STUDY OF LTPP LABORATORY RESILIENT MODULUS TEST DATA AND RESPONSE CHARACTERISTICS, FINAL REPORT

PUBLICATION NO. FHWA-RD-02-051
OCTOBER 2002

U.S. Department of Transportation
Federal Highway Administration
Research, Development, and Technology
Turner-Fairbank Highway Research Center
6300 Georgetown Pike
McLean, VA 22101-2296

Foreword

The elastic or resilient modulus of pavement materials is an important material property in any mechanistically based design/analysis procedure for flexible pavements. Repeated load resilient modulus tests are being performed on all unbound materials and soils of the Specific Pavement Studies (SPS) and General Pavement Studies (GPS) test sections that are in the Federal Highway Administration (FHWA) Long Term Pavement Performance (LTPP) program in accordance with LTPP test protocol P46. Previous studies have shown that the resilient modulus test results can be affected by sampling technique, testing procedure, and errors that can occur during the testing program. Thus, the FHWA sponsored a detailed review of the resilient modulus test results that have a Level E status in the LTPP database, i.e., they have passed all levels of the quality control (QC) checks.

This report documents the first comprehensive review and evaluation of the resilient modulus test data measured on pavement materials and soils recovered from the LTPP test sections. The resilient modulus test data were found generally to be in excellent condition with less than 10 percent of the tests exhibiting potential anomalies or discrepancies in the data.

The resilient modulus data were further investigated to evaluate relationships between resilient modulus and the physical properties of the unbound materials and soils. The primary result from these studies is that the resilient modulus can be reasonably predicted from the physical properties included in the LTPP database, but there is a bias present in the calculated values. Thus, until additional test results become available to improve or confirm these relationships, it is recommended that at least some laboratory tests be performed to measure the resilient modulus for unbound pavement materials and soils.

T. Paul Teng, P.E.
Director
Office of Infrastructure
Research and Development

Notice

This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Government assumes no liability for its contents or use thereof. This report does not constitute a standard, specification, or regulation.

The United 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