Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

PUBLICATION NO. FHWA-HRT-23-046 JULY 2023 

Variability in the Engineering Properties 

of Open-Graded Aggregate Backfills: 

A Large-Scale Direct Shear 

Round-Robin Study
FOREWORD

Open-graded aggregates (OGAs) are a common civil engineering material used in the 

construction of roads and bridges. Their unit weight and shear strength are important parameters 

that transportation agencies must consider during design, yet little is known about the variability 

of those parameters. To address this gap, the Federal Highway Administration initiated a 

round-robin study in which six laboratories tested three commonly used OGAs from five 

different quarries for gradation, density, and shear strength using large-scale direct shear devices.

This report presents and analyzes the results from this interlaboratory study and discusses the 

sensitivity of the physical and mechanical parameters for OGAs. The results of this study should 

assist State and local transportation agencies, design consultants, contractors, and researchers in 

determining appropriate design parameters and understanding their reliability.

Jean Nehme, Ph.D., P.E.

Director, Office of Infrastructure

Research and Development

Notice

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

(USDOT) in the interest of information exchange. The U.S. Government assumes no liability for 

the use of the information contained in this document.

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

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

objective of the document. 

Quality Assurance Statement

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

Government, industry, and the public in a manner that promotes public understanding. Standards 

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its 

information. FHWA periodically reviews quality issues and adjusts its programs and processes to 

ensure continuous quality improvement. 
TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.

FHWA-HRT-23-046

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

4. Title and Subtitle

Variability in the Engineering Properties of Open-Graded 

Aggregate Backfills: A Large-Scale Direct Shear Round-Robin 

Study

5. Report Date

July 2023

6. Performing Organization Code

7. Author(s)

Jennifer E. Nicks (ORCID: 0000-0001-7230-3578), Michael T. 

Adams (ORCID: 0000-0003-2358-4128), Nicholas Culbreth 

(ORCID: 0000-0003-0434-230X), and Thomas Gebrenegus 

(ORCID: 0000-0002-5742-6411) 

8. Performing Organization Report No.

9. Performing Organization Name and Address 

Office of Infrastructure R&D

FHWA Research, Development and Technology

6300 Georgetown Pike

McLean, VA 22101

10. Work Unit No.

11. Contract or Grant No.

693JJ320F000160/693JJ319D000057

12. Sponsoring Agency Name and Address 

Office of Research, Development, and Technology 

Federal Highway Administration

6300 Georgetown Pike

McLean, VA 22101-2296

13. Type of Report and Period

Final Report; February 2019– July 2023

14. Sponsoring Agency Code

HRDI-40

15. Supplementary Notes

The contracting officer’s representative was Michael T. Adams (HRDI-10; 0000-0003-2358-4128).

16. Abstract

Open-graded aggregates (OGAs) are a common type of structural backfill used to build a variety of transportation 

earthworks. Therefore, the Federal Highway Administration (FHWA) has made a concerted effort over the past 

decade to better understand and quantify the strength-deformation characteristics of OGAs through large-scale 

direct shear (LSDS) testing performed on a wide variety of stone sizes. However, all of this testing was 

performed using a single type of LSDS device, primarily conducted by a single laboratory technician, with OGAs 

generally obtained from a single quarry. To address these limitations and better understand the variability 

expected for OGAs across the country, FHWA initiated a round-robin study that included sieve, maximum and 

minimum density, and LSDS tests. In the study, six laboratories tested three stone size classifications (No. 57, 

No. 68, and No. 8) from five quarries with different mineralogy, meaning 90 OGAs were evaluated. Ottawa 

20-30 sand was also included as standard soil for comparison. A statistical analysis of all the data for key 

geotechnical design parameters was then performed to determine mean values, standard deviations, coefficients 

of variation, and suggested statistical distribution types. This report details the testing program; results from all 

the laboratory tests performed and from the statistical analyses, including the sensitivity of engineering properties 

to different factors; and the impact on design, with suggested values for preliminary design provided.

17. Key Words

Open-graded aggregates, structural backfill, largescale direct shear, coefficient of variation, friction 

angle, dilation angle, shear strength, dry unit 

weight

18. Distribution Statement

No restrictions. No restrictions. This document is available 

to the public through the National Technical Information 

Service, Springfield, VA 22161. http://www.ntis.gov

19. Security Classif. (of this report) 

Unclassified

20. Security Classif. (of this page) 

Unclassified

21. No. of Pages

257

22. Price

N/A

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

TABLE OF CONTENTS

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

Background ............................................................................................................................ 3

Engineering Properties of Structural Backfills ................................................................. 3

Variability of Physical Properties and Characteristics ....................................................... 5

Variability of Shear Strength ............................................................................................. 5

DS Testing ......................................................................................................................... 7

DS Devices ......................................................................................................................... 7

DS Test Procedures ............................................................................................................ 8

Report Overview .................................................................................................................... 9

CHAPTER 2. TEST PROGRAM ............................................................................................. 11

Materials ............................................................................................................................... 11

OS-20-30 ........................................................................................................................... 11

OGAs ............................................................................................................................... 11

OGA Sampling ................................................................................................................. 13

Laboratory Testing .............................................................................................................. 14

Sequence of Round-Robin Testing .................................................................................. 14

Sequence of Laboratory Testing ...................................................................................... 15

Sample Preparation .......................................................................................................... 15

Initial Sieve Testing ......................................................................................................... 15

Minimum and Maximum Density Testing ....................................................................... 15

LSDS Testing ................................................................................................................... 16

Post-Shear Sieve Testing ................................................................................................. 18

AIMS2 Testing ................................................................................................................. 19

Micro-Deval Testing ........................................................................................................ 19

CHAPTER 3. TEST RESULTS ............................................................................................... 21

Physical Properties and Characteristics ............................................................................ 21

Particle Size ..................................................................................................................... 21

As-Received Gradations .................................................................................................. 21

Post-LSDS Gradations ...................................................................................................... 26

Dry Unit Weight .............................................................................................................. 28

Bulk Dry Specific Gravity ............................................................................................... 32

Particle Characteristics ..................................................................................................... 33

Angularity ........................................................................................................................ 33

Sphericity ......................................................................................................................... 34

F&E Values ...................................................................................................................... 35

Surface TX ....................................................................................................................... 36

Abrasion Resistance and Durability ................................................................................. 37

Shear Strength and Deformation ....................................................................................... 38

OS-20-30 .......................................................................................................................... 39

No. 57 OGAs ................................................................................................................... 46

No. 68 OGAs ................................................................................................................... 55

No. 8 OGAs ..................................................................................................................... 64

Summary ............................................................................................................................... 73
iv

CHAPTER 4. ANALYSIS OF RESULTS ............................................................................... 75

Distribution Types ............................................................................................................... 75

Dry Unit Weight .............................................................................................................. 77

Friction Angles ................................................................................................................. 79

Secant Friction Angle ...................................................................................................... 79

Tangent Friction Angle .................................................................................................... 82

Residual Friction Angle ................................................................................................... 84

Constant Volume Friction Angle ..................................................................................... 86

Maximum Dilation Angle ................................................................................................ 88

Summary .......................................................................................................................... 90

Impact of Stone Size, Mineralogy, and Laboratory .......................................................... 91

DS Testing Devices and Procedures ................................................................................... 95

Box Shape ........................................................................................................................ 95

Box Mobility .................................................................................................................... 96

Base of the Loading Platen .............................................................................................. 97

Connection Between the Load Platen and Normal Load ................................................. 98

Specimen Versus Box Dimensions ................................................................................... 99

Vertical Displacement Measurements .............................................................................. 99

Application of Normal Load ............................................................................................ 99

Data Collection Frequency ............................................................................................ 100

Setting the Shear Gap ..................................................................................................... 100

Specimen Compaction ................................................................................................... 101

Test Reports Versus Analyzed Data .............................................................................. 101

Design Implications ............................................................................................................ 102

CHAPTER 5. CONCLUSIONS .............................................................................................. 107

Gradation ............................................................................................................................ 107

Dry Unit Weight and Bulk Dry Specific Gravity ............................................................ 108

Particle Shape Characteristics .......................................................................................... 108

Particle Durability ............................................................................................................. 109

Shear Strength .................................................................................................................... 109

LSDS Devices and Procedures .......................................................................................... 110

Lessons Learned ................................................................................................................. 111

Geotechnical Design Application ...................................................................................... 112

Next Steps and Future Research ...................................................................................... 113

APPENDIX A. SAMPLE PREPARATION PROTOCOL AND INSTRUCTIONS .......... 115

Test Samples (AASHTO No. 8, No. 68, and No. 57) ....................................................... 115

Sample Preparation ........................................................................................................... 115

Sample Reduction .............................................................................................................. 115

Sieve Analysis (ASTM C136) and Maximum/Minimum Index (Relative) Density 

(ASTM D4253 and D4254) ................................................................................................ 116

LSDS Testing (ASTM D3080) ........................................................................................... 117

Sample Preparation ........................................................................................................ 117

LSDS Test Setup ............................................................................................................ 118

Post-LSDS Sieve Analysis ............................................................................................. 118

Test Data ............................................................................................................................. 118
v 

APPENDIX B. PRE- AND POST-SHEAR SIEVE ANALYSIS ......................................... 119

No. 57 ................................................................................................................................... 119

No. 68 ................................................................................................................................... 125

No. 8 ..................................................................................................................................... 130

APPENDIX C. AIMS2 PARTICLE CHARACTERISTIC RESULTS .............................. 135

OS-20-30 .............................................................................................................................. 135

No. 57 OGAS ...................................................................................................................... 135

No. 68 OGAS ...................................................................................................................... 144

No. 8 OGAS ........................................................................................................................ 152

APPENDIX D. LSDS TEST RESULTS ................................................................................. 163

OS-20-30 .............................................................................................................................. 163

No. 57 OGAS ...................................................................................................................... 166

No. 68 OGAS ...................................................................................................................... 187

No. 8 OGAS ........................................................................................................................ 207

APPENDIX E. AD TEST AND ANOVA ANALYSIS .......................................................... 227

AD Test ............................................................................................................................... 227

ANOVA ............................................................................................................................... 229

ACKNOWLEDGMENTS ....................................................................................................... 235

REFERENCES ......................................................................................................................... 237
vi 

LIST OF FIGURES

Figure 1. Photo. OGAs as structural backfill in a geosynthetic reinforced soil abutment. ............ 1

Figure 2. Photo. LSDS devices at TFHRC. ................................................................................... 2

Figure 3. Illustration. Basic types of DS boxes, as described by Shibuya et al. (1997). ............... 8

Figure 4. Photos. Rock types for the OGAs evaluated. ............................................................... 12

Figure 5. Photo. Stockpile of aggregates at TFHRC for random sampling. ................................. 14

Figure 6. Schematics. LSDS device configurations for each laboratory with dimensions in 

inches. ................................................................................................................................. 18

Figure 7. Charts. Gradation curves for the as-received LI OGAs. .............................................. 23

Figure 8. Chart. D85 for LI OGAs. ............................................................................................... 26

Figure 9. Chart. Breakage index results for LI OGAs. ................................................................ 28

Figure 10. Chart. γd95 values for LI OGAs. .................................................................................. 32

Figure 11. Charts. Shear stress versus horizontal strain for OS-20-30. ....................................... 40

Figure 12. Charts. Vertical strain versus horizontal strain for OS-20-30. ................................... 41

Figure 13. Chart. Secant friction angles for OS-20-30. ............................................................... 43

Figure 14. Chart. Linear Mohr-Coulomb failure envelopes for OS-20-30. ................................. 44

Figure 15. Chart. Maximum dilation angle for OS-20-30. .......................................................... 46

Figure 16. Charts. Shear stress versus horizontal strain for No. 57-LI. ....................................... 47

Figure 17. Charts. Vertical strain versus horizontal strain for No. 57-LI. ................................... 48

Figure 18. Chart. Peak shear stress versus εh,peak for No. 57 OGAs. ........................................... 50

Figure 19. Chart. Secant friction angles for No. 57-LI. ............................................................... 51

Figure 20. Chart. Linear Mohr-Coulomb failure envelopes for No. 57-LI. ................................. 53

Figure 21. Chart. Maximum dilation angle for No. 57-LI. .......................................................... 55

Figure 22. Charts. Shear stress versus horizontal strain for No. 68-LI. ....................................... 56

Figure 23. Charts. Vertical strain versus horizontal strain for No. 68-LI. ................................... 57

Figure 24. Chart. Peak shear stress versus εh,peak for No. 68 OGAs. ............................................ 58

Figure 25. Chart. Secant friction angles for No. 68-LI. ............................................................... 60

Figure 26. Chart. Linear Mohr-Coulomb failure envelopes for No. 68-LI. ................................. 62

Figure 27. Chart. Maximum dilation angle for No. 68-LI. .......................................................... 64

Figure 28. Charts. Shear stress versus horizontal strain for No. 8-LI. ......................................... 65

Figure 29. Charts. Vertical strain versus horizontal strain for No. 8 OGAs. ............................... 66

Figure 30. Chart. Peak shear stress versus εh,peak for No. 8 OGAs. ............................................. 67

Figure 31. Chart. Secant friction angles for No. 8-LI. ................................................................. 69

Figure 32. Chart. Linear Mohr-Coulomb failure envelopes for No. 8-LI. ................................... 70

Figure 33. Chart. Maximum dilation angle for No. 8-LI. ............................................................ 73

Figure 34. Chart. Histogram of γd95 with idealized normal distribution curve overlayed. .......... 77

Figure 35. Chart. Normal probability plot for γd95. ...................................................................... 78

Figure 36. Chart. Relationship between γd95 and Gsb. ................................................................. 79

Figure 37. Chart. Histogram of φs with idealized normal distribution curve overlayed. ............. 80

Figure 38. Charts. Normal probability plots for φs. ..................................................................... 82

Figure 39. Chart. Histogram for φt with idealized normal curve overlayed. ............................... 83

Figure 40. Chart. Normal probability plot for φt. ......................................................................... 84

Figure 41. Chart. Histogram for φt,r with idealized normal distribution curve overlayed. .......... 85

Figure 42. Chart. Normal probability plot for φt,r. ....................................................................... 86
vii 

Figure 43. Chart. Histogram for φcv with idealized normal distribution curve overlayed. .......... 87

Figure 44. Chart. Normal probability plot for φcv. ....................................................................... 88

Figure 45. Chart. Histograms for ψmax with idealized normal distribution curve overlayed. ...... 89

Figure 46. Chart. Standard normal variable plots for ψmax. ......................................................... 90

Figure 47. Chart. Normal distribution curves for φt per stone size. ............................................. 92

Figure 48. Charts. No. 68 stress-strain curves by mineralogy for all laboratories. ...................... 93

Figure 49. Charts. No. 68 vertical-horizontal strain curves by mineralogy for all 

laboratories. ........................................................................................................................ 94

Figure 50. Chart. Impact of box mobility on the strength-dilatancy relationship. ....................... 97

Figure 51. Illustrations. Types of loading platen bases. ............................................................... 98

Figure 52. Charts. Comparison of φt and φs. ............................................................................. 104

Figure 53. Chart. Residual versus constant volume friction angle. ............................................ 105

Figure 54. Chart. Extrapolated cumulative distributions for dry unit weight at 95RD. ............ 106

Figure 55. Chart. Extrapolated cumulative distributions for tangent friction angle. ................. 106

Figure 56. Illustration. Sampling procedure using a quartering method. .................................. 116

Figure 57. Chart. AIMS2 cumulative angularity distributions for OS-20-30. ........................... 135

Figure 58. Charts. AIMS2 cumulative distributions for No. 57-BA. ........................................ 137

Figure 59. Charts. AIMS2 cumulative distributions for No. 57-DI. ......................................... 138

Figure 60. Charts. AIMS2 cumulative distributions for No. 57-GG. ........................................ 140

Figure 61. Charts. AIMS2 cumulative distributions for No. 57-LI. .......................................... 141

Figure 62. Charts. AIMS2 cumulative distributions for No. 57-SI. .......................................... 143

Figure 63. Charts. AIMS2 cumulative distributions for No. 68-BA. ........................................ 145

Figure 64. Charts. AIMS2 cumulative distributions for No. 68-DI. .......................................... 147

Figure 65. Charts. AIMS2 cumulative distributions for No. 68-GG. ........................................ 148

Figure 66. Charts. AIMS2 cumulative distributions for No. 68-LI. .......................................... 150

Figure 67. Charts. AIMS2 cumulative distributions for No. 68-SI. .......................................... 151

Figure 68. Charts. AIMS2 cumulative distributions for No. 8-BA. .......................................... 154

Figure 69. Charts. AIMS2 cumulative distributions for No. 8-DI. ............................................ 155

Figure 70. Charts. AIMS2 cumulative distributions for No. 8-GG. .......................................... 157

Figure 71. Charts. AIMS2 cumulative distributions for No. 8-LI. ............................................ 158

Figure 72. Charts. AIMS2 cumulative distributions for No. 8-SI. ............................................ 160

Figure 73. Charts. Shear stress versus horizontal strain for OS-20-30. ..................................... 163

Figure 74. Charts. Vertical strain versus horizontal strain for OS-20-30. ................................. 164

Figure 75. Chart. Linear Mohr-Coulomb failure envelopes for OS-20-30. ............................... 165

Figure 76. Charts. Shear stress versus horizontal strain for No. 57-BA. ................................... 167

Figure 77. Charts. Vertical strain versus horizontal strain for No. 57-BA. ............................... 168

Figure 78. Chart. Linear Mohr-Coulomb failure envelopes for No. 57-BA. ............................. 169

Figure 79. Charts. Shear stress versus horizontal strain for No. 57-DI. .................................... 171

Figure 80. Charts. Vertical strain versus horizontal strain for No. 57-DI. ................................ 172

Figure 81. Chart. Linear Mohr-Coulomb failure envelopes for No. 57-DI. .............................. 173

Figure 82. Charts. Shear stress versus horizontal strain for No. 57-GG. ................................... 175

Figure 83. Charts. Vertical strain versus horizontal strain for No. 57-GG. ............................... 176

Figure 84. Chart. Linear Mohr-Coulomb failure envelopes for No. 57-GG. ............................. 177

Figure 85. Charts. Shear stress versus horizontal strain for No. 57-LI. ..................................... 179

Figure 86. Charts. Vertical strain versus horizontal strain for No. 57-LI. ................................. 180

Figure 87. Chart. Linear Mohr-Coulomb failure envelopes for No. 57-LI. ............................... 181
viii

Figure 88. Charts. Shear stress versus horizontal strain for No. 57-SI. ..................................... 183

Figure 89. Charts. Vertical strain versus horizontal strain for No. 57-SI. ................................. 184

Figure 90. Chart. Linear Mohr-Coulomb failure envelopes for No. 57-SI. ............................... 185

Figure 91. Charts. Shear stress versus horizontal strain for No. 68-BA. ................................... 187

Figure 92. Charts. Vertical strain versus horizontal strain for No. 68-BA. ............................... 188

Figure 93. Chart. Linear Mohr-Coulomb failure envelopes for No. 68-BA. ............................. 189

Figure 94. Charts. Shear stress versus horizontal strain for No. 68-DI. .................................... 191

Figure 95. Charts. Vertical strain versus horizontal strain for No. 68-DI. ................................ 192

Figure 96. Chart. Linear Mohr-Coulomb failure envelopes for No. 68-DI. .............................. 193

Figure 97. Charts. Shear stress versus horizontal strain for No. 68-GG. ................................... 195

Figure 98. Charts. Vertical strain versus horizontal strain for No. 68-GG. ............................... 196

Figure 99. Chart. Linear Mohr-Coulomb failure envelopes for No. 68-GG. ............................. 197

Figure 100. Charts. Shear stress versus horizontal strain for No. 68-LI. ................................... 199

Figure 101. Charts. Vertical strain versus horizontal strain for No. 68-LI. ............................... 200

Figure 102. Chart. Linear Mohr-Coulomb failure envelopes for No. 68-LI. ............................. 201

Figure 103. Charts. Shear stress versus horizontal strain for No. 68-SI. ................................... 203

Figure 104. Charts. Vertical strain versus horizontal strain for No. 68-SI. ............................... 204

Figure 105. Chart. Linear Mohr-Coulomb failure envelopes for No. 68-SI. ............................. 205

Figure 106. Charts. Shear stress versus horizontal strain for No. 8-BA. ................................... 207

Figure 107. Charts. Vertical strain versus horizontal strain for No. 8-BA. ............................... 208

Figure 108. Chart. Linear Mohr-Coulomb failure envelopes for No. 8-BA. ............................. 209

Figure 109. Charts. Shear stress versus horizontal strain for No. 8-DI. .................................... 211

Figure 110. Charts. Vertical strain versus horizontal strain for No. 8-DI. ................................ 212

Figure 111. Chart. Linear Mohr-Coulomb failure envelopes for No. 8-DI. .............................. 213

Figure 112. Charts. Shear stress versus horizontal strain for No. 8-GG. ................................... 215

Figure 113. Charts. Vertical strain versus horizontal strain for No. 8-GG. ............................... 216

Figure 114. Chart. Linear Mohr-Coulomb failure envelopes for No. 8-GG. ............................. 217

Figure 115. Charts. Shear stress versus horizontal strain for No. 8-LI. ..................................... 219

Figure 116. Charts. Vertical strain versus horizontal strain for No. 8-LI. ................................. 220

Figure 117. Chart. Linear Mohr-Coulomb failure envelopes for No. 8-LI. ............................... 221

Figure 118. Charts. Shear stress versus horizontal strain for No. 8-SI. ..................................... 223

Figure 119. Charts. Vertical strain versus horizontal strain for No. 8-SI. ................................. 224

Figure 120. Chart. Linear Mohr-Coulomb failure envelopes for No. 8-SI. ............................... 225
ix

LIST OF TABLES

Table 1. Reported variabilities of select physical properties and characteristics. ......................... 5

Table 2. ASTM C778 OS-20-30 gradation requirements (ASTM 2017). ................................... 11

Table 3. Selected AASHTO M 43-05 stone size designations (AASHTO 2018a). .................... 12

Table 4. OGA sample nomenclature. ........................................................................................... 13

Table 5. Round-robin test order. .................................................................................................. 15

Table 6. LSDS device and testing configurations. ....................................................................... 17

Table 7. As-received gradation test results per AASHTO M 43-05 specifications. .................... 24

Table 8. D85 (inch) for as-received OGAs. .................................................................................. 25

Table 9. Breakage index (percent). .............................................................................................. 27

Table 10. Dry unit weights for No. 57 OGAs. ............................................................................. 29

Table 11. Dry unit weights for No. 68 OGAs. ............................................................................. 30

Table 12. Dry unit weights for No. 8 OGAs. ............................................................................... 31

Table 13. Reported bulk dry specific gravities for the OGAs. .................................................... 33

Table 14. Summary of AIMS2 weighted averages for angularity. .............................................. 34

Table 15. Summary of AIMS2 weighted averages for SP. .......................................................... 35

Table 16. Summary of AIMS2 weighted averages for F&E values. ........................................... 36

Table 17. Summary of AIMS2 weighted averages for texture. ................................................... 37

Table 18. Durability results for the OGA rock types. .................................................................. 38

Table 19. Peak shear parameters for OS-20-30. .......................................................................... 42

Table 20. Shear strength parameters for OS-20-30. .................................................................... 42

Table 21. Selection of n-point centered moving averages for ψmax computation. ....................... 45

Table 22. Maximum dilation angles for OS-20-30. ..................................................................... 46

Table 23. Peak shear stress parameters for No. 57 OGAs. .......................................................... 49

Table 24. Shear strength parameters for No. 57 OGAs. .............................................................. 52

Table 25. Maximum dilation angles for No. 57 OGAs. ............................................................... 54

Table 26. Peak shear stress parameters for No. 68 OGAs. .......................................................... 59

Table 27. Shear strength parameters for No. 68 OGAs. .............................................................. 61

Table 28. Maximum dilation angles for No. 68 OGAs. ............................................................... 63

Table 29. Peak shear stress parameters for No. 8 OGAs. ............................................................ 68

Table 30. Shear strength parameters for No. 8 OGAs. ................................................................ 71

Table 31. Maximum dilation angles for No. 8 OGAs. ................................................................. 72

Table 32. Summary of key, average OGA results and basic statistics. ....................................... 74

Table 33. Histogram parameters. ................................................................................................. 76

Table 34. Summary of suggested statistics for key OGA design parameters. ............................. 91

Table 35. Proposed default values for key geotechnical design parameters. ............................. 113

Table 36. Selected AASHTO M 43 aggregate designations (AASHTO 2005). ........................ 117

Table 37. Pre- and post-shear sieving data for No. 57-BA. ....................................................... 120

Table 38. Pre- and post-shear sieving data for No. 57-DI. ........................................................ 121

Table 39. Pre- and post-shear sieving data for No. 57-GG. ....................................................... 122

Table 40. Pre- and post-shear sieving data for No. 57-LI. ......................................................... 123

Table 41. Pre- and post-shear sieving data for No. 57-SI. ......................................................... 124

Table 42. Pre- and post-shear sieving data for No. 68-BA. ....................................................... 125

Table 43. Pre- and post-shear sieving data for No. 68-DI. ........................................................ 126

Table 44. Pre- and post-shear sieving data for No. 68-GG. ....................................................... 127
x 

Table 45. Pre- and post-shear sieving data for No. 68-LI. ......................................................... 128

Table 46. Pre- and post-shear sieving data for No. 68-SI. ......................................................... 129

Table 47. Pre- and post-shear sieving data for No. 8-BA. ......................................................... 130

Table 48. Pre- and post-shear sieving data for No. 8-DI. .......................................................... 131

Table 49. Pre- and post-shear sieving data for No. 8-GG. ......................................................... 132

Table 50. Pre- and post-shear sieving data for No. 8-LI. ........................................................... 133

Table 51. Pre- and post-shear sieving data for No. 8-SI. ........................................................... 134

Table 52. Summary of AIMS2 weighted averages for No. 57 OGAs. ...................................... 143

Table 53. Summary of AIMS2 weighted average F&E values for No. 57 OGAs. .................... 144

Table 54. Summary of AIMS2 weighted averages for No. 68 OGAs. ...................................... 152

Table 55. Summary of AIMS2 weighted average F&E values for No. 68 OGAs. .................... 152

Table 56. Summary of AIMS2 weighted averages for No. 8 OGAs. ........................................ 160

Table 57. Summary of AIMS2 weighted average F&E values for No. 8 OGAs. ...................... 161

Table 58. Summary of LSDS results for OS-20-30. .................................................................. 166

Table 59. Summary of LSDS results for No. 57-BA. ................................................................ 170

Table 60. Summary of LSDS results for No. 57-DI. ................................................................. 174

Table 61. Summary of LSDS results for No. 57-GG. ................................................................ 178

Table 62. Summary of LSDS results for No. 57-LI. .................................................................. 182

Table 63. Summary of LSDS results for No. 57-SI. .................................................................. 186

Table 64. Summary of LSDS results for No. 68-BA. ................................................................ 190

Table 65. Summary of LSDS results for No. 68-DI. ................................................................. 194

Table 66. Summary of LSDS results for No. 68-GG. ................................................................ 198

Table 67. Summary of LSDS results for No. 68-LI. .................................................................. 202

Table 68. Summary of LSDS results for No. 68-SI. .................................................................. 206

Table 69. Summary of LSDS results for No. 8-BA. .................................................................. 210

Table 70. Summary of LSDS results for No. 8-DI. ................................................................... 214

Table 71. Summary of LSDS results for No. 8-GG. .................................................................. 218

Table 72. Summary of LSDS results for No. 8-LI. .................................................................... 222

Table 73. Summary of LSDS results for No. 8-SI. .................................................................... 226

Table 74. AD* p-values for normal distributions. ..................................................................... 228

Table 75. AD test results for key parameters. ............................................................................ 228

Table 76. Grouped AD results for nonnormal key parameters. ................................................. 229

Table 77. LSDS test results for tangent friction angle by factor. .............................................. 230

Table 78. Test results from the two-factor ANOVA without replicates analysis. ..................... 231

Table 79. Summary of AD normality test results for datasets within each factor. .................... 232

Table 80. Levene’s test for selected parameters by factor. ........................................................ 233
xi 

LIST OF ABBREVIATIONS

AASHTO American Association of State Highway and Transportation Officials

AD Anderson-Darling

AIMS2 Aggregate Imaging Measurement System 2 

ANOVA analysis of variance

AR acceptable range

ASTM American Society for Testing and Materials

BA basalt

COV coefficient of variation

DI diabase

DS direct shear

FHWA Federal Highway Administration

F&E flat and elongated

GA gradient angularity

GG granite-gneiss

K-S Kolmogorov-Smirnov

L.A. Los Angeles 

LI limestone

LRFD load and resistance factor design

LSDS large-scale direct shear

LVDT linear variable differential transformer

OGA open-graded aggregate 

OS-20-30 Ottawa 20-30 sand

RD relative density

SI siltstone

SP sphericity

TFHRC Turner-Fairbank Highway Research Center

TX texture 

ZDA zero dilation angle 

95RD 95 percent relative density
xii 

LIST OF SYMBOLS

Δh change in horizontal displacement

Δt sampling frequency 

Δvmax maximum change in vertical displacement

εh,peak horizontal strain at peak shear

εh,peak,5psi horizontal strain at peak shear at 5-psi target applied normal stress

εh,peak,10psi horizontal strain at peak shear at 10-psi target applied normal stress

εh,peak,15psi horizontal strain at peak shear at 15-psi target applied normal stress

εh,peak,30psi horizontal strain at peak shear at 30-psi target applied normal stress

γ unit weight of the aggregates

γd95 dry unit weight at 95 percent relative density 

γdmax maximum dry unit weight

γdmin minimum dry unit weight

σh lateral earth pressure

σn applied normal stress

τ shear strength

τinitial initial shear stress values before the shear phase 

τpeak,5psi peak shear stress at 5-psi target applied normal stress

τpeak,10psi peak shear stress at 10-psi target applied normal stress

τpeak,15psi peak shear stress at 15-psi target applied normal stress

τpeak,30psi peak shear stress at 30-psi target applied normal stress

τr residual shear stress at 20 percent horizonal strain

φ friction angle

φcv constant volume friction angle 

φcv,fixed constant volume friction angle under fixed upper shear box conditions 

φcv,mobile constant volume friction angle under mobile upper shear box conditions 

φs secant, or peak friction angle 

φs,5psi secant, or peak friction angle at 5-psi target applied normal stress 

φs,10psi secant, or peak friction angle at 10-psi target applied normal stress

φs,15psi secant, or peak friction angle at 15-psi target applied normal stress

φs,30psi secant, or peak friction angle at 30-psi target applied normal stress

φt tangent friction angle 

φt,r residual tangent friction angle

ψ dilation angle 

ψmax maximum dilation angle 

ψmax,5psi maximum dilation angle at 5-psi target applied normal stress 

ψmax,10psi maximum dilation angle at 10-psi target applied normal stress 

ψmax,15psi maximum dilation angle at 15-psi target applied normal stress 

ψmax,30psi maximum dilation angle at 30-psi target applied normal stress

BI breakage index

ca apparent cohesion

D85 particle diameter at which 85 percent of the sample is finer, by mass

dmax maximum grain size

EH horizontal earth pressure load
xiii

EV vertical pressure from dead load of earth fill

Gsb bulk dry specific gravity 

H0 null hypothesis 

H1 alternative hypothesis 

Ka active earth pressure coefficient

Ku kurtosis 

L length of particle

n number of samples or points 

s standard deviation

S thickness of particle

Sk skewness

W histogram’s optimal bin width

Wi initial (i.e., as-received) percentage retained for each sieve size evaluated

Wf final (i.e., post-shear) percentage retained for each sieve size evaluated

x̄ mean

Z standard normal variable

z depth

1 

CHAPTER 1. INTRODUCTION

Open-graded aggregates (OGAs) are a common type of structural backfill used to build a variety 

of transportation earthworks (e.g., retaining walls, embankments, and bridge abutments) 

(figure 1). Early application of OGAs began in the 1950s as surface courses for asphalt 

pavements (Kandhal and Mallick 1999). The use of OGAs in transportation construction is still 

evolving with applications related to pavement bases and subbases, portland cement pervious 

concrete, and structural backfills (Mallick et al. 2000; Nicks et al. 2015; Tao and 

Abu-Farsakh 2008; Tyson and Tayabji 2012; Younger et al. 1994). OGAs are most often 

produced from the blasting of rock in quarries. The blasted rock is then crushed and sorted into 

aggregates of different sizes per the material specifications for a project. 

