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Publication Number: FHWA-RD-02-051

Study of LTPP Laboratory Resilient Modulus Test Data and Response Characteristics, Final Report

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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 State 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.:

4. Title and Subtitle: Study of LTPP Laboratory Resilient Modulus Test Data and Response Characteristics

5. Report Date: OCTOBER 2002

6. Performing Organization Code:

7. Author(s): Amber Yau and Harold L. Von Quintus

8. Performing Organization Report No.: 3032.1

9. Performing Organization Name and Address: Fugro-BRE, 8613 Cross Park Drive, Austin, TX 78754

10. Work Unit No. (TRAIS): C6B

11. Contract or Grant No.: DTFH61-95-C-00028

12. Sponsoring Agency Name and Address: Office of Engineering R & D Federal Highway Administration, 6300 Georgetown Pike, McLean, Virginia 22101-2296

13. Type of Report and Period Covered: June 2000-October 2001 Final Report

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, VA 22161.

19. Security Classification (of this report): Unclassified

20. Security Classification (of this page): Unclassified

21. No. of Pages: 173

22. Price:

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


SI* (MODERN METRIC) CONVERSION FACTORS

Approximate Conversions to SI Units

Length:
inches (in) multiply by 25.4 to get millimeters (mm)
feet (ft) multiply by 0.305 to get meters (m)
yards (yd) multiply by 0.914 to get meters (m)
miles (mi) multiply by 1.61 to get kilometers (km)

Area:
square inches (in2) multiply by 645.2 to get square millimeters (mm2)
square feet (ft2) multiply by 0.093 to get square meters (m2)
square yard (yd2) multiply by 0.836 to get square meters (m2)
acres (ac) multiply by 0.405 to get hectares (ha)
square miles (mi2) multiply by 2.59 to get square kilometers (km2)

Volume:
fluid ounces (fl oz) multiply by 29.57 to get milliliters (mL)
gallons (gal) multiply by 3.785 to get liters (L)
cubic feet (ft3) multiply by 0.028 to get cubic meters (m3)
cubic yards (yd3) multiply by 0.765 to get cubic meters (m3)
NOTE: volumes greater than 1000 L shall be shown in m3

Mass:
ounces (oz) multiply by 28.35 to get grams (g)
pounds (lb) multiply by 0.454 to get kilograms (kg)
short tons - 2000 lb (T) multiply by 0.907 to get megagrams or "metric ton" (Mg or "t")

Temperature (exact degrees):
Fahrenheit (°F) multiply by 5 (F-32)/9 or (F-32)/1.8 to get Celsius (°C)

Illumination:
foot-candles (fc) multiply by 10.76 to get lux (lx)
foot-Lamberts (fl) multiply by 3.426 to get candela/m2 (cd/m2)

Force and Pressure or Stress:
poundforce (lbf) multiply by 4.45 to get newtons (N)
poundforce per square inch (lbf/in2) multiply by 6.89 to get kilopascals (kPa)

Approximate Conversions From SI Units

Length:
millimeters (mm) multiply by 0.039 to get inches (in)
meters (m) multiply by 3.28 to get feet (ft)
meters (m) multiply by 1.09 to get yards (yd)
kilometers (km) multiply by 0.621 to get miles (mi)

Area:
square millimeters (mm2) multiply by 0.0016 to get square inches (in2)
square meters (m2) multiply by 10.764 to get square feet (ft2)
square meters (m2) multiply by 1.195 to get square yards (yd2)
hectares (ha) multiply by 2.47 to get acres (ac)
square kilometers (km2) multiply by 0.386 to get square miles (mi2)

Volume:
milliliters (mL) multiply by 0.034 to get fluid ounces (fl oz)
liters (L) multiply by 0.264 to get gallons (gal)
cubic meters (m3) multiply by 35.314 to get cubic feet (ft3)
cubic meters (m3) multiply by 1.307 to get cubic yards (yd3)

Mass:
grams (g) multiply by 0.035 to get ounces (oz)
kilograms (kg) multiply by 2.202 to get pounds (lb)
megagrams or "metric ton" (Mg or "t") multiply by 1.103 to get short tons - 2000 lb (T)

Temperature (exact degrees):
Celsius (°C) multiply by 1.8C+32 to get Fahrenheit (°F)

Illumination:
lux (lx) multiply by 0.0929 to get foot-candles (fc)
candela/m2 (cd/m2) multiply by 0.2919 to get foot-Lamberts (fl)

Force and Pressure or Stress:
newtons (N) multiply by 0.225 to get poundforce (lbf)
kilopascals (kPa) multiply by 0.145 to get poundforce per square inch (lbf/in2)

*SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380.
(Revised March 2002)


TABLE OF CONTENTS

1. INTRODUCTION

BACKGROUND
STUDY OBJECTIVES
SCOPE OF REPORT

2. REVIEW OF RESILIENT MODULUS TEST DATA

IDENTIFICATION OF MISSING RESILIENT MODULUS TESTS
RESILIENT MODULUS CONSTITUTIVE EQUATION
IDENTIFICATION OF TEST DATA ANOMALIES

3. EFFECT OF SAMPLING TECHNIQUE ON RESILIENT MODULUS

DATA GROUPS EVALUATED - SOURCES OF VARIABILITY IDENTIFICATION OF OUTLIERS
COMPARISON OF RESILIENT MODULUS TEST RESULTS
Effect of Stress State
Unbound Aggregate Layers - Test Pit Versus Auger Samples
Soils - Test Pit Versus Auger Samples
Soils - Shelby Tubes (Undisturbed) Versus Recompacted (Disturbed) Samples
SUMMARY

4. EFFECT OF PHYSICAL PROPERTIES ON RESILIENT MODULUS

PHYSICAL PROPERTIES USED IN STUDY
STATISTICAL PROCEDURE
CORRELATION STUDY FOR MODEL DEVELOPMENT
Effect of Material/Soil Type
Unbound Aggregate Base/Subbase Materials
Subgrade Soils
SUMMARY

5. SUMMARY AND FUTURE RECOMMENDATIONS

FINDINGS AND OBSERVATIONS
RECOMMENDATIONS

APPENDIX A: SUMMARY OF k-COEFFICIENTS FOR THE LTPP RESILIENT MODULUS TESTS

APPENDIX B: GEOGRAPHICAL EXAMPLES OF THE DIFFERENT TYPES OF ANOMALIES IDENTIFIED IN THE RESILIENT MODULUS TEST DATA

APPENDIX C: SUMMARY OF THE FLAGGED RESILIENT MODULUS TESTS BY ANOMALY TYPE

APPENDIX D: PARAMETERS AND THEIR VALUES INCLUDED IN THE NONLINEAR REGRESSION RELATING RESILIENT MODULUS TO PHYSICAL PROPERTIES

APPENDIX E: RESULTS FROM NONLINEAR OPTIMIZATION REGRESSION STUDY RELATING RESILENT MODULUS TO PHYSICAL PROPERTIES

REFERENCES


LIST OF TABLES

1. Summary of completed and missing resilient modulus tests as of the October 2000 LTPP data release

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

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

4. Summary of identified anomaly types

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

6. Results of ANOVA to determine if the resilient modulus ratio (auger versus test pit test specimens) is a function of stress

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

8. Summary of the student t-test on the difference between augured and test pit samples for the base/subbase materials and subgrade soils

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

10. Summary of ANOVA to determine effect of sampling technique (Shelby tube versus auger) on resilient modulus

11. Summary of the student t-test on the difference between disturbed and undisturbed samples for the subgrade soils

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

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

14. Summary of the MR physical property regression variables

15. Summary of the physical properties that were found to be important for predicting resilient modulus for each material and soil type

16. k-values determined from nonlinear regression analyses of LTPP resilient modulus test of unbound materials

17. Resilient modulus tests showing characteristics of exhibiting test specimen distortion or excessive softening

18. Resilient modulus tests showing significant effect of confining pressure

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

20. Resilient modulus tests exhibiting localized softening or disturbance of the specimen during the test or LVDT movement

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

22. Resilient modulus tests showing resilient modulus is independent of confining pressure at the lowest vertical stress

23. Resilient modulus tests with potential data entry error

24. Summary of the LTPP data used in the nonlinear regression study of resilient modulus for all granular base and subbase material data set

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

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

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

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

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

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

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

32. Summary of the LTPP data used in the nonlinear regression study of resilient modulus for all subgrade soils data set

33. Summary of the LTPP data used in the nonlinear regression study of resilient modulus for the gravel subgrade soils data set

34. Summary of the LTPP data used in the nonlinear regression study of resilient modulus for the sand subgrade soils data set

35. Summary of the LTPP data used in the nonlinear regression study of resilient modulus for the silt subgrade soils data set

36. Summary of the LTPP data used in the nonlinear regression study of resilient modulus for the clay subgrade soils data set

37. Results from the nonlinear optimization regression study for all base and subbase material types combined

38. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 302 - uncrushed gravel

39. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 303 - crushed stone

40. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 304 - crushed gravel

41. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 306 - sand

42. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 307 - fine-grained soil-aggregate mixture

43. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 308 - coarse-grained soil-aggregate mixture

44. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 309 - fine-grained soil

45. Results from the nonlinear optimization regression study for the combined subgrade soil data set

46. Results from the nonlinear optimization regression study for the LTPP gravel subgrade soil data set

47. Results from the nonlinear optimization regression study for the LTPP sand subgrade soil data set

48. Results from the nonlinear optimization regression study for the LTPP silt subgrade soil data set

49. Results from the nonlinear optimization regression study for the LTPP clay subgrade soil data set


LIST OF FIGURES

1. Distribution of the k-coefficients of constitutive equation 3, assuming k6 =0, for the entire LTPP resilient modulus database

2. Distribution of the k-coefficients of constitutive equation 3, assuming k6 =0, for the unbound aggregate base and subbase materials

3. Distribution of the k-coefficients of constitutive equation 3, assuming k6 =0, for the coarse-grained subgrade soils

4. Distribution of the k-coefficients of constitutive equation 3, assuming k6 =0, for the fine-grained subgrade soils

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

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

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

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

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

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

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

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

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

14. Sample from test section 010102, layer 1, at the leave end exhibits specimen distortion or excess softening

15. Sample from test section 171003, layer 1, at the leave end shows significant effect of confining pressure on resilient modulus

16. Sample from test section 014129, layer 1, at the leave end shows sudden drop and then increase in resilient modulus.

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

18. Sample from test section 473108, layer 1, at the leave end shows higher confining pressures result in lower resilient modulus

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

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

21. Graphical comparison of the predicted and measured resilient modulus for the crushed stone base materials

22. Graphical comparison of the predicted and measured resilient modulus for the crushed gravel base materials

23. Graphical comparison of the predicted and measured resilient modulus for the uncrushed gravel base materials

24. Graphical comparison of the predicted and measured resilient modulus for the sand base materials

25. Graphical comparison of the predicted and measured resilient modulus for the coarse-grained soil-aggregate base materials

26. Graphical comparison of the predicted and measured resilient modulus for the fine-grained soil-aggregate base materials

27. Graphical comparison of the predicted and measured resilient modulus for the fine-grained soil base materials

28. Graphical comparison of the predicted and measured resilient modulus for the coarse-grained gravel soils

29. Graphical comparison of the predicted and measured resilient modulus for the coarse-grained sand soils

30. Graphical comparison of the predicted and measured resilient modulus for the fine-grained silt soils

31. Graphical comparison of the predicted and measured resilient modulus for the fine-grained clay soils

32. Graphical comparison of the resilient modulus predicted from the data sets for crushed stone materials sampled from the test pit and auger locations

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

34. Sample from test section 010111, layer 1, at the leave end exhibits specimen distortion or excess softening

35. Sample from test section 063030, layer 1, at the approach end exhibits specimen distortion or excess softening

36. Sample from test section 067455, layer 1, at the approach end exhibits specimen distortion or excess softening

37. Sample from test section 370212, layer 1, at the approach end exhibits specimen distortion or excess softening

38. Sample from test section 179327, layer 1, at the approach end shows significant effect of confining pressure on resilient modulus.

39. Sample from test section 295403, layer 1, at the approach end shows significant effect of confining pressure on resilient modulus.

40. Sample from test section 296067, layer 1, at the approach end shows significant effect of confining pressure on resilient modulus

41. Sample from test section 289030, layer 1, at the leave end shows significant effect of confining pressure on resilient modulus

42. Sample from test section 123811, layer 1, at the leave end shows sudden drop and then increase in resilient modulus

43. Sample from test section 280508, layer 1, at the leave end shows sudden drop and then increase in resilient modulus

44. Sample from test section 283089, layer 1, at the leave end shows sudden drop and then increase in resilient modulus

45. Sample from test section 483875, layer 1, at the leave end shows sudden drop and then increase in resilient modulus

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

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

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

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

50. Sample from test section 014125, layer 1, at the approach end shows higher confining pressures result in lower resilient modulus

51. Sample from test section 014127, layer 1, at the leave end shows higher confining pressures result in lower resilient modulus

52. Sample from test section 473109, layer 1, at the leave end shows higher confining pressures result in lower resilient modulus

53. Sample from test section 481047, layer 1, at the leave end shows higher confining pressures result in lower resilient modulus

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

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

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

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

58. Sample from test section 014073, layer 3, at the approach end shows possible data entry error

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

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

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

62. Residuals, R, for the combined resilient modulus prediction equation for all base and subbase materials

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

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

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

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

67. Residuals, R, for the fine-grained soil-aggregate mixture (LTPP material code 307) resilient modulus prediction equation

68. Residuals, R, for the coarse-grained soil-aggregate mixture (LTPP material code 308) resilient modulus prediction equation

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

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

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

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

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

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


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, "Development of Design Procedure for New and Rehabilitated 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.(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 "recoverable" strain that occurs when the applied load is removed from the test specimen.

MR (resilient modulus) equals sigmad divided by varepsilonr (Equation 1)

Where:

sigmad = applied deviator stress in a repeated load triaxial test.
varepsilonr = 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.

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 "cleaned" 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.


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 TypeSoil TypeNo. of Tests RequiredNo. of Tests CompletedNo. of Tests Missing
Subgrade Soil All18861347594
Subgrade SoilClay652513168
Subgrade SoilGravel262123140
Subgrade SoilRock24321
Subgrade SoilSand765580208
Subgrade SoilSilt16911655
Subgrade SoilUnknown14122
Granular SubbaseAll685259427
Granular BaseAll956385573
UnknownUnknown--23--
Total 352720141594


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.

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.


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.

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 "universal" constitutive equation provided a very good fit to the LTPP MR test data.(3) The specific equation used is given below:

Equation 2: resilient modulus equals regression constant 1 times atmospheric pressure times (bulk stress divided by atmospheric pressure) to the regression constant 2 times [sigma lower case D divided by atmospheric pressure] to the K lower case 3.

(Equation 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)

Equation 3: resilient modulus equals regression constant 1 times atmospheric pressure times [(bulk stress minus (3 times regression constant 6)) divided by atmospheric pressure] to the regression constant 2 times [octahedral shear stress divided by (atmospheric pressure plus 1)] to the regression constant 3.

(Equation 3)

where:

Pa = atmospheric pressure.
theta = bulk stress: theta = sigma1 + sigma2 + sigma3. (Equation 4)
sigma1 = major principal stress.
sigma2 = intermediate principal stress = sigma3 for MR test on cylindrical specimen.
sigma3 = minor principal stress/confining pressure.
Tauoct = octahedral shear stress:
Equation 5: octahedral shear stress equals one third times the square root of [(major principal stress minus intermediate principal stress) squared plus (major principal stress minus (minor principal stress divided by confining pressure) squared plus (intermediate principal stress minus the (minor principal stress divided by confining pressure)squared].

(Equation 5)


k1, k2, k3, k6 = regression constants.

Coefficient k1 is proportional to Young's modulus. Thus, the values for k1 should be positive since MR can never be negative. Increasing the volumetric stress (theta) 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 material's 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 k-coefficients are presented in appendix A.


Observation: Coefficient k6 in equation 3 was found to be zero for more than 50 percent of the MR tests.

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 bi-normal 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).


Figure 1. Distribution of the k-coefficients of constitutive equation 3, assuming k6 = 0, for the entire LTPP resilient modulus database.
Figure 1. Distribution of the K-coefficients of constitutive equation 3, assuming K subscript 6 equals 0, for the entire LTPP resilient modulus database. K 1 Quantiles: 100.0 Percent (maximum) equals 2.7055, 99.5 Percent equals 2.1431, 97.5 Percent equals 1.5692, 90.0 Percent equals 1.2637, 75.0 Percent (quartile) equals 1.0150, 50.0 Percent (median) equals 0.8036, 25.0 Percent (quartile) equals 0.6391, 10.0 Percent equals 0.5174, 2.5 Percent equals 0.3913, 0.5 Percent equals 0.2629, 0.0 Percent (minimum) equals 0.1583; Moments: Mean equals 0.855, Standard Deviation equals 0.313, Standard Error Mean equals 0.007, Upper 95 Percent Mean equals 0.869, Lower 95 Percent Mean equals 0.841, N equals 1920.00, Sum Weights equals 1920.00. K 2: Quantiles: 100.0 Percent (maximum) equals 1.3450, 99.5 Percent equals 0.9747, 97.5 Percent equals 0.8275, 90.0 Percent equals 0.7299, 75.0 Percent (quartile) equals 0.6335, 50.0 Percent (median) equals 0.4824, 25.0 Percent (quartile) equals 0.2570, 10.0 Percent equals 0.1710, 2.5 Percent equals 0.0902, 0.5 Percent equals 0.0000, 0.0 Percent (minimum) equals 0.0000; Moments: Mean equals 0.457, Standard Deviation equals 0.219, Standard Error Mean equals 0.005, Upper 95 Percent Mean equals 0.467, Lower 95 Percent Mean equals 0.447, N equals 1920.00, Sum Weights equals 1920.00. K 3: Quantiles: 100.0 Percent (maximum) equals 0.0000, 99.5 Percent equals 0.0000, 97.5 Percent equals 0.000, 90.0 Percent equals 0.0000, 75.0 Percent (quartile) equals negative 0.0948, 50.0 Percent (median) equals negative 0.6536, 25.0 Percent (quartile) equals negative 1.6649, 10.0 Percent equals negative 2.6841, 2.5 Percent equals negative 3.9364, 0.5 Percent equals negative 5.1932, 0.0 Percent (minimum) negative 6.5304; Moments: Mean equals negative .033, Standard Deviation 1.132, Standard Error Mean equals 0.026, Upper 95 Percent Mean equals negative 0.983, Lower 95 Percent equals Mean negative 1.084, N 1920.00, Sum Weights 1920.00.


