES USED IN STUDY 

The anomalies identified in chapter 2 were removed from the data set based on the April and 

October 2000 data releases that were used in a nonlinear optimization regression analysis 

relating the physical properties of the test specimen to the MR from the constitutive equation. 

The classification data (including gradation, Atterberg limits, density, moisture, optimum 

density, moisture contents, and other physical properties) were extracted from the LTPP database 

of unbound materials. For most LTPP test sections, the strength (e.g., CBR and R-value) of a 

material or soil is unavailable in the database. Table 14 summarizes all the variables used in the 

regression analysis and the IMS tables from which the data were extracted. The range, mean, 
 38

and median values for each of these variables are included in appendix D for the base and 

subbase materials and subgrade soils. 

Table 14. Summary of the MR physical property regression variables. 

Variable Description Table(s) From the IMS 

k1 (MPa) Regression constant of MR constitutive equation -- 

k2 Regression constant of MR constitutive equation -- 

k3 Regression constant of MR constitutive equation -- 

P3/8", % Percentage passing 3/8” sieve TST_SS01_UG01_UG02 

PNo. 4, % Percentage passing No. 4 sieve TST_SS01_UG01_UG02 

PNo. 40, % Percentage passing No. 40 sieve TST_SS01_UG01_UG02 

PNo. 200, % Percentage passing No. 200 sieve TST_SS01_UG01_UG02 

% Silt Percentage of silt TST_SS02_UG03 

% Clay Percentage of clay TST_SS02_UG03 

LL, % Liquid limit of soil TST_UG04_SS03 

PI, % Plasticity index of soil TST_UG04_SS03 

wopt, % Optimum water content TST_UG05_SS05 

Υd, opt (kg/m3) Maximum dry unit weight of soil TST_UG05_SS05 

ws, % Water content of the test specimen TST_UG07_SS07_A, 

TST_UG07_SS07_B 

Υs (kg/m3) Dry density of the test specimen TST_UG07_SS07_A, 

TST_UG07_SS07_B 

1 in = 25.4 mm 

STATISTICAL PROCEDURE 

A nonlinear optimization regression analysis was performed using SASÆ statistical analysis 

system software relating the physical properties (listed in table 14) of the test specimen to the MR

used in the constitutive equation on the ìcleanî data set. A stepwise regression analysis was 

initially performed relating the physical properties to the resilient modulus to identify the 

important variables. The procedure combined the forward and backward stepwise regression 

methods. 

A variable (physical property) with a 0.25 probability was selected to enter the regression and 

was removed with a 0.1 probability to stay. The regression started with no variables in the 

model. The F statistics were calculated for each independent variable. The variable with the 

most significant level greater than 0.25 was entered into the model first. All variables were 

entered individually with this entry criterion. The variables already in the model did not 

necessarily remain, because after a variable is added, the stepwise method considers all the 

variables already included and deletes any variable that does not yield an F statistic at a level of 

significance greater than 0.1. The process was completed when no more variables outside the 

model had a level of significance greater than 0.25 to enter and 0.1 to delete. 

CORRELATION STUDY FOR MODEL DEVELOPMENT 

As discussed in chapter 3, the base/subbase materials should be analyzed separately from the 

subgrade materials. The base/subbase materials were grouped by material code from LTPP 

terminology for pavement materials and soils. The crushed stone and uncrushed gravel materials 
 39

were separated into auger and test pit samples to see the effect of sampling technique as 

discussed in chapter 3. The subgrade material was grouped by material type (clay, gravel, silt, 

and sand) and the clay soils were further grouped into: (1) disturbed samples and (2) undisturbed 

samples. 

The test specimens from the Shelby tubes were taken at various depths through the sampling 

tubes, while the samples from which the physical properties were measured were confined to the 

top 0.3 m of the subgrade. As a result, the resilient modulus tests and some of the physical 

property tests could have been performed on entirely different soils. Von Quintus and 

Killingsworth identified this fact as a problem in completing similar correlations in 1996.(3) 

Thus, the undisturbed test specimens (Shelby tube samples) were not included in the correlations 

between resilient modulus and physical properties. 

Appendix E summarizes the properties that were found to be important and the resulting 

statistical measures of the correlation for each of the data groups analyzed. Table 15 presents an 

overall summary of those physical properties that were found to be important for each material 

and soil. Observations from these correlation studies are noted below: 

• The maximum or optimum dry unit weight was found to be important for all base and 

subbase material types, with the exception of the fine-grained soil (LTPP material code 

309); while the optimum moisture content and percent passing the 3/8-in (9.5 mm) sieve 

were found to be important for most coarse-grained base materials. 

• The plasticity index and the percent passing the No. 40 sieve were the only properties 

found to be important for the fine-grained soil base material group (LTPP material code 

309). 

• The water content and percent clay for the test specimen are important for all soil groups. 

• The liquid limit is important for all soils except the silt group, while the percent silt is 

important for all soils except the gravel group. 

 
Table 15. Summary of the physical properties that were found to be important for predicting resilient modulus 

soil type. 

Independent Base/Subbase Material Variable 303, 

Crushed Stone 

304, Crushed Gravel 

302, Uncrushed Gravel 

306, Sand 308, 

CoarseGrained SoilAggr. Mixture 

307, FineGrained SoilAggr. Mixture 

309, FineGrained Soil 

Gravel Sand 

Percent passing 3/8-in sieve, P3/8 

√

√

√

√

√

√

√

Percent passing No. 4 sieve, P4 

√

√

√

Percent passing No. 40 sieve, P40 

√

√

√

√

√

Percent passing No. 200 sieve, P200 

√

√

√

√

Percent Clay, %Clay 

√

√

Percent Silt, %Silt 

√

Liquid Limit, LL 

√

√

√

√

√

√

Plasticity Index, PI 

√

√

√

√

√

Water content of test specimen, 

Ws

√

√

√

√

√

Dry density of test specimen, 

γs 

√

√

√

√

√

Optimum water content, 

Wopt

√

√

√

√

√

√

Maximum dry unit weight, 

γopt

√

√

√

√

√

√

√

Number of 

MR

Tests 

109 49 81 66 187 32 92 122 50

1 in = 25.4 mm 

40
 41

Effect of Material/Soil Type 

Dividing the base/subbase materials by material code improves the regression statistics from the 

overall base/subbase model (see appendix E). When the crushed stone material was separated 

into auger and test pit samples, as recommended in chapter 3, some improvement was observed. 

However, this improvement is inconclusive and debatable because the greater correlation may be 

the result of the smaller sample size. The uncrushed gravel was not separated into auger and test 

pit samples due to a limited number of data points (refer to table 5). 

Sorting the subgrade by soil type also improved the regression statistics as compared to the 

overall soil model (see appendix E). The subgrade materials were not classified in accordance 

with AASHTO, because the number of data points was limited for some of the classifications. 

Sampling technique (auger versus test pit samples) did not improve the regression statistics. The 

remaining part of this chapter presents the regression equations that resulted from the nonlinear 

optimization for each base material type and soil group. The residuals (bias) for each of the 

prediction models are provided in appendix E. The symbols used in the following equations 

were defined in chapter 2 (equation 3) and in table 15. 

Unbound Aggregate Base/Subbase Materials 

Crushed Stone Materials ñ LTPP Material Code 303

[ ] ( )

opt opt

opt

opt opt

LL W

a

oct

P

P LL W x

a

R opt opt a

p

p

M P LL W p

γ

γ γ

τ

θ

γ

1.1720 0.0082 0.0014 0.0005

2.2159 0.0016 0.0008 0.038 0.0006 2.4 10

3 / 8

1

*

0.7632 0.0084 0.0088 0.0371 0.0001 *

40

2 7 3 / 8

− − − +































 − + − − +





 





+





 





= + + − −

−

 (6) 

Number of points = 853 

Mean squared error = 1699.6 

Se = 41.23 

Sy = 87.42 

Se/Sy = 0.4716 

Figure 21 shows a comparison of the measured and predicted resilient modulus using equation 6 

at the appropriate stress states used to test crushed stone base materials. 
 42

Crushed Gravel ñ LTPP Material Code 304

( )

s

opt

s opt

a

oct P

LL PI W x

a

a

opt

s

opt s

R

p p

p

P

x

P LL PI W W

M

γ γ γ

θ τ

γ

γ

4.9555 0.0057 0.0075 0.0470 0.0022 2.8 10 3.514 0.0016

40

2

6

3 / 8

1

0.0013 2.6 10

0.8282 0.0065 0.0114 0.0004 0.0187 0.0036

40

2 6 − + 





























 − − − − +

−





 



  +



 







































 −

− − + + − + +

=

−

 

 (7) 

Number of points = 404 

Mean squared error = 854.4 

Se = 29.23 

Sy = 66.74 

Se/Sy = 0.4380 

Figure 22 shows a comparison of the measured and predicted resilient modulus using equation 7 

at the appropriate stress states used to test crushed gravel base materials. 

Uncrushed Gravel ñ LTPP Material Code 302

( )































 − + + −































 +















 − − +





 





+





 



































 = − + −

opt

s opt opt

opt

s

opt

s s

W

W

W

a

oct

W

W

P

a

a

opt

s

R s

p

p

p W

W

M

0.5979 0.0349 0.0004 0.5166

0.4960 0.0074 0.0007 1.6972 0.1199

1

1.8961 0.0014 0.1184 *

200

γ

γ

γ γ

τ

θ

γ

 (8) 

Number of points = 461 

Mean squared error = 475.9 

Se = 21.81 

Sy = 63.05 

Se/Sy = 0.3460 

Figure 23 shows a comparison of the measured and predicted resilient modulus using equation 8 

at the appropriate stress states used to test crushed gravel base materials. 
 43

 

Figure 21. Graphical comparison of the predicted and measured resilient modulus for the 

crushed stone base materials. 

Figure 22. Graphical comparison of the predicted and measured resilient modulus for the 

crushed gravel base materials. 

Base/Subbase Material 303,

Crushed Stone

0

100

200

300

400

500

600

0 100 200 300 400 500 600

Mr (observed), MPa

M =f(physical properties) r

Base/Subbase Material 304,

Crushed Gravel

0

100

200

300

400

500

600

0 100 200 300 400 500 600

Mr (observed), MPa

M =f(physical properties) r
 44

Sand ñ LTPP Material Code 306

( ) P LL PI

a

oct P

P LL PI x

a

a

opt

R

p p

p PM P LL PI x

opt 1.1148 0.0053 0.0095 0.0325 7.2 10 0.4508 0.0029 0.0185 0.0798

40

2

7

3 / 8

3 / 8

40

2

7 3/ 8

1

0.2786 0.0097 0.0219 0.0737 1.8 10 *

− + − + 



































− − + +

−





 



  +



 



































 = − + + − +

−

θ τ

γ

λ (9) 

Number of points = 519 

Mean squared error = 512.7 

 Se = 22.64 

 Sy = 51.61 

 Se/Sy = 0.4388 

Figure 24 shows a comparison of the measured and predicted resilient modulus using equation 9 

at the appropriate stress states used to test sand base materials. 

Coarse-Grained Soil-Aggregate Mixture ñ LTPP Material Code 308

( )





































− − +





































−















 − − + −

−

−

−

−





 





+





 











































 −















+













 − +

− + − + + +

=

40

2

7 200

40

2

7 200

0.1906 0.0026 8.1 10

0.7833 0.0060 0.0081 0.0001 0.1483 2.7 10

40

2

7

6

3 / 8 4 200

1

*

0.0426 1.6456 0.3932 8.2 10

0.5856 0.0130 0.0174 0.0027 0.0149 1.6 10

P

P x

a

oct

P x W

W

P PI

a

opt a

opt

s

opt

s

s

opt

R

opt

opt

opt

s

opt

p

p

p

P

x

W

W W

P P P PI x

M

γ

γ

γ

τ

θ

γ

γ

γ

γ

 (10) 

Number of points = 2,323 

Mean squared error = 1883.9 

 Se = 43.40 

 Sy = 80.19 

 Se/Sy = 0.5413 

Figure 25 shows a comparison of the measured and predicted resilient modulus using equation 

10 at the appropriate stress states used to test coarse-grained soil-aggregate base materials. 
 45

Figure 23. Graphical comparison of the predicted and measured resilient modulus for the 

uncrushed gravel base materials. 

Figure 24. Graphical comparison of the predicted and measured resilient modulus for the sand 

base materials. 

Base/Subbase Material 302,

Uncrushed Gravel

0

50

100

150

200

250

300

350

400

450

0 100 200 300 400

Mr (observed), MPa

M =f(physical properties) r

Base/Subbase Material 306,

Sand

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350

Mr (observed), MPa

M =f(physical properties) r
 46

Figure 25. Graphical comparison of the predicted and measured resilient modulus for the coarsegrained soil-aggregate base materials. 

Figure 26. Graphical comparison of the predicted and measured resilient modulus for the finegrained soil-aggregate base materials. 

 Base/Sub base Material 308, 

 Coarse-Grained Soil-Agg. 

0

100

200

300

400

500

600

0 100 200 300 400 500 600

Mr (observed), MPa

M =f(physical properties) r

Mixture 

 Base/Subbase Material 307,

Fine-Grained Soil-Agg. 

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350

Mr (observed), MPa

M =f(physical properties) r

Mixture 
 47

Fine-Grained Soil-Aggregate Mixture ñ LTPP Material Code 307































 + + − 





























 − − +





 



  +



 



































 = − + + + − +

opt

s

opt

s P LL

a

oct

P P

a

a

opt

s

R opt

p p

M P P LL W p

γ

γ

γ

λ

θ τ

γ

γ

0.4951 0.0141 0.0061 1.3941 0.9303 0.0293 0.0036 3.8903

4 200

4 200 3 / 8

1

0.7668 0.0051 0.0128 0.0030 0.0510 1.1729 *

 (11) 

Number of points = 390 

Mean squared error = 588.2 

 Se = 24.25 

 Sy = 49.37 

 Se/Sy = 0.4912 

Figure 26 shows a comparison of the measured and predicted resilient modulus using equation 

11 at the appropriate stress states used to test fine-grained soil-aggregate base materials. 

Fine-Grained Soil ñ LTPP Material Code 309

[ ]

( ) ( ) PI

a

oct

P PI

a

R a p p

M P PI p

0.6668 0.0007 0.0139 0.1667 0.0207

40 0.8409 0.0004 0.0161 1

− 40 − − −





 



  +



 



 = + +

θ τ

 (12) 

Number of points = 1,079 

Mean squared error = 1,167 

 Se = 34.16 

 Sy = 62.80 

 Se/Sy = 0.5440 

Figure 27 shows a comparison of the measured and predicted resilient modulus using equation 

12 at the appropriate stress states used to test fine-grained soil base materials. 
 48

Figure 27. Graphical comparison of the predicted and measured resilient modulus for the finegrained soil base materials. 

Subgrade Soils 

Coarse-Grained Gravel Soils

[ ] ( )

( ) ( )

( ) ( ) s

s

P Clay LL PI W

a

oct

P Clay LL PI W

a

R s a

p

p

M P Clay LL W p

1.5167 0.0302 0.0435 % 0.0626 0.0377 0.2353

0.3311 0.0010 0.0019 % 0.0050 0.0072 0.0093

3 / 8

3 / 8

3 / 8

1

*

1.3429 0.0051 0.0124 % 0.0053 0.0231 *

− + + + −

+ − − − +





 





+





 





= − + + −

τ

θ (13) 

Number of points = 957 

Mean squared error = 301.3 

 Se = 17.36 

 Sy = 26.81 

 Se/Sy = 0.6474 

 

Base/Subbase Material 309, 

Fine-Grained Soil

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350 400

Mr (observed), MPa

M =f(physical properties) r
 49

Figure 28 shows a comparison of the measured and predicted resilient modulus using equation 

13 at the appropriate stress states used to test coarse-grained gravel soils. 

Coarse-Grained Sand Soils

[ ( ) ]

() ( ) ( )

() ( ) 





























 −















 − + − − + + − − − +































 +















 + − − − − + − −





 





+





 





= − + + + − −

− −

opt

s

opt

s opt s

opt

s

opt

s opt s

W

W P P P Silt Clay LL W

a

oct

W

W P x P Silt Clay LL W x

a

R opt s a

p

p

M P P Clay LL W p

3.5677 0.1142 0.0839 0.1249 0.1030 % 0.1191 % 0.0069 0.0103 0.0017 4.3177 1.1095

0.5670 0.0045 2.98 10 0.0043 % 0.0102 % 0.0041 0.0014 3.41 10 0.4582 0.1779

3 / 8 4

3 / 8 4 200

5 4 5 3 / 8

1

*

3.2868 0.0412 0.0267 0.0137 % 0.0083 0.0379 0.0004 *

λ

γ γ

γ

γ γ

τ

θ

γ

 (14) 

Number of points = 3,117 

Mean squared error = 357.7 

 Se = 18.91 

 Sy = 24.79 

 Se/Sy = 0.7630 

Figure 29 shows a comparison of the measured and predicted resilient modulus using equation 

14 at the appropriate stress states used to test coarse-grained sand soils. 

Fine-Grained Silt Soils

[ ] ( )

( )

( ) ( ) PI Ws Silt

a

oct

PI

a

R s a

p

p

M Clay PI W p

0.2218 0.0047 % 0.0849 0.1399

0.5097 0.0286

1

1.0480 0.0177 % 0.0279 0.370 *

− + + −

−





 





+





 



 = + + −

τ

θ

 (15) 

Number of points = 464 

Mean squared error = 193.0 

 Se = 13.89 

 Sy = 24.71 

 Se/Sy = 0.5622 

Figure 30 shows a comparison of the measured and predicted resilient modulus using equation 

15 at the appropriate stress states used to test fine-grained silt soils. 
 50

Figure 28. Graphical comparison of the predicted and measured resilient modulus for the coarsegrained gravel soils. 

Figure 29. Graphical comparison of the predicted and measured resilient modulus for the coarsegrained sand soils. 

 Subgrade, Gravel

0

50

100

150

200

250

0 50 100 150 200 250

Mr (observed), MPa

M =f(physical properties), MPa r

 

Subgrade, Sand

0

50

100

150

200

250

0 50 100 150 200 250

Mr (observed), MPa

M =f(physical properties), MPa r
 51

Fine-Grained Clay Soils

[ ] ( )

( )

( ) 





























 − + − + + − − + −

− + − − −





 





+





 



 = + −

opt

s

opt opt s

opt

W

W

P P P Silt LL W

a

oct

P P P LL W

a

R s a

p

p

M Clay W p

1.4258 0.0288 0.0303 0.0521 0.0251 % 0.0535 0.0672 0.0026 0.0025 0.6055

0.5193 0.0073 0.0095 0.0027 0.0030 0.0049

4 40 200

4 40 200

1

1.3577 0.0106 % 0.0437 *

γ γ

τ

θ

 (16) 

Number of points = 1,484 

Mean squared error = 557.9 

 Se = 23.62 

 Sy = 29.22 

 Se/Sy = 0.8082 

Figure 31 shows a comparison of the measured and predicted resilient modulus using equation 

16 at the appropriate stress states used to test fine-grained clay soils. 

SUMMARY 

The results from the nonlinear optimization regression study were compared to those from earlier 

studies. The statistical parameters for some of the unbound aggregate base and subbase layers 

improved, indicating that the defined anomalies and use of nonlinear regression techniques were 

important. In summary, the physical properties show fair to good correlations between the 

physical properties and MR. The following are some of the more important findings from these 

correlation studies: 

• Several key factors affect the correlation between the material physical properties of the 

pavement materials and soils and MR. For example, recompacting the materials may have 

changed some of the physical features of the test specimens from what was measured for the 

bulk samples. 

• The statistics for all models were generally fair to good for both the unbound aggregate 

materials and the subgrade soils. Breaking the data groups into subgroups by sampling 

technique did improve on the regression statistics. Most of the se/sy terms are less than 0.7. 

The base materials generally have better statistical parameters than the soils. 

• The primary result from these correlation studies is that the resilient modulus from 

constitutive equation 3 can be reasonably predicted from the physical properties that are 

included in the LTPP database. 

• The physical properties of percent clay and test specimen moisture content or density are 

important for all soil groups. 

• Percent silt was an important property for all soil groups, except for the gravelly soils. 
 52

Figure 30. Graphical comparison of the predicted and measured resilient modulus for the finegrained silt soils. 

Figure 31. Graphical comparison of the predicted and measured resilient modulus for the finegrained clay soils. 

Subgrade, Silt

0

50

100

150

200

250

0 50 100 150 200 250

Mr (observed), MPa

M =f(physical properties), MPa r

Subgrade, Clay

0

50

100

150

200

250

0 50 100 150 200 250

Mr (observed), MPa

M =f(physical properties), r MPa
 53

Figure 32 shows a comparison of the calculated MR between the test pit and augered samples 

using the regression equations to estimate the k-coefficients. A bias is present in the calculated 

MR values between the test pit and augered samples and supports the previous observation that 

there is an effect of sampling technique for the crushed stone base materials included in the 

LTPP database. 

Figure 33 shows the comparison of the predicted MR using the regression models developed for 

the different sampling techniques for sand. The error in the calculated MR using the physical 

properties overshadows any difference caused by the different sampling techniques used. 

The physical properties correlated to the resilient modulus varied between the different 

base/subbase material groups. No one physical property was included for all material types. 

However, the liquid limit, plasticity index, and the amount of material passing the smaller sieve 

sizes are important for the lower strength unbound base/subbase materials, while a measure of 

the moisture content and density are important for the higher strength materials. The amount of 

material passing the larger sieve sizes are related to the resilient modulus of the unbound 

base/subbase materials with the larger aggregate particles, as expected. 

Until additional test results become available to improve or confirm these relationships, it is 

recommended that at least some resilient modulus tests be performed to measure the MR for 

unbound pavement materials and soils. 

 

Figure 32. Comparison of the resilient modulus predicted from the data sets for crushed stone 

materials sampled from the test pit and auger locations. 

Resilient Modulus for Crushed Stone (material code = 303)

0

50

100

150

200

250

300

350

400

450

500

0 50 100 150 200 250 300 350 400 450 500

Mr Predicted (Test Pit)

Mr Predicted (Auger)
 54

Figure 33. Graphical comparison of the calculated MR using the regressed k-coefficients from 

the physical properties of the sand soil group sampled from augers and test pits. 

Resilient Modulus for Sand

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140

Mr Predicted (Test Pit)

Mr Predicted (Auger)
 55

CHAPTER 5. SUMMARY AND FUTURE RECOMMENDATIONS 

Repeated-load resilient modulus tests are being performed on all unbound pavement materials 

and soils from the SPS and GPS test sections included in FHWAís LTPP program in accordance 

with LTPP test protocol P46. The overall goal of this study was to complete a detailed review of 

the LTPP MR data and to identify potential anomalies and bias in those data. To accomplish that 

goal, correlation studies and regression analysis were completed in evaluating MR test results. 

The correlation and regression studies included: 

• Regression of the k-coefficients of equation 3. 

• Comparison of the distributions of each k-coefficient for different data groups to identify any 

bias or differences between different data sets. 

• Identification of the physical properties and other parameters that affect the response 

characteristics of the materials and soils tested. 

FINDINGS AND OBSERVATIONS 

The following is a summary of the findings and recommendations from this study: 

• A total of 2,014 MR tests of unbound pavement materials and soils have a Level E data status, 

while 1,594 tests have not yet obtained a Level E status in the LTPP database as of the 

October 2000 data release. It is expected that the number of completed MR tests with a Level 

E status will significantly increase in future data releases. 

• Constitutive equation 3 was found to be an excellent fit to the MR test results included in the 

LTPP database. Specifically, almost 92 percent of the LTPP MR test results have response 

characteristics that can be accurately simulated by constitutive equation 3. Constitutive 

equation 3 is the equation selected for use in development of the 2002 Design Guide. It is 

important to note that the values for the k1 coefficient reported herein from the regression 

studies were determined using units of kPa for the pressure and stress parameters and units of 

MPa for the MR. 

• Coefficient k6 (pore-water pressure or cohesion term) in equation 3 was found to be zero for 

more than 50 percent of the MR tests. The non-zero values of k6 were highly variable and 

have a uniform distribution. Thus, k6 was assumed to be zero for all of the correlation studies 

and analyses performed on the MR test data. This assumption should be checked and 

confirmed as additional MR test results reach a Level E data status in the LTPP database. 

• Coefficient k3 was found to be zero for nearly 25 percent of the MR tests performed on the 

unbound aggregate base/subbase materials and about 10 percent of the tests performed on the 

coarse-grained subgrade soils. 
 56

• There were 185 MR tests (approximately 8 percent) that were flagged with potential 

anomalies. Most of the anomalous tests (103 of 185 flagged tests) were defined as a type 4 

anomaly. A type 4 anomaly exhibits a different stress sensitivity between the different 

confining pressures. Some of these differences are large enough that the higher confining 

pressure will result in a lower MR than a lower confining pressure at the same repeated 

vertical load. Samples that exhibit this type of anomaly should be retested. 

• Sampling technique (auger versus test pit samples) does have an effect on the MR test results 

for the uncrushed gravel and crushed stone base/subbase materials. No significant difference 

was found between the augered and test pit samples of the other base/subbase materials. 

• Sampling technique also has an effect on the MR test results for the subgrade soils. However, 

only one of the k-coefficients regressed from the MR test data for the augered and test pit 

samples were found to be different for the coarse-grained soils and no difference was found 

for the fine-grained soils. Conversely, at least one of the k-coefficients was found to be 

different for all soil groups when comparing undisturbed and disturbed test specimens. 

Multiple k-coefficients (including k1) were found to be different for the clay soils. Thus, it 

appears that there is a significant difference in the MR test results for selected data groups that 

can be attributed to, or explained by, the use of different sampling techniques. These data 

groups include undisturbed versus disturbed test specimens for the clay soils and augered 

versus test pit specimens for the crushed stone base/subbase materials. At a minimum, these 

data groups should be considered as different populations of MR test data. 

• The physical properties correlated to resilient modulus varied between the different materials 

and soils. No one physical property was included for all materials and soils. However, the 

following summarizes the properties related to the k-coefficients for many of the data groups: 

! Liquid limit, plasticity index, and the amount of material passing the smaller sieve sizes 

were found to be important as related to the resilient modulus for the lower strength 

unbound aggregate base/subbase materials, while the moisture content and density were 

important as related to the higher strength materials. 

! The amount of material passing the larger sieve sizes was important for the unbound 

aggregate base/subbase materials with larger aggregates. 

! Percent clay and test specimen moisture content or density are important for all soil 

groups. 

! Percent silt was important for all soil groups except gravel. 

• The statistics for all models relating the resilient modulus to physical properties were fair to 

good for most data groups. Breaking the data groups into subgroups by sampling technique 

and material or soil type did improve on the regression statistics. Thus, the primary result 

from these regression studies is that the resilient modulus can be reasonably predicted from 

those physical properties that are included in the LTPP database. It should be noted that 
 57

these correlation and regression studies did not consider any effect that may have been 

caused by the use of different testing contractors. 

RECOMMENDATIONS 

Two important recommendations are a result of this study: 

1. The review process identified in chapter 2 should be performed on the resilient modulus test 

results after each test is completed. In other words, the review process to identify anomalous 

data should become a part of the QC process, but the review should be performed 

immediately after testing. Retests can then be scheduled and performed for those tests that 

are flagged. 

2. The findings and observations from this study should be verified and confirmed after all MR

tests have been completed, checked through the QC process, and have reached a Level E data 

status in the LTPP database. 

The final recommendation or suggestion is to determine if there is any effect or bias in the 

resilient modulus test results between the different testing contractors (i.e., operator- or 

equipment-dependent). The bias for each prediction model was provided in appendix E. The 

resilient modulus data should be studied in more detail to identify any causes of the bias that 

appear to be material- and/or stress-state-dependent. 

 

59

APPENDIX A. 

SUMMARY OF k-COEFFICIENTS FOR THE LTPP RESILIENT MODULUS TESTS 

Appendix A, table 16, provides a tabulation of the k-coefficients that were determined for each 

resilient modulus test using nonlinear regression techniques for the “universal” constitutive 

equation. Various statistical parameters are also tabulated for each test. These statistical 

parameters include the following: 

 RMSE = Root Mean Squared Error 

 MSE = Mean Squared Error 

R2

 Se/Sy
60
61

Table 16. k-values determined from nonlinear regression analyses of LTPP resilient modulus 

test of unbound materials. 