OGAs are classified per the American Association of State Highway and Transportation 

Officials (AASHTO) M 43-05 Standard Specification for Sizes of Aggregate for Road and 

Bridge Construction (AASHTO 2018a). The maximum grain size (dmax) under the AASHTO 

M 43–05 specification ranges from 0.375 to 4 inches, although for most structural backfill 

applications, dmax is limited to 1.5 inches (AASHTO 2018a). Because of their relatively large 

void ratios and limited amounts of fine content, OGAs have excellent drainage characteristics, 

low frost-heave potential, easy placement during construction, quick quality assurance for 

compaction, and relatively lower unit weight compared to conventional, well-graded backfills. 

Source: FHWA.

Figure 1. Photo. OGAs as structural backfill in a geosynthetic reinforced soil abutment.

Over the past decade, the Federal Highway Administration (FHWA) has made a concerted effort 

to better understand and quantify the engineering properties of OGAs. Strength-deformation 

characteristics, such as shear strength (τ) (i.e., friction angle) and dilation behavior (i.e., dilation 
2 

angle), which were assessed using large-scale laboratory testing devices, were of primary interest

(Nicks and Adams 2013; Nicks et al. 2015; Gebrenegus et al. 2015; Gebrenegus et al. 2017; 

Nicks et al. 2021). For large-scale direct shear (LSDS) testing in particular, all of the testing 

conducted by FHWA was performed on a single type of LSDS device (figure 2) in FHWA’s 

Geotechnical Laboratory at the Turner-Fairbank Highway Research Center (TFHRC). In 

addition, the OGAs evaluated, ranging from an AASHTO No. 5 to an AASHTO No. 10, largely 

came from a single source with identical mineralogy. 

Source: FHWA.

Figure 2. Photo. LSDS devices at TFHRC.

To address the limitations in previous FHWA studies, including use of a single type of LSDS 

device, limited OGA rock types, and a single laboratory technician conducting the tests, FHWA 

initiated an interlaboratory, round-robin study. The purpose of this study was to evaluate the 

variability of engineering properties for three common OGA gradations (i.e., No. 57, No. 68, and 

No. 8). TFHRC and five other laboratories in the United States with LSDS devices were 

included in the study. Each laboratory was sent three OGA gradations obtained from five 

different quarries. Each quarry had different geologic conditions and mineralogy (i.e., basalt 

(BA), diabase (DI), granite-gneiss (GG), limestone (LI), and siltstone (SI)). Each laboratory 

therefore tested 15 different OGAs; for 6 laboratories, a total of 90 OGAs were evaluated in this 

study. 

Each laboratory measured the as-received gradation of each OGA; minimum and maximum dry 

unit weights; secant, tangent, residual, and constant volume friction angles; apparent cohesion 

(ca); and maximum dilation angles. A statistical analysis of all the relevant data was also 

performed to determine mean (x̄) values, standard deviations (s), and coefficients of variation

(COV). The associated statistical distributions for the key engineering parameters were also 

determined. 
3 

The results of this interlaboratory study can be used by designers to assess more reasonable 

values for geotechnical designs, by agencies to update or develop relevant material 

specifications, and by contractors to select structural backfills for a project. Additionally, 

researchers can use the results to evaluate the reliability of various design methods and calibrate 

load and resistance factors in the framework of load and resistance factor design (LRFD). The 

results may also lay the foundation for the development of new test standards and specifications 

for LSDS testing of structural backfills like OGAs by organizations like AASHTO and ASTM

International. 

BACKGROUND

The engineering properties of construction materials like soils and aggregates play a large role in 

the design of transportation earthworks. These properties impact calculations related to lateral 

earth pressure (σh), nominal bearing resistance, settlement, lateral deformation, and more. 

Therefore, using appropriate input values for geotechnical design parameters such as friction 

angle, cohesion, and unit weight is of utmost importance. Oftentimes, in the absence of testing, 

preliminary, or default, values for these parameters are used. For example, a typical default value 

of 34 degrees is frequently specified by designers for the friction angle of any soil or aggregate 

used as a structural backfill. Another alternative for coarse-grained materials is to perform 

conventional testing on a reduced size sample, prepared either through scalping or a parallel 

gradation technique. In either case (i.e., using a default value or using a scalped sample), the 

tradeoff is that the actual strength of the coarse-grained soils (e.g., OGAs) could be 

underestimated, and/or the dominant behaviors of such materials during shear, such as crushing, 

rearrangement or interlocking, and dilation may not be captured. 

The introduction of LSDS devices in geotechnical laboratory testing addresses many of these 

concerns. However, even with larger devices, other uncertainties arise in measuring design 

properties. For example, no existing industry standards (i.e., AASHTO, ASTM) specify the 

“correct” configuration of a LSDS device (e.g., fixity of the stationary box, connection between 

the platen and the normal load, application of load), and no noted differences in the associated 

test procedures, which were initially developed for soils, exist (e.g., gap size, strain rate). Since 

no common industry standard controls the device configuration and test procedure, their 

influence on the sample behavior during shear, and thus the measured parameters, is not well 

known. 

A conservative design is generally associated with high construction costs or, at the very least, an 

underestimation of in-service performance. The discussion in the following paragraphs 

demonstrates wide variations in engineering properties of OGAs illustrating how unrealistic 

default values could be if applied blindly. For example, previous work by FHWA suggested that 

an estimate of 40 degrees for the friction angle may be more appropriate for OGAs (Nicks et al. 

2015) compared to the conventional default value of 34 degrees; this difference represents a 

nearly 30 percent decrease in computed σh values. 

Engineering Properties of Structural Backfills

Since soils (and rocks) are naturally occurring materials, their fundamental behavior is not as 

well understood or as straightforward as manmade materials. Manmade materials like steel or 

concrete can be engineered to specifically suit design requirements. To combat this issue for 
4 

most transportation earthworks, and to achieve a more desired behavior, structural backfills are 

often used as an alternative to the native material at a site. These backfills can be better 

controlled and have better engineering properties. 

Common structural backfills include well-graded materials and OGAs. Well-graded backfills are 

recommended for applications such as mechanically stabilized earth walls (Berg et al. 2009), 

whereas OGAs for geotechnical infrastructure applications were introduced only recently in 

FHWA guidance for geosynthetic reinforced soil abutments and integrated bridge systems 

(Adams et al. 2011). The key physical and strength-deformation characteristics of structural 

backfills, such as unit weight and τ, are thought to largely depend on the gradation (e.g., 

maximum aggregate size, uniformity, fines content), saturation level, shape (e.g., angularity, 

sphericity (SP), texture (TX), durability (e.g., abrasion resistance, soundness), and mineralogy of 

the material. 

While all structural backfills are commonly assumed to be free draining, and thus will not result 

in a buildup of hydrostatic pressures against the back of retaining walls (Gomez et al. 2014), the 

unit weight and shear strength may still be impacted by the presence of water. The maximum dry 

unit weight of structural backfills is measured using a Standard/Modified Proctor test (AASHTO 

T 99/AASHTO T 180) for well-graded aggregates and a vibratory table test (ASTM 

D4253/ASTM D4254) for OGAs (AASHTO 2018a, AASHTO 2018b, ASTM 2016b, and 

ASTM 2016c). Well-graded aggregates naturally result in higher unit weights than OGAs. For 

example, based on standard Proctor tests for 16 well-graded aggregates commonly used in 

Virginia, maximum dry unit weights ranged from 131.8 to 155.8 lb/ft3

 (Hossain and Lane 2015). 

In contrast, maximum dry unit weights of 101.3 to 115.9 lb/ft3

 have been reported by Nicks et 

al. (2015) and Nicks et al. (2018) for OGAs.

Shear strength is traditionally determined through triaxial tests (ASTM D7181) and/or direct 

shear (DS) tests (ASTM D3080) (ASTM 2011b, ASTM 2011a). For structural backfills, 

large-scale versions of the test devices are required. Focusing solely on LSDS tests of structural 

backfills, tangent friction angles (φt) up to 54 degrees for well-graded aggregates used in 

geosynthetic reinforced soil applications, have been reported (Adams and Nicks 2018; 

Abu-Hejleh et al. 2000). The strength of OGAs is similar, with reported friction angles ranging 

from 37 to 58 degrees (Nicks and Adams 2013; Nicks et al. 2015; Nicks et al. 2021; 

Stallings 2020; Abu-Farsakh et al. 2020). These results indicate that structural backfills are 

stronger than the conservative default value of 34 degrees commonly used in preliminary design 

calculations.

Regardless of the backfill type and the methods to measure their engineering properties, large 

uncertainties in these properties can result from many disparate sources. According to Phoon and 

Kulhawy (1999), three primary sources of uncertainty exist: inherent variability, measurement 

error, and transformation uncertainty. Of particular interest to this study is measurement error, 

and, to some degree, the inherent variability in blasting and sampling of the aggregate stockpile. 

Variability in measurements is related to equipment, procedure(s), operator(s), and random 

testing effects related to inaccuracies and error; an interlaboratory study is one approach to 

quantify measurement errors. Examples related to the variability of physical properties and 

characteristics and the τ of soils and aggregates are presented in the following subsections. 
5 

Variability of Physical Properties and Characteristics

The physical properties and characteristics of interest in this study were unit weight (i.e., 

density), aggregate shape factors, and abrasion resistance. Limited studies are available in the 

literature on the variability of these physical properties (Yoshimi and Tohno 1973; Hamidi et 

al. 2013; Ganji 2019; Gates et al. 2011; Cuelho et al. 2007; Hossain et al. 2007). Therefore, the 

variabilities often reported by the standard test procedures can serve as a guide for assessing the 

x̄, s, COV, and acceptable range (AR) of values for the applicable parameter (table 1). 

Table 1. Reported variabilities of select physical properties and characteristics.

Parameter Soil Type

Variability Between Laboratories

x̄ S Reference

COV 

(%) AR

Minimum 

dry unit 

weight Poorly graded sand

97.54 lb/ft3 2.63 lb/ft3 2.70 7.3 lb/ft3 D4254 

(ASTM 2016c)

Maximum 

dry unit 

weight

116.9 lb/ft3 1.8 lb/ft3 1.54 5.1 lb/ft3 D4253 

(ASTM 2016b)

Angularity

Gravel

(0.5 inches) 

2777.9 119.3 4.3 12.2% Gates et al.

(2011)

SP 0.69 0.0133 1.9 7.4% Gates et al.

(2011)

TX 233.6 16.3 7.0 20.0% Gates et al.

(2011)

MicroDeval+ 

abrasion

resistance

— 5% 0.5% 10 28% T 327-12 

(AASHTO 2020)

L.A. 

abrasion 

resistance

21% 1.11% 5.3 15%

— — — 6.4 18.1% C535

(ASTM 2016a)

—Not specified. +Statistics provided are for the lowest and highest aggregate abrasion loss reported in AASHTO T 327 

(AASHTO 2020b).

Variability of Shear Strength 

The mechanical properties of interest in this study were τ (i.e., friction angle and ca) and 

maximum dilation angle. Several researchers have investigated the sources of τ variability, as 

measured through DS testing. Some of the investigated sources of variability include the size and 

shape of the specimen (Cerato and Lutenegger 2006; Bareither et al. 2008b; Wu et al. 2008; 

Dadkhah et al. 2010; Sobol et al. 2015; Altaf et al. 2016), the gap size between the upper and 

lower shear boxes (Kim et al. 2012), and the shear displacement rate (Mamo and Dey 2014). All 

these studies were based on sand samples except for the study by Sobol et al. (2015), where

recycled concrete aggregates were tested. 

On the effect of specimen size, Cerato and Lutenegger (2006) found that the measured friction 

angles generally decreased with an increase in box size; friction angles were up to 10 degrees 
6 

higher in a 2.4-inch (60 mm) box than in a 12-inch (305 mm) box. Bareither et al. (2008a) also 

reported a decrease in friction angle with an increase in specimen size, but the effect was much 

smaller; an average tangent friction angle of 42.6 degrees was obtained for the 2.5 inch (64 mm) 

square box compared to a 40.5-degree angle for the 12-inch (305 mm) square box. The effect of 

specimen/box shape on friction angles was reported by Altaf et al. (2016) who found that using a 

circular shear box resulted in friction angles 2 to 3 degrees higher compared to a square shear 

box. To evaluate the effect of gap size between the upper and lower DS boxes, Kim et al. (2012) 

performed tests using seven types of sand at six different gap sizes ranging from 0.008 inch 

(0.2 mm) to 0.16 inch (4.0 mm). The results of this study indicated that the peak shear strength 

generally decreased with an increase in opening size due to outflow of the sands between the 

gap. On the effect of shear displacement rate, Mamo and Dey (2014) investigated the influence 

of different strain rates (i.e., 0.0014, 0.0069, and 0.035 percent lateral displacement per second) 

for sand specimens prepared at 70 percent and 85 percent relative densities (RDs). The tangent 

friction angle increased slightly with an increase in strain rate; from 42.5 to 46.5 degrees at 

70 percent RD and from 44.8 to 48.2 degrees at 85 percent RD. 

There have been limited round-robin studies to quantify the variability of shear strength

parameters and, to a lesser degree, deformation behavior of granular materials (Converse 1952; 

Bareither et al. 2008b). In the work reported by Converse (1952), seven laboratories performed 

stress- and strain-controlled DS tests on Ottawa 20-30 sand (OS-20-30) in loose and dense states; 

the findings from only the strain-controlled DS tests from three laboratories are presented herein. 

For the dense sands, the measured peak friction angles ranged from 29.3 to 43.2 degrees, with an 

average of 36.1 degrees and a COV of 19.1 percent; for sands tested in the loose state, peak 

friction angles were lower, ranging from 23.8 to 32.0 degrees, with an average and COV of 

27.5 degrees and 14.9 percent, respectively. Residual (i.e., ultimate) friction angles were also 

computed for OS-20-30, and COVs of 18.6 and 21.9 percent were reported for the loose and 

dense states, respectively. Converse (1952) suggested that the variability in the measured friction 

angles was associated with the details of the equipment and procedures, such as loading methods 

and rates, shear box dimensions, specimen thickness, and the gap size between shear boxes. The 

work eventually led to the development of a standard test method for DS testing of soils (i.e., 

ASTM D3080) (ASTM 2011a). 

The interlaboratory study conducted by Bareither et al. (2008b) included 10 laboratories. Each

laboratory performed inundated DS testing on four homogeneous granular backfill materials. All 

the materials were classified as poorly graded (i.e., open-graded) sands. Eight of the shear boxes 

were circular and two were square. The results from this study showed variability in the MohrCoulomb failure envelopes and the resulting tangent friction angles (with COVs ranging from 

8.6 to 15.3 percent). This study also reported a wide variation in volume change behavior (i.e., 

dilation and contraction) among the laboratories; however, the dilation angles were not 

quantified. Based on the results presented in this study, interlaboratory variability was also 

observed through the dilation angle, the maximum vertical strain at peak shear stress, and the 

horizontal strain where the maximum contraction of the sample occurred. The same sources of 

variability discussed earlier, including sample thickness, gap size, and displacement rate, along 

with differences in the frequency of data collection, attributed to the variability of 

strength-deformation behavior in their interlaboratory study. 

Greco (2016) provided a theoretical basis to evaluate uncertainties and variabilities in cohesion 

and friction coefficient values as measured through DS testing and included an extensive 
7 

literature review documenting reported values by other researchers. In Greco’s literature review, 

the COV for the friction coefficient (and thus friction angle) was reported to be between 10 and 

20 percent for a wide range of soils—from clays to rock fills. The reported COV for cohesion 

was between 20 and 60 percent. The variabilities for both strength parameters were generally 

considered inherent due to variations resulting simply from the magnitude of normal stress 

applied during DS testing but were also partially attributed to measurement error.

In order to have a comprehensive understanding of the variability due to measurement error, 

interlaboratory studies should include and document different configurations of DS devices so 

their influence can be analyzed. Configurations of interest include the connection between the 

normal load and the loading platen, the connection between the loading platen and the upper 

shear box, the mobility of the upper box relative to the specimen during shear, and so on. The 

following subsections highlight some of these variations in DS testing and DS device 

configurations. 

DS Testing 

A DS test is commonly used to determine the shear strength and dilation behavior of soils and 

aggregates. Despite its limitations in having a predetermined horizontal failure plane and 

nonhomogeneous stress state, DS tests are popular in practice due to their operational simplicity 

and the wide spectrum of geomaterials that they can test without the need for highly specialized 

personnel (Taylor 1953; Shibuya et al. 1997; Cerato and Lutenegger 2006). DS tests have been 

in use for nearly three quarters of a century, and their history for engineering applications is well 

documented by Matthews (1988). 

DS Devices

Shibuya et al. (1997) and Kim et al. (2012) reviewed the types of DS devices that have been used 

since the 1950s and classified them into three different types (i.e., types A, B, and C), based on 

the configuration of the upper box, loading platen, and ram (figure 3). In type A, devised by 

Skempton and Bishop (1950), the top platen is connected to the loading ram with a hinge or ball 

bearing and is independent of the mobile upper shear box. Type B, devised by Jewell and Wroth 

(1987), is like type A except for the fixity of the top platen with respect to the loading ram and 

the mobile upper shear box. In type C, the upper shear box is fixed and independent of the top 

platen, which is fixed to the loading ram. 
8 

Source: FHWA.

Figure 3. Illustration. Basic types of DS boxes, as described by Shibuya et al. (1997).

ASTM D3080 includes the following requirements, which dictate the size of the DS device 

relative to the size of the soil sample being tested (ASTM 2011a): 

• The sample width or diameter must be at least 2 inches (50.8 mm). 

• The minimum sample thickness must be approximately 0.5 inches (12.7 mm) but no less 

than six times the maximum particle size (dmax). 

• The minimum sample width or diameter to thickness ratio must be 2 to 1. 

• The width of the specimen must be at least 10 times dmax. 

DS Test Procedures

DS testing is commonly performed per ASTM D3080 or AASHTO T 236 (ASTM 2011a; 

AASHTO 2018). Both test procedures determine the consolidated drained shear strength of a soil 

in DS by deforming the specimen along a predesignated horizontal shear plane between the two 

shear box halves. However, some differences between the two standards related to shearing, 

inundation, gap size, and data collection frequency exist. For example, the ASTM method is 

performed in single shear with optional inundation, whereas the AASHTO method may be 

performed in either single shear or in double shear under inundation. Another difference is that 

the tests in ASTM are displacement controlled, whereas in the AASHTO method, stresscontrolled tests are also allowed. For simplicity, only ASTM D3080 is further discussed in this 

report (ASTM 2011a). 

Note that DS tests were originally developed to test soils; therefore, the impact of the associated 

test procedures within ASTM D3080 for structural backfills, such as OGAs, has not been fully 

evaluated, but modifications to the test procedure have been noted by FHWA in the past (Nicks

et al. 2015). Regardless of the soil or aggregate being tested, the primary test procedures that can 

impact the results of DS testing include the following: the compaction level of the specimen; the 

filling of the shear box with water; the time allotted for the consolidation stage; the gap size 

 
9 

between the two shear box halves; the selection of the shear displacement rate; and the frequency

of data collection.

REPORT OVERVIEW

Given the limited work performed on OGAs and whether the variability found for soils is 

accurate for these structural backfills, this FHWA round-robin study is timely and will aid in a 

better understanding of the behavior of OGAs during shear in different LSDS devices and the 

resulting variability of their engineering properties. The information and key findings from this 

study serve to assist owners in selecting reliable design parameters when OGAs are specified for 

a project. The chapters in this report are organized as follows:

• Chapter 2 describes the test program, including the materials, sampling methods, and 

laboratory tests and associated procedures followed as part of the round-robin study. 

• Chapter 3 provides all of the test results defining the physical properties and 

characteristics (e.g., particle size, particle breakage, dry unit weight, bulk dry specific 

gravity, shape factors, and abrasion resistance and durability) and the 

strength-deformation characteristics (e.g., friction and dilation angles) of the OGAs 

evaluated; results from the standard OS-20-30 are also presented as a baseline for 

comparison. Basic statistics such as x̄, s, and COV are presented for each parameter 

evaluated. 

• Chapter 4 presents the in-depth analysis of the results, including the determination of 

parameter distribution types through histograms, normal probability plots, and a 

goodness-of-fit test; an investigation into the impact of stone size, mineralogy, and 

laboratory on the results through analysis of variance (ANOVA); and insights into the 

influence various LSDS device characteristics and procedures have on the results. Given 

the analysis, implications to geotechnical practice are also presented.

• Chapter 5 summarizes the main conclusions and key findings from the study. Lessons 

learned from setting up a round-robin study and the subsequent data analysis are also 

presented, along with future research plans. 

• Appendixes A–E are provided to deliver all the results for each OGA tested by each 

laboratory (i.e., round-robin test instructions, pre- and post-shear sieve data, AIMS2 and 

LSDS data), along with additional information and steps to detail the analysis presented 

in chapter 4.

11 

CHAPTER 2. TEST PROGRAM

This chapter provides details on the test program employed in this study. It includes the materials 

selected, the sampling procedures for those materials, the various laboratory tests performed to 

determine the physical characteristics and shear strength of the materials, and key details of the 

six independent laboratories participating in this round-robin study. Differences between the test 

devices used by the laboratories are noted. 

MATERIALS

The materials included in the interlaboratory round-robin study were OGAs; however, 

OS-20-30 was also included as a standard soil for a comparison of the results between the 

different laboratories. 

OS-20-30 

OS-20-30 is a standard sand per ASTM C778; it is a naturally rounded, poorly graded silica sand 

mined from the areas of Ottawa, IL and Le Sueur, MN. As the name suggests, OS-20-30 has a 

gradation that predominantly passes a No. 20 sieve but is retained on a No. 30 sieve (table 2) 

(ASTM 2017). Bags of OS-20-30 were procured and delivered by the supplier directly to each 

laboratory for testing.

Table 2. ASTM C778 OS-20-30 gradation requirements (ASTM 2017). 

Sieve Particle Size (inches) Percent Passing

No. 16 0.046 100

No. 20 0.033 85–100

No. 30 0.024 0–5

OGAs

Three types of OGAs meeting the AASHTO M 43-05 specifications were selected for this study: 

No. 57, No. 68, and No. 8 (table 3) (AASHTO 2018a). These specific OGA classifications were 

chosen to span the range of the AASHTO M 43-05 gradations more commonly used in 

geotechnical applications (AASHTO 2018a). Since quarries around the country vary in geology, 

five different rock types for each OGA gradation were evaluated in this study, all obtained from 

different quarries in Virginia. These rock types included BA, DI, GG, LI, and SI, which 

represent the entire spectrum of geologic rock formations, including igneous, metamorphic, and 

sedimentary rocks. The five selected rock types (figure 4) were verified through petrographic 

analysis performed by the Aggregate and Petrography Laboratory at TFHRC following modified 

ASTM C295 procedures (ASTM 2018). 
12 

Table 3. Selected AASHTO M 43-05 stone size designations (AASHTO 2018a).

Sieve Particle Size (inches) 

Percent Passing

No. 57 No. 68 No. 8 

1.5 inches 1.5 100 — — 

1 inch 1.0 95–100 100 — 

3/4 inch 0.75 — 90–100 — 

1/2 inch 0.50 25–60 — 100 

3/8 inch 0.375 — 30–65 85–100 

No. 4 0.187 0–10 5–25 10–30 

No. 8 0.093 0–5 0–10 0–10 

No. 16 0.046 — 0–5 0–5 

—Not specified.

Source: FHWA.

Figure 4. Photos. Rock types for the OGAs evaluated.
13 

The total number of OGAs tested by each laboratory was 15 (i.e., 3 OGA stone size 

classifications, each with 5 different rock types). Nomenclature was established for each 

combination of aggregate and rock type (see table 4). The identity of the participating 

laboratories is withheld in this report; instead, each of the six laboratories included in this 

round-robin study was assigned an alphanumeric designation (i.e., L01, L02, L03, L04, L05, and 

L06), which was incorporated at the end of the sample IDs shown in table 4

(e.g., No. 57-BA-L01). This study resulted in a total number of 90 samples tested. 

Table 4. OGA sample nomenclature.

Stone Size Rock Type Sample ID

No. 57 

Basalt No. 57-BA

Diabase No. 57-DI

Granite-Gneiss No. 57-GG

Limestone No. 57-LI

Siltstone No. 57-SI

No. 68 

Basalt No. 68-BA

Diabase No. 68-DI

Granite-Gneiss No. 68-GG

Limestone No. 68-LI

Siltstone No. 68-SI

No. 8 

Basalt No. 8-BA

Diabase No. 8-DI

Granite-Gneiss No. 8-GG

Limestone No. 8-LI

Siltstone No. 8-SI

OGA Sampling

Each OGA was first delivered in 5-ton stockpiles to TFHRC. To ensure consistency among the 

OGA samples delivered to and tested by each laboratory, a procedure was established to 

randomly collect samples from the bottom, middle, and top layers of the stockpiles. Four 5-gal 

buckets were filled for each laboratory (figure 5). On average, approximately 275 lb of each 

OGA were sent to each laboratory for testing. As will be discussed in the Initial Sieve Testing

section later in this chapter, each laboratory performed a sieve analysis on the as-received 

samples. The variation in these initial gradations will be noted in chapter 3. 
14 

Source: FHWA.

Figure 5. Photo. Stockpile of aggregates at TFHRC for random sampling. 

LABORATORY TESTING

Six commercial and research laboratories participated in the round-robin study. Six is the 

minimum number required for interlaboratory studies per ASTM C802; this number allows for a 

reasonable evaluation of reproducibility for a given construction material test method

(ASTM 2014). 

Sequence of Round-Robin Testing

Six rounds of testing were conducted in this study. The sequence of materials sent to each 

laboratory is shown in table 5. The OGAs were selected for the first five rounds because the 

primary objective of the study was to define the variability of their physical properties and 

characteristics and shear strength. The last round (i.e., round 6) was specifically selected to 

further evaluate the test devices in each laboratory using a standard soil (i.e., OS-20-30). 
15 

Table 5. Round-robin test order.

Round No. Soil Type Rock Type

1 OGA DI

2 OGA LI

3 OGA GG

4 OGA BA

5 OGA SI

6 OS-20-30 Quartz

Sequence of Laboratory Testing

OGA testing for this study included the following in sequential order: sieve testing on the 

as-received materials; minimum and maximum density testing; LSDS testing; and post-shear

sieve testing. While not included in the interlaboratory study, FHWA also separately 

characterized the shape (i.e., angularity, SP, percentage of flat and elongated (F&E) particles, 

and TX) and abrasion resistance for each rock type using the aggregate image measurement 

system 2 (AIMS2) and the Micro-Deval devices at TFHRC, respectively. For the OS-20-30, only 

LSDS testing was performed by each laboratory; however, FHWA performed all other 

applicable tests (e.g., sieve analysis, minimum and maximum density testing, and AIMS2).

Sample Preparation

FHWA developed a protocol and set of instructions for consistent preparation of each OGA test 

sample by each laboratory (appendix A). The basic steps for each laboratory included first oven 

drying all four buckets received for each OGA sample at 212 °F and then blending and 

separating the oven-dried OGAs to appropriate test sizes using a quartering method as per 

AASHTO T 248—Method B (AASHTO 2014). 

Initial Sieve Testing

Dry sieving was performed on the as-received samples per ASTM C136 (2019). This action 

facilitated a comparison with the AASHTO M 43-05 gradation specifications for a given sample. 