Figure 2. Distribution of the k-coefficients of constitutive equation 3, assuming k6 = 0, for the unbound aggregate base and subbase materials.
Figure 2. Distribution of the K coefficients of constitutive equation 3, assuming K subscript 6 equals 0, for the unbound aggregate base and subbase materials. K 1 MRK12000STAT: Quantiles: 100.0 Percent (maximum) equals 1.8474, 99.5 Percent equals 1.8002, 97.5 Percent equals 1.4835, 90.0 Percent equals 1.2097, 75.0 Percent (quartile) equals 1.0498, 50.0 Percent (median) equals 0.8527, 25.0 Percent (quartile) equals 0.6778, 10.0 Percent equals 0.5267, 2.5 Percent equals 0.4105, 0.5 Percent equals 0.3013, 0.0 Percent (minimum) equals 0.2809; Moments: Mean equals 0.8732, Standard Deviation equals 0.2726, Standard Error Mean equals 0.0133, Upper 95 Percent Mean equals 0.8993, Lower 95 Percent Mean equals 0.8472, N equals 423.0000, Sum Weights equals 423.0000. K 2 MRK12000STAT: Quantiles: 100.0 Percent (maximum) equals 1.0622, 99.5 Percent equals 1.0211, 97.5 Percent equals 0.9025, 90.0 Percent equals 0.7712, 75.0 Percent (quartile) equals 0.7000, 50.0 Percent (median) equals 0.6280, 25.0 Percent (quartile) equals 0.5646, 10.0 Percent equals 0.4867, 2.5 Percent equals 0.2738, 0.5 Percent equals 0.1880, 0.0 Percent (minimum) equals 0.1741; Moments: Mean equals 0.6261, Standard Deviation equals 0.1330, Standard Error Mean equals 0.0065, Upper 95 Percent Mean equals 0.6388, Lower 95 Percent Mean equals 0.6134, N equals 423.0000, Sum Weights equal 423.0000. K 3 MRK12000STAT: Quantiles: 100.0 Percent (maximum) equals 0.0000, 99.5 Percent equals 0.0000, 97.5 Percent equals 0.000, 90.0 Percent equals 0.0000, 75.0 Percent (quartile) equals negative 0.0000, 50.0 Percent (median) equals negative 0.1294, 25.0 Percent (quartile) equals negative 0.2606, 10.0 Percent equals negative 0.4007, 2.5 Percent equals negative 0.6245, 0.5 Percent equals negative 0.8154, 0.0 Percent (minimum) equals negative 2.8978; Moments: Mean equals negative 0.1696, Standard Deviation equals 0.2148, Standard Error Mean equals 0.0104, Upper 95 Percent Mean equals negative 0.1490, Lower 95 Percent Mean equals negative 0.1901, N equals 423.0000, Sum Weights equal 423.0000.


Figure 3. Distribution of the k-coefficients of constitutive equation 3, assuming k6 = 0, for the coarse-grained subgrade soils.
Figure 3. Distribution of the K coefficients of constitutive equation 3, assuming K subscript 6 equals 0, for the coarse grained subgrade soils. K 1 MRK12000STAT K6EQl0_property: Quantiles: 100.0 Percent (maximum) equals 1.8894, 99.5 Percent equals 1.8408, 97.5 Percent equals 1.4490, 90.0 Percent equals 1.1558, 75.0 Percent (quartile) equals 0.9294, 50.0 Percent (median) equals 0.7635, 25.0 Percent (quartile) equals 0.6094, 10.0 Percent equals 0.5050, 2.5 Percent equals 0.4284, 0.5 Percent equals 0.3736, 0.0 Percent (minimum) equals 0.3727; Moments: Mean equals 0.8019, Standard Deviation equals 0.2661, Standard Error Mean equals 0.0166, Upper 95 Percent Mean equals 0.8345, Lower 95 Percent Mean equals 0.7692, N equals 257.0000, Sum Weights equal 257.0000. K 2 MRK12000STAT K6EQl0_property: Quantiles: 100.0 Percent (maximum) equals 0.89552, 99.5 Percent equals 0.88562, 97.5 Percent equals 0.79432, 90.0 Percent equals 0.71210, 75.0 Percent (quartile) equals 0.62000, 50.0 Percent (median) equals 0.44597, 25.0 Percent (quartile) equals 0.28199, 10.0 Percent equals 0.19680, 2.5 Percent equals 0.14334, 0.5 Percent equals 0.09506, 0.0 Percent (minimum) equals 0.08290; Moments: Mean equals 0.4521, Standard Deviation equals 0.1927, Standard Error Mean equals 0.0120, Upper 95 Percent Mean equals 0.4758, Lower 95 Percent Mean equals 0.4284, N equals 257.0000, Sum Weights equal 257.0000. K 3 MRK12000STAT K6EQl0_property: Quantiles: 100.0 Percent (maximum) equals 0.0000, 99.5 Percent equals 0.0000, 97.5 Percent equals 0.000, 90.0 Percent equals negative 0.1401, 75.0 Percent (quartile) equals negative 0.6423, 50.0 Percent (median) equals negative 1.0518, 25.0 Percent (quartile) equals negative 1.5820, 10.0 Percent equals negative 2.2226, 2.5 Percent equals negative 2.8804, 0.5 Percent equals negative 3.0199, 0.0 Percent (minimum) equals negative 3.0230; Moments: Mean equals negative 1.1401, Standard Deviation equals 0.7365, Standard Error Mean equals 0.0459, Upper 95 Percent Mean equals negative 1.0496, Lower 95 Percent Mean equals negative 1.2305, N equals 257.0000, Sum Weights equal 257.0000.


Figure 4. Distribution of the k-coefficients of constitutive equation 3, assuming k6 = 0, for the fine-grained subgrade soils.
Figure 4. Distribution of the K coefficients of constitutive equation 3, assuming K subscript 6 equals 0, for the fine grained subgrade soils. K 1 MRK12000STAT K6eql0_property: Quantiles - 100.0 Percent (maximum) equals 1.8391, 99.5 Percent equals 1.8391, 97.5 Percent equals 1.7168, 90.0 Percent equals 1.3225, 75.0 Percent (quartile) equals 1.0925, 50.0 Percent (median) equals 0.8037, 25.0 Percent (quartile) equals 0.6565, 10.0 Percent equals 0.5867, 2.5 Percent equals 0.4459, 0.5 Percent equals 0.2750, 0.0 Percent (minimum) 0.2750; Moments: Mean equals 0.8962, Standard Deviation 0.3133, Standard Error Mean equals 0.0306, Upper 95 Percent Mean equals 0.9568, Lower 95 Percent equals Mean 0.8356, N 105.0000, Sum Weights 105.0000. K 2 MRK12000STAT K6eql0_property: Quantiles - 100.0 Percent (maximum) equals 0.85065, 99.5 Percent equals 0.85065, 97.5 Percent equals 0.66573, 90.0 Percent equals 0.53715, 75.0 Percent (quartile) equals 0.34959, 50.0 Percent (median) equals 0.24320, 25.0 Percent (quartile) equals 0.17651, 10.0 Percent equals 0.13522, 2.5 Percent equals 0.05900, 0.5 Percent equals 0.00034, 0.0 Percent (minimum) 0.00034; Moments: Mean equals 0.2824, Standard Deviation 0.1552, Standard Error Mean equals 0.0151, Upper 95 Percent Mean equals 0.3124, Lower 95 Percent equals Mean 0.2523, N 105.0000, Sum Weights 105.0000. K 3 MRK12000STAT K6eql0_property: Quantiles: 100.0 Percent (maximum) equals 0.0000, 99.5 Percent equals 0.0000, 97.5 Percent equals 0.000, 90.0 Percent equals negative 0.1749, 75.0 Percent (quartile) equals negative 0.8130, 50.0 Percent (median) equals negative 1.3993, 25.0 Percent (quartile) equals negative 2.2409, 10.0 Percent equals negative 3.1481, 2.5 Percent equals negative 4.3063, 0.5 Percent equals negative 4.9793, 0.0 Percent (minimum) negative 4.9793; Moments: Mean equals negative 1.5764, Standard Deviation 1.1014, Standard Error Mean equals 0.1075, Upper 95 Percent Mean equals negative 1.3632, Lower 95 Percent Mean equals negative 1.7895, N 105.0000, Sum Weights 105.0000.


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.

Coefficient
Type
Unbound
Base-Subbase Materials
Coarse-Grained Soils
Fine-Grained Soils
k1 Median
0.853
0.764
0.804
k1 Mean
0.873
0.802
0.896
k1 Standard Deviation
0.2726
0.2661
0.3133
k2 Median
0.628
0.446
0.243
k2 Mean
0.626
0.452
0.282
k2 Standard Deviation
0.1330
0.1927
0.1552
k3 Median
-0.129
-1.052
-1.399
k3 Mean
-0.170
-1.140
-1.576
k3 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.


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 5. Comparison of measured and predicted resilient modulus (from regressed K values of the constitutive equation from measured resilient modulus data) for the crushed stone materials (material code equals 303) sampled from the test pit locations. The resilient modulus measured is graphed on the horizontal axis and the resilient modulus predicted on the vertical axis. As shown, the constitutive equation provides an excellent fit to the LTPP resilient modulus test data.


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.
Figure 6. Comparison of measured and predicted resilient modulus (from regressed K values of the constitutive equation from measured resilient modulus data) for the crushed stone materials (material code equals 303) sampled from the auger locations. The resilient modulus measured is graphed on the horizontal axis and the resilient modulus predicted on the vertical axis. As shown, the constitutive equation provides an excellent fit to the LTPP resilient modulus test data.


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 7. Graphical comparison of the calculated resilient modulus (using the regressed K coefficients of the constitutive equation from the LTPP test results) to the measured resilient modulus for the gravel soils. The resilient modulus measured is graphed on the horizontal axis and the resilient modulus calculated on the vertical axis. As shown, the constitutive equation provides an excellent fit to the LTPP resilient modulus test data.


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.
Figure 8. Graphical comparison of the calculated resilient modulus (using the regressed K coefficients of the constitutive equation from the LTPP test results) to the measured resilient modulus for the clay soils. The resilient modulus measured is graphed on the horizontal axis and the resilient modulus calculated on the vertical axis. As shown, the constitutive equation provides an excellent fit to the LTPP resilient modulus test data.


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:

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.
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.

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.

STATE CODE
SHRP ID
LAYER NO.
TEST NO.
LOC. NO.
SAMPLE NO.
R2
SE/SY
MATL CODE
N Cycles
Correlations with MR BULK STRESS
Correlations with MR 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


Figure 9. Repeated-load resilient modulus test results for section 014073, layer 3, at the approach end.
Figure 9. Repeated load resilient modulus test results for section 014073, layer 3, at the approach end (material code equals 308, coarse soil aggregate mixture). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, is graphed on the vertical axis. The graph for a confining pressure of 20.7 kilopascals is a nearly straight line between 3 data points, beginning at a resilient modulus of about 70 megapascals and a pressure of 15 kilopascals and ending at about 100 megapascals/55 kilopascals. The graph for a confining pressure of 34.5 kilopascals is a nearly straight line between 3 data points, beginning at about 110 megapascals/30 kilopascals and ending at about 150 megapascals/95 kilopascals. The graph for a confining pressure of 68.9 kilopascals is a straight line between 3 data points, beginning at about 160 megapascals/60 kilopascals and ending at about 210 megapascals/190 kilopascals. The graph for a confining pressure of 103.4 kilopascals is a nearly straight line between 3 data points, beginning at about 200 megapascals/60 kilopascals and ending at about 260 megapascals/190 kilopascals. The resilient modulus test from test section 014073 is characteristic of a coarse grained soil. The resilient modulus increases with increasing confining pressure as expected. However, the incremental change in resilient modulus 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.


Figure 10. Repeated-load resilient modulus test results for section 480802, layer 3, at the leave end.
Figure 10. Repeated load resilient modulus test results for section 480802, layer 3, at the leave end (material code equals 302, uncrushed gravel). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, is graphed on the vertical axis. The graph for a confining pressure of 13.8 kilopascals is a nearly straight line between 5 data points, beginning at about 77 megapascals and 12 kilopascals and ending at about 80 megapascals and 63 kilopascals. The graph for a pressure of 27.6 kilopascals is a nearly straight line between 5 data points, beginning at about 80 megapascals and 12 kilopascals and ending at about 83 megapascals and 63 kilopascals. The graph for a pressure of 41.3 kilopascals is a nearly straight line between 5 data points, beginning at about 70 megapascals and 12 kilopascals and ending at about 70 megapascals and 63 kilopascals. This figure shows that the resilient modulus 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 resilient modulus increases between the first two repeated vertical stresses applied to the test specimen, but then continues to decrease with increasing repeated vertical stresses.


Figure 11. Repeated-load resilient modulus test results for section 352007, layer 2, at the approach end.
Figure 11. Repeated load resilient modulus test results for section 352007, layer 2, at the approach end (material code equals 309, fine grained soil). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, is graphed on the vertical axis. The graph for a confining pressure of 13.8 kilopascals is a curving line between 5 data points, decreasing and then flat, beginning at a resilient modulus of about 63 megapascals and pressure of 13 kilopascals and ending at about 55 megapascals/60 kilopascals. The graph for a pressure of 27.6 kilopascals is a curving line between 5 data points, decreasing and then flat, beginning at about 75 megapascals/13 kilopascals and ending at about 67 megapascals/62 kilopascals. The graph for a pressure of 41.4 kilopascals is a curving line between 5 data points, decreasing and then flat, beginning at about 87 megapascals/12 kilopascals and ending at about 72 megapascals/62 kilopascals. The resilient modulus test on section 352007 initially was flaged (see table 3). This figure 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 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.


Figure 12. Repeated-load resilient modulus test results for section 390209, layer 2, at the approach end.
Figure 12. Repeated load resilient modulus test results for section 390209, layer 2, at the approach end (Material Code equals 303, Crushed Stone). The Repeated Vertical Pressure, kilopascals, is graphed on the horizontal axis and the Resilient Modulus, megapascals, is graphed on the vertical axis. The graph for a confining pressure of 20.8 kilopascals is a straight line between 2 data points, beginning at a resilient modulus of about 125 megapascals and pressure of 35 kilopascals and ending at about 140 megapascals/55 kilopascals. The graph for a pressure of 33.2 kilopascals is a nearly straight line between 3 data points, beginning at about 148 megapascals/30 kilopascals and ending at about 180 megapascals/95 kilopascals. The graph for a pressure of 69.3 kilopascals is a nearly straight line between 3 data points, beginning at about 235 megapascals/65 kilopascals and ending at about 280 megapascals/190 kilopascals. The graph for a pressure of 103.5 kilopascals is a straight line between 3 data points, beginning at about 260 megapascals/65 kilopascals and ending at about 330 megapascals/190 kilopascals. The graph for a pressure of 137.8 kilopascals is a straight line between 2 data points, beginning at about 335 megapascals/95 kilopascals and ending at about 350 megapascals/125 kilopascals. This figure for test section 390209 was not flagged. This graph of non flagged data is provided for comparative purposes.


Figure 13. Repeated-load resilient modulus test results for section 481093, layer 2, at the approach end.
Figure 13. Repeated load resilient modulus test results for section 481093, layer 2, at the approach end (material code equals 303, crushed stone). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, is graphed on the vertical axis. The graph for a confining pressure of 20.7 kilopascals is a nearly straight line between 3 data points, beginning at a resilient modulus of about 40 megapascals and pressure of 15 kilopascals and ending at about 55 megapascals/55 kilopascals. The graph for a confining pressure of 34.5 kilopascals is a nearly straight line between 3 data points, beginning at about 55 megapascals/25 kilopascals and ending at about 90 megapascals/95 kilopascals. The graph for a confining pressure of 68.9 kilopascals is a nearly straight line between 3 data points, beginning at about 120 megapascals/65 kilopascals and ending at about 160 megapascals/190 kilopascals. The graph for a confining pressure of 103.4 kilopascals is a straight line between 3 data points, beginning at about 150 megapascals/65 kilopascals and ending at about 200 megapascals/190 kilopascals. The graph for a confining pressure of 137.9 kilopascals is a nearly straight line between 3 data points, beginning at about 200 megapascals/95 kilopascals and ending at about 260 megapascals/255 kilopascals. This figure for test section 481093 was not flaged. This graph of non-flaged data is provided for comparative purposes.


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


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., "possible anomalous data"), 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 soil's 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 anomaly's initial description for each flagged test.]


Observation: Almost 92 percent of the LTPP MR tests have response characteristics that are accurately simulated by the "universal" constitutive equation selected for the 2002 Design Guide.


Figure 14. Sample from test section 010102, layer 1, at the leave end exhibits specimen distortion or excess softening.
Figure 14. Sample from test section 010102, layer 1, at the leave end exhibits specimen distortion or excess softening (material code equals 131, silty clay). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, is graphed on the vertical axis. The graph for a confining pressure of 13.8 kilopascals is a curved line between 5 data points, beginning at a resilient modulus of about 69 megapascals and a pressure of 15 kilopascals, peaking at about 74 megapascals/39 kilopascals, and ending at about 68 megapascals/63 kilopascals. The graph for a confining pressure of 27.6 kilopascals is a curved line between 5 data points, beginning at about 73 megapascals/15 kilopascals, peaking at about 78 megapascals/39 kilopascals, and ending at about 73 megapascals/64 kilopascals. The graph for a confining pressure of 41.3 kilopascals is a curved line between 5 data points, beginning at about 77 megapascals/15 kilopascals, peaking at about 83 megapascals/26 kilopascals, and ending at about 73 megapascals/64 kilopascals. Type 1 Anomaly Example - This test shows that the resilient modulus 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.


Figure 15. Sample from test section 171003, layer 1, at the leave end shows significant effect of confining pressure on resilient modulus.
Figure 15. Sample from test section 171003, layer 1, at the leave end shows significant effect of confining pressure on resilient modulus (material code equals 102, lean clay). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, is graphed on the vertical axis. The graph for a confining pressure of 13.8 kilopascals is a curved line between 5 data points, beginning at a resilient modulus of about 20 megapascals and a pressure of 15 kilopascals, decreasing to about 13 megapascals/37 kilopascals, and ending at about 15 megapascals/62 kilopascals. The graph for a confining pressure of 27.7 kilopascals is a curved line between 5 data points, beginning at about 23 megapascals/15 kilopascals, steadily decreasing and ending at about 16 megapascals/62 kilopascals. The graph for a confining pressure of 41.5 kilopascals is a nearly straight line between 5 data points, beginning at about 35 megapascals/15 kilopascals, and ending at about 16 megapascals/62 kilopascals. Type 2 anomaly example: 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 resilient modulus 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.


Figure 16. Sample from test section 014129, layer 1, at the leave end shows sudden drop and then increase in resilient modulus.
Figure 16. Sample from test section 014129, layer 1, at the leave end shows sudden drop and then increase in resilient modulus (material code equals 215, silty sand with gravel). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, is graphed on the vertical axis. The graph for a confining pressure of 13.8 kilopascals is a sharply dropping then slowly rising line between 5 data points, beginning at a resilient modulus of about 98 megapascals and a pressure of 15 kilopascals, decreasing to about 68 megapascals/25 kilopascals, and ending at about 79 megapascals/63 kilopascals. The graph for a confining pressure of 27.6 kilopascals is a nearly straight line between 5 data points, beginning at about 79 megapascals/15 kilopascals, and ending at about 75 megapascals/63 kilopascals. The graph for a confining pressure of 41.4 kilopascals is a nearly straight line between 5 data points, beginning at about 78 megapascals/15 kilopascals, and ending at about 65 megapascals/62 kilopascals. Type 3 Anomaly Example - This test shows a sudden drop and then increase in the resilient modulus for the highest confining pressure, while the resilient modulus slightly decreases with increasing repeated vertical loads for the two lower confining pressures. This anomaly can be characteristic of re zeroing the LVDT 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.


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.
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 (material code equals 217, clayey sand with gravel). The Repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis. The graph for a confining pressure of 13.8 kilopascals is a slowly dropping then rising line between 5 data points, beginning at a resilient modulus of about 62 megapascals and a pressure of 15 kilopascals, decreasing to about 57 megapascals/50 kilopascals, and ending at about 60 megapascals/62 kilopascals. The graph for a confining pressure of 27.6 kilopascals is a steadily rising line between 5 data points, beginning at about 57 megapascals/15 kilopascals, and ending at about 73 megapascals/63 kilopascals. The graph for a confining pressure of 41.4 kilopascals is a slowly dropping then rising line between 5 data points, beginning at about 68 megapascals/15 kilopascals, decreasing to about 64 megapascals/25 kilopascals, and ending at about 75 megapascals/63 kilopascals. Type 4 anomaly example: The change in resilient modulus 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.