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points Std Dev(MR) RMSE MSE R2 Se/Sy

1 0101 1 2 B6 BS06 0.7371 0.1236 -0.7748 15 4.1656 2.0358 4.1447 0.9991 0.4887

1 0102 1 2 B7 BS07 0.7810 0.1497 -0.4579 15 4.3337 2.4088 5.8023 0.9990 0.5558

1 0103 1 2 B5 BS05 0.7471 0.1952 -1.2825 15 5.9738 1.9974 3.9898 0.9991 0.3344

1 0106 1 2 B4 BS04 0.7514 0.1787 -0.2832 15 4.6260 1.8647 3.4770 0.9994 0.4031

1 0107 1 2 B1 BS01 0.6701 0.2137 -1.0366 15 4.9454 1.4704 2.1620 0.9994 0.2973

1 0108 1 2 B2 BS02 0.7619 0.1612 -0.4410 15 4.1196 1.6944 2.8708 0.9995 0.4113

1 0111 1 2 B3 BS03 0.7628 0.1344 -0.2691 15 4.1827 2.7063 7.3239 0.9988 0.6470

1 0502 1 1 TP1 BS55 0.6190 0.3902 0.0000 15 9.0806 1.9745 3.8986 0.9992 0.2174

1 0502 2 1 TP1 BG56 0.6188 0.5133 -0.0405 15 33.6647 1.1438 1.3084 0.9999 0.0340

1 0502 2 2 TP1 BG56 0.5948 0.4399 0.0000 15 9.8985 1.9707 3.8836 0.9991 0.1991

1 1001 2 2 TP1 BG56 0.7172 0.7705 -0.0458 15 78.1141 6.6861 44.7042 0.9987 0.0856

1 1001 2 2 TP1 BG57 0.7268 0.7067 -0.1472 15 62.5584 5.6975 32.4613 0.9988 0.0911

1 1011 1 1 A1 TS01 0.8228 0.1655 -2.2042 15 9.7575 4.6641 21.7535 0.9946 0.4780

1 1011 1 2 A2 TS03 1.7600 0.4354 -3.1476 15 25.0337 4.9273 24.2783 0.9984 0.1968

1 1011 2 1 BA* BG** 0.9145 0.5503 0.0000 15 57.9386 4.5896 21.0643 0.9994 0.0792

1 1011 2 2 BA* BG** 0.9613 0.6280 -0.1737 15 65.4470 5.6762 32.2189 0.9992 0.0867

1 1011 3 1 BA* BG** 0.5700 0.9897 0.0000 15 103.5283 6.7758 45.9112 0.9990 0.0654

1 1019 1 1 A1 TS02 1.2501 0.4131 -1.2442 15 15.3623 5.3629 28.7604 0.9978 0.3491

1 1019 1 2 A2 TS03 0.5343 0.4178 0.0000 15 8.9320 3.2359 10.4713 0.9971 0.3623

1 1019 2 1 BA* BG** 0.9962 0.6250 0.0000 15 80.1910 17.8706 319.3589 0.9934 0.2229

1 1019 2 2 TP1 BG55 0.7799 0.6658 -0.1396 15 61.1355 6.8790 47.3208 0.9984 0.1125

1 1021 1 1 A1 TS01 0.8648 0.5048 -2.3817 15 12.6630 4.1558 17.2709 0.9963 0.3282

1 1021 1 2 A2 TS03 1.2172 0.2507 -2.9302 15 15.9592 5.0640 25.6442 0.9966 0.3173

1 1021 2 1 BA* BG** 0.9483 0.6619 -0.1447 15 72.2560 4.8052 23.0902 0.9994 0.0665

1 1021 2 2 TP1 BG55 0.8984 0.7054 -0.2732 15 70.3500 8.9635 80.3441 0.9979 0.1274

1 3028 1 1 BA* BS** 1.2131 0.2656 0.0000 15 24.3307 21.2344 450.8977 0.9750 0.8727

1 3028 1 2 BA* BS** 1.8894 0.2760 -2.2448 15 20.6635 2.8790 8.2887 0.9996 0.1393

1 3028 2 1 BA* BG** 1.4464 0.5184 -0.0799 15 77.6224 17.7199 313.9942 0.9956 0.2283

1 3028 2 2 BA* BG** 1.2310 0.7180 -0.6733 15 76.8463 22.2049 493.0587 0.9905 0.2890

1 3028 3 1 BA* BG** 1.0271 0.6810 0.0000 15 90.4006 11.0833 122.8406 0.9979 0.1226

1 3028 3 2 BA* BG** 1.5955 0.5814 0.0000 15 110.8525 14.2134 202.0195 0.9982 0.1282

1 3998 1 2 BA* BS** 1.0637 0.3231 -1.0555 15 10.6735 3.7247 13.8734 0.9986 0.3490

1 3998 3 1 BA1 BG** 0.9738 0.5864 -0.2905 15 52.9351 6.8765 47.2866 0.9985 0.1299

1 3998 3 2 BA4 BG04 0.8006 0.6053 -0.2377 14 45.7415 3.5012 12.2582 0.9994 0.0765

1 4007 1 1 BA* BS** 0.8141 0.4355 -3.0154 15 12.1330 4.3485 18.9090 0.9944 0.3584

1 4007 1 2 BA* BS** 1.3948 0.2649 -2.8767 15 17.6589 2.3832 5.6795 0.9994 0.1350

1 4007 2 1 BA* BG** 0.9494 0.5808 -0.1435 15 57.4057 7.0918 50.2932 0.9985 0.1235

1 4007 2 2 BA* BG** 0.8383 0.5634 0.0000 15 54.5472 10.8640 118.0265 0.9959 0.1992

1 4007 3 1 BA* BG** 1.3816 0.5590 0.0000 15 91.1401 12.7308 162.0725 0.9979 0.1397

1 4007 3 2 BA* BG** 0.9497 0.7222 0.0000 15 94.7404 13.2385 175.2568 0.9969 0.1397

1 4073 1 1 BA* BS** 0.9002 0.1355 -0.2725 15 6.4609 5.2374 27.4301 0.9968 0.8106

1 4073 1 2 A2 TS03 0.7229 0.1997 0.0000 15 16.3509 15.4884 239.8912 0.9618 0.9473

1 4073 3 1 BA* BG** 0.9836 0.2466 0.0000 15 84.1259 81.9652 6718.2890 0.7186 0.9743

1 4073 3 2 BA* BG** 0.8174 0.7952 -0.1003 15 90.1776 6.7010 44.9029 0.9990 0.0743

1 4084 1 1 A1 TS01 0.8795 0.1582 -0.4664 15 5.0256 2.5857 6.6857 0.9991 0.5145

1 4084 1 2 BA* BS** 1.0375 0.2973 -0.5501 15 10.1901 4.1911 17.5656 0.9984 0.4113

1 4084 2 1 BA* BG** 0.5990 0.7892 -0.1143 15 63.8606 3.1233 9.7553 0.9996 0.0489

1 4084 2 2 BA* BG** 0.7972 0.5885 0.0000 15 69.4017 50.4695 2547.1710 0.9121 0.7272

1 4084 3 1 BA* BG** 0.6778 0.7146 0.0000 15 64.6516 9.1687 84.0648 0.9970 0.1418

1 4084 3 2 BA* BG** 0.7800 0.8275 -0.0167 15 97.7705 5.2889 27.9730 0.9995 0.0541

1 4125 1 1 BA* BS** 0.8059 0.1801 -0.3696 15 7.6389 6.1378 37.6726 0.9944 0.8035

1 4125 1 2 BA* BS** 1.1292 0.2901 -1.0669 15 10.8659 4.6570 21.6877 0.9980 0.4286

1 4125 2 1 BA* BG** 0.8139 0.6263 -0.1825 15 53.9916 5.5835 31.1760 0.9989 0.1034

1 4125 2 2 BA* BG** 1.1805 0.5535 -0.7258 15 43.2580 15.0289 225.8680 0.9924 0.3474

1 4126 1 1 A1 TS01 0.7751 0.2980 -1.6994 15 8.9400 4.5929 21.0945 0.9951 0.5137

1 4126 1 2 BA* BS** 0.7809 0.4647 -1.1358 15 10.8483 3.5572 12.6540 0.9977 0.3279

1 4126 2 1 BA* BG** 1.0471 0.6218 0.0000 15 80.4536 7.2282 52.2470 0.9990 0.0898

1 4126 2 2 BA* BG** 0.6490 0.7825 0.0000 15 73.9168 7.9356 62.9744 0.9980 0.1074

1 4127 1 1 A1 TS01 1.1422 0.3306 -2.7938 15 14.2538 2.6335 6.9355 0.9990 0.1848

1 4127 1 2 BA* BS** 1.3265 0.0829 -1.7482 15 13.6162 6.0374 36.4507 0.9969 0.4434

1 4127 2 1 BA* BG** 0.7026 0.7705 0.0000 15 77.0454 8.5414 72.9563 0.9980 0.1109

1 4127 2 2 BA* BG** 0.5337 0.7125 0.0000 15 52.2137 16.6248 276.3824 0.9845 0.3184

1 4129 1 1 BA* BS** 1.1543 0.3027 -2.8987 15 15.1453 3.7856 14.3305 0.9979 0.2499

1 4129 1 2 TP1 BS55 0.8461 0.1659 -0.9872 15 7.4661 5.4494 29.6957 0.9951 0.7299

1 4129 2 2 TP1 BG56 0.8022 0.8315 -0.6935 15 62.8943 5.7104 32.6087 0.9989 0.0908
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