It also allowed for an analysis of the range and variability in OGA gradations meeting the 

specification as well as an evaluation of the impact of gradation (i.e., stone size) on the strengthdeformation characteristics of OGAs. In addition, the gradation curves provided the aggregate 

size in which 85 percent of the material is smaller (D85); D85 is used by FHWA to define the gap 

size between the upper and lower shear boxes in LSDS testing (Nicks and Adams 2013).

Minimum and Maximum Density Testing

The minimum dry unit weight (γdmin) and maximum dry unit weight (γdmax) for each OGA sample 

were determined using Method A of ASTM D4254-16 and Method 1A of ASTM D4253-16 

(vibratory table method), respectively (ASTM 2016c, ASTM 2016b). As allowed by the ASTM 

D4253-16 standard (ASTM 2016b), all but one of the laboratories performed the maximum 

density tests using a shake table. L05 used a universal testing machine as the platform instead. 

Most of the laboratories (i.e., L01, L03, L04, and L06) conducted the maximum density tests at a 
16 

frequency of 60 Hz for a duration of 8 min such that the mold had a double amplitude of vertical 

vibration of 0.013 inch. L05 cycled at 50 Hz with a peak-to-peak amplitude of 0.019 inches, and 

L02 did not characterize or report the frequency or amplitude used in their testing. The results of 

these tests allowed for the determination of the dry unit weight at 95 percent relative density 

(γd95) for each OGA sample (equation 1); γd95 was specified as the target dry unit weight for 

LSDS testing.

(1) 

Where 95RD denotes 95 percent relative density.

LSDS Testing

LSDS tests were performed per ASTM D3080 (2011) to determine the secant (φs), tangent (φt), 

residual tangent (φt,r), and constant volume (φcv) friction angles, along with the maximum 

dilation angles (ψmax) and ca for each sample type. The following testing conditions were 

specified:

• All shear tests were performed under dry conditions (i.e., no saturation of the samples).

• Placement of the OGAs in the shear box required compaction to 95RD for each sample.

• A constant shear rate of 0.015 inch/min was maintained throughout the test for all

samples.

• The gap between the upper and lower boxes was set at D85 for each sample.

• The applied normal stress (σn) values were 5, 10, 15, and 30 psi to cover the typical stress

ranges for most geotechnical applications where OGAs are used.

• The end point for termination of each LSDS test was set at 20 percent horizontal strain

(e.g., 2.4 inches for a 12-inch square box).

Each laboratory included in the round-robin study had a different type of LSDS device. The 

configurations for each device are presented in table 6 with the corresponding schematics shown 

in figure 6. Key differences between the LSDS devices included the mobility of the upper shear 

box, the connection between the loading platen and the normal load, the shear box dimensions, 

the number of linear variable differential transformers (LVDTs) to measure vertical 

deformations, the method of load application for normal and shear loads, and the capacity of the 

load cells used to measure the loads (table 6). Other differences not necessarily related to the 

LSDS device itself included the sample dimensions for testing and the frequency of data 

collection for load and displacement.
17 

Table 6. LSDS device and testing configurations.

Lab ID 

and 

Type+

LSDS 

Specimen 

Shape

Upper 

Shear 

Box 

Mobility

Base of 

Top 

Platen/ 

Spacer

Connection 

Between 

Loading 

Platen and 

Normal 

Load

Nominal 

Bottom 

Shear Box 

Dimensions

(inch × inch

× inch)*

Nominal 

Specimen 

Dimensions

(inch × inch × 

inch)*

Number 

of 

Vertical 

LVDTs++

Normal 

Load 

Application

and 

Capacity 

(kips)

Horizontal 

Load

Application

and Capacity 

(kips)

Typical 

Time Step 

for Data 

Collection 

(s) 

L01

(C) Square Mobile Smooth Fixed 12 × 12 × 12 12 × 12 × 6 4 

Micro 

stepper 

motor (50.0) 

Micro stepper 

motor (50.0) 16

L02

(C/R) Square Fixed Grooved Not fixed 12 × 12 × 8 12 × 12 × 7 3 

Airbag/

Hydraulic**

(14.4/20.0) 

Hydraulic 

(12.5) 24

L03

(C) Square Mobile Grooved Not fixed 15 × 12 × 6 12 × 12 × 6 2 

Dead 

weight/ 

Airbag*** 

(20.0) 

Step motor 

system (20.0) 80^

L04

(C) Square Mobile Textured Fixed 12 × 12 × 7.5 12 × 12 × 6 1 Hydraulic (20.0) 

Hydraulic 

(12.0) 200^

L05

(R) Circular Fixed Smooth Fixed 12 × 8 12 × 7.5 1 Hydraulic (45.0) 

Hydraulic 

(67.4) 1 

L06

(R) Square Fixed Smooth Not fixed 12 × 12 × 8 12 × 12 × 7.5 4 

Micro 

stepper 

motor (20.0) 

Micro stepper 

motor (20.0) 40

+C = commercial; R = research. 

*Interior dimensions shown as length × width × height (square specimen) or diameter × height (circular specimen). ++Results presented in the report represent averages of all LVDT measurements.

**Airbag for the DI OGAs; hydraulic loading for all other OGA rock types. 

***Dead weight was used for 5 and 10 psi normal stresses; airbag was used for 15 and 30 psi normal stresses. ^

Actual time step varied at different intervals throughout testing; representative value shown. 
18 

Source: FHWA.

*Dead weight for lower normal loads.

Figure 6. Schematics. LSDS device configurations for each laboratory with dimensions in

inches.

Post-Shear Sieve Testing

After LSDS testing, dry sieve tests per ASTM C136 (2019) were again performed by each 

laboratory on each OGA sample. The sample for post-shear sieve testing was prepared by 

 
19 

blending the aggregates used for each of the four-point LSDS test series into a single pile and 

performing the same sample reduction procedure used previously. This sequence of events 

allowed for an evaluation of particle breakage after each OGA type was sheared to failure (i.e., 

20 percent horizontal strain). While this information is not used in design, it does provide an 

indication of the strength of the aggregates and may allow for the evaluation of the differences 

between different LSDS devices.

AIMS2 Testing

The AIMS2 device at TFHRC was used to characterize the shape factors (e.g., angularity, SP, 

percentage of F&E particles, and TX) for each OGA rock type (i.e., BA, DI, GG, LI, and SI) and 

the OS-20-30. This testing was performed solely by FHWA. The shape factors of the materials 

tested should be independent of the laboratory and were not a key variable in the round-robin 

study. In addition, the variability of AIMS2 results has already been established as part of the 

development/refinement of the device, as research performed by Gates et al. (2011) explains 

(noted in chapter 1). AIMS2 testing was performed per AASHTO T 381 (2018e). 

Micro-Deval Testing

Since different geologic sources were selected for this study, the abrasion resistance of each 

OGA rock type was evaluated solely by FHWA to determine their relative durability and the 

potential impact on τ. The quarries provided results of Los Angeles (L.A.) abrasion testing and 

magnesium sulfate soundness testing for the OGAs delivered (shown in chapter 3). To 

supplement those results, the abrasion resistance of each rock type (e.g., BA, DI, GG, LI, and SI) 

was also evaluated solely by FHWA using a Micro-Deval apparatus at TFHRC. Micro-Deval 

testing was performed in accordance with AASHTO T 327-12 (AASHTO 2020). 

The Micro-Deval test is typically recommended as a test to measure the abrasion resistance of 

aggregate, while the L.A. abrasion test is better suited as an indirect measure of aggregate 

strength; the sulfate soundness test is widely used to predict the freeze-thaw durability of 

aggregates (Weyers et al. 2005). While not included in the round-robin study, the variability of 

abrasion resistance has already been established (noted in chapter 1).

21 

CHAPTER 3. TEST RESULTS

This chapter presents the physical properties, characteristics, and shear strength of OS-20-30 and 

the three types of OGAs (No. 57, No. 68, and No. 8) tested in the round-robin study. Properties 

not tested by the participant laboratories in the round-robin study were either tested by the 

FHWA Geotechnical Laboratory or came from aggregate stockpile reports by the source 

quarries.

PHYSICAL PROPERTIES AND CHARACTERISTICS

The key physical properties and characteristics tested included particle size and dry unit weight 

as tested by the participant laboratories; the bulk dry specific gravity of each OGA as tested by 

the source quarries; and particle shape (e.g., angularity, SP, percentage of F&E particles, and 

TX), abrasion resistance, and durability as tested by FHWA and source quarries.

Particle Size

Each laboratory conducted dry sieving to characterize the size, uniformity, and variability of the 

as-received OGA gradations. In addition, dry sieving was conducted by each laboratory after 

each four-point LSDS test to roughly quantify the amount of breakage the OGAs experienced as 

a result of shearing to failure (i.e., 20 percent horizontal strain). Dry sieving of OS-20-30 was 

performed solely by FHWA before its delivery to each laboratory. Complete sieve analysis 

results are provided in appendix B. 

As-Received Gradations 

To illustrate the sieve analysis results, the as-received gradation curves for No. 57-LI, No. 68-LI, 

and No. 8-LI are presented in figure 7. 
22 

Source: FHWA.

A. No. 57-LI.

Source: FHWA.

B. No. 68-LI.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
23 

Source: FHWA.

C. No. 8-LI.

Figure 7. Charts. Gradation curves for the as-received LI OGAs.

Note that the AASHTO M 43-05 stone size limits are indicated by vertical bars on the charts at 

the appropriate sieve sizes for comparison. All laboratories, save L06, often included 

intermediate sieves not explicitly required to test for M 43-05 compliance. Nine of the fifteen 

OGAs tested were found by at least one laboratory to not comply with the M 43-05 stone size 

supplied by the source quarries (table 7), although the differences per sieve size was generally 

small (appendix B). The largest discrepancies were found for the GG and SI aggregates, whereby 

18 of the 24 samples did not meet the specification which could suggest quarry practice resulted 

in the noncompliance. 

The noted deviations in the as-received gradation results may also be in part due to variability in 

the stockpiles or due to FHWA packaging procedures when preparing samples from the initial 

5-ton stockpiles delivered by the source quarries. In addition, natural segregation of the 

aggregates during delivery and specimen preparation by the participant laboratories could be 

another source of deviation. Regardless, the results presented in this chapter and the analyses in 

chapter 4 assume that each sample met the appropriate M 43-05 classification for reporting 

purposes (i.e., No. 57, No. 68, or No. 8). Any impacts resulting from noncompliance, however, 

were considered when evaluating the results of all subsequent testing.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
24 

Table 7. As-received gradation test results per AASHTO M 43-05 specifications.

Stone Size Sample ID L01 L02 L03 L04 L05 L06

No. 57 

No. 57-BA ✓ ✓ ✓ ✓ ✓ ✓

No. 57-DI ✓ ✓ ✓ ✓ ✓ ✓

No. 57-GG ✓    ✓ ✓

No. 57-LI ✓ ✓ ✓ ✓ ✓ ✓

No. 57-SI ✓   ✓ ✓ 

No. 68 

No. 68-BA ✓ ✓ ✓ ✓ ✓ ✓

No. 68-DI ✓ ✓ ✓   ✓

No. 68-GG ✓  ✓ ✓  ✓

No. 68-LI ✓  ✓ ✓ ✓ ✓

No. 68-SI ✓ ✓ ✓ ✓ ✓ ✓

No. 8 

No. 8-BA ✓ ✓  ✓ ✓ 

No. 8-DI ✓ ✓ ✓ ✓ ✓ ✓

No. 8-GG ✓    ✓ 

No. 8-LI ✓  ✓ ✓ ✓ ✓

No. 8-SI      

✓ = compliance with the specification;  = noncompliance with the specification.
25 

Beyond testing simply for AASHTO M 43-05 compliance, the as-received sieving data were also 

used to determine relevant gradation parameters for each OGA, namely the D85, or the particle 

size where 85 percent of particles are smaller (table 8).

Table 8. D85 (inch) for as-received OGAs.

Avg. = average.

Figure 8 illustrates the variability of the D85 values presented in table 8. The D85 for each OGA 

sample was used to set the gap size between the upper and lower shear boxes during LSDS 

testing, hence its variability is of primary importance to this study. All laboratories found similar 

D85 values for the OGAs, indicating relatively uniform gradations among the laboratories (and 

thus gap sizes for LSDS testing). The largest variability in gradation occurred for the No. 57 

OGAs, with an average COV of 7.5 percent. Sieve analysis for OS-20-30 was performed solely 

by FHWA, with a D85 (i.e., gap size) of 0.032 inches provided directly to each participant 

laboratory. Sieve analysis for the as-received OS-20-30 was not requested by the participant 

laboratories since the purpose was simply to evaluate differences in behavior due to the LSDS 

device and laboratory procedures using a standard soil. 

Stone 

Size Sample ID L01 L02 L03 L04 L05 L06 x̄ s COV (%)

No. 57 

No. 57-BA 0.73 0.78 0.72 0.75 0.87 0.88 0.79 0.07 8.9

No. 57-DI 0.73 0.72 0.70 0.71 0.84 0.86 0.76 0.07 9.2

No. 57-GG 0.84 0.73 0.85 0.80 0.87 0.90 0.83 0.06 7.2

No. 57-LI 0.77 0.78 0.76 0.76 0.87 0.91 0.81 0.06 7.4

No. 57-SI 0.75 0.86 0.66 0.81 0.85 0.84 0.80 0.08 10.0

No. 57-Avg. 0.76 0.77 0.74 0.77 0.86 0.88 0.80 0.06 7.5

No. 68 

No. 68-BA 0.73 0.65 0.64 0.63 0.66 0.68 0.67 0.04 6.0

No. 68-DI 0.70 0.61 0.68 0.69 0.67 0.68 0.67 0.03 4.5

No. 68-GG 0.60 0.61 0.66 0.63 0.63 0.66 0.63 0.02 3.2

No. 68-LI 0.62 0.60 0.60 0.60 0.63 0.65 0.62 0.02 3.2

No. 68-SI 0.66 0.65 0.61 0.67 0.66 0.68 0.66 0.02 3.0

No. 68-Avg. 0.66 0.62 0.64 0.64 0.65 0.67 0.65 0.02 3.1

No. 8 

No. 8-BA 0.37 0.36 0.43 0.36 0.36 0.37 0.38 0.03 7.9

No. 8-DI 0.36 0.35 0.34 0.35 0.35 0.36 0.35 0.01 2.9

No. 8-GG 0.39 0.37 0.40 0.40 0.37 0.37 0.38 0.02 5.3

No. 8-LI 0.34 0.35 0.35 0.34 0.34 0.36 0.35 0.01 2.9

No. 8-SI 0.37 0.35 0.36 0.35 0.36 0.37 0.36 0.01 2.8

No. 8-Avg. 0.37 0.36 0.38 0.36 0.36 0.37 0.37 0.01 2.7
26 

Source: FHWA.

Figure 8. Chart. D85 for LI OGAs.

Post-LSDS Gradations

For each OGA type tested, the sheared samples after LSDS testing under the four target normal 

stresses were then blended and sieved to determine the post-shear gradation (see appendix B). 

The change in the post-shear gradation was evaluated using the breakage index (BI) described by 

Marsal (1967) (equation 2). 

(2) 

Where Wi and Wf are the initial (i.e., as-received) and final (i.e., post-shear) percentages retained 

for each sieve size evaluated, respectively. 

Only the positive changes in percent retained values were summed to determine the BI for each 

sample (table 9). 

 

 

 

 
27 

Table 9. Breakage index (percent).

Stone 

Size Sample ID L01 L02 L03 L04 L05 L06 x̄ s

COV 

(percent)

No. 57 

No. 57-BA 10.0 9.3 4.3 7.0 1.6 0.4 5.4 4.0 74.1

No. 57-DI 3.0 — 7.6 14.4 2.6 0.0 5.5 5.7 103.6

No. 57-GG 8.1 14.8 7.0 6.0 6.0 0.0 7.0 4.8 68.6

No. 57-LI 6.0 10.3 14.6 4.0 1.7 0.2 6.1 5.4 88.5

No. 57-SI 5.9 21.5 10.2 9.1 9.5 1.4 9.6 6.7 69.8

No. 57-Avg. 6.6 14.0 8.7 8.1 4.3 0.4 7.0 4.6 65.7

No. 68 

No. 68-BA 7.3 6.4 10.5 2.0 7.7 3.7 6.3 3.0 47.6

No. 68-DI 4.0 — 10.4 12.5 3.3 7.5 7.5 4.0 53.3

No. 68-GG 4.2 3.1 13.7 13.0 15.3 0.1 8.2 6.5 79.3

No. 68-LI 3.7 2.9 5.7 7.0 2.4 0.9 3.8 2.2 57.9

No. 68-SI 4.0 15.3 6.5 7.0 3.8 0.6 6.2 5.0 80.6

No. 68-Avg. 4.6 6.9 9.4 8.3 6.5 2.6 6.4 2.5 39.1

No. 8 

No. 8-BA 9.3 4.6 17.8 13.7 2.3 4.6 8.7 6.0 69.0

No. 8-DI 2.0 — 8.4 5.0 4.9 0.6 4.2 3.0 71.4

No. 8-GG 3.2 2.4 3.0 11.2 5.6 9.1 5.8 3.6 62.1

No. 8-LI 7.2 2.8 9.2 10.0 2.7 4.8 6.1 3.2 52.5

No. 8-SI 3.0 8.4 4.0 7.5 2.2 4.4 4.9 2.5 51.0

No. 8-Avg. 4.9 4.6 8.5 9.5 3.5 4.7 6.0 2.4 40.0

—Not measured/evaluated.

The highest BI values were generally found by L03 and L04, whereas the lowest BI values were 

generally found by L05 and L06. The largest variability in breakage occurred for the No. 57 

OGAs, with an average COV of 65.7 percent. To illustrate the difference in breakage results, bar 

charts for the No. 57-LI, No. 68-LI, and No. 8-LI are presented in figure 9. 
28 

Source: FHWA.

Figure 9. Chart. Breakage index results for LI OGAs.

Dry Unit Weight 

Participant laboratories were instructed to test the γdmax and γdmin of the OGAs per ASTM D4253 

(ASTM 2016b) and D4254 (ASTM 2016c), respectively. The dry unit weight at 95 percent 

relative density (γd95) for each OGA was then calculated by the participating laboratories using 

equation 1 (chapter 2). The dry unit weight results were consistent across the laboratories for all 

OGAs for each particular rock type (table 10 through table 12). 

 

 

 

 
29 

Table 10. Dry unit weights for No. 57 OGAs. 

Parameter Sample ID L01 L02 L03 L04 L05 L06 x̄ s 

COV 

(%) 

γdmin (lb/ft3) 

No. 57-BA 96.8 98.4 97.1 97.0 93.6 98.3 96.9 1.7 1.8

No. 57-DI 95.0 98.1 101.7 97.5 96.3 96.2 97.5 2.3 2.4

No. 57-GG 89.0 92.6 90.7 89.5 84.3 89.4 89.3 2.8 3.1

No. 57-LI 84.3 84.4 86.7 87.1 83.2 86.3 85.3 1.6 1.9

No. 57-SI 90.6 87.8 89.1 88.3 87.7 88.3 88.6 1.1 1.2

No. 57-Avg. 91.1 92.3 93.1 91.9 89.0 91.7 91.5 1.4 1.5

γdmax (lb/ft3) 

No. 57-BA 110.5 114.0 109.2 108.7 112.7 114.2 111.6 2.4 2.2

No. 57-DI 106.7 110.9 110.9 110.8 110.8 110.4 110.1 1.7 1.5

No. 57-GG 99.6 103.2 102.2 97.7 100.1 104.6 101.2 2.6 2.6

No. 57-LI 97.3 99.4 98.6 96.3 101.7 99.7 98.8 1.9 1.9

No. 57-SI 105.0 106.4 101.9 100.9 102.4 106.1 103.8 2.3 2.2

No. 57-Avg. 103.8 106.8 104.6 102.9 105.5 107.0 105.1 1.6 1.5

γd95 (lb/ft3) 

No. 57-BA 109.7 113.1 108.5 108.5 111.6 113.3 110.8 2.2 2.0

No. 57-DI 106.0 110.2 110.4 110.1 110.0 109.6 109.4 1.7 1.6

No. 57-GG 99.0 102.7 101.6 97.3 99.1 103.7 100.6 2.5 2.5

No. 57-LI 96.6 98.5 97.9 95.8 100.5 98.9 98.0 1.7 1.7

No. 57-SI 104.2 105.2 101.2 100.2 101.5 105.1 102.9 2.2 2.1

No. 57-Avg. 103.1 105.9 103.9 102.4 104.5 106.1 104.3 1.5 1.4
30 

Table 11. Dry unit weights for No. 68 OGAs. 

Parameter Aggregate L01 L02 L03 L04 L05 L06 x̄ s 

COV 

(%) 

γdmin (lb/ft3) 

No. 68-BA 100.1 97.0 100.8 99.1 98.2 101.8 99.5 1.8 1.8

No. 68-DI 95.9 100.0 100.2 96.3 98.1 95.8 97.7 2.0 2.0

No. 68-GG 86.6 94.5 88.5 89.7 89.2 90.6 89.9 2.6 2.9

No. 68-LI 88.1 85.9 89.5 85.3 84.0 87.6 86.7 2.0 2.3

No. 68-SI 93.6 89.2 92.5 89.3 88.4 90.6 90.6 2.1 2.3

No. 68-Avg. 92.9 93.3 94.3 91.9 91.6 93.3 92.9 1.0 1.1

γdmax (lb/ft3) 

No. 68-BA 116.7 119.1 118.6 115.4 118.8 119.9 118.1 1.7 1.4

No. 68-DI 112.3 115.7 111.2 110.6 111.1 112.7 112.3 1.9 1.7

No. 68-GG 102.0 105.9 104.7 102.6 107.4 105.0 104.6 2.0 1.9

No. 68-LI 98.7 103.4 102.1 100.0 104.9 104.4 102.3 2.5 2.4

No. 68-SI 107.0 106.8 105.0 103.7 105.2 105.0 105.5 1.2 1.1

No. 68-Avg. 107.3 110.2 108.3 106.5 109.5 109.4 108.5 1.4 1.3

γd95 (lb/ft3) 

No. 68-BA 115.8 117.8 117.6 114.5 117.6 118.8 117.0 1.6 1.4

No. 68-DI 111.5 114.8 110.6 109.8 110.4 111.7 111.5 1.8 1.6

No. 68-GG 101.0 105.3 103.8 101.9 106.3 104.1 103.7 2.0 1.9

No. 68-LI 98.1 102.3 101.4 99.2 103.6 103.4 101.3 2.3 2.3

No. 68-SI 106.3 105.8 104.3 102.9 104.2 104.1 104.6 1.2 1.1

No. 68 Avg. 106.5 109.2 107.5 105.7 108.4 108.4 107.6 1.3 1.2
31 

Table 12. Dry unit weights for No. 8 OGAs.

Parameter Aggregate L01 L02 L03 L04 L05 L06 x̄ s

COV 

(%)

γdmin (lb/ft3) 

No. 8-BA 94.6 94.4 94.3 91.8 93.1 96.8 94.2 1.7 1.8

No. 8-DI 87.4 94.7 91.8 86.1 91.1 85.6 89.5 3.6 4.0

No. 8-GG 87.3 95.2 88.7 85.7 87.4 88.1 88.7 3.3 3.7

No. 8-LI 78.8 83.3 81.2 78.7 80.6 80.6 80.5 1.7 2.1

No. 8-SI 88.0 85.1 85.2 84.8 84.8 85.6 85.6 1.2 1.4

No. 8-Avg. 87.2 90.5 88.2 85.4 87.4 87.3 87.7 1.7 1.9

γdmax (lb/ft3) 

No. 8-BA 112.7 113.2 113.9 106.4 112.8 117.6 112.8 3.6 3.2

No. 8-DI 103.7 105.9 106.5 102.8 107.0 106.1 105.3 1.7 1.6

No. 8-GG 100.1 106.3 103.6 98.5 102.3 104.6 102.6 2.9 2.8

No. 8-LI 96.5 100.3 98.9 96.8 102.7 100.8 99.3 2.4 2.4

No. 8-SI 101.9 104.8 103.0 97.6 101.4 103.2 102.0 2.4 2.4

No. 8 Avg. 103.0 106.1 105.2 100.4 105.2 106.5 104.4 2.3 2.2

γd95 (lb/ft3) 

No. 8-BA 111.6 112.1 112.7 105.6 111.6 116.3 111.7 3.5 3.1

No. 8-DI 102.5 105.2 105.7 102.0 106.1 104.8 104.4 1.7 1.6

No. 8-GG 99.5 105.6 102.7 97.8 101.4 103.7 101.8 2.8 2.8

No. 8-LI 95.4 99.3 97.8 95.7 101.4 99.5 98.2 2.3 2.3

No. 8-SI 101.1 103.6 102.0 96.9 100.4 102.1 101.0 2.3 2.3

No. 8 Avg. 102.0 105.2 104.2 99.6 104.2 105.3 103.4 2.2 2.1

This consistency indicates relatively uniform levels of target compaction (i.e., γd95) for LSDS 

testing; see figure 10 as an example. The target unit weight (i.e., γd95) for LSDS testing of 

OS‐20‐30 was provided to each laboratory based on density testing performed solely by FHWA; 

the γd95 for OS-20-30 was 111.0 lb/ft3, and the minimum and maximum dry densities for OS-20-

30 were 98.9 and 111.7 lb/ft3, respectively. 
32 

Source: FHWA.

Figure 10. Chart. γd95 values for LI OGAs.

Bulk Dry Specific Gravity

The bulk dry specific gravity (Gsb) of each OGA was provided directly by the source quarries 

(table 13). The Gsb refers to the ratio of the dry unit weight of the aggregate to the weight of 

water of equal volume. The heaviest rock types were BA and DI, with average Gsb values of 

2.922 and 2.923, respectively; GG was generally the lightest, with an average Gsb of 2.704. 

 

 

 

 

 
33 

Table 13. Reported bulk dry specific gravities for the OGAs.

Stone Size Sample ID Gsb

No. 57 

No. 57-BA 2.923 

No. 57-DI 2.936 

No. 57-GG 2.685 

No. 57-LI 2.716 

No. 57-SI 2.737 

No. 68 

No. 68-BA 2.928 

No. 68-DI 2.908 

No. 68-GG 2.730 

No. 68-LI 2.722 

No. 68-SI 2.737 

No. 8 

No. 8-BA 2.914 

No. 8-DI 2.925 

No. 8-GG 2.697 

No. 8-LI 2.722 

No. 8-SI 2.727 

Particle Characteristics

FHWA performed AIMS2 testing on each OGA sample to evaluate gradient angularity (GA), 

SP, F&E values, and TX. For OS-20-30, FHWA only performed AIMS2 GA testing. SP, F&E, 

and TX could not be evaluated for OS-20-30, per AASHTO T 381, due to the relatively fine 

particle size. Full AIMS2 results for each sample are provided in appendix C. 

Angularity

The cumulative angularity for each sieve size was evaluated individually (appendix C). A 

stockpile approach was taken whereby the weighted average GA indexes were calculated by 

summing the individual angularity results per sieve multiplied by the percentage of material 

retained on that sieve. The weighted AIMS2 GA index results (table 14) show that all tested 

OGAs have low angularity (i.e., average GA index ≤ 3,300, per AASHTO R 91-18) 

(AASHTO 2018b). The AIMS2 results classified OS-20-30 as also having low angularity, 

although the weighted average GA index is an order of magnitude lower than the OGAs 

(table 14). The variability of angularity measurements per sample ID was not evaluated in the 

round-robin study; however, when all OGAs evaluated in this study were combined, the mean 

GA index was 3,069, with a COV of 3.7 percent. 
34 

Table 14. Summary of AIMS2 weighted averages for angularity. 

Stone Size Sample ID Average GA Index GA Classification

No. 57

No. 57-BA 2,948 Low

No. 57-DI 2,957 Low

No. 57-GG 2,934 Low

No. 57-LI 3,177 Low

No. 57-SI 3,031 Low

No. 57-Avg. 3,009 Low

No. 68

No. 68-BA 2,956 Low

No. 68-DI 2,936 Low

No. 68-GG 3,158 Low

No. 68-LI 3185 Low

No. 68-SI 3147 Low

No. 68-Avg. 3,076 Low

No. 8

No. 8-BA 3,131 Low

No. 8-DI 2,922 Low

No. 8-GG 3,147 Low

No. 8-LI 3,209 Low

No. 8-SI 3,192 Low

No. 8-Avg. 3,120 Low

OS-20-30 OS-20-30 674 Low

Sphericity

AIMS2 SP testing was conducted in a similar fashion to angularity, resulting in weighted 

average SP indexes for each OGA (table 15). All OGAs were classified as having medium SP 

(i.e., average SP index between 0.3 and 0.7, per AASHTO R 91-18) (AASHTO 2018b). The 

variability of these SP measurements per sample ID was not evaluated in the round-robin study; 

however, when all OGAs evaluated in this study were combined, the mean SP index was 0.579, 

with a COV of 5 percent. 
35 

Table 15. Summary of AIMS2 weighted averages for SP. 

Stone Size Sample ID Average SP Index SP Classification

No. 57 

No. 57-BA 0.568 Medium

No. 57-DI 0.588 Medium

No. 57-GG 0.607 Medium

No. 57-LI 0.541 Medium

No. 57-SI 0.595 Medium

No. 57-Avg. 0.580 Medium

No. 68 

No. 68-BA 0.626 Medium

No. 68-DI 0.614 Medium

No. 68-GG 0.577 Medium

No. 68-LI 0.527 Medium

No. 68-SI 0.612 Medium

No. 68-Avg. 0.591 Medium

No. 8 

No. 8-BA 0.556 Medium

No. 8-DI 0.567 Medium

No. 8-GG 0.576 Medium

No. 8-LI 0.547 Medium

No. 8-SI 0.580 Medium

No. 8-Avg. 0.565 Medium

F&E Values

The F&E values refer to the ratio of particle length (L) to thickness (S). Table 16 provides the 

distribution of the F&E values for different L/S ratios; F&E values greater than 5:1 are indicative 

of an exceptionally elongated shape. The No. 8 OGAs had the highest average percentages for 

F&E values of 3:1, 4:1, and 5:1 (i.e., the least spherical) while No. 57 OGAs had the least. The 

DI and GG OGAs exhibited the least F&E of greater than 5:1 percent. 
36 

Table 16. Summary of AIMS2 weighted averages for F&E values. 