Figure 18. Sample from test section 473108, layer 1, at the leave end shows higher confining pressures result in lower resilient modulus.
Figure 18. Sample from test section 473108, layer 1, at the leave end shows higher confining pressures result in lower resilient modulus (material code equals 114, sandy lean clay). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis. The graph for a confining pressure of 13.8 kilopascals is a steadily dropping line between 5 data points, beginning at a resilient modulus of about 70 megapascals and a pressure of 12 kilopascals, and ending at about 38 megapascals/62 kilopascals. The graph for a confining pressure of 27.6 kilopascals is a steadily dropping line between 5 data points, beginning at about 70 megapascals/12 kilopascals, and ending at about 38 megapascals/62 kilopascals. The graph for a confining pressure of 41.4 kilopascals is a dropping then flattening line between 5 data points, beginning at about 57 megapascals/12 kilopascals, and ending at about 36 megapascals/62 kilopascals. Type 5 anomaly example: 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.


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.
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 (material code equals 216, silty sand with gravel). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis. The graph for a confining pressure of 13.8 kilopascals is a rising then flattening line between 5 data points, beginning at a resilient modulus of about 105 megapascals and a pressure of 13 kilopascals, and ending at about 130 megapascals/62 kilopascals. The graph for a confining pressure of 27.6 kilopascals is a rising then flattening line between 5 data points, beginning at about 105 megapascals/13 kilopascals, and ending at about 143 megapascals/62 kilopascals. The graph for a confining pressure of 41.4 kilopascals is a rising then flattening line between 5 data points, beginning at about 105 megapascals/13 kilopascals, and ending at about 150 megapascals/62 kilopascals. Type 6 anomaly example: 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.


Figure 20. Sample from test section 473104, layer 2, at the approach end shows possible data entry error.
Figure 20. Sample from test section 473104, layer 2, at the approach end shows possible data entry error (material code equals 303, crushed stone). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis. The graph for a confining pressure of 20.7 kilopascals is a nearly straight line between 3 data points, beginning at a resilient modulus of about 77 megapascals and a pressure of 15 kilopascals, and ending at about 110 megapascals/55 kilopascals. The graph for a confining pressure of 34.5 kilopascals is a nearly straight line between 3 data points, beginning at about 130 megapascals/25 kilopascals, and ending at about 185 megapascals/95 kilopascals. The graph for a confining pressure of 68.9 kilopascals is a nearly straight line between 3 data points, beginning at about 255 megapascals/67 kilopascals, and ending at about 280 megapascals/190 kilopascals. The graph for a confining pressure of 103.4 kilopascals is a nearly straight line between 3 data points, beginning at about 285 megapascals/67 kilopascals, and ending at about 345 megapascals/190 kilopascals. The graph for a confining pressure of 137.9 kilopascals is a sharply dropping then sharply rising line between 3 data points, beginning at 350 megapascals/95 kilopascals, dropping to 0 megapascals/0 kilopascals, and rising to about 405 megapascals/255 kilopascals. Type 7 Anomaly Example: 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.



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 thin-walled 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 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 k-coefficients 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.

Pavement Layer Type Material Code/Type*
No. of Tests - Auger
No. of Tests - Test Pit
No. of Tests - Shelby Tube
Total Number of Tests
Base/Subbase All

405

212

NA

617

Base/Subbase 302, Uncrushed Gravel

48

33

NA

81

Base/Subbase 303, Crushed Stone

63

46

NA

109

Base/Subbase 304, Crushed Gravel

32

17

NA

49

Base/Subbase 306, Sand

47

19

NA

66

Base/Subbase 307, Fine-Grained Soil-Aggregate Mixture

22

10

NA

32

Base/Subbase 308, Coarse-Grained Soil-Aggregate Mixture

127

60

NA

187

Base/Subbase 309, Fine-Grained Soil

65

27

NA

92

Subgrade Soil All

476

319

456

1251

Subgrade Soil Gravel

78

32

12

122

Subgrade Soil Sand

223

150

136

509

Subgrade Soil Silt

42

34

32

108

Subgrade Soil Clay

133

103

276

512

Total Number of Tests  

881

531

456

1868

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 Shapiro-Wilk W Test.(5) The data for some of the groups were not distributed normally. These data then 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 - 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)
Base/Subbase Materials All 0.0238 Yes - Vertical Loads
Base/Subbase Materials 302, Uncrushed Gravel 0.3769 No
Base/Subbase Materials 303, Crushed Stone 0.2874 No
Base/Subbase Materials 304, Crushed Gravel 0.4809 No
Base/Subbase Materials 306, Sand 0.0123 Yes - Confinement
Base/Subbase Materials 307, Fine-Grained Soil-Aggregate Mixture 0.9112 No
Base/Subbase Materials 308, Coarse-Grained Soil-Aggregate Mixture 0.0022 Yes - Vertical Loads
Base/Subbase Materials 309, Fine-Grained Soil 0.1057 No
Subgrade Soils All 0.1598 No
Subgrade Soils Gravel 0.4932 No
Subgrade Soils Sand 0.6691 No
Subgrade Soils 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).


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: ka divided by ktp = 1 or MRa divided by MRtp = 1

HA: ka divided by ktp does not equal 1
or MRa divided by MRtp does not equal 1

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.


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)
Base/Subbase Materials All Low 0.9706 0.9763 0.1875 0.2022 Accept
Base/Subbase Materials All Medium 1.0000 1.0092 0.1264 0.4308 Accept
Base/Subbase Materials All High 1.0000 1.0111 0.1183 0.3146 Accept
Base/Subbase Materials 302, Uncrushed Gravel All values 1.0253 1.0438 0.1712 <0.0001 REJECT
Base/Subbase Materials 303, Crushed Stone All values 0.9527 0.9391 0.1621 <0.0001 REJECT
Base/Subbase Materials 304, Crushed Gravel All values 1.0444 1.0323 0.1841 0.0670 Accept
Base/Subbase Materials 306, Sand Low 0.9706 1.0540 0.1882 0.4143 Accept
Base/Subbase Materials 306, Sand Medium 1.0000 0.9971 0.0539 0.8759 Accept
Base/Subbase Materials 306, Sand High 0.9563 0.9735 0.0664 0.2652 Accept
Base/Subbase Materials 307, Fine-Grained Soil-Aggregate Mixture All values 1.0041 1.0494 0.1660 0.0145 REJECT
Base/Subbase Materials 308, Coarse-Grained Soil-Aggregate Mixture Low 0.9592 0.9321 0.2097 0.0720 Accept
Base/Subbase Materials 308, Coarse-Grained Soil-Aggregate Mixture Medium 1.0000 1.0124 0.1307 0.5631 Accept
Base/Subbase Materials 308, Coarse-Grained Soil-Aggregate Mixture High 1.0327 1.0253 0.1666 0.3303 Accept
Base/Subbase Materials 309, Fine-Grained Soil All values 1.0092 1.0331 0.1264 <0.0001 REJECT
Subgrade Soils All All values 1.0476 1.0600 0.2810 <0.0001 REJECT
Subgrade Soils Gravel All values 1.2226 1.2437 0.2690 <0.0001 REJECT
Subgrade Soils Sand All values 1.0099 0.9990 0.2016 0.8980 Accept
Subgrade Soils 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.


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.

Material/Soil Type k1(1) k2(1) k3(1)
Base/Subbase Materials All 0.2378 0.5846 0.5070
Base/Subbase Materials 302, Uncrushed Gravel 0.0260 0.0850 0.3919
Base/Subbase Materials 303, Crushed Stone 0.0350 0.1868 0.0025
Base/Subbase Materials 304, Crushed Gravel 0.5228 0.7903 0.5193
Base/Subbase Materials 306, Sand 0.3149 0.1512 0.7767*
Base/Subbase Materials 307, Fine-Grained Soil-Aggregate Mixture 0.4134 0.3213 0.8316
Base/Subbase Materials 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
Subgrade Soils All 0.0328 0.0013 0.6553
Subgrade Soils Gravel 0.0710 0.9120 0.0169
Subgrade Soils Sand 0.8287 0.0050 0.3052
Subgrade Soils Silt 0.1059 0.1569 0.2512
Subgrade Soils Clay 0.1153 0.1594 0.9407
(1) Student t-Test Probability (Prob > |t|)
*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.

Material/Soil Type k1* k2* k3* MR Values; Hypothesis, MRa/MRtp = 1
Base/Subbase MaterialsAllAcceptAcceptAcceptAccept
Base/Subbase Materials302REJECTAcceptAcceptREJECT
Base/Subbase Materials303REJECTAcceptREJECTREJECT
Base/Subbase Materials304AcceptAcceptAcceptAccept
Base/Subbase Materials306AcceptAcceptAcceptAccept
Base/Subbase Materials307AcceptAcceptAcceptREJECT
Base/Subbase Materials308AcceptAcceptREJECTAccept
Base/Subbase Materials309AcceptAcceptAcceptREJECT
Subgrade SoilAllREJECTREJECTAcceptREJECT
Subgrade SoilGravelAcceptAcceptREJECTREJECT
Subgrade SoilSandAcceptREJECTAcceptAccept
Subgrade SoilSiltAcceptAcceptAcceptREJECT
Subgrade SoilClayAcceptAcceptAcceptREJECT
*k-Values; Hypothesis, ka/ktp = 1



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.

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: ka = kST or MRa = MRST
HA: ka does not equal kST or MRa does not equal MRST

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 Type Prob.>F Variances 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<0.0001No<0.0001---6.034REJECT
Gravel0.0045No<0.0001---11.653REJECT
Sand<0.0001No0.2725----0.514Accept
Silt0.5582Yes---<0.00019.964REJECT
Clay0.9484Yes---<0.000110.582REJECT


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.

Material Typek1k2k3
All0.7475<0.0001*<0.0001*
Clay0.03140.8948*0.0002
Gravel0.50800.23790.0001
Sand0.88650.01220.7961*
Silt0.9978*0.1687<0.0001
(1) Student t-Test Probability (Prob > |t|)
* 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.


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.

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 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
* k-Value; Hypothesis, ka = kst


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.

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:

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.


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

Sampling Technique Material/Soil Type Consistently Different Results or Different Populations of Data Borderline - Dependent on Type of Data Used Consistently Indifferent Results or Populations of Data are the Same
Auger Versus Test Pit Base and Subbase 302, Uncrushed gravel 307, Fine-grained soil-aggregate mixture 304, Crushed gravel
Auger Versus Test Pit Base and Subbase 303, Crushed stone 309, Fine-grained soil 306, Sand
Auger Versus Test Pit Base and Subbase     308, Coarse-grained soil-aggregate mixture
Auger Versus Test Pit Subgrade Soils None Gravel Sand
Auger Versus Test Pit Subgrade Soils   Silt  
Auger Versus Test Pit Subgrade Soils   Clay  
Undisturbed (Shelby Tubes) Versus Disturbed (Auger) Subgrade Soil Clay Gravel Sand
Undisturbed (Shelby Tubes) Versus Disturbed (Auger) Subgrade Soil   Silt  



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 materials' 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 material's 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, 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
Upsilond, 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
Upsilons (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 SAS® 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 "clean" 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 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:


Table 15. Summary of the physical properties that were found to be important for predicting resilient modulus for each material and soil type.

Independent Variable 303, Crushed Stone 304, Crushed Gravel 302, Uncrushed Gravel 306, Sand 308, Coarse-Grained Soil-Aggr. Mixture 307, Fine-Grained Soil-Aggr. Mixture 309, Fine-Grained Soil Gravel Sand Silt Clay
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, gammas   * *   * *     *   *
Optimum water content, Wopt * * *   * *     *   *
Maximum dry unit weight, gammaopt * * * * * *     *   *
Number of MR Tests 109 49 81 66 187 32 92 122 509 108 512
1 in = 25.4 mm


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 - LTPP Material Code 303

Equation 6: resilient modulus equals [0.7632 plus (0.0084 times the percentage passing the three eighths inch sieve) plus (0.0088 times the liquid limit of soil) minus (0.0371 times the optimum water content) minus (0.0001 times maximum dry unit weight of soil)] times atmospheric pressure times [bulk stress divided by atmospheric pressure] to the [2.2159 minus (0.0016 times percentage passing the three eighths inch sieve) plus (0.0008 times the liquid limit of soil) minus (0.038 times optimum water content) minus (0.0006 times maximum dry unit weight of soil) plus (2.4 times (10 to the negative 7) times (maximum dry unit weight of soil squared divided by the percentage passing the number 40 sieve)] times [(octahedral shear stress divided by atmospheric pressure) plus 1] to the [negative 1.1720 minus (0.0082 times the liquid limit of soil) minus (0.0014 times optimum water content) plus (0.0005 times maximum dry unit weight of soil)].

(Equation 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.

Crushed Gravel - LTPP Material Code 304

Equation 7: resilient modulus equals [negative 0.8282 minus (0.0065 times percentage passing the three eights inch sieve) plus (0.0114 times the liquid limit of soil) plus (0.0004 times plasticity index of soil) minus (0.0187 times optimum water content) plus (0.0036 times the water content of the test specimen) plus (0.0013 times the dry density of the test specimen) minus (2.6 time (10 to the negative 6) times (maximum dry weight unit of soil squared divided by the percentage passing the number 40 sieve] times atmospheric pressure times [bulk stress divided by atmospheric pressure] to the [negative 4.9555 minus (0.0057 times liquid limit of soil) minus (0.0075 times plasticity index of soil) minus (0.0470 times the water content of the test specimen) minus (0.0022 times maximum dry unit weight of soil) plus (2.8 time (10 to the negative 6) times (maximum dry unit weight of soil squared divided by percentage passing the number 40 sieve)] times [(octahedral shear stress divided by atmospheric pressure) plus1] to the [negative 3.514 plus (0.0016 times the dry density of the test specimen)].

(Equation 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 - LTPP Material Code 302

Equation 8: resilient modulus equals [negative 1.8961 plus (0.0014 times the dry density of the test specimen) minus (0.1184 times (the water content of the test specimen divided by optimum water content))] times atmospheric pressure times [bulk stress divided by atmospheric pressure] to the [0.4960 minus (0.0074 times percentage passing number 200 sieve) minus (0.0007 times the dry density of the test specimen) plus (1.6972 times (the dry density of the test specimen divided by maximum dry unit weight of soil)) plus (0.1199 times (the water content of the test specimen divided by optimum water content)] times [(octahedral shear stress divided by atmospheric pressure) plus 1] to the [negative 0.5979 plus (0.0349 times optimum water content) plus (0.0004 times maximum dry unit weight of soil) minus (0.5166 times (the water content of the test specimen divided by optimum water content)].

(Equation 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.


Figure 21. Graphical comparison of the predicted and measured resilient modulus for the crushed stone base materials.

Figure 21. Graphical comparison of the predicted and measured resilient modulus for the crushed stone base materials (Base/Subbase Material 303, Crushed Stone). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the resilient modulus equals f (physical properties) on the vertical axis. This figure 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.


Figure 22. Graphical comparison of the predicted and measured resilient modulus for the crushed gravel base materials.

Figure 22. Graphical comparison of the predicted and measured resilient modulus for the crushed gravel base materials (base/subbase material 304, crushed gravel). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the resilient modulus equals f (physical properties) on the vertical axis. This figure 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.


Sand - LTPP Material Code 306

Equation 9: resilient modulus equals [negative 0.2786 plus (0.0097 times percentage passing three eighths inch sieve) plus (0.0219 times liquid limit of soil) minus (0.0737 times plasticity index of soil) plus (1.8 times (10 to the negative 7) times (maximum dry unit weight of soil squared divided by percentage passing the number 40 sieve))] times atmospheric pressure times [(bulk stress divided by atmospheric pressure) to the (1.1148 minus (0.0053 times percentage passing three eighths inch sieve) minus (0.0095 times liquid limit of soil) plus (0.0325 times plasticity index of soil) plus (7.2 times (10 to the negative 7) times (maximum dry unit weight of soil squared divided by percentage passing the number 40 sieve))] times [((octahedral shear stress divided by atmospheric pressure) plus1) to the (negative 0.4508 plus (0.0029 times percentage passing three eighths inch sieve) minus (0.0185 times liquid limit of soil) plus (0.0798 times plasticity index of soil))].

(Equation 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 - LTPP Material Code 308

Equation 10: resilient modulus equals [negative 0.5856 plus (0.0130 times percentage passing three eighths inch sieve) minus (0.0174 times percentage passing number 4 sieve) plus (0.0027 times percentage passing number 200 sieve) plus (0.0149 times plasticity index of soil) plus (1.6 times (10 to the negative 6) times maximum dry unit weight of soil) minus (0.0426 times the water content of the test specimen) plus (1.6456 times (the dry density of the test specimen divided by maximum dry unit weight of soil)) plus (0.3932 times (the water content of the test specimen divided by optimum water content)) minus (8.2 times (10 to the negative 7) times (maximum dry unit weight of soil squared divided by percentage passing the number 40 sieve)] times atmospheric pressure times [(bulk stress divided by atmospheric pressure) to the (0.7833 minus (0.0060 times percentage passing number 200 sieve) minus (0.0081 times plasticity index of soil) plus (0.0001 times maximum dry unit weight of soil) minus (0.1483 times (the water content of the test specimen divided by optimum water content)) minus (2.7 times (10 to the negative 7) times (maximum dry unit weight of soil squared divided by percentage passing the number 40 sieve))] times [((octahedral shear stress divided by atmospheric pressure) plus1) to the (negative 0.1906 minus (0.0026 times percentage passing number 200 sieve) plus (8.1 times (10 to the negative 7) times (maximum dry unit weight of soil squared divided by percentage passing the number 40 sieve))].

(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.


Figure 23. Graphical comparison of the predicted and measured resilient modulus for the uncrushed gravel base materials.

Figure 23. Graphical comparison of the predicted and measured resilient modulus for the uncrushed gravel base materials (base/subbase material 302, uncrushed gravel). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the resilient modulus equals the function of (physical properties) on the vertical axis. This figure 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.


Figure 24. Graphical comparison of the predicted and measured resilient modulus for the sand base materials.

Figure 24. Graphical comparison of the predicted and measured resilient modulus for the sand base materials (base/subbase material 306, sand). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the resilient modulus equals the function of (physical properties) on the vertical axis. This figure shows a comparison of the measured and predicted resilient modulus using equation 9 at the appropriate stress states used to test sand base materials.


Figure 25. Graphical comparison of the predicted and measured resilient modulus for the coarse-grained soil-aggregate base materials.

Figure 25. Graphical comparison of the predicted and measured resilient modulus for the coarse grained soil aggregate base materials (base/subbase material 308, coarse grained soil aggregate mixture). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the resilient modulus equals the function of (physical properties) on the vertical axis. This figure 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.


Figure 26. Graphical comparison of the predicted and measured resilient modulus for the fine-grained soil-aggregate base materials.