1 4129 3 1 BA* BG** 1.1371 0.6745 0.0000 15 100.0928 7.6607 58.6858 0.9992 0.0765

1 4129 3 2 TP1 BG55 1.0055 0.6922 0.0000 15 91.2690 10.4864 109.9647 0.9981 0.1149

1 4155 1 1 BA* BS** 1.0195 0.7429 -0.7080 15 28.4700 15.6947 246.3234 0.9799 0.5513

1 4155 1 2 A2 TS03 2.0801 0.4302 -2.2159 15 26.3755 5.4274 29.4568 0.9989 0.2058

1 4155 2 1 BA* BG** 1.2935 0.5532 0.0000 15 84.6003 16.1815 261.8409 0.9961 0.1913

1 4155 2 2 BA* BG** 1.1041 0.6834 -0.0930 15 92.5873 6.6830 44.6630 0.9993 0.0722

1 5008 1 1 A1 TS01 1.0711 0.2380 -3.5698 15 16.1103 5.9652 35.5836 0.9927 0.3703

1 5008 1 2 A2 TS03 0.7008 0.3522 -1.7352 15 8.1650 3.1471 9.9044 0.9972 0.3854

1 6012 1 1 A1 TS01 0.6492 0.3830 -0.5643 15 8.5206 3.4496 11.8995 0.9973 0.4049

1 6012 1 2 A2 TS03 0.7752 0.5601 -1.7078 15 11.9012 3.1382 9.8480 0.9979 0.2637

1 6012 2 1 BA* BG** 0.8778 0.5954 -0.1138 15 57.2686 4.1081 16.8766 0.9995 0.0717

1 6012 2 2 TP1 BG55 1.0494 0.7489 -0.4188 15 80.4753 15.7269 247.3352 0.9952 0.1954

1 6019 1 1 A1 TS01 0.7928 0.3903 -0.9354 15 9.8595 3.9358 15.4902 0.9973 0.3992

1 6019 1 2 BA* BS** 0.8190 0.4979 -0.6530 15 12.7906 2.6269 6.9006 0.9990 0.2054

1 6019 2 1 BA* BG** 0.7012 0.7925 -0.3774 15 61.9985 3.7865 14.3375 0.9995 0.0611

1 6019 2 2 BA* BG** 0.8196 0.6743 -0.2775 15 57.5630 5.5761 31.0933 0.9989 0.0969

4 0114 1 2 B309 BS09 1.3826 0.2588 -1.5020 15 12.2991 1.9360 3.7482 0.9997 0.1574

4 0115 1 2 B303 BS03 0.9022 0.5984 -2.0181 15 14.4413 3.1117 9.6824 0.9983 0.2155

4 0213 1 2 B311 BS11 0.8746 0.5885 -2.1306 15 13.6249 2.7469 7.5452 0.9986 0.2016

4 0216 1 2 B306 BS06 0.9361 0.5105 -1.9370 15 13.0978 2.5639 6.5734 0.9989 0.1957

4 0217 1 2 B309 BS09 0.7398 0.6783 -1.8964 15 13.2388 2.6095 6.8093 0.9984 0.1971

4 0222 1 2 B303 BS03 0.9586 0.6219 -2.2077 14 15.2084 1.9614 3.8471 0.9994 0.1290

4 0223 1 2 B308 BS08 0.8278 0.7128 -1.8388 14 16.0995 3.0501 9.3029 0.9983 0.1895

4 0608 1 2 B* BS** 0.6853 0.4443 -1.5710 15 8.7977 2.7190 7.3927 0.9980 0.3091

4 1001 1 1 BA* BS** 0.4998 0.4101 -1.1300 15 5.9936 1.5315 2.3456 0.9989 0.2555

4 1001 1 2 TP1 BS91 0.7853 0.3092 -0.9687 15 7.4687 2.2560 5.0894 0.9991 0.3021

4 1003 1 1 BA* BS** 0.8319 0.3211 -1.1004 15 7.9000 1.4748 2.1751 0.9996 0.1867

4 1003 1 2 TP1 BS92 0.7813 0.2274 -1.4264 15 6.6783 1.6462 2.7100 0.9994 0.2465

4 1006 1 1 BA* BS** 0.6460 0.4283 -1.5221 15 8.2016 2.5962 6.7405 0.9979 0.3166

4 1006 1 2 TP1 BS92 0.8157 0.2828 -0.9575 15 7.1581 2.2317 4.9804 0.9992 0.3118

4 1006 2 2 TP1 BG91 0.4255 0.5981 -0.0512 15 28.7498 1.3155 1.7306 0.9998 0.0458

4 1007 1 1 BA* BS** 0.7197 0.2933 -1.0219 15 6.8125 2.6900 7.2359 0.9984 0.3949

4 1007 1 2 TP1 BS91 0.6616 0.5148 -1.5365 15 9.4708 1.8007 3.2424 0.9991 0.1901

4 1015 1 1 BA* BS** 0.9300 0.2290 0.0000 15 8.3995 3.0906 9.5517 0.9990 0.3679

4 1015 1 2 TP1 BS92 1.0206 0.1451 0.0000 15 7.1933 4.7344 22.4147 0.9981 0.6582

4 1016 2 1 BA* BG** 0.8553 0.4920 -0.4112 15 32.5506 10.2399 104.8550 0.9940 0.3146

4 1017 1 1 BA* BS** 1.0919 0.1256 0.0000 15 10.0247 8.6811 75.3617 0.9945 0.8660

4 1018 1 2 TP1 BS92 0.3435 0.3740 -2.3961 15 4.2840 1.1042 1.2193 0.9983 0.2578

4 1018 2 1 BA* BG** 1.0551 0.2786 -0.1404 15 21.7065 1.3288 1.7656 0.9999 0.0612

4 1021 1 1 BA* BS** 0.5579 0.6154 -1.3122 15 9.7458 2.1006 4.4126 0.9984 0.2155

4 1021 1 2 TP1 BS92 0.5287 0.6330 -1.6658 15 9.1766 2.3003 5.2912 0.9977 0.2507

4 1022 1 2 TP1 BS93 0.9034 0.2029 0.0000 15 7.0697 2.2604 5.1096 0.9995 0.3197

4 1024 1 1 BA* BS** 1.0553 0.2244 0.0000 15 10.2502 5.3602 28.7313 0.9978 0.5229

4 1024 1 2 TP1 BS92 1.0418 0.1763 -0.5128 15 5.7677 1.3073 1.7091 0.9998 0.2267

4 1024 2 1 BA* BG** 1.3847 0.2193 0.0000 15 26.1743 6.0040 36.0478 0.9989 0.2294

4 1034 1 2 TP1 BS92 0.7936 0.3787 -1.5099 15 8.9016 2.0526 4.2131 0.9991 0.2306

4 1036 1 2 TP1 BS70 0.7304 0.2685 -0.7325 15 6.2587 2.2873 5.2318 0.9990 0.3655

4 1062 1 1 BA* BS** 0.6933 0.2804 -0.2882 15 6.8334 2.6882 7.2262 0.9986 0.3934

4 1065 1 1 BA* BS** 0.8859 0.2622 -0.4837 15 7.4782 2.4435 5.9709 0.9993 0.3268

4 6053 1 1 BA* BS** 0.7658 0.3751 -1.3903 15 8.3569 1.4713 2.1647 0.9995 0.1761

4 6053 1 2 TP1 BS92 0.7798 0.3288 -0.6940 15 7.9809 2.5445 6.4745 0.9989 0.3188

4 6054 1 1 BA* BS** 0.6366 0.5542 -1.5157 15 9.7897 2.1944 4.8154 0.9986 0.2242

4 6054 1 2 TP1 BS92 0.6613 0.5143 -1.2380 15 9.6204 2.0383 4.1547 0.9989 0.2119

4 6054 2 1 BA* BG** 0.4914 0.5684 -0.0938 15 29.7610 4.0400 16.3213 0.9982 0.1357

4 6055 1 1 BA1 BS63 0.8699 0.2678 -0.5267 15 7.7263 3.1824 10.1275 0.9987 0.4119

4 6060 1 2 TP1 BS92 1.0603 0.1957 -0.7465 15 6.7068 1.7628 3.1075 0.9997 0.2628

62
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

4 7079 1 1 TP1 BG92 0.7094 0.1720 0.0000 15 4.9828 2.2408 5.0212 0.9991 0.4497

4 7614 1 1 BA* BS** 0.5153 0.6683 -1.1108 15 10.0887 1.9554 3.8236 0.9985 0.1938

4 7614 1 2 BA* BS** 0.5464 0.6406 -1.4908 15 9.7356 2.2565 5.0919 0.9980 0.2318

5 0809 1 1 A1 TS01 1.1977 0.2272 -1.3215 15 9.5534 1.3115 1.7199 0.9998 0.1373

5 0809 1 2 B2 BS02 1.0976 0.2637 -1.6926 15 10.3730 1.5268 2.3312 0.9997 0.1472

5 0810 1 2 B3 BS03 0.7958 0.4785 -1.7610 15 10.6583 2.0967 4.3962 0.9991 0.1967

5 3011 1 2 A2 TS03 0.8035 0.1570 -0.8411 15 6.0174 4.0411 16.3302 0.9972 0.6716

5 3048 1 1 A1 TS01 0.5393 0.4559 -4.7896 15 8.1492 1.5051 2.2654 0.9979 0.1847

5 3048 1 2 A2 TS03 0.7728 0.0727 -0.0652 15 4.3403 3.9048 15.2474 0.9977 0.8997

5 3058 1 1 A1 TS02 0.7875 0.2825 -3.7571 15 10.8575 1.4862 2.2089 0.9992 0.1369

5 3058 1 2 A2 TS04 0.5751 0.5593 -1.4822 15 8.7576 1.4011 1.9631 0.9993 0.1600

5 3059 1 1 A1 TS01 0.7745 0.3783 -0.6541 15 8.9815 1.3285 1.7650 0.9997 0.1479

5 3059 1 2 A2 TS03 0.6421 0.5358 -0.8646 15 10.3293 1.8870 3.5607 0.9991 0.1827

5 3073 1 1 BA* BS** 1.2130 0.1555 -0.9743 15 11.1471 8.3210 69.2397 0.9945 0.7465

5 3073 1 2 A2 TS03 1.7246 0.4174 -1.9475 15 20.9955 3.3692 11.3516 0.9994 0.1605

5 3073 2 2 BA* BG** 0.7711 0.5753 -0.0042 15 51.6329 3.3592 11.2845 0.9996 0.0651

5 3073 3 2 BA* BG** 0.9091 0.6159 -0.5333 15 44.9817 8.4644 71.6458 0.9970 0.1882

5 3074 1 1 A1 TS01 0.5447 0.4050 -3.2925 15 7.6239 2.2466 5.0474 0.9966 0.2947

5 3074 1 2 A2 TS03 0.6514 0.3682 -2.2002 15 8.1929 3.0916 9.5578 0.9965 0.3773

5 4019 1 1 A1 TS01 0.5482 0.4429 -0.8866 15 7.3601 1.6951 2.8734 0.9990 0.2303

5 4019 1 2 A2 TS03 0.4647 0.4165 -0.4198 15 6.4343 1.2036 1.4486 0.9994 0.1871

5 4019 2 1 BA* BG** 0.5626 0.6400 -0.0409 15 43.5697 2.2207 4.9314 0.9997 0.0510

5 4019 2 2 BA* BG** 0.6635 0.6286 -0.2518 15 42.0982 3.3810 11.4309 0.9993 0.0803

5 4021 1 1 A1 TS01 0.5824 0.0000 -0.7731 15 7.4661 6.9580 48.4139 0.9841 0.9319

5 4021 1 2 A2 TS03 0.9402 0.4058 -3.6363 15 13.8192 4.1893 17.5499 0.9956 0.3031

5 4021 2 1 BA* BG** 0.9836 0.6125 -0.3278 15 56.0750 7.3651 54.2453 0.9984 0.1313

5 4021 2 2 BA* BG** 0.9931 0.6600 -0.3497 15 63.3222 8.7766 77.0290 0.9980 0.1386

5 4021 3 1 BA1 BG01 0.8281 0.5985 0.0000 15 60.2221 5.7339 32.8770 0.9989 0.0952

5 4021 3 2 BA* BG** 1.0234 0.6369 -0.0277 15 79.9328 3.0210 9.1261 0.9998 0.0378

5 4023 1 2 A2 TS03 0.4008 0.0827 -3.4340 15 5.6273 2.6811 7.1881 0.9909 0.4764

5 4046 1 1 A1 TS01 0.6732 0.1544 -1.9907 15 6.6833 2.0732 4.2980 0.9985 0.3102

5 4046 1 2 A2 TS03 0.8173 0.2922 -3.8799 15 11.5293 1.5947 2.5429 0.9991 0.1383

5 5803 1 1 BA* BS** 0.6256 0.1622 0.0000 15 5.4467 4.0120 16.0961 0.9964 0.7366

5 5803 1 2 BA* BS** 0.7263 0.2834 -0.1316 15 7.5957 2.7507 7.5666 0.9988 0.3621

5 5803 2 2 BA* BG** 0.8995 0.5434 -0.7994 15 30.2501 10.1542 103.1070 0.9935 0.3357

5 5805 1 1 BA* BS** 1.6165 0.3330 -1.6501 15 16.8797 3.4987 12.2411 0.9994 0.2073

5 5805 1 2 BA* BS** 0.6384 0.2468 0.0000 15 7.3310 4.5288 20.5105 0.9958 0.6178

6 1253 1 1 BA* BS** 0.8830 0.2074 0.0000 15 8.3341 5.0314 25.3147 0.9972 0.6037

6 2002 1 1 BA* BS** 0.5407 0.4460 -1.4504 15 6.8813 1.6833 2.8334 0.9988 0.2446

6 2004 1 1 BA* BS** 0.5721 0.4024 -2.1477 15 7.3549 2.4186 5.8499 0.9972 0.3288

6 2004 2 1 BA* BG** 0.4943 0.6108 -0.1061 15 33.3267 2.5404 6.4536 0.9994 0.0762

6 2004 2 2 TP1 BG91 0.5026 0.6098 -0.0964 15 34.1735 1.8080 3.2689 0.9997 0.0529

6 2038 1 1 BA* BS** 0.4972 0.6936 -2.3137 15 8.8919 1.8030 3.2507 0.9981 0.2028

6 2038 1 2 TP1 BS92 0.6524 0.5741 -2.5869 15 10.1151 2.1687 4.7034 0.9982 0.2144

6 2051 1 2 TP1 BG55 1.0052 0.1877 0.0000 15 7.7662 3.5491 12.5962 0.9989 0.4570

6 2053 1 1 A1 TS01 0.8825 0.1566 -0.2485 15 4.6260 1.5040 2.2621 0.9997 0.3251

6 2647 2 1 BA* BG** 0.5444 0.5276 -0.1809 15 27.2446 4.3768 19.1567 0.9980 0.1607

6 3010 1 2 BA* BS** 1.3127 0.2247 0.0000 15 14.8622 10.1830 103.6940 0.9949 0.6852

6 3013 1 1 BA* BS** 0.8532 0.2000 -0.5983 15 5.7296 2.4640 6.0711 0.9991 0.4300

6 3013 1 2 BA* BS** 0.4936 0.6305 -1.0905 15 9.0275 1.4499 2.1021 0.9991 0.1606

6 3019 1 1 BA* BS** 0.7663 0.4057 -0.2891 15 10.4449 1.4168 2.0072 0.9997 0.1356

6 3019 1 2 BA* BS** 0.7604 0.2688 -1.5229 15 7.2058 2.1095 4.4500 0.9990 0.2927

6 3019 2 1 BA* BG** 0.5335 0.5526 -0.1776 15 28.8139 3.7393 13.9823 0.9985 0.1298

6 3019 2 2 BA* BG** 1.0167 0.2303 -0.2524 15 14.1596 4.1284 17.0438 0.9989 0.2916

6 3021 1 1 BA* BS** 0.5388 0.5868 -1.5125 15 8.7723 2.0862 4.3521 0.9982 0.2378

6 3021 1 2 BA* BS** 0.5064 0.6617 -1.0518 15 9.8043 1.9581 3.8342 0.9985 0.1997

63
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

6 3021 2 1 BA* BG** 0.4928 0.6465 -0.2440 15 32.9003 2.5309 6.4056 0.9994 0.0769

6 3021 2 2 BA* BG** 0.5105 0.5973 -0.2913 15 28.6124 4.7970 23.0112 0.9974 0.1677

6 3024 1 1 BA* BS** 0.5822 0.5992 -1.2084 15 9.9676 2.4363 5.9355 0.9981 0.2444

6 3024 1 2 BA* BS** 0.7776 0.2866 -1.3810 15 7.5612 2.8038 7.8610 0.9983 0.3708

6 3030 1 1 BA* BS** 0.8068 0.1653 -1.0192 15 5.8611 2.9328 8.6010 0.9984 0.5004

6 3030 1 2 BA* BS** 0.9139 0.1248 -0.9845 15 6.0340 2.8551 8.1513 0.9988 0.4732

6 3042 1 1 A1 TS01 0.6981 0.2199 -0.9301 15 5.3745 2.4178 5.8458 0.9986 0.4499

6 3042 1 2 A2 TS03 0.9515 0.2904 -0.8062 15 8.4724 2.3378 5.4654 0.9993 0.2759

6 6044 1 1 BA* BS** 0.9247 0.1324 0.0000 15 5.4406 3.0952 9.5801 0.9990 0.5689

6 6044 1 2 TP1 BS93 0.7369 0.1989 -2.3643 15 8.2537 1.3385 1.7916 0.9994 0.1622

6 7452 1 2 A2 TS03 0.6432 0.3418 -1.2512 15 6.7767 2.2228 4.9408 0.9985 0.3280

6 7455 1 1 BA1 BS01 0.8728 0.1182 0.0000 15 4.6547 2.7182 7.3885 0.9991 0.5840

6 7456 1 2 A2 TS03 0.8811 0.0643 -0.4024 15 2.4339 0.8551 0.7311 0.9999 0.3513

6 7493 1 1 BA* BS** 0.5549 0.6356 -1.0915 15 10.2181 1.9574 3.8316 0.9987 0.1916

6 8149 1 2 TP1 BS91 0.9513 0.1694 -0.1897 15 5.8538 2.5974 6.7465 0.9993 0.4437

6 8150 1 2 TP1 BS92 0.4707 0.6219 -1.1504 15 8.4080 1.6630 2.7654 0.9987 0.1978

6 8150 2 1 BA* BG** 0.4453 0.6237 -0.1413 15 30.1870 2.5970 6.7446 0.9992 0.0860

6 8151 1 2 TP1 BS91 0.5315 0.5758 -0.8936 15 9.1063 1.2846 1.6502 0.9994 0.1411

6 8153 1 1 BA* BS** 0.7594 0.1639 -0.7032 15 4.4315 1.7877 3.1959 0.9994 0.4034

6 8153 1 2 TP1 BS94 0.6883 0.1763 -2.0942 15 7.0488 0.9471 0.8969 0.9997 0.1344

6 8153 1 3 TP1 BG93 1.1350 0.1914 -0.3936 15 10.6225 4.4039 19.3948 0.9988 0.4146

6 8153 2 2 TP1 BG93 0.4428 0.5861 -0.0425 15 29.6008 1.1971 1.4332 0.9998 0.0404

6 8153 2 3 TP1 BG93 1.1350 0.1914 -0.3936 15 10.6225 4.4039 19.3948 0.9988 0.4146

6 8153 3 2 TP1 BG92 0.4420 0.5875 -0.0444 15 29.5751 1.1627 1.3520 0.9998 0.0393

6 8201 1 1 BA* BS** 0.5413 0.5647 -1.9937 15 8.5161 2.6525 7.0357 0.9966 0.3115

6 8201 1 2 TP1 BS92 0.6662 0.3175 0.0000 15 8.0593 1.9978 3.9911 0.9993 0.2479

6 8201 2 2 TP1 BG91 0.5414 0.6000 -0.2937 15 30.4806 4.0225 16.1808 0.9984 0.1320

6 8202 1 1 BA* BS** 0.4824 0.7120 -1.1406 15 9.9833 1.5382 2.3662 0.9990 0.1541

6 8202 1 2 TP1 BS91 0.3727 0.5896 -1.0324 15 6.6640 2.0966 4.3955 0.9967 0.3146

6 8534 1 1 BA* BS** 0.7072 0.2134 -1.4977 15 5.9096 0.5461 0.2982 0.9999 0.0924

6 8534 1 2 TP1 BS93 0.4252 0.3246 -2.6240 15 5.2915 1.2751 1.6259 0.9984 0.2410

6 8534 2 2 TP1 BG92 0.5610 0.5810 -0.0542 15 36.5819 1.4494 2.1009 0.9998 0.0396

6 8535 1 1 A1 TS01 0.5029 0.3376 -1.9250 15 5.5908 1.4715 2.1653 0.9987 0.2632

6 8535 1 2 A2 TS03 0.5417 0.3562 -1.3171 15 5.7005 1.3056 1.7045 0.9993 0.2290

6 9048 1 1 BA* BS** 0.5375 0.6285 -1.3856 15 9.4481 2.1530 4.6355 0.9982 0.2279

6 9048 1 2 BA* BS** 0.5465 0.6292 -1.3501 15 9.8377 2.8307 8.0129 0.9970 0.2877

6 9049 1 1 A1 TS01 0.7127 0.1235 -0.9651 15 4.0178 0.4537 0.2059 1.0000 0.1129

6 9049 1 2 A2 TS03 0.7360 0.1862 -1.2697 15 5.4746 1.1072 1.2259 0.9997 0.2022

8 0214 1 2 B2 BG02 1.1189 0.3250 -2.0816 14 12.3003 2.1884 4.7892 0.9994 0.1779

8 0217 1 2 B4 BG04 1.3112 0.1767 -1.4419 15 10.2377 1.1300 1.2770 0.9999 0.1104

8 0219 1 2 B3 BG03 1.3788 0.2140 -1.6695 15 12.2618 1.6644 2.7703 0.9998 0.1357

8 0221 1 2 B6 BG06 0.9585 0.1916 -2.3908 15 10.6023 0.9962 0.9925 0.9998 0.0940

8 0223 1 2 B7 BG07 0.6255 0.7108 -0.9095 14 13.8320 1.6283 2.6513 0.9994 0.1177

8 0224 1 2 B5 BG05 1.2216 0.2435 -1.5363 15 10.7491 1.4619 2.1371 0.9998 0.1360

8 0501 1 1 B* BS** 1.1849 0.2166 -1.2534 15 9.0370 1.0671 1.1387 0.9999 0.1181

8 0505 1 1 TP2 BS91 1.3927 0.2213 -0.9915 15 9.7688 0.9878 0.9757 0.9999 0.1011

8 0508 1 1 B* BS** 0.9520 0.1973 -2.2349 15 10.0915 1.3494 1.8208 0.9997 0.1337

8 1029 1 1 A1 TS01 0.9247 0.2617 -0.2430 15 8.4363 2.9342 8.6097 0.9991 0.3478

8 1029 1 1 BA* BS** 0.5784 0.2836 -1.3818 15 5.3301 1.4073 1.9804 0.9992 0.2640

8 1029 1 2 TP1 BS93 0.4591 0.6161 -1.8004 15 7.6083 1.8823 3.5430 0.9978 0.2474

8 1047 1 1 A1 TS01 0.8582 0.2892 -2.0809 15 9.2864 1.6277 2.6493 0.9994 0.1753

8 1047 1 1 BA* BS** 0.9428 0.1879 -0.1674 15 6.1085 1.5757 2.4828 0.9997 0.2579

8 1047 1 2 TP1 BS94 0.8107 0.1773 -1.0178 15 5.3966 1.3862 1.9216 0.9997 0.2569

8 1047 2 2 TP1 BS94 0.8763 0.1689 -0.6857 15 7.6830 4.4079 19.4298 0.9973 0.5737

8 1053 1 2 A2 JS03 0.5975 0.3772 -1.4540 15 6.5444 1.0662 1.1369 0.9996 0.1629

8 1053 1 2 TP1 BS93 0.7768 0.1609 -1.4560 15 6.2503 1.3835 1.9141 0.9996 0.2213

64
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

8 1057 1 2 A2 TS03 0.3642 0.3101 -3.3758 15 5.0775 1.3795 1.9029 0.9969 0.2717

8 1057 1 2 TP1 BG93 0.6293 0.3166 -1.8557 15 6.7153 1.2149 1.4759 0.9995 0.1809

8 2008 1 1 A1 TS01 0.6497 0.3169 -3.1272 15 8.5790 1.4344 2.0575 0.9990 0.1672

8 2008 1 1 BA* BS** 0.6313 0.1892 -1.2603 15 4.9058 1.7088 2.9201 0.9991 0.3483

8 2008 1 2 TP1 BS93 0.6182 0.1704 -0.9772 15 4.2235 1.8128 3.2863 0.9990 0.4292

8 2008 2 2 TP1 BG92 1.3752 0.2144 0.0000 15 24.9279 4.2035 17.6696 0.9995 0.1686

8 6002 1 1 A1 TS01 0.8081 0.1188 -1.0092 15 5.0351 1.9369 3.7515 0.9993 0.3847

8 6002 1 1 BA* BS** 0.6856 0.1867 -2.6215 15 8.1211 0.9616 0.9247 0.9996 0.1184

8 6002 1 2 A2 TS03 0.6370 0.1238 -1.4454 15 5.0803 1.4370 2.0649 0.9993 0.2829

8 6002 1 2 TP1 BS92 0.7331 0.1433 -0.7818 15 3.9857 1.2319 1.5176 0.9997 0.3091

8 6013 1 1 BA* BS** 0.6407 0.3661 -0.3677 15 7.8237 2.1590 4.6613 0.9990 0.2760

8 6013 1 2 TP1 BS93 1.1514 0.2051 0.0000 15 9.4315 3.7882 14.3503 0.9991 0.4017

8 6013 2 1 BA* BG** 0.5359 0.5580 -0.0894 15 31.8523 1.9124 3.6571 0.9997 0.0600

8 6013 2 2 TP1 BG** 0.5387 0.5594 -0.0662 15 32.7039 2.0364 4.1469 0.9996 0.0623

8 7035 1 1 BA* BS** 0.6074 0.3382 -2.7277 15 7.6669 1.2863 1.6546 0.9992 0.1678

8 7035 1 2 A2 TS04 0.5484 0.2235 -1.7124 15 5.3745 2.0893 4.3652 0.9979 0.3887

8 7035 1 2 BA* BS** 0.6203 0.1806 -1.0651 15 4.4668 1.7725 3.1418 0.9990 0.3968

8 7035 2 1 BA* BG** 0.4811 0.5986 -0.0881 15 31.9707 1.6310 2.6602 0.9997 0.0510

8 7035 3 1 BA* BG** 0.4806 0.5932 -0.0714 15 31.7352 2.3839 5.6831 0.9994 0.0751

8 7035 3 2 BA* BG** 0.7105 0.4240 -0.2531 15 23.7531 3.3991 11.5540 0.9990 0.1431

8 7036 1 1 A1 TS01 0.3881 0.5582 -2.8959 15 6.0929 1.7446 3.0437 0.9963 0.2863

8 7036 1 1 BA* BS** 0.7979 0.2077 0.0000 15 6.1412 0.8793 0.7732 0.9999 0.1432

8 7036 1 2 A2 TS03 0.4793 0.3088 -2.6789 15 5.9745 1.3679 1.8710 0.9985 0.2289

8 7036 1 2 BA* BS** 0.7042 0.2395 -1.0344 15 5.5403 1.7052 2.9077 0.9993 0.3078

8 7776 1 1 BA* BS** 0.7249 0.3053 -0.6783 15 6.7273 1.4822 2.1968 0.9996 0.2203

8 7776 1 1 BA1 BS01 0.9382 0.2499 -0.7301 15 7.2585 1.9369 3.7517 0.9995 0.2669

8 7776 1 2 BA* BS** 0.7562 0.2275 -0.5597 15 5.4362 1.6924 2.8641 0.9995 0.3113

8 7776 2 1 BA* BG** 1.0640 0.2134 -0.1404 15 15.5649 3.2166 10.3466 0.9994 0.2067

8 7781 1 1 A1 TS01 0.6418 0.2204 -0.8799 15 4.7539 1.7793 3.1659 0.9991 0.3743

8 7781 1 1 BA* BS** 0.7049 0.1353 -0.9915 15 4.6731 2.1478 4.6132 0.9989 0.4596

8 7781 1 2 BA* BS** 0.7338 0.3807 -1.6433 15 8.3478 1.8657 3.4807 0.9991 0.2235

8 7783 1 2 TP1 BS93 0.2536 0.0824 -3.0950 15 3.7771 1.9410 3.7673 0.9876 0.5139

8 9019 1 1 A1 TS01 0.3696 0.3750 -0.8599 15 4.1346 0.9031 0.8155 0.9994 0.2184

8 9019 1 1 BA* BS** 0.9485 0.2802 0.0000 15 12.3508 7.5625 57.1918 0.9947 0.6123

8 9019 1 2 A2 TS03 0.6984 0.2732 -1.9740 15 7.3140 1.5861 2.5157 0.9992 0.2169

8 9019 1 2 BA* BS** 0.4042 0.5291 -2.3357 15 6.0922 2.1659 4.6913 0.9955 0.3555

8 9020 1 2 BA* BS** 1.0004 0.1542 -0.7844 15 5.6627 1.8133 3.2881 0.9996 0.3202

9 4008 1 1 BA3 BS03 0.6505 0.3644 0.0000 15 9.8329 4.6889 21.9862 0.9958 0.4769

9 4008 1 2 BA* BS** 0.5737 0.8205 -0.9856 15 14.2618 2.4301 5.9052 0.9984 0.1704

9 4020 1 1 BA2 BS02 0.7663 0.7455 -1.2817 15 16.2299 2.4766 6.1335 0.9989 0.1526

9 4020 2 1 BA* BG** 0.5391 0.7107 -0.0837 15 48.4510 2.8189 7.9459 0.9995 0.0582

9 5001 1 1 BA2 BS02 0.5722 0.7457 0.0000 15 19.1067 10.7988 116.6134 0.9767 0.5652

10 0102 1 1 B2 BS02 0.4871 0.5315 -0.9233 15 7.7870 2.0947 4.3880 0.9981 0.2690

10 0102 1 2 B9 BS09 0.5034 0.5382 -0.2964 15 9.2644 1.3894 1.9306 0.9994 0.1500

10 0102 1 3 A5 TS09 0.5967 0.5457 -0.2679 15 11.1688 1.5807 2.4987 0.9994 0.1415

10 0103 1 2 B10 BS10 0.5404 0.5512 -0.6219 15 9.3859 1.5664 2.4536 0.9992 0.1669

10 0103 1 3 A9 TS17 0.5965 0.5502 -0.3580 15 10.9991 1.6094 2.5901 0.9994 0.1463

10 0103 1 1 B3 BS03 0.8096 0.1229 -0.2659 15 3.9677 2.4820 6.1605 0.9991 0.6256

10 0104 1 1 B7 BS07 0.4675 0.6321 -0.4759 15 9.7209 1.2112 1.4671 0.9994 0.1246

10 0107 1 1 B1 BS01 0.6174 0.4327 -0.9619 15 8.0131 2.3818 5.6729 0.9984 0.2972

10 0107 1 2 B8 BS08 0.4873 0.5850 -0.1576 15 10.2251 1.7274 2.9838 0.9990 0.1689

10 0107 1 3 A2 TS03 0.5169 0.5536 0.0000 15 10.8724 2.4980 6.2399 0.9983 0.2298

10 0108 1 1 B5 BS05 0.5706 0.5549 -1.3240 15 8.9576 2.1710 4.7134 0.9983 0.2424

10 0108 1 3 A14 TS28 0.5804 0.4935 -2.2309 15 8.1387 2.0369 4.1491 0.9981 0.2503

10 0112 1 1 B11 BS11 0.5580 0.5114 -0.7176 15 8.8172 2.0666 4.2710 0.9987 0.2344

10 0112 1 2 B4 BS04 0.8166 0.2650 -0.9352 15 7.2230 3.1764 10.0897 0.9983 0.4398

65
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

10 0201 1 2 B12 BS06 0.4610 0.5518 -0.4218 15 8.5228 1.8790 3.5306 0.9986 0.2205

10 0201 1 3 A17 TS33 0.5080 0.5210 0.0000 15 10.0048 2.0051 4.0205 0.9988 0.2004

10 0201 2 1 B6 BG06 0.4745 0.6041 -0.2803 15 9.9403 1.6500 2.7226 0.9990 0.1660

10 0202 1 1 B3 BG03 0.5146 0.6021 -0.3152 15 10.8641 3.0002 9.0010 0.9972 0.2762

10 0202 1 2 B9 BS03 0.5223 0.5351 -0.7636 15 8.5846 1.8367 3.3736 0.9988 0.2140

10 0204 1 3 A2 TS03 0.5974 0.4958 0.0000 15 11.5726 3.8093 14.5104 0.9969 0.3292

10 0204 2 2 B1 BG01 0.5278 0.6023 -0.5789 15 10.1254 1.4023 1.9663 0.9994 0.1385

10 0207 1 1 B10 BS04 0.7416 0.3477 -1.4035 15 8.0000 2.5807 6.6600 0.9985 0.3226

10 0207 1 3 A11 TS21 0.5275 0.4735 0.0000 15 9.5334 2.4055 5.7863 0.9984 0.2523

10 0207 2 2 B4 BG04 0.5149 0.5627 -0.4112 15 9.5877 1.3647 1.8625 0.9994 0.1423

10 0211 1 2 B11 BS05 0.6758 0.3955 -1.1849 15 8.0196 2.5438 6.4710 0.9983 0.3172

10 0211 1 3 A14 TS27 0.5715 0.4488 0.0000 15 9.6174 1.8783 3.5280 0.9992 0.1953

10 0212 1 1 B2 BG02 0.5013 0.5471 -0.3572 15 9.1963 1.3752 1.8911 0.9994 0.1495