Stone Size

Flat and Elongated Distribution (%)

L/S ≥ 1:1 L/S > 2:1 L/S > 3:1 L/S > 4:1 L/S > 5:1 

No. 57

No. 57-BA 98.0 73.3 33.6 13.8 7.7

No. 57-DI 96.8 79.6 42.3 16.9 3.6

No. 57-GG 99.4 68.5 23.8 10.8 2.0

No. 57-LI 96.9 80.9 38.6 16.6 7.2

No. 57-SI 93.8 81.6 43.1 20.4 8.8

No. 57-Avg. 97.0 76.8 36.3 15.7 5.9

No. 68

No. 68-BA 86.4 67.8 30.1 12.0 6.3

No. 68-DI 94.2 85.6 43.8 16.8 4.7

No. 68-GG 95.9 81.5 46.0 18.1 7.5

No. 68-LI 90.1 87.6 66.5 32.9 11.6

No. 68-SI 92.0 82.6 45.7 20.3 9.4

No. 68-Avg. 91.7 81.0 46.4 20.0 7.9

No. 8

No. 8-BA 80.6 73.4 57.1 38.9 21.8

No. 8-DI 82.6 78.3 49.1 22.0 9.3

No. 8-GG 92.0 83.6 50.8 31.1 11.4

No. 8-LI 74.2 67.8 50.1 31.8 19.9

No. 8-SI 76.8 72.2 46.9 23.8 16.4

No. 8-Avg. 81.2 75.1 50.8 29.5 15.8

Surface TX

AIMS2 surface roughness measurements and weighted average TX indexes were prepared for all 

OGAs (table 17). TX classifications ranged from medium (i.e., average TX index values between 

260 and 550 per AASHTO R 91-18) to high (i.e., average TX index values between 550 and 

1,000) roughness without an obvious trend associated with stone size. Mineralogy appeared to be 

a larger factor; SI OGAs had consistently lower (i.e., smoother) average TX index values, while 

GG OGAs had the highest roughness within each stone size. The variability of these TX 

measurements per sample ID was not evaluated in the round-robin study. However, when all 

OGAs evaluated in this study were combined, the mean TX index was 485, with a COV of 

25.2 percent.
37 

Table 17. Summary of AIMS2 weighted averages for texture.

Stone Size Sample ID Average TX Index TX Classification

No. 57 

No. 57-BA 335 Medium 

No. 57-DI 523 Medium 

No. 57-GG 633 High

No. 57-LI 479 Medium 

No. 57-SI 261 Medium 

No. 57-Avg. 446 Medium 

No. 68 

No. 68-BA 483 Medium 

No. 68-DI 571 High

No. 68-GG 628 High

No. 68-LI 552 High

No. 68-SI 336 Medium 

No. 68-Avg. 514 Medium 

No. 8 

No. 8-BA 518 Medium 

No. 8-DI 582 High

No. 8-GG 630 High

No. 8-LI 366 Medium 

No. 8-SI 372 Medium 

No. 8-Avg. 494 Medium 

Abrasion Resistance and Durability

L.A. abrasion and magnesium sulfate soundness results were provided by the source quarries for 

the respective rock types delivered (table 18). In addition, Micro-Deval tests were performed by 

FHWA to further characterize the abrasion and impact resistance of the OGA rock types 

(table 18). SI OGAs saw the lowest percent mass loss during both Micro-Deval and L.A. 

abrasion testing. Conversely, GG experienced the highest mass loss during both abrasion tests. 

BA OGAs experienced the least percent mass loss after magnesium sulfate soundness tests, 

while GG had the highest mass loss. The combined results indicate that SI was the most durable 

rock type, while GG was the least. The variability of these abrasion resistance and durability 

measurements was not evaluated in the round-robin study; however, as reported in chapter 1, a 

COV of 5.3 to 10.0 percent may be expected for the Micro-Deval and L.A. Abrasion results. 
38 

Table 18. Durability results for the OGA rock types.

Rock Type

Percent Mass Loss

Micro-Deval L.A. Abrasion*

Magnesium Sulfate 

Soundness*

BA 10.3 13.7** 0.40 

DI 5.5 13.0 1.20 

GG 11.2 36.0 1.30 

LI 10.2 12.0 0.70 

SI 5.3 12.0 0.50 

*Data were provided by the quarries for each OGA delivered. 

**Average value for the OGAs is reported; No. 8‐BA and No. 68-BA = 14.0, whereas No. 57-BA = 13.0.

SHEAR STRENGTH AND DEFORMATION

The mechanical properties of soils and aggregates primarily relate to the strength and 

deformation characteristics during loading (Borowicka 1961). To this end, participant 

laboratories were instructed to conduct LSDS testing per ASTM D3080 (2011). All the samples 

were subject to four LSDS tests. The tests were performed at target applied normal stresses (σn) 

of 5, 10, 15, and 30 psi. The direct LSDS test outputs include normal load, shear load, horizontal 

displacement/strain, and vertical displacement/strain. From these measurements, the derived 

shear strength parameters include the following: 

a. Secant (i.e., peak) friction angle (φs) at each target applied σn (e.g., secant, or peak 

friction angle at 5-psi target applied normal stress (φs,5psi), secant, or peak friction angle at 

10-psi target applied normal stress (φs,10psi), secant, or peak friction angle at 15-psi target 

applied normal stress (φs,15psi), secant, or peak friction angle at 30-psi target applied 

normal stress (φs,30psi)); 

b. Tangent friction angle (φt) and ca based on a linear Mohr-Coulomb failure envelope; 

c. Residual tangent friction angle at 20 percent horizontal strain (φt,r) based on a linear 

Mohr-Coulomb failure envelope; 

d. Constant volume friction angle (φcv) based on the zero dilation angle approach. A detailed 

description of the data reduction approaches, and key definitions of the extracted strength 

parameters used in this report, are referenced in Nicks et al. (2015). 

The τ of a soil/aggregate (equation 3) is a function of the σn, friction angle (φ), and cohesion 

value (c).

(3) 

The design requirements for a project, plus engineering judgment, will determine which friction 

angle to use to evaluate τ (e.g., secant, tangent, residual tangent, or constant volume). Friction 

angles are a function of interparticle sliding, crushing, rearrangement, and the dilation of the 

particles during shear (Rowe 1962); interlocking of the particles during shear has also been 
39 

found to contribute to friction angle (Guo and Su 2007). Many of these mechanisms can be 

captured by measuring the deformation behavior during LSDS testing (i.e., the vertical and 

horizontal displacement/strain). The vertical displacement during the shearing process typically 

indicates contraction (i.e., compression) of the specimen, followed by expansion of the specimen 

(i.e., dilation), until a general leveling off at large horizontal displacements.

Since all LSDS tests were performed under dry conditions (i.e., no saturation), total stress 

parameters are presented herein; however, effective stress parameters could also have been 

equivalently used because the pore water pressure was zero in all cases. Representative graphs 

illustrating the results of LSDS tests are presented in this section, including the baseline OS-20-

30 and Nos. 57-, 68-, and 8-LI OGAs. All LSDS stress-strain and strain-strain plots are presented 

in appendix D. 

In the data reduction and analysis of the LSDS results, note that no area corrections were applied 

to the reported results for normal and shear stresses since that was not standard practice among 

the participating laboratories. Corrections were also not applied for the shear or deformation 

resistance of the LSDS devices themselves since that also was not standard practice among the 

participating laboratories. The vertical strain results represent an average of all LVDT 

measurements, initialized to zero at the start of shear. For laboratories with only one LVDT 

(table 6), the results are presented directly as reported, initialized to zero at the start of shear. 

Positive values of vertical strain indicate compression whereas negative values indicate dilation. 

The shear stress was initialized to zero at the start of shear for each laboratory (see appendix D 

for those initial values post-consolidation, pre-shear). The impact of applying or not applying 

corrections to LSDS data was not evaluated in this study; however, the characteristic trends 

found through the results would remain similar regardless. 

OS-20-30 

The shear stress-horizontal strain curves for OS-20-30 are presented in figure 11; corresponding 

vertical-horizontal strain curves are shown in figure 12. Based on these results, the peak shear 

stress, horizontal strain at peak shear (εh,peak), secant, tangent, residual tangent, φcv, and maximum 

dilation angle were determined. 
40 

Source: FHWA.

Figure 11. Charts. Shear stress versus horizontal strain for OS-20-30.

 

 

 
41 

Source: FHWA.

Figure 12. Charts. Vertical strain versus horizontal strain for OS-20-30. 

Peak Shear Stress

Classical results for a densely packed soil sample would show a sharp peak in shear stress 

followed by strain softening (Holtz and Kovacs 1981). This expected behavior was consistently 

seen in L04, L05, and L06 shear-strain curves (figure 11); however, not all results indicated this 

behavior. For example, although the target density for LSDS testing was the same for all 

laboratories (i.e., γd95 = 111.0 lb/ft3

), the results from L02 at lower σn exhibited the behavior of a 

loosely packed sample whereby the shear stress continued to gradually increase with no shear 

softening (figure 11). Excluding L02’s anomalously high values for εh,peak at these lower normal 

stresses, the interlaboratory variability of εh,peak was relatively large, with COVs of 50 percent or 

greater (table 19). In addition to differences in the characteristic shapes of the shear 

stress-horizontal strain curves, the magnitude of peak shear stresses (τpeak) varied between these 

laboratories, with COVs decreasing with increasing σn, ranging from 26.0 to 12.7 percent 

(table 19). 

 

 

 
42 

Table 19. Peak shear parameters for OS-20-30. 

Parameter L01 L02 L03 L04 L05 L06 x̄ s

COV

(percent)

Peak Shear 

Stress

(psi)

τpeak,5psi 4.1 5.0 3.7 4.2 5.6 7.3 5.0 1.3 26.0

τpeak,10psi 7.5 8.4 7.3 7.2 10.1 12.1 8.8 2.0 22.7

τpeak,15psi 10.8 13.3 10.7 10.8 14.2 14.3 12.4 1.8 14.5

τpeak,30psi 20.6 25.9 21.0 21.2 26.7 26.6 23.7 3.0 12.7

Horizontal 

Strain at Peak 

Shear Stress 

(percent)

εh,peak,5psi 1.5 18.8 3.3 1.0 1.1 1.3 4.5 7.1 157.8

εh,peak,10psi 2.2 14.7 3.2 0.8 0.8 1.6 3.9 5.4 138.5

εh,peak,15psi 1.4 2.6 3.8 1.2 1.2 1.6 2.0 1.0 50.0

εh,peak,30psi 1.4 2.5 4.0 1.3 1.1 1.5 2.0 1.1 55.0

εh,peak = horizontal strain at peak shear.

εh,peak,5psi = horizontal strain at peak shear at 5-psi target applied normal stress. 

εh,peak,10psi = horizontal strain at peak shear at 10-psi target applied normal stress.

εh,peak,15psi = horizontal strain at peak shear at 15-psi target applied normal stress.

εh,peak,30psi = horizontal strain at peak shear at 30-psi target applied normal stress.

Secant Friction Angle 

The secant friction angle (φs) for each target σn was also calculated (table 20).

Table 20. Shear strength parameters for OS-20-30. 

Parameter L01 L02 L03 L04 L05 L06 x̄ s 

COV

(percent)

Secant Friction Angle 

(degree)

φs,5psi 39.4 45.3 36.8 39.8 48.3 55.8 44.2 7.1 16.1

φs,10psi 36.9 40.0 36.0 35.8 45.4 50.3 40.7 5.9 14.5

φs,15psi 35.8 41.5 35.6 35.7 43.5 43.6 39.3 4.0 10.2

φs,30psi 34.5 40.8 35.0 35.3 41.6 41.5 38.1 3.5 9.2

Mohr-Coulomb 

Parameters

ca (psi) 0.9 0.5 0.4 0.5 1.6 3.7 1.3 1.3 100.0

φt (deg) 33.4 40.3 34.6 34.5 40.0 37.1 36.7 3.0 8.2

φt,r (deg) 29.2 36.5 26.2 29.7 28.4 31.1 30.2 3.5 11.6

Constant Volume 

Friction Angle (degree) φcv 32.4 48.4 34.3 41.1 44.7 -0.7 33.4 17.8 53.3

As expected, all laboratories (excepting L02) saw a decrease in φs as the target σn increased from 

5 psi to 30 psi (figure 13).
43 

Source: FHWA.

Figure 13. Chart. Secant friction angles for OS-20-30. 

The mean (x̄), standard deviation (s), and COV between the laboratories were computed for each 

parameter (table 20). The variability of φs was lower than the variability of τpeak, with COVs 

ranging from 9.2 to 16.1 percent. 

Tangent Friction Angle 

Tangent friction angle (φt) and ca values, presented in table 20, were derived from the linear 

Mohr-Coulomb failure envelopes (figure 14). Regardless of the behavior during shear, the 

resulting φt had generally low variability, with a mean φt of 36.7 degrees and a COV of 

8.2 percent. Ultimately, φt results were less variable than those of φs. Apparent cohesion (ca) 

appeared in the assumed linear failure envelopes for all laboratories (table 20), despite OS-20-30 

being cohesionless. Variability of ca was high, with a mean of 1.3 psi and a COV of 100 percent. 

However, ca would not be considered in design. 

 

 

 

 

 

 
44 

Source: FHWA.

Figure 14. Chart. Linear Mohr-Coulomb failure envelopes for OS-20-30. 

Residual Friction Angle 

Using the residual, or “fully softened,” shear stresses (τr) (i.e., τ at 20-percent horizontal strain) 

to develop linear Mohr-Coulomb failure envelopes, the tangent of the residual friction angles 

(φt,r) were calculated (table 20). In the case of φt,r, all failure envelopes were force-fit to have 

zero cohesion. The mean φt,r was 30.2 degrees, with a COV of 11.6 percent. 

Constant Volume Friction Angle 

Another strength parameter evaluated was the constant volume friction angle (φcv) that 

corresponds to φs at zero dilation. Peak secant friction angles for each target σn were plotted 

against their corresponding maximum dilation angles (ψmax); the y-intercept of the best-fit line 

through those plotted points is the φcv (table 20). Relatively large variability was found for this 

parameter, ranging from −0.7 to 48.4 degrees, with a mean φcv of 33.4 degrees and a COV of 

53.3 percent. 

Maximum Dilation Angle 

As described in the preceding subsection, a key parameter needed to determine the φcv was the 

maximum dilation angle (ψmax). Maximum dilation angles were calculated with the equation ψmax

= tan−1

(Δvmax/Δh), where Δvmax and Δh are the maximum change in vertical displacement and the 

constant change in horizontal displacement, respectively. To ensure uniformity in determining 

Δvmax for a consistent Δh between the laboratories, differing “n-point” centered moving averages 

were used to analyze the data. This method of analysis was required because the sampling 

 

 

 

 

 

 

 

 
45 

frequency, or time step (Δt), for data collection varied widely between the laboratories (table 21). 

Centered moving averages targeting a 0.02-inch Δh were selected so that results from this study 

could be directly compared to previous FHWA work on characterizing OGAs (Nicks et al. 

2015). It is worth noting that L04 had a particularly variable Δt that continuously increased 

during their tests. While the overall average Δh was 0.05 inches for L04, Δh was closer to the 

0.02-inch target during the early stages of the test where maximum dilation typically occurred.

Table 21. Selection of n-point centered moving averages for ψmax computation.

Laboratory ID 

Δt

+

(s)

Δh+

(inch)

Required

n-point

Actual

n-point

Actual

n-point

Δh (inch)

L01 16 0.004 6 7 0.024 

L02 24 0.006 4.3 5 0.024 

L03 80 0.02 2 1 0.02 

L04 200 0.05 1.4 1 0.05 

L05 1 0.00025 81 81 0.02 

L06 40 0.01 3 3 0.02 +Typical values (table 6). 

The vertical-horizontal strain curves (figure 12) and thus the computed maximum dilation angles 

(table 22), showed considerable variation in deformation behavior during shear. COVs for ψmax

ranged from 38.1 to 49.7 percent, with means ranging from 12.5 to 15.4 degrees. 
46 

Table 22. Maximum dilation angles for OS-20-30. 

Parameter L01 L02 L03 L04 L05 L06 x̄ s 

COV 

(percent) 

ψmax,5psi (degree) 9.6 10.6 14.4 5.7 15.2 19.3 12.5 4.8 38.4 

ψmax,10psi (degree) 5.9 14.3 15.6 21.8 18.4 16.4 15.4 5.3 34.4 

ψmax,15psi (degree) 8.7 14.3 9.6 24.2 16.9 14.7 14.7 5.6 38.1 

ψmax,30psi (degree) 7.7 19.6 4.9 24.2 15.3 15.0 14.5 7.2 49.7 

In general, ψmax is expected to decrease with increasing σn; however, all laboratories diverged 

from the expected trend to varying degrees (figure 15). This divergence may be due to issues 

with measuring vertical deformation that could also be impacted by the mobility and rigidity of 

the LSDS device, or due to issues with the data collection frequency. 

Source: FHWA.

Figure 15. Chart. Maximum dilation angle for OS-20-30. 

No. 57 OGAs 

The shear stress-horizontal strain curves and corresponding vertical-horizontal strain curves for 

the No. 57 OGAs are all presented in appendix D; No. 57-LI was selected as a representative 

sample (figure 16 and figure 17, respectively) to illustrate the main findings in this section. 

Recall that the vertical strain results presented represent an average of all LVDT measurements.

 

 

 

 

 

 

 
47 

Source: FHWA.

Figure 16. Charts. Shear stress versus horizontal strain for No. 57-LI.

 

 

 
48 

Source: FHWA.

Figure 17. Charts. Vertical strain versus horizontal strain for No. 57-LI.

Peak Shear Stress

The classical sharp peak in shear stress followed by strain softening that was observed in some 

OS-20-30 results (figure 11) is not well pronounced for the No. 57 samples (e.g., figure 16). 

COVs for τpeak were also higher for No. 57 OGAs compared to OS-20-30, ranging from about 

30 to 80 percent (table 23); increasing σn continued to correlate with lower COVs. 

In addition, the location of τpeak occurred at much larger horizontal strain (εh,peak) than with the 

OS-20-30. On average, εh,peak ranged from 6.3 to 11.1 percent, with increasing εh,peak as σn

increased (table 23); interlaboratory COVs ranged from 33.3 to 78.5 percent (table 23).

 

 

 
49 

Table 23. Peak shear stress parameters for No. 57 OGAs.

Parameter Sample ID L01 L02 L03 L04 L05 L06 x̄ s

COV 

(%)

τpeak,5psi (psi)

No. 57-BA 7.3 7.0 10.0 7.0 34.0 15.3 13.4 10.6 79.1

No. 57-DI 9.7 16.1 7.4 5.8 19.9 13.7 12.1 5.4 44.6

No. 57-GG 6.9 12.3 7.4 5.5 15.8 18.6 11.1 5.3 47.7

No. 57-LI 9.3 16.1 7.8 6.9 19.6 18.2 13.0 5.6 43.1

No. 57-SI 7.8 16.3 7.5 5.9 22.3 20.0 13.3 7.1 53.4

τpeak,10psi (psi)

No. 57-BA 14.5 16.1 15.3 12.3 44.5 30.2 22.2 12.7 57.2

No. 57-DI 16.9 24.3 15.5 11.5 37.6 28.4 22.4 9.7 43.3

No. 57-GG 13.7 23.9 14.9 10.3 24.5 21.9 18.2 6.0 33.0

No. 57-LI 16.1 23.4 15.3 10.8 29.0 28.3 20.5 7.5 36.6

No. 57-SI 13.5 19.4 14.3 10.7 34.0 27.5 19.9 9.1 45.7

τpeak,15psi (psi)

No. 57-BA 22.3 26.4 21.5 18.8 55.0 42.2 31.0 14.4 46.5

No. 57-DI 23.0 35.8 21.6 16.7 38.9 33.5 28.3 9.0 31.8

No. 57-GG 20.6 29.6 21.3 14.4 30.7 34.1 25.1 7.5 29.9

No. 57-LI 22.9 34.9 22.0 14.4 38.8 30.8 27.3 9.1 33.3

No. 57-SI 18.7 37.7 20.6 15.8 46.8 29.4 28.2 12.2 43.3

τpeak,30psi (psi)

No. 57-BA 39.1 54.1 40.7 35.7 77.7 66.2 52.3 16.9 39.1

No. 57-DI 41.9 61.8 38.6 30.7 60.7 64.6 49.7 14.4 41.9

No. 57-GG 35.0 55.2 37.2 30.5 50.8 52.6 43.6 10.5 35.0

No. 57-LI 41.0 65.6 37.5 32.6 51.7 53.1 46.9 12.2 41.0

No. 57-SI 35.9 55.6 37.4 32.7 71.9 50.3 47.3 15.0 35.9

εh,peak,5psi (%)

No. 57-BA 3.6 14.8 7.4 6.3 7.0 7.2 7.7 3.7 48.1

No. 57-DI 3.3 12.5 5.8 2.1 7.2 7.1 6.3 3.7 58.7

No. 57-GG 3.3 13.9 8.1 4.6 6.1 4.0 6.7 3.9 58.2

No. 57-LI 5.2 11.7 7.9 5.0 8.0 6.2 7.3 2.5 34.2

No. 57-SI 4.3 19.0 6.0 3.3 6.6 7.0 7.7 5.7 74.0

εh,peak,10psi (%)

No. 57-BA 4.6 12.8 7.6 2.5 6.6 6.5 6.8 3.5 51.5

No. 57-DI 4.7 9.7 9.9 2.9 8.2 6.8 7.0 2.8 40.0

No. 57-GG 5.1 16.7 7.8 3.3 6.4 5.6 7.5 4.8 64.0

No. 57-LI 5.9 12.1 7.3 3.3 10.1 8.6 7.9 3.1 39.2

No. 57-SI 4.3 19.9 4.1 2.9 13.4 12.8 9.6 6.8 70.8

εh,peak,15psi (%)

No. 57-BA 4.7 20.0 8.7 2.5 11.0 7.7 9.1 6.1 67.0

No. 57-DI 6.3 19.9 8.3 2.5 9.3 7.3 8.9 5.9 66.3

No. 57-GG 6.3 18.4 7.4 2.9 9.4 6.9 8.6 5.3 61.6

No. 57-LI 7.3 19.8 8.7 2.5 10.2 7.1 9.3 5.8 62.4

No. 57-SI 4.4 19.8 4.7 2.5 7.1 8.8 7.9 6.2 78.5

εh,peak,30psi (%)

No. 57-BA 7.3 19.3 10.4 3.3 8.3 8.8 9.6 5.3 55.2

No. 57-DI 8.2 13.2 7.9 3.8 10.9 6.8 8.5 3.3 38.8

No. 57-GG 5.8 15.2 9.1 5.0 9.8 10.5 9.2 3.7 40.2

No. 57-LI 7.6 18.2 11.5 10.0 10.3 8.8 11.1 3.7 33.3

No. 57-SI 5.2 17.5 8.8 5.4 12.7 14.1 10.6 5.0 47.2
50 

Each τpeak and corresponding εh,peak for the No. 57 OGAs are plotted in figure 18. Of further note 

is L02’s distinct plateau in vertical strain for 5 and 10 psi, along with anomalous sample 

compression for 15 and 30 psi during the No. 57-LI tests, as seen in figure 17. Anomalous or 

potentially erroneous data such as these present an additional, and difficult to quantify, source of 

variability.

Source: FHWA.

Figure 18. Chart. Peak shear stress versus εh,peak for No. 57 OGAs. 

Secant Friction Angle 

All laboratories, save L04, continued to show the expected trend of φs decreasing as σn increased 

for No. 57-LI (figure 19).

 

 

 

 

 

 

 

 
51 

Source: FHWA.

Figure 19. Chart. Secant friction angles for No. 57-LI.

Across all No. 57 OGAs tested, average secant friction angles (φs) ranged from 54.5 to 66.0 

degrees, with COVs ranging from 11.9 to 18.3 percent (table 24), dramatically lower than the 

variability of τpeak (table 23).

 

 

 

 

 

 
52 

Table 24. Shear strength parameters for No. 57 OGAs. 

Parameter Sample ID L01 L02 L03 L04 L05 L06 x̄ s

COV 

(percent)

φs,5psi

(degree)

No. 57-BA 55.7 54.3 63.4 54.4 81.6 71.9 63.6 11.2 17.6

No. 57-DI 62.7 72.7 55.8 49.4 75.9 69.9 64.4 10.3 16.0

No. 57-GG 54.2 67.9 56.1 47.8 72.4 74.9 62.2 11.0 17.7

No. 57-LI 61.6 72.8 57.4 54.0 75.7 74.7 66.0 9.5 14.4

No. 57-SI 57.3 72.9 56.4 49.5 77.4 76.0 64.9 11.9 18.3

φs,10psi

(degree)

No. 57-BA 55.5 58.1 56.9 50.8 77.3 71.7 61.7 10.4 16.9

No. 57-DI 59.5 67.7 57.2 49.1 75.1 70.6 63.2 9.6 15.2

No. 57-GG 53.8 67.3 56.2 45.7 67.8 65.5 59.4 8.9 15.0

No. 57-LI 58.1 66.8 56.8 47.1 71.0 70.5 61.7 9.4 15.2

No. 57-SI 53.4 62.8 55.0 46.9 73.6 70.0 60.3 10.3 17.1

φs,15psi

(degree)

No. 57-BA 56.0 60.4 55.1 51.3 74.7 70.4 61.3 9.3 15.2

No. 57-DI 56.9 67.3 55.3 48.1 68.9 65.9 60.4 8.2 13.6

No. 57-GG 53.9 63.1 54.9 43.8 63.9 66.2 57.6 8.4 14.6

No. 57-LI 56.8 66.7 55.7 43.8 68.8 64.0 59.3 9.2 15.5

No. 57-SI 51.3 68.3 53.9 46.6 72.2 63.0 59.2 10.2 17.2

φs,30psi

(degree)

No. 57-BA 52.5 61.0 53.6 50.0 68.9 65.6 58.6 7.7 13.1

No. 57-DI 54.4 64.1 52.1 45.6 63.7 65.1 57.5 8.0 13.9

No. 57-GG 49.4 61.5 51.1 45.4 59.5 60.3 54.5 6.8 12.5

No. 57-LI 53.8 65.4 51.4 47.4 59.9 60.5 56.4 6.7 11.9

No. 57-SI 50.1 61.7 51.3 47.5 67.4 59.2 56.2 7.8 13.9

ca (psi)

No. 57-BA 1.9 -2.5 3.3 1.1 26.9 8.9 6.6 10.6 160.6

No. 57-DI 3.8 6.9 2.4 1.5 16.8 5.4 6.1 5.6 91.8

No. 57-GG 2.4 5.2 2.7 0.1 9.8 10.6 5.1 4.3 84.3

No. 57-LI 3.4 4.8 3.1 0.4 16.1 12.3 6.7 6.1 91.0

No. 57-SI 2.1 7.6 2.2 0.1 14.4 14.0 6.7 6.3 94.0

φt

(degree)

No. 57-BA 51.5 62.1 51.2 49.2 59.9 63.1 56.2 6.2 11.0

No. 57-DI 51.9 61.5 50.7 44.5 56.3 63.1 54.7 7.0 12.8

No. 57-GG 47.9 59.1 49.5 45.0 54.0 54.7 51.7 5.2 10.1

No. 57-LI 51.6 63.6 49.4 46.4 51.2 53.5 52.6 5.9 11.2

No. 57-SI 48.4 58.6 49.8 47.2 63.0 50.0 52.8 6.4 12.1

φr

(degree)

No. 57-BA 38.5 59.9 47.2 32.3 61.7 59.2 49.8 12.4 24.9

No. 57-DI 41.3 64.5 46.2 30.4 56.5 55.7 49.1 12.3 25.1

No. 57-GG 38.4 59.5 46.0 34.7 49.0 58.2 47.6 10.1 21.2

No. 57-LI 47.9 65.2 46.6 39.8 56.9 59.0 52.6 9.4 17.9

No. 57-SI 37.0 62.5 47.2 33.9 64.8 59.3 50.8 13.4 26.4

φcv

(degree)

No. 57-BA 49.3 61.3 61.6 37.7 57.0 56.8 54.0 9.1 16.9

No. 57-DI 38.2 — 65.8 44.2 54.8 55.0 51.6 10.7 20.7

No. 57-GG 41.3 52.1 50.4 43.1 48.5 52.3 48.0 4.7 9.8

No. 57-LI 20.7 65.9 46.8 47.0 47.0 51.7 46.5 14.6 31.4

No. 57-SI 38.8 65.7 50.9 42.0 54.1 50.7 50.4 9.5 18.8

—Not measured/evaluated.
53 

Tangent Friction Angle 

Tangent friction angles (φt) and ca values, presented in table 24, were derived from the linear 

Mohr-Coulomb failure envelopes (e.g., figure 20). Interlaboratory variability in φt was low for 

the No. 57 OGAs; COVs were between 10.1 and 12.8 percent (table 24). Although the COVs are 

similar to those found for OS-20-30, the magnitude of φt were 15° to 20° higher than the mean φt 

for OS-20-30 (table 20), ranging from 51.7 to 56.2 degrees, on average (table 24). 

Source: FHWA.

Figure 20. Chart. Linear Mohr-Coulomb failure envelopes for No. 57-LI.

Residual Friction Angle 

Average residual, tangent friction angles (φt,r) ranged from 47.6 to 52.6 degrees; COVs ranged 

from 17.9 to 26.4 percent (table 24).

Constant Volume Friction Angle 

Constant volume friction angles (φcv) ranged, on average, from 46.5 to 54.0 degrees (table 24). 