Figure 26. Graphical comparison of the predicted and measured resilient modulus for the fine grained soil aggregate base materials (base/subbase material 307, fine grained soil aggregate mixture). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the resilient modulus equals the function of (physical properties) on the vertical axis. This figure 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-Aggregate Mixture - LTPP Material Code 307

Equation 11: resilient modulus equals [negative 0.7668 plus (0.0051 times percentage passing number 4 sieve) plus (0.0128 times percentage passing number 200 sieve) plus 0.0030 times liquid limit of soil) minus (0.0510 times optimum water content plus (1.1729 times (the dry density of the test specimen divided by maximum dry unit weight of soil))] times atmospheric pressure times times [(bulk stress divided by atmospheric pressure) to the (0.4951 minus (0.0141 times percentage passing number 4 sieve) minus (0.0061 times percentage passing number 200 sieve) plus (1.3941 times (dry density of test specimen divided by maximum dry unit weight of soil)] times [((octahedral shear stress divided by atmospheric pressure) plus1) to the (0.9303 plus (0.0293 times percentage passing three eighths inch sieve) plus (0.0036 times liquid limit of soil) minus (3.8903 times (the dry density of the test specimen divided by maximum dry unit weight of soil))].

(Equation 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 - LTPP Material Code 309

Equation 12: resilient modulus equals [0.8409 plus (0.0004 times percentage passing the number 40 sieve) plus (0.0161 times plasticity index of soil)] times atmospheric pressure times [(bulk stress divided by atmospheric pressure) to the (0.6668 minus (0.0007 times percentage passing the number 40 sieve) minus (0.0139 times plasticity index of soil))] times [((octahedral shear stress divided by atmospheric pressure) plus1) to the (0.1667 minus (0.0207 times plasticity index of soil))].

(Equation 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.


Figure 27. Graphical comparison of the predicted and measured resilient modulus for the fine-grained soil base materials.

Figure 27. Graphical comparison of the predicted and measured resilient modulus for the fine grained soil base materials (base/subbase material 309, fine grained soil). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the resilient modulus equals the function of (physical properties) on the vertical axis. This figure 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.


Subgrade Soils

Coarse-Grained Gravel Soils

Equation 13: resilient modulus equals [1.3429 minus (0.0051 times percentage passing three eighths inch sieve) plus (0.0124 times percentage clay) plus (0.0053 times liquid limit of soil) minus (0.0231 times the water content of the test specimen)] times atmospheric pressure times [(bulk stress divided by atmospheric pressure) to the (0.3311 plus (0.0010 times percentage passing three eighths inch sieve) minus (0.0019 times percentage clay) minus (0.0050 time liquid limit of soil) minus (0.0072 times plasticity index of soil) plus (0.0093 times the water content of the test specimen))] times [((octahedral shear stress divided by atmospheric pressure) plus1) to the (1.5167 minus (0.0302 times percentage passing three eighths inch sieve) plus (0.0435 times percentage clay) plus (0.00626 times liquid limit of soil) plus (0.0377 times plasticity index of soil) minus (0.2353 times the water content of the test specimen))].

(Equation 13)

Number of points = 957
Mean squared error = 301.3
Se = 17.36
Sy = 26.81
Se/Sy = 0.6474

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

Equation 14: resilient modulus equals [3.2868 minus (0.0412 times percentage passing three eighths inch sieve) plus (0.0267 times percentage passing number 4 sieve) plus (0.0137 times percentage clay) plus (0.0083 times liquid limit of soil) minus (0.0379 times optimum water content) minus (0.0004 times the dry density of the test specimen)] times atmospheric pressure times [(bulk stress divided by atmospheric pressure) to the (0.5670 plus (0.0045 times percentage passing three eighths inch sieve) minus (2.98 times (10 to the negative 5) times percentage passing number 4 sieve) minus (0.0043 times percent silt) minus (0.0102 times percentage clay) minus (0.0041 times liquid limit of soil) plus (0.0014 times optimum water content) minus (3.41 times (10 to the negative 5) times the dry density of the test specimen) minus (0.4582 times (the dry density of the test specimen divided by maximum dry unit weight of soil)) plus (0.1779 times (the water content of the test specimen divided by optimum water content))] times [((octahedral shear stress divided by atmospheric pressure) plus 1) to the (negative 3.5677 plus (0.1142 times percentage passing three eighths inch sieve) minus (0.0839 times percentage passing number 4 sieve) minus (0.1249 times percentage passing the number 200 sieve) plus (0.1030 times percentage silt) plus (0.1191 times percentage clay) minus (0.0069 times liquid limit of soil) minus (0.0103 times optimum water content) minus (0.0017 times the dry density of the test specimen) plus (4.3177 times (the dry density of the test specimen divided by maximum dry unit weight of soil)) minus (1.1095 times (the water content of the test specimen divided by optimum water content))].

(Equation 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

Equation 15: resilient modulus equals [1.0480 plus (0.0177 times percentage clay) plus (0.0279 times plasticity index of soil) minus (0.370 times the water content of the test specimen)] times atmospheric pressure times [(bulk stress divided by atmospheric pressure) to the (0.5097 minus (0.0286 times plasticity index of soil)] times [((octahedral shear stress divided by atmospheric pressure) plus 1) to the (0.2218 plus (0.0047 times percent silt) plus (0.0849 times plasticity index of soil) minus (0.1399 times the water content of the test specimen))].

(Equation 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.


Figure 28. Graphical comparison of the predicted and measured resilient modulus for the coarse-grained gravel soils.

Figure 28. Graphical comparison of the predicted and measured resilient modulus for the coarse-grained gravel soils (subgrade, gravel). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the resilient modulus equals the function of (physical properties), megapascals on the vertical axis. This figure 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.


Figure 29. Graphical comparison of the predicted and measured resilient modulus for the coarse-grained sand soils.

Figure 29. Graphical comparison of the predicted and measured resilient modulus for the coarse-grained sand soils (subgrade, sand). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the resilient modulus equals the function of (physical properties), megapascals on the vertical axis. This figure 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 Clay Soils

Equation 16: resilient modulus equals [1.3577 plus (0.0106 times percentage clay) minus (0.0437 times the water content of the test specimen)] times atmospheric pressure times [(bulk stress divided by atmospheric pressure) to the (0.5193 minus (0.0073 times percentage passing number 4 sieve) plus (0.0095 times percentage passing the number 40 sieve) minus (0.0027 times percentage passing number 200 sieve) minus (0.0030 times liquid limit of soil) minus (0.0049 times optimum water content))] times [((octahedral shear stress divided by atmospheric pressure) plus 1) to the (1.4258 minus (0.0288 times percentage passing number 4 sieve) plus (0.0303 times percentage passing the number 40 sieve) minus (0.0521 times percentage passing number 200 sieve) plus (0.0251 times percent silt) plus (0.0535 times liquid limit of soil) minus (0.0672 times optimum water content) minus (0.0026 times maximum dry unit weight of soil) plus (0.0025 times the dry density of the test specimen) minus (0.6055 times (the water content of the test specimen divided by optimum water content))].

(Equation 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:


Figure 30. Graphical comparison of the predicted and measured resilient modulus for the fine-grained silt soils.

Figure 30. Graphical comparison of the predicted and measured resilient modulus for the fine grained silt soils (subgrade, silt). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the resilient modulus equals the function of (physical properties), megapascals on the vertical axis. This figure 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.


Figure 31. Graphical comparison of the predicted and measured resilient modulus for the fine-grained clay soils.

Figure 31. Graphical comparison of the predicted and measured resilient modulus for the fine grained clay soils (Subgrade, clay). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the resilient modulus equals the function of (physical properties), megapascals on the vertical axis. This figure 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.


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 MrR 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.

Figure 32. Comparison of the resilient modulus predicted from the data sets for crushed stone materials sampled from the test pit and auger locations (material code 303, crushed stone). The resilient modulus predicted (test pit) is graphed on the horizontal axis and the resilient modulus predicted (auger) on the vertical axis. This figure shows a comparison of the calculated resilient modulus between the test pit and augered samples using the regression equations to estimate the K coefficients. A bias is present in the calculated resilient modulus 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. 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.

Figure 33. Graphical comparison of the calculated resilient modulus using the regressed K coefficients from the physical properties of the sand soil group sampled from augers and test pits (resilient modulus for sand). The resilient modulus predicted (test pit) is graphed on the horizontal axis and the resilient modulus predicted (auger) on the vertical axis. This figure shows the comparison of the predicted resilient modulus using the regression models developed for the different sampling techniques for sand. The error in the calculated resilient modulus using the physical properties overshadows any difference caused by the different sampling techniques used.



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 FHWA's 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:

FINDINGS AND OBSERVATIONS

The following is a summary of the findings and recommendations from this study:

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.


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


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.
k1k2k3No.
Points
Std
Dev(MR)
RMSEMSER2Se/Sy
1010112B6BS060.73710.1236-0.7748154.16562.03584.14470.99910.4887
1010212B7BS070.78100.1497-0.4579154.33372.40885.80230.99900.5558
1010312B5BS050.74710.1952-1.2825155.97381.99743.98980.99910.3344
1010612B4BS040.75140.1787-0.2832154.62601.86473.47700.99940.4031
1010712B1BS010.67010.2137-1.0366154.94541.47042.16200.99940.2973
1010812B2BS020.76190.1612-0.4410154.11961.69442.87080.99950.4113
1011112B3BS030.76280.1344-0.2691154.18272.70637.32390.99880.6470
1050211TP1BS550.61900.39020.0000159.08061.97453.89860.99920.2174
1050221TP1BG560.61880.5133-0.04051533.66471.14381.30840.99990.0340
1050222TP1BG560.59480.43990.0000159.89851.97073.88360.99910.1991
1100122TP1BG560.71720.7705-0.04581578.11416.686144.70420.99870.0856
1100122TP1BG570.72680.7067-0.14721562.55845.697532.46130.99880.0911
1101111A1TS010.82280.1655-2.2042159.75754.664121.75350.99460.4780
1101112A2TS031.76000.4354-3.14761525.03374.927324.27830.99840.1968
1101121BA*BG**0.91450.55030.00001557.93864.589621.06430.99940.0792
1101122BA*BG**0.96130.6280-0.17371565.44705.676232.21890.99920.0867
1101131BA*BG**0.57000.98970.000015103.52836.775845.91120.99900.0654
1101911A1TS021.25010.4131-1.24421515.36235.362928.76040.99780.3491
1101912A2TS030.53430.41780.0000158.93203.235910.47130.99710.3623
1101921BA*BG**0.99620.62500.00001580.191017.8706319.35890.99340.2229
1101922TP1BG550.77990.6658-0.13961561.13556.879047.32080.99840.1125
1102111A1TS010.86480.5048-2.38171512.66304.155817.27090.99630.3282
1102112A2TS031.21720.2507-2.93021515.95925.064025.64420.99660.3173
1102121BA*BG**0.94830.6619-0.14471572.25604.805223.09020.99940.0665
1102122TP1BG550.89840.7054-0.27321570.35008.963580.34410.99790.1274
1302811BA*BS**1.21310.26560.00001524.330721.2344450.89770.97500.8727
1302812BA*BS**1.88940.2760-2.24481520.66352.87908.28870.99960.1393
1302821BA*BG**1.44640.5184-0.07991577.622417.7199313.99420.99560.2283
1302822BA*BG**1.23100.7180-0.67331576.846322.2049493.05870.99050.2890
1302831BA*BG**1.02710.68100.00001590.400611.0833122.84060.99790.1226
1302832BA*BG**1.59550.58140.000015110.852514.2134202.01950.99820.1282
1399812BA*BS**1.06370.3231-1.05551510.67353.724713.87340.99860.3490
1399831BA1BG**0.97380.5864-0.29051552.93516.876547.28660.99850.1299
1399832BA4BG040.80060.6053-0.23771445.74153.501212.25820.99940.0765
1400711BA*BS**0.81410.4355-3.01541512.13304.348518.90900.99440.3584
1400712BA*BS**1.39480.2649-2.87671517.65892.38325.67950.99940.1350
1400721BA*BG**0.94940.5808-0.14351557.40577.091850.29320.99850.1235
1400722BA*BG**0.83830.56340.00001554.547210.8640118.02650.99590.1992
1400731BA*BG**1.38160.55900.00001591.140112.7308162.07250.99790.1397
1400732BA*BG**0.94970.72220.00001594.740413.2385175.25680.99690.1397
1407311BA*BS**0.90020.1355-0.2725156.46095.237427.43010.99680.8106
1407312A2TS030.72290.19970.00001516.350915.4884239.89120.96180.9473
1407331BA*BG**0.98360.24660.00001584.125981.96526718.28900.71860.9743
1407332BA*BG**0.81740.7952-0.10031590.17766.701044.90290.99900.0743
1408411A1TS010.87950.1582-0.4664155.02562.58576.68570.99910.5145
1408412BA*BS**1.03750.2973-0.55011510.19014.191117.56560.99840.4113
1408421BA*BG**0.59900.7892-0.11431563.86063.12339.75530.99960.0489
1408422BA*BG**0.79720.58850.00001569.401750.46952547.17100.91210.7272
1408431BA*BG**0.67780.71460.00001564.65169.168784.06480.99700.1418
1408432BA*BG**0.78000.8275-0.01671597.77055.288927.97300.99950.0541
1412511BA*BS**0.80590.1801-0.3696157.63896.137837.67260.99440.8035
1412512BA*BS**1.12920.2901-1.06691510.86594.657021.68770.99800.4286
1412521BA*BG**0.81390.6263-0.18251553.99165.583531.17600.99890.1034
1412522BA*BG**1.18050.5535-0.72581543.258015.0289225.86800.99240.3474
1412611A1TS010.77510.2980-1.6994158.94004.592921.09450.99510.5137
1412612BA*BS**0.78090.4647-1.13581510.84833.557212.65400.99770.3279
1412621BA*BG**1.04710.62180.00001580.45367.228252.24700.99900.0898
1412622BA*BG**0.64900.78250.00001573.91687.935662.97440.99800.1074
1412711A1TS011.14220.3306-2.79381514.25382.63356.93550.99900.1848
1412712BA*BS**1.32650.0829-1.74821513.61626.037436.45070.99690.4434
1412721BA*BG**0.70260.77050.00001577.04548.541472.95630.99800.1109
1412722BA*BG**0.53370.71250.00001552.213716.6248276.38240.98450.3184
1412911BA*BS**1.15430.3027-2.89871515.14533.785614.33050.99790.2499
1412912TP1BS550.84610.1659-0.9872157.46615.449429.69570.99510.7299
1412922TP1BG560.80220.8315-0.69351562.89435.710432.60870.99890.0908
1415522BA*BG**1.10410.6834-0.09301592.58736.683044.66300.99930.0722
1500811A1TS011.07110.2380-3.56981516.11035.965235.58360.99270.3703
1500812A2TS030.70080.3522-1.7352158.16503.14719.90440.99720.3854
1601211A1TS010.64920.3830-0.5643158.52063.449611.89950.9973 0.4049
1601212A2TS030.77520.5601-1.70781511.90123.13829.84800.99790.2637
1601221BA*BG**0.87780.5954-0.11381557.26864.108116.87660.99950.0717
1601222TP1BG551.04940.7489-0.41881580.475315.7269247.33520.99520.1954
1601911A1TS010.79280.3903-0.9354159.85953.935815.49020.99730.3992
1601912BA*BS**0.81900.4979-0.65301512.79062.62696.90060.99900.2054
1601921BA*BG**0.70120.7925-0.37741561.99853.786514.33750.99950.0611
1601922BA*BG**0.81960.6743-0.27751557.56305.576131.09330.99890.0969
4011412B309BS091.38260.2588-1.50201512.29911.93603.74820.99970.1574
4011512B303BS030.90220.5984-2.01811514.44133.11179.68240.99830.2155
4021312B311BS110.87460.5885-2.13061513.62492.74697.54520.99860.2016
4021612B306BS060.93610.5105-1.93701513.09782.56396.57340.99890.1957
4021712B309BS090.73980.6783-1.89641513.23882.60956.80930.99840.1971
4022212B303BS030.95860.6219-2.20771415.20841.96143.84710.99940.1290
4022312B308BS080.82780.7128-1.83881416.09953.05019.30290.99830.1895
4060812B*BS**0.68530.4443-1.5710158.79772.71907.39270.99800.3091
4100111BA*BS**0.49980.4101-1.1300155.99361.53152.34560.99890.2555
4100112TP1BS910.78530.3092-0.9687157.46872.25605.08940.99910.3021
4100311BA*BS**0.83190.3211-1.1004157.90001.47482.17510.99960.1867
4100312TP1BS920.78130.2274-1.4264156.67831.64622.71000.99940.2465
4100611BA*BS**0.64600.4283-1.5221158.20162.59626.74050.99790.3166
4100612TP1BS920.81570.2828-0.9575157.15812.23174.98040.99920.3118
4100622TP1BG910.42550.5981-0.05121528.74981.31551.73060.99980.0458
4100711BA*BS**0.71970.2933-1.0219156.81252.69007.23590.99840.3949
4100712TP1BS910.66160.5148-1.5365159.47081.80073.24240.99910.1901
4101511BA*BS**0.93000.22900.0000158.39953.09069.55170.99900.3679
4101512TP1BS921.02060.14510.0000157.19334.734422.41470.99810.6582
4101621BA*BG**0.85530.4920-0.41121532.550610.2399104.85500.99400.3146
4101711BA*BS**1.09190.12560.00001510.02478.681175.36170.99450.8660
4101812TP1BS920.34350.3740-2.3961154.28401.10421.21930.99830.2578
4101821BA*BG**1.05510.2786-0.14041521.70651.32881.76560.99990.0612
4102111BA*BS**0.55790.6154-1.3122159.74582.10064.41260.99840.2155
4102112TP1BS920.52870.6330-1.6658159.17662.30035.29120.99770.2507
4102212TP1BS930.90340.20290.0000157.06972.26045.10960.99950.3197
4102411BA*BS**1.05530.22440.00001510.25025.360228.73130.99780.5229
4102412TP1BS921.04180.1763-0.5128155.76771.30731.70910.99980.2267
4102421BA*BG**1.38470.21930.00001526.17436.004036.04780.99890.2294
4103412TP1BS920.79360.3787-1.5099158.90162.05264.21310.99910.2306
4103612TP1BS700.73040.2685-0.7325156.25872.28735.23180.99900.3655
4106211BA*BS**0.69330.2804-0.2882156.83342.68827.22620.99860.3934
4106511BA*BS**0.88590.2622-0.4837157.47822.44355.97090.99930.3268
4605311BA*BS**0.76580.3751-1.3903158.35691.47132.16470.99950.1761
4605312TP1BS920.77980.3288-0.6940157.98092.54456.47450.99890.3188
4605411BA*BS**0.63660.5542-1.5157159.78972.19444.81540.99860.2242
4605412TP1BS920.66130.5143-1.2380159.62042.03834.15470.99890.2119
4605421BA*BG**0.49140.5684-0.09381529.76104.040016.32130.99820.1357
4605511BA1BS630.86990.2678-0.5267157.72633.182410.12750.99870.4119
4606012TP1BS921.06030.1957-0.7465156.70681.76283.10750.99970.2628
4707911TP1BG920.70940.17200.0000154.98282.24085.02120.99910.4497
4761411BA*BS**0.51530.6683-1.11081510.08871.95543.82360.99850.1938
4761412BA*BS**0.54640.6406-1.4908159.73562.25655.09190.99800.2318
5080911A1TS011.19770.2272-1.3215159.55341.31151.71990.99980.1373
5080912B2BS021.09760.2637-1.69261510.37301.52682.33120.99970.1472
5081012B3BS030.79580.4785-1.76101510.65832.09674.39620.99910.1967
5301112A2TS030.80350.1570-0.8411156.01744.041116.33020.99720.6716
5304811A1TS010.53930.4559-4.7896158.14921.50512.26540.99790.1847
5304812A2TS030.77280.0727-0.0652154.34033.904815.24740.99770.8997
5305811A1TS020.78750.2825-3.75711510.85751.48622.20890.99920.1369
5305812A2TS040.57510.5593-1.4822158.75761.40111.96310.99930.1600
5305911A1TS010.77450.3783-0.6541158.98151.32851.76500.99970.1479
5305912A2TS030.64210.5358-0.86461510.32931.88703.56070.99910.1827
5307311BA*BS**1.21300.1555-0.97431511.14718.321069.23970.99450.7465
5307312A2TS031.72460.4174-1.94751520.99553.369211.35160.99940.1605
5307322BA*BG**0.77110.5753-0.00421551.63293.359211.28450.99960.0651
5307332BA*BG**0.90910.6159-0.53331544.98178.464471.64580.99700.1882
5307411A1TS010.54470.4050-3.2925157.62392.24665.04740.99660.2947
5307412A2TS030.65140.3682-2.2002158.19293.09169.55780.99650.3773
5401911A1TS010.54820.4429-0.8866157.36011.69512.87340.99900.2303
5401912A2TS030.46470.4165-0.4198156.43431.20361.44860.99940.1871
5401921BA*BG**0.56260.6400-0.04091543.56972.22074.93140.99970.0510
5401922BA*BG**0.66350.6286-0.25181542.09823.381011.43090.99930.0803
5402111A1TS010.58240.0000-0.7731157.46616.958048.41390.98410.9319
5402112A2TS030.94020.4058-3.63631513.81924.189317.54990.99560.3031
5402121BA*BG**0.98360.6125-0.32781556.07507.365154.24530.99840.1313
5402122BA*BG**0.99310.6600-0.34971563.32228.776677.02900.99800.1386
5402131BA1BG010.82810.59850.00001560.22215.733932.87700.99890.0952
5402132BA*BG**1.02340.6369-0.02771579.93283.02109.12610.99980.0378
5402312A2TS030.40080.0827-3.4340155.62732.68117.18810.99090.4764
5404611A1TS010.67320.1544-1.9907156.68332.07324.29800.99850.3102
5404612A2TS030.81730.2922-3.87991511.52931.59472.54290.99910.1383
5580311BA*BS**0.62560.16220.0000155.44674.012016.09610.99640.7366
5580312BA*BS**0.72630.2834-0.1316157.59572.75077.56660.99880.3621
5580322BA*BG**0.89950.5434-0.79941530.250110.1542103.10700.99350.3357
5580511BA*BS**1.61650.3330-1.65011516.87973.498712.24110.99940.2073
5580512BA*BS**0.63840.24680.0000157.33104.528820.51050.99580.6178
6125311BA*BS**0.88300.20740.0000158.33415.031425.31470.99720.6037
6200211BA*BS**0.54070.4460-1.4504156.88131.68332.83340.99880.2446
6200411BA*BS**0.57210.4024-2.1477157.35492.41865.84990.99720.3288
6200421BA*BG**0.49430.6108-0.10611533.32672.54046.45360.99940.0762
6200422TP1BG910.50260.6098-0.09641534.17351.80803.26890.99970.0529
6203811BA*BS**0.49720.6936-2.3137158.89191.80303.25070.99810.2028
6203812TP1BS920.65240.5741-2.58691510.11512.16874.70340.99820.2144
6205112TP1BG551.00520.18770.0000157.76623.549112.59620.99890.4570
6205311A1TS010.88250.1566-0.2485154.62601.50402.26210.99970.3251
6264721BA*BG**0.54440.5276-0.18091527.24464.376819.15670.99800.1607
6301012BA*BS**1.31270.22470.00001514.862210.1830103.69400.99490.6852
6301311BA*BS**0.85320.2000-0.5983155.72962.46406.07110.99910.4300
6301312BA*BS**0.49360.6305-1.0905159.02751.44992.10210.99910.1606
6301911BA*BS**0.76630.4057-0.28911510.44491.41682.00720.99970.1356
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88164511BA*BS**0.55750.5673-1.8587149.13783.03549.21360.99600.3322
88164512TPBS551.05140.3470-2.47341513.50244.200517.64420.99720.3111
88164611BA*BS**0.86830.3856-2.88351512.18594.403819.39340.99500.3614
88164612TPBS550.62090.4368-1.5422158.11052.99428.96520.99700.3692
88164712TPBS550.93170.2328-1.5853159.12514.003616.02890.99740.4387
89102111BA*BS**0.82470.5784-1.02411513.87632.07894.32160.99930.1498
89102112TPBS550.69930.5953-0.79181512.70251.99843.99340.99920.1573
89112511BA*BS**0.80090.7689-1.38461517.25522.45226.01350.99900.1421
89112512TPBS550.65210.6448-0.79631512.86121.91433.66460.99920.1488
89112521BA*BG**0.69020.6806-0.08181557.38033.476012.08290.99950.0606
89112522TPBG570.74170.6761-0.22351554.70112.91818.51510.99970.0533
89112711BA*BS**0.71830.5634-0.92761512.10002.82637.98780.99840.2336
89112721BA3BG030.57670.7112-0.32181543.44762.66717.11340.99950.0614
89112722TPBG560.53730.7512-0.32051544.50184.057516.46320.99890.0912
89300111BA*BS**0.52240.6329-0.79701510.27111.55812.42760.99920.1517
89300112BA*BS**0.64670.6037-0.88121511.78302.22014.92890.99880.1884
89300122BA*BG**0.59240.6600-0.21481542.39013.929215.43840.99900.0927
89300211BA*BS**0.80470.5151-1.43861512.18004.383919.21830.99640.3599
89301511BA*BS**0.60020.6961-0.61661513.53662.47076.10420.99860.1825
89301512BA*BS**0.81640.5880-1.05651514.06352.80417.86290.99880.1994
89901811BA*BS**0.72450.4851-0.58271511.16632.17254.71980.99920.1946
89901812BA*BS**0.71800.4582-0.70451510.60773.872814.99830.99720.3651
90640011TP*BS**0.91570.6394-1.11301516.69422.64276.98410.99910.1583
90640012TP*BS**0.82820.5789-1.13811513.67062.48516.17570.99900.1818
90640531TP*BG**0.74610.7024-0.01781568.13383.839714.74340.99950.0564
90640532TP*BG**1.46880.5246-0.27431568.139416.7181279.49520.99550.2454
90680111TP*BS**1.52000.2122-1.29961511.73801.40061.96170.99990.1193
90680112TP*BS**0.98870.31400.00001511.95753.636513.22410.99890.3041
* - Reference to LTPP Database Code List
** - Reference to LTPP Database Code List