10 0212 1 2 B8 BS02 0.5802 0.5153 -0.8925 15 8.9857 2.0707 4.2878 0.9987 0.2304

10 1201 1 1 BA** BS** 0.9346 0.5452 -1.4123 14 14.1229 4.2089 17.7146 0.9977 0.2980

10 1201 1 2 BA** BS** 0.8074 0.5196 -0.7583 15 12.9585 2.8740 8.2597 0.9988 0.2218

10 1201 2 1 BA1 BG03 0.6557 0.7192 -0.3295 14 50.8403 3.7755 14.2546 0.9993 0.0743

10 4002 2 1 BA* BG** 0.8164 0.6761 -0.3259 15 55.3411 6.6851 44.6902 0.9984 0.1208

10 4002 2 2 BA* BG** 0.6919 0.7114 -0.3183 15 52.1586 3.7721 14.2287 0.9993 0.0723

10 5004 2 1 BA2 BG02 0.6689 0.7362 -0.1552 14 58.6943 3.1649 10.0163 0.9996 0.0539

10 5004 2 2 BA* BG** 0.7930 0.6578 -0.2301 14 55.4522 5.1026 26.0365 0.9990 0.0920

10 5005 1 1 BA1 BS01 0.7943 0.6288 -1.1734 15 14.2839 2.7062 7.3232 0.9988 0.1895

10 5005 1 2 BA6 BS06 0.6353 0.5872 0.0000 15 15.0943 5.9591 35.5111 0.9936 0.3948

10 5005 2 1 BA* BG** 0.7074 0.7208 -0.2847 15 55.6949 4.2563 18.1164 0.9993 0.0764

12 0101 1 1 B5 BS05 0.5973 0.5024 0.0000 15 11.2088 1.6014 2.5645 0.9994 0.1429

12 0104 1 2 B4 BS04 0.6657 0.4732 0.0000 15 11.9236 2.6877 7.2239 0.9987 0.2254

12 0106 1 2 B2 BS02 0.6817 0.4674 -0.2324 15 11.4547 3.4737 12.0663 0.9978 0.3033

12 0107 1 2 B1 BS01 0.6119 0.6186 -0.1422 15 13.6845 2.0042 4.0167 0.9992 0.1465

12 0112 1 2 B3 BS03 0.6652 0.5724 -0.2718 15 13.2259 1.9549 3.8217 0.9993 0.1478

12 1030 1 1 A1 TS01 0.7635 0.8401 -1.0871 15 20.2395 7.2234 52.1774 0.9917 0.3569

12 1030 1 2 TP1 BS55 1.0741 0.5049 0.0000 15 20.5735 3.9253 15.4082 0.9990 0.1908

12 1030 2 1 BA* BG** 1.1649 0.5985 -0.2235 15 69.8153 3.9118 15.3021 0.9997 0.0560

12 1030 2 2 TP1 BG56 1.0276 0.5576 0.0000 15 66.2582 6.3145 39.8731 0.9991 0.0953

12 1030 3 1 BA* BG** 0.7311 0.7292 -0.0214 15 71.7623 12.6045 158.8739 0.9953 0.1756

12 1030 3 2 TP1 BG55 0.9320 0.6805 0.0000 15 82.1426 10.4899 110.0383 0.9978 0.1277

12 1370 2 1 BA* BG** 0.7739 0.7513 -0.2882 15 68.6942 11.3641 129.1437 0.9959 0.1654

12 1370 2 2 TP1 BG56 0.7039 0.6223 0.0000 15 53.6308 5.1446 26.4664 0.9989 0.0959

12 1370 3 2 TP1 BG55 0.9465 0.7224 -0.1113 15 86.1236 6.7845 46.0291 0.9991 0.0788

12 3804 1 1 A1 TS01 0.9070 0.6862 -1.3881 15 17.4432 3.6151 13.0690 0.9982 0.2073

12 3804 1 2 BA* BS** 0.9657 0.5709 -0.2772 15 19.2490 3.2761 10.7328 0.9991 0.1702

12 3811 1 1 BA* BS** 1.2626 0.2499 0.0000 15 15.9368 10.9476 119.8507 0.9937 0.6869

12 3811 1 2 A2 TS03 1.0453 0.3358 -0.8567 15 12.0285 6.0151 36.1813 0.9964 0.5001

12 3811 2 1 BA* BG** 0.8395 0.6029 -0.2223 15 51.1611 3.7397 13.9853 0.9995 0.0731

12 3811 2 2 BA* BG** 0.5468 0.6922 0.0000 15 49.2982 6.4105 41.0949 0.9976 0.1300

12 3995 1 1 A1 TS01 0.6758 0.6123 -0.3224 15 14.8891 3.4067 11.6056 0.9980 0.2288

12 3995 1 2 TP1 BS55 0.8587 0.4460 0.0000 15 14.8411 4.6674 21.7851 0.9977 0.3145

12 3995 2 2 TP1 BG56 0.8732 0.5308 0.0000 15 51.7569 3.2508 10.5679 0.9996 0.0628

12 3995 3 1 BA* BG** 0.5862 0.7820 0.0000 15 66.3438 22.8761 523.3177 0.9800 0.3448

12 3995 3 2 TP1 BG55 1.0498 0.6834 0.0000 15 93.5001 14.8367 220.1285 0.9965 0.1587

12 3996 1 1 BA* BS** 1.1853 0.5631 -0.3406 15 22.7466 3.7254 13.8786 0.9992 0.1638

12 3996 1 2 A2 TS03 0.7946 0.6264 -0.6460 15 16.2255 3.5180 12.3766 0.9982 0.2168

12 3996 2 1 BA* BG** 1.2738 0.5697 -0.2774 15 66.8735 7.1835 51.6032 0.9990 0.1074

12 3996 2 2 TP1 BG56 1.1808 0.6139 -0.1975 15 75.3561 5.1741 26.7718 0.9995 0.0687

12 3996 3 2 TP1 BG55 1.2266 0.5697 -0.2059 15 68.3164 10.4957 110.1605 0.9979 0.1536

12 3997 1 1 BA* BS** 0.9690 0.4790 -0.2001 15 16.4152 3.3933 11.5143 0.9990 0.2067

12 3997 1 2 A2 TS02 0.5257 0.7256 -1.0220 15 11.7866 1.6129 2.6014 0.9991 0.1368

66
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

12 3997 2 1 BA* BG** 0.6290 0.8039 -0.3322 15 58.9405 4.6904 21.9994 0.9990 0.0796

12 3997 2 2 TP1 BG56 0.6511 0.7805 -0.2947 15 59.1027 4.8368 23.3942 0.9990 0.0818

12 3997 3 1 BA* BG** 0.9810 0.6149 0.0000 15 87.3458 56.1647 3154.4790 0.9313 0.6430

12 3997 3 2 TP1 BG55 1.8166 0.6821 -0.3972 15 119.9431 11.8271 139.8806 0.9989 0.0986

12 4000 1 1 A1 TS01 0.7079 0.1281 0.0000 15 13.2043 12.7528 162.6327 0.9723 0.9658

12 4000 1 2 A2 TS04 0.6955 0.5877 -0.3577 15 14.1808 2.9421 8.6558 0.9985 0.2075

12 4057 1 1 A1 TS01 1.0015 0.6071 -0.2501 15 22.2544 7.1691 51.3967 0.9959 0.3221

12 4057 1 2 A2 TS03 1.1368 0.7373 -0.6570 15 28.9109 8.2250 67.6514 0.9956 0.2845

12 4057 2 1 BA* BG** 1.1329 0.5996 -0.1200 15 73.9796 3.5863 12.8614 0.9998 0.0485

12 4057 2 2 BA* BG** 1.1356 0.5978 -0.1918 15 70.0804 5.2201 27.2492 0.9994 0.0745

12 4059 1 1 A1 TS01 0.7213 0.5814 0.0000 15 17.4465 7.2319 52.3008 0.9926 0.4145

12 4059 1 2 BA* BS** 0.8018 0.3872 -0.3412 15 11.6937 6.1376 37.6695 0.9948 0.5249

12 4059 2 1 BA* BG** 1.6715 0.5319 -0.4455 15 68.3669 12.1150 146.7725 0.9979 0.1772

12 4059 2 2 BA* BG** 1.5439 0.5875 -0.3898 15 77.7682 7.6240 58.1253 0.9992 0.0980

12 4096 1 1 A1 TS01 0.5874 0.6335 0.0000 15 14.8558 4.6186 21.3318 0.9956 0.3109

12 4096 1 2 A2 TS03 0.6756 0.8444 -0.6089 15 19.4696 4.5569 20.7655 0.9964 0.2341

12 4096 2 1 BA* BG** 0.8613 0.5729 -0.1239 15 52.0244 3.7153 13.8037 0.9995 0.0714

12 4096 2 2 TP1 BG55 0.5867 0.7227 -0.1420 15 51.8209 1.8257 3.3332 0.9998 0.0352

12 4097 1 1 A1 TS01 0.8105 0.4330 -0.4685 15 11.8615 3.5622 12.6895 0.9982 0.3003

12 4097 1 2 A2 TS03 1.1159 0.5017 -1.1770 15 16.3963 4.1717 17.4031 0.9984 0.2544

12 4099 1 1 BA* BS** 0.9644 0.5428 0.0000 15 20.0649 4.5685 20.8710 0.9983 0.2277

12 4099 1 2 TP1 BS55 1.0681 0.5000 0.0000 13 21.3952 3.1893 10.1714 0.9993 0.1491

12 4099 2 1 BA* BG** 0.9989 0.6266 -0.1209 15 69.0869 3.5593 12.6688 0.9997 0.0515

12 4099 2 2 TP1 BG56 1.0873 0.5745 -0.0372 15 71.0889 3.6850 13.5794 0.9997 0.0518

12 4099 3 1 BA* BG** 1.0777 0.5905 -0.1316 15 67.4197 7.5809 57.4708 0.9987 0.1124

12 4100 1 1 A1 TS01 0.5159 0.5230 0.0000 15 10.5456 3.3422 11.1702 0.9968 0.3169

12 4100 1 2 A2 TS03 0.5491 0.5933 0.0000 15 12.4663 2.5676 6.5927 0.9984 0.2060

12 4100 2 1 BA* BG** 0.8429 0.6516 -0.3325 15 53.9442 4.1538 17.2545 0.9994 0.0770

12 4100 2 2 TP1 BG55 0.8432 0.5865 -0.0964 15 53.9411 2.6795 7.1797 0.9997 0.0497

12 4101 1 1 A1 TS01 0.4948 0.6069 -0.6083 15 9.7897 1.1690 1.3665 0.9995 0.1194

12 4101 1 2 A2 TS03 0.5166 0.5130 -0.4348 15 9.1641 3.1218 9.7458 0.9968 0.3407

12 4101 2 1 BA* BG** 1.0272 0.6928 -0.3993 15 69.2829 6.7941 46.1596 0.9989 0.0981

12 4101 2 2 TP1 BG56 0.7937 0.7175 -0.2933 15 62.0190 3.8732 15.0015 0.9995 0.0625

12 4101 3 1 BA* BG** 1.4702 0.4829 -0.2496 15 60.6487 9.7178 94.4349 0.9984 0.1602

12 4101 3 2 TP1 BG55 1.0903 0.5542 -0.0534 15 66.7345 9.8639 97.2973 0.9979 0.1478

12 4102 1 1 A1 TS02 0.5231 0.4857 0.0000 15 13.8822 10.2642 105.3530 0.9713 0.7394

12 4102 1 2 A2 TS03 0.4947 0.7199 -0.6812 15 11.7526 2.8602 8.1807 0.9971 0.2434

12 4102 2 1 BA* BG** 0.9817 0.6666 -0.1654 15 73.8272 3.6918 13.6293 0.9997 0.0500

12 4102 2 2 TP1 BG56 0.9340 0.6579 -0.1694 15 69.4508 6.6583 44.3335 0.9989 0.0959

12 4102 3 1 BA* BG** 1.0586 0.6259 -0.1294 15 73.0574 8.9601 80.2832 0.9983 0.1226

12 4102 3 2 TP1 BG55 1.0933 0.5949 0.0000 15 77.8220 11.9144 141.9525 0.9974 0.1531

12 4103 1 1 BA* BS** 0.6491 0.6565 0.0000 15 33.0970 29.0194 842.1244 0.8766 0.8768

12 4103 1 2 TP1 BS55 0.8813 0.6075 -0.3588 14 18.7143 2.0665 4.2704 0.9996 0.1104

12 4103 2 1 BA* BG** 1.3077 0.6478 0.0000 15 107.1725 12.7980 163.7882 0.9981 0.1194

12 4103 2 2 BA* BG** 1.3077 0.6478 0.0000 15 107.1725 12.7980 163.7882 0.9981 0.1194

12 4103 2 2 TP1 BG56 1.4307 0.5687 -0.2639 15 75.8032 16.7789 281.5308 0.9958 0.2213

12 4103 3 1 BA* BG** 0.2985 1.0083 0.0000 15 55.7031 7.1588 51.2488 0.9960 0.1285

12 4103 3 2 TP1 BG55 0.3982 1.0622 0.0000 15 84.1613 5.0229 25.2297 0.9991 0.0597

12 4105 1 1 BA* BS** 0.9902 0.5251 -0.3831 15 17.5494 3.3652 11.3245 0.9990 0.1918

12 4105 1 2 BA* BS** 0.8644 0.6456 -0.3097 15 19.2942 2.9455 8.6757 0.9991 0.1527

12 4105 2 1 BA* BG** 0.9147 0.6413 -0.1892 15 63.5754 2.7306 7.4561 0.9998 0.0430

12 4105 2 2 BA* BG** 0.9363 0.5835 -0.1520 15 57.1025 3.0922 9.5615 0.9997 0.0542

12 4105 3 1 BA* BG** 1.1295 0.6654 -0.2417 15 79.3272 10.5297 110.8754 0.9980 0.1327

12 4105 3 2 BA* BG** 1.2034 0.5859 0.0000 15 83.1151 16.2179 263.0190 0.9958 0.1951

12 4106 1 1 A1 TS01 0.7348 0.7280 -0.4088 15 18.9957 4.8558 23.5786 0.9965 0.2556

12 4106 1 2 A2 TS03 0.8087 0.6480 -0.2570 15 18.8068 4.1161 16.9422 0.9980 0.2189

67
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

12 4106 2 1 BA* BG** 0.7192 0.8682 0.0000 15 108.7992 58.5846 3432.1540 0.9310 0.5385

12 4106 2 2 TP1 BG56 0.9003 0.6710 -0.2002 15 66.7200 3.0393 9.2374 0.9997 0.0456

12 4106 3 1 BA* BG** 1.1197 0.5430 0.0000 15 95.5868 69.3999 4816.3440 0.9070 0.7260

12 4106 3 2 TP1 BG55 1.1762 0.7253 -0.1736 15 102.0559 6.7128 45.0612 0.9994 0.0658

12 4107 1 1 A1 TS01 0.6872 0.5268 0.0000 15 14.7283 5.9662 35.5950 0.9943 0.4051

12 4107 2 1 BA* BG** 1.1597 0.7404 -0.1617 15 106.3249 9.6466 93.0578 0.9988 0.0907

12 4108 2 1 BA* BG** 0.8199 0.6055 -0.0285 15 58.4847 2.6824 7.1953 0.9998 0.0459

12 4108 2 2 TP1 BG55 0.8789 0.6536 -0.3168 15 56.9647 3.7440 14.0179 0.9995 0.0657

12 4136 1 2 TP1 BS55 0.8085 0.4982 0.0000 15 15.1585 1.1706 1.3704 0.9998 0.0772

12 4153 2 1 BA* BG** 1.2416 0.7259 -0.2695 15 100.7053 8.0287 64.4608 0.9992 0.0797

12 4153 2 2 TP1 BG55 1.2721 0.6403 -0.2794 15 82.4839 6.7410 45.4406 0.9993 0.0817

12 4154 2 1 BA* BG** 1.1643 0.4996 0.0000 15 62.6633 9.4596 89.4846 0.9981 0.1510

12 4154 2 2 TP1 BG55 1.1360 0.4973 -0.0894 15 56.3619 7.5011 56.2666 0.9986 0.1331

12 9054 3 2 TP1 BG55 0.5994 1.0198 -0.1789 15 102.6889 8.1423 66.2965 0.9985 0.0793

13 0507 1 1 BA* BS** 0.9499 0.3930 -1.8450 15 11.4068 3.0205 9.1235 0.9985 0.2648

13 0507 2 1 BA* BG** 1.0362 0.6794 -0.2521 14 77.5624 5.6562 31.9925 0.9993 0.0729

13 0509 2 2 BA* BG** 1.0046 0.6334 -0.1394 15 70.8226 3.8759 15.0225 0.9997 0.0547

13 1001 2 1 BA* BG** 0.6046 0.8342 -0.1435 15 69.6931 2.4606 6.0544 0.9998 0.0353

13 1001 2 2 TP1 BG55 0.8146 0.7086 -0.1135 15 70.9952 3.9226 15.3864 0.9996 0.0553

13 1004 2 1 BA* BG** 0.8050 0.8342 -0.3270 15 80.9104 6.9782 48.6952 0.9988 0.0862

13 1004 2 2 TP1 BG55 0.7927 0.5838 -0.0444 15 52.7293 3.6009 12.9665 0.9995 0.0683

13 1005 2 2 TP1 BG55 0.9928 0.5953 -0.2068 15 59.5105 5.7688 33.2787 0.9991 0.0969

13 1031 2 1 BA* BG** 0.8214 0.5996 -0.4204 15 42.0999 8.9091 79.3714 0.9962 0.2116

13 1031 2 2 TP1 BG55 0.3498 1.0213 -0.6299 15 43.9569 4.9407 24.4102 0.9976 0.1124

13 3007 2 1 BA* BG** 0.9088 0.7512 -0.0006 15 94.9349 9.6074 92.3022 0.9984 0.1012

13 3007 2 2 TP1 BG55 0.9234 0.7572 0.0000 15 99.2485 3.7725 14.2316 0.9998 0.0380

13 3016 2 1 BA3 BG03 0.9990 0.6250 -0.0824 15 72.5807 7.0308 49.4323 0.9989 0.0969

13 3016 2 2 BA* BG** 0.6669 0.7000 -0.0929 15 57.7468 5.5427 30.7210 0.9987 0.0960

13 3019 2 1 BA* BG** 0.4957 0.6388 0.0000 15 40.1800 4.8493 23.5156 0.9981 0.1207

13 3019 2 2 BA* BG** 0.6419 0.6839 -0.0113 15 57.4828 4.1381 17.1239 0.9993 0.0720

13 4111 2 1 BA* BG** 0.4531 0.9688 -0.3873 15 60.2849 7.0552 49.7762 0.9973 0.1170

13 4111 2 2 TP1 BG55 1.2044 0.5349 -0.1181 15 65.0076 10.4045 108.2534 0.9978 0.1601

13 4119 2 1 BA* BG** 0.6039 0.6786 -0.0545 15 51.9033 4.9568 24.5703 0.9987 0.0955

13 4119 2 2 BA* BG** 1.0735 0.6537 -0.1402 15 79.4028 5.7009 32.4999 0.9994 0.0718

15 1003 1 1 BA* BS** 1.1801 0.2744 0.0000 15 14.2170 7.7635 60.2712 0.9964 0.5461

15 1003 1 2 TP1 BS93 0.8037 0.2713 -1.9778 15 8.4386 1.6830 2.8324 0.9993 0.1994

15 1006 1 2 TP1 BS93 0.8282 0.2533 -1.5392 15 7.6364 2.0750 4.3055 0.9991 0.2717

16 1005 1 1 BA* BS** 0.8133 0.1709 -0.8203 15 5.0351 1.8550 3.4410 0.9994 0.3684

16 1005 1 2 TP1 BS92 0.5412 0.4771 -1.4878 15 7.4495 2.3277 5.4183 0.9977 0.3125

16 1005 2 1 BA* BG** 0.4444 0.6073 -0.0347 15 31.3161 3.0125 9.0752 0.9990 0.0962

16 1009 1 1 BA* BS** 0.6956 0.3369 -1.2859 15 7.1661 2.1588 4.6603 0.9988 0.3013

16 1009 1 2 TP1 BS92 0.5343 0.5533 -2.0868 15 8.0575 2.0946 4.3874 0.9978 0.2600

16 1010 1 1 BA* BS** 0.4761 0.7369 -0.7215 15 10.9948 1.4424 2.0805 0.9992 0.1312

16 1010 1 2 TP1 BS92 0.4972 0.6362 -0.8064 15 9.7003 1.8796 3.5330 0.9987 0.1938

16 1020 1 1 BA* BS** 0.6778 0.2134 -0.4236 15 4.8472 2.0117 4.0467 0.9991 0.4150

16 1020 1 2 TP1 BS93 0.5297 0.5317 -2.4055 15 7.8619 2.0733 4.2987 0.9975 0.2637

16 3017 1 1 BA* BS** 0.6379 0.4009 -1.4634 15 7.6108 2.4823 6.1619 0.9981 0.3262

16 3017 1 2 BA* BS** 0.5082 0.5484 -1.0714 15 8.1807 2.2643 5.1271 0.9979 0.2768

16 3023 1 1 BA* BS** 0.6797 0.2082 -1.0948 15 5.0972 1.7088 2.9202 0.9992 0.3353

16 3023 1 2 BA* BS** 0.5490 0.5495 -1.2113 15 8.6421 2.2628 5.1203 0.9981 0.2618

16 3023 2 1 BA* BG** 0.8836 0.2666 -0.1515 15 16.9276 3.1961 10.2148 0.9992 0.1888

16 5025 1 2 BA* BS** 0.8766 0.2593 -0.9251 15 7.1760 2.3484 5.5150 0.9992 0.3273

16 6027 1 2 TP1 BS93 1.4416 0.2028 0.0000 15 16.3454 12.3673 152.9498 0.9937 0.7566

16 9032 1 2 TP1 BS92 0.4390 0.1143 -4.2765 15 7.0326 2.1370 4.5666 0.9933 0.3039

16 9034 1 2 TP1 BS91 0.5695 0.7125 -1.7816 15 10.8869 2.3033 5.3054 0.9980 0.2116

17 1002 1 1 A1 TS01 1.3479 0.2225 -1.7115 15 12.2467 1.5635 2.4446 0.9998 0.1277

68
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

17 1002 1 2 TP* BS** 0.7694 0.7533 -4.0159 15 14.2552 3.3959 11.5320 0.9956 0.2382

17 1003 1 1 BA* BS** 0.8986 0.2605 -1.6956 15 8.4724 0.9582 0.9182 0.9998 0.1131

17 1003 1 2 TP* BS** 0.3314 0.7253 -4.3621 15 6.2427 2.3750 5.6405 0.9872 0.3804

17 4074 1 1 BA* BS** 0.6099 0.2265 -0.5543 15 4.4508 1.7885 3.1987 0.9991 0.4018

17 4074 1 2 BA* BS** 1.6972 0.3568 -0.8437 15 17.5860 1.9087 3.6430 0.9999 0.1085

17 4082 1 1 A1 TS01 0.9277 0.0669 -1.7470 15 8.4504 0.8743 0.7644 0.9999 0.1035

17 4082 1 2 A2 TS03 0.8998 0.2462 -3.5207 15 12.6540 1.6305 2.6587 0.9992 0.1289

17 5020 1 1 A1 TS01 0.4670 0.1470 -3.8974 15 6.9946 0.9860 0.9722 0.9988 0.1410

17 5020 1 2 A2 TS03 1.1749 0.2575 -2.7268 15 14.3371 1.2611 1.5903 0.9998 0.0880

17 5151 1 1 BA* BS** 0.6819 0.7680 -0.7372 15 16.5946 2.5366 6.4344 0.9988 0.1529

17 5151 1 2 BA* BS** 0.7360 0.7417 -1.1850 15 15.6336 2.3824 5.6759 0.9990 0.1524

17 5217 1 1 A1 TS01 0.6774 0.1698 -3.3220 15 9.2644 1.1282 1.2728 0.9994 0.1218

17 5217 2 1 BA* BG** 0.8709 0.6651 -0.0736 15 69.5484 3.1945 10.2050 0.9997 0.0459

17 5217 2 2 BA* BG** 0.7451 0.6239 0.0000 15 56.5062 4.3643 19.0473 0.9993 0.0772

17 5423 1 1 A1 TS01 1.0361 0.1443 -1.6573 15 8.9427 1.3387 1.7921 0.9998 0.1497

17 5423 1 2 A2 TS03 1.4215 0.3107 -1.6122 15 14.0604 1.9613 3.8465 0.9997 0.1395

17 5453 1 1 A1 TS01 0.8921 0.3810 -4.5791 15 14.6102 3.1721 10.0621 0.9963 0.2171

17 5453 1 2 A2 TS03 1.2888 0.1400 -2.6957 15 15.7843 1.1936 1.4247 0.9998 0.0756

17 5843 1 1 A1 TS01 0.9798 0.1512 -1.9692 15 9.4602 1.0294 1.0596 0.9998 0.1088

17 5843 1 2 A2 TS03 1.3123 0.1087 -1.4823 15 10.4129 1.3978 1.9538 0.9998 0.1342

17 5849 1 1 BA* BS** 1.5837 0.3030 -1.2764 15 14.5645 2.2465 5.0468 0.9997 0.1542

17 5849 1 2 TP* BS** 1.3882 0.3634 -2.2505 15 16.5394 3.1663 10.0255 0.9992 0.1914

17 5854 1 1 BA* BS** 0.2378 0.0231 -2.0798 15 3.3094 2.2278 4.9629 0.9856 0.6732

17 5854 1 2 A2 TS03 1.1069 0.1574 -2.2795 15 11.9754 1.0224 1.0453 0.9999 0.0854

17 5869 1 1 BA* BS** 0.9555 0.5101 -2.8228 14 14.1501 3.1949 10.2077 0.9979 0.2258

17 5908 1 1 BA* BS** 1.2271 0.3164 -1.8914 15 12.7384 0.9803 0.9609 0.9999 0.0770

17 5908 1 2 A2 TS03 1.1184 0.2961 -3.5981 15 16.0926 1.8435 3.3986 0.9994 0.1146

17 6050 1 1 BA* BS** 0.5312 0.4764 -5.0924 15 8.9320 1.4586 2.1276 0.9975 0.1633

17 6050 1 2 TP1 BS** 1.3150 0.2621 -0.9935 14 9.3291 1.0072 1.0144 0.9999 0.1080

17 6050 2 1 BA* BG** 0.8542 0.6403 0.0000 15 67.3355 6.1253 37.5189 0.9990 0.0910

17 6050 2 2 TP* BG** 1.0270 0.5903 0.0000 15 71.1082 5.7426 32.9779 0.9993 0.0808

17 6050 3 1 BA* BG** 1.0193 0.7123 -0.0121 15 96.3697 5.9577 35.4946 0.9994 0.0618

17 6050 3 2 TP* BG** 1.2085 0.5660 0.0000 14 74.4341 6.2652 39.2524 0.9994 0.0842

17 7937 1 1 BA* BS** 0.7524 0.3875 -2.9406 15 10.3680 2.7066 7.3259 0.9975 0.2611

17 7937 1 2 A2 TS03 0.4952 0.4619 -4.4102 15 8.3478 2.7544 7.5866 0.9914 0.3300

17 7937 2 1 BA* BG** 0.6658 0.5978 -0.0450 15 45.4803 8.8611 78.5189 0.9959 0.1948

17 7937 2 2 TP* BG** 0.5436 0.7482 -0.0841 15 52.4847 8.8776 78.8126 0.9957 0.1691

17 9267 1 2 BA* BS** 0.6401 0.6992 -0.5095 15 14.7535 1.3112 1.7193 0.9997 0.0889

17 9327 1 1 A2 TS03 0.7987 0.2157 -3.6060 15 11.3381 0.8968 0.8042 0.9997 0.0791

17 9327 1 1 BA* BS** 0.3284 0.2792 -3.6669 14 5.5589 3.1555 9.9571 0.9787 0.5676

17 9327 2 1 BA* BG** 0.9241 0.5903 0.0000 15 64.0460 2.9739 8.8442 0.9998 0.0464

17 9327 2 2 TP* BG** 0.8682 0.5603 -0.0696 15 52.2651 7.1054 50.4874 0.9982 0.1360

18 1028 1 1 A1 TS01 1.0185 0.2041 -3.9905 15 15.4858 3.0842 9.5120 0.9976 0.1992

18 1028 1 2 A2 TS03 1.4511 0.2260 -0.8881 15 10.0773 1.0247 1.0499 0.9999 0.1017

18 1037 1 1 BA* BS** 0.2130 0.4021 0.0000 15 4.3622 3.0453 9.2739 0.9839 0.6981

18 1037 1 2 TP* BS** 0.3652 0.3284 -2.6868 15 5.9362 4.0843 16.6813 0.9775 0.6880

18 2008 1 2 A2 TS03 2.2960 0.3122 -2.1867 14 21.8729 2.7116 7.3526 0.9998 0.1240

18 2009 2 1 BA1 BG01 1.3611 0.4370 -0.5682 14 37.4322 13.9977 195.9342 0.9941 0.3739

18 2009 2 2 TP* BG** 2.3228 0.3086 -1.1605 13 36.0690 22.8971 524.2750 0.9892 0.6348

18 3002 1 1 A1 TS01 1.2879 0.3377 -1.7600 15 13.6057 1.6677 2.7812 0.9998 0.1226

18 3002 1 2 A2 TS03 0.9382 0.2318 -2.0386 15 9.5444 1.0347 1.0707 0.9998 0.1084

18 3002 2 1 BA* BG** 0.9557 0.6382 0.0000 14 69.4903 3.1152 9.7045 0.9998 0.0448

18 3002 2 2 TP* BG** 1.0218 0.6626 -0.0370 14 76.4659 4.3353 18.7947 0.9996 0.0567

18 3003 1 1 BA* BS** 0.3717 0.7565 -1.5394 15 8.9240 4.9152 24.1593 0.9807 0.5508

18 3003 1 2 TP* BS** 0.4990 0.8898 -0.9009 15 14.0401 2.2433 5.0324 0.9983 0.1598

18 3030 1 1 A1 TS01 1.9430 0.3907 -1.6994 15 22.5046 5.3663 28.7969 0.9990 0.2385

69
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

18 3030 1 2 TP* BS** 1.1469 0.3549 -4.5930 15 18.2983 2.5840 6.6769 0.9985 0.1412

18 3031 1 1 A1 TS01 1.3715 0.1639 -1.9271 15 13.1501 1.3828 1.9121 0.9998 0.1052

18 3031 1 2 A2 TS03 0.8333 0.2519 -4.4471 15 13.0738 1.6140 2.6049 0.9989 0.1235

18 4021 1 1 A1 TS01 1.0102 0.5087 -5.5454 15 17.6751 4.9346 24.3500 0.9914 0.2792

18 4021 1 2 TP* BS** 1.3495 0.3534 -4.1962 15 20.7422 2.4830 6.1655 0.9991 0.1197

18 4042 1 1 BA* BS** 1.2089 0.3601 -1.8826 15 13.8914 2.8705 8.2395 0.9992 0.2066

18 4042 1 2 BA* BS** 0.6107 0.6534 -1.3516 15 11.2059 2.3325 5.4403 0.9984 0.2081

18 5022 1 1 BA* BS** 0.7935 0.6230 -2.7372 13 11.2278 2.9441 8.6679 0.9974 0.2622

18 5022 1 2 A2 TS04 1.5391 0.2834 -1.3788 15 13.8058 1.8257 3.3333 0.9998 0.1322

18 5043 1 1 BA* BS** 1.1261 0.2032 -2.3606 15 12.4491 1.2976 1.6838 0.9998 0.1042

18 5043 1 2 BA* BS** 0.8842 0.3176 -4.2421 15 13.7885 2.8014 7.8476 0.9972 0.2032

18 5043 2 1 BA* BG** 0.6851 0.7196 -0.2192 15 56.5018 3.3685 11.3468 0.9995 0.0596

18 5043 2 2 BA* BG** 0.5903 0.7128 -0.1781 15 49.1084 5.7173 32.6873 0.9982 0.1164

18 5518 1 1 BA* BS** 0.6409 0.7795 -0.9907 15 15.1877 3.1805 10.1157 0.9977 0.2094

18 5518 1 2 BA* BS** 0.5421 0.8955 -2.2834 15 12.2338 1.6973 2.8807 0.9987 0.1387

18 5518 2 1 BA* BG** 0.8349 0.6897 -0.1683 14 61.7587 4.0735 16.5930 0.9995 0.0660

18 5518 2 2 BA* BG** 1.0768 0.4659 0.0000 15 52.0478 8.0773 65.2426 0.9982 0.1552

18 5528 1 1 BA* BS** 0.5961 1.3450 -5.0231 15 15.8556 5.7838 33.4519 0.9792 0.3648

18 5528 2 1 BA* BG** 0.5415 0.7558 -0.2264 14 46.4155 2.8352 8.0383 0.9995 0.0611

18 5528 2 2 BA* BG** 0.5918 0.7527 -0.2666 15 51.4652 3.1689 10.0419 0.9995 0.0616

18 5538 1 1 BA* BS** 0.6547 0.7629 -0.8125 15 15.6929 3.5963 12.9334 0.9974 0.2292

18 5538 1 2 BA* BS** 0.6262 0.7890 -0.8639 15 15.3877 2.2576 5.0969 0.9989 0.1467