Variability in φcv for the No. 57 OGAs was generally greater than the other τ parameters, with 

COVs up to 31.4 percent (table 24). However, this range in variability is still markedly lower 

than the COV of 53.3 percent found for φcv in the OS-20-30 tests (table 20). Of note is that 

vertical displacement measurements were not measured by L02 in round one (i.e., DI); 

accordingly, φcv and ψmax values from L02 for DI OGAs are not available for consideration. 

 

 

 

 

 

 

 

 
54 

Maximum Dilation Angle 

Using the n-point centered moving average approach (table 21), ψmax was computed for the 

No. 57 OGAs (table 25).

Table 25. Maximum dilation angles for No. 57 OGAs.

Parameter Sample ID L01 L02 L03 L04 L05 L06 x̄ s

COV 

(percent)

ψmax,5psi

(degree) 

No. 57-BA 18.9 25.6 28.5 32.6 25.9 25.1 26.1 4.5 17.2

No. 57-DI 26.7 — 19.4 35.8 24.4 21.2 25.5 6.4 25.1

No. 57-GG 18.4 19.6 23.7 43.5 18.7 23.2 24.5 9.6 39.2

No. 57-LI 20.5 18.0 21.1 20.7 19.4 20.0 20.0 1.1 5.5

No. 57-SI 16.1 13.0 28.3 33.0 20.3 21.3 22.0 7.5 34.1

ψmax,10psi

(degree) 

No. 57-BA 23.3 3.5 28.5 28.8 25.0 20.8 21.7 9.4 43.3

No. 57-DI 24.6 — 22.4 25.6 20.7 19.8 22.6 2.5 11.1

No. 57-GG 16.4 18.4 36.2 24.7 15.9 17.2 21.5 7.9 36.7

No. 57-LI 19.7 15.3 24.5 30.1 17.2 17.1 20.7 5.6 27.1

No. 57-SI 15.2 15.2 28.3 29.2 16.4 13.4 19.6 7.1 36.2

ψmax,15psi

(degree) 

No. 57-BA 17.8 9.7 38.3 31.0 17.0 20.2 22.3 10.4 46.6

No. 57-DI 23.2 — 23.8 19.3 15.5 16.5 19.7 3.8 19.3

No. 57-GG 18.4 13.8 18.0 19.8 15.1 15.0 16.7 2.4 14.4

No. 57-LI 19.3 0.0 22.6 17.7 15.1 10.8 14.3 8.0 55.9

No. 57-SI 12.3 12.5 39.2 24.7 16.7 11.1 19.4 10.9 56.2

ψmax,30psi

(degree) 

No. 57-BA 15.1 8.4 26.1 24.7 15.6 15.0 17.5 6.7 38.3

No. 57-DI 17.7 — 24.0 20.8 10.2 13.2 17.2 5.6 32.6

No. 57-GG 11.8 11.4 12.7 13.5 8.4 7.8 10.9 2.3 21.1

No. 57-LI 16.8 0.0 11.3 11.3 8.8 7.8 9.3 5.5 59.1

No. 57-SI 10.1 11.0 20.7 22.8 11.6 7.4 13.9 6.3 45.3

—Not measured/evaluated.

Except for the results from L03 and L04, the expected downward trend of ψmax with increasing σn

was found (figure 21).
55 

Source: FHWA.

Figure 21. Chart. Maximum dilation angle for No. 57-LI.

On average, ψmax ranged from 9.3 to 26.1 degrees. COVs for ψmax trended upward as σn

increased, with the lowest COV of 5.5 percent at 5 psi and the highest of 59.1 percent at 30 psi 

(table 25). 

No. 68 OGAs 

The shear stress-horizontal strain curves and corresponding vertical-horizontal strain curves for 

the No. 68 OGAs are all presented in appendix D; No. 68-LI was selected as a representative 

sample (figure 22 and figure 23, respectively) to illustrate the main findings in this section. 

Recall that the vertical strain results presented represent an average of all LVDT measurements.

 

 

 

 

 

 

 
56 

Source: FHWA.

Figure 22. Charts. Shear stress versus horizontal strain for No. 68-LI. 

 

 

 
57 

Source: FHWA.

Figure 23. Charts. Vertical strain versus horizontal strain for No. 68-LI. 

 

 

 
58 

Peak Shear Stress

Broadly, the stress-strain curves for No. 68 OGAs are smoother than those of the No. 57 OGAs 

(appendix D). Sharp shear peaks and post-peak strain softening are minimal, continuing to 

diverge from classical expectations for densely packed samples; each τpeak and corresponding 

εh,peak for all No. 68 samples are plotted in figure 24. 

Source: FHWA.

Figure 24. Chart. Peak shear stress versus εh,peak for No. 68 OGAs. 

The No. 68 OGAs had a broad range of COVs for τpeak, ranging from 27.9 to 84.6 percent 

(table 26). Similarly, COVs for εh,peak ranged from 32.7 to 83.1 percent (table 26)—similar to that 

of the No. 57 OGAs—with average εh,peak values ranging from 5.2 to 10 percent (table 26). 

 

 

 

 

 

 

 

 
59 

Table 26. Peak shear stress parameters for No. 68 OGAs.

Parameter Sample ID L01 L02 L03 L04 L05 L06 x̄ s 

COV 

(percent)

τpeak,5psi

(psi)

No. 68-BA 7.6 6.8 9.1 7.5 39.5 26.8 16.2 13.7 84.6

No. 68-DI 8.5 13.8 6.7 6.1 24.7 22.9 13.8 8.2 59.4

No. 68-GG 7.7 11.8 6.4 6.2 16.8 14.9 10.6 4.6 43.4

No. 68-LI 8.0 10.1 6.6 5.6 22.3 19.8 12.1 7.2 59.5

No. 68-SI 7.3 14.4 7.4 5.8 27.9 23.4 14.4 9.3 64.6

τpeak,10psi

(psi)

No. 68-BA 13.8 14.1 14.2 10.6 51.2 33.6 22.9 16.1 70.3

No. 68-DI 16.6 23.4 14.1 10.9 33.8 30.6 21.6 9.3 43.1

No. 68-GG 13.2 18.7 13.7 9.5 34.8 19.3 18.2 8.9 48.9

No. 68-LI 14.9 18.4 13.8 9.5 29.6 33.8 20.0 9.6 48.0

No. 68-SI 13.4 21.5 14.5 12.4 44.7 32.6 23.2 13.0 56.0

τpeak,15psi

(psi)

No. 68-BA 21.3 24.3 21.6 18.5 64.2 46.7 32.8 18.5 56.4

No. 68-DI 22.8 32.0 21.3 14.6 39.8 44.2 29.1 11.5 39.5

No. 68-GG 18.3 23.6 19.5 15.3 40.0 25.0 23.6 8.8 37.3

No. 68-LI 21.0 28.1 19.3 14.8 38.6 42.5 27.4 11.1 40.5

No. 68-SI 20.6 35.5 20.2 15.2 53.3 44.3 31.5 15.3 48.6

τpeak,30psi

(psi)

No. 68-BA 36.8 52.8 37.6 34.2 101.3 68.9 55.3 26.1 47.2

No. 68-DI 40.6 48.8 36.0 27.4 63.9 66.4 47.2 15.6 33.1

No. 68-GG 35.7 44.4 35.4 27.3 60.1 37.4 40.1 11.2 27.9

No. 68-LI 37.0 47.4 36.2 27.5 58.6 58.0 44.1 12.7 28.8

No. 68-SI 35.5 56.8 36.5 29.6 89.0 71.4 53.1 23.6 44.4

εh,peak,5psi

(percent)

No. 68-BA 4.3 17.1 5.3 10.0 3.8 5.8 7.7 5.1 66.2

No. 68-DI 2.9 11.0 5.8 2.5 5.5 7.8 5.9 3.2 54.2

No. 68-GG 3.5 8.0 5.1 3.3 6.0 5.5 5.2 1.7 32.7

No. 68-LI 3.0 16.4 5.9 2.1 7.1 7.1 6.9 5.1 73.9

No. 68-SI 3.2 16.9 6.1 3.3 6.3 7.2 7.2 5.0 69.4

εh,peak,10psi

(percent)

No. 68-BA 4.5 9.8 6.7 2.1 5.9 7.3 6.1 2.6 42.6

No. 68-DI 4.9 10.6 9.1 2.1 6.4 7.9 6.8 3.1 45.6

No. 68-GG 4.5 18.4 6.7 1.3 5.3 6.3 7.1 5.9 83.1

No. 68-LI 5.2 19.5 11.4 2.9 7.7 8.3 9.2 5.8 63.0

No. 68-SI 4.4 20.0 4.9 3.8 6.8 19.8 10.0 7.8 78.0

εh,peak,15psi

(percent)

No. 68-BA 3.9 18.7 7.2 2.5 5.7 7.3 7.6 5.8 76.3

No. 68-DI 4.2 13.5 8.0 2.5 10.6 7.3 7.7 4.0 51.9

No. 68-GG 4.1 12.9 9.0 3.3 5.3 5.9 6.8 3.6 52.9

No. 68-LI 5.5 14.0 9.3 3.8 7.7 7.9 8.0 3.5 43.8

No. 68-SI 4.7 19.7 5.7 3.3 5.1 7.8 7.7 6.1 79.2

εh,peak,30psi

(percent)

No. 68-BA 4.8 19.8 6.7 3.8 8.5 7.8 8.6 5.8 67.4

No. 68-DI 5.8 19.2 13.1 2.5 6.5 8.4 9.3 6.0 64.5

No. 68-GG 4.3 15.4 8.2 3.8 6.1 8.1 7.7 4.2 54.5

No. 68-LI 7.1 17.1 12.1 3.3 6.3 7.5 8.9 4.9 55.1

No. 68-SI 4.1 15.9 7.8 3.8 8.5 8.8 8.2 4.4 53.7
60 

Secant Friction Angle 

The expected inverse correlation between φs and σn was generally found for No. 68 OGAs tested; 

however, the trend was not consistent among the laboratories (figure 25).

Source: FHWA.

Figure 25. Chart. Secant friction angles for No. 68-LI.

Average secant friction angles (φs) for the No. 68 OGAs ranged from 52.1 to 65.0 degrees, with 

COVs ranging from 13.6 to 21.0 percent (table 27); these COVs are slightly lower and slightly 

higher than those for the No. 57 OGAs, respectively (table 24).

 

 

 

 

 

 
61 

Table 27. Shear strength parameters for No. 68 OGAs.

Parameter Sample ID L01 L02 L03 L04 L05 L06 x̄ s

COV 

(percent)

φs,5psi 

(degree)

No. 68-BA 56.8 53.6 61.1 56.2 82.8 79.4 65.0 12.8 19.7

No. 68-DI 59.6 70.0 53.1 50.6 78.6 77.7 64.9 12.2 18.8

No. 68-GG 56.8 67.0 52.0 51.1 73.4 71.4 62.0 9.9 16.0

No. 68-LI 58.0 63.6 52.8 48.2 77.4 75.8 62.6 12.0 19.2

No. 68-SI 55.8 70.9 56.0 49.0 79.8 77.9 64.9 13.0 20.0

φs,10psi 

(degree)

No. 68-BA 54.0 54.6 54.8 46.6 78.9 73.4 60.4 12.7 21.0

No. 68-DI 58.9 66.9 54.7 47.4 73.5 71.9 62.2 10.3 16.6

No. 68-GG 53.0 61.8 53.8 43.6 74.0 62.6 58.1 10.4 17.9

No. 68-LI 56.1 61.5 54.1 43.5 71.3 73.5 60.0 11.3 18.8

No. 68-SI 53.2 65.1 55.5 51.2 77.4 72.9 62.6 11.0 17.6

φs,15psi 

(degree)

No. 68-BA 54.8 58.3 55.2 50.9 76.8 72.2 61.4 10.5 17.1

No. 68-DI 56.7 64.9 54.8 44.2 69.3 71.2 60.2 10.2 16.9

No. 68-GG 50.6 57.5 52.4 45.5 69.4 59.1 55.8 8.3 14.9

No. 68-LI 54.5 61.9 52.2 44.5 68.8 70.6 58.8 10.2 17.3

No. 68-SI 53.9 67.1 53.4 45.4 74.3 71.3 60.9 11.6 19.0

φs,30psi 

(degree)

No. 68-BA 50.8 60.4 51.4 48.7 73.5 66.5 58.6 10.0 17.1

No. 68-DI 53.5 58.4 50.2 42.4 64.9 65.7 55.9 9.0 16.1

No. 68-GG 50.0 56.0 49.7 42.3 63.5 51.3 52.1 7.1 13.6

No. 68-LI 51.0 57.6 50.3 42.5 62.9 62.7 54.5 8.0 14.7

No. 68-SI 49.8 62.2 50.6 44.6 71.4 67.2 57.6 10.8 18.8

ca (psi)

No. 68-BA 2.4 -3.5 3.4 1.2 26.8 18.4 8.1 11.8 145.7

No. 68-DI 3.2 9.1 2.2 2.1 17.3 14.7 8.1 6.7 82.7

No. 68-GG 1.9 5.1 1.7 1.7 14.0 10.6 5.8 5.3 91.4

No. 68-LI 3.1 3.8 1.5 1.1 15.5 17.0 7.0 7.2 102.9

No. 68-SI 2.4 6.3 2.5 1.9 18.0 14.0 7.5 6.9 92.0

φt

(degree)

No. 68-BA 49.3 61.8 48.9 47.7 68.1 59.6 55.9 8.5 15.2

No. 68-DI 51.5 53.7 49.1 40.2 57.2 60.3 52.0 7.0 13.5

No. 68-GG 48.3 52.5 48.7 40.6 57.9 42.1 48.4 6.4 13.2

No. 68-LI 48.9 55.9 49.4 41.5 55.4 55.2 51.1 5.6 11.0

No. 68-SI 48.3 59.7 48.9 42.8 67.2 62.6 54.9 9.6 17.5

φr (degree)

No. 68-BA 38.0 58.8 45.5 34.6 61.8 58.0 49.5 11.7 23.6

No. 68-DI 43.0 58.9 45.7 28.1 53.7 59.6 48.2 11.9 24.7

No. 68-GG 37.2 56.3 44.1 31.1 53.7 45.0 44.6 9.6 21.5

No. 68-LI 42.3 58.1 45.9 31.8 56.7 59.0 49.0 10.9 22.2

No. 68-SI 38.0 62.9 45.7 33.4 62.0 63.6 50.9 13.6 26.7

φcv (degree)

No. 68-BA 43.8 60.0 43.1 50.8 63.2 50.2 51.9 8.3 16.0

No. 68-DI 44.2 — 48.8 38.9 51.1 51.8 47.0 5.4 11.5

No. 68-GG 37.3 49.6 45.8 39.8 51.9 43.9 44.7 5.6 12.5

No. 68-LI 42.4 45.9 50.2 38.7 50.8 54.1 47.0 5.8 12.3

No. 68-SI 32.2 56.4 51.8 26.1 62.3 54.2 47.2 14.5 30.7

—Not measured/evaluated. 
62 

Tangent Friction Angle 

Interlaboratory variability for φt results remained relatively low for the No. 68 OGAs, with φt

ranging, on average, from 48.4 to 55.9 degrees (table 27); COVs ranged from 11.0 to 17.5 

percent (table 27). Apparent cohesion (ca) was still present in the linear Mohr-Coulomb failure 

envelopes (e.g., figure 26), with COVs up to 145.7 percent (table 27).

Source: FHWA.

Figure 26. Chart. Linear Mohr-Coulomb failure envelopes for No. 68-LI. 

Residual Friction Angle 

Compared to φt, φt,r had higher variability; COVs ranged from 21.5 to 26.7 percent (table 27). 

Average residual, tangent friction angles (φt,r) ranged from 44.6 to 50.9 degrees—again, less than 

the No. 57 OGAs. 

Constant Volume Friction Angle 

Constant volume friction angles (φcv) ranged, on average, from 44.7 to 51.9 degrees (table 27). 

Variability in φcv for the No. 68 OGAs was in line with that of the No. 57 OGAs; the minimum 

COV was 11.5 percent, while the maximum was 30.7 percent (table 27). 

Maximum Dilation Angle

Using the n-point centered moving average approach (table 21), ψmax was computed for the No. 

68 OGAs (table 28).

 

 

 

 

 

 

 

 
63 

Table 28. Maximum dilation angles for No. 68 OGAs.

Parameter Sample ID L01 L02 L03 L04 L05 L06 x̄ s

COV 

(percent)

ψmax,5psi

(degree) 

No. 68-BA 17.6 22.8 23.0 30.1 31.0 26.1 25.1 5.0 19.9

No. 68-DI 24.3 — 22.1 26.6 22.4 24.3 23.9 1.8 7.5

No. 68-GG 18.6 21.6 19.9 33.0 22.1 20.4 22.6 5.2 23.0

No. 68-LI 19.8 10.7 25.5 35.0 23.3 20.8 22.5 7.9 35.1

No. 68-SI 16.8 12.5 30.8 31.8 28.3 24.6 24.1 7.9 32.8

ψmax,10psi

(degree) 

No. 68-BA 15.1 9.5 23.6 33.0 26.5 23.6 21.9 8.4 38.4

No. 68-DI 25.3 — 20.0 30.1 18.2 19.4 22.6 5.0 22.1

No. 68-GG 16.1 14.1 23.1 23.7 21.2 14.5 18.8 4.4 23.4

No. 68-LI 16.3 10.0 23.2 21.8 16.9 18.2 17.7 4.7 26.6

No. 68-SI 16.0 13.0 33.9 33.4 23.4 18.2 23.0 8.9 38.7

ψmax,15psi

(degree) 

No. 68-BA 16.6 5.3 16.6 20.8 22.0 19.9 16.9 6.1 36.1

No. 68-DI 21.9 — 32.3 15.6 15.0 17.9 20.5 7.1 34.6

No. 68-GG 12.5 9.3 17.3 12.7 16.8 12.0 13.4 3.1 23.1

No. 68-LI 18.5 11.8 10.4 26.6 15.3 14.8 16.2 5.8 35.8

No. 68-SI 14.6 11.0 45.6 26.6 19.2 17.7 22.5 12.5 55.6

ψmax,30psi

(degree) 

No. 68-BA 9.8 4.2 15.4 22.8 16.4 15.1 14.0 6.3 45.0

No. 68-DI 15.4 — 11.7 11.3 11.2 13.1 12.5 1.8 14.4

No. 68-GG 12.5 8.6 19.6 10.2 11.8 5.1 11.3 4.8 42.5

No. 68-LI 11.8 8.5 5.6 12.7 10.9 8.4 9.7 2.6 26.8

No. 68-SI 13.2 11.7 26.6 24.7 14.5 13.7 17.4 6.5 37.4

—Not measured/evaluated.

The downward trend in ψmax associated with increasing σn was more pronounced, and sporadic, 

among the No. 68 results (figure 27).
64 

Source: FHWA.

Figure 27. Chart. Maximum dilation angle for No. 68-LI.

On average, ψmax ranged from 9.7 to 25.1 degrees (table 28); COVs for ψmax ranged from 7.5 to 

55.6 percent. 

No. 8 OGAs

The shear stress-horizontal strain curves and corresponding vertical-horizontal strain curves for 

the No. 8 OGAs are all presented in appendix D; No. 8-LI was selected as a representative 

sample (figure 28 and figure 29, respectively) to illustrate the main findings in this section. 

Recall that the vertical strain results presented represent an average of all LVDT measurements.

 

 

 

 

 

 

 
65 

Source: FHWA.

Figure 28. Charts. Shear stress versus horizontal strain for No. 8-LI. 

 

 

 
66 

Source: FHWA.

Figure 29. Charts. Vertical strain versus horizontal strain for No. 8 OGAs.

Peak Shear Stress

The stress-strain curves for the No. 8 OGAs are the smoothest of the OGA samples, although the 

same general lack of distinct shear peaks and strain softening persists (appendix D). Each No. 8 

OGA’s τpeak and corresponding εh,peak are plotted in figure 30. 

 

 

 
67 

Source: FHWA.

Figure 30. Chart. Peak shear stress versus εh,peak for No. 8 OGAs. 

COVs for τpeak are from 27.7 to 85.2 percent (table 29), consistent with that of the coarser OGAs 

tested (table 23 and table 26). Similarly, εh,peak was, on average, between 4.9 and 10.0 percent, 

with COVs ranging from 40.8 to 98.3 percent (table 29). 

 

 

 

 

 

 

 

 
68 

Table 29. Peak shear stress parameters for No. 8 OGAs.

Parameter

Sample 

ID L01 L02 L03 L04 L05 L06 x̄ s

COV 

(percent)

τpeak,5psi (psi)

No. 8-BA 7.4 5.3 5.1 5.8 24.4 29.0 12.8 10.9 85.2

No. 8-DI 7.2 7.2 5.8 5.9 16.5 16.4 9.8 5.2 53.1

No. 8-GG 6.4 9.1 5.5 5.0 11.8 15.5 8.9 4.1 46.1

No. 8-LI 6.8 9.8 5.5 5.5 18.6 23.2 11.6 7.5 64.7

No. 8-SI 6.8 8.3 5.8 6.0 21.9 14.2 10.5 6.4 61.0

τpeak,10psi

(psi)

No. 8-BA 13.5 14.4 9.7 12.0 37.3 33.1 20.0 12.0 60.0

No. 8-DI 13.8 18.4 10.5 10.2 26.9 25.3 17.5 7.3 41.7

No. 8-GG 11.7 13.5 10.0 8.3 22.4 17.9 14.0 5.3 37.9

No. 8-LI 12.9 17.5 10.4 9.6 28.2 38.0 19.4 11.4 58.8

No. 8-SI 11.9 18.2 11.7 9.7 32.2 26.5 18.4 9.2 50.0

τpeak,15psi

(psi)

No. 8-BA 20.6 21.8 14.5 16.1 51.4 44.6 28.2 15.7 55.7

No. 8-DI 17.9 27.0 16.3 15.0 37.0 38.5 25.3 10.5 41.5

No. 8-GG 16.2 21.5 15.0 12.7 35.3 32.2 22.2 9.5 42.8

No. 8-LI 18.6 26.2 15.7 13.3 37.7 45.2 26.1 12.9 49.4

No. 8-SI 16.7 25.7 16.1 13.7 47.6 39.8 26.6 14.1 53.0

τpeak,30psi

(psi)

No. 8-BA 36.9 37.6 26.7 29.6 76.6 60.1 44.6 19.6 43.9

No. 8-DI 32.2 45.3 29.0 26.5 48.5 59.2 40.1 12.9 32.2

No. 8-GG 29.6 37.3 27.3 22.1 46.8 42.7 34.3 9.5 27.7

No. 8-LI 33.6 45.9 28.0 24.9 58.7 69.9 43.5 18.0 41.4

No. 8-SI 32.5 50.4 28.0 27.9 68.6 61.6 44.8 17.9 40.0

εh,peak,5psi

(percent)

No. 8-BA 2.3 17.6 4.7 1.5 4.2 5.5 6.0 5.9 98.3

No. 8-DI 2.8 13.9 3.9 2.1 4.4 5.3 5.4 4.3 79.6

No. 8-GG 3.3 8.3 5.3 2.5 5.7 4.5 4.9 2.0 40.8

No. 8-LI 4.7 12.0 7.5 3.8 4.0 7.3 6.6 3.1 47.0

No. 8-SI 4.3 12.3 4.0 2.1 5.2 5.6 5.6 3.5 62.5

εh,peak,10psi

(percent)

No. 8-BA 2.4 19.9 10.4 2.9 5.7 6.3 7.9 6.5 82.3

No. 8-DI 3.6 11.1 6.4 2.9 4.7 5.9 5.8 2.9 50.0

No. 8-GG 3.8 13.8 7.3 2.9 4.8 5.3 6.3 4.0 63.5

No. 8-LI 4.3 12.9 10.1 2.5 5.0 8.4 7.2 3.9 54.2

No. 8-SI 3.3 20.0 5.5 2.1 5.2 7.4 7.3 6.5 89.0

εh,peak,15psi

(percent)

No. 8-BA 3.6 17.5 9.1 2.1 4.9 5.8 7.2 5.6 77.8

No. 8-DI 4.4 13.8 6.1 2.9 6.2 6.5 6.7 3.8 56.7

No. 8-GG 4.3 12.4 6.2 2.9 5.5 6.8 6.4 3.3 51.6

No. 8-LI 5.8 19.3 9.4 3.3 6.2 9.1 8.9 5.6 62.9

No. 8-SI 4.9 20.0 6.8 2.9 6.1 7.5 8.0 6.1 76.3

εh,peak,30psi

(percent)

No. 8-BA 3.5 19.7 6.4 1.7 6.0 6.5 7.3 6.4 87.7

No. 8-DI 5.6 13.8 8.5 3.3 6.6 8.1 7.7 3.5 45.5

No. 8-GG 4.1 15.5 10.0 2.5 7.6 6.2 7.7 4.7 61.0

No. 8-LI 7.2 20.0 11.7 5.4 6.9 8.9 10.0 5.3 53.0

No. 8-SI 4.1 16.6 8.2 3.3 6.7 9.7 8.1 4.8 59.3
69 

Secant Friction Angle 

The No. 8 OGAs continue to follow the classically expected trend of decreasing φs associated 

with increasing σn (e.g., figure 31). Average secant friction angles (φs) for the No. 8 OGAs 

ranged from 47.8 to 60.9 degrees, with COVs ranging from 16.7 to 26.8 percent (table 30). These 

φs values are generally lower than the No. 68 (table 27) and No. 57 (table 24) results; on the 

other hand, COVs for the No. 8 OGAs are generally higher than the COVs of the larger OGA 

stone sizes.

Source: FHWA.

Figure 31. Chart. Secant friction angles for No. 8-LI.

Tangent Friction Angle 

Variability remained low for φt with COVs from 15.2 to 19.5 percent (table 30); average φt 

values range from 44.8 to 51.8 degrees, slightly less than those found for No. 57 (table 24) and 

No. 68 (table 27). As with the previous OGA stone sizes, ca is still present in the linear MohrCoulomb failure envelopes (e.g., figure 32). 

 

 

 

 

 

 
70 

Source: FHWA.

Figure 32. Chart. Linear Mohr-Coulomb failure envelopes for No. 8-LI.

Residual Friction Angle

Like the other OGAs, variability in φt,r was greater than that of φt with COVs ranging from 19.5 

to 25.8 percent (table 30). Average φt,r values ranged from 40.8 to 48.6 degrees, following the 

same general downward trend in friction angle with stone size. 

 

 

 

 

 

 

 

 
71 

Table 30. Shear strength parameters for No. 8 OGAs.

Parameter

Sample 

ID L01 L02 L03 L04 L05 L06 x̄ s

COV 

(percent)

φs,5psi

(degree) 

No. 8-BA 55.9 46.6 45.5 49.3 78.4 80.2 59.3 15.9 26.8

No. 8-DI 55.3 55.4 49.4 49.7 73.1 73.0 59.3 10.9 18.4

No. 8-GG 51.8 61.3 47.8 44.9 67.0 72.2 57.5 11.0 19.1

No. 8-LI 53.8 62.9 47.6 47.9 75.0 77.9 60.9 13.3 21.8

No. 8-SI 53.5 58.9 49.4 50.3 77.1 70.6 60.0 11.4 19.0

φs,10psi

(degree) 

No. 8-BA 53.4 55.2 44.3 50.2 75.0 73.2 58.6 12.6 21.5

No. 8-DI 54.0 61.5 46.3 45.7 69.6 68.4 57.6 10.6 18.4

No. 8-GG 49.4 53.5 44.9 39.8 65.9 60.8 52.4 9.8 18.7

No. 8-LI 52.3 60.2 46.2 43.8 70.5 75.3 58.1 12.9 22.2

No. 8-SI 50.1 61.2 49.4 44.0 72.8 69.3 57.8 11.7 20.2

φs,15psi

(degree) 

No. 8-BA 54.0 55.4 44.1 47.1 73.7 71.4 57.6 12.3 21.4

No. 8-DI 50.0 61.0 47.5 45.0 68.0 68.7 56.7 10.6 18.7

No. 8-GG 47.2 55.1 45.0 40.2 67.0 65.0 53.3 11.0 20.6

No. 8-LI 51.2 60.2 46.4 41.6 68.3 71.7 56.6 12.1 21.4

No. 8-SI 48.0 59.7 47.0 42.4 72.5 69.3 56.5 12.6 22.3

φs,30psi

(degree) 

No. 8-BA 50.9 51.4 41.7 44.6 68.6 63.5 53.5 10.6 19.8

No. 8-DI 47.1 56.5 44.0 41.5 58.3 63.1 51.8 8.7 16.8

No. 8-GG 44.6 51.2 42.3 36.4 57.3 54.9 47.8 8.0 16.7

No. 8-LI 48.2 56.8 43.0 39.7 62.9 66.8 52.9 11.0 20.8

No. 8-SI 47.3 59.2 43.0 42.9 66.4 64.0 53.8 10.7 19.9

ca (psi)

No. 8-BA 1.9 0.9 1.1 1.9 16.6 22.7 7.5 9.6 128.0

No. 8-DI 3.1 2.5 1.5 2.1 13.9 9.2 5.4 5.0 92.6

No. 8-GG 2.2 3.2 1.4 1.7 8.8 10.1 4.6 3.9 84.8

No. 8-LI 2.1 3.3 1.5 1.7 12.1 17.3 6.3 6.7 106.3

No. 8-SI 1.5 0.7 2.4 1.0 14.8 7.6 4.7 5.6 119.1

φt

(degree) 

No. 8-BA 49.7 51.4 40.8 42.9 64.0 51.8 50.1 8.2 16.4

No. 8-DI 44.4 55.8 42.8 39.4 50.7 59.6 48.8 7.9 16.2

No. 8-GG 42.6 48.9 41.0 34.5 53.4 48.5 44.8 6.8 15.2

No. 8-LI 46.7 55.2 41.8 37.7 57.7 60.8 50.0 9.3 18.6

No. 8-SI 45.8 58.9 40.9 41.5 61.7 61.7 51.8 10.1 19.5

φr

(degree) 

No. 8-BA 37.1 52.0 38.5 33.4 52.3 51.1 44.1 8.6 19.5

No. 8-DI 39.5 55.9 39.5 30.2 49.8 54.7 44.9 10.2 22.7

No. 8-GG 36.3 49.8 38.8 27.8 47.2 44.6 40.8 8.1 19.9

No. 8-LI 40.5 57.4 38.9 35.2 55.8 63.7 48.6 11.8 24.3

No. 8-SI 37.0 59.2 40.0 31.2 52.5 59.1 46.5 12.0 25.8

φcv 

(degree) 

No. 8-BA 37.0 59.1 39.8 34.3 58.2 35.3 44.0 11.5 26.1

No. 8-DI 37.9 — 41.2 40.4 51.2 52.4 44.6 6.7 15.0

No. 8-GG 38.1 45.3 44.3 35.4 50.1 49.4 43.8 5.9 13.5

No. 8-LI 46.0 53.4 45.9 34.6 50.6 58.8 48.2 8.2 17.0

No. 8-SI 42.5 66.6 43.5 31.9 53.9 56.8 49.2 12.3 25.0

—Not measured/evaluated.
72 

Constant Volume Friction Angle 

Constant volume friction angles (φcv) ranged, on average, from 43.8 to 49.2 degrees; COVs 

ranged from 13.5 to 26.1 percent, suggesting the variability of φcv for the No. 8 OGAs was in line 

with that of the other OGAs (table 30).