Appendix B. GRAPHICAL EXAMPLES OF THE DIFFERENT TYPES OF ANOMALIES IDENTIFIED IN THE RESILIENT MODULUS TEST DATA

Appendix B provides graphical examples of the different types of anomalies identified in the resilient modulus test data. The following gives a brief description of the graphical examples included in this appendix:


Figure 34. Sample from test section 010111, layer 1, at the leave end exhibits specimen distortion or excess softening.

Figure 34. Sample from test section 010111, layer 1, at the leave end exhibits specimen distortion or excess softening (material code 131, silty clay). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.3. This figure shows excess softening or potential disturbance of the test specimen for the higher vertical loads. These resilient modulus tests could be


Figure 35. Sample from test section 063030, layer 1, at the approach end exhibits specimen distortion or excess softening.

Figure 35. Sample from test section 063030, layer 1, at the approach end exhibits specimen distortion or excess softening (material code 267, clayey gravel with sand). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.3. This figure shows excess softening or potential disturbance of the test specimen for the higher vertical loads. These resilient modulus tests could be


Figure 36. Sample from test section 067455, layer 1, at the approach end exhibits specimen distortion or excess softening.

Figure 36. Sample from test section 067455, layer 1, at the approach end exhibits specimen distortion or excess softening (material code 117, gravelly lean clay with sand). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.3. This figure shows excess softening or potential disturbance of the test specimen for the higher vertical loads. These resilient modulus tests could be


Figure 37. Sample from test section 370212, layer 1, at the approach end exhibits specimen distortion or excess softening.

Figure 37. Sample from test section 370212, layer 1, at the approach end exhibits specimen distortion or excess softening (material code 145, sandy silt). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.3. This figure shows excess softening or potential disturbance of the test specimen for the higher vertical loads. These resilient modulus tests could be


Figure 38. Sample from test section 179327, layer 1, at the approach end shows significant effect of confining pressure on resilient modulus.

Figure 38. Sample from test section 179327, layer 1, at the approach end shows significant effect of confining pressure on resilient modulus (material code 108, lean clay with sand). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.9, 27.7, and 41.6. This figure provides graphical examples of the resilient modulus tests with a significant effect of the confining pressure that varies with the vertical loads used in the test program. These tests could be


Figure 39. Sample from test section 295403, layer 1, at the approach end shows significant effect of confining pressure on resilient modulus.

Figure 39. Sample from test section 295403, layer 1, at the approach end shows significant effect of confining pressure on resilient modulus (material code 214, silty sand). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.9, 27.6, and 41.4. this figure provides graphical examples of the resilient modulus tests with a significant effect of the confining pressure that varies with the vertical loads used in the test program. These tests could be


Figure 40. Sample from test section 296067, layer 1, at the approach end shows significant effect of confining pressure on resilient modulus.

Figure 40. Sample from test section 296067, layer 1, at the approach end shows significant effect of confining pressure on resilient modulus (material code 217, clayey sand with gravel). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 14.3, 27.9, and 41.5. this figure provides graphical examples of the resilient modulus tests with a significant effect of the confining pressure that varies with the vertical loads used in the test program. These tests could be


Figure 41. Sample from test section 289030, layer 1, at the leave end shows significant effect of confining pressure on resilient modulus.

Figure 41. Sample from test section 289030, layer 1, at the leave end shows significant effect of confining pressure on resilient modulus (material code 102, lean clay). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.4. this figure provides graphical examples of the resilient modulus tests with a significant effect of the confining pressure that varies with the vertical loads used in the test program. These tests could be


Figure 42. Sample from test section 123811, layer 1, at the leave end shows sudden drop and then increase in resilient modulus.

Figure 42. Sample from test section 123811, layer 1, at the leave end shows sudden drop and then increase in resilient modulus (material code 216, silty sand with gravel). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.4. this figure provides graphical examples of the resilient modulus tests with a sudden drop and then an increase in the resilient modulus measured at increasing vertical loads.


Figure 43. Sample from test section 280508, layer 1, at the leave end shows sudden drop and then increase in resilient modulus.

Figure 43. Sample from test section 280508, layer 1, at the leave end shows sudden drop and then increase in resilient modulus (material code 102, lean clay). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.4. this figure provides graphical examples of the resilient modulus tests with a sudden drop and then an increase in the resilient modulus measured at increasing vertical loads.


Figure 44. Sample from test section 283089, layer 1, at the leave end shows sudden drop and then increase in resilient modulus.

Figure 44. Sample from test section 283089, layer 1, at the leave end shows sudden drop and then increase in resilient modulus (material code 114, sandy lean clay). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.4. this figure provides graphical examples of the resilient modulus tests with a sudden drop and then an increase in the resilient modulus measured at increasing vertical loads.


Figure 45. Sample from test section 483875, layer 1, at the leave end shows sudden drop and then increase in resilient modulus.

Figure 45. Sample from test section 483875, layer 1, at the leave end shows sudden drop and then increase in resilient modulus (material code 108, lean clay with sand). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.4. this figure provides graphical examples of the resilient modulus tests with a sudden drop and then an increase in the resilient modulus measured at increasing vertical loads.


Figure 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.

Figure 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 (material code 214, silty sand). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.4. This figure provides graphical examples of the resilient modulus tests with relationships between resilient modulus and vertical loads for different confining pressures that intersect or have completely different stress sensitivity effects.


Figure 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.

Figure 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 (material code 101, clay). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.4. This figure provides graphical examples of the resilient modulus tests with relationships between resilient modulus and vertical loads for different confining pressures that intersect or have completely different stress sensitivity effects.


Figure 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.

Figure 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 (material code 102, lean clay). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.4. This figure provides graphical examples of the resilient modulus tests with relationships between resilient modulus and vertical loads for different confining pressures that intersect or have completely different stress sensitivity effects.


Figure 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.

Figure 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 (material code 267, clayey gravel with sand). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.4. this figure provides graphical examples of the resilient modulus tests with relationships between resilient modulus and vertical loads for different confining pressures that intersect or have completely different stress sensitivity effects.


Figure 50. Sample from test section 014125, layer 1, at the approach end shows higher confining pressures result in lower resilient modulus.

Figure 50. Sample from test section 014125, layer 1, at the approach end shows higher confining pressures result in lower resilient modulus (Material code 217, clayey sand with gravel). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.4. This figure provides graphical examples of the resilient modulus tests where the higher confining pressures result in a lower resilient modulus.


Figure 51. Sample from test section 014127, layer 1, at the leave end shows higher confining pressures result in lower resilient modulus.

Figure 51. Sample from test section 014127, layer 1, at the leave end shows higher confining pressures result in lower resilient modulus (material code 308, coarse soil aggregate mixture). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 20.7, 34.5, 68.9, 103.4, and 137.9. this figure provides graphical examples of the resilient modulus tests where the higher confining pressures result in a lower resilient modulus.


Figure 52. Sample from test section 473109, layer 1, at the leave end shows higher confining pressures result in lower resilient modulus.

Figure 52. Sample from test section 473109, layer 1, at the leave end shows higher confining pressures result in lower resilient modulus (material code 114, sandy lean clay). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.4. This figure provides graphical examples of the resilient modulus tests where the higher confining pressures result in a lower resilient modulus.


Figure 53. Sample from test section 481047, layer 1, at the leave end shows higher confining pressures result in lower resilient modulus.

Figure 53. Sample from test section 481047, layer 1, at the leave end shows higher confining pressures result in lower resilient modulus (material code 107, clay with sand). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.4. This figure provides graphical examples of the resilient modulus tests where the higher confining pressures result in a lower resilient modulus.


Figure 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.

Figure 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 (material code 215, silty sand with gravel). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.4. this figure provides graphical examples of the resilient modulus tests where the resilient modulus is independent of the confining pressure at the lowest vertical load used in the test program.


Figure 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.

Figure 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 (material code 145, sandy silt). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.3. This figure provides graphical examples of the resilient modulus tests where the resilient modulus is independent of the confining pressure at the lowest vertical load used in the test program.


Figure 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.

Figure 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 (material code 145, sandy silt). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.3. this figure provides graphical examples of the resilient modulus tests where the resilient modulus is independent of the confining pressure at the lowest vertical load used in the test program.


Figure 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.

Figure 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 (material code 267, clayey gravel with sand). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 13.8, 27.6, and 41.3. This figure provides graphical examples of the resilient modulus tests where the resilient modulus is independent of the confining pressure at the lowest vertical load used in the test program.


Figure 58. Sample from test section 014073, layer 3, at the approach end shows possible data entry error.

Figure 58. Sample from test section 014073, layer 3, at the approach end shows possible data entry error (material code 308, coarse soil aggregate mixture). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 20.7, 34.5, 68.9, 103.4, and 137.9. This figure provides graphical examples of the resilient modulus tests with possible data entry errors.


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

Figure 59. Sample from test section 014084, layer 2, at the leave end shows possible data entry error (material code 308, coarse soil aggregate mixture). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 20.7, 34.5, 68.9, 103.4, and 137.9. This figure provides graphical examples of the resilient modulus tests with possible data entry errors.


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

Figure 60. Sample from test section 124106, layer 2, at the approach end shows possible data entry error (material code 309, fine grained soil). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 20.7, 34.5, 68.9, 103.4, and 137.9. This figure provides graphical examples of the resilient modulus tests with possible data entry errors.


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

Figure 61. Sample from test section 124106, layer 3, at the approach end shows possible data entry error (material code 308, soil aggregate mixture). The repeated vertical pressure, kilopascals, is graphed on the horizontal axis and the resilient modulus, megapascals, on the vertical axis for confining pressures, kilopascals, of 20.7, 34.5, 68.9, 103.4, and 137.9. this figure provides graphical examples of the resilient modulus tests with possible data entry errors.



Appendix C: SUMMARY OF THE FLAGGED RESILIENT MODULUS TESTS BY ANOMALY TYPE

Appendix C, tables 17 through 23, provides listings of all the resilient modulus tests that were flagged with the potential anomalies graphically presented in appendix B.


Table 17. Resilient modulus tests showing characteristics of exhibiting test specimen distortion or excessive softening.

State
Code
SHRP
ID
Layer
No.
Test
No.
Loc.
No.
Sample
No.
R-
Squared
SE/SYMatl
Code
No. of
Cycles
Correlations
with MR - theta
Correlations
with MR - tauoct
FlagComment
1010212B7BS070.99900.5558131150.6274-0.16701Failure
1011112B3BS030.99880.6470131150.70760.02591Failure
1407311BA*BS**0.99680.8106215150.55780.00581Failure
1415511BA*BS**0.97990.5513214150.82440.15241Lowest confining pressure curve behaves (concaves up) totally different from the other two (concave down).
6604411BA*BS**0.99900.5689145150.82650.56201Failure
6745511BA1BS010.99910.5840117150.80150.51041Failure
10010311B3BS030.99910.6256202150.7127-0.00371Failure, first point of highest and mid confinement coincide.
30812911BA*BS**0.99910.5361117150.85560.63801Failure at confining pressure of 41.4 kPa.
37021211B5BS050.99890.6214145150.78590.42441Failure
42160611BA2BS020.99510.9337117150.33270.05071Failure with interweaving pattern.
42161811BA*BS**0.97100.9836120150.21680.67991Failure with interweaving pattern. Possible seating problem at initial stages for 41.4-kPa and 27.6-kPa confining pressure.
51146411BA*BS**0.98460.9502135150.29580.54691Failure, first point on the 41.4-kPa curve lies below the other two curves. This could be due to a seating problem with the sample at 41.4 kPa.
81281212A2TS010.99840.7180108150.73140.18911Failure
* - Reference to LTPP Database Code List
** - Reference to LTPP Database Code List


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

State
Code
SHRP
ID
Layer
No.
Test
No.
Loc.
No.
Sample
No.
R-
Squared
SE/SYMatl
Code
No. of
Cycles
Correlations
with MR - theta
Correlations
with MR - tauoct
FlagComment
17100312TP*BS**0.98720.3804102150.3379-0.55642All seem to merge at end.
17932711BA*BS**0.97870.567610814-0.0863-0.69862All merged at end.
18300311BA*BS**0.98070.5508216150.74810.10582 
18552811BA*BS**0.97920.3648217150.5770-0.27472 
27408212TP*BS**0.98140.5051217140.79760.06512Highest confining pressure curve/shape is a mirror image of the other two confining pressures.
28903012A2TS030.98070.4484102150.7436-0.08352Highest confining pressure shows failure, big gap between it and the other two curves.
29540311BA*BS**0.98670.4476214150.84940.23302Failure at highest confining pressure (41.4 kPa).
29541311BA*BS**0.95060.7765145140.63100.90242Points on 27.6 kPa and 41.4 kPa seem to merge at the end.
29606711BA*BS**0.99420.2934217150.4942-0.44352 
36101112TPBS550.98280.9800265140.0196-0.14062All merged at end.
39301311A1TS020.98760.4303108150.0386-0.72832Highest and mid confining pressure merged at end.
48104711A1TS010.98550.5817107150.74130.16832Weaving of 13.8-kPa and 27.6-kPa confining pressure curves.
48105622TP1BG560.98900.4795308150.84620.44552Highest confining pressure concave down and all others concave up.
48355911BA*BS**0.99410.5077214150.7649-0.05472Big gap between highest confining pressure (concave down) and the other two (concave up).
48528411BA*BS**0.99280.5328216150.4744-0.37902First and last points of curves 13.8 kPa and 27.6 kPa coincide.
* - Reference to LTPP Database Code List
** - Reference to LTPP Database Code List


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

State
Code
SHRP
ID
Layer
No.
Test
No.
Loc.
No.
Sample
No.
R-
Squared
SE/SYMatl
Code
No. of
Cycles
Correlations
with MR - theta
Correlations
with MR - tauoct
FlagComment
1412912TP1BS550.99510.7299215150.2770-0.41283Leak in membrane suspected for highest confining pressure.
12381112A2TS030.99640.5001216150.7180-0.06323Highest confining pressure went down and up, the other two not very stress-sensitive.
28050812A9TS030.99830.5757102150.81190.130532nd point of highest confining pressure plot below mid confining pressure.
28308912A2TS030.99500.5721114150.7298-0.12153Mid confining pressure very close to lowest confining pressure; 3rd point actually went below.
45102411A1TS010.99660.3753217150.4722-0.49433There is a sudden dip in the data at 41.4-kPa confining pressure after which the curve becomes normal; also there might be some initial seating problem at a confining pressure of 41.4 kPa.
48105611A1TS020.99900.6303108150.3895-0.47173Curve 41.4 kPa dips suddenly and also has an initial seating problem.
48105622TP1BG550.98630.4299308150.82150.61613Curve 137.9 kPa suddenly dips, probably due to membrane rupture.
48106112A2TS040.99810.5205108150.4530-0.493031st two points of highest confining pressure coincide with the mid confining pressure.
48106912A2TS030.99830.6191103150.72590.09833Highest confining pressure very close to mid confining pressure; 2nd point actually went below.
48387512A2TS040.99810.5205108150.4530-0.49303Highest confining pressure has a sudden dip in the middle; probably due to defective sample (air voids ?).
* - Reference to LTPP Database Code List
** - Reference to LTPP Database Code List


Table 20. Resilient modulus tests exhibiting localized softening or disturbance of the specimen during the test or LVDT movement.