18 5538 2 1 BA* BG** 0.6834 0.5664 -0.1700 15 38.8131 6.4711 41.8752 0.9975 0.1667

18 5538 2 2 BA* BG** 0.7562 0.4858 -0.1272 15 35.0845 6.5490 42.8899 0.9975 0.1867

18 6012 1 1 A1 TS01 1.4520 0.1806 -2.2634 15 15.7662 1.1087 1.2292 0.9999 0.0703

18 6012 1 2 A2 TS03 1.3473 0.2058 -3.0076 15 17.5070 1.3145 1.7279 0.9998 0.0751

18 9020 1 1 A1 TS02 1.8770 0.3469 -0.7316 15 19.4777 3.0350 9.2112 0.9997 0.1558

18 9020 1 2 A2 TS04 1.5309 0.1642 -1.3203 15 11.3356 1.6831 2.8328 0.9998 0.1485

18 9020 2 1 BA* BG** 0.8442 0.5724 -0.0204 15 54.5464 6.2601 39.1891 0.9987 0.1148

18 9020 2 2 BA* BG** 0.6308 0.7969 -0.1728 15 64.1682 4.6479 21.6026 0.9992 0.0724

19 0102 1 3 A5 TS10 1.4885 0.2082 -0.7352 14 9.2961 0.7045 0.4963 1.0000 0.0758

19 0103 1 3 A1 TS02 2.1248 0.2735 0.0000 15 21.6801 3.3727 11.3749 0.9998 0.1556

19 0106 1 3 A13 TS26 0.8838 0.1107 -3.3215 15 12.2909 1.2949 1.6768 0.9995 0.1054

19 0110 1 3 A10 TS20 1.2411 0.1176 -1.4465 15 9.7311 1.8654 3.4797 0.9997 0.1917

19 0110 1 3 A11 TS22 1.3405 0.1687 -1.1501 15 9.0827 1.5498 2.4019 0.9998 0.1706

19 0112 1 3 A9 TS18 1.6401 0.1607 -0.4726 15 8.2393 1.6502 2.7231 0.9999 0.2003

19 1044 1 1 BA* BS** 1.6966 0.2525 -1.3993 12 12.4633 1.4705 2.1623 0.9999 0.1180

19 1044 1 2 A2 TS03 2.0502 0.2428 -0.8598 15 15.2075 2.8095 7.8932 0.9998 0.1847

19 3006 1 1 A1 TS01 0.9369 0.1784 -3.9041 15 13.9932 1.9829 3.9321 0.9988 0.1417

19 3006 1 2 A2 TS03 1.4405 0.2547 -2.2705 15 15.9696 1.7289 2.9892 0.9998 0.1083

19 3009 1 1 BA* BS** 0.7151 0.7334 -1.4018 15 14.5448 2.0739 4.3010 0.9991 0.1426

19 3009 1 2 BA* BS** 0.8679 0.4185 -1.8791 14 10.7663 2.3589 5.5645 0.9989 0.2191

19 3009 2 2 BA* BG** 0.9315 0.4114 -0.5268 15 24.1217 7.9768 63.6300 0.9959 0.3307

19 3009 2 1 BA* BG** 2.1712 0.3023 -0.3806 15 38.1122 4.4926 20.1835 0.9997 0.1179

19 3028 1 1 BA* BS** 1.1183 0.2181 -2.5405 15 12.9861 1.2676 1.6069 0.9998 0.0976

19 3028 1 2 BA* BS** 0.8075 0.2894 -3.0993 15 10.5754 1.2393 1.5358 0.9995 0.1172

19 3033 1 1 A1 TS01 1.2537 0.2884 -2.1453 15 13.4837 2.4316 5.9129 0.9994 0.1803

19 3033 1 2 A2 TS03 1.4562 0.2610 -1.8767 15 14.4529 2.0627 4.2547 0.9997 0.1427

19 3055 1 1 A1 TS01 0.7844 0.1595 -2.7298 15 9.4542 0.7456 0.5560 0.9998 0.0789

19 3055 1 2 TP* BS** 1.6817 0.2754 -1.7494 15 16.1413 1.5473 2.3941 0.9999 0.0959

19 3055 2 1 BA* BG** 0.8248 0.7487 -0.1108 15 80.6146 7.5650 57.2297 0.9986 0.0938

19 3055 2 2 TP* BG** 0.6546 0.7635 -0.0902 15 65.5517 4.1582 17.2907 0.9994 0.0634

19 5042 1 2 BA* BS** 0.9288 0.5303 -2.7635 15 13.7502 2.3804 5.6664 0.9988 0.1731

19 5042 1 1 BA* BS** 1.2637 0.3349 -1.3799 15 12.7373 2.2182 4.9203 0.9996 0.1741

19 5046 1 1 BA* BS** 0.9709 0.6113 -1.9458 15 15.6701 2.9761 8.8572 0.9987 0.1899

19 5046 1 2 TP* BS** 1.0231 0.5057 -1.7480 15 14.2972 3.2284 10.4228 0.9987 0.2258

70
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

19 6049 1 1 A1 TS01 0.8254 0.1955 -3.3212 15 11.3103 2.1609 4.6693 0.9985 0.1911

19 6049 1 2 TP* BS** 1.0164 0.1962 -3.3031 15 13.8351 1.5015 2.2546 0.9995 0.1085

19 6150 1 1 BA* BS* 1.2065 0.2198 -1.2748 15 9.2849 0.4994 0.2494 1.0000 0.0538

19 6150 1 2 A2 TS03 0.4963 0.6050 -4.1992 15 8.4976 1.7196 2.9569 0.9970 0.2024

19 6150 2 1 BA* BG** 1.5332 0.3766 -0.5671 14 33.7438 13.8003 190.4490 0.9948 0.4090

19 6150 2 2 BA* BG** 1.6464 0.4173 -0.5915 14 40.4489 12.1557 147.7598 0.9967 0.3005

19 9126 1 1 A1 TS01 1.2189 0.3434 -2.9238 15 16.0036 2.5706 6.6081 0.9991 0.1606

19 9126 1 2 A2 TS03 0.8953 0.3317 -4.0784 15 13.3944 1.6416 2.6948 0.9991 0.1226

19 9126 3 1 BA* BG** 0.7340 0.8203 -0.1035 15 83.6418 8.1848 66.9905 0.9984 0.0979

19 9126 3 2 TP* BG** 0.8565 0.5750 0.0000 15 56.6504 11.3103 127.9232 0.9958 0.1997

20 0101 1 3 A5 TS12 0.9228 0.2176 -2.1077 14 9.1198 1.1220 1.2589 0.9998 0.1230

20 0110 1 3 A23 TS53 1.0282 0.3089 -2.0891 15 11.2622 2.2341 4.9913 0.9993 0.1984

20 0203 1 2 B1 BS01 1.1307 0.2483 -1.0144 15 8.7788 1.4964 2.2392 0.9998 0.1705

20 1005 1 1 A1 TS01 0.9171 0.0998 -2.8131 15 11.7648 0.8882 0.7888 0.9998 0.0755

20 1005 1 2 A2 TS03 1.0058 0.2793 -3.0416 15 13.2970 1.2214 1.4917 0.9997 0.0919

20 1006 1 1 BA* BS* 1.0688 0.3618 -2.5638 15 13.5425 2.8128 7.9117 0.9988 0.2077

20 1006 1 2 TP* BS** 0.5343 0.3354 -2.1834 15 6.4991 2.5681 6.5950 0.9963 0.3951

20 1009 1 2 TP* BS** 1.4287 0.2558 -2.7932 15 17.8480 2.7120 7.3549 0.9993 0.1519

20 1009 1 1 BA* BS** 0.5444 0.7363 -1.9292 15 10.6355 2.4440 5.9731 0.9974 0.2298

20 1010 1 1 A1 TS01 0.8326 0.3336 -2.3971 15 9.9990 1.6626 2.7641 0.9993 0.1663

20 1010 1 2 A2 TS03 0.9594 0.3163 -2.9697 15 12.6818 2.0378 4.1528 0.9991 0.1607

20 3013 1 1 A1 TS01 1.1909 0.1432 -1.1052 15 7.6014 0.8713 0.7592 0.9999 0.1146

20 3013 1 2 BA* BS** 1.0051 0.1964 -1.7240 15 9.1026 1.4938 2.2315 0.9997 0.1641

20 3015 1 1 A1 TS01 1.1866 0.1883 -1.1641 15 8.3484 1.1655 1.3584 0.9999 0.1396

20 3015 1 2 BA* BS** 0.9001 0.2254 -1.3863 15 7.3082 0.8490 0.7207 0.9999 0.1162

20 3060 1 1 BA* BS** 1.0383 0.3049 -1.9478 15 10.9510 1.4304 2.0462 0.9997 0.1306

20 3060 1 2 A2 TS03 0.8682 0.2030 -2.7581 15 10.6802 0.8186 0.6701 0.9998 0.0766

20 4016 1 1 BA* BS** 1.3182 0.1903 -0.9351 15 8.4555 1.0999 1.2099 0.9999 0.1301

20 4016 1 2 A2 TS03 0.8293 0.2439 -3.0881 15 10.9427 1.0727 1.1506 0.9996 0.0980

20 4016 2 1 BA* BG** 0.9342 0.5967 0.0000 15 65.9965 4.3712 19.1073 0.9995 0.0662

20 4052 1 1 BA* BS** 0.6744 0.5186 -1.9799 13 9.6190 1.3937 1.9425 0.9994 0.1449

20 4052 1 2 BA* BS** 0.6321 0.6997 -0.7172 15 13.8640 2.4230 5.8709 0.9987 0.1748

20 4053 1 1 BA* BS** 0.8396 0.4462 -3.5158 15 12.6201 3.0494 9.2991 0.9971 0.2416

20 4053 1 2 A2 TS03 0.8677 0.2452 -5.5103 15 14.7351 2.5128 6.3142 0.9969 0.1705

20 4054 1 1 A1 TS01 1.0542 0.1421 -1.7260 15 9.2772 0.8409 0.7071 0.9999 0.0906

20 4054 1 2 BA* BS** 0.9615 0.2514 -0.9968 15 7.5498 1.5755 2.4823 0.9997 0.2087

20 4063 1 1 A1 TS02 0.6180 0.3951 -4.0257 15 9.5802 2.1407 4.5824 0.9969 0.2234

20 4063 1 2 BA* BS** 0.8238 0.6084 -2.3082 15 13.1022 2.1113 4.4577 0.9990 0.1611

20 4067 1 1 BA* BS** 0.5004 0.1924 -5.4471 15 8.3854 0.8444 0.7131 0.9989 0.1007

20 4067 1 2 A2 TS04 1.4136 0.1418 -1.2489 15 9.9226 1.7860 3.1896 0.9998 0.1800

20 4067 3 1 BA* BG** 0.5290 0.8166 -0.2554 13 47.7971 3.0617 9.3741 0.9995 0.0641

20 4067 3 2 TP* BG** 0.7695 0.6528 -0.0573 14 56.2055 2.8450 8.0940 0.9997 0.0506

20 6026 1 1 A1 TS01 1.3415 0.1781 -1.0188 15 8.7244 1.9034 3.6229 0.9998 0.2182

20 6026 1 2 A2 TS04 1.4843 0.2690 -0.5641 15 12.1988 1.9063 3.6340 0.9998 0.1563

20 7073 1 1 BA* BS** 0.7014 0.6221 -0.6926 15 13.5394 1.8848 3.5526 0.9993 0.1392

20 7073 1 2 BA* BS** 0.6359 0.7141 -0.7743 15 14.1462 1.2418 1.5421 0.9997 0.0878

20 7073 2 2 BA* BG** 1.0509 0.4321 0.0000 15 45.7356 4.2702 18.2344 0.9994 0.0934

20 7073 2 1 BA* BG** 0.6247 0.7330 -0.2781 15 51.2025 2.2313 4.9787 0.9997 0.0436

20 7085 1 1 A1 TS01 0.6522 0.2634 -3.6317 15 9.2618 0.8985 0.8073 0.9995 0.0970

20 7085 1 2 A2 TS03 1.0001 0.1866 -2.0313 15 9.9657 0.8299 0.6887 0.9999 0.0833

20 7085 2 2 BA* BG** 0.9166 0.6488 -0.2080 15 62.9350 5.1951 26.9889 0.9992 0.0825

20 7085 2 1 BA* BG** 1.1409 0.5790 -0.4235 15 54.8568 7.9566 63.3077 0.9983 0.1450

20 9037 1 1 A1 TS02 0.6495 0.4006 -3.3312 15 9.2880 1.9667 3.8678 0.9980 0.2117

20 9037 1 2 A2 TS03 0.8944 0.4029 -3.3992 15 12.8256 2.0650 4.2644 0.9988 0.1610

20 9037 2 1 BA* BG** 0.7377 0.7179 0.0000 15 70.8941 5.5094 30.3536 0.9991 0.0777

20 9037 2 2 BA* BG** 1.5178 0.3971 0.0000 15 58.9320 4.4759 20.0333 0.9997 0.0759

71
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

21 1010 1 1 BA* BS** 1.3140 0.3828 -1.5136 14 14.3787 1.6804 2.8238 0.9998 0.1169

21 1010 1 2 TP* BS** 1.5693 0.2436 -1.3492 15 13.1105 1.7836 3.1812 0.9998 0.1360

21 1010 2 1 BA* BG** 0.9395 0.7345 0.0000 15 93.9695 6.0900 37.0880 0.9994 0.0648

21 1010 2 2 TP* BG** 1.0459 0.6707 0.0000 15 89.6545 10.0747 101.5000 0.9983 0.1124

21 1034 1 1 BA* BS** 1.2691 0.1488 -1.4909 15 10.5483 2.9698 8.8194 0.9992 0.2815

21 1034 1 2 TP* BS** 1.5143 0.2963 -0.8791 15 13.4625 2.5721 6.6158 0.9997 0.1911

21 3016 1 1 BA* BS** 1.2755 0.3655 -3.9170 15 19.1833 1.5922 2.5350 0.9996 0.0830

21 3016 1 2 BA* BS** 1.4503 0.2515 -2.0894 15 15.4633 2.7497 7.5611 0.9994 0.1778

21 3016 3 1 BA* BG** 1.2765 0.6587 -0.2201 14 85.0612 5.2495 27.5576 0.9996 0.0617

21 4025 2 1 BA* BG** 1.8262 0.5918 -0.8477 14 68.0482 21.4827 461.5070 0.9933 0.3157

21 4025 2 2 BA* BG** 1.0295 0.5355 0.0000 15 61.0209 10.5917 112.1837 0.9972 0.1736

21 6040 1 1 BA* BS** 1.8454 0.1822 0.0000 15 17.9828 13.0745 170.9435 0.9957 0.7271

21 6040 1 2 TP* BS** 1.7626 0.3400 -0.1478 12 21.5062 3.0622 9.3770 0.9997 0.1424

21 6040 2 1 BA* BG** 0.7885 0.7352 -0.0396 15 76.3275 5.6096 31.4680 0.9992 0.0735

21 6040 2 2 TP* BG** 0.9805 0.6050 0.0000 15 70.4505 6.2345 38.8694 0.9991 0.0885

21 6043 1 2 TP1 BS** 1.1778 0.2814 -1.5852 15 11.1283 2.1033 4.4240 0.9996 0.1890

21 6043 2 1 BA* BG** 0.8953 0.7648 0.0000 15 95.9820 6.9636 48.4916 0.9991 0.0726

21 6043 2 2 TP* BG** 0.7641 0.7552 -0.0122 15 78.9523 7.0479 49.6732 0.9987 0.0893

22 0113 1 1 B6 BS06 1.0059 0.1915 0.0000 15 9.4617 6.2752 39.3779 0.9966 0.6632

22 0113 3 2 B12 BG12 0.7163 0.2062 -0.6477 15 4.8137 1.7752 3.1514 0.9994 0.3688

22 0117 1 2 B5 BS05 0.7686 0.1458 0.0000 15 4.8028 2.5121 6.3109 0.9991 0.5231

22 0118 1 2 B4 BS04 0.8679 0.1866 0.0000 15 7.4066 4.4189 19.5269 0.9978 0.5966

22 0118 2 1 B10 BG10 0.6805 0.3283 -1.0674 15 6.6490 1.6997 2.8890 0.9993 0.2556

22 0119 1 2 B1 BS01 0.6042 0.2110 -0.2100 15 4.4753 1.6793 2.8201 0.9993 0.3752

22 0119 2 1 B7 BG07 0.4108 0.5374 -0.7097 15 6.8020 1.1648 1.3567 0.9992 0.1712

22 0121 1 2 B2 BS02 0.4437 0.4391 -0.4960 15 6.3456 1.7877 3.1957 0.9985 0.2817

22 0124 1 1 B3 BS03 0.8404 0.1335 0.0000 15 5.1390 3.0860 9.5235 0.9988 0.6005

22 4001 1 1 BA* BS** 1.4944 0.8507 -2.3484 15 32.2921 11.1757 124.8952 0.9923 0.3461

22 4001 1 2 BA* BS** 1.3809 0.3573 -0.5343 15 15.8033 4.5453 20.6596 0.9990 0.2876

22 4001 2 1 BA* BG** 0.6173 0.6772 -0.3508 15 41.1482 6.8960 47.5550 0.9969 0.1676

23 0506 1 2 TP1 BS55 0.5087 0.5699 -0.0732 15 10.6158 1.2952 1.6776 0.9995 0.1220

23 0506 2 2 TP1 BG56 0.4848 0.5852 -0.0566 15 31.7366 1.3996 1.9590 0.9998 0.0441

23 1012 1 1 BA* BS** 0.6022 0.5781 0.0000 15 13.3442 2.7335 7.4722 0.9985 0.2048

23 1012 1 2 TP BS55 0.6974 0.6371 -1.5406 15 12.6867 4.1763 17.4412 0.9958 0.3292

23 1012 2 1 BA* BG** 0.5464 0.7491 -0.2655 14 48.4540 3.9740 15.7924 0.9990 0.0820

23 1026 1 2 TP BS55 0.8330 0.6087 -0.9905 15 14.8574 1.8059 3.2613 0.9995 0.1215

23 3013 1 2 BA* BS** 0.6755 0.6278 -0.4215 15 14.2368 1.9750 3.9005 0.9993 0.1387

23 3013 2 1 BA* BG** 0.6736 0.6746 -0.1825 15 51.0720 3.2040 10.2659 0.9995 0.0627

23 3014 1 1 BA* BS** 0.7205 0.7498 -0.9058 15 16.4056 2.2938 5.2613 0.9991 0.1398

23 7023 1 1 BA** BS** 0.6913 0.6144 0.0000 14 16.4290 3.1704 10.0515 0.9985 0.1930

23 7023 1 2 BA* BS** 0.7092 0.6402 0.0000 15 17.3940 4.0928 16.7511 0.9976 0.2353

24 1632 2 1 BA* BG** 0.5811 0.6991 -0.0579 15 52.1860 2.9777 8.8666 0.9995 0.0571

24 1632 2 2 TP BG55 0.7274 0.6283 -0.2507 15 46.4612 4.1235 17.0034 0.9992 0.0888

24 1634 1 2 TP BS55 0.8622 0.6097 -0.6792 15 16.6796 3.7889 14.3557 0.9982 0.2272

24 1634 2 1 BA1 BG03 1.2617 0.5666 -0.4912 15 55.4963 11.5692 133.8464 0.9969 0.2085

24 2401 3 1 BA2 BG02 1.1044 0.4425 -0.0430 15 48.3967 11.6601 135.9578 0.9961 0.2409

24 2401 3 2 TP BG55 1.3128 0.5367 -0.4288 15 55.4645 13.6206 185.5200 0.9959 0.2456

24 2805 2 1 BA* BG** 0.8228 0.5139 -0.1333 15 41.6713 3.4960 12.2221 0.9994 0.0839

24 5807 2 1 BA* BG** 0.8824 0.5890 -0.2614 15 49.5448 7.9898 63.8367 0.9976 0.1613

24 5807 2 2 BA5 BG05 0.8888 0.5661 -0.0848 15 54.0839 8.5424 72.9731 0.9976 0.1579

25 1002 1 2 TP BS55 0.7155 0.6381 -0.8656 15 14.1209 3.4568 11.9492 0.9978 0.2448

25 1004 1 1 BA3 BS03 0.6026 0.6496 0.0000 14 15.8268 4.9782 24.7828 0.9953 0.3145

26 0120 1 2 B1 BS01 1.4818 0.3113 -2.9054 13 18.9804 1.3988 1.9567 0.9998 0.0737

26 0121 2 1 B9 BG01 1.0702 0.7188 -0.0101 14 94.1332 18.6328 347.1815 0.9945 0.1979

26 0122 1 1 B4 BS04 1.4366 0.2674 -1.4395 15 12.6822 1.5319 2.3466 0.9998 0.1208

26 0218 1 2 B6 BS06 1.4717 0.2640 -1.5980 15 13.6706 2.1813 4.7582 0.9997 0.1596

72
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

26 0219 1 1 B7 BS07 1.3374 0.3864 -2.0730 13 16.3868 1.8866 3.5591 0.9997 0.1151

26 0219 2 2 B14 BG14 1.4301 0.3172 -2.8978 15 18.5673 1.8217 3.3184 0.9997 0.0981

26 0220 1 1 B3 BS03 1.3238 0.2598 -3.4381 14 18.7605 1.3376 1.7890 0.9998 0.0713

26 0222 1 2 B5 BS05 1.0187 0.4008 -4.7503 14 16.9487 2.5285 6.3933 0.9981 0.1492

26 0224 1 2 B2 BS02 1.1615 0.2411 -3.9661 15 17.3543 1.8745 3.5138 0.9993 0.1080

26 0224 2 2 B9 BG09 1.4414 0.3682 -2.1885 14 14.3291 0.8665 0.7509 0.9999 0.0605

26 1001 1 1 BA* BS** 0.7635 0.6178 -0.6505 15 15.6683 5.5531 30.8369 0.9952 0.3544

26 1001 2 1 BA* BG** 1.2137 0.5162 0.0000 15 68.2490 8.0786 65.2642 0.9988 0.1184

26 1001 2 2 TP* BG** 0.9975 0.6751 -0.0387 15 84.1689 3.2104 10.3066 0.9998 0.0381

26 1004 1 1 BA* BS** 0.9051 0.6812 -1.0068 14 18.9593 4.0895 16.7237 0.9980 0.2157

26 1004 1 2 TP* BS** 0.8749 0.6533 -0.9488 15 18.2227 6.8059 46.3206 0.9941 0.3735

26 1004 2 2 TP* BG** 0.6441 0.7193 -0.0274 15 61.1261 3.4596 11.9692 0.9995 0.0566

26 1010 1 1 BA* BS** 0.2186 0.7104 0.0000 15 7.3937 4.4017 19.3749 0.9726 0.5953

26 1010 1 2 TP* BS** 0.2849 0.1893 -0.9044 15 4.5930 4.2497 18.0598 0.9752 0.9253

26 1010 2 1 BA* BG** 0.6960 0.6713 -0.1122 15 54.7890 2.8313 8.0163 0.9997 0.0517

26 1010 2 2 TP* BG** 0.5464 0.8224 -0.4050 13 46.1708 2.4887 6.1938 0.9996 0.0539

26 1010 3 1 BA* BG** 1.0904 0.5005 0.0000 15 58.7963 5.2456 27.5165 0.9993 0.0892

26 1010 3 2 TP* BG** 0.8491 0.7005 0.0000 15 78.0328 5.7623 33.2042 0.9992 0.0738

26 1012 1 1 BA* BS** 0.7369 0.7053 -0.7929 15 16.5840 4.7026 22.1141 0.9963 0.2836

26 1012 1 2 A2 TS04 1.2862 0.1626 -1.5326 15 10.3473 0.7875 0.6201 0.9999 0.0761

26 1012 2 1 BA* BG** 0.7927 0.5511 -0.1813 15 42.9293 6.8693 47.1871 0.9978 0.1600

26 1012 2 2 TP* BG** 0.6790 0.8114 -0.4863 15 57.6894 6.7627 45.7343 0.9981 0.1172

26 1012 3 2 TP* BG** 0.8505 0.6235 -0.2292 15 54.2979 6.9024 47.6425 0.9983 0.1271

26 1013 1 1 BA* BS** 0.7225 0.7486 -0.6051 15 17.5857 1.6345 2.6716 0.9996 0.0929

26 1013 2 1 BA* BG** 0.5853 0.7240 -0.1627 15 50.5296 5.9401 35.2853 0.9981 0.1176

26 1013 2 2 TP* BG** 0.6525 0.6243 -0.0706 15 46.6640 5.2572 27.6385 0.9986 0.1127

26 1013 3 1 BA* BG** 0.5752 0.6509 0.0000 15 46.6444 7.1070 50.5094 0.9970 0.1524

26 1013 3 2 TP* BG** 0.6082 0.7773 -0.2590 15 55.6492 4.4721 19.9998 0.9991 0.0804

26 3069 1 1 BA* BS** 0.7556 0.7524 -0.6701 14 18.7552 1.8128 3.2862 0.9995 0.0967

26 3069 1 2 TP* BS** 0.7152 0.7789 -0.7880 13 16.3911 1.1601 1.3459 0.9998 0.0708

26 4015 1 1 BA* BS** 1.2632 0.3423 -3.0715 15 17.2530 3.4649 12.0054 0.9985 0.2008

26 4015 1 2 TP* BS** 1.0766 0.4109 -3.9369 15 16.3745 1.6421 2.6964 0.9994 0.1003

26 4015 2 1 BA* BG** 0.6861 0.6778 -0.0540 15 57.0374 5.6369 31.7743 0.9987 0.0988

26 4015 2 2 TP* BG** 0.9150 0.5608 -0.0688 15 55.2729 5.8685 34.4389 0.9989 0.1062

26 5363 2 1 BA* BG** 0.9378 0.4957 0.0000 15 49.7299 4.4243 19.5743 0.9993 0.0890

26 5363 2 2 TP* BG** 0.7150 0.6980 -0.0108 15 64.8101 3.5763 12.7899 0.9996 0.0552

26 5363 3 1 BA* BG** 0.8545 0.6235 -0.1165 15 58.9102 8.5503 73.1082 0.9977 0.1451

26 5363 3 2 TP* BG** 0.5204 0.6969 0.0000 15 47.1990 6.1308 37.5861 0.9976 0.1299

26 6016 1 1 BA* BS** 0.6990 0.6532 -0.5370 15 14.8837 2.0780 4.3179 0.9992 0.1396

26 6016 2 2 TP* BG** 1.2267 0.4050 -0.0344 15 47.4821 9.3367 87.1732 0.9978 0.1966

26 6016 2 1 BA* BG** 0.7111 0.7467 -0.3196 15 58.7317 2.7828 7.7439 0.9997 0.0474

26 6016 3 1 BA* BG** 0.6625 0.6839 -0.1188 15 53.2955 7.4471 55.4593 0.9975 0.1397

26 6016 3 2 TP* BG** 0.7712 0.7104 -0.1748 14 59.9572 3.6474 13.3032 0.9995 0.0608

26 7072 1 1 BA* BS** 0.6671 0.8126 -1.0981 14 15.5712 1.8731 3.5084 0.9992 0.1203

26 7072 1 2 TP* BS** 2.3352 0.2824 -0.8111 14 18.2108 1.3008 1.6921 1.0000 0.0714

26 7072 2 1 BA* BG** 0.7257 0.7702 -0.3289 15 62.3880 4.9261 24.2666 0.9991 0.0790

26 7072 2 2 TP* BG** 0.5510 0.8236 -0.0397 15 65.5310 5.3964 29.1217 0.9988 0.0824

26 7072 3 1 BA* BG** 1.3205 0.4923 0.0000 15 69.2262 9.2379 85.3392 0.9985 0.1334

26 7072 3 2 TP* BG** 0.8766 0.7457 0.0000 15 89.4937 7.4010 54.7755 0.9989 0.0827

26 9029 2 1 BA* BG** 0.5808 0.7716 -0.2813 15 51.7133 3.0769 9.4670 0.9995 0.0595

26 9029 3 1 BA* BG** 0.7054 0.6211 0.0000 15 52.7891 6.2922 39.5924 0.9983 0.1192

26 9029 3 2 BA* BG** 0.7859 0.5949 0.0000 15 55.0050 6.3423 40.2248 0.9985 0.1153

27 1016 1 1 BA* BS** 0.7571 0.6718 -0.7353 15 15.7782 1.5184 2.3057 0.9996 0.0962

27 1016 1 2 TP* BS** 0.6648 0.7455 -0.7598 15 15.4873 1.7236 2.9706 0.9994 0.1113

27 1016 2 1 BA* BG** 0.7940 0.6779 0.0000 15 68.8309 5.3381 28.4953 0.9992 0.0776

27 1016 2 2 TP* BG** 0.6633 0.6964 0.0000 15 60.3926 3.9359 15.4914 0.9994 0.0652

73
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

27 1018 1 1 BA* BS** 0.7145 0.6922 -0.7367 15 15.3431 1.6328 2.6662 0.9995 0.1064

27 1018 1 2 TP* BS** 0.5661 0.8358 -0.8654 15 14.7254 1.3619 1.8547 0.9995 0.0925

27 1018 2 1 BA* BG** 0.7521 0.6316 -0.2637 15 47.3867 7.7311 59.7703 0.9973 0.1632

27 1018 2 2 TP* BG** 0.4830 0.8376 -0.3472 14 45.5099 4.0817 16.6607 0.9987 0.0897

27 1019 2 1 BA* BG** 0.7410 0.6698 -0.0688 15 60.1734 3.5661 12.7168 0.9995 0.0593

27 1019 2 2 TP* BG** 0.9804 0.5447 0.0000 15 59.7106 7.0383 49.5374 0.9987 0.1179

27 1028 1 1 BA* BS** 0.7300 0.7753 -1.1021 15 16.7724 2.1937 4.8124 0.9991 0.1308

27 1028 1 2 TP* BS** 0.7891 0.8533 -1.4552 15 18.7266 2.1106 4.4548 0.9993 0.1127

27 1029 1 1 BA* BS** 0.7796 0.5804 -1.1021 15 12.9773 2.0276 4.1110 0.9993 0.1562

27 1029 1 2 TP* BS** 0.7419 0.6791 -0.9346 15 15.0403 1.8658 3.4814 0.9994 0.1241

27 1085 1 1 BA* BS** 1.7532 0.2988 -2.2666 15 19.7383 2.2788 5.1930 0.9997 0.1155

27 1085 1 2 A2 TS03 1.5602 0.3192 -1.0676 15 14.9418 3.3932 11.5138 0.9995 0.2271

27 3003 1 1 A1 TS01 1.4477 0.2800 -1.1707 15 12.5463 2.1119 4.4602 0.9997 0.1683

27 3003 1 2 A2 TS03 1.5063 0.2453 -1.3728 15 12.5982 1.2990 1.6875 0.9999 0.1031

27 3003 2 1 BA* BG** 0.8425 0.6046 -0.2097 14 48.8306 4.1211 16.9831 0.9993 0.0844

27 3003 2 2 TP* BG** 0.5108 0.8536 -0.0885 15 63.0153 4.2206 17.8133 0.9992 0.0670

27 3013 1 2 TP* BS** 0.6015 0.7370 -1.1199 12 12.5224 1.0219 1.0442 0.9997 0.0816

27 4033 1 1 C6 BS01 0.5412 0.7300 -1.0006 13 12.1560 1.7003 2.8911 0.9990 0.1399

27 4033 1 2 TP* BS** 0.6682 0.7574 -1.5541 15 13.8753 2.4022 5.7707 0.9985 0.1731

27 4034 1 1 TP* BS** 0.7241 0.6873 -0.7904 15 15.0627 1.7392 3.0247 0.9995 0.1155

27 4034 1 2 TP* BS** 0.6477 0.5919 -0.9236 15 11.6202 2.5074 6.2868 0.9985 0.2158

27 4034 2 1 TP* BG** 0.7621 0.6335 -0.0142 15 58.7706 4.4924 20.1821 0.9993 0.0764

27 4034 2 2 TP* BG** 0.6644 0.7182 -0.0591 15 60.9059 6.7047 44.9524 0.9983 0.1101

27 4037 1 1 C6 BS01 0.8953 0.6661 -1.5409 15 16.1770 2.9636 8.7830 0.9987 0.1832

27 4037 1 2 TP* BS** 0.4114 0.7488 0.0000 15 11.9312 1.6108 2.5947 0.9990 0.1350

27 4037 2 2 TP* BG** 0.9164 0.6053 0.0000 15 66.4647 5.3933 29.0877 0.9992 0.0811

27 4040 1 1 A1 TS01 0.9116 0.1902 -2.5367 15 10.5348 0.8562 0.7330 0.9998 0.0813

27 4040 1 2 A2 TS03 0.8461 0.1965 -3.2454 15 11.3921 1.2857 1.6531 0.9995 0.1129

27 4040 2 1 BA* BG** 0.4578 0.8095 -0.0486 15 52.3923 4.5158 20.3924 0.9987 0.0862

27 4040 2 2 TP* BG** 0.5690 0.7350 -0.0515 15 54.5549 5.2740 27.8148 0.9986 0.0967

27 4054 1 1 BA* BS** 0.6709 0.7337 -0.9679 15 14.7367 1.7097 2.9232 0.9994 0.1160