Maximum Dilation Angle 

Using the n-point centered moving average approach (table 21), ψmax was computed for the No. 8 

OGAs (table 31).

Table 31. Maximum dilation angles for No. 8 OGAs.

—Not measured/evaluated.

Parameter 

Sample

ID L01 L02 L03 L04 L05 L06 x̄ s 

COV 

(percent) 

ψmax,5psi

(degree) 

No. 8-BA 19.2 35.7 15.4 25.6 26.9 26.7 24.9 7.0 28.1 

No. 8-DI 21.8 — 16.0 45.0 22.6 22.6 25.6 11.2 43.8 

No. 8-GG 15.9 12.5 17.1 31.0 18.3 22.3 19.5 6.5 33.3 

No. 8-LI 14.1 14.5 10.7 21.8 20.6 21.5 17.2 4.7 27.3 

No. 8-SI 12.3 14.4 17.4 30.6 23.8 21.1 19.9 6.7 33.7 

ψmax,10psi

(degree) 

No. 8-BA 16.6 9.1 18.3 30.1 21.9 22.4 19.7 7.0 35.5 

No. 8-DI 19.8 — 17.5 24.5 15.3 18.1 19.0 3.5 18.4 

No. 8-GG 14.7 12.5 31.5 12.4 17.1 16.4 17.4 7.2 41.4 

No. 8-LI 13.8 11.6 12.4 11.3 16.9 16.4 13.7 2.4 17.5 

No. 8-SI 14.3 12.5 40.0 22.8 20.2 17.5 21.2 9.9 46.7 

ψmax,15psi

(degree) 

No. 8-BA 18.3 23.6 18.8 26.6 19.4 20.8 21.3 3.2 15.0 

No. 8-DI 17.1 — 13.6 15.3 13.8 15.5 15.1 1.4 9.3 

No. 8-GG 9.8 10.8 8.7 11.6 13.9 10.5 10.9 1.8 16.5 

No. 8-LI 9.5 8.9 5.4 13.5 15.3 14.2 11.1 3.8 34.2 

No. 8-SI 9.8 12.7 23.5 19.8 17.7 16.4 16.7 4.9 29.3 

ψmax,30psi

(degree) 

No. 8-BA 14.5 21.0 14.9 19.8 14.3 16.9 16.9 2.9 17.2 

No. 8-DI 11.1 — 8.7 11.3 9.4 13.0 10.7 1.7 15.9 

No. 8-GG 8.7 6.0 11.7 6.8 8.8 9.3 8.6 2.0 23.3 

No. 8-LI 4.7 6.0 10.0 11.3 10.4 9.2 8.6 2.6 30.2 

No. 8-SI 7.7 12.3 14.8 16.7 13.3 11.5 12.7 3.1 24.4 
73 

As expected, ψmax generally decreased as σn increased (e.g., figure 33).

Source: FHWA.

Figure 33. Chart. Maximum dilation angle for No. 8-LI.

On average, ψmax ranged from 8.6 to 25.6 degrees (table 31); COVs for ψmax ranged from 9.3 to 

46.7 percent. 

SUMMARY

The round-robin interlaboratory testing program provided data on the physical properties and τ

of select OGAs often used in road and bridge construction. From the dataset, the variability of 

key design parameters was found; a summary of the basic statistics (e.g., mean, standard 

deviation, and COV) for each OGA (and the entire dataset, as applicable) is provided in table 32. 

The findings indicated that OGA gradation (e.g., D85) and unit weight (e.g., γd95) results between 

the laboratories were relatively consistent, suggesting that the gap size and target density 

specified for LSDS testing were not significant factors in the strength-deformation differences 

found between the laboratories. These differences were made clear in the larger variability found 

for the resulting friction angles, whether secant (φs), tangent (φt), residual, tangent (φt,r), or 

constant volume (φcv), and the resulting maximum dilation angles (Ψmax) (table 32). This 

variability in LSDS strength results was further highlighted when OS-20-30 was tested by each 

laboratory (table 20 and table 22), emphasizing the impact of LSDS box characteristics on the 

strength-deformation behavior and the derived results for soils and aggregates. Further analysis 

on the type of statistical distribution each parameter follows (e.g., normal, lognormal), the 

significance of LSDS devices and mineralogy of OGAs on the results, and the implications of 

these results found on geotechnical design, are presented in chapter 4.

 

 

 

 

 

 

 
74 

Table 32. Summary of key, average OGA results and basic statistics.

Parameter Sample ID x̄ s

COV 

(%) Reference

D85

(inch) 

No. 57-Avg. 0.80 0.07 8.8 table 8

No. 68-Avg. 0.65 0.03 4.6 table 8

No. 8-Avg. 0.36 0.02 5.6 table 8

γd95

(lb/ft3) 

No. 57-Avg. 104.3 5.4 5.2 table 10

No. 68-Avg. 107.6 6.1 5.7 table 11

No. 8-Avg. 103.4 5.2 5.0 table 12

φs

+

(degree) 

No. 57-Avg. 60.4 9.1 15.1 N/A

No. 68-Avg. 59.9 10.4 17.4 N/A

No. 8-Avg. 56.1 11.0 19.6 N/A

All-Avg. 58.8 10.2 17.4 N/A

φt

(degree) 

No. 57-Avg. 53.6 6.0 11.2 table 24

No. 68-Avg. 52.4 7.5 14.3 table 27

No. 8-Avg. 49.1 8.3 16.9 table 30

All-Avg. 51.7 7.3 14.1 N/A

φt,r

(degree) 

No. 57-Avg. 50.0 10.9 21.8 table 24

No. 68-Avg. 48.4 11.0 22.7 table 27

No. 8-Avg. 45.0 9.9 22.0 table 30

All-Avg. 47.8 10.6 22.2 N/A

φcv 

(degree) 

No. 57-Avg. 50.0 9.8 19.6 table 24

No. 68-Avg. 47.6 8.4 17.6 table 27

No. 8-Avg. 46.0 9.0 19.6 table 30

All-Avg. 47.9 9.1 18.9 N/A

ψmax+

(degree) 

No. 57-Avg. 19.2 7.7 39.9 N/A

No. 68-Avg. 18.8 7.5 39.6 N/A

No. 8-Avg. 16.5 6.9 42.1 N/A

All-Avg. 18.2 7.4 40.5 N/A +Combined values over the range of σn values (i.e., 5 to 30 psi).

N/A = not applicable.
75 

CHAPTER 4. ANALYSIS OF RESULTS

The results presented in the previous chapter suggest that the variability of physical properties 

and characteristics is relatively low; for example, COVs for γd95 ranged from 1.1 to 3.1 percent 

for the OGAs (table 10 through table 12). The variability of shear strength (i.e., friction and 

dilation angles), however, was found to be higher; for example, COVs for φt ranged from 10.1 to 

19.5 percent for the OGAs (table 24, table 27, and table 30). This chapter will evaluate potential 

reasons for the interlaboratory variability, primarily as these reasons relate to differences in the 

LSDS devices and test procedures at each of the laboratories. In addition, statistical methods

such as standard normal variable plots and Anderson-Darling (AD) tests were employed to 

further analyze the distribution of the datasets for dry unit weight and shear strength within the 

context of probabilistic design. Finally, ANOVA was performed to evaluate the impact of the 

laboratory (i.e., LSDS device) and sample type (i.e., stone size and mineralogy) on the variability 

of results.

DISTRIBUTION TYPES

The basic statistics of all data in chapter 3 were reported in terms of mean, standard deviation, 

and COV. To further characterize the design parameters of interest (i.e., dry unit weight at 95RD

(selected as representative of field conditions), friction angles, and maximum dilation angle) 

statistically, an evaluation of the distribution type (e.g., normal, lognormal) was performed. This 

section presents varying approaches to determine the type of distribution that best fits the 

measured and/or derived data presented in chapter 3, including frequency histograms, normal 

probability plots, and AD tests to determine the goodness of fit for selected distribution types.

Histograms are the most common way to represent scattered data graphically

(Baecher and Christian 2003). The y-axis in any histogram is the frequency, or number, of data 

points that fall into a certain, selected bin size (or bin width) on the x-axis. To maintain 

consistency in developing histograms for the relevant design parameters evaluated in this study 

(i.e., γd95, φs, φt, φt,r, φcv, and ψmax), Scott’s normal reference rule was selected to calculate each 

histogram’s optimal bin width (W) as a function of the associated standard deviation (s) and 

sample size (n) per equation 4 (Scott 1979). 

 (4) 

As the name implies, Scott’s normal reference rule generates bin widths that approximate normal 

distributions in an unbiased manner (Scott 1979). While the exact distribution of the data was 

unknown before the histograms were developed, this method of selecting bin widths for each 

parameter evaluated only required inputs that were known in this study (i.e., s and n); see 

table 33. In all cases, the starting bin value in the histograms was set to the minimum value 

measured for each parameter (table 33). The histograms presented in this section are also 

overlayed with an idealized normal distribution curve as computed from the x̄ and s of the plotted 

parameter. Note that each histogram combines the entire dataset for the parameter evaluated (i.e., 

no distinction is made between stone size, mineralogy, laboratory, or σn) and is not truncated for 

the purposes of illustrating the fit with the data. 
76 

Table 33. Histogram parameters.

Parameter Units Min. Max. Mode++ Median x̄ s n W Ku Sk

γd95 lb/ft3 95.4 118.8 101.4 

(111.6) 104.1 105.1 5.8 90 4.5 −0.5 0.5 

φs

+ deg 36.4 82.8 49.4 56.8 58.8 10.4 360 5.1 −1.0 0.2 

φt deg 34.5 68.1 48.9 51.0 51.7 7.5 90 5.8 −0.7 0.1 

φt,r deg 27.8 65.2 47.2 47.2 47.8 10.7 90 8.3 −1.3 −0.1

φcv deg 20.7 66.6 

39.8 

(44.2) 49.1 47.7 9.0 86 7.1 0.1 −0.2

ψmax+ deg 3.5 45.6 12.5 17.2 18.3 7.3 346 3.6 0.9 0.8 +Combined values over the range of σn values(i.e., 5 to 30 psi). ++For bimodal distributions, first mode (second mode) identified.

Table 33 also includes additional parameters for a full characterization of a given (untruncated) 

histogram, including mode, median, kurtosis (Ku), and skewness (Sk). In a perfectly normal 

distribution, the mode, median, and mean (x̄) are equal, and the Ku and Sk are zero. The values of 

Ku and Sk are properties of the distribution used to evaluate how peaked or flat and how skewed 

or symmetrical the tails of the distribution are, respectively (Selezneva et al. 2002). A positive 

and negative Ku value indicates a relatively peaked and flat distribution, respectively, whereas a 

positive and negative Sk value corresponds to a distribution with an asymmetric tail extending 

more toward the right (i.e., positive skew) and left (i.e., negative skew), respectively. Equation 5 

and equation 6 were used to determine Ku and Sk of each parameter (Uzielli et al. 2006).

(5) 

(6) 

Another graphical method to evaluate the distribution of the data for each parameter is to 

develop normal probability plots. This method of evaluation requires transforming the 

probability of the data into standard normal variables (Z) and then plotting those Z values versus 

the corresponding measured data and versus data predicted, assuming a given distribution type 

(e.g., normal, lognormal) (Allen et al. 2005). Each set of data was first arranged in ascending 

order, and a numeric rank (i), starting from 1, was assigned to each value. The Z was computed 

as the inverse of the standard normal cumulative distribution, or Z = NORMSINV (i/(n+1)), for 

each value and then plotted against the corresponding measured data. Theoretical normal and 

lognormal distributions for the datasets were then compared within the normal probability plot to 

evaluate the best-fit distribution. Note that the mean and standard deviation of each dataset were 

log-transformed and the inverse of the lognormal was computed to determine the predicted 

lognormal distribution for comparison. 

Finally, the AD test was adopted to perform a goodness-of-fit test (Anderson and Darling 1954). 

AD tests are nonparametric tests where the null hypothesis states that the data follow a specified 
77 

distribution. Conversely, the alternative hypothesis would be that the data do not follow a 

specified distribution. Normal and lognormal were tested with an alpha (i.e., threshold p-value) 

of 0.05. A p-value less than or equal to the alpha of 0.05 corresponds to at least a 95-percent 

confidence level that random chance, based on the mean and standard deviation of the dataset, 

would generate results at least as extreme as those observed. If the p-value from the statistic test 

is greater than 0.05, the null hypothesis should be accepted. Summarized steps for the AD test 

are shown in appendix E. 

Dry Unit Weight 

The γdmin and γdmax for each OGA sample were measured by each laboratory; these measured unit 

weights were then used to compute the γd95 for each sample (table 10 through table 12). Since 

γd95 was used as the target density for LSDS testing and is most representative of compacted 

conditions in the field, only its histogram, based on the values in table 33, is presented in this 

subsection. Visual observation of the histogram indicates that the calculated γd95 for all OGAs 

evaluated in this study are not normally distributed (figure 34). This finding is also evidenced by 

the nonequality of values among the mode, median, and mean (table 33). The Ku and Sk values 

(table 33) indicated a relatively flat distribution with positive skew, respectively.

Source: FHWA.

Figure 34. Chart. Histogram of γd95 with idealized normal distribution curve overlayed.

The normal probability plot for γd95 is shown in figure 35, along with the predicted normal and 

lognormal distributions of the dataset for comparison. The measured γd95 data were not in good 

agreement with either the predicted normal or lognormal distribution curves. This fact is 

unsurprising given the diversity of source quarries and AASHTO stone sizes tested. There is a 

distinct break in the normal probability plot between 106 and 108 lb/ft3 that corresponds to a 

change in mineralogy.

 

 

 
78 

Source: FHWA.

Figure 35. Chart. Normal probability plot for γd95. 

All γd95 values in excess of 108 lb/ft3 are composed of mafic mineralogy (i.e., DI and BA), with 

Gsb values above 2.9 versus the lighter sedimentary or felsic mineralogy (i.e., GG, LI, and SI), 

which had Gsb values around 2.7 (figure 36).

 

 

 

 
79 

Source: FHWA.

Figure 36. Chart. Relationship between γd95 and Gsb. 

The AD test for γd95 was initially performed for the entire 90-point dataset. The test found that 

the entirety of γd95 does not follow a normal distribution (i.e., p-value = 0.00) or a lognormal 

distribution (p-value = 0.01) (appendix E). However, separating the 90-point dataset into lighter 

(i.e., GG, LI, and SI) and heavier weight (i.e., BA and DI) OGAs in the AD test resulted in two 

normal distribution curves with p-values of 0.30 and 0.40, respectively (appendix E). As such, 

the bimodal nature of γd95 would be best represented by two separate normal distributions with 

x̄ = 101.4 lb/ft3

 and s = 2.9 lb/ft3 for the lighter sedimentary or felsic mineralogy evaluated, in 

contrast to x̄ = 110.8 lb/ft3 and s = 4.3 lb/ft3 for the heavier mafic mineralogy. The mean of 105.1 

(table 33) is an appropriate approximation of γd95 for preliminary design in the absence of 

mineralogy information. A selection of OGAs covering a more continuous spectrum of bulk dry 

specific gravities may reveal a singular normal distribution curve.

Friction Angles 

The secant (φs), tangent (φt), residual tangent (φt,r), and constant volume (φcv) friction angles were 

all determined for each sample; a summary of these strength parameters for all OGAs are shown 

in table 24, table 27, and table 30 in chapter 3. 

Secant Friction Angle

To evaluate the distribution of φs, all of the values (table 24, table 27, and table 30) were 

combined over the range of σn values (i.e., 5 to 30 psi) into a single, 360-point dataset to 

 

 

 

 

 

 

 

 
80 

determine the overall statistics of the parameter (table 33). Visual observation of the histogram 

for the combined φs dataset (figure 37) suggests that φs for all OGAs evaluated in this study are 

not normally distributed. Similarly, evaluation of the mode, median, and mean, along with the Ku

and Sk values (table 33), indicate nonnormality of the φs parameter.

Source: FHWA.

Figure 37. Chart. Histogram of φs with idealized normal distribution curve overlayed.

The normal probability plot for φs is shown in figure 38-A, along with the predicted normal and 

lognormal distributions of the dataset for comparison. The measured φs data were not in good 

agreement with either predicted distribution curve. In addition, there appears to be two distinct 

groupings present in the data (figure 38-A)—as was the case with γd95. Further investigation 

revealed that L01, L03, and L04 are overwhelmingly located to the left of the inflection point at 

approximately 58 degrees (figure 38-B); likewise, most points to the right of 58 degrees were 

from L02, L05, and L06. These left and right groupings coincide with mobile and fixed upper 

shear boxes, respectively (table 6).

 

 

 
81 

Source: FHWA.

A. All data with predicted distributions.

 

 

 

 
82 

Source: FHWA.

B. All data by box mobility. 

Figure 38. Charts. Normal probability plots for φs. 

The AD test for φs performed for the combined 360-point dataset indicated that neither 

distribution type fit the φs data. Additional AD testing according to the upper box fixity 

groupings showed that φs followed normal behavior (p-value = 0.16) within the fixed upper box 

group (i.e., L02, L05, and L06). The φs remained neither normally nor lognormally distributed 

for the mobile upper box group (i.e., L01, L03, and L04) (appendix E). This analysis lends 

credence to devices with fixed upper boxes, yet further research is still needed, particularly 

considering that the laboratories with fixed upper boxes in this study were research-based 

laboratories, whereas the mobile upper box results were from commercial laboratories (table 6). 

Therefore, φs is best approximated by a normal distribution where x̄ = 67.1 degrees and s = 7.1 

degrees for data collected from fixed upper boxes. Additional distribution types (e.g., Weibull, 

beta, etc.) would need to be checked for data collected from mobile upper boxes based on 

x̄ = 50.5 degrees and s = 5.1 degrees.

Tangent Friction Angle

The φt for each OGA sample was determined assuming a linear Mohr-Coulomb failure envelope 

(table 24, table 27, and table 30); a total number of 90 data points were used to establish the 

histogram for φt (figure 39). The calculated values of Ku (i.e., 0.7) and Sk (i.e., 0.1) shown in 

 

 

 
83 

table 33 indicate a relatively flat, but fairly symmetrical, distribution. The mode, median, and 

mean are not equal; however, their differences are relatively small, particularly with respect to 

the standard deviation of the parameter (table 33). These observations suggest that φt could 

reasonably be assumed to be a normal distribution; however, further evaluations were performed, 

as discussed next. 

Source: FHWA.

Figure 39. Chart. Histogram for φt with idealized normal curve overlayed.

The normal probability plot for φt, along with the predicted normal and lognormal distribution 

curves, are shown in figure 40. Both distribution types visually fit the data fairly well. However, 

the predicted normal distribution better represents the full spectrum of values, while the 

predicted lognormal distribution better fits the lower tail of values. To determine if normality (or 

lognormality) can be reasonably assumed for φt, a goodness-of-fit test was performed.

The AD test for φt was based on the 90-point dataset. Similar to the observations from the normal 

probability plot (figure 40), both normal and lognormal distributions reasonably fit the frequency 

distribution of φt (appendix E). Since normality was found (i.e., p-value > 0.05), φt can 

statistically be approximated, assuming a normal distribution with x̄ = 67.1 degrees and s = 7.1 

degrees for the OGAs evaluated in this study. This finding also suggests that incorporating the 

spectrum of φs values in determining φt offsets nonnormality in the broader φs dataset. This

finding is corroborated by the lower COV of φt compared to φs (table 32).

 

 

 
84 

Source: FHWA.

Figure 40. Chart. Normal probability plot for φt. 

Residual Friction Angle

The histogram for φt,r is shown in figure 41; 90 data points (table 24, table 27, and table 30) were 

used to establish the φt,r histogram. Visual and numerical observation of the histogram indicates 

φt,r follows a relatively flat distribution (i.e., Ku = −1.3) with minimal negative Sk (i.e., Sk = −0.1). 

In addition, the mode, median, and mean for φt,r were practically equal (table 33); the Sk and Ku

values also suggests that φt,r generally follows a uniform distribution (i.e., nonnormal). 

 

 

 

 
85 

Source: FHWA.

Figure 41. Chart. Histogram for φt,r with idealized normal distribution curve overlayed.

The normal probability plot, along with the predicted normal and lognormal distribution curves 

for φt,r, is shown in figure 42. Neither predicted distribution type visually matches the data well 

across the entire dataset. Therefore, in the absence of testing higher order distribution types, φt,r

can reasonably be approximated assuming a uniform distribution over the range of values (i.e., 

27.8–65.2 degrees) found within this study. The AD test for φt,r was based on 90-point dataset. 

The findings strongly suggested that neither normal nor lognormal distributions fit the data. 

However, φt,r can be approximated with a uniform distribution with x̄ = 46.5 degrees and 

s = 10.8 degrees given the descriptive statistics for φt,r (table 33). 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
86 

Source: FHWA.

Figure 42. Chart. Normal probability plot for φt,r. 

Constant Volume Friction Angle

The histogram for φcv, along with the overlayed normal distribution curve, is shown in figure 43

based on 86 data points (table 24, table 27, and table 30). Visual observation of the histogram 

shows the data are skewed to the left (figure 43). The frequency distribution was found to be 

bimodal (table 33); however, unlike γd95, this frequency distribution was likely just a factor of the 

sample size because, within the entire dataset, there were only two values at each mode. 

Regardless, the modes, median, and mean are unequal (table 33). However, Ku and Sk indicate 

similarities with a normal distribution.

 

 

 

 
87 

Source: FHWA.

Figure 43. Chart. Histogram for φcv with idealized normal distribution curve overlayed.

The normal probability plot for φcv, along with the predicted normal and lognormal distribution 

curves, are illustrated in figure 44. The data generally fit well with a normal distribution, except 

for two data points at the extreme lower tail; therefore, φcv can reasonably be captured by 

assuming a normal distribution. The AD normality test for φcv was based on the 86-point dataset 

and found a p-value of 0.70 (appendix E); this finding agrees with the observations found in the 

normal probability plot (figure 44). Therefore, φcv is normally distributed with x̄ = 47.7 degrees 

and s = 9.0 degrees.

 

 

 

 

 

 

 

 

 

 

 

 

 

 
88 

Source: FHWA.

Figure 44. Chart. Normal probability plot for φcv. 

Maximum Dilation Angle

To evaluate the distribution of ψmax, all of the values (table 25, table 28, and table 31) were 

combined over the range of σn values (i.e., 5 to 30 psi) into a single, 346-point dataset to 

determine the overall statistics of the parameter (table 33). Visual observation of the histogram 

for the combined ψmax dataset (figure 45) suggests that ψmax for all OGAs evaluated in this study 

are not normally distributed, with the data more skewed to the right. The descriptive statistics 

(table 33) indicate unequal mode, median, and mean with Ku and Sk indicating a relatively 

peaked distribution and positive skew, respectively. 

 

 

 

 
89 

Source: FHWA.

Figure 45. Chart. Histograms for ψmax with idealized normal distribution curve overlayed.

The normal probability plot for the combined 346-point ψmax dataset, along with the predicted 

normal and lognormal distribution curves, are illustrated in figure 46. The results show that the 

idealized lognormal distribution fits better than the normal distribution, particularly at the lower 

tail of the data. The AD test results for ψmax, however, demonstrate that ψmax is not normally (or 

lognormally) distributed when all laboratories are considered (appendix E). 

 

 

 

 

 

 

 

 

 

 

 

  
90 

Source: FHWA.

Figure 46. Chart. Standard normal variable plots for ψmax. 

Further investigation of the data showed that ψmax is highly sensitive to the n-point centered 

moving average selected (table 21), as evidenced by the elevated ψmax values found by L03 and 

L04 (table 25, table 28, and table 31), which required no manipulation of the data 

(i.e., n point = 1) because of their low frequency of data collection. Separating the broader ψmax

dataset into laboratories where ψmax was calculated using multipoint moving averages (i.e., L01, 

L02, L05, and L06) and laboratories where no data smoothing was performed (i.e., L03 and L04) 

resulted in normal behavior among both groups, with p-values of 0.621 and 0.076, respectively 

(appendix E). As such, ψmax is best approximated by a normal distribution with x̄ = 16.2 degrees 

and s = 5.4 based on the smoothed dilation data from L01, L02, L05, and L06. Notably, much 

like φs and φt, the nonnormality of the broader ψmax and φs datasets is mitigated in the calculation 

of φcv. 

Summary

The researchers made use of descriptive statistics and graphical approaches such as histograms 

and normal probability plots, along with more formal goodness-of-fit tests (e.g., AD) to evaluate 

the underlying distribution of the key physical properties and characteristics and shear strengths 

evaluated in the round-robin study. Based on that analysis, table 34 provides suggested 

 

 

 

 
91 

distribution types that reasonably fit the data best. Depending on the accuracy needed, higher 

order distribution types, such as Weibull and beta distributions, could be tested to evaluate their 

suitability.

Table 34. Summary of suggested statistics for key OGA design parameters.

Parameter n Distribution Type x̄ s

γd95+ (lb/ft3) 54 Bimodal normal 101.4 2.9 

36 110.8 4.3 

φs

^

 (degree) 180 Normal 67.1 7.1 

φt (degree) 90 Normal 51.7 7.5 

φt,r (degree) 90 Uniform 46.5 10.8 

φcv (degree) 86 Normal 47.7 9.0 

ψmax* (degree) 226 Normal 16.2 5.4 

+Statistics based on sedimentary/felsic mineralogy (top) and mafic mineralogy (bottom).

^Statistics based on the fixed upper shear box group.

*Statistics based on calculations with multipoint moving averages.

IMPACT OF STONE SIZE, MINERALOGY, AND LABORATORY

Within this round-robin study, the primary variables included stone size (i.e., No. 57, No. 68, and 

No. 8), mineralogy (i.e., BA, DI, GG, LI, and SI) and laboratory (i.e., L01–L06). Stone size and 

mineralogy relate to the inherent variability of the OGAs, while laboratory relates to the 

measurement variability. Each of these variables, whether alone or in combination with one 

another, can impact the resulting dry unit weights, friction angles, and maximum dilation angles.

The results suggested that stone size does play a minor role in the measured and computed 

parameters, as evidenced by the means and COVs for the key OGA parameters evaluated, such 

as γd95, φs, φt, φt,r, and φcv (table 32). On average, the No. 8 OGAs resulted in lower values with 

slightly more variability compared to the larger No. 57 OGAs; for example, figure 47 shows the 

normal distribution curves for φt based on stone size. This general trend supports the previous 

findings by Nicks et al. (2015). Whether this fact is solely a result of stone size, the larger 

percentage of F&E particles for the No. 8 OGAs (table 16), or a factor of the ratio between stone 

size and LSDS box/cylinder size would need further evaluation. 
92 

Source: FHWA.

Figure 47. Chart. Normal distribution curves for φt per stone size.

Similar to stone size, observations of the LSDS results (e.g., figure 48 and figure 49) suggest that 

mineralogy is not a significant factor in the strength variability found in the study. This finding is 

particularly notable given the previously discussed presence of two distinct clusters of bulk dry 

specific gravity and corresponding γd95 values. 

When the differences are compared in shear stress—horizontal strain behavior due to 

mineralogy, the variability of responses seems to be more pronounced for L05 and L06 

(figure 48); however, the vertical—horizontal strain data show variability across the board 

(figure 49). Generally, the vertical—horizontal strain response appears to correlate with the peak 

shear stress. The samples with higher peak shear stress exhibited steeper dilation behavior, 

particularly for BA and SI mineralogy. The largest impact, therefore, appears to come from 

measurement variability, namely the differences in LSDS devices between the laboratories. The 

researchers performed an ANOVA on the LSDS results to statistically investigate the 

significance of the inherent variability (e.g., stone size and mineralogy) and measurement 

variability (e.g., different LSDS devices). 

 

 
93 

Source: FHWA.

Figure 48. Charts. No. 68 stress-strain curves by mineralogy for all laboratories. 

 

 

 

 
94 

Source: FHWA.

Figure 49. Charts. No. 68 vertical-horizontal strain curves by mineralogy for all 

laboratories. 

ANOVA is a common statistical analysis method used to compare the differences between the 

means of measurement data (Casella and Berger 2002). The following two factors were 

considered in the ANOVA analysis: Factor A—sample type (e.g., stone size and mineralogy); 

and Factor B—testing laboratory (e.g., LSDS device, operator). The two-factor without 

 

 

 

 
95 

replication ANOVA approach was employed to analyze the data (Zaiontz 2020). A three-factor 

ANOVA approach could have been employed instead, splitting the sample type factor into 

separate stone size and mineralogy factors; however, with the relatively limited dataset for those 

factors, combining them into one factor was considered reasonable by the research team. 