State
Code
SHRP
ID
Layer
No.
Test
No.
Loc.
No.
Sample
No.
R-
Squared
SE/SYMatl
Code
No. of
Cycles
Correlations
with MR - theta
Correlations
with MR - tauoct
FlagComment
01302811BA*BS**0.97500.8727216150.48300.83604Highest confining pressure test plot below other two tests at beginning, possible problem with seating of specimen; all show failure at end.
01407312A2TS030.96180.9473215150.33340.90814Higher confining pressure test plot below lower confining pressure test at beginning, possible problem with seating of specimen.
01408411A1TS010.99910.5145216150.7123-0.15114Lowest and highest confining pressure show failure, mid confining pressure not sensitive to stress.
01412611A1TS010.99510.5137214150.4255-0.49754Highest confining pressure test plot below mid confining pressure test at beginning, possible problem with seating of specimen.
04101512TP1BS920.99810.6582267150.75760.75864First point of highest confining pressure plot below lowest confining pressure, seating problem suspected for specimen.
04101711BA*BS**0.99450.8660267150.50150.95384Highest confining pressure test plot below other two tests at beginning, possible problem with seating of specimen.
05301112A2TS030.99720.6716133150.4038-0.42374Failure at highest confining pressure.
05304812A2TS030.99770.8997102150.45300.117041st point of highest confining pressure plot below lowest confining pressure test.
05307311BA*BS**0.99450.7465265150.2842-0.46304Highest confining pressure test went wild!
05402111A1TS010.98410.931926515-0.1699-0.34714Highest confining pressure test went wild!
05580311BA*BS**0.99640.7366217150.72010.43264Each confining test weaves in and out with the others.
05580512BA*BS**0.99580.6178282150.79470.59354Mid confining pressure behaves (concaves down) totally different from the other two (concave up).
08778312TP1BS930.98760.513921615-0.2180-0.79204Three confining pressures close to each other.
12400011A1TS010.97230.9658214150.19210.48814Leak in membrane for highest confining pressure, it almost coincides with the lowest confining pressure.
12405912BA*BS**0.99480.5249202150.86100.24604Mid confining pressure behaves differently from the other two, possible rupture of membrane in the middle of the test.
12410211A1TS020.97130.7394204150.68840.86064Beginning of highest confining pressure plot below the other two, Seating problem?
12410311BA*BS**0.87660.8768214150.48530.95434Each confining test weaves in and out with the others.
15100311BA*BS**0.99640.5461145150.83460.844241st point of highest confining pressure plot below mid confining pressure test.
16602712TP1BS930.99370.7566255150.65920.927341st point of all confining pressures are out of order, possible problem with seating of sample.
17585411BA*BS**0.98560.673210815-0.2648-0.68124All merged at end.
21604011BA*BS**0.99570.7271108150.68580.906241st half of highest confining pressure plot below mid confining pressure.
22011812B4BS040.99780.5966101150.79860.820341st point of highest confining pressure plot below mid confining pressure test.
28101611A1TS010.98870.3869214150.85820.164041st point of highest confining pressure plot below mid confining pressure, big gap between the lowest and the other two curves.
28301812A2TS030.99590.5013214150.1695-0.65904Highest confining pressure below mid confining pressure except last point.
28308111A1TS010.99310.7821216150.1502-0.48994Highest confining pressure crossing the other two curves.
28309011A1TS010.98850.6523143150.2925-0.525041st point of highest confining pressure plot below lowest confining pressure test.
28309711A1TS010.96931.000014115-0.2393-0.01134Highest confining pressure crossing the other two curves.
28309911A1TS010.99600.8400103150.4192-0.12494Highest confining pressure crossing the other two curves.
34103312TPBS550.99650.5103267150.5167-0.415241st point of highest confining pressure plot below mid confining pressure test.
35102211A1TS010.99430.4376204150.4313-0.492341st point of highest confining pressure plot below mid confining pressure test.
35211811A1TS010.99440.8583214150.49300.77394Data points at different confining pressures form a weaving pattern.
35301011A1TS010.99070.5846202150.83010.699341st point of highest confining pressure plots below mid & lowest confining pressure test.
37102412TPBS550.98740.5150214140.0140-0.70774Data points of confining pressures 13.8 kPa and 27.6 kPa form a weaving pattern.
37135212TPBS550.99271.0000141150.05700.09804Data points at different confining pressures form a weaving pattern.
37180312TPBS550.99600.5124144150.4728-0.467341st point of highest confining pressure plot below mid confining pressure test.
37199211BA*BS**0.99810.5061215150.5541-0.37624Data points of confining pressures 41.4 kPa and 27.6 kPa form a weaving pattern.
37282512TPBS550.99640.8159204150.5545-0.00934Data points of confining pressures 41.4 kPa and 27.6 kPa form a weaving pattern.
37301111BA*BS**0.99620.6789216150.6536-0.00904Data points of confining pressures 41.4 kPa and 27.6 kPa form a weaving pattern.
37503711BA*BS**0.98650.6047215150.2836-0.546541st point of highest confining pressure plot below mid confining pressure test.
40011612B2BS020.99870.5134113150.85430.670441st point of highest confining pressure plot below mid confining pressure test.
40408712BA*BS**0.93190.9479108150.32590.92724Weaving pattern seen.
40416111A1TS010.98140.9226214150.41720.82174Weaving pattern seen.
40416112A2TS030.98330.8917214150.49120.16784Weaving pattern seen and soil seems to be stress-insensitive.
40416611BA*BS**0.99170.8673114150.50240.80404Data at confining pressure of 41.4 kPa weaves through the data at the other two confining pressures.
40502112A2TS010.98480.943326515-0.3253-0.33164Data at confining pressure of 41.4 kPa weaves through the data at the other two confining pressures.
40601012BA*BS**0.99710.5426217150.7421-0.03174Data points at confining pressure of 41.4 kPa weave through the data points at a confining pressure of 27.6 kPa.
40702412A2TS030.98970.7258214150.1761-0.54844First point of highest confining pressure plot below lowest confining pressure, seating problem suspected for specimen.
42159712TPBS550.97970.8934111150.45100.87844Curves 41.4 kPa and 27.6 kPa lower than the curve at 13.8 kPa during initial stages of the test. Could be a seating problem or leak in pressure during the initial stages of the test.
42159812BA6BS060.91620.9553217150.30770.92224Curves 41.4 kPa and 27.6 kPa lower than the curve at 13.8 kPa during initial stages of the test. Could be a seating problem or leak in pressure during the initial stages of the test.
42160512TPBS550.98890.438826714-0.1774-0.80894First point on the 41.4-kPa curve which is slightly below the first point on the 27.6 kPa curve. Initial seating problem for 41.4 kPa?
42169011BA*BS**0.99440.6388146150.80850.34734Weaving pattern, with seating problem for a pressure of 27.6 kPa. Also the soil seems to stress-insensitive.
42703712BA*BS**0.99770.5600267150.5678-0.33264Weaving pattern, with seating problem for a pressure of 41.1. Also, the soil seems stress-insensitive.
42902712BA*BS**0.99800.6105267150.5527-0.32644Weaving pattern, with seating problem for a pressure of 27.6 kPa. Also, the soil seems stress-insensitive.
45100812A2TS030.98290.8335214150.58160.63834Weaving pattern, with seating problem for a pressure of 41.4 kPa. Also, the soil seems stress-insensitive during the latter part of the test.
45101121BA*BG**0.98620.3155308150.95210.89934Weaving pattern. The first point at every pressure is below the curve at an immediately lower pressure. Probably seating problems at the initial stages of the test.
47102912TP1BS550.99530.6113217150.3157-0.54094Seating problem with 41.4 kPa.
47200812A2TS030.99240.7033131150.1024-0.61794Seating problem with 41.4 kPa.
47310111A1TS010.98030.9283109150.37800.58984Weaving pattern with the 41.4-kPa curve lower than that of 27.6 kPa. Probable initial seating problems and also a leak in pressure at 41.4 kPa.
47602211A1TS010.99590.4761114150.4705-0.45574Curves at pressure 41.4 kPa and 27.6 kPa weave through each other. Leak in pressure at level 41.4 kPa?
48080113A5TS090.99830.6001145150.7146-0.05444Failure with seating problem at 41.4 kPa?
48104621BA*BG**0.98320.3962309130.93360.82574Seating problem with 34.5 and 68.9 kPa?
48106911BA*BS**0.99930.7093103150.72230.374841st point of highest and lowest confining pressure coincide.
48109211BA*BS**0.99091.000014315-0.17100.14234All three curves cross each other.
48109412TP1BS550.99290.5702217150.81590.71394Mid confining pressure crosses the other two curves.
48111112A2TS030.98370.9019216150.44190.87324All three curves cross each other.
48111111A1TS010.99100.9958216150.0569-0.07434Highest confining pressure crosses the other two curves.
48111312A2TS030.95130.9895114150.17900.78524All three curves cross each other.
48111611A1TS010.99570.9128114150.40040.29414All three curves cross each other.
48113012A2TS030.97980.9423109150.33520.91554Highest confining pressure below mid confining pressure and crosses the lowest confining pressure curve.
48118112BA*BS**0.98290.7838114150.60340.75674Mid confining pressure crosses the other two curves.
48118312A2TS030.99400.8556114150.3563-0.18814Highest confining pressure below mid confining pressure and crosses the lowest confining pressure curve.
48300311A1TS010.99590.9410103150.40180.51684All three curves cross each other.
48301012BA*BS**0.99880.783410215-0.0756-0.55814All three curves are very close and cross each other.
48357911A1TS010.99850.5796114150.76670.20494Highest confining pressure crosses mid confining pressure.
48358912A2TS030.99270.7455214150.68810.60334Highest confining pressure crosses the other two curves.
48360911A1TS010.99810.5103101150.1417-0.64044Highest confining pressure crosses the other two curves.
48360912A2TS030.97970.8954101150.43500.88874All three curves are very close and cross each other.
48368912A2TS030.97660.8534113150.56660.72544Lowest confining pressure crosses the other two curves and data entry error for mid confining pressure.
48372911A1TS010.99410.6437102150.6323-0.18694Highest confining pressure (concave down) crossed the other two (concave up).
48374911A1TS020.99730.8904216150.49790.52384All three curves cross each other.
48374912A2TS030.98901.000021615-0.00340.13664Highest confining pressure (concave down) crossed the other two (concave up).
48376911BA*BS**0.99750.6711215150.6232-0.18804Highest confining pressure (concave down) crossed the other two (concave up).
48377911A1TS010.99310.588510915-0.1265-0.75174Lowest confining pressure crosses mid confining pressure.
48414211A1TS010.99430.7639216150.65600.51294First point of highest confining pressure plot below lowest confining pressure, seating problem suspected for specimen.
48502611A1TS010.99591.000010315-0.10730.39154All three curves cross each other.
48515411A1TS020.98001.000021615-0.30150.20444Leak in pressure for the highest confining pressure, hence it crosses the other two curves.
48527811BA*BS**0.99630.6317217150.6168-0.00054Leak in pressure for 41.4-kPa sample, hence it falls below the 27.6-kPa curve. Could be due to rupture in membrane.
48531012BA*BS**0.98880.6436214150.76880.80894First point of 27.6 kPa falls below that of 13.8 kPa. This could be due to a seating problem for the sample at 27.6 kPa.
48532312A2TS030.96880.9522108150.31800.83224Curves 27.6 kPa and 41.4 kPa fall below curve 13.8 kPa for the first half of the test and during the second half, curve 41.4 kPa is below curve 27.6 kPa. This could be due to seating problems or leak in pressure.
48533412A2TS030.99400.5232114150.2214-0.60714First point of 27.6 kPa falls below that of 13.8 kPa. This could be due to a seating problem for the sample at 27.6 kPa. Also, the last points on the 13.8-kPa and 27.6-kPa curves coincide.
48533512BA*BS**0.97330.9192108150.38900.73254Curves 27.6 kPa and 41.4 kPa fall below curve 13.8 kPa for the first half of the test and during the second half, curve 41.4 kPa is below curve 27.6 kPa. This could be due to seating problems or leak in pressure.
48533612A2TS030.97080.9971108150.13340.48124All three curves cross each other. The material is also stress-insensitive.
48617911A1TS010.99130.7866216150.3214-0.31234Curve 27.6 kPa falls below curve 13.8 kPa during the latter part of the test. This could be due to membrane rupture or leak in pressure.
48900512A2TS020.99680.8181118150.62010.69094Seating problems with samples at 27.6 kPa and 41.4 kPa.
49100812TP1BS920.98920.9980114150.11210.08014Curves 27.6 kPa and 13.8 kPa seem to be almost the same. All the curves cross each other.
51500912BA*BS**0.99810.5779267150.81430.72934Highest confining pressure crosses mid confining pressure.
54164012TPBS550.98270.472326715-0.2536-0.80974First point on curve 41.4 kPa lies below the other two curves. This is probably due to a seating problem. The last points on the middle and high confining pressures coincide with each other.
54400311BA*BS**0.99680.5450265150.5032-0.42474First point on the highest confinement curve is below that on the mid confining pressure curve. Due to a seating problem? Soil is stress insensitive.
54700812BA*BS**0.99660.6189108150.5514-0.31454First point on the highest confinement curve is below that on the mid confining pressure curve. Due to a seating problem? Soil is stress insensitive.
54700811BA*BS**0.99680.5393108150.5152-0.41784First point on the highest confinement curve is below that on the mid confining pressure curve. Due to a seating problem Soil is stress insensitive.
72412211BA*BS**0.99640.5956267150.70280.07974The 41.4-kPa curve falls below the 27.6-kPa curve during the second half of the test. Could be due to membrane rupture.
87162011BA*BS**0.99750.5387102150.0715-0.71344First point on the highest confinement curve is below that on the mid & low confining pressure curves. Due to a seating problem?
87281111BA*BS**0.99170.716413115-0.4051-0.70924First point on the highest confinement curve is below that on the mid & low confining pressure curves. Due to a seating problem?
* - Reference to LTPP Database Code List
** - Reference to LTPP Database Code List


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

State
Code
SHRP
ID
Layer
No.
Test
No.
Loc.
No.
Sample
No.
R-
Squared
SE/SYMatl
Code
No. of
Cycles
Correlations
with MR - theta
Correlations
with MR - tauoct
FlagComment
1412511BA*BS**0.99440.8035217150.51650.01415Leak in membrane suspected for highest confining pressure, not sensitive to stress for the other two.
1412722BA*BG**0.98450.3184308150.95790.91185Leak in membrane suspected for 34.5-kPa and 68.9-kPa confining pressure.
12399531BA*BG**0.98000.3448308150.95510.8834520.7-kPa confining pressure above 34.5-kPa confining pressure and behaves differently from all confining pressures.
28101612A2TS030.98870.5853214150.4356-0.40205Highest confining pressure below mid confining pressure.
28402411BA*BS**0.99040.8564108150.53510.73705Highest confining pressure below mid confining pressure, 2nd point of all three curves coincide.
40301812A2TS030.99280.549010215-0.5167-0.79625Out of order and some weaving seen.
47310812TP1BS550.98990.413611415-0.6332-0.88915Curve at pressure of 41.4 kPa is lower than the curve at 13.8 kPa.
47310912TP1BS550.98800.636211415-0.6952-0.77305Curve at pressure of 41.4 kPa is lower than the curve at 13.8 kPa. Also the last points of all curves merge at one single point.
48080232B4BG010.99241.000030215-0.41630.04455Curve at pressure 41.4 kPa is lower than the curves at 13.8 kPa and 27.6 kPa. The soil is stress-insensitive.
48104712A2TS030.99750.600810715-0.1202-0.74635Curve 41.4 kPa below curve 26.7 kPa
48900511A1TS010.99390.921811815-0.6583-0.36405Curve 41.4 kPa is below the curves at 13.8 kPa and 27.6 kPa. Also, the curves at 13.8 kPa and 27.6 kPa cross each other, which may be due to seating problems with the sample at 27.6 kPa.
* - Reference to LTPP Database Code List
** - Reference to LTPP Database Code List


Table 22. Resilient modulus tests showing resilient modulus is independent of confining pressure at the lowest vertical stress.