27 4054 1 2 BA* BS** 0.7898 0.8614 -1.4658 14 17.7177 1.6678 2.7817 0.9996 0.0941

27 4054 2 1 BA* BG** 1.0646 0.5307 0.0000 15 62.4086 6.8673 47.1599 0.9989 0.1100

27 4054 2 2 BA* BG** 0.7552 0.6763 0.0000 15 64.9811 7.9268 62.8338 0.9980 0.1220

27 4055 1 1 BA* BS** 0.8370 0.6106 -1.0765 15 14.8269 2.7212 7.4048 0.9989 0.1835

27 4055 1 2 TP* BS** 0.6854 0.5817 -0.8830 15 11.9929 2.2371 5.0048 0.9989 0.1865

27 4055 2 2 TP* BG** 0.6695 0.7695 -0.2960 15 58.3902 7.7278 59.7194 0.9976 0.1323

27 4082 1 1 A1 TS01 0.9684 0.2068 -2.6811 15 11.5540 1.1560 1.3364 0.9997 0.1001

27 4082 1 2 TP* BS** 0.3577 0.9497 -1.4417 14 10.0952 5.0992 26.0017 0.9814 0.5051

27 5076 1 1 BA* BS** 1.1417 0.3884 -2.1105 15 13.7096 2.4614 6.0586 0.9993 0.1795

27 5076 1 2 BA* BS** 1.3797 0.2945 -1.8713 15 14.0601 1.3203 1.7431 0.9999 0.0939

27 5076 2 1 BA* BG** 0.7697 0.5864 -0.0996 15 48.7001 6.3801 40.7062 0.9983 0.1310

27 5076 2 2 BA* BG** 0.3297 0.9073 -0.1510 15 43.6744 4.0163 16.1309 0.9984 0.0920

27 6251 1 1 BA* BS** 0.7261 0.6619 -0.8628 15 14.4888 1.7593 3.0952 0.9994 0.1214

27 6251 1 2 TP* BS** 0.6138 0.8872 -1.7640 15 14.5455 1.8369 3.3740 0.9990 0.1263

27 6251 2 2 TP* BG** 0.7751 0.6919 0.0000 15 70.1171 4.1232 17.0004 0.9995 0.0588

27 6300 1 1 A1 TS01 1.1684 0.2273 -3.1249 15 15.4081 1.7242 2.9730 0.9995 0.1119

27 6300 1 2 TP* BS** 1.4667 0.3651 -2.4260 15 17.8144 2.3072 5.3234 0.9996 0.1295

27 7090 1 1 BA* BS** 0.6077 0.3404 -3.8486 15 9.0333 1.6799 2.8222 0.9981 0.1860

27 7090 2 1 BA* BG** 0.6938 0.5582 -0.0688 15 41.7675 5.5503 30.8056 0.9983 0.1329

27 7090 2 2 TP* BG** 0.7152 0.6393 -0.2359 15 47.8012 4.7170 22.2499 0.9989 0.0987

27 7090 3 1 BA* BG** 0.6122 0.6561 -0.5419 14 31.8438 4.4535 19.8337 0.9985 0.1399

27 7090 3 2 TP* BG** 0.4889 0.7558 -0.3140 15 40.9719 7.1768 51.5069 0.9958 0.1752

27 9075 1 1 BA* BS** 0.8421 0.2536 -0.8485 15 6.3636 0.7034 0.4947 0.9999 0.1105

27 9075 1 2 BA* BS** 1.1881 0.2096 -1.2414 15 8.8678 0.6159 0.3793 1.0000 0.0695

28 0501 1 1 A1 TS01 0.4296 0.7504 -0.4600 15 10.9965 1.7604 3.0991 0.9987 0.1601

74
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

28 0501 1 2 A2 TS04 0.2136 0.4305 -1.7715 15 2.9488 1.3894 1.9306 0.9943 0.4712

28 0503 1 1 A7 TS01 0.5346 0.5908 0.0000 15 12.8612 4.6447 21.5732 0.9945 0.3611

28 0504 1 2 BA* BS** 1.3927 0.1484 -1.3025 15 10.1278 2.0865 4.3534 0.9997 0.2060

28 0506 1 1 A5 TS01 0.5916 0.5060 -1.2199 15 8.4808 2.1701 4.7095 0.9985 0.2559

28 0507 1 1 A3 TS01 1.1560 0.6145 -0.7763 15 21.9812 6.6461 44.1702 0.9969 0.3024

28 0508 1 1 A8 TS01 0.6763 0.5245 -3.0140 15 10.1980 2.5687 6.5980 0.9973 0.2519

28 0508 1 2 A9 TS03 0.6411 0.1921 -0.2812 15 4.7929 2.7593 7.6139 0.9983 0.5757

28 0509 1 1 A6 TS01 0.9214 0.3365 -4.0909 15 13.5794 2.9234 8.5465 0.9975 0.2153

28 1001 1 1 A1 TS01 0.4830 0.4098 -4.9710 15 7.4909 1.7125 2.9327 0.9961 0.2286

28 1001 1 2 A2 TS03 0.6843 0.0033 -3.7063 15 10.3694 2.0291 4.1173 0.9977 0.1957

28 1001 2 1 BA* BG** 1.2394 0.4378 -0.3516 15 40.4610 11.0430 121.9489 0.9964 0.2729

28 1001 2 2 BA4 BG** 0.6769 0.7374 -0.2764 15 55.9691 4.4790 20.0615 0.9991 0.0800

28 1016 1 1 A1 TS01 0.5635 0.8344 -1.4185 15 15.1789 5.8728 34.4901 0.9887 0.3869

28 1016 1 2 A2 TS03 0.9632 0.4011 -1.9807 15 14.5104 8.4931 72.1324 0.9887 0.5853

28 1016 2 1 BA* BG** 0.7199 0.6171 -0.1429 15 48.1306 4.3071 18.5509 0.9991 0.0895

28 1016 2 2 TP1 BG55 0.7488 0.5864 -0.1679 15 45.5534 2.7471 7.5464 0.9996 0.0603

28 1802 1 1 BA* BS** 0.8968 0.3915 -0.4663 15 11.5882 3.4637 11.9969 0.9986 0.2989

28 1802 1 2 A2 TS03 0.7525 0.3040 -0.0600 15 9.2941 4.4133 19.4774 0.9971 0.4749

28 1802 2 1 BA* BG** 1.2030 0.4672 -0.1977 15 49.0857 7.2767 52.9502 0.9986 0.1482

28 1802 2 2 TP1 BG55 0.9001 0.6394 -0.1210 15 65.0943 6.6476 44.1907 0.9988 0.1021

28 2807 1 1 A1 TS01 0.3856 0.6519 -3.2137 15 6.5407 1.7095 2.9225 0.9964 0.2614

28 2807 1 2 A2 TS03 0.9370 0.2147 -2.8659 15 11.2559 1.9621 3.8497 0.9992 0.1743

28 3018 1 1 A1 TS01 0.7536 0.4199 -1.3997 15 9.0963 2.0228 4.0918 0.9991 0.2224

28 3018 1 2 A2 TS03 0.9323 0.2198 -1.7576 15 9.8522 4.9390 24.3937 0.9959 0.5013

28 3081 1 1 A1 TS01 0.7610 0.1258 -1.0848 15 7.3569 5.7537 33.1050 0.9931 0.7821

28 3081 1 2 A2 TS03 0.7022 0.5815 -1.3703 15 11.4155 1.8482 3.4158 0.9992 0.1619

28 3082 1 1 A1 TS01 0.9479 0.5542 0.0000 15 19.7653 2.3317 5.4368 0.9995 0.1180

28 3082 1 2 A2 TS03 0.8337 0.4984 0.0000 15 16.2211 5.4201 29.3771 0.9967 0.3341

28 3083 1 1 A1 TS01 0.6474 0.4511 0.0000 15 11.0247 2.2784 5.1912 0.9990 0.2067

28 3083 1 2 A2 TS03 0.6062 0.5550 -0.1346 15 12.3327 1.5799 2.4960 0.9995 0.1281

28 3085 1 1 BA* BS** 1.4489 0.2148 -0.9126 15 10.5546 3.7374 13.9683 0.9992 0.3541

28 3087 1 1 BA3 BS03 0.8903 0.6372 -0.8657 14 17.5893 2.3582 5.5609 0.9993 0.1341

28 3087 1 2 BA* BS** 0.7258 0.3482 0.0000 13 10.4311 2.9281 8.5736 0.9987 0.2807

28 3089 1 1 A1 TS01 0.7743 0.4456 -2.3509 15 10.3427 2.4650 6.0764 0.9984 0.2383

28 3089 1 2 A2 TS03 0.7370 0.3363 -0.9617 15 8.6839 4.9681 24.6817 0.9950 0.5721

28 3090 1 1 A1 TS01 0.6065 0.2834 -1.8594 15 8.2271 5.3669 28.8039 0.9885 0.6523

28 3090 1 2 A2 TS02 0.7514 0.4839 -2.0114 15 10.2794 2.3089 5.3308 0.9986 0.2246

28 3090 2 1 BA* BG** 0.9484 0.5388 0.0000 15 58.3285 9.8922 97.8550 0.9972 0.1696

28 3090 2 2 BA* BG** 1.2587 0.6058 -0.4254 15 65.0352 10.5074 110.4063 0.9978 0.1616

28 3090 3 1 BA* BG** 0.7073 0.9193 -0.0673 15 106.5282 7.6451 58.4479 0.9989 0.0718

28 3090 3 2 BA* BG** 0.8222 0.6158 0.0000 15 81.5996 56.1786 3156.0310 0.9075 0.6885

28 3091 1 1 A1 TS01 0.9539 0.4315 -0.7337 15 13.7137 6.0720 36.8695 0.9960 0.4428

28 3091 1 2 A2 TS03 0.6823 0.4351 0.0000 14 11.8952 2.9579 8.7491 0.9985 0.2487

28 3093 1 1 BS* BS** 0.7523 0.5735 -0.4220 15 14.3968 1.9019 3.6171 0.9995 0.1321

28 3093 1 2 BA* BS** 0.8434 0.3937 -0.8469 15 10.2153 3.1608 9.9909 0.9985 0.3094

28 3094 1 1 A1 TS01 1.5502 0.6160 -4.2283 15 27.2839 9.6517 93.1548 0.9905 0.3538

28 3094 1 2 A2 TS02 0.7404 0.4200 0.0000 15 12.8719 5.7306 32.8400 0.9953 0.4452

28 3097 1 1 A1 TS01 0.5048 0.0000 -0.0175 15 9.3960 9.3958 88.2817 0.9693 1.0000

28 3097 1 2 A2 TS03 0.5593 0.6087 -3.1221 15 9.0685 1.9423 3.7724 0.9978 0.2142

28 3097 3 1 BA* BG** 0.9806 0.7369 -0.2088 15 86.7918 8.8876 78.9887 0.9985 0.1024

28 3097 3 2 BA* BG** 0.9068 0.7638 -0.1300 15 91.3346 7.5634 57.2049 0.9989 0.0828

28 3099 1 1 A1 TS01 0.5174 0.1286 -0.4072 15 3.9182 3.2914 10.8335 0.9960 0.8400

28 3099 1 2 A2 TS03 0.5807 0.2052 -2.6455 15 7.3937 3.0364 9.2196 0.9949 0.4107

28 4024 1 1 BA* BS** 0.7762 0.1760 0.0000 15 9.6051 8.2256 67.6604 0.9904 0.8564

28 4024 1 2 A2 TS03 0.5100 0.3021 -2.2208 15 6.0765 2.2798 5.1975 0.9967 0.3752

28 5006 1 1 A1 TS01 1.0949 0.2238 -2.6408 15 12.9780 3.0408 9.2464 0.9986 0.2343

75
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

28 5006 1 2 A2 TS03 0.8565 0.2252 -3.6845 15 11.8816 2.4900 6.2003 0.9980 0.2096

28 5025 1 1 BA* BS** 0.9304 0.4181 -0.5371 15 12.6144 3.1695 10.0460 0.9989 0.2513

28 5025 1 2 BA* BS** 0.9196 0.2927 -0.5659 15 8.9272 3.9180 15.3509 0.9982 0.4389

28 5025 2 1 BA* BG** 1.2468 0.5861 0.0000 15 87.0926 6.7758 45.9121 0.9993 0.0778

28 5025 2 2 BA* BG** 1.1200 0.6862 -0.1840 15 88.7097 9.4346 89.0116 0.9985 0.1064

28 5803 1 2 BA* BS** 0.7222 0.3697 0.0000 15 11.3984 5.4634 29.8484 0.9954 0.4793

28 5805 1 1 BA* BS** 0.6256 0.5485 0.0000 15 13.5636 4.3057 18.5387 0.9965 0.3174

28 5805 1 2 BA* BS** 0.8535 0.2995 -1.7143 15 9.4375 4.0607 16.4892 0.9968 0.4303

28 5805 2 1 BA* BG** 0.7525 0.6732 -0.2135 15 55.6776 3.6392 13.2441 0.9995 0.0654

28 5805 2 2 BA* BG** 0.6319 0.7589 -0.2775 15 55.0203 3.4368 11.8119 0.9995 0.0625

28 7012 1 1 BA2 BS02 0.9665 0.3616 -1.6515 15 10.7051 2.7175 7.3847 0.9989 0.2538

28 7012 1 2 A2 TS03 0.4493 0.4766 0.0000 15 8.6674 3.8543 14.8555 0.9944 0.4447

28 7012 2 1 BA* BG** 0.7754 0.5459 0.0000 15 48.1845 6.9962 48.9466 0.9979 0.1452

28 7012 2 2 BA* BG** 0.6465 0.5989 0.0000 15 46.2632 3.2678 10.6787 0.9994 0.0706

28 7012 3 1 BA* BG** 1.0775 0.6422 -0.1267 15 79.6098 8.1694 66.7398 0.9987 0.1026

28 7012 3 2 BA* BG** 0.6694 0.5714 -0.0622 15 42.1163 5.1458 26.4788 0.9985 0.1222

28 9030 1 1 A1 TS01 0.5855 0.5830 -1.6244 15 9.6100 3.0490 9.2965 0.9966 0.3173

28 9030 1 2 A2 TS03 0.9572 1.0500 -2.5503 15 25.9545 11.6392 135.4719 0.9807 0.4484

29 0603 1 2 TP7 BS07 0.7049 0.4336 -2.0065 15 8.8544 1.9018 3.6168 0.9989 0.2148

29 0605 1 2 TP5 BS05 1.1613 0.1806 -1.9226 15 11.1343 1.4382 2.0683 0.9998 0.1292

29 0607 1 2 TP1 BS01 1.2712 0.1479 -1.2551 15 8.9719 1.7118 2.9304 0.9998 0.1908

29 0608 1 2 TP3 BS03 0.9406 0.1876 -1.5575 15 7.7907 1.0183 1.0369 0.9998 0.1307

29 0608 2 2 TP3 BG03 0.8897 0.4855 0.0000 14 45.7283 16.6274 276.4708 0.9888 0.3636

29 1002 1 1 BA* BS** 2.2555 0.3205 -1.0017 13 19.8262 2.5669 6.5889 0.9998 0.1295

29 1002 2 1 BA* BG** 0.6787 0.7076 0.0000 15 63.1432 7.7860 60.6218 0.9978 0.1233

29 1002 2 2 TP* BG** 0.6757 0.6406 0.0000 15 53.1658 6.9456 48.2409 0.9979 0.1306

29 1005 2 1 BA* BG** 0.8208 0.6707 0.0000 15 69.5521 7.4657 55.7371 0.9985 0.1073

29 1005 2 2 TP* BG** 0.6483 0.8938 -0.0367 15 90.5061 8.1123 65.8088 0.9984 0.0896

29 1008 1 1 A1 TS02 1.2151 0.4634 -3.2285 15 17.8213 2.9713 8.8286 0.9988 0.1667

29 1008 1 2 A2 TS04 1.3415 0.2402 -2.4097 15 15.2300 1.5926 2.5363 0.9998 0.1046

29 1008 2 1 BA* BG** 1.3623 0.4655 0.0000 15 66.4470 16.0703 258.2561 0.9956 0.2419

29 1010 1 1 BA* BS** 2.3257 0.3104 -0.4505 13 24.1425 5.5821 31.1604 0.9994 0.2312

29 1010 2 2 TP* BG** 0.6512 0.7504 0.0000 15 67.2327 7.9067 62.5153 0.9979 0.1176

29 4036 1 1 A1 TS01 1.0374 0.2343 -2.6844 15 12.4835 1.7344 3.0082 0.9995 0.1389

29 4036 1 2 BA* BS** 1.3092 0.2385 -1.1929 15 10.0560 0.7493 0.5614 1.0000 0.0745

29 4036 2 1 BA* BG** 0.8372 0.6580 0.0000 15 69.4966 5.3582 28.7099 0.9992 0.0771

29 4036 2 2 BA* BG** 0.9379 0.6573 -0.1898 15 66.8932 4.0826 16.6680 0.9996 0.0610

29 4069 1 1 BA* BS** 0.7065 0.6609 -0.4527 15 15.5970 3.0304 9.1836 0.9985 0.1943

29 4069 1 2 BA* BS** 0.6859 0.8918 -0.9959 12 18.2657 3.5880 12.8736 0.9977 0.1964

29 4069 2 1 BA* BG** 0.7332 0.6173 -0.2456 15 44.9813 6.5533 42.9457 0.9979 0.1457

29 5000 1 1 A1 TS01 0.9256 0.1323 -2.3526 15 10.3150 0.9680 0.9370 0.9998 0.0938

29 5000 2 1 BA* BG** 0.8774 0.6656 -0.0273 15 72.5356 5.8178 33.8464 0.9992 0.0802

29 5000 2 2 BA* BG** 0.8525 0.7155 0.0000 15 81.5036 5.3840 28.9875 0.9994 0.0661

29 5047 1 1 BA* BS** 0.6935 0.3517 -1.9299 15 7.7724 1.3191 1.7402 0.9995 0.1697

29 5047 1 2 BA* BS** 0.9456 0.3450 -2.4405 15 11.3356 1.0444 1.0907 0.9998 0.0921

29 5058 1 2 BA* BS** 0.7524 0.2320 -2.9214 15 9.4557 0.9426 0.8886 0.9997 0.0997

29 5081 1 2 A2 TS04 1.1171 0.0606 -0.9467 15 6.0906 0.7289 0.5312 0.9999 0.1197

29 5081 1 1 BA* BS** 0.9644 0.1864 -1.9737 15 9.4299 1.2547 1.5743 0.9997 0.1331

29 5091 1 1 A1 TS02 0.7057 0.1451 -3.2496 15 9.6125 1.0902 1.1884 0.9995 0.1134

29 5091 1 2 A2 TS03 0.8396 0.2428 -2.9690 15 10.6695 1.1016 1.2135 0.9996 0.1032

29 5393 1 1 A1 TS02 1.4920 0.2024 -2.0448 15 15.0593 1.6159 2.6112 0.9998 0.1073

29 5393 2 1 BA* BG** 0.7257 0.7392 -0.3216 15 57.9131 6.7310 45.3067 0.9982 0.1162

29 5393 2 2 TP* BG** 0.8813 0.6496 -0.4566 15 50.5395 8.2776 68.5194 0.9974 0.1638

29 5403 1 1 BA* BS** 0.3236 0.8099 -1.1268 15 8.5646 3.8331 14.6930 0.9867 0.4476

29 5403 1 2 TP* BS** 0.4875 0.8351 -1.8453 15 10.8921 2.6887 7.2290 0.9964 0.2468

29 5413 1 1 BA* BS** 0.1583 0.6566 0.0000 14 5.6276 4.3697 19.0940 0.9506 0.7765

76
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

29 5413 1 2 BA* BS** 0.5343 0.7912 -1.9114 15 11.0121 2.1423 4.5896 0.9980 0.1945

29 6067 1 1 BA* BS** 0.8896 0.7517 -3.5453 15 16.3716 4.8038 23.0761 0.9942 0.2934

29 6067 1 2 TP* BS** 0.8678 0.7015 -3.6541 15 15.3058 4.0251 16.2016 0.9955 0.2630

29 6067 2 1 BA* BG** 0.8021 0.7135 0.0000 15 75.9444 5.1494 26.5163 0.9993 0.0678

29 6067 2 2 TP* BS** 0.7277 0.7680 0.0000 15 78.0581 7.4258 55.1421 0.9985 0.0951

29 7054 1 1 BA* BS** 1.4209 0.3180 -2.1790 12 13.0802 0.7556 0.5709 1.0000 0.0578

29 7054 1 2 BA* BS** 1.6696 0.2102 -1.3860 15 13.3442 1.5837 2.5081 0.9999 0.1187

29 7054 2 2 BA* BG** 1.0058 0.5377 0.0000 15 60.0267 10.1294 102.6042 0.9973 0.1687

29 7073 1 1 A1 TS01 0.7707 0.3347 -5.1748 15 12.9541 1.3913 1.9359 0.9989 0.1074

29 7073 1 2 A2 TS03 1.1225 0.1654 -2.2798 15 12.1784 1.3835 1.9142 0.9997 0.1136

29 7073 3 2 BA* BG** 1.4402 0.4837 -0.1764 15 63.3902 14.0779 198.1872 0.9966 0.2221

30 1001 1 1 BA* BS** 0.8632 0.1528 -0.9899 15 5.6627 2.2048 4.8611 0.9992 0.3894

30 6004 1 1 BA* BS** 0.6669 0.2432 -2.4667 15 7.7226 1.3104 1.7172 0.9993 0.1697

30 6004 1 2 TP1 BS93 0.8320 0.1334 -1.6088 15 7.1760 1.4691 2.1583 0.9996 0.2047

30 6004 2 2 TP1 BG92 0.5146 0.5290 -0.2255 15 24.9023 4.2754 18.2788 0.9977 0.1717

30 7066 1 1 BA* BS** 0.6669 0.2432 -2.4667 15 7.7226 1.3104 1.7172 0.9993 0.1697

30 7075 1 2 TP1 BS93 0.6023 0.2563 -2.7520 15 7.4514 1.4447 2.0873 0.9989 0.1939

30 7076 2 1 BA* BG** 0.4187 0.6012 -0.4023 15 21.7755 4.3598 19.0076 0.9966 0.2002

30 7076 2 2 TP1 BG93 0.2809 0.8542 -0.3448 15 29.2977 1.4241 2.0281 0.9996 0.0486

30 7088 1 1 BA* BS** 0.7415 0.1513 -1.2324 15 5.4493 1.7719 3.1395 0.9993 0.3252

30 7088 1 2 TP1 BS93 0.9762 0.1447 -0.3559 15 4.9694 2.3714 5.6234 0.9994 0.4772

30 8129 1 1 BA* BS** 1.0897 0.1394 0.0000 15 6.5625 3.5179 12.3759 0.9991 0.5361

31 0113 1 3 A17 TS33 0.9527 0.2803 -1.0314 15 7.9180 0.6568 0.4314 0.9999 0.0830

31 0115 1 3 A8 TS16 0.7421 0.4491 -2.4975 13 10.2100 1.2588 1.5846 0.9995 0.1233

31 0115 1 2 B3 BS03 0.9652 0.3697 -0.8094 15 10.5198 1.2057 1.4537 0.9998 0.1146

31 0116 1 1 B5 BS05 1.0765 0.1833 -0.8971 12 5.8672 0.6441 0.4148 1.0000 0.1098

31 0120 1 3 A11 TS22 0.7922 0.2468 -1.8877 15 7.7078 0.9509 0.9043 0.9998 0.1234

31 0124 1 2 B1 BS01 0.7360 0.3377 -2.7693 14 9.6077 0.7949 0.6319 0.9998 0.0827

31 3018 1 1 BA* BS** 0.6827 0.8523 -1.1184 15 17.2605 2.4041 5.7798 0.9988 0.1393

31 3018 1 2 TP* BS** 0.7840 0.8169 -1.2018 15 18.5336 2.1622 4.6752 0.9993 0.1167

31 3023 1 1 BA* BS** 0.7441 0.7108 -0.9261 15 15.6880 1.7926 3.2133 0.9995 0.1143

31 3023 1 2 TP* BS** 0.6779 0.7220 -0.4899 13 15.1514 1.2281 1.5081 0.9997 0.0811

31 3023 2 2 TP* BG** 0.6834 0.6123 -0.1004 15 46.9521 4.2287 17.8815 0.9991 0.0901

31 3024 1 1 BA* BS** 1.1275 0.3020 -1.5126 15 10.7282 1.6009 2.5629 0.9997 0.1492

31 3024 1 2 TP* BS** 0.6338 0.4853 -2.8514 15 9.1610 2.0618 4.2508 0.9981 0.2251

31 3028 1 1 BA* BS** 1.0009 0.1676 -2.2151 15 10.5388 1.1265 1.2690 0.9998 0.1069

31 3028 1 2 A2 TS03 0.9545 0.1654 -2.4789 15 11.1995 0.7506 0.5634 0.9999 0.0670

31 3033 1 1 BA* BS** 0.9545 0.5284 -1.7917 12 12.3469 0.9881 0.9764 0.9999 0.0800

31 3033 1 2 TP* BS** 0.6171 0.7665 -1.1180 15 13.7834 2.8737 8.2582 0.9979 0.2085

31 4019 1 1 A1 TS01 0.9180 0.1886 -1.7982 15 8.4177 0.7255 0.5263 0.9999 0.0862

31 4019 1 2 A2 TS04 0.5789 0.2259 -3.1061 15 7.5423 0.8853 0.7837 0.9995 0.1174

31 5052 1 1 A1 TS02 1.2649 0.2288 -1.3382 15 10.1099 0.9002 0.8103 0.9999 0.0890

31 5052 1 2 TP1 BS55 0.9413 0.2472 -1.7577 15 8.8759 1.4139 1.9992 0.9997 0.1593

31 6700 1 1 BA* BS** 0.5489 0.4015 -2.4837 15 7.1214 1.6574 2.7470 0.9984 0.2327

31 6700 1 2 TP1 BS** 0.3902 0.4593 -2.7419 15 5.6543 1.7948 3.2212 0.9962 0.3174

31 6701 1 1 BA* BS** 0.5232 1.0135 -3.1041 15 12.3211 1.9729 3.8923 0.9977 0.1601

31 6701 1 2 TP1 BS55 0.7962 0.6268 -0.6755 15 15.6783 1.5852 2.5127 0.9996 0.1011

31 6702 1 1 BA* BS** 0.7452 0.7673 -2.3411 15 14.4677 2.5028 6.2641 0.9984 0.1730

31 6702 1 2 TP* BS** 0.6271 0.7658 -2.2391 15 12.1624 2.3043 5.3097 0.9981 0.1895

31 7005 1 1 BA* BS** 0.5740 0.5377 -1.9149 15 8.5010 1.9488 3.7978 0.9984 0.2292

31 7005 1 2 BA* BS** 0.6827 0.5896 -1.8517 15 10.8422 2.0928 4.3798 0.9987 0.1930

31 7005 2 1 BA* BG** 0.7557 0.7040 -0.1716 15 61.9387 3.7489 14.0542 0.9995 0.0605

31 7005 2 2 BA* BG** 0.6823 0.7349 -0.2183 15 58.1916 3.5337 12.4867 0.9995 0.0607

31 7017 1 1 BA* BS** 1.0963 0.2533 -1.7314 15 10.3150 1.3966 1.9506 0.9998 0.1354

31 7017 1 2 TP* BS** 0.8180 0.2451 -2.8582 15 10.2167 0.9774 0.9553 0.9997 0.0957

31 7017 2 2 TP* BG** 0.7653 0.5134 -0.1536 15 37.8804 5.5099 30.3590 0.9983 0.1455

77
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

31 7040 1 1 A1 TS02 0.6558 0.1907 -2.1733 15 6.7844 0.5449 0.2969 0.9999 0.0803

31 7040 1 2 TP1 BS** 0.6510 0.1307 -1.0998 13 4.0997 0.6884 0.4740 0.9999 0.1679

31 7040 2 1 BA* BG** 0.7887 0.6180 -0.0098 15 58.3264 4.4061 19.4138 0.9993 0.0755

31 7040 2 2 TP* BG** 0.8222 0.5398 -0.0242 15 48.6055 4.3531 18.9496 0.9992 0.0896

31 7050 1 1 BA* BS** 0.6882 0.2449 -2.8732 15 8.6509 1.3074 1.7092 0.9993 0.1511

31 7050 1 2 TP* BS** 0.7362 0.1835 -2.8416 15 9.1298 0.8446 0.7134 0.9997 0.0925

31 7050 2 2 TP* BG** 0.5955 0.6446 -0.2215 15 40.3730 5.9077 34.9003 0.9976 0.1463

32 0101 1 2 B26 BS01 0.5965 0.7717 -1.9526 15 12.0147 2.5560 6.5330 0.9977 0.2127

32 0105 1 2 B31 BS06 0.5774 0.7375 -1.9775 15 11.2470 2.2511 5.0675 0.9980 0.2002

32 0106 1 2 B27 BS02 1.2794 0.2343 -1.5824 15 11.3339 1.7717 3.1388 0.9997 0.1563

32 0109 1 2 B28 BS03 0.7370 0.5980 -2.1861 15 11.8912 3.1952 10.2093 0.9972 0.2687

32 0111 1 2 B30 BS05 1.2431 0.2367 -1.4671 15 10.5573 1.3104 1.7171 0.9999 0.1241

32 1020 1 1 BA* BS** 0.5320 0.6989 -0.6981 15 11.7400 1.3112 1.7191 0.9995 0.1117

32 1020 1 2 TP1 BS92 0.6278 0.6056 -1.2972 15 10.7296 2.3186 5.3759 0.9985 0.2161

32 1021 1 1 BA* BS** 0.8756 0.1361 -0.3087 15 4.2404 2.0614 4.2493 0.9995 0.4861

32 1021 1 2 TP1 BS93 0.4802 0.3284 -2.1831 15 5.5222 1.3584 1.8452 0.9987 0.2460

32 1021 2 1 BA* BG** 0.5125 0.5064 -0.3604 15 20.9655 6.0519 36.6260 0.9946 0.2887

32 1030 1 1 BA* BS** 1.1115 0.1956 -0.0890 15 7.9144 2.4045 5.7818 0.9996 0.3038

32 1030 1 2 TP1 BS71 1.0128 0.2753 -0.4842 15 9.0143 2.8766 8.2746 0.9992 0.3191

32 2027 1 1 BA* BS** 0.6036 0.4453 -1.6384 15 7.8090 2.3743 5.6373 0.9980 0.3040

32 2027 1 2 TP1 BS93 0.4681 0.5335 -1.6621 15 7.0495 1.9534 3.8157 0.9978 0.2771

32 3010 1 2 BA* BS** 0.4898 0.3852 -1.1293 15 5.3940 0.8337 0.6951 0.9997 0.1546

32 7084 2 1 BA* BG** 0.6450 0.4418 -0.2098 15 23.9131 4.1919 17.5716 0.9983 0.1753

34 0503 1 2 TP2 BS56 0.7614 0.2402 -0.5386 15 6.0828 2.5897 6.7068 0.9988 0.4258

34 0505 1 2 TP1 BS55 0.5751 0.5115 -0.8372 15 8.9618 2.3731 5.6316 0.9983 0.2648

34 0505 2 2 TP1 BG55 0.9100 0.7671 -0.3020 15 79.3859 4.7504 22.5663 0.9995 0.0598

34 0801 1 2 B1 BS01 0.4990 0.6526 -0.4719 15 11.0871 3.0075 9.0452 0.9970 0.2713

34 0802 1 1 B2 BS02 0.5312 0.5392 -0.1860 15 10.1831 1.8512 3.4268 0.9990 0.1818

34 1011 1 2 TP BS55 0.7084 0.5922 -0.6944 15 13.0464 1.9333 3.7376 0.9993 0.1482

34 1031 1 1 BA* BS** 0.7516 0.6361 -1.0440 15 13.9755 1.9745 3.8986 0.9993 0.1413

34 1031 1 2 TP BS55 0.6511 0.4797 -0.4137 15 10.4845 2.2398 5.0168 0.9990 0.2136

34 1033 1 1 BA* BS** 0.8907 0.2220 -0.3252 13 6.3063 3.3177 11.0073 0.9987 0.5261

34 1033 1 2 TP BS55 1.0464 0.2820 -1.2799 15 10.7814 5.5022 30.2746 0.9965 0.5103

34 4042 2 1 BA* BG** 0.6578 0.6752 -0.1177 15 52.5478 4.1776 17.4526 0.9992 0.0795

35 0101 1 2 B1 BS01 0.8437 0.1740 0.0000 15 7.9791 5.8879 34.6669 0.9958 0.7379

35 0102 1 3 A2 TS03 0.5317 0.2421 0.0000 15 4.9971 1.7731 3.1439 0.9991 0.3548

35 0103 1 2 B2 BS02 0.7778 0.3042 0.0000 15 5.6753 3.8139 14.5455 0.9975 0.6720

35 0105 1 2 B3 BS03 0.7277 0.1732 0.0000 15 6.5538 4.6474 21.5980 0.9965 0.7091

35 0106 1 3 A9 TS17 0.3991 0.2297 -1.2502 15 3.2704 1.0192 1.0388 0.9992 0.3116

35 0107 1 2 B4 BS04 0.6822 0.2334 0.0000 15 6.3042 2.3610 5.5744 0.9990 0.3745