As with the AD approach, an alpha of 0.05 was selected to determine F-critical thresholds. If the 

F-statistic of the target factor is less than the corresponding F-critical then the null hypothesis 

(H0) is validated. In this case, H0 states that no statistically significant influence on the physical 

properties and shear strength due to the considered factor (e.g., sample type or laboratory) exist. 

The alternative hypothesis (H1) is that the examined factor is significant enough to impact the 

physical or strength parameter results of the OGAs. If the F-statistic exceeds the F-critical, then 

H0 is rejected and H1 is accepted. Summarized steps for computing the F-statistic and F-critical 

for each parameter evaluated, the full ANOVA results, and the procedures needed to ensure that 

the major assumptions for the two-factor ANOVA test were satisfied are provided in appendix E. 

The ANOVA analysis indicates that H0 was rejected for γd95 whereby γd95 was found to be 

statistically sensitive to both sources of variability (i.e., the sample type and the laboratory). 

However, the results suggest that sample type significantly outweighs the variability due to the 

laboratory performing the density test (appendix E). Similarly, the sample type and laboratory 

are also statistically significant sources of variability for every strength and dilatancy parameter 

except φcv, which was statistically impacted only by the laboratory performing the LSDS test 

(appendix E). Unlike the γd95 ANOVA results, however, the laboratory performing the test plays 

a more profound role than the sample type for all strength and dilatancy parameters. Given the 

wide range of device characteristics within this round-robin study (table 6), it is not surprising 

that the laboratory performing the test plays a significant role in the variability found. 

DS TESTING DEVICES AND PROCEDURES 

The LSDS devices used by each laboratory in this round-robin study were all configured 

differently (table 6 and figure 6), yet most devices met the ASTM D3080 requirements dictating 

the size of the device relative to the size of the sample (ASTM 2011a). The exception was L05 

and L06 where the diameter/width-to-thickness ratios deviated slightly from the minimum of 2:1 

per ASTM D3080; both laboratories utilized a ratio of 1.6:1 instead. The impact of this 

diameter/width to thickness ratio, as well as other device characteristics and/or the associated test 

procedures, on the variability in the resulting strength-deformation characteristics reported in 

chapter 3 needs further investigation. 

Box Shape

Four of the six laboratories had square-shaped LSDS boxes, one laboratory (i.e., L03) had a 

rectangular-shaped LSDS box, and one laboratory (i.e., L05) used a circular device; however, the 

nominal width/diameter of all specimens within the LSDS device were the same (i.e., 12 inches).

There was no apparent difference in the measured shear responses of L03 and L05 that would 

indicate the nonsquare shape played a role. In fact, the results of L05 with a cylindrical device

tended to most closely match the results of L06 which had a square device (e.g., figure 16, 

figure 17, figure 22, figure 23, figure 28, and figure 29). In terms of this study, particularly when 
96 

area corrections were not applied to the results, box shape alone likely did not play a role in the 

variability of the results. 

Box Mobility 

One of the most notable differences between the LSDS devices was the mobility of the upper 

shear box (i.e., restrained or unrestrained). The test devices from L01, L03, and L04 had mobile 

upper boxes that could theoretically move vertically during shear, while L02, L05, and L06 had 

fixed upper boxes (figure 6). The mobility of the upper box can also influence the gap size 

between the two shear boxes; a mobile box could allow the gap to fluctuate during shear, 

whereas a fixed box would result in a constant gap size during shear. In addition, larger frictional 

forces could develop between the specimen and the walls of the box due to the specimen’s 

volume change during shear when the upper box is fixed versus mobile due to the restraint 

(Shibuya et al. 1997; Lings and Dietz 2004; Liu et al. 2005). These frictional forces could then 

result in a larger imposed vertical stress at the shear interface not captured by the load cell at the 

top of the specimen measuring the applied normal load; therefore, the reported friction angles 

from devices with a fixed upper box would be higher than those from devices with a mobile 

upper box. This hypothesis could potentially explain the higher reported values of shear strength 

parameters for the laboratories with a fixed upper box in this study (i.e., L02, L05, and L06) as 

shown in table 24, table 27, and table 30 from chapter 3. 

In addition, φs does not follow normal or lognormal distribution curves when all laboratories are 

combined (figure 38); however, by grouping the datasets according to box mobility, normal 

behavior was clearly found (appendix E). The differences between the laboratories with fixed 

versus mobile upper boxes is also clearly reflected in the strength-dilatancy relationships for all 

the OGAs evaluated in this round-robin study (figure 50). Devices with a fixed upper box 

exhibited relatively low scatter when grouped together (i.e., R2 ≈ 0.4), resulting in a φcv of 55.3 

degrees. In contrast, the strength-dilatancy relationship for laboratories with mobile upper boxes 

has excessive scatter (i.e., R2 ≈ 0.08) and resulted in a lower φcv of 47.0 degrees. 

The coefficients (i.e., slopes) relating secant friction angle to maximum dilation angle were also 

different between fixed (i.e., 0.75) and mobile (i.e., 0.18) upper boxes (figure 50). Based on the 

strength-dilatancy relationships found for different dense sands in axisymmetric and plane strain 

conditions, Bolton (1986) suggested a coefficient of 0.8 between secant friction angle and 

maximum dilation angle (i.e., φs = φcv + 0.8ψmax). This coefficient also roughly estimated the 

LSDS strength-dilatancy of OGAs from an earlier FHWA study (Nicks et al. 2018). The OGA 

results from fixed upper boxes in this round-robin study fit well with this past work, lending 

further credence to that device characteristic; however, further research is needed to fully 

investigate the impact of box mobility and its influence on aggregate behavior during LSDS 

testing. 
97 

Source: FHWA.

Figure 50. Chart. Impact of box mobility on the strength-dilatancy relationship.

Base of the Loading Platen 

The base of the loading platen is in direct contact with the sample and can be smooth, grooved, 

or textured (figure 51). The base boundaries for L01, L05, and L06 are smooth, L02 and L03 are 

grooved, and L04 is textured; the exact details of the grooved and TX platens used are unknown. 

The impact of the base boundaries has not been investigated for LSDS devices; however, Kittu 

and Bernhardt (2017) investigated this factor in standard DS testing and found that the boundary 

of the platen base seemed to have minimal impact on the soil behavior during shear and the 

resulting friction angle. It is, therefore, difficult to specifically state the effect of boundary 

textures on the testing devices considered in this study. Two of the three laboratories with 

smooth boundaries produced results having the highest shear strength. However, other factors 

involved (e.g., box mobility) might explain those results. Further investigation isolating the 

boundary’s impact would need to be performed for LSDS testing to determine the influence on 

the overall response of OGAs during shear. 

 

 

 

 

 

 
98 

Source: FHWA.

A. Smooth base. 

Source: FHWA.

B. Grooved base.

Source: FHWA.

C. Textured base.

Figure 51. Illustrations. Types of loading platen bases.

Connection Between the Load Platen and Normal Load 

The nature of the connection between the load platen and the normal load application (e.g., fixed 

or hinged) is another potential source of variability. Fixing the platen to the normal load, as done 

by L01, L04, and L05, should eliminate any tilting of the platen that may occur during shear. The 

use of ball bearings instead, as done by L02 and L06, could allow for rotation of the platen as the 

sample shears. Note that L03 is unique because the normal load was applied by either dead 

weight or an airbag dead weight would theoretically limit any tilting, whereas an airbag might 

allow tilting. The impact of this connection could not readily be discerned with the dataset, but 

the impact of platen tilting, and the resulting change in normal pressure distribution across the 

sample, needs further research.

 
99 

Specimen Versus Box Dimensions

For all laboratories, the specimen dimensions were different from the box dimensions (table 6). 

Spacers were used by L01, L02, and L04 to limit the sample height within the box to 6 inches. 

No spacers were needed for the L03 device. The use of spacers served to reduce the amount of 

aggregate required for testing while meeting the ASTM D3080 requirements (i.e., the minimum 

specimen diameter/width -to- thickness ratio of 2:1). On the other hand, L05 and L06 both had 

the tallest specimens at 7.5 inches, leaving a 0.5-inch inset for the load platen within the upper 

box (or cylinder in the case of L05). The 2:1 ratio for specimen width to thickness per ASTM 

D3080 was, therefore, not met by L05 and L06; however, considering that the height of 

aggregates above and below the shear zone is nearly equal for all laboratories, the effect of this 

height difference could be minimal. 

Another difference in specimen versus box dimensions was found for L03. Unlike those for the 

other laboratories, the lower box of L03 was larger than the upper box by 3 inches (table 6). The 

rationale for this device configuration is to ensure a constant contact area throughout shear, 

eliminating any need for area corrections. The impact of this factor on the results is not readily 

apparent; therefore, additional testing isolating this device characteristic is needed. 

Vertical Displacement Measurements 

ASTM D3080 requires measurement of both horizontal and vertical displacements throughout 

the test; however, not all participant laboratories routinely measured vertical displacement as part 

of their standard practice (i.e., L02 and L04). For example, L02, which had routinely used an 

airbag to distribute the vertical load to the specimen, retrofitted its device between rounds one 

(i.e., DI) and two (i.e., LI) to switch from the airbag to hydraulic pressure. The retrofitting then 

allowed for vertical displacement measurements. This change created some issues; L02’s 

retrofitted LVDTs often bottomed out, leading to plateauing of its vertical displacement results 

(e.g., figure 17). Anomalous compression of the sample was also reported for No. 57-LI-L02 at 

15 and 30 psi (figure 17); this result may be an error in the sign convention of the LVDT 

measurements, but without confirmation, the data were reported as is. Ultimately, this anomaly 

highlights the potential errors that can occur in measuring and reporting vertical displacement 

data.

The number and locations of vertical displacement measurements using LVDTs were also 

different. L01 and L06 used four LVDTs located close to the four corners of the square shaped 

load platen, with the average reported. The remaining laboratories had fewer LVDTs (table 6) 

and located them around the platen’s center; the average vertical displacement was reported if 

there was more than one LVDT. 

Application of Normal Load 

The method of applying and measuring the normal loads/pressures is another source of 

differences between the laboratories. The different methods primarily influence the distribution 

of the load/pressure to the shear plane and the consistency in load/pressure throughout the 

duration of the test. The methods of applying the load/pressure in the study included dead 

weight, an airbag, hydraulic load, and a microstepper motor (table 6). Dead weight, used by L03 
100 

for the lower normal stresses (i.e., 5 and 10 psi), is considered the most accurate but is generally 

applicable only at lower target normal stresses due to the difficulty and danger of stacking large 

weights. Airbags, used by L02 in round one (i.e., DI) and L03 for higher normal stresses (i.e., 15 

and 30 psi), are considered next best in the sense that the pressure is more evenly distributed 

across the surface of the sample; however, there were no noticeable differences in shear response 

between the tests with an airbag and the other methods of normal load application for L02 and 

L03. Hydraulic and microstepper motors are also capable of applying loads with accuracy; 

however, depending on the rotation of the load platen (i.e., fixed or hinged), stresses may 

redistribute across the surface of the sample during testing. In addition, the fixity of the upper 

box may result in more load reaching the horizontal shear plane due to the frictional forces along 

the sidewalls, as discussed in the Box Mobility section. These aspects were not explicitly 

evaluated in the round-robin study but may be sources of potential variability in the results. 

Regardless of the method of normal load application, the consistency in load/pressure throughout 

the duration of the test is another factor. For example, L04 set the target normal pressure at the 

start of their tests and manually adjusted, as needed, based on the digital readout. Unfortunately, 

the pressure measurements throughout the duration of the test were not supplied by L04, limiting 

evaluation of any changes. Similarly, real-time normal pressure data were absent for L02, 

leading to uncertainty about its consistency throughout shear testing. The unique shear stress—

horizontal strain results from L02 whereby the curve never reaches a distinct peak could 

potentially be a result of such inconsistent normal stresses during testing; however, there is no 

way to verify one way or the other for the purposes of this study. The other laboratories, save 

L03 when using dead weight, had automated normal loading systems. Based on the results from 

this study, no obvious trend that shows an increase or decrease in stress-strain and/or dilation 

response in relation to one of these identified factors exists.

Data Collection Frequency

All laboratories satisfied the minimum data readings in accordance with ASTM D3080; 

however, there was a big difference in the amount of data collected per test. The amount of data 

collected ranged from close to 10,000 data points for L05 to 33 data points for L04. The typical 

time step, or frequency, for data collection for each lab is shown in table 6. The frequency of 

data collection has an impact on the degree of smoothness of the stress-strain curve and the 

vertical-horizontal strain curves. As indicated in table 21, different n-point centered moving 

averages were used to achieve a similar degree of data collection frequency among the vertical 

and horizontal deformation measurements. Without this approach, the computed dilation angles 

varied significantly simply due to the distance/time between data points. The approach also had 

an impact on the distribution of the ψmax dataset, which did not fit predicted normal nor 

lognormal distributions according to the AD tests (appendix E). Normality was found by 

separating the broader ψmax dataset into laboratories where ψmax was calculated using multipoint 

moving averages (i.e., L01, L02, L05, and L06) and laboratories without any data smoothing 

(i.e., L03 and L04) (appendix E).

Setting the Shear Gap

Per ASTM D3080, after consolidation of the specimen, the shear box halves should be separated 

to create a gap (i.e., D85 in this study) before shear is initiated; however, there was inconsistency 
101 

in this practice among the laboratories (ASTM 2011a). L01, L05, and L06 applied the shear gap 

after consolidation, L02 and L03 before consolidation, and L04 before sample placement. The 

primary reason for L02, L03, and L04 setting the gap earlier was the configuration of their LSDS 

devices; the devices did not allow for setting the gap during the test. Setting the shear gap before 

the consolidation phase may have an impact on the aggregate behavior during shear and thus the 

results.

When establishing the gap before sample placement, as in the case of L04, side flow of the 

aggregates within the gap and/or weakening in the shear plane may occur during compaction. 

This gap setting procedure could potentially be a reason for their unique and consistent results 

for exhibiting early failure, although this idea needs further investigation (e.g., figure 18, 

figure 24, and figure 30). There was no clear trend in shear response associated with whether the 

shear gap was applied before or after consolidation in this study. Of note, however, is that 

relatively large tensile loads were registered for L06 as a result of setting the gap 

post-consolidation (see appendix D). While these initial loads were “zeroed out” in the data 

reduction approach employed in this study, the influence of those tensile loads needs further 

investigation. Initial shear stress values before the shear phase (τinitial) for all performed LSDS 

tests are reported in appendix D. 

Specimen Compaction 

To maintain consistency between the laboratories, test instructions were prepared outlining the 

sampling procedures and compaction requirements before testing (appendix A). The target 

density for compaction was specified as γd95, which, based on the results from the round-robin 

study, had low variability across the laboratories (see table 10 through table 12). The compaction 

of the aggregates was performed in three lifts by all laboratories, except for L05 and L06, which 

compacted the stones in five lifts. All laboratories besides L02 hand tamped the OGAs (and 

OS-20-30) to the target density during sample compaction. L02 vibrated its samples to the target 

density, and it is not clear how this process may factor into the overall response of the aggregates 

during shear, provided the target density was still achieved. A distinct difference in the stressstrain behavior and the volumetric response of the samples, however, was found in the results 

produced by L02, despite sharing similar features with L05 and L06. Specifically, the 

stress‐strain curves from L02 exhibited ductile behavior compared to the more brittle responses 

found by L05 and L06. Further evaluation on the impact of the compaction procedure, 

particularly the uniformity of density throughout the specimen, is therefore warranted. 

Test Reports Versus Analyzed Data

The test reports submitted by the laboratories for both the physical and mechanical tests were 

carefully examined to verify the accuracy and reliability of the data. A few irregularities were 

identified on some reports and subsequently corrected before analysis. This finding of 

irregularities highlights the fact that users requesting LSDS tests should independently verify 

(i.e., spot check) the results in the test report. It is also important to note that test reports typically 

provide the results as is without any corrections or manipulations (e.g., zeroing out of the initial 

shear stress, zeroing out of the initial vertical displacement measurement, area corrections, etc.) 

included. These corrections and manipulations can all impact the resulting friction angle(s) 

measured versus reported.
102 

Sometimes what is not included in the test report is also important. Data from the consolidation 

phase, normal load/pressure versus time, and data from each LVDT (if more than one) are not 

commonly included, yet this information can prove valuable in the context of interpreting LSDS 

results. In addition, details about the LSDS device (e.g., upper box mobility, smoothness of the 

platen base, connection between the normal load and the platen, specimen versus box 

dimensions, etc.) are often absent in the test reports; however, given the broad range of LSDS 

devices available around the country, and their significant impact on the results, these details 

may be essential to note or verify with the laboratory. 

DESIGN IMPLICATIONS

In the AASHTO LRFD Bridge Design Specifications, which govern most highway geotechnical 

structures, the resistance factors for each design model (e.g., bearing resistance, sliding, etc.) 

have been either empirically or statistically calibrated (AASHTO 2020). The variability of the 

design parameters within each model (e.g., unit weight, friction angle, etc.), however, are not 

individually accounted for in those calibration efforts. By including the variability of 

geotechnical design parameters, the reliability of each design equation can be better defined. 

When OGAs are used as a structural backfill, the basic statistics (table 33) and suggested 

distribution type (table 34) defined for each parameter found through this round-robin study 

could then be used as inputs in future resistance factor calibration efforts for geotechnical design 

models. Similarly, AASHTO (2020) provides permanent load factors for the vertical pressure 

from the dead load of earth fill (i.e., EV) and the horizontal earth pressure load (i.e., EH); 

however, those factors were developed for traditional soils. Similar efforts could be employed to 

calibrate OGA-specific load factors if needed. 

To highlight the impact of parameter variability on geotechnical design, consider a simple 

example of calculating the σh due to a dry OGA backfill behind a vertical retaining wall with a 

level backslope (equation 7). 

(7) 

Where: 

γ = the unit weight of the aggregate, assumed to equal γd95 for this example.

z = the depth below the top of the retaining wall.

Ka = the active earth pressure coefficient based on the friction angle (φ) of the aggregate, 

assumed to equal φt for this example. 

The depth (z) can reasonably be assumed as a deterministic value; therefore, equation 7 includes 

two variable parameters (i.e., γ and φ). To approximate the COV of the lateral pressure using the 

known statistical results (table 33) of the design parameters (i.e., γd95 and φt) based on the overall 

datasets, the delta method was adopted (Casella and Berger 2002). The results of this analysis 

indicated that the COV of the design model (equation 7) is around 42 percent compared to COVs 

of 5.5 and 14.5 percent for γd95 and φt, respectively. This model variability would change if the 

parameter statistics changed. For example, if the specified OGA was known to be a LI, then the 

statistics of γd95 could be based on the bimodal normal distribution for lighter sedimentary 
103 

mineralogy instead (table 34). This change would result in a lower COV for the design model. 

This propagation of errors is important to consider when calibrating design models. 

In that example, φt was used; however, another friction angle (e.g., secant, residual tangent, or 

constant volume) could be substituted, depending on the design situation. Note that by 

substituting a different friction angle, the statistics of that parameter would thus change the 

variability of equation 7. The decision on which friction angle to use in design remains. As 

mentioned in chapter 3, the design requirements for a project, plus engineering judgment, will 

often determine which friction angle to use to evaluate τ. For instance, if the applied loads are 

well defined and not expected to change throughout the design life of the structure, then use of a 

secant friction angle determined from a single LSDS test under that applied normal load may be 

appropriate. When the loads are more uncertain or may change across the design life of the 

structure, then use of a tangent friction angle determined through a three- or four-point LSDS test 

under a reasonable range of applied normal loads may be appropriate. This method mitigates the 

influence of LSDS device design on φs. Note that the findings from this round-robin study 

suggest that the secant friction angle determined at the highest σn in the range specified to 

determine the tangent friction angle gives similar values between the two, regardless of the 

LSDS device used (figure 52). In other words, the tangent friction angle could perhaps be 

defined solely by conducting a single LSDS test at the highest normal stress that would have 

been specified and then simply determining the corresponding secant friction angle; however, 

further research is needed to validate this potential finding. 
104 

Source: FHWA.

Figure 52. Charts. Comparison of φt and φs. 

The residual friction angle is often used when large deformations are expected in the design, 

such as in areas with slope stability concerns or in areas of seismic activity. Constant volume 

friction angles represent the critical state, or the lower bound of shear resistance; their use may 

be appropriate when the structure behaves with Poisson’s ratio near 0.5 (e.g., geosynthetic 

reinforced soil) and/or when lateral deformations need to be similarly controlled. Generally, φcv

should be close, if not slightly greater than, φt,r; the results of this study showed this general 

relationship (figure 53), albeit with some variability.

 

 

 
105 

Source: FHWA.

Figure 53. Chart. Residual versus constant volume friction angle.

To extrapolate the cumulative distributions of the design parameters evaluated (based on the 

90‐point dataset collected in this study), Monte Carlo simulations can be performed based on the 

mean, standard deviation, and distribution type (table 33 and table 34). For example, 10,000 data 

points were generated using the Monte Carlo method for γd95 and φt to evaluate their extrapolated 

(normal) cumulative distributions (figure 54 and figure 55). Note that the combined γd95 dataset 

was simulated using a normal distribution for illustrative purposes only. Additional simulations 

are plotted to illustrate the influence of OGA specific gravity and box fixity on γd95 and φt, 

respectively. Note that OGAs with Gsb less than 2.8 are considered “lightweight,” while OGAs 

with Gsb greater than 2.8 are considered “heavyweight” (within figure 54). These extrapolated 

cumulative distributions could then be used to evaluate the probability of exceedance for any 

proposed OGA design value. In the examples for γd95 and φt, 95.6 lb/ft3 and 39.1 degrees, 

respectively, represent values that have a 95 percent probability of exceedance (i.e., only a 

5 percent chance that values smaller than those would be found). 

 

 

 

 

 

 

 

 
106 

Source: FHWA.

Figure 54. Chart. Extrapolated cumulative distributions for dry unit weight at 95RD.

Source: FHWA.

Figure 55. Chart. Extrapolated cumulative distributions for tangent friction angle.

 

 

 

 

 

 

 

 
107 

CHAPTER 5. CONCLUSIONS

FHWA initiated a six-laboratory round-robin study to evaluate the variability of physical 

properties and characteristics and shear strength for three common OGA gradations (i.e., No. 57, 

No. 68, and No. 8) from five different rock sources (i.e., BA, DI, GG, LI, and SI). In total, 90 

OGAs were evaluated as part of this study. OS-20-30 was also included as a standard soil for 

further comparison. Testing for physical properties and characteristics by each laboratory 

included sieve analysis (both on the as-received samples and the post-shear tested samples) and 

minimum and maximum dry density testing (chapter 2). In addition, FHWA performed AIMS2 

and Micro-Deval testing (chapter 2), with bulk dry specific gravity, L.A. Abrasion, and 

magnesium sulfate soundness results provided directly by the source quarries (chapter 3). LSDS 

testing was then performed by each laboratory (chapter 2) to determine the τ of the OGAs (and 

OS-20-30), namely the strength-deformation characteristics. Test instructions were provided to 

each laboratory to ensure consistency during sample preparation and testing (appendix A). 

The key results from all tests (chapter 3), alongside further quantitative statistical analyses 

(chapter 4), provided insights into the degree of interlaboratory variability of the physical and 

strength parameters of OGAs and the factors impacting these parameters (e.g., stone size, 

mineralogy, and laboratory). A summary of the basic statistics (e.g., mean, standard deviation, 

and COV) for each OGA (and the entire dataset, as applicable) are provided in table 32. 

Understanding this variability is important for designers to assess more reasonable values for 

geotechnical designs, agencies in the development of material specifications, contractors in their 

selection of structural backfills, and researchers to evaluate the reliability of various design 

methods and to calibrate load and resistance factors in the framework of LRFD. Additionally, the 

results of this study suggest that modifications to ASTM D3080 are needed when aggregates are 

tested. A summary of the key results and findings from this study is provided in the following 

subsection below.

GRADATION

Key findings related to gradation include the following: 

• The sieve analysis (appendix B) indicated many of the delivered OGAs were not 

compliant with the AASHTO M 43 size specifications (table 7); however, this finding 

was based on only one sieve test per laboratory. 

• The interlaboratory variability of D85 was relatively low, with COVs ranging, on average, 

between 2.7 percent for the No. 8 OGAs and 7.5 percent for the No. 57 OGAs (table 8). 

The low variability in D85 suggests that similar gap sizes were set in LSDS testing by 

each laboratory. 

• The breakage index (BI) was computed by comparing the post-shear with the initial 

gradations (table 9); the largest variability in breakage occurred for the No. 57 OGAs, 

with an average COV of 65.7 percent. 
108 

• The BI potentially provides insights on the LSDS devices used and the impact that

crushing may have had on strength-deformation characteristics. For example, L03 and

L04 generally demonstrated the highest BI values and had lower friction angles than L05

and L06, which had the lowest BI values (table 9).

DRY UNIT WEIGHT AND BULK DRY SPECIFIC GRAVITY

Key findings related to the dry unit weight and bulk dry specific gravity include the following: 

• Researchers used three different methods to measure unit weight (chapter 2); however,

the low variability of γd95 within individual sample types (maximum COV of 3.1 percent)

suggests that compacted OGA density was not sensitive to the device or test procedure.

• Researchers found the variability in γdmin and γdmax for OGAs to be similar to the

variability other researchers found for poorly graded sands (table 1).

• Variability of γd95 between sample types was significant, despite low variability within

each stone size-mineralogy combination. Compacted unit weight is heavily influenced by

the bulk dry specific gravity (table 13) and thus the mineralogy of the stones; BA and DI

OGAs are significantly denser than LI and GG.

• The distribution of the entire γd95 dataset was not normal. However, two overlapping

normal distributions were revealed when the lighter, felsic metamorphic (i.e., GG) and

sedimentary mineralogy (i.e., LI and SI) were normality tested separately from the

denser, mafic igneous mineralogy (i.e., BA and DI).

• The two-factor ANOVA analysis found that γd95 was significantly dependent on the

sample type and, to a lesser degree, the laboratory performing the test (appendix E). The

laboratory variability found by ANOVA is a product of ranking within the data. L02 and

L06 routinely found the highest γd95 values; meanwhile, L04 and L01 consistently found

the lowest. This aspect of variability is not captured in the COVs of γd95.

PARTICLE SHAPE CHARACTERISTICS

Key findings related to the particle shape characteristics include the following:

• AIMS2 tests were performed by FHWA to evaluate the particle characteristics such as

angularity, SP, F&E particles, and TX (appendix C).

• The angularity index was classified as low for all OGAs evaluated (and the OS-20-30)

(table 14). This low classification is contrary to the expectation that a crushed,

manufactured rock is angular. Since AIMS2 classifications were developed for pavement

materials, there may be a need to update those classifications for structural backfills.

• The SP index was designated as medium for all OGAs (table 15); however, when the

F&E values were evaluated (table 16), it was found that the No. 8 had the largest

percentage of F&E particles, while No. 57 had the lowest percentage.
109 

• Texture was noticeably dependent on mineralogy, unlike the other shape factors 

(table 17): SI OGAs consistently had the lowest TX index (classified as medium), while 

GG OGAs exhibited the roughest TX index (classified as high).

PARTICLE DURABILITY

Key findings related to particle durability include the following: 

• Particle durability was evaluated through Micro-Deval, L.A. abrasion, and magnesium 

sulfate soundness tests (table 18); tests were performed by FHWA and the source 

quarries.

• The data showed that the OGAs with SI and GG exhibited the most and least durability, 

respectively, regardless of the type of test (table 18). 

SHEAR STRENGTH 

Key findings related to shear strength include the following: 

• LSDS tests were generally conducted per ASTM D3080 under the following test 

conditions: dry moisture state, shear gap set at D85, target compaction at 95RD, fixed 

strain rate at 0.015 inches per min, four imposed σn levels (i.e., 5, 10, 15, and 30 psi), and 

termination of the tests at 20 percent horizontal strain. All LSDS results are presented in 

appendix D. 

• The LSDS results showed markedly pronounced differences in the shear stress—

horizontal strain and vertical-horizontal strain responses between the laboratories for all 

stone sizes (e.g., figure 16, figure 17, figure 22, figure 23, figure 28, and figure 29) and 

the OS-20-30 (figure 11 and figure 12). These results are a strong indication that the 

variability is highly laboratory dependent. 

• The horizontal strain corresponding to the peak shear stress (εh,peak) for OGAs was 

considerably higher (about 5 to 11 percent, on average) than that for the OS-20-30 (about 

1 to 3 percent); see table 19, table 23, table 26, and table 29.

• Secant friction angles (φs) over the range of 5 to 30 psi ranged from 36.4 to 82.8 degrees, 

and tangent friction angles (φt) ranged from 34.5 to 68.1 degrees (table 33); those LSDS 

devices that had a fixed upper box were on the upper end of the range. Meanwhile, 

devices with a mobile upper box were on the lower end of the range (figure 38).

• The variability of φt,r was the highest of all OGA friction angles evaluated (i.e., average 

COV of 22 percent), followed by φcv (average COV of 19 percent), φs, (average COV of 

17 percent) and φt (average COV of 14 percent); see table 32. Less variability was found 

for OS-20-30 (table 20) compared to OGAs. 

• The variability in τ found for OGAs was similar to the variability found by other 

researchers for sands and other granular materials (see chapter 1).
110 

• Dilation angles for each stone size ranged from about 16 to 19 degrees (table 32); 

however, COVs up to 42 percent were found. This relatively high variability may be a 

function of the n-point centered moving average approach that was employed to achieve 

consistency in comparing LSDS results (table 21); n-points specific to the laboratory 

device would have resulted in different dilation angles for each laboratory. 

• An evaluation of the strength-dilatancy relationships showed that results produced by 

fixed upper boxes matches well with past work (i.e., φs = φcv + 0.8ψmax), resulting in an 

overall φcv of 55.3 degrees (figure 50).

• Based on AD tests (appendix E), φt and φcv were normally distributed; φt,r exhibited a 

uniform distribution (table 34). In contrast, ψmax and φs were not normally distributed 

when all laboratories were evaluated together.

• Additional φs AD tests where laboratories were grouped by upper shear box fixity found 

that φs was normally distributed for the three laboratories (i.e., L02, L05, and L06) with 

fixed upper shear boxes. 