State
Code
SHRP
ID
Layer
No.
Test
No.
Loc.
No.
Sample
No.
R-
Squared
SE/SYMatl
Code
No. of
Cycles
Correlations
with MR - theta
Correlations
with MR - tauoct
FlagComment
6125311BA*BS**0.99720.6037267150.82090.742361st points of all confining pressures are about the same.
9500111BA2BS020.97670.5652215150.83530.706861st points of all confining pressures are about the same.
12381111BA*BS**0.99370.6869216150.72990.722561st points of all confining pressures are about the same.
22011311B6BS060.99660.6632101150.74090.862261st points of highest confining pressure plot coincide with mid confining pressure test.
22011712B5BS050.99910.5231101150.85660.566261st points of highest confining pressure plot coincide with mid confining pressure test.
22012411B3BS030.99880.6005101150.79280.823661st points of highest confining pressure plot coincide with mid confining pressure test.
35010112B1BS010.99580.7379114150.66990.888361st points of highest confining pressure plot below mid & lowest confining pressure test.
35010512B3BS030.99650.7091103150.70000.883761st points of highest confining pressure plot below mid confining pressure test (the first points at all confining pressures. Start at almost the same point).
40011712B3BS030.99640.6047113150.79270.849961st points of highest and mid confining pressure test coincide.
40012012B5BS050.99710.5888113150.80660.770461st points of highest and mid confining pressure test coincide.
40012312B6BS060.99260.7377113150.67920.91406The first points at all confining pressure start at almost the same point.
48080111B2BS020.99850.5336145150.84790.72356First and the last points of confining pressures 27.6 kPa and 41.3 kPa coincide.
48080211B1BS010.99510.7011145150.71760.87376Initial point is the same for all three curves.
48213311A1TS010.99840.5330103150.7112-0.123761st points of highest and mid confining pressure coincide.
49100612TP1BS920.99780.5413267150.83440.61606Initial points on curves 13.8 kPa and 27.6 kPa coincide. Also, the second point on the 41.4-kPa curve looks like a data entry error.
56603111BA*BS**0.99670.6675267150.75330.84946First point on all three curves coincide.
56603111BA*BS**0.99670.6675267150.75330.84946First point on all three curves coincide.
56603112TP1BS910.99840.5475267150.83970.74156First points on the mid and high confining pressures coincide.
56777212TP1BS910.99910.5443267150.6069-0.27316First points on the mid and high confining pressures coincide. First point on the low curve does not exactly coincide with the other two, but is very close.
72412212BA*BS**0.98720.7199267150.69640.81966First point on all three curves coincide.
81180511BA*BS**0.99930.4547137150.4926-0.45176First points on the mid and high confining pressures coincide. Failure?
* - Reference to LTPP Database Code List
** - Reference to LTPP Database Code List


Table 23. Resilient modulus tests with potential data entry error.

State
Code
SHRP
ID
Layer
No.
Test
No.
Loc.
No.
Sample
No.
R-
Squared
SE/SYMatl
Code
No. of
Cycles
Correlations
with MR - theta
Correlations
with MR - tauoct
FlagComment
1407331BA*BG**0.71860.9743308150.20390.88297Both Mr and stress at zero for highest confining pressure, data entry error?! But it's at Level E!!??
1408422BA*BG**0.91210.7272308150.73950.82407Leak in membrane suspected for 34.5-kPa and 68.9-kPa confining pressure, zero data point for 103.4-kPa confining pressure.
12399731BA*BG**0.93130.6430308150.78560.75037Zero data point for 103.4-kPa confining pressure.
12410631BA*BG**0.90700.7260308150.69180.77117Zero data point for 137.9-kPa confining pressure.
12410621BA*BG**0.93100.5385309150.84890.91267Zero data point for 103.4-kPa confining pressure.
28309032BA*BG**0.90750.6885308150.73190.82657Zero point for highest confining pressure.
47310421BA*BG**0.90520.6603303150.75070.82147Zero point for a pressure of 137.9 kPa.
48386511BA*BS**0.96950.6396114150.72380.58627Zero point for lowest confining pressure.
48916732BA4BG040.90320.6839308150.73960.90237Initial zero point for curve 137.9 kPa.
* - Reference to LTPP Database Code List
** - Reference to LTPP Database Code List



Appendix D: PARAMETERS AND THEIR VALUES INCLUDED IN THE NONLINEAR REGRESSION RELATING RESILIENT MODULUS TO PHYSICAL PROPERTIES

Appendix D, tables 24 through 39, provides a summary of the minimum, maximum, mean, and median values for each parameter included in the nonlinear optimization regression study to determine the relationship and effect between resilient modulus and physical properties. Tables 24 through 31 include the data sets for the base and subbase materials, while tables 31 through 36 include the data sets for the subgrade soils. The following defines the parameters used in these tables.

P3/8 - Percent passing the 3/8-in [9.5-mm] sieve.
PNo. 4 - Percent passing the No. 4 sieve.
PNo. 40 - Percent passing the No. 40 sieve.
PNo. 200 - Percent passing the No. 200 sieve.
LL - Liquid limit.
PI - Plasticity index.
Wopt - Optimum water content of material.
deltad,opt - Maximum dry unit weight of material.
Ws - Water content of test specimen.
deltas - Dry unit weight of test specimen.
%Silt - Percent by weight of silt in the material.
%Clay - Percent by weight of clay in the material.


Table 24. Summary of the LTPP data used in the nonlinear regression study of resilient modulus for all granular base and subbase material data set.

LTPP BASE MATL. CODE: All Granular Base & Subbase Materials
No. of Resilient Modulus Tests: 423

ParametersMinMaxMedianMean
P3/8"39.0100.079.078.9
PNo. 421.0100.065.067.6
PNo. 408.098.038.042.4
PNo. 2001.796.114.117.5
LL0.060.00.07.5
PI0.037.00.01.9
wopt%4.019.08.08.2
gammad, opt (kg/m3)1666.12467.12114.62097.0
ws%3.120.57.68.0
gammas (kg/m3)1557.02391.62000.01978.8
gammas/gammad,opt0.801.060.950.94
ws/wopt0.361.460.980.98
(gammad,opt)2/PNo. 4030172.0665211.9117421.0140388.9


Table 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.

LTPP BASE MATL. CODE: 302 - Uncrushed Gravel
No. of Resilient Modulus Tests: 31

ParametersMinMaxMedianMean
P3/8"60.090.076.076.6
PNo. 432.081.059.061.2
PNo. 409.045.025.025.6
PNo. 2003.518.16.98.5
LL0.023.00.03.0
PI0.08.00.00.7
wopt%5.010.06.06.7
gammad, opt (kg/m3)2018.52371.02194.72190.1
ws%3.713.86.06.4
gammas (kg/m3)1882.12215.52057.02049.9
gammas/gammad,opt0.891.000.940.94
ws/wopt0.621.380.980.95
(gammad,opt)2/PNo. 4093439.9535209.3193843.1215727.5


Table 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.

LTPP BASE MATL. CODE: 303 - Crushed Stone
No. of Resilient Modulus Tests: 57

ParametersMinMaxMedianMean
P3/8"39.090.064.063.5
PNo. 421.077.049.046.9
PNo. 408.047.025.025.6
PNo. 2003.032.412.213.4
LL0.027.00.06.1
PI0.08.00.01.3
wopt%4.011.06.06.4
gammad, opt (kg/m3)1874.32354.92242.82218.6
ws%3.112.96.36.6
gammas(kg/m3)1723.62236.22095.22082.3
gammas/gammad,opt0.801.000.940.94
ws/wopt0.521.421.001.03
(gammad,opt)2/PNo. 4074747.9665211.9198342.0220732.2


Table 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.

LTPP BASE MATL. CODE: 304 - Crushed Gravel
No. of Resilient Modulus Tests: 27

ParametersMinMaxMedianMean
P3/8"49.098.069.069.5
PNo. 430.091.053.053.7
PNo. 408.069.028.028.2
PNo. 2003.559.912.316.3
LL0.033.00.09.7
PI0.016.00.02.1
wopt%5.011.06.07.2
gammad, opt (kg/m3)1986.52419.02194.72195.3
ws%4.311.35.96.9
gammas (kg/m3)1875.82285.82061.62072.8
gammas/gammad,opt0.920.960.940.94
ws/wopt0.691.300.950.96
(gammad,opt)2/PNo. 4057189.9584658.9172031.6210196.2


Table 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.

LTPP BASE MATL. CODE: 306 - Sand
No. of Resilient Modulus Tests: 35

ParametersMinMaxMedianMean
P3/8"80.0100.098.094.6
PNo. 469.0100.095.091.1
PNo. 4028.097.059.060.9
PNo. 2001.732.39.410.5
LL0.026.00.02.0
PI0.04.00.00.1
wopt%5.016.010.09.5
gammad, opt (kg/m3)1666.12226.81906.41943.0
ws%5.014.79.18.9
gammas (kg/m3)1574.62108.91797.31831.5
gammas/gammad,opt0.900.970.950.94
ws/wopt0.551.210.960.95
(gammad,opt)2/PNo. 4030172.0151323.764972.078238.9


Table 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.

LTPP BASE MATL. CODE: 307 - Fine-Grained Soil-Aggregate Mixture
No. of Resilient Modulus Tests: 26

ParametersMinMaxMedianMean
P3/8"59.0100.092.089.0
PNo. 447.099.085.583.0
PNo. 4032.080.050.551.4
PNo. 2007.264.832.529.3
LL0.060.00.012.8
PI0.037.00.04.5
wopt%4.017.08.08.5
gammad, opt (kg/m3)1794.22226.82082.62065.3
ws%3.716.67.78.1
gammas (kg/m3)1726.42096.81968.71962.3
gammas/gammad,opt0.920.970.960.95
ws/wopt0.871.100.940.95
(gammad,opt)2/PNo. 4043914.4139740.784267.387798.8


Table 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.

LTPP BASE MATL. CODE: 308 - Coarse-Grained Soil-Aggregate Mixture
No. of Resilient Modulus Tests: 155

ParametersMinMaxMedianMean
P3/8"45.0100.075.075.3
PNo. 434.099.061.062.1
PNo. 4013.090.036.037.3
PNo. 2001.937.015.917.4
LL0.044.00.010.4
PI0.018.00.02.7
wopt%4.019.08.08.5
gammad, opt (kg/m3)1682.12451.12114.62099.8
ws%3.520.57.98.5
gammas (kg/m3)1557.02332.02005.51985.3
gammas/gammad,opt0.851.060.950.95
ws/wopt0.361.460.991.01
(gammad,opt)2/PNo. 4037058.9412457.8117658.0141567.2


Table 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.

LTPP BASE MATL. CODE: 309 - Fine-Grained Soil
No. of Resilient Modulus Tests: 72

ParametersMinMaxMedianMean
P3/8"58.0100.094.592.3
PNo. 436.0100.089.587.4
PNo. 4020.098.066.067.2
PNo. 2004.196.118.023.9
LL0.030.00.05.4
PI0.012.00.01.6
wopt%5.013.09.09.0
gammad, opt (kg/m3)1746.22467.11986.52001.8
ws%4.714.28.38.5
gammas (kg/m3)1608.32391.61871.01889.8
gammas/gammad,opt0.861.010.940.94
ws/wopt0.451.290.960.95
(gammad,opt)2/PNo. 4033188.6304324.258296.369574.2


Table 32. Summary of the LTPP data used in the nonlinear regression study of resilient modulus for all subgrade soils data set.

LTPP BASE MATL. CODE: All Subgrade Soils
No. of Resilient Modulus Tests: 404

ParametersMinMaxMedianMean
P3/8"53.0100.096.092.3
PNo. 430.0100.092.087.4
PNo. 4018.099.071.069.3
PNo. 2001.099.035.040.2
% Silt0.092.723.226.6
% Clay0.075.510.313.5
LL0.073.022.019.7
PI0.046.05.07.9
wopt%6.095.012.013.2
gammad, opt (kg/m3)352.42226.81890.41865.5
ws%3.033.211.612.7
gammas (kg/m3)1215.82160.01804.51790.3
gammas/gammad,opt0.8164.2310.9570.966
ws/wopt0.2391.3570.9730.964
(gammad,opt)2/PNo. 401380.2275475.049524.358883.4


Table 33. Summary of the LTPP data used in the nonlinear regression study of resilient modulus for the gravel subgrade soils data set.

LTPP BASE MATL. CODE: Gravel
No. of Resilient Modulus Tests: 64

ParametersMinMaxMedianMean
P3/8"53.099.079.078.7
PNo. 430.099.065.066.5
PNo. 4018.097.047.048.3
PNo. 2009.561.129.431.8
% Silt4.155.520.922.2
% Clay0.732.88.79.8
LL0.050.026.023.7
PI0.027.07.08.2
wopt%7.026.011.012.6
gammad, opt (kg/m3)1457.82226.81978.51921.9
ws%6.825.511.412.3
gammas (kg/m3)1377.62160.01869.61838.3
gammas/gammad,opt0.8641.0300.9580.957
ws/wopt0.7461.2440.9710.977
(gammad,opt)2/PNo. 4036839.8275475.076995.789477.2


Table 34. Summary of the LTPP data used in the nonlinear regression study of resilient modulus for the sand subgrade soils data set.

LTPP BASE MATL. CODE: Sand
No. of Resilient Modulus Tests: 209

ParametersMinMaxMedianMean
P3/8"65.0100.096.093.7
PNo. 445.0100.092.089.4
PNo. 4026.099.065.066.0
PNo. 2001.074.024.325.4
% Silt0.055.015.917.1
% Clay0.028.07.18.3
LL0.065.00.010.7
PI0.026.00.03.4
wopt%6.033.011.011.3
gammad, opt (kg/m3)1361.72194.71922.41913.3
ws%3.033.210.410.6
gammas (kg/m3)1249.42141.41839.51831.9
gammas/gammad,opt0.8651.0560.9570.957
ws/wopt0.2501.1670.9600.938
(gammad,opt)2/PNo. 4022074.1151773.257600.062402.6


Table 35. Summary of the LTPP data used in the nonlinear regression study of resilient modulus for the silt subgrade soils data set.

LTPP BASE MATL. CODE: Silt
No. of Resilient Modulus Tests: 31

ParametersMinMaxMedianMean
P3/8"85.0100.097.094.6
PNo. 464.0100.094.090.8
PNo. 4050.099.082.081.5
PNo. 20034.799.061.265.6
% Silt28.092.748.955.6
% Clay2.819.08.89.8
LL0.052.018.015.3
PI0.015.00.02.6
wopt%7.032.013.014.1
gammad, opt (kg/m3)1409.82210.81842.31845.2
ws%6.633.112.314.0
gammas (kg/m3)1366.52098.31778.11775.0
gammas/gammad,opt0.9261.0480.9530.962
ws/wopt0.7711.1820.9850.983
(gammad,opt)2/PNo. 4022165.470263.040329.243567.6


Table 36. Summary of the LTPP data used in the nonlinear regression study of resilient modulus for the clay subgrade soils data set.

LTPP BASE MATL. CODE: Clay
No. of Resilient Modulus Tests: 100

ParametersMinMaxMedianMean
P3/8"74.0100.099.097.5
PNo. 454.0100.098.095.3
PNo. 4038.099.088.085.9
PNo. 2007.098.466.668.5
% Silt3.371.239.440.1
% Clay3.175.526.028.0
LL0.073.035.037.1
PI0.046.015.518.7
wopt%8.095.016.017.5
gammad, opt (kg/m3)352.42114.61730.21735.7
ws%7.928.716.816.9
gammas (kg/m3)1215.82027.91666.71677.3
gammas/gammad,opt0.8164.2310.9570.993
ws/wopt0.2391.3571.0001.003
(gammad,opt)2/PNo. 401380.263686.035848.636696.0



Appendix E. RESULTS FROM NONLINEAR OPTIMIZATION REGRESSION STUDY RELATING RESILIENT MODULUS TO PHYSICAL PROPERTIES

Appendix E provides a summary from the nonlinear regression study that was used to identify the relationship or effect of physical properties of the materials on the resilient modulus by material type. Tables 37 through 49 identify the physical properties considered to be important and list the coefficients for each parameter, along with resulting statistics from the regression study for each base material and soil type.

Figures 62 through 74 provide a graphical comparison of the residuals (MR[Predicted]-MR[Observed]) by base material and soil type. As shown by the models, there is a modulus-dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.


Table 37. Results from the nonlinear optimization regression study for all base and subbase material types combined.

Material: All Base and Subbase Materials Combined

Model Type Coefficient theta Exponent tauoct Exponent
Model Parameters Intercept 12.8140 -8.9652 -2.7735
Model Parameters P3/8" 0.0083 -- --
Model Parameters PNo. 4 -0.0139 0.0023 0.0007
Model Parameters PNo. 40 -- -- --
Model Parameters PNo. 200 0.0036 -0.0019 -0.0054
Model Parameters % Silt -- -- --
Model Parameters % Clay -- -- --
Model Parameters LL -0.0055 0.0041 0.0007
Model Parameters PI 0.0206 -0.0168 --
Model Parameters wopt% -- -- --
Model Parameters gammad, opt (kg/m3) -0.0056 0.0042 0.0010
Model Parameters ws% -0.0431 -- --
Model Parameters gammas (kg/m3) 0.0054 -0.0045 -0.0005
Model Parameters gammas/gammad,opt -10.9427 9.7625 1.7644
Model Parameters ws/wopt 0.1150 0.1251 -0.0969
Model Parameters (gammad,opt)2/PNo. 40 -8.14E-07 4.29E-07 --
Statistics MSE   1871.79  
Statistics se   43.264  
Statistics sy   75.312  
Statistics se/sy   0.5745  
Statistics R2   --  
Statistics No. of Points   6329  


Table 38. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 302 - uncrushed gravel.

Material: LTPP Base and Subbase Material Code 302:Uncrushed Gravel

Model Type Coefficient theta Exponent tauoct Exponent
Model Parameters Intercept -1.8961 0.4960 -0.5979
Model Parameters P3/8" -- -- --
Model Parameters PNo. 4 -- -- --
Model Parameters PNo. 40 -- -- --
Model Parameters PNo. 200 -- -0.0074 --
Model Parameters % Silt -- -- --
Model Parameters % Clay -- -- --
Model Parameters LL -- -- --
Model Parameters PI -- -- --
Model Parameters wopt% -- -- 0.0349
Model Parameters gammad, opt (kg/m3) -- -- 0.0004
Model Parameters ws% -- -- --
Model Parameters gammas (kg/m3) 0.0014 -0.0007 --
Model Parameters gammas/gammad,opt -- 1.6972 --
Model Parameters ws/wopt -0.1184 0.1199 -0.5166
Model Parameters (gammad,opt)2/PNo. 40 -- -- --
Statistics MSE   475.85  
Statistics se   21.814  
Statistics sy   63.045  
Statistics se/sy   0.346  
Statistics R2   --  
Statistics No. of Points   461  


Table 39. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 303 - crushed stone.

Material: LTPP Base and Subbase Material Code 303:Crushed Stone

Model Type Coefficient theta Exponent tauoct Exponent
Model Parameters Intercept 0.7632 2.2159 -1.1720
Model Parameters P3/8" 0.0084 -0.0016 --
Model Parameters PNo. 4 -- -- --
Model Parameters PNo. 40 -- -- --
Model Parameters PNo. 200 -- -- --
Model Parameters % Silt -- -- --
Model Parameters % Clay -- -- --
Model Parameters LL 0.0088 0.0008 -0.0082
Model Parameters PI -- -- --
Model Parameters wopt% -0.0371 -0.0380 -0.0014
Model Parameters gammad, opt (kg/m3) -0.0001 -0.0006 0.0005
Model Parameters ws% -- -- --
Model Parameters gammas (kg/m3) -- -- --
Model Parameters gammas/gammad,opt -- -- --
Model Parameters ws/wopt -- -- --
Model Parameters (gammad,opt)2/PNo. 40 -- 2.4E-07 --
Statistics MSE   1699.64  
Statistics se   41.227  
Statistics sy   87.416  
Statistics se/sy   0.4716  
Statistics R2   --  
Statistics No. of Points   853  


Table 40. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 304 - crushed gravel.