35 0108 1 3 A11 TS21 0.4910 0.1442 -1.0136 15 3.0907 0.9621 0.9256 0.9995 0.3113

35 0109 1 2 B5 BS05 0.6704 0.1364 0.0000 15 3.7696 1.7358 3.0130 0.9994 0.4605

35 0110 1 3 A14 TS27 0.7783 0.3229 0.0000 15 10.1957 4.3493 18.9161 0.9974 0.4266

35 0111 1 2 B6 BS06 0.6016 0.3769 -0.6062 15 7.0933 1.8948 3.5904 0.9990 0.2671

35 0112 1 3 A17 TS33 0.5187 0.2317 -0.7539 15 3.8545 1.3528 1.8300 0.9993 0.3510

35 1002 1 2 TP1 BS55 0.9051 0.4221 -0.8276 15 11.2834 2.2779 5.1888 0.9993 0.2019

35 1002 2 2 TP1 BG55 0.9707 0.6487 -0.0935 15 73.9881 5.9341 35.2135 0.9992 0.0802

35 1003 1 1 BA* BS** 1.2015 0.4417 -0.0646 15 19.8538 3.8564 14.8721 0.9992 0.1942

35 1003 2 1 BA* BG** 0.7762 0.7697 -0.1357 15 78.3228 4.2805 18.3231 0.9995 0.0547

35 1003 2 2 TP1 BG55 1.3095 0.3860 0.0000 15 49.8529 12.8881 166.1037 0.9963 0.2585

35 1005 1 2 TP1 BS55 1.0627 0.2438 -1.0162 15 8.1912 1.7384 3.0222 0.9997 0.2122

35 1005 2 1 BA* BG** 0.7366 0.7375 0.0000 15 75.4685 8.2614 68.2504 0.9981 0.1095

35 1005 2 2 TP1 BG55 0.8802 0.6531 -0.0940 15 67.7448 5.1798 26.8300 0.9993 0.0765

35 1022 1 1 A1 TS01 0.9878 0.4068 -2.2316 15 13.5446 5.9267 35.1262 0.9943 0.4376

35 1022 1 2 A2 TS03 0.8339 0.4387 -1.8656 15 10.4348 2.3617 5.5776 0.9989 0.2263

35 1022 2 1 BA* BG** 0.6392 0.8025 0.0000 15 77.4217 10.4941 110.1256 0.9966 0.1355

78
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

35 1022 2 2 TP1 BG55 0.7352 0.7532 0.0000 15 78.5264 5.2192 27.2399 0.9993 0.0665

35 1112 1 1 BA* BS** 0.8417 0.4699 0.0000 15 15.2222 4.4575 19.8690 0.9978 0.2928

35 1112 1 2 TP1 BS55 0.8456 0.5132 -0.1217 15 15.7918 2.8769 8.2768 0.9991 0.1822

35 1112 2 1 BA* BG** 0.9479 0.8044 -0.5377 15 76.7049 4.8738 23.7542 0.9995 0.0635

35 1112 2 2 TP1 BG55 1.0553 0.6409 -0.5854 15 54.3913 12.5249 156.8721 0.9953 0.2303

35 2006 1 1 A1 TS01 0.5038 0.6525 -0.5448 15 10.9666 1.4940 2.2320 0.9992 0.1362

35 2006 1 2 A2 TS03 0.6805 0.6776 -1.4607 15 12.8656 2.5914 6.7151 0.9983 0.2014

35 2006 2 1 BA* BG** 0.5394 0.7011 -0.2255 15 42.2135 3.7086 13.7537 0.9990 0.0879

35 2006 2 2 TP1 BG55 0.5955 0.6705 -0.2082 15 43.6172 3.9785 15.8286 0.9990 0.0912

35 2007 2 1 BA* BS** 0.8077 0.3957 -1.6296 15 9.6288 2.7639 7.6391 0.9984 0.2870

35 2007 2 2 TP1 BS55 0.6662 0.4153 -1.0251 15 8.5245 3.2107 10.3085 0.9974 0.3766

35 2118 1 1 A1 TS01 0.2731 0.1298 0.0000 15 2.5598 2.1970 4.8269 0.9944 0.8583

35 2118 1 2 TP1 BS55 0.5064 0.2923 -0.2238 15 5.5136 2.4358 5.9334 0.9979 0.4418

35 2118 2 1 BA* BG** 0.6992 0.6753 -0.2370 15 51.0614 3.8876 15.1132 0.9993 0.0761

35 2118 2 2 TP1 BG56 0.6065 0.6786 -0.1466 15 47.8181 2.3394 5.4728 0.9997 0.0489

35 2118 3 1 BA* BG** 0.8368 0.6790 0.0000 15 74.9557 5.2642 27.7122 0.9993 0.0702

35 2118 3 2 TP1 BG55 0.9554 0.6672 -0.1183 15 75.1762 4.7487 22.5504 0.9995 0.0632

35 3010 1 1 A1 TS01 0.7204 0.4099 0.0000 15 13.4100 7.8390 61.4499 0.9907 0.5846

35 3010 1 2 A2 TS03 0.6200 0.5703 -1.0452 15 10.6650 3.9780 15.8242 0.9957 0.3730

35 3010 2 1 BA* BG** 0.9575 0.6966 -0.0228 15 87.5216 7.6745 58.8976 0.9989 0.0877

35 3010 2 2 BA* BG** 0.6851 0.7610 0.0000 15 74.5450 12.4774 155.6846 0.9953 0.1674

35 6033 1 1 BA* BS** 0.9073 0.3140 -0.8156 15 9.0543 3.4644 12.0018 0.9984 0.3826

35 6033 1 2 A2 TS03 0.7294 0.8171 -1.3477 15 17.4512 3.7982 14.4267 0.9972 0.2177

35 6033 2 1 BA* BG** 0.6598 0.6857 0.0000 15 59.8510 8.0811 65.3044 0.9974 0.1350

35 6033 2 2 TP1 BG55 0.4777 0.7270 0.0000 15 47.3977 2.8824 8.3081 0.9994 0.0608

35 6035 1 1 A1 TS01 0.7396 0.1481 -2.0998 15 8.3569 3.8169 14.5685 0.9956 0.4567

35 6035 1 2 TP1 BS55 1.0431 0.2668 -1.5392 15 10.0157 3.3195 11.0192 0.9986 0.3314

35 6035 3 1 BA3 BG03 0.8740 0.5158 -0.0205 15 48.6443 4.9770 24.7702 0.9991 0.1023

35 6035 3 2 TP1 BG55 0.3365 0.8375 0.0000 15 43.2443 6.3093 39.8069 0.9960 0.1459

35 6401 1 1 A1 TS01 1.0291 0.5537 -2.8297 15 15.2862 3.4135 11.6521 0.9981 0.2233

35 6401 1 2 A2 TS03 0.8011 0.6618 -1.5567 15 14.1495 0.9985 0.9970 0.9998 0.0706

35 6401 3 1 BA* BG** 0.9800 0.6441 0.0000 15 80.7271 15.9003 252.8196 0.9948 0.1970

35 6401 3 2 TP1 BG** 0.9800 0.6441 0.0000 15 80.7271 15.9003 252.8196 0.9948 0.1970

36 0801 1 2 B1 BS01 0.4623 0.5655 -0.1668 15 9.3412 1.6278 2.6499 0.9990 0.1743

36 0802 1 2 B2 BS02 0.4891 0.6660 -0.6244 15 10.5343 2.4175 5.8445 0.9979 0.2295

36 1008 1 1 BA* BS** 0.8533 0.5917 -1.5578 15 13.8609 3.4739 12.0682 0.9980 0.2506

36 1008 1 2 TP BS55 0.6464 0.4130 -1.2083 15 8.2883 3.4294 11.7609 0.9967 0.4138

36 1011 1 1 BA* BS** 1.2531 0.2721 -1.8965 15 14.2170 6.1444 37.7537 0.9964 0.4322

36 1011 1 2 TP BS55 0.3868 0.0434 -0.5088 14 5.0715 4.9699 24.6996 0.9828 0.9800

36 1644 1 1 BA* BS** 0.7869 0.7098 -1.1339 15 16.3051 2.3951 5.7367 0.9991 0.1469

36 4018 1 1 BA* BS** 1.2293 0.4279 -1.1935 15 15.2980 4.0828 16.6694 0.9987 0.2669

37 0201 1 3 A2 TS02 0.4533 0.3225 -1.3388 15 4.9924 2.3729 5.6306 0.9966 0.4753

37 0206 1 3 A8 TS08 0.5075 0.2494 -2.1239 15 5.5917 1.6271 2.6475 0.9983 0.2910

37 0207 1 3 A11 TS11 0.3071 0.5937 -1.8885 15 4.9981 1.4187 2.0128 0.9971 0.2839

37 0210 1 3 A5 TS05 0.5609 0.2707 -0.9501 15 5.0398 2.1611 4.6702 0.9983 0.4288

37 0212 1 1 B5 BS05 0.7789 0.1193 0.0000 15 4.3337 2.6932 7.2531 0.9989 0.6214

37 0212 1 3 A14 TS14 0.4674 0.2894 -2.4036 15 5.6044 1.7037 2.9026 0.9977 0.3040

37 0801 1 2 B1 BS01 0.7232 0.6717 -0.5640 15 15.8361 2.0406 4.1641 0.9993 0.1289

37 0802 1 2 B2 BS02 0.6942 0.7289 -1.1240 15 15.0513 3.4940 12.2078 0.9975 0.2321

37 1006 1 1 BA2 BS02 0.9164 0.3319 -3.1837 15 12.7709 4.0516 16.4157 0.9960 0.3173

37 1006 1 2 TP BS55 0.8226 0.2487 -2.5525 15 10.6225 4.7713 22.7656 0.9939 0.4492

37 1006 2 1 BA1 BG01 0.9826 0.6171 -0.1741 15 63.9775 9.1950 84.5476 0.9978 0.1437

37 1006 2 2 TP1 BG55 1.0125 0.6169 -0.1279 15 69.1116 4.5007 20.2563 0.9995 0.0651

37 1024 1 2 TP BS55 0.3320 0.2857 -3.2671 14 4.9725 2.5609 6.5584 0.9874 0.5150

37 1024 2 1 BA* BG** 0.7243 0.7045 -0.2415 15 56.4088 7.4521 55.5338 0.9978 0.1321

37 1028 1 2 TP BS55 0.5957 0.5871 0.0000 14 13.8604 2.8360 8.0429 0.9984 0.2046

79
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

37 1030 1 2 TP BS55 0.5776 0.5130 0.0000 15 11.7039 4.0470 16.3786 0.9963 0.3458

37 1040 2 1 BA* BG** 0.6688 0.6185 -0.0045 15 50.1581 5.3333 28.4436 0.9987 0.1063

37 1040 2 2 TP BG55 0.8254 0.6915 -0.2682 15 60.5673 8.3977 70.5219 0.9977 0.1387

37 1352 1 2 TP BS55 0.6910 0.0000 0.0000 15 6.2336 6.2335 38.8571 0.9927 1.0000

37 1801 1 2 TP BS55 0.8054 0.2202 -2.9237 15 10.5320 3.3995 11.5569 0.9964 0.3228

37 1803 1 2 TP BS55 0.8492 0.2879 -1.4407 15 9.1823 4.7054 22.1410 0.9960 0.5124

37 1803 2 1 BA* BG** 0.6012 0.6739 0.0000 15 52.1425 12.4341 154.6067 0.9923 0.2385

37 1803 2 2 TP BG55 0.7949 0.7390 -0.4169 15 59.3161 7.6911 59.1527 0.9979 0.1297

37 1817 1 1 BA* BS** 0.9124 0.3333 -3.4651 15 13.2190 4.0068 16.0547 0.9956 0.3031

37 1817 1 2 TP BS55 0.9654 0.1769 -2.5638 15 11.9084 4.0678 16.5471 0.9967 0.3416

37 1992 1 1 BA* BS** 0.8120 0.2192 -0.9444 15 6.5814 3.3311 11.0965 0.9981 0.5061

37 2819 1 1 BA* BS** 0.5632 0.2011 -2.2567 15 6.3456 1.9793 3.9177 0.9979 0.3119

37 2819 1 2 TP BS55 0.7508 0.0614 -1.7706 15 7.5939 3.4340 11.7925 0.9968 0.4522

37 2825 1 2 TP BS55 0.5958 0.1375 -0.2998 15 4.4379 3.6210 13.1116 0.9964 0.8159

37 3008 1 1 BA* BS** 0.6223 0.3402 -2.8894 15 8.7603 3.6009 12.9661 0.9935 0.4110

37 3008 1 2 BA* BS** 0.6704 0.4799 -2.2577 15 9.8624 3.8740 15.0077 0.9948 0.3928

37 3011 1 1 BA* BS** 0.9754 0.2170 -0.4908 15 8.8436 6.0037 36.0446 0.9962 0.6789

37 3011 1 2 TP BS55 1.2689 0.2668 -1.9342 15 13.4837 4.6206 21.3501 0.9980 0.3427

37 3044 2 1 BA* BG** 0.7047 0.5818 -0.3382 15 36.6513 8.7532 76.6182 0.9952 0.2388

37 3044 2 2 BA* BG** 0.8331 0.5646 -0.3174 15 41.5713 7.4481 55.4742 0.9974 0.1792

37 3807 1 1 BA* BS** 0.7188 0.4839 -2.9830 15 11.3129 4.6917 22.0120 0.9919 0.4147

37 3807 1 2 TP BS55 0.7263 0.4405 -3.2208 15 10.9731 3.9086 15.2769 0.9940 0.3562

37 5037 1 1 BA* BS** 0.6293 0.3403 -2.3543 15 9.3646 5.6625 32.0642 0.9865 0.6047

37 5037 1 2 BA* BS** 0.8095 0.1422 -2.6958 15 10.5456 4.1501 17.2232 0.9949 0.3935

37 5827 1 1 BA* BS** 0.6703 0.4708 -2.8276 15 10.0631 3.8618 14.9137 0.9938 0.3838

37 5827 1 2 TP BS55 0.6923 0.2928 -2.4503 15 9.2849 4.4524 19.8240 0.9928 0.4795

38 0219 1 3 A14 TS27 0.7657 0.1591 -1.6992 15 6.5843 0.5169 0.2671 0.9999 0.0785

38 0219 1 3 A14 TS28 0.5685 0.1507 -2.8057 13 6.5594 0.4256 0.1811 0.9999 0.0649

38 0221 1 3 A20 TS40 0.7199 0.1386 -1.8029 13 5.1078 0.5500 0.3025 0.9999 0.1077

38 0221 1 3 A21 TS42 0.7785 0.2271 -2.2288 15 8.2173 0.4454 0.1983 0.9999 0.0542

38 0221 3 3 B13 BG12 1.0296 0.5450 0.0000 14 59.1369 6.0983 37.1893 0.9990 0.1031

38 0223 3 3 B12 BG11 1.0719 0.6569 -0.0664 14 78.4702 4.4137 19.4806 0.9996 0.0562

38 3005 2 1 BA* BG** 0.9006 0.3575 -0.7161 15 16.3261 6.2887 39.5482 0.9964 0.3852

38 3006 1 1 BA* BS** 0.6977 0.6230 -3.1469 15 11.4280 2.4777 6.1392 0.9976 0.2168

38 3006 1 2 TP* BS** 0.6985 0.5303 -2.2198 15 10.0854 1.7994 3.2379 0.9990 0.1784

38 3006 2 1 BA* BG** 0.6527 0.6024 -0.0942 15 43.1805 6.8477 46.8905 0.9973 0.1586

38 3006 2 2 TP* BG** 0.3656 0.8232 -0.0286 15 43.6899 5.1463 26.4848 0.9976 0.1178

39 0101 2 2 B16 BG16 1.3235 0.6547 0.0000 14 101.9413 9.9099 98.2065 0.9988 0.0972

39 0102 2 2 B18 BG18 1.3342 0.6330 0.0000 14 95.7167 5.3768 28.9097 0.9996 0.0562

39 0106 1 2 B2 BS02 1.5063 0.3014 -0.9646 14 12.3440 1.8809 3.5379 0.9998 0.1524

39 0107 1 1 B3 BS03 1.1437 0.2312 -2.5223 15 13.2773 1.6224 2.6320 0.9996 0.1222

39 0108 1 1 B5 BS05 1.0460 0.2559 -1.6620 15 9.7165 1.2973 1.6829 0.9998 0.1335

39 0108 2 2 B19 BG19 0.9477 0.5841 -0.0283 14 58.5248 4.9704 24.7051 0.9993 0.0849

39 0203 2 2 B23 BG23 1.3221 0.5554 -0.0436 14 76.0211 5.9199 35.0458 0.9994 0.0779

39 0204 3 1 B19 BG19 1.2464 0.5372 0.0000 14 70.0611 5.6160 31.5398 0.9994 0.0802

39 0209 2 1 B22 BG22 1.2262 0.6116 0.0000 13 78.9295 5.7591 33.1673 0.9995 0.0730

39 0210 2 1 B20 BG20 0.7285 0.8353 0.0000 14 83.3119 4.4737 20.0137 0.9995 0.0537

39 0211 1 2 B6 BS06 1.3626 0.3090 -0.2987 15 13.9226 2.9887 8.9323 0.9996 0.2147

39 0803 1 3 A4 TS07 1.8490 0.2425 -1.3345 15 15.1620 1.7963 3.2267 0.9999 0.1185

39 0804 1 3 A1 TS13 1.3505 0.2300 -1.9049 15 13.1974 1.9383 3.7568 0.9997 0.1469

39 0804 3 1 B6 BG06 1.0810 0.6542 -0.0182 13 76.6177 4.2136 17.7548 0.9997 0.0550

39 0809 3 2 B7 BG07 1.1805 0.5990 0.0000 14 78.2695 4.3249 18.7047 0.9997 0.0553

39 0810 1 2 B4 BS04 1.0565 0.2802 -3.9932 15 15.7864 2.1498 4.6215 0.9989 0.1362

39 0810 3 2 B8 BG08 1.0751 0.6261 -0.0474 14 73.1927 6.4980 42.2246 0.9991 0.0888

39 3013 1 1 A1 TS02 0.5991 0.3751 -4.0511 15 9.6988 4.1732 17.4159 0.9876 0.4303

39 3013 1 2 A2 TS03 0.8795 0.3858 -5.8718 15 15.3849 3.1500 9.9227 0.9949 0.2047

80
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

39 3801 1 1 BA* BS** 1.5905 0.2845 -2.3499 15 18.1764 1.4295 2.0435 0.9999 0.0786

39 3801 1 2 BA* BS** 1.3816 0.4328 -1.4045 14 15.2036 1.2717 1.6172 0.9999 0.0836

39 4031 1 1 BA* BS** 1.8391 0.2655 -2.0338 15 19.1379 1.7028 2.8994 0.9999 0.0890

39 4031 1 2 B* BS** 1.5370 0.3557 -1.6368 14 14.1414 1.3570 1.8416 0.9999 0.0960

39 4031 2 1 BA* BG** 0.9639 0.5048 -0.1818 15 45.3001 10.8097 116.8488 0.9958 0.2386

39 4031 2 2 BA* BG** 0.7575 0.6792 0.0000 15 65.7124 6.2888 39.5489 0.9988 0.0957

39 5003 1 1 BA* BS** 1.2735 0.2940 -3.2631 14 14.7829 1.5177 2.3035 0.9997 0.1027

39 5003 1 2 BA* BG** 1.3413 0.2548 -2.8297 15 16.8755 1.7787 3.1639 0.9997 0.1054

39 5003 2 1 BA* BG** 1.1465 0.4724 0.0000 15 56.8831 8.3130 69.1059 0.9984 0.1461

39 5003 2 2 BA* BG** 0.7158 0.7927 -0.1822 15 72.2603 3.7138 13.7924 0.9996 0.0514

39 5010 1 2 BA* BS** 0.9527 0.4270 -2.8889 15 13.4263 3.7567 14.1131 0.9970 0.2798

39 7021 1 1 BA* BS** 1.0532 0.4167 -4.3618 15 16.5995 1.2925 1.6707 0.9996 0.0779

39 7021 1 2 BA* BS** 1.2614 0.1805 -2.4099 15 14.3301 1.8556 3.4432 0.9996 0.1295

39 7021 2 1 BA* BG** 0.7853 0.5365 0.0000 15 46.8231 6.0738 36.8907 0.9984 0.1297

39 7021 2 2 BA* BG** 0.6546 0.7917 -0.2778 15 61.4396 3.4390 11.8264 0.9995 0.0560

39 9006 1 1 A1 TS02 0.7979 0.1969 -4.7725 15 12.9144 1.5188 2.3068 0.9988 0.1176

39 9006 1 2 BA* BS** 1.1796 0.2895 -1.3390 14 10.6948 1.0943 1.1974 0.9999 0.1023

39 9006 2 1 BA* BG** 0.6696 0.7168 -0.1912 15 55.2714 5.6925 32.4043 0.9986 0.1030

39 9006 2 2 BA* BG** 0.7314 0.6309 -0.0579 15 53.6655 5.3642 28.7742 0.9988 0.1000

39 9022 1 1 BA* BS** 0.9700 0.2885 -2.2142 15 10.7029 1.6258 2.6431 0.9995 0.1519

39 9022 1 2 BA* BS** 1.2538 0.2363 -1.3040 14 8.8109 1.5731 2.4748 0.9998 0.1785

40 0114 1 2 B1 BS01 0.6288 0.2585 -0.3183 15 5.6036 2.1666 4.6943 0.9989 0.3867

40 0116 1 2 B2 BS02 0.7489 0.1739 0.0000 15 5.5532 2.8508 8.1271 0.9987 0.5134

40 0117 1 2 B3 BS03 0.8804 0.2326 0.0000 15 9.4557 5.7176 32.6911 0.9964 0.6047

40 0120 1 2 B5 BS05 0.8234 0.2199 0.0000 15 8.2045 4.8307 23.3353 0.9971 0.5888

40 0121 1 3 A14 TS27 0.5877 0.0915 -1.7329 15 5.5403 1.8775 3.5251 0.9985 0.3389

40 0122 1 2 B4 BS04 0.7352 0.2144 -0.0206 15 6.2618 2.5809 6.6610 0.9989 0.4122

40 0123 1 2 B6 BS06 1.0303 0.2341 0.0000 15 13.1087 9.6699 93.5063 0.9926 0.7377

40 0124 1 3 A17 TS33 0.5897 0.0185 -1.1002 15 4.3894 2.0908 4.3715 0.9984 0.4763

40 1015 1 1 A1 TS01 1.0432 0.1972 -1.7187 15 9.2633 1.3513 1.8261 0.9998 0.1459

40 1015 1 2 A2 TS03 0.5881 0.3653 -0.1026 15 8.6658 4.0718 16.5793 0.9960 0.4699

40 1017 1 1 A1 TS01 1.7708 0.4159 -1.3840 15 23.2895 11.2262 126.0274 0.9951 0.4820

40 1017 1 2 A2 TS03 0.7012 0.6516 -1.5159 15 12.5003 2.0748 4.3050 0.9990 0.1660

40 3018 1 1 A1 TS01 0.5833 0.5169 -4.2692 15 9.3121 2.2222 4.9381 0.9963 0.2386

40 3018 1 2 A2 TS03 0.2960 0.0000 -2.1828 15 3.5950 1.9737 3.8954 0.9928 0.5490

40 4086 1 1 A1 TS01 0.5422 0.6520 -4.0088 15 8.9576 2.6429 6.9847 0.9946 0.2950

40 4086 1 2 A2 TS03 0.5464 0.5555 -2.6984 15 8.3427 1.9925 3.9701 0.9978 0.2388

40 4087 1 1 A1 TS01 1.7265 0.2555 -0.6188 15 13.4423 1.6242 2.6379 0.9999 0.1208

40 4087 1 2 BA* BS** 0.5161 0.2697 0.0000 15 16.0911 15.2534 232.6666 0.9319 0.9479

40 4088 1 2 BA* BS** 0.5991 0.2581 -1.9140 15 6.3004 2.2542 5.0814 0.9978 0.3578

40 4155 1 1 A1 TS01 0.7895 0.5631 -3.6829 15 12.2987 2.4675 6.0887 0.9980 0.2006

40 4155 1 2 BA* BS** 0.9793 0.4536 -2.3316 15 13.0311 3.0449 9.2715 0.9985 0.2337

40 4157 1 1 BA* BS** 0.6765 0.5117 -0.6596 15 11.3167 3.7357 13.9554 0.9971 0.3301

40 4157 1 2 BA* BS** 0.6748 0.6605 -1.3037 15 12.5993 2.2571 5.0945 0.9988 0.1791

40 4158 1 1 BA* BS** 0.6912 0.5342 -1.9908 15 10.6815 3.6615 13.4066 0.9961 0.3428

40 4158 1 2 BA* BS** 0.6080 0.3899 -1.3724 15 7.5637 3.3252 11.0572 0.9963 0.4396

40 4160 1 1 A1 TS01 0.5848 0.3835 -5.9611 15 9.3646 3.3566 11.2667 0.9885 0.3584

40 4160 1 2 A2 TS02 1.0501 0.4262 -1.7440 15 13.0136 3.2212 10.3762 0.9987 0.2475

40 4160 2 1 BA* BG** 0.9827 0.3492 -0.0154 15 32.0665 7.2453 52.4938 0.9977 0.2259

40 4160 2 2 BA* BG** 0.9216 0.5836 -0.0393 15 61.3965 9.6157 92.4612 0.9973 0.1566

40 4161 1 1 A1 TS01 0.6876 0.1714 0.0000 15 11.0000 10.1482 102.9855 0.9814 0.9226

40 4161 1 2 A2 TS03 0.5642 0.1977 -0.0065 15 8.8452 7.8870 62.2048 0.9833 0.8917

40 4162 1 1 A1 TS01 1.2183 0.5652 -1.8572 15 18.4623 2.9331 8.6030 0.9992 0.1589

40 4162 1 2 A2 TS03 0.7156 0.2577 -1.8255 15 7.3988 2.8343 8.0331 0.9977 0.3831

40 4164 1 1 BA* BS** 0.7598 0.5080 -0.8089 15 12.1212 3.8623 14.9177 0.9974 0.3186

40 4164 1 2 A2 TS03 0.7977 0.6125 -1.1781 15 14.0655 2.1484 4.6156 0.9992 0.1527

81
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

40 4166 1 1 BA* BS** 0.6403 0.1545 0.0000 15 7.2230 6.2647 39.2470 0.9917 0.8673

40 4166 1 2 A2 TS03 0.7740 0.1165 -2.2322 15 8.4046 4.0599 16.4826 0.9957 0.4831

40 5021 1 2 A2 TS01 0.5350 0.0000 -0.6667 15 6.6961 6.3165 39.8978 0.9848 0.9433

40 6010 1 1 BA* BS** 1.1617 0.2813 -1.0623 15 10.2850 3.1847 10.1424 0.9991 0.3096

40 6010 1 2 BA* BS** 1.0072 0.2751 -0.6287 15 9.8899 5.3661 28.7954 0.9971 0.5426

40 7024 1 1 A1 TS01 0.6482 0.4314 -2.7779 15 9.1781 3.3174 11.0053 0.9953 0.3614

40 7024 1 2 A2 TS03 0.7882 0.1866 -1.5423 15 9.4466 6.8567 47.0143 0.9897 0.7258

41 2002 1 1 A1 TS01 0.1994 0.5385 -2.2799 15 3.1045 1.3327 1.7760 0.9932 0.4293

41 2002 1 2 A2 TS03 0.3939 0.4940 -2.0941 15 5.5609 1.7347 3.0092 0.9971 0.3119

41 5005 1 1 A1 TS01 0.4772 0.2917 -2.2655 15 5.3426 1.1851 1.4045 0.9990 0.2218

41 5005 1 2 A2 TS03 0.5785 0.1770 -2.9179 15 7.1401 0.9754 0.9513 0.9994 0.1366

41 5006 1 1 A1 TS01 0.5503 0.2553 -2.4153 15 6.2731 1.1852 1.4048 0.9992 0.1889

41 5006 1 1 BA* BS** 0.6064 0.1979 -0.8382 15 3.9976 1.2551 1.5752 0.9995 0.3140

41 5006 1 2 BA* BS** 0.2850 0.7409 -2.7081 15 5.3247 1.4871 2.2114 0.9956 0.2793

41 5006 2 1 BA* BG** 1.0135 0.1741 0.0000 15 14.1320 1.6635 2.7673 0.9998 0.1177

41 5006 2 2 BA* BG** 1.0411 0.1936 0.0000 15 16.4050 1.2461 1.5528 0.9999 0.0760

41 5006 3 2 BA* BG** 0.5314 0.5185 -0.1905 15 25.6261 4.5654 20.8425 0.9976 0.1782

41 5008 1 1 BA* BS** 0.8025 0.2465 -0.8242 15 6.1389 1.6796 2.8210 0.9995 0.2736

41 5008 1 2 BA* BS** 1.0517 0.1759 -0.1054 15 6.4417 1.1887 1.4129 0.9999 0.1845

41 5022 1 2 BA6 BS16 0.9010 0.2600 -1.0831 15 7.3860 1.5785 2.4915 0.9996 0.2137

41 6011 1 1 A1 TS01 0.5741 0.2144 -1.1075 15 4.1952 0.7865 0.6185 0.9998 0.1875

41 6011 1 2 A2 TS03 0.4429 0.2012 -2.0200 15 4.3665 0.6748 0.4554 0.9996 0.1545

41 7018 1 1 BA* BS** 0.6390 0.1580 -2.3917 15 7.1201 0.7665 0.5875 0.9997 0.1076

41 7018 1 2 BA* BS** 0.9140 0.1529 -0.0717 15 5.1195 1.5882 2.5225 0.9997 0.3102

41 7019 1 1 BA* BS** 0.8883 0.1998 0.0000 15 8.9560 6.1635 37.9882 0.9959 0.6882

41 7019 1 2 BA* BS** 1.0430 0.2763 0.0000 15 11.7100 4.9578 24.5801 0.9981 0.4234

41 7025 1 2 A2 TS05 0.7142 0.2945 -4.7190 15 11.2517 2.2405 5.0198 0.9970 0.1991

42 0603 1 2 B5 BS05 0.8429 0.2252 0.0000 15 7.9144 3.8112 14.5250 0.9983 0.4815

42 0608 1 2 BA6 BS06 0.7779 0.2264 -0.5420 15 5.8285 2.4156 5.8350 0.9990 0.4144

42 1597 1 1 BA1 BS01 1.2179 0.2240 -1.3571 15 11.1283 5.2052 27.0944 0.9976 0.4677

42 1597 1 2 TP BS55 0.9290 0.2135 0.0000 15 16.1797 14.4547 208.9396 0.9797 0.8934

42 1598 1 2 BA6 BS06 0.8814 0.2810 0.0000 15 30.5068 29.1444 849.3943 0.9162 0.9553

42 1599 1 1 BA* BS** 1.1976 0.2726 -1.4671 15 11.2610 3.5947 12.9217 0.9988 0.3192

42 1599 1 2 TP BS55 0.8779 0.3119 -1.6200 15 9.2788 3.2764 10.7350 0.9981 0.3531

42 1605 1 1 BA2 BS02 1.1296 0.2423 -2.7411 15 14.5193 4.8309 23.3378 0.9965 0.3327

42 1605 1 2 TP BS55 0.7416 0.1876 -3.6869 14 11.3205 4.9672 24.6734 0.9889 0.4388

42 1606 1 1 BA2 BS02 1.0593 0.0861 -0.1187 15 8.2531 7.7058 59.3792 0.9951 0.9337

42 1606 1 2 BA5 BS04 1.3631 0.2563 0.0000 15 13.9993 5.7341 32.8805 0.9985 0.4096

42 1608 1 1 BA1 BS01 1.1241 0.2083 -0.5573 15 8.1766 4.0561 16.4521 0.9987 0.4961

42 1613 1 1 BA* BS** 0.6696 0.6107 -2.6245 15 11.0678 3.2580 10.6148 0.9961 0.2944

42 1613 1 2 BA* BS** 0.7219 0.4706 -2.2170 14 10.8923 4.4822 20.0902 0.9940 0.4115

42 1613 2 1 BA1 BG01 0.8608 0.7675 -0.4527 15 67.4814 8.4253 70.9859 0.9980 0.1249

42 1614 1 1 BA* BS** 1.1678 0.3567 -1.9054 14 14.4923 5.3291 28.3991 0.9970 0.3677

42 1614 1 2 BA* BS** 1.4264 0.2147 -1.4519 15 12.0917 3.1325 9.8123 0.9993 0.2591

42 1614 2 1 BA* BG** 0.6597 0.6437 -0.2470 15 43.8404 3.1860 10.1506 0.9994 0.0727

42 1617 1 1 BA* BS** 1.7221 0.4466 -2.7154 15 24.0327 4.9292 24.2971 0.9985 0.2051

42 1617 1 2 BA* BS** 1.0380 0.3248 -3.0124 15 14.5857 5.1336 26.3537 0.9950 0.3520

42 1618 1 1 BA* BS** 0.8466 0.0940 0.0000 15 15.7954 15.5357 241.3591 0.9710 0.9836

42 1618 2 1 BA* BG** 0.7340 0.7223 -0.4796 14 51.9994 6.8455 46.8612 0.9979 0.1316

42 1623 1 1 BA* BS** 1.1494 0.3166 -1.3721 15 11.2787 2.9156 8.5008 0.9992 0.2585

42 1623 1 2 BA5 BS05 0.8315 0.4185 -2.4920 15 11.2998 3.8210 14.5999 0.9964 0.3381

42 1627 1 1 BA* BS** 1.1344 0.2458 -0.7043 15 9.5244 4.5863 21.0340 0.9983 0.4815

42 1627 1 2 BA* BS** 1.0536 0.4409 -2.0805 15 14.1108 4.6979 22.0705 0.9970 0.3329

42 1690 1 1 BA* BS** 1.1688 0.2724 0.0000 15 14.9389 9.5433 91.0754 0.9944 0.6388

42 1690 1 2 BA* BS** 0.7380 0.3412 -0.9247 15 7.9361 3.3480 11.2092 0.9977 0.4219

42 3044 1 1 BA1 BS01 1.4695 0.4205 -3.1776 15 21.3035 4.6973 22.0645 0.9979 0.2205

82
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

42 5020 1 2 BA5 BS04 0.8639 0.5063 -1.0841 15 12.5725 2.1072 4.4404 0.9994 0.1676

42 7025 1 1 BA* BS** 0.8528 0.4199 -2.2559 15 12.2311 5.5955 31.3100 0.9931 0.4575

42 7025 1 2 BA* BS** 0.8620 0.6210 -2.3223 15 14.6346 5.3154 28.2534 0.9942 0.3632

42 7025 2 2 BA* BG** 1.2372 0.5122 -0.4399 15 47.7571 9.7326 94.7229 0.9975 0.2038

42 7037 1 1 BA* BS** 1.2869 0.2822 -1.3211 15 12.1342 4.1306 17.0618 0.9987 0.3404

42 7037 1 2 BA* BS** 1.0692 0.2131 -0.8617 15 8.6850 4.8633 23.6512 0.9977 0.5600

42 7037 2 1 BA3 BG03 0.8159 0.5241 0.0000 15 47.6005 7.7802 60.5310 0.9975 0.1634

42 7037 2 2 BA5 BG05 1.3511 0.4294 -0.4827 15 38.1261 10.7165 114.8433 0.9967 0.2811

42 9027 1 2 BA* BS** 1.1214 0.1738 -0.7099 15 7.8782 4.8097 23.1334 0.9980 0.6105

45 1008 1 1 A1 TS01 0.9584 0.5623 -2.6292 15 14.5498 2.1731 4.7222 0.9991 0.1494

45 1008 1 2 A2 TS03 0.6119 0.2568 0.0000 15 10.4462 8.7071 75.8142 0.9829 0.8335

45 1008 2 1 BA* BG** 0.5487 0.7521 -0.1001 15 53.7453 3.4792 12.1046 0.9994 0.0647

45 1008 2 2 TP1 BG55 0.8435 0.7367 -0.2961 15 69.2724 4.6863 21.9612 0.9994 0.0677

45 1011 1 1 BA* BS** 0.8791 0.5004 -0.7119 15 13.6214 2.7876 7.7706 0.9990 0.2046

45 1011 1 2 BA* BS** 0.8041 0.4662 -0.4398 15 12.4319 2.7275 7.4393 0.9990 0.2194

45 1011 2 1 BA* BG** 0.8686 0.6486 0.0000 15 74.1676 23.4012 547.6161 0.9862 0.3155

45 1011 2 2 BA* BG** 1.2357 0.5509 0.0000 15 77.7528 15.0246 225.7375 0.9963 0.1932

45 1024 1 1 A1 TS01 0.9860 0.3844 -2.0542 15 12.5254 4.7007 22.0968 0.9966 0.3753

45 1024 1 2 TP1 BS55 1.0778 0.2189 -2.2483 15 12.5007 5.0386 25.3870 0.9963 0.4031

45 1024 2 1 BA* BG** 0.5058 0.7978 -0.0066 15 59.2241 4.5845 21.0178 0.9989 0.0774

45 1024 2 2 TP1 BG55 0.4304 0.8535 -0.0496 15 56.2340 2.7222 7.4102 0.9995 0.0484

45 1025 1 1 A1 TS01 0.6298 0.4025 0.0000 15 9.8305 3.0734 9.4456 0.9981 0.3126

45 1025 1 2 A2 TS03 0.8716 0.4924 -5.2213 15 14.2812 3.3376 11.1398 0.9954 0.2337

45 1025 2 1 BA* BG** 0.6765 0.6035 -0.0609 15 46.7493 2.7040 7.3115 0.9996 0.0578

45 1025 2 2 TP1 BG** 0.8929 0.6805 -0.1293 15 71.4322 4.1134 16.9201 0.9996 0.0576

45 3012 1 1 A1 TS01 0.5775 0.3749 -3.0666 15 8.2779 2.7739 7.6948 0.9953 0.3351

45 3012 1 2 A2 TS03 0.5603 0.4095 -4.3981 15 9.0701 3.0086 9.0518 0.9921 0.3317

45 5017 1 1 A1 TS01 0.8494 0.4346 -0.7402 15 11.7830 3.8878 15.1153 0.9979 0.3300

45 5017 1 2 BA* BS** 0.7194 0.5896 0.0000 14 16.9997 5.2463 27.5236 0.9961 0.3086

45 5034 1 1 A1 TS01 0.9504 0.5001 -1.5595 15 13.9786 5.3898 29.0500 0.9959 0.3856

45 5034 1 2 A2 TS03 0.7599 0.4244 -1.8524 15 9.7174 2.9941 8.9644 0.9978 0.3081

45 5035 1 1 A1 TS01 0.6324 0.7250 -1.3138 15 13.1283 2.5475 6.4899 0.9983 0.1940

45 5035 1 2 A2 TS03 0.8516 0.3949 -0.4930 15 11.6157 4.5648 20.8377 0.9973 0.3930

45 7019 1 1 A1 TS01 0.8309 0.3925 -1.7864 15 10.6064 4.5556 20.7534 0.9958 0.4295

45 7019 1 2 A2 TS03 0.4102 0.6064 -1.0110 15 7.4814 1.8731 3.5086 0.9979 0.2504

46 0804 1 3 A5 TS10 1.0014 0.1792 -0.5826 15 5.6290 1.2340 1.5228 0.9998 0.2192

46 0804 1 3 A6 TS12 1.0125 0.2113 -1.1664 14 7.4543 1.4291 2.0425 0.9998 0.1917

46 3009 1 1 A1 TS02 1.5606 0.2006 -1.1031 15 10.9052 1.2399 1.5373 0.9999 0.1137

46 3009 2 1 BA* BG** 0.8673 0.5690 -0.2010 15 49.3638 16.8450 283.7539 0.9892 0.3412

46 3009 2 2 TP* BG** 0.6031 0.7497 -0.0289 15 60.9481 5.8817 34.5944 0.9986 0.0965

46 3010 1 1 BA* BS** 0.9322 0.3758 -2.7217 15 12.0752 2.3515 5.5293 0.9988 0.1947

46 3010 1 2 TP* BS** 1.0380 0.4275 -3.1172 15 14.6385 2.8377 8.0523 0.9985 0.1938

46 3010 2 1 BA* BG** 0.5338 0.7779 -0.1845 15 51.6920 5.5391 30.6814 0.9983 0.1072

46 3010 2 2 TP* BG** 0.5876 0.6184 -0.0587 15 41.9237 8.9799 80.6390 0.9948 0.2142

46 3012 1 2 TP* BS** 1.2348 0.2422 -2.5427 15 14.5183 1.8950 3.5911 0.9996 0.1305

46 3012 2 2 TP* BG** 0.8957 0.5861 0.0000 15 61.4029 8.3851 70.3101 0.9980 0.1366

46 3013 1 1 BA* BS** 0.8050 0.4527 -2.8605 15 11.3293 2.3970 5.7457 0.9983 0.2116

46 3013 1 2 TP* BS** 0.4566 0.9315 -2.9497 15 10.2363 3.2072 10.2859 0.9923 0.3133

46 3013 2 1 BA* BG** 0.8500 0.5165 0.0000 15 48.3228 9.9216 98.4390 0.9962 0.2053

46 3013 2 2 TP* BG** 0.8512 0.5507 -0.0674 15 50.3168 11.1993 125.4248 0.9954 0.2226

46 3052 1 1 A1 TS01 0.8446 0.1040 -1.6726 15 7.2552 0.3888 0.1512 1.0000 0.0536

46 3052 1 2 A2 TS03 0.9241 0.2112 -1.8830 15 8.9443 1.6171 2.6149 0.9995 0.1808

46 3052 2 1 BA* BG** 0.7146 0.7893 -0.4298 15 59.4961 12.6767 160.6987 0.9939 0.2131

46 3052 2 2 TP* BG** 0.6374 0.8206 -0.3821 15 59.1952 11.2968 127.6171 0.9946 0.1908

46 3053 1 1 TP* BS56 1.7962 0.3681 0.0000 15 25.0367 6.0484 36.5830 0.9991 0.2416

46 3053 1 2 TP* BS55 1.2268 0.4501 -2.1052 14 15.7522 1.4936 2.2308 0.9998 0.0948

83
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

46 3053 2 1 TP* BG** 0.8185 0.7113 0.0000 15 77.8152 3.4433 11.8566 0.9997 0.0443

46 3053 2 2 TP* BG55 1.1884 0.5823 -0.2036 14 64.9293 6.3667 40.5343 0.9991 0.0981

46 5020 1 1 BA* BS** 2.7055 0.4640 -0.8565 12 35.1499 3.1575 9.9701 0.9999 0.0898

46 5020 1 2 TP* BS** 1.5206 0.6009 -1.0997 12 23.2240 3.4530 11.9230 0.9995 0.1487

46 5025 1 1 A1 TS01 0.8830 0.1689 -2.5597 15 10.2432 0.6086 0.3704 0.9999 0.0594

46 5025 1 2 A2 TS03 0.5766 0.1952 -1.9920 15 5.6501 0.7813 0.6104 0.9997 0.1383

46 5025 2 1 BA* BG** 0.9986 0.5352 -0.1822 14 48.4778 5.0833 25.8399 0.9991 0.1049

46 5025 2 2 TP* BG** 0.5190 0.7112 -0.1280 15 44.2861 6.6796 44.6170 0.9969 0.1508

46 5040 1 1 A1 TS01 0.7909 0.2828 -3.0264 15 10.2181 0.8014 0.6423 0.9998 0.0784

46 5040 1 2 TP* BS** 0.7266 0.3868 -2.9324 15 9.8406 1.8869 3.5602 0.9987 0.1917

46 5040 2 1 BA* BG** 0.6632 0.6993 0.0000 15 60.6216 5.1603 26.6284 0.9990 0.0851

46 5040 2 2 TP* BG** 0.5935 0.7513 -0.0979 15 57.3438 4.4212 19.5467 0.9991 0.0771

46 5040 3 1 BA* BG** 0.6328 0.7042 0.0000 15 58.7378 3.1279 9.7837 0.9996 0.0533

46 5040 3 2 TP* BG** 0.5499 0.7878 -0.2430 14 48.8398 5.3293 28.4011 0.9983 0.1091

46 6600 1 1 TP1 BS55 1.1863 0.2317 -0.5790 15 8.3740 0.9404 0.8844 0.9999 0.1123

46 6600 1 2 TP2 BS56 1.0023 0.1514 -1.3986 14 7.8296 1.0442 1.0904 0.9999 0.1334

46 7049 1 1 A1 TS01 1.5136 0.1861 -1.2292 15 10.9340 1.3506 1.8242 0.9999 0.1235

46 7049 1 2 TP1 BS** 0.8353 0.1960 -1.7720 15 7.5593 0.7829 0.6129 0.9999 0.1036

46 7049 2 1 BA* BG** 0.5622 0.6946 -0.1306 15 45.9112 8.3765 70.1656 0.9957 0.1825

46 7049 2 2 TP* BG** 0.6955 0.6255 -0.3226 15 41.5335 7.9110 62.5833 0.9964 0.1905

46 9106 1 1 BA* BS** 1.1870 0.2524 -0.6165 15 9.0984 1.9959 3.9837 0.9997 0.2194

46 9106 1 2 A2 TS04 1.0458 0.1937 -1.6813 15 9.1558 0.9413 0.8860 0.9999 0.1028

46 9106 2 2 TP* BG** 0.5238 0.7802 -0.1904 14 51.4747 6.8047 46.3046 0.9974 0.1322

46 9106 2 1 BA* BG** 1.8358 0.3683 -0.5697 15 36.7206 4.5272 20.4955 0.9996 0.1233

46 9197 1 1 BA* BS** 1.4855 0.2598 -0.7724 15 11.5107 1.0718 1.1488 0.9999 0.0931

46 9197 2 1 BA* BG** 0.7879 0.6616 -0.0875 15 61.4780 4.2921 18.4225 0.9994 0.0698

46 9197 2 2 TP* BG** 1.0141 0.5245 -0.1141 15 53.3287 3.6552 13.3603 0.9996 0.0685

46 9197 3 1 BA* BG** 0.9735 0.5689 -0.2246 15 53.2131 5.0722 25.7276 0.9992 0.0953

46 9197 3 2 TP* BG** 0.8925 0.5091 0.0000 15 49.3730 4.7788 22.8370 0.9992 0.0968

47 1023 1 1 A1 TS01 1.0786 0.2218 -3.0252 15 13.8537 2.1721 4.7179 0.9992 0.1568

47 1023 1 2 A2 TS03 1.2949 0.3683 -3.3139 15 18.9807 6.8685 47.1759 0.9939 0.3619

47 1023 2 2 BA* BG** 0.8648 0.6731 0.0000 15 77.8210 24.1529 583.3605 0.9860 0.3104

47 1028 1 1 A1 TS01 1.2481 0.2578 -1.5370 15 12.3083 5.3024 28.1152 0.9976 0.4308

47 1028 1 2 A2 TS03 0.8043 0.0949 -2.3105 15 9.0333 2.7403 7.5091 0.9980 0.3034

47 1028 2 1 BA* BG** 1.1137 0.6494 0.0000 15 91.8633 10.7345 115.2304 0.9982 0.1169

47 1028 2 2 TP1 BG55 0.9327 0.7073 0.0000 15 88.5205 6.8098 46.3732 0.9991 0.0769

47 1029 1 1 BA* BS** 0.8849 0.4230 -2.1874 15 11.8374 4.9107 24.1146 0.9952 0.4148

47 1029 1 2 TP1 BS55 1.4501 0.2150 -1.2842 15 14.3676 8.7824 77.1311 0.9953 0.6113

47 1029 2 1 BA* BG** 0.7273 0.8019 -0.0465 15 84.0687 5.7557 33.1284 0.9992 0.0685

47 1029 2 2 TP1 BG55 1.0711 0.5600 -0.0865 15 63.9161 10.5702 111.7286 0.9974 0.1654

47 2001 1 1 A1 TS01 0.7135 0.3533 -3.6649 15 10.2850 1.9889 3.9558 0.9982 0.1934

47 2001 1 2 A2 TS03 0.9409 0.3478 -3.0080 15 12.7809 3.8818 15.0685 0.9966 0.3037

47 2008 1 1 A1 TS01 0.8779 0.5949 -3.0326 15 14.5350 4.7821 22.8686 0.9945 0.3290

47 2008 1 2 A2 TS03 0.7039 0.1426 -1.4181 15 7.5574 5.3151 28.2505 0.9924 0.7033

47 3075 1 2 TP1 BS55 0.8884 0.3764 -1.6948 15 10.2725 2.9924 8.9542 0.9984 0.2913

47 3075 2 2 TP1 BG55 0.6575 0.8543 0.0000 15 87.4282 6.0281 36.3380 0.9991 0.0689

47 3101 1 1 A1 TS01 0.7853 0.1677 0.0000 15 12.8767 11.9530 142.8747 0.9803 0.9283

47 3101 1 2 A2 TS03 0.9733 0.0706 -3.1421 15 14.5104 5.9779 35.7349 0.9917 0.4120

47 3101 2 1 BA* BG** 1.2076 0.5647 -0.1090 15 71.6649 7.9968 63.9488 0.9988 0.1116

47 3101 2 2 TP1 BG55 1.8474 0.5231 -0.2039 15 90.9057 24.5441 602.4151 0.9943 0.2700

47 3104 1 1 A1 TS01 0.8583 0.3951 -2.5626 15 11.4247 3.5042 12.2792 0.9971 0.3067

47 3104 1 2 A2 TS03 1.0671 0.7672 -3.6486 15 19.6622 3.4665 12.0164 0.9979 0.1763

47 3104 2 1 BA* BG** 1.0306 0.6849 0.0000 15 118.1427 78.0074 6085.1500 0.9052 0.6603

47 3104 2 2 TP1 BG55 0.7363 0.7146 0.0000 15 70.9373 10.2498 105.0592 0.9969 0.1445

47 3108 1 1 A1 TS01 0.6470 0.4496 -2.0586 15 8.7325 2.7688 7.6660 0.9973 0.3171

47 3108 1 2 TP1 BS55 0.7829 0.0000 -3.3939 15 12.4377 5.1447 26.4681 0.9899 0.4136

84
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

47 3108 2 1 BA* BG** 0.7518 0.8033 -0.1174 15 82.3921 3.3388 11.1474 0.9997 0.0405

47 3108 2 2 TP1 BG** 1.1590 0.6200 0.0000 15 87.5784 8.8720 78.7129 0.9988 0.1013

47 3109 1 1 A1 TS01 0.8278 0.3696 -3.5625 15 11.8201 2.9844 8.9068 0.9971 0.2525

47 3109 1 2 TP1 BS55 0.8609 0.0000 -1.9870 15 11.6292 7.3989 54.7442 0.9880 0.6362

47 3109 2 2 TP1 BG55 0.7034 0.9260 -0.1367 15 100.6816 3.0394 9.2379 0.9998 0.0302

47 3110 1 1 A1 TS01 1.0502 0.1794 -3.1042 15 14.4364 5.4579 29.7884 0.9943 0.3781

47 3110 2 2 TP1 BG55 0.9401 0.7373 -0.0074 15 95.8770 6.5525 42.9347 0.9993 0.0683

47 6015 1 1 A1 TS01 0.6318 0.5032 -3.4845 15 9.6273 2.6672 7.1137 0.9963 0.2770

47 6015 1 2 A2 TS03 0.5653 0.4175 -2.0241 15 7.4948 2.9248 8.5545 0.9960 0.3902

47 6015 2 1 BA* BG** 0.8159 0.7663 -0.1549 15 79.6900 5.2476 27.5375 0.9993 0.0659

47 6015 2 2 TP1 BG55 1.1750 0.5796 0.0000 15 81.5816 8.9494 80.0916 0.9986 0.1097

47 6022 1 1 A1 TS01 0.8717 0.3258 -1.6146 15 10.0830 4.8007 23.0465 0.9959 0.4761

47 6022 1 2 A2 TS03 0.7641 0.4143 -2.3112 15 10.0105 3.2069 10.2841 0.9971 0.3204

47 6022 2 2 TP1 BG55 1.1636 0.6405 0.0000 15 93.6808 8.1064 65.7136 0.9990 0.0865

47 9024 1 1 BA* BG** 0.7471 0.9837 -0.3424 15 107.1057 7.8765 62.0396 0.9988 0.0735

47 9024 1 2 TP1 BG55 1.1186 0.5635 0.0000 15 73.0364 6.8620 47.0864 0.9991 0.0940

47 9025 2 1 BA* BG** 0.6103 0.6752 0.0000 15 54.4923 14.4041 207.4771 0.9900 0.2643

47 9025 2 2 TP1 BG55 1.2069 0.5885 -0.0494 15 81.7582 9.9364 98.7320 0.9984 0.1215

48 0001 1 1 BA* BS** 1.1825 0.1390 -0.7944 15 6.3343 1.8259 3.3341 0.9997 0.2883

48 0001 1 2 TP1 BS55 2.4171 0.4522 -2.1555 15 36.0592 18.5955 345.7918 0.9909 0.5157

48 0001 2 1 BA* BG** 1.2829 0.5166 0.0000 15 73.5065 13.5510 183.6289 0.9969 0.1844

48 0001 2 2 TP1 BG55 1.5222 0.6143 -0.1842 15 97.9238 14.9166 222.5048 0.9976 0.1523

48 0113 1 2 B7 BS07 0.5169 0.5114 0.0000 15 10.0631 2.6437 6.9890 0.9980 0.2627

48 0116 1 2 B10 BS10 0.5240 0.5196 0.0000 15 10.4722 3.0734 9.4456 0.9974 0.2935

48 0117 1 2 B8 BS08 0.5169 0.5384 0.0000 15 10.5978 2.4509 6.0069 0.9983 0.2313

48 0119 1 2 B3 BS03 0.5116 0.5199 0.0000 15 10.1840 2.6951 7.2636 0.9979 0.2646

48 0121 1 2 B4 BS04 0.4944 0.5622 0.0000 15 10.6762 2.8146 7.9218 0.9976 0.2636

48 0123 1 2 B9 BS09 0.5120 0.4813 0.0000 15 9.2633 1.7556 3.0822 0.9991 0.1895

48 0801 1 1 B2 BS02 0.8722 0.1827 0.0000 15 6.9158 3.6900 13.6163 0.9985 0.5336

48 0801 1 2 B3 BS03 0.7152 0.1898 -0.1431 15 5.1111 2.3524 5.5338 0.9990 0.4603

48 0801 1 3 A5 TS09 0.6076 0.1794 -0.4282 15 4.1610 2.4970 6.2349 0.9983 0.6001

48 0801 3 2 B5 BG02 0.7867 0.2624 -0.5323 15 6.6812 2.4791 6.1460 0.9990 0.3711

48 0801 3 3 B6 BG03 0.8143 0.2526 -0.5981 15 6.6102 2.4686 6.0938 0.9991 0.3734

48 0802 1 1 B1 BS01 0.9765 0.2118 0.0000 15 10.5884 7.4231 55.1028 0.9951 0.7011

48 0802 1 3 A1 TS01 0.5835 0.1785 -0.9326 15 4.0036 1.7313 2.9974 0.9990 0.4324

48 0802 3 2 B4 BG01 0.7746 0.0000 0.0000 15 7.1301 7.1301 50.8381 0.9924 1.0000

48 1039 1 1 BA* BS** 0.6196 0.2150 -1.8082 15 5.7130 1.1450 1.3111 0.9995 0.2004

48 1039 1 2 A2 TS03 0.8759 0.3008 -1.4755 15 8.3049 1.6820 2.8292 0.9995 0.2025

48 1039 3 1 BA* BG** 0.8631 0.5002 -0.3710 15 33.7749 4.9935 24.9346 0.9987 0.1478

48 1046 1 1 A1 TS01 0.2690 0.4162 0.0000 15 4.7580 2.3261 5.4108 0.9941 0.4889

48 1046 1 2 TP1 BS55 0.9175 0.1621 -1.5803 15 7.5706 1.1793 1.3908 0.9998 0.1558

48 1046 2 1 BA* BG** 0.5926 0.6244 0.0000 13 42.0988 16.6814 278.2681 0.9832 0.3962

48 1046 2 2 TP1 BG56 0.9471 0.4889 -0.8175 15 26.5594 10.2416 104.8895 0.9931 0.3856

48 1046 3 2 TP1 BG55 0.9946 0.6148 0.0000 15 75.0062 8.4506 71.4128 0.9985 0.1127

48 1047 1 1 A1 TS01 0.1957 0.5812 -1.0967 15 3.9545 2.3003 5.2916 0.9855 0.5817

48 1047 1 2 A2 TS03 0.7547 0.0755 -1.0669 15 5.6753 3.4096 11.6253 0.9975 0.6008

48 1048 1 1 A1 TS01 0.5724 0.3698 -1.4262 15 6.2640 1.4335 2.0549 0.9992 0.2288

48 1048 1 2 A2 TS03 0.5912 0.1241 -1.3962 15 4.7759 2.1736 4.7244 0.9982 0.4551

48 1049 1 1 A1 TS01 1.0273 0.1630 -1.6539 15 8.9400 2.2006 4.8426 0.9993 0.2462

48 1049 1 2 BA* BS** 0.9918 0.2778 0.0000 15 11.1612 4.5471 20.6765 0.9982 0.4074

48 1050 1 1 A1 TS01 1.5581 0.2048 -1.6032 15 13.8254 2.5861 6.6878 0.9996 0.1871

48 1050 1 2 A2 TS04 1.4249 0.2317 -1.3411 15 11.8615 3.3286 11.0797 0.9993 0.2806

48 1050 3 2 TP1 BG55 1.1191 0.6722 0.0000 15 97.1308 10.5492 111.2865 0.9984 0.1086

48 1056 1 1 A1 TS02 0.7251 0.1003 -0.6057 15 3.6029 2.2711 5.1577 0.9990 0.6303

48 1056 1 2 A2 TS03 0.6485 0.1412 -2.2270 15 5.9666 1.6549 2.7388 0.9990 0.2774

48 1056 2 1 BA* BG** 0.4747 0.7532 0.0000 15 50.1248 6.6977 44.8590 0.9971 0.1336

85
Table 16. k-values determined from nonlinear regression analyses of LTPP 

resilient modulus test of unbound materials (continued).

State 

Code

SHRP 

ID

Layer 

No.

Test 

No.

Loc. 

No.

Sample 

No. k1 k2 k3

No. 

Points

Std 

Dev(MR) RMSE MSE R2 Se/Sy

48 1056 2 2 TP1 BG55 0.8513 0.4880 -0.4002 15 35.8626 15.4161 237.6548 0.9863 0.4299

48 1056 2 2 TP1 BG56 0.7956 0.4463 -0.6084 15 23.5245 11.2791 127.2175 0.9890 0.4795

48 1060 1 1 A1 TS01 0.6443 0.3365 -2.3882 15 7.7133 2.0621 4.2522 0.9983 0.2673

48 1060 1 2 A2 TS03 0.7981 0.1751 0.0000 15 5.6172 2.3073 5.3238 0.9993 0.4108

48 1060 3 1 BA* BG** 0.4672 0.9551 -0.0712 15 74.4472 4.3246 18.7024 0.9993 0.0581

48 1061 1 1 A1 TS02 0.8909 0.4123 -1.3360 15 10.8153 2.6377 6.9574 0.9989 0.2439

48 1061 1 2 A2 TS04 0.8356 0.1845 -1.0435 15 6.4016 3.3320 11.1023 0.9981 0.5205

48 1061 2 1 BA* BG** 0.8527 0.5775 0.0000 15 57.9665 7.5989 57.7437 0.9981 0.1311

48 1061 2 2 TP1 BG55 1.0719 0.5824 -0.4320 15 51.7045 10.9626 120.1779 0.9964 0.2120

48 1065 1 1 A1 TS01 0.5213 0.5976 -1.6932 15 8.5312 1.6362 2.6770 0.9988 0.1918

48 1065 1 2 A2 TS03 0.4962 0.2820 -2.2360 15 5.7801 1.8836 3.5480 0.9977 0.3259

48 1065 2 1 BA* BG** 0.7229 0.7348 -0.5081 15 50.2397 7.6681 58.7990 0.9973 0.1526

48 1068 1 1 BA2 BS02 0.8729 0.1775 -1.6186 15 7.3374 1.2804 1.6394 0.9997 0.1745

48 1068 1 2 TP1 BS55 0.6051 0.0593 -1.8845 15 5.6804 1.0365 1.0744 0.9995 0.1825

48 1068 3 1 BA* BG** 0.6203 0.6740 -0.0205 15 53.5868 3.6333 13.2006 0.9994 0.0678

48 1068 3 2 TP1 BG55 0.5156 0.8304 -0.0221 15 64.2182 5.0362 25.3634 0.9989 0.0784

48 1069 1 1 BA* BS** 0.7532 0.0771 0.0000 15 3.0000 2.1279 4.5279 0.9993 0.7093

48 1069 1 2 A2 TS03 0.4375 0.1681 -0.2736 15 2.9681 1.8376 3.3768 0.9983 0.6191

48 1069 1 2 TP1 BS55 1.0704 0.1992 -0.9432 15 7.2355 1.9804 3.9220 0.9996 0.2737

48 1070 1 1 BA* BS** 0.8122 0.1334 -0.9318 15 4.5743 0.8297 0.6885 0.9999 0.1814

48 1070 1 2 A2 TS03 0.5886 0.1441 -2.6538 15 7.5826 2.9387 8.6362 0.9952 0.3876

48 1076 1 1 A1 TS01 0.8602 0.4952 -1.1453 15 12.4281 3.8649 14.9375 0.9978 0.3110

48 1076 1 2 A2 TS03 0.8243 0.5250 -1.6402 15 12.0704 2.5359 6.4308 0.9988 0.2101

48 1077 1 1 A1 TS03 0.7623 0.4403 -1.0167 15 10.6064 4.7174 22.2535 0.9958 0.4448

48 1077 1 2 TP1 BS55 0.6875 0.4037 -0.8742 15 8.4515 2.6379 6.9586 0.9984 0.3121

48 1077 2 2 TP1 BG55 1.1532 0.6336 -0.0656 15 86.5221 5.9036 34.8525 0.9994 0.0682

48 1087 1 1 A1 TS02 1.0534 0.5543 -2.1209 15 16.5135 5.2940 28.0269 0.9963 0.3206

48 1087 1 2 A2 TS04 0.9902 0.4640 -1.8606 15 12.9144 2.5636 6.5719 0.9991 0.1985

48 1087 2 1 BA* BG** 1.0699 0.4313 -0.0371 15 45.4053 9.7455 94.9744 0.9971 0.2146

48 1087 2 2 TP1 BG55 0.8091 0.6580 -0.1574 15 60.5297 5.1602 26.6275 0.9991 0.0853

48 1092 1 1 BA* BS** 0.6858 0.0000 0.0000 15 6.8958 6.8958 47.5524 0.9909 1.0000

48 1092 1 2 A2 TS03 0.5586 0.1308 -1.3361 15 4.4110 2.1759 4.7348 0.9980 0.4933

48 1092 2 1 BA* BG** 1.2075 0.6778 -0.1562 15 95.8562 11.6279 135.2075 0.9981 0.1213

48 1092 2 2 TP1 BG56 1.0069 0.7279 -0.1513 15 90.0656 7.9083 62.5408 0.9989 0.0878

48 1092 3 2 TP1 BG55 0.8162 0.9196 -0.1491 15 113.9006 5.2890 27.9736 0.9996 0.0464

48 1093 1 1 BA* BS** 0.8755 0.5979 -1.6241 15 14.1202 2.5389 6.4461 0.9990 0.1798

48 1093 1 2 A2 TS03 0.8456 0.2368 -2.8365 15 9.9976 1.2405 1.5390 0.9996 0.1241

48 1093 2 1 BA* BG** 0.4777 0.8992 0.0000 15 70.9626 3.8067 14.4906 0.9994 0.0536

48 1094 1 1 BA* BS** 1.6352 0.1700 -1.2629 15 12.5691 4.8236 23.2669 0.9989 0.3838

48 1094 1 2 TP1 BS55 1.3982 0.3655 0.0000 15 23.0356 13.1342 172.5080 0.9929 0.5702

48 1094 2 1 BA* BG** 1.5853 0.6592 -0.2348 15 110.3281 11.0771 122.7017 0.9989 0.1004

48 1094 2 2 TP1 BG55 1.4927 0.7425 -0.5738 15 101.3282 21.6068 466.8531 0.9947 0.2132

48 1096 1 1 A1 TS01 0.6131 0.3404 -2.4188 15 7.3179 1.8548 3.4402 0.9985 0.2535

48 1096 1 2 A2 TS03 0.7918 0.1782 0.0000 15 5.6172 2.2089 4.8791 0.9993 0.3932

48 1096 2 1 BA* BG** 1.1299 0.6115 -0.0809 15 78.6232 9.6798 93.6992 0.9983 0.1231

48 1096 2 2 TP1 BG55 1.4170 0.6724 0.0000 15 131.5498 47.2433 2231.9330 0.9802 0.3591

48 1109 1 1 A1 TS01 0.8706 0.0230 -2.1721 15 9.5529 1.7616 3.1032 0.9993 0.1844

48 1109 1 2 A2 TS03 0.7174 0.2844 -2.2452 15 7.7410 1.5772 2.4875 0.9992 0.2037

48 1111 1 1 A1 TS01 0.5797 0.0165 -0.1335 15 5.7046 5.6809 32.2726 0.9910 0.9958

48 1111 1 2 A2 TS03 0.5305 0.1816 0.0000 15 8.1504 7.3507 54.0324 0.9837 0.9019

48 1111 2 1 BA* BG** 0.8135 0.6991 -0.6209 15 47.2577 6.7876 46.0711 0.9979 0.1436

48 1111 2 2 TP1 BG55 0.9247 0.6744 -0.5227 15 54.4180 5.4616 29.8294 0.9990 0.1004

48 1113 1 1 A1 TS01 1.4862 0.5646 -0.4100 15 27.9782 2.8598 8.1783 0.9997 0.1022

48 1113 1 2 A2 TS03 0.6508 0.0979 0.0000 15 15.7788 15.6134 243.7787 0.9513 0.9895

48 1113 2 1 BA* BG** 0.6822 0.6823 -0.0883 15 56.8836 3.4954 12.2182 0.9995 0.0614

48 1113 2 2 BA* BG** 0.5870 0.6988 -0.3355 15 42.5607 4.2733 18.2612 0.9988 0.1004

86