Material: LTPP Base and Subbase Material Code 304:Crushed Gravel

Model Type Coefficient theta Exponent tauoct Exponent
Model Parameters Intercept -0.8292 4.9555 -3.5141
Model Parameters P3/8" -0.0065 -- --
Model Parameters PNo. 4 -- -- --
Model Parameters PNo. 40 -- -- --
Model Parameters PNo. 200 -- -- --
Model Parameters % Silt -- -- --
Model Parameters % Clay -- -- --
Model Parameters LL 0.0114 -0.0057 --
Model Parameters PI 0.0004 -0.0075 --
Model Parameters wopt% -0.0187 -- --
Model Parameters gammad, opt (kg/m3) -- -- --
Model Parameters ws% 0.0036 -0.0470 --
Model Parameters gammas (kg/m3) 0.0013 -0.0022 0.0016
Model Parameters gammas/gammad,opt -- -- --
Model Parameters ws/wopt -- -- --
Model Parameters (gammad,opt)2/PNo. 40 -2.6E-06 2.8E-06 --
Statistics MSE   854.398  
Statistics se   29.230  
Statistics sy   66.743  
Statistics se/sy   0.4380  
Statistics R2   --  
Statistics No. of Points   404  


Table 41. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 306 - sand.

Material: LTPP Base and Subbase Material Code 306:Sand

Model Type Coefficient theta Exponent tauoct Exponent
Model Parameters Intercept -0.2786 1.1148 -0.4508
Model Parameters P3/8" 0.0097 -0.0053 0.0029
Model Parameters PNo. 4 -- -- --
Model Parameters PNo. 40 -- -- --
Model Parameters PNo. 200 -- -- --
Model Parameters % Silt -- -- --
Model Parameters % Clay -- -- --
Model Parameters LL 0.0219 -0.0095 -0.0185
Model Parameters PI -0.0737 0.0325 0.0798
Model Parameters wopt% -- -- --
Model Parameters gammad, opt (kg/m3) -- -- --
Model Parameters ws% -0.0431 -- --
Model Parameters gammas (kg/m3) -- -- --
Model Parameters gammas/gammad,opt -- -- --
Model Parameters ws/wopt -- -- --
Model Parameters (gammad,opt)2/PNo. 40 1.8E-07 7.2E-07 --
Statistics MSE   512.674  
Statistics se   22.642  
Statistics sy   51.605  
Statistics se/sy   0.4388  
Statistics R2   --  
Statistics No. of Points   519  


Table 42. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 307 - fine-grained soil-aggregate mixture.

Material: LTPP Base and Subbase Material Code 307:Fine-Grained Soil-Aggregate Mix
Recalibrated Coefficient with Mr Equation

Model Type Coefficient theta Exponent tauoct Exponent
Model Parameters Intercept -0.7668 0.4951 0.9303
Model Parameters P3/8" -- -- 0.0293
Model Parameters PNo. 4 0.0051 -0.0141 --
Model Parameters PNo. 40 -- -- --
Model Parameters PNo. 200 0.0128 -0.0061 --
Model Parameters % Silt -- -- --
Model Parameters % Clay -- -- --
Model Parameters LL 0.0030 -- 0.0036
Model Parameters PI -- -- --
Model Parameters wopt% -0.0510 -- --
Model Parameters gammad, opt (kg/m3) -- -- --
Model Parameters ws% -- -- --
Model Parameters gammas (kg/m3) -- -- --
Model Parameters gammas/gammad,opt 1.1729 1.3941 -3.8903
Model Parameters ws/wopt -- -- --
Model Parameters (gammad,opt)2/PNo. 40 -- -- --
Statistics MSE   588.20  
Statistics se   24.253  
Statistics sy   49.371  
Statistics se/sy   0.4912  
Statistics R2   --  
Statistics No. of Points   390  


Table 43. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 308 - coarse-grained soil-aggregate mixture.

Material: Base and Subbase Material 308:Coarse-Grained Soil-Aggregate Mixture

Model Type Coefficient theta Exponent tauoct Exponent
Model Parameters Intercept -0.5856 0.7833 -0.1906
Model Parameters P3/8" 0.0130 -- --
Model Parameters PNo. 4 -0.0174 -- --
Model Parameters PNo. 40 -- -- --
Model Parameters PNo. 200 0.0027 -0.0060 -0.0026
Model Parameters % Silt -- -- --
Model Parameters % Clay -- -- --
Model Parameters LL -- -- --
Model Parameters PI 0.0149 -0.0081 --
Model Parameters wopt% -- -- --
Model Parameters gammad, opt (kg/m3) 1.6E-06 0.0001 --
Model Parameters ws% -0.0426 -- --
Model Parameters gammas (kg/m3) -- -- --
Model Parameters gammas/gammad,opt 1.6456 -- --
Model Parameters ws/wopt 0.3932 -0.1483 --
Model Parameters (gammad,opt)2/PNo. 40 -8.2E-07 -2.7E-07 8.1E-07
Statistics MSE   1883.89  
Statistics se   43.404  
Statistics sy   80.186  
Statistics se/sy   0.5413  
Statistics R2   --  
Statistics No. of Points   2323  


Table 44. Results from the nonlinear optimization regression study for the LTPP base and subbase material code data set 309 - fine-grained soil.

Material: LTPP Base and Subbase Material Code 309:Fine-Grained Soil

Model Type Coefficient theta Exponent tauoct Exponent
Model Parameters Intercept 0.8409 0.6668 -0.1667
Model Parameters P3/8" -- -- --
Model Parameters PNo. 4 -- -- --
Model Parameters PNo. 40 0.0004 -0.0007 --
Model Parameters PNo. 200 -- -- --
Model Parameters % Silt -- -- --
Model Parameters % Clay -- -- --
Model Parameters LL -- -- --
Model Parameters PI 0.0161 -0.0139 -0.0207
Model Parameters wopt% -- -- --
Model Parameters gammad, opt (kg/m3) -- -- --
Model Parameters ws% -- -- --
Model Parameters gammas (kg/m3) -- -- --
Model Parameters gammas/gammad,opt -- -- --
Model Parameters ws/wopt -- -- --
Model Parameters (gammad,opt)2/PNo. 40 -- -- --
Statistics MSE   1167.03  
Statistics se   34.162  
Statistics sy   62.8  
Statistics se/sy   0.5440  
Statistics R2   --  
Statistics No. of Points   1079  


Table 45. Results from the nonlinear optimization regression study for the combined subgrade soil data set.

Material: All Subgrade Soils Combined

Model Type Coefficient theta Exponent tauoct Exponent
Model Parameters Intercept 0.9848 0.4808 9.6691
Model Parameters P3/8" -0.0050 -0.0037 -0.0302
Model Parameters PNo. 4 -- 0.0062 0.0065
Model Parameters PNo. 40 0.0011 -0.0016 0.0192
Model Parameters PNo. 200 -- -0.0008 -0.0115
Model Parameters % Silt -- -- --
Model Parameters % Clay 0.0085 -0.0018 0.0040
Model Parameters LL 0.0089 -0.0078 0.0075
Model Parameters PI -0.0094 0.0019 0.0401
Model Parameters wopt% -- -- 0.0020
Model Parameters gammad, opt (kg/m3) -- -- -0.0039
Model Parameters ws% -0.0235 0.0111 -0.2750
Model Parameters gammas (kg/m3) -- -- --
Model Parameters gammas/gammad,opt -- -0.1232 -0.7177
Model Parameters ws/wopt 0.3290 -0.0009 1.0262
Model Parameters (gammad,opt)2/PNo. 40 -- -- 5.28E-06
Statistics MSE   449.184  
Statistics se   21.194  
Statistics sy   26.574  
Statistics se/sy   0.7975  
Statistics R2   --  
Statistics No. of Points   6022  


Table 46. Results from the nonlinear optimization regression study for the LTPP gravel subgrade soil data set.

Material: Gravel Subgrade Soils

Model Type Coefficient theta Exponent tauoct Exponent
Model Parameters Intercept 1.3429 0.3311 1.5167
Model Parameters P3/8" -0.0051 0.0010 -0.0302
Model Parameters PNo. 4 -- -- --
Model Parameters PNo. 40 -- -- --
Model Parameters PNo. 200 -- -- --
Model Parameters % Silt -- -- --
Model Parameters % Clay 0.0124 -0.0019 0.0435
Model Parameters LL 0.0053 -0.0050 0.0626
Model Parameters PI -- -0.0072 0.0377
Model Parameters wopt% -- -- --
Model Parameters gammad, opt (kg/m3) -- -- --
Model Parameters ws% -0.0231 0.0093 -0.2353
Model Parameters gammas (kg/m3) -- -- --
Model Parameters gammas/gammad,opt -- -- --
Model Parameters ws/wopt -- -- --
Model Parameters (gammad,opt)2/PNo. 40 -- -- --
Statistics MSE   301.322  
Statistics se   17.359  
Statistics sy   26.812  
Statistics se/sy   0.6474  
Statistics R2   --  
Statistics No. of Points   957  


Table 47. Results from the nonlinear optimization regression study for the LTPP sand subgrade soil data set.

Material: Sand Subgrade Soils

Model Type Coefficient theta Exponent tauoct Exponent
Model Parameters Intercept 3.2868 0.5670 -3.5677
Model Parameters P3/8" -0.0412 0.0045 0.1142
Model Parameters PNo. 4 0.0267 -2.98E-05 -0.0839
Model Parameters PNo. 40 -- -- --
Model Parameters PNo. 200 -- -- -0.1249
Model Parameters % Silt -- -0.0043 0.1030
Model Parameters % Clay 0.0137 -0.0102 0.1191
Model Parameters LL 0.0083 -0.0041 -0.0069
Model Parameters PI -- -- --
Model Parameters wopt% -0.0379 0.0014 -0.0103
Model Parameters gammad, opt (kg/m3) -- -- --
Model Parameters ws% -- -- --
Model Parameters gammas (kg/m3) -0.0004 -3.41E-05 -0.0017
Model Parameters gammas/gammad,opt -- -0.4582 4.3177
Model Parameters ws/wopt -- 0.1779 -1.1095
Model Parameters (gammad,opt)2/PNo. 40 -- -- --
Statistics MSE   357.7155648  
Statistics se   18.91337  
Statistics sy   24.787  
Statistics se/sy   0.7630  
Statistics R2   --  
Statistics No. of Points   3117  


Table 48. Results from the nonlinear optimization regression study for the LTPP silt subgrade soil data set.

Material: Silt Subgrade Soils

Model Type Coefficient theta Exponent tauoct Exponent
Model Parameters Intercept 1.0480 0.5097 -0.2218
Model Parameters P3/8" -- -- --
Model Parameters PNo. 4 -- -- --
Model Parameters PNo. 40 -- -- --
Model Parameters PNo. 200 -- -- --
Model Parameters % Silt -- -- 0.0047
Model Parameters % Clay 0.0177 -- --
Model Parameters LL -- -- --
Model Parameters PI 0.0279 -0.0286 0.0849
Model Parameters wopt% -- -- --
Model Parameters gammad, opt (kg/m3) -- -- --
Model Parameters ws% -0.0370 -- -0.1399
Model Parameters gammas (kg/m3) -- -- --
Model Parameters gammas/gammad,opt -- -- --
Model Parameters ws/wopt -- -- --
Model Parameters (gammad,opt)2/PNo. 40 -- -- --
Statistics MSE   193.03  
Statistics se   13.894  
Statistics sy   24.714  
Statistics se/sy   0.5622  
Statistics R2   --  
Statistics No. of Points   464  


Table 49. Results from the nonlinear optimization regression study for the LTPP clay subgrade soil data set.

Material: Clay Subgrade Soils

Model Type Coefficient theta Exponent tauoct Exponent
Model Parameters Intercept 1.3577 0.5193 1.4258
Model Parameters P3/8" -- -- --
Model Parameters PNo. 4 -- -0.0073 -0.0288
Model Parameters PNo. 40 -- 0.0095 0.0303
Model Parameters PNo. 200 -- -0.0027 -0.0521
Model Parameters % Silt -- -- 0.0251
Model Parameters % Clay 0.0106-- -- --
Model Parameters LL -- -0.0030 0.0535
Model Parameters PI -- -- --
Model Parameters wopt% -- -0.0049 -0.0672
Model Parameters gammad, opt (kg/m3) -- -- -0.0026
Model Parameters ws% -0.0437 -- --
Model Parameters gammas (kg/m3) -- -- -0.0025
Model Parameters gammas/gammad,opt -- -- --
Model Parameters ws/wopt -- -- -0.6055
Model Parameters (gammad,opt)2/PNo. 40 -- -- --
Statistics MSE   557.918  
Statistics se   23.620  
Statistics sy   29.224  
Statistics se/sy   0.8082  
Statistics R2   --  
Statistics No. of Points   1484  


Figure 62. Residuals, R, for the combined resilient modulus prediction equation for all base and subbase materials.

Figure 62. Residuals, R, for the combined resilient modulus prediction equation for all base and subbase materials. Base/subbase, resilient modulus equals the function of (physical properties). R, megapascals equals 51.091 minus 0.131 resilient modulus (observed). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the Residuals on the vertical axis. This figure provides a graphical comparison of the residuals by base material and soil type. As shown by the models, there is a modulus dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.


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

Figure 63. Residuals, R, for the uncrushed gravel (LTPP material code 302) resilient modulus prediction equation. Base/subbase material 302, uncrushed gravel, resilient modulus equals the function of (physical properties). R, megapascals equals 16.185 minus 0.1039 resilient modulus (observed). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the Residuals on the vertical axis. This figure provides a graphical comparison of the residuals by base material and soil type. As shown by the models, there is a modulus dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.


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

Figure 64. Residuals, R, for the crushed stone (LTPP material code 303) resilient modulus prediction equation. Base/subbase material 303, crushed stone, resilient modulus equals the function of (physical properties). R, megapascals equals 40.254 minus 0.2119 resilient modulus (observed). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the residuals on the vertical axis. This figure provides a graphical comparison of the residuals by base material and soil type. As shown by the models, there is a modulus dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.


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

Figure 65. Residuals, R, for the crushed gravel (LTPP material code 304) resilient modulus prediction equation. Base/subbase material 304, crushed gravel, resilient modulus equals the function of (physical properties). R, megapascals equals 19.535 minus 0.1402 resilient modulus (observed). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the residuals on the vertical axis. This figure provides a graphical comparison of the residuals by base material and soil type. As shown by the models, there is a modulus dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.


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

Figure 66. Residuals, R, for the sand (LTPP material code 306) resilient modulus prediction equation. Base/subbase material 306, sand, resilient modulus equals the function of (physical properties). R, megapascals equals 22.913 minus 0.1797 resilient modulus (observed). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the residuals on the vertical axis. This figure provides a graphical comparison of the residuals by base material and soil type. As shown by the models, there is a modulus dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.


Figure 67. Residuals, R, for the fine-grained soil-aggregate mixture (LTPP material code 307) resilient modulus prediction equation.

Figure 67. Residuals, R, for the fine grained soil aggregate mixture (LTPP material code 307) resilient modulus prediction equation. Base/subbase material 307, fine grained soil aggregate mix, resilient modulus equals the function of (physical properties). R, megapascals equals 26.335 minus 0.2117 resilient modulus (observed). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the residuals on the vertical axis. This figure provides a graphical comparison of the residuals by base material and soil type. As shown by the models, there is a modulus dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.


Figure 68. Residuals, R, for the coarse-grained soil-aggregate mixture (LTPP material, code 308) resilient modulus prediction equation.

Figure 68. Residuals, R, for the coarse grained soil aggregate mixture (LTPP material, code 308) resilient modulus prediction equation. Base/subbase material 308, coarse grained soil aggregate mix, resilient modulus equals the function of (physical properties). R, megapascals equals 46.835 minus 0.2854 resilient modulus (observed). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the residuals on the vertical axis. This figure provides a graphical comparison of the residuals by base material and soil type. As shown by the models, there is a modulus dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.


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

Figure 69. Residuals, R, for the fine grained soil (LTPP material code 309) resilient modulus prediction equation. Base/subbase 309, fine grained soil, resilient modulus equals the function of (physical properties). R, megapascals equals 45.662 minus 0.2888 resilient modulus observed). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the residuals on the vertical axis. This figure provides a graphical comparison of the residuals by base material and soil type. As shown by the models, there is a modulus dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.


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

Figure 70. Residuals, R, for the resilient modulus prediction equation for all subgrade soils. Subgrade, resilient modulus equals the function of (physical properties). R, megapascals equals 45.633 minus 0.627 resilient modulus (observed). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the Residuals on the vertical axis. This figure provides a graphical comparison of the residuals by base material and soil type. As shown by the models, there is a modulus dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.


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

Figure 71. Residuals, R, for the gravel soils resilient modulus prediction equation. Subgrade, gravel, resilient modulus equals the function of (physical properties). R, megapascals equals 29.306 minus 0.3781 resilient modulus (observed). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the residuals on the vertical axis. This figure provides a graphical comparison of the residuals by base material and soil type. As shown by the models, there is a modulus dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.


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

Figure 72. Residuals, R, for the sand soils resilient modulus prediction equation. Subgrade, Sand, resilient modulus equals the function of (physical properties). R, megapascals equals 40.407 minus 0.5752 resilient modulus (observed). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the residuals on the vertical axis. This figure provides a graphical comparison of the residuals by base material and soil type. As shown by the models, there is a modulus dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.


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

Figure 73. Residuals, R, for the silt soils resilient modulus prediction equation. Subgrade, silt, resilient modulus equals the function of (physical properties). R, megapascals equals 19.511 minus 0.2992 resilient modulus (observed). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the residuals on the vertical axis. This figure provides a graphical comparison of the residuals by base material and soil type. As shown by the models, there is a modulus dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.


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

Figure 74. Residuals, R, for the clay soils resilient modulus prediction equation. Subgrade, clay, resilient modulus equals the function of (physical properties). R, megapascals equals 49.744 minus 0.6454 resilient modulus (observed). The resilient modulus (observed), megapascals, is graphed on the horizontal axis and the residuals on the vertical axis. This figure provides a graphical comparison of the residuals by base material and soil type. As shown by the models, there is a modulus dependent bias. Determining the cause of the bias was beyond the scope of work for this study. Thus, the residuals and their resilient modulus dependence are presented for the consideration of future users of the LTPP resilient modulus database and computed parameters from this study.



REFERENCES

  1. American Association of State Highway and Transportation Officials, AASHTO Guide for Design of Pavement Structures, Washington, D.C., 1993.
  2. Alavi, S.T., T. Merport, J. Wilson, A. Groeger, and A. Lopez, LTPP Materials Characterization Program: Resilient Modulus of Unbound Materials (LTPP Protocol P46) - Laboratory Startup and Quality Control Procedure, Report No. FHWA-RD-96-176, Federal Highway Administration, U.S. Department of Transportation, Washington, D.C., January 1997.
  3. Von Quintus, H. and B. Killingsworth, Analyses Relating to Pavement Material Characterizations and Their Effects on Pavement Performance, Report No. FHWA-RD-97-085, Federal Highway Administration, U.S. Department of Transportation, Washington, D.C., 1998.
  4. "Unbound Materials Characterization Utilizing LTPP Data," Unpublished Interim Task Report, NCHRP Project 1-37A, Development of the 2002 Design Guide for the Design of New and Rehabilitated Pavement Structures, National Cooperative Highway Research Program, National Research Council, Washington, D.C., August 2000.
  5. Mason, Robert L., Richard F. Gunst, and James L. Hess, Statistical Design and Analysis of Experiments With Applications to Engineering and Science, John Wiley & Sons, New York City, N.Y., 1989.
  6. Darter, Michael I., Harold L. Von Quintus, Emmanuel B. Owusu-Antwi, and Jane Jiang, Systems for Design of Highway Pavements, Final Report for NCHRP Project 1-32, National Cooperative Highway Research Program, National Research Council, Washington, D.C., May 1997.
  7. Santha, B. Lanka, Resilient Modulus of Subgrade Soils: Comparison of Two Constitutive Equations, TRR No. 1462, Transportation Research Board, National Research Council, Washington, D.C., 1994.


The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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