• ψmax was reevaluated by grouping laboratories with similar data collection frequencies. 

AD testing showed ψmax followed a normal distribution for data with both high (L01, 

L02, L05, and L06) and low (L03 and L04) data collection frequency groups. Collection 

frequency and data smoothing (table 21) clearly influence ψmax. 

• The two-factor ANOVA showed that all friction and dilation angles were significantly 

impacted by sample type (i.e., stone size and mineralogy) and laboratory, although the 

laboratory far outweighed the sample type in terms of significance (appendix E).

LSDS DEVICES AND PROCEDURES 

Conclusions regarding LSDS devices and procedures include the following: 

• There were six unique LSDS devices with varying configurations included in the study 

(figure 6); however, other configurations likely exist nationally and internationally. The 

key differences in this study, summarized in table 6, were box shape, upper shear box 

mobility, base smoothness of the loading platen, connection between the loading platen 

and normal load, box and specimen dimensions, number of LVDTs to measure vertical 

displacement, and application of normal load. 

• Procedural differences in conducting LSDS tests included the frequency of data 

collection (i.e., sampling rate), timing of setting the shear gap, and method of specimen 

compaction (chapter 4).

• Whether the upper shear box was fixed was the most influential LSDS device 

configuration variable on OGA strength results. The strength-dilatancy relationships 

showed that the devices with a fixed upper box had less scatter and were closer to 

conventional expectations (figure 50). Further AD tests performed on φs found that the 
111 

data from laboratories with fixed upper boxes followed a normal distribution. In contrast, 

laboratories with mobile upper boxes remained neither normal nor lognormal behavior. 

• The main conclusion is that LSDS testing needs to be standardized to reduce variability; 

particularly, standard device configurations should be developed and used. This

standardization would require either modifications to ASTM D3080 to account for 

differences in larger devices or the development of a new standard for LSDS testing.

LESSONS LEARNED

Setting up a round-robin study seems straightforward: Select a certain number of laboratories, 

the test method(s) to follow, and the sample(s) to test. Unfortunately, a complete picture is 

typically only clear in hindsight, after the results are in. Particular to this study, as data analysis 

proceeded and knowledge of LSDS testing improved, researchers found that there was more to 

the LSDS test than just a box of rocks. Setting up this interlaboratory study and evaluating the 

resulting data imparted some general wisdom about best practices. Going forward, researchers

would benefit from doing the following in setting up similar round-robin studies: 

• Conduct an extensive literature review and/or an industry survey in advance. This 

practice would have helped better identify the laboratories (and thus LSDS devices) to 

select for the round-robin. Before the study, the seemingly subtle differences in LSDS 

device configurations were not well understood but may have led to different 

laboratories/devices being selected to ensure those differences could be quantified 

through the results.

• Set up site visits and/or phone calls with the laboratories before the start of the study. 

This practice would have allowed for more extensive discussions to better understand 

their devices and test practices and to explain the requirements for consistency in testing. 

Clearly communicating the test instructions (appendix A) verbally could have clarified 

the procedures, avoided delays, and reduced unexpected sources of variability.

• Be specific in the data outputs expected from the laboratories. While the test instructions 

(appendix A) provided a list of data to be submitted by each lab, there was not enough 

specificity to clearly identify the level of detail expected. For example, it was assumed 

that consolidation data would be provided since that is part of the LSDS tests; however, 

most laboratories do not record or store this information. Similarly, photos were 

requested to document the laboratory procedures; however, photos do not fully express 

everything, so having written procedures or descriptions would have been helpful. 

• Start with a standard soil (e.g., OS-20-30) to identify any potential issues and iron out the 

kinks before testing the samples of interest. In this study, OS-20-30 was included at the 

end of the round-robin to help decipher the OGA results, but some of the pitfalls could 

have been avoided from the beginning. 

• Develop troubleshooting protocols for what to do if things do not go as planned. In this 

study, for example, many of the sieve tests suggested the OGAs delivered to the 

laboratories did not meet the AASHTO M 43 specifications; while the test instructions 
112 

(appendix A) briefly told the laboratories to stop and await further instructions, there 

were not internal procedures on how to handle noncompliance, resulting in a case-bycase determination to move forward. 

• Verify results from the laboratories providing them. During lab report evaluation, some 

inconsistencies were found that could have been overlooked in a typical review. 

• Request any clarifications from the laboratories in a straightforward, concise manner to 

avoid back-and-forth correspondence and reduce delays. Once questions were raised, the 

laboratories were immediately contacted for an answer resulting in multiple requests for 

information. This back-and-forth could have best been conducted by planning and 

consolidating all inquiries for more efficient responses. 

• Begin data reduction and analysis procedures before all the data is collected. Clearly 

analyze the data early so trends or anomalies for intra- and interlaboratory reliability can 

be identified early on. Some discrepancies in internal data analyses were found after the 

fact. These discrepancies could have been corrected before additional testing began. 

• Independently check the data, both from the laboratories providing the results and from 

in-house data reduction and analysis efforts; everyone makes mistakes. This data 

validation will ensure data quality from the beginning. Including this type of procedure 

early on would have avoided going back and forth with this large amount of data and thus 

limiting delays. 

• Develop clear data management protocols (e.g., file names, file structure, formats, file 

organization, version control, etc.) before starting any study. The quantity of data 

collected was by no means considered “big data”; however, the datasets were large 

enough that the files required time-consuming restructuring that could have been avoided 

with advanced and thoughtful planning. 

GEOTECHNICAL DESIGN APPLICATION

Ultimately, the variability of measured design parameters has an impact on the resulting design. 

Key findings from this study through a design implication lens are as follows:

• The comparison of φs and φt from all LSDS tests indicated that, at the highest normal 

stress level (i.e., 30 psi), the two parameters were similar regardless of the laboratory 

performing the LSDS test (figure 52). The practical application of this finding is that a 

secant friction angle from a single test at the highest normal stress of a test series may 

sufficiently represent the tangent friction angle. Additional research is needed to verify 

this result for all potential ranges of σn. 

• Both φt,r and φcv are generally conservative measures of strength; as expected, these 

parameters were found to be nearly equal in magnitude (figure 53).
113 

• The variability of a design parameter is different from the variability of a design model 

that uses that parameter; this propagation of errors should be considered when any design 

model is calibrated.

• Suggested values for γd95 and φt are proposed (table 35) based on extrapolated cumulative 

distribution functions established from 10,000 data points generated using a Monte-Carlo 

approach (chapter 4). A range for γd95 that encompasses the middle 90 percent of the 

combined dataset is provided in the absence of mineralogy information for the specified 

OGA on a project (figure 54). The suggested default value of 40 degrees for φt closely 

represents a 95-percent probability of being exceeded based on the combined dataset in 

this round-robin study (figure 55). This default value agrees with past FHWA research 

recommendations for OGAs by Nicks et al. (2018), despite the variability in LSDS 

testing this round-robin study found. 

Table 35. Proposed default values for key geotechnical design parameters.

Parameter Suggested Values

γd95 96–115 lb/ft3

φt 40 degrees 

NEXT STEPS AND FUTURE RESEARCH

With all the results collected in this round-robin study, the next immediate step is to archive the 

data for public use. The FHWA InfoMaterialsTM web portal is one centralized gateway to 

infrastructure research and materials testing data that could be used for this purpose

(FHWA 2022). In addition, the data will be further mined to identify the influence of intrinsic 

factors (e.g., particle shape characteristics, unit weight, stone size, durability, etc.) on τ of OGAs. 

A nonlinear multivariate regression analysis could also be performed on the data to develop 

correlations between parameters. Regardless, the impact of LSDS devices and test procedures for 

structural backfills was profound, suggesting standardization for testing the strength of larger 

materials is needed. This avenue of research will be further investigated through experimental 

and numerical studies to home in on the most appropriate device configurations for producing 

repeatable and reliable results, with the aim of taming the wild west of LSDS testing.

115 

APPENDIX A. SAMPLE PREPARATION PROTOCOL AND INSTRUCTIONS

It is understood that many testing laboratories have their own internal procedures for DS testing; 

however, to maintain consistency in both sample preparation and key test procedures, the 

following test instructions were sent to each laboratory at the beginning of the round-robin study. 

TEST SAMPLES (AASHTO NO. 8, NO. 68, AND NO. 57)

Each lab will receive a pallet containing four 5-gal buckets for each aggregate type; a total of 

12 buckets. Sample identification labels are attached on the outside of the bucket and inside the 

bucket. Use this label code in the indentation of the aggregate types and related test results. 

Please complete the testing of each aggregate one at a time, before proceeding to the next 

aggregate sample. 

Please take photographs of the aggregates, test devices, sample preparation, and test procedures 

used in this project for reporting and publications requirements. A permission release form will 

be provided. 

SAMPLE PREPARATION

For each aggregate type, all buckets should be emptied and placed in an oven at 110 °C to 

evaporate any moisture in the aggregates and to determine the dry mass needed for each planned 

test. 

SAMPLE REDUCTION

The oven-dried aggregates for each aggregate type should be poured onto a tarp to produce a 

mini, uncontaminated stockpile, then mixed thoroughly, with samples collected for sieve analysis 

and density tests using a quartering sample reduction method, as per AASHTO T 248—Method 

B Quartering (AASHTO 2014) (figure 56). The samples used for sieve analysis and density 

testing must be mixed thoroughly and blended back with the original source. 
116 

Source: FHWA.

Figure 56. Illustration. Sampling procedure using a quartering method.

SIEVE ANALYSIS (ASTM C136) AND MAXIMUM/MINIMUM INDEX (RELATIVE) 

DENSITY (ASTM D4253 AND D4254)

Grain size analysis must be conducted by each lab first for each aggregate to ensure the 

laboratory has the correct samples (i.e., meets AASHTO specifications) before density and 

LSDS testing is conducted. To have a compatible comparison with the AASHTO M 43-05 

aggregate designation, use the sieves that match with the sieve numbers indicated in table 36 for 

each aggregate type (AASHTO 2018a). If the sieve results of the aggregates do not fall within 

the limits of the specifications, immediately contact FHWA, and do not conduct any additional 

tests.
117 

Table 36. Selected AASHTO M 43 aggregate designations (AASHTO 2005). 

Sieve No.

Particle Size

(inches)

Percent Passing Through Sieve

No. 57 No. 68 No. 8

1.5 inch 1.5 100 — —

1 inch 1.0 95–100 100 —

3/4 inch 0.75 — 90–100 —

1/2 inch 0.50 25–60 — 100

3/8 inch 0.375 — 30–65 85–100

No. 4 0.187 0–10 5–25 10–30

No. 8 0.093 0–5 0–10 0–10

No. 16 0.046 — 0–5 0–5

—Not specified.

Note: Please submit all initial sieve analysis results before commencing the LSDS tests, 

regardless of whether the aggregates meet the specifications or not.

Following the concurrence of the aggregates’ gradation with the AASHTO designation, the 

minimum density test should be performed first, followed by the maximum density test.

LSDS TESTING (ASTM D3080) 

Test instructions related to sample preparation, compaction procedures, and LSDS test setup 

protocols are listed in the following subsections. 

Sample Preparation 

After testing the aggregate for the density and sieve analysis, blend them back in the original 

four-bucket pile. The quartering method should be used again to thoroughly mix the aggregates 

again before LSDS testing. 

Fill a bucket by taking aggregate from each quarter until the required target dry mass is reached 

to achieve the dry maximum index density of 95 percent. Repeat this step to fill the three 

remaining buckets. Each bucket will be used to perform a single point of the LSDS shear test. If 

there is not enough material to conduct virgin samples for each point of the LSDS shear test, then 

blend the samples back together to complete the final test.
118 

LSDS Test Setup

The testing procedures related to the sample compaction and DS tests are as follows:

1. Avoid unreasonable breakdown of the aggregate during the compaction process (such as 

with a mechanical or vibratory device). For instance, instead of using vibratory hammers, 

the aggregates can be compacted in four to five layers using a wooden hammer. 

2. Adhere to the following parameters and procedures for each of the LSDS shear tests:

a. Shear rate: 0.015 inch/min. 

b. Density: 95 percent relative density (based on minimum and maximum index 

densities).

c. Shear gap: D85 determined from the sieve analysis for each aggregate type.

d. Normal stress increments: 5, 10, 15, and 30 psi. 

e. Determination of failure: Terminate the test at 20 percent horizontal strain, or 2.4 

inches, regardless of whether the peak shear stress occurs before this termination 

point. 

Post-LSDS Sieve Analysis

At the end of the four-point test series for each aggregate type, reblend the aggregates back into a 

single source, four-bucket pile, and resample to perform the posttest sieve analysis.

TEST DATA

Submit a separate summary report for each aggregate type that include the following data: 

1. Initial sieve analysis data and results.

2. Minimum and maximum density data and results.

3. LSDS test results: 

a. Summary information of the results.

b. Disclosure of any anomalies.

c. Both the raw and reduced data files for each aggregate type. The raw data must 

include the horizontal strain, the vertical strain, the horizontal load/stress, the vertical 

load/stress, and the elapsed time.

4. Post-sieve analysis data and results.

5. Photos to document the procedure.
119 

APPENDIX B. PRE- AND POST-SHEAR SIEVE ANALYSIS

This following appendix contains the pre- (i.e., as-received) and post-shear sieve analysis for all 

tested aggregates. Sieving results are presented as percent passing values. The AASHTO M 43 

specifications per sieve size are also included in each table for each aggregates’ respective stone 

size (AASHTO 2005). Aggregates are presented in descending gradation coarseness followed by 

mineralogy in alphabetic order. 

NO. 57 

The pre- and post-shear sieving data for the No. 57 OGAs are presented in table 37 through 

table 41.
120 

Table 37. Pre- and post-shear sieving data for No. 57-BA.

Sieve 

No.

Sieve 

Size 

(inches)

No. 57 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 100 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 100 100 100 100 100 100 100 100 100

1.5 inch 1.5 100 100 100 100 100 100 100 100 100 100 100 100 100

1 inch 1.0 95-100 100 100 100 100 100 100 100 100 99.6 99.1 100 99.9

3/4 inch 0.75 — 88.0 84.0 83.8 75.5 88.0 91.3 85.0 83.0 79.7 79.4 — — 

1/2 inch 0.5 25–60 37.0 37.0 30.1 26.9 49.3 50.9 34.0 27.0 29.0 29.9 34.8 33.2

3/8 inch 0.375 — 17.0 12.0 6.1 4.5 24.2 26.7 12.0 8.0 9.4 10.4 — — 

No. 4 0.187 0–10 4.0 5.0 0.5 1.5 3.8 5.0 2.0 1.0 1.1 2.0 3.1 2.3

No. 8 0.0937 0–5 2.0 2.0 0.5 1.5 1.5 1.7 1.0 1.0 0.5 1.3 1.7 1.3

No. 16 0.0469 — 1.0 1.0 0.5 1.4 1.1 1.2 1.0 1.0 0.5 1.0 — — 

No. 30 0.0234 — 1.0 1.0 0.5 1.4 1.0 1.1 1.0 1.0 — — — — 

No. 50 0.0117 — 1.0 1.0 0.5 1.4 0.9 1.0 1.0 1.0 — — — — 

No. 100 0.0059 — 1.0 1.0 0.5 1.3 0.8 0.9 1.0 1.0 — — — — 

No. 200 0.0029 — 0.7 0.7 0.5 1.3 0.7 0.9 0.4 0.3 0.4 0.7 0.8 0.7

—No data. 
121 

Table 38. Pre- and post-shear sieving data for No. 57-DI.

Sieve 

No.

Sieve 

Size 

(inches)

No. 57 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 — 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 — 100 100 100 100 100 100 100 100

1.5 inch 1.5 100 100 100 100 — 100 100 100 100 100 100 100 100

1 inch 1.0 95-100 100 100 100 — 100 99.5 99.0 100 99.6 99.5 100 100

3/4 inch 0.75 — 88.0 88.0 89.4 — 92.8 90.4 91.0 95.0 88.8 90.1 — — 

1/2 inch 0.5 25–60 36.0 35.0 42.3 — 41.5 46.0 40.0 54.0 40.9 43.4 47.6 51.7

3/8 inch 0.375 — 13.0 11.0 13.5 — 16.4 19.9 17.0 28.0 13.0 15.3 — — 

No. 4 0.187 0–10 2.0 1.0 1.5 — 3.1 3.4 3.0 8.0 1.4 2.4 2.7 4.9

No. 8 0.0937 0–5 1.0 1.0 1.3 — 1.9 1.2 2.0 3.0 0.6 0.7 1.4 2.5

No. 16 0.0469 — 1.0 0.0 1.2 — 1.7 0.9 1.0 2.0 0.6 0.5 — — 

No. 30 0.0234 — 0.0 0.0 1.2 — 1.6 0.8 1.0 2.0 — — — — 

No. 50 0.0117 — 0.0 0.0 1.2 — 1.4 0.8 1.0 2.0 — — — — 

No. 100 0.0059 — 0.0 0.0 1.1 — 1.0 0.7 1.0 1.0 — — — — 

No. 200 0.0029 — 0.0 0.0 1.0 — 0.6 0.5 0.6 1.0 0.0 0.0 0.0 1.2

—No data.
122 

Table 39. Pre- and post-shear sieving data for No. 57-GG.

Sieve 

No.

Sieve 

Size 

(inches)

No. 57 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 100 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 100 100 100 100 100 100 100 100 100

1.5 inch 1.5 100 100 100 100 100 100 100 100 100 100 100 100 100

1 inch 1.0 95-100 100 100 100 100 99.5 98.7 100 100 99.7 99.0 99.4 99.5

3/4 inch 0.75 — 86.0 85.0 86.6 71.9 72.3 76.5 80.0 84.0 80.1 72.1 — — 

1/2 inch 0.5 25–60 35.0 31.0 20.7 13.3 19.2 20.1 23.0 26.0 29.3 20.8 27.4 34.2

3/8 inch 0.375 — 18.0 12.0 4.6 3.0 6.8 5.9 6.0 6.0 8.0 4.0 — — 

No. 4 0.187 0–10 7.0 8.0 0.7 0.4 4.1 4.8 3.0 1.0 4.1 0.9 1.2 5.2

No. 8 0.0937 0–5 5.0 7.0 0.4 0.4 3.6 4.0 2.0 1.0 3.3 0.4 1.0 3.9

No. 16 0.0469 — 5.0 6.0 0.4 0.3 3.2 3.4 2.0 1.0 2.9 0.4 — — 

No. 30 0.0234 — 4.0 5.0 0.4 0.3 3.0 3.3 2.0 1.0 — — — — 

No. 50 0.0117 — 3.0 4.0 0.4 0.3 2.5 2.9 2.0 1.0 — — — — 

No. 100 0.0059 — 2.0 3.0 0.3 0.3 1.7 2.3 1.0 1.0 — — — — 

No. 200 0.0029 — 0.5 1.6 0.3 0.2 0.7 0.6 0.9 0.3 0.9 0.2 0.4 0.9

—No data.
123 

Table 40. Pre- and post-shear sieving data for No. 57-LI.

Sieve 

No.

Sieve 

Size 

(inches)

No. 57 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 100 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 100 100 100 100 100 100 100 100 100

1.5 inch 1.5 100 100 100 100 100 100 100 100 100 100 100 100 100

1 inch 1.0 95-100 99.0 99.0 100 100 99.3 99.0 100 100 99.2 99.8 98.8 99.0

3/4 inch 0.75 — 83.0 77.0 84.9 95.1 83.9 88.7 84.0 87.0 78.8 78.8 — — 

1/2 inch 0.5 25–60 29.0 28.0 33.7 42.1 31.0 45.3 34.0 36.0 30.4 31.5 25.3 33.2

3/8 inch 0.375 — 8.0 8.0 9.4 12.9 11.1 24.4 12.0 13.0 7.1 7.6 — — 

No. 4 0.187 0–10 1.0 1.0 1.1 0.9 2.8 9.6 3.0 2.0 0.6 0.4 1.5 5.5

No. 8 0.0937 0–5 1.0 1.0 0.9 0.5 2.1 6.4 2.0 1.0 0.5 0.2 1.2 4.1

No. 16 0.0469 — 0.3 0.3 0.9 0.5 1.7 4.7 1.0 1.0 0.5 0.2 — — 

No. 30 0.0234 — 0.3 0.3 0.9 0.5 1.5 3.6 1.0 1.0 — — — — 

No. 50 0.0117 — 0.3 0.3 0.9 0.5 1.2 2.6 1.0 1.0 — — — — 

No. 100 0.0059 — 0.3 0.3 0.8 0.5 0.7 1.4 1.0 1.0 — — — — 

No. 200 0.0029 — 0.3 0.3 0.8 0.4 0.3 0.7 0.7 0.3 0.1 0.1 0.0 1.4

—No data. 
124 

Table 41. Pre- and post-shear sieving data for No. 57-SI.

Sieve 

No.

Sieve 

Size 

(inches)

No. 57 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 100 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 100 100 100 100 100 100 100 100 100

1.5 inch 1.5 100 100 100 100 100 100 100 100 100 100 100 100 100

1 inch 1.0 95-100 98.0 98.0 93.1 100 100 98.2 98.0 100 95.9 98.4 97.0 98.4

3/4 inch 0.75 — 85.0 85.0 76.9 73.6 91.2 87.6 80.0 85.0 75.3 84.6 — — 

1/2 inch 0.5 25–60 56.0 61.0 40.4 48.4 70.6 61.6 49.0 58.0 50.6 57.9 60.4 60.6

3/8 inch 0.375 — 40.0 44.0 24.5 35.8 52.8 45.0 34.0 40.0 34.3 37.5 — — 

No. 4 0.187 0–10 5.0 7.0 2.1 5.0 6.6 6.1 4.0 5.0 4.6 4.4 6.9 7.1

No. 8 0.0937 0–5 1.0 1.0 0.6 1.3 0.7 1.7 1.0 1.0 0.5 0.4 1.1 1.4

No. 16 0.0469 — 1.0 1.0 0.6 1.1 0.5 1.1 1.0 1.0 0.3 0.3 — — 

No. 30 0.0234 — 0.1 1.0 0.6 1.1 0.5 0.7 1.0 1.0 — — — — 

No. 50 0.0117 — 0.1 1.0 0.6 1.0 0.4 0.6 1.0 1.0 — — — — 

No. 100 0.0059 — 0.1 0.1 0.6 1.0 0.2 0.4 1.0 1.0 — — — — 

No. 200 0.0029 — 0.1 0.1 0.6 1.0 0.0 0.4 0.2 0.3 0.2 0.2 0.4 0.6

—No data.
125 

NO. 68 

The pre- and post-shear sieving data for the No. 68 OGAs are presented in table 42 through table 46. 

Table 42. Pre- and post-shear sieving data for No. 68-BA.

Sieve 

No.

Sieve 

Size 

(inches)

No. 68 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 100 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 100 100 100 100 100 100 100 100 100

1.5 inch 1.5 — 100 100 100 100 100 100 100 100 100 100 — — 

1 inch 1.0 100 100 100 100 100 100 100 100 100 100 100 100 100

3/4 inch 0.75 90-100 95.0 95.0 94.6 96.8 93.8 96.9 95.0 95.0 93.3 94.3 92.0 95.6

1/2 inch 0.5 — 65.0 70.0 77.2 78.4 71.7 81.1 70.0 71.0 67.8 72.6 — — 

3/8 inch 0.375 30–65 44.0 51.0 60.7 66.1 54.9 65.4 53.0 53.0 46.6 52.4 53.0 54.0

No. 4 0.187 5–25 10.0 14.0 15.7 18.6 13.5 20.3 13.0 14.0 9.8 17.5 14.5 15.6

No. 8 0.0937 0–10 2.0 3.0 2.3 3.4 2.7 4.6 2.0 2.0 0.8 2.0 2.4 2.8

No. 16 0.0469 0–5 1.0 2.0 1.1 2.2 1.5 2.6 1.0 1.0 0.4 0.8 1.2 1.3

No. 30 0.0234 — 1.0 1.0 1.0 1.9 1.3 2.1 1.0 1.0 — — — — 

No. 50 0.0117 — 1.0 1.0 1.0 1.8 1.2 1.8 1.0 1.0 — — — — 

No. 100 0.0059 — 1.0 1.0 1.0 1.7 1.1 1.7 1.0 1.0 — — — — 

No. 200 0.0029 — 0.7 1.0 0.9 1.6 1.0 1.5 0.8 0.5 0.3 0.6 0.8 0.7

—No data. 
126 

Table 43. Pre- and post-shear sieving data for No. 68-DI.

Sieve 

No.

Sieve 

Size 

(inches)

No. 68 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 — 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 — 100 100 100 100 100 100 100 100

1.5 inch 1.5 — 100 100 100 — 100 100 100 100 100 100 — — 

1 inch 1.0 100 100 100 100 — 100 100 100 100 100 100 100 100

3/4 inch 0.75 90-100 92.0 92.0 95.7 — 94.8 93.9 92.0 94.0 93.8 92.9 94.7 94.1

1/2 inch 0.5 — 48.0 47.0 71.5 — 55.3 45.2 52.0 62.0 49.7 49.0 — — 

3/8 inch 0.375 30–65 31.0 28.0 58.1 — 33.3 24.3 32.0 44.0 30.2 26.7 41.1 35.1

No. 4 0.187 5–25 5.0 4.0 18.6 — 5.0 4.1 4.0 10.0 4.9 3.2 6.6 7.5

No. 8 0.0937 0–10 1.0 1.0 8.2 — 2.3 1.6 1.0 3.0 0.9 0.5 1.6 3.1

No. 16 0.0469 0–5 0.0 1.0 0.8 — 2.0 1.2 1.0 2.0 0.9 0.4 1.3 2.4

No. 30 0.0234 — 0.0 0.0 0.7 — 1.9 1.0 1.0 2.0 — — — — 

No. 50 0.0117 — 0.0 0.0 0.6 — 1.7 0.9 1.0 1.0 — — — — 

No. 100 0.0059 — 0.0 0.0 0.6 — 1.2 0.8 1.0 1.0 — — — — 

No. 200 0.0029 — 0.0 0.0 0.5 — 0.5 0.6 0.5 1.0 0.0 0.0 0.0 1.3

—No data.
127 

Table 44. Pre- and post-shear sieving data for No. 68-GG.

Sieve 

No.

Sieve 

Size 

(inches)

No. 68 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 100 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 100 100 100 100 100 100 100 100 100

1.5 inch 1.5 — 100 100 100 100 100 100 100 100 100 100 — — 

1 inch 1.0 100 100 100 100 100 100 100 100 100 100 100 100 100

3/4 inch 0.75 90-100 100 100 99.4 98.8 99.6 99.2 100 100 99.7 94.9 99.4 99.6

1/2 inch 0.5 — 67.0 66.0 58.0 58.5 53.0 58.0 65.0 74.0 60.9 68.7 — — 

3/8 inch 0.375 30–65 48.0 47.0 39.7 37.4 31.1 25.8 42.0 55.0 36.8 45.7 37.1 41.5

No. 4 0.187 5–25 8.0 11.0 3.8 2.4 6.9 8.9 5.0 14.0 2.7 13.2 5.2 8.1

No. 8 0.0937 0–10 5.0 6.0 0.8 0.4 4.8 5.1 2.0 7.0 0.2 7.1 2.3 3.8

No. 16 0.0469 0–5 5.0 5.0 0.7 0.4 4.2 4.7 2.0 5.0 0.2 5.9 1.8 2.9

No. 30 0.0234 — 4.0 4.0 0.7 0.4 3.8 3.7 1.0 4.0 — — — — 

No. 50 0.0117 — 3.0 3.0 0.7 0.4 3.2 3.0 1.0 3.0 — — — — 

No. 100 0.0059 — 2.0 2.0 0.6 0.3 2.2 2.8 1.0 2.0 — — — — 

No. 200 0.0029 — 1.0 1.2 0.5 0.2 0.9 1.2 0.3 1.2 0.1 1.4 0.6 0.7

—No data.
128 

Table 45. Pre- and post-shear sieving data for No. 68-LI.

Sieve 

No.

Sieve 

Size 

(inches)

No. 68 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 100 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 100 100 100 100 100 100 100 100 100

1.5 inch 1.5 — 100 100 100 100 100 100 100 100 100 100 — — 

1 inch 1.0 100 100 100 100 100 100 100 100 100 100 100 100 100

3/4 inch 0.75 90-100 100 98.0 100 98.2 99.4 97.2 100 99.0 99.0 98.6 99.5 99.8

1/2 inch 0.5 — 67.0 64.0 83.5 81.7 72.8 70.6 71.0 74.0 64.7 66.5 — — 

3/8 inch 0.375 30–65 46.0 42.0 66.0 65.4 53.9 52.0 48.0 54.0 39.1 41.1 45.9 47.9

No. 4 0.187 5–25 9.0 5.0 16.4 17.0 13.6 8.2 10.0 14.0 6.6 7.1 8.6 11.1

No. 8 0.0937 0–10 2.0 0.0 4.2 3.5 5.4 1.1 3.0 4.0 1.0 1.1 2.2 3.4

No. 16 0.0469 0–5 1.0 0.0 2.4 1.8 3.5 0.9 2.0 2.0 0.8 0.6 1.4 2.0

No. 30 0.0234 — 1.0 0.0 1.9 1.5 2.4 0.9 1.0 1.0 — — — — 

No. 50 0.0117 — 1.0 0.0 1.7 1.4 1.7 0.8 1.0 1.0 — — — — 

No. 100 0.0059 — 0.3 0.0 1.5 1.3 0.8 0.5 1.0 1.0 — — — — 

No. 200 0.0029 — 0.3 0.0 1.5 1.2 0.3 0.3 0.5 0.4 0.5 0.2 0.0 0.7

—No data.
129 

Table 46. Pre- and post-shear sieving data for No. 68-SI.

Sieve No.

Sieve 

Size 

(inches)

No. 68 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 100 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 100 100 100 100 100 100 100 100 100

1.5 inch 1.5 — 100 100 100 100 100 100 100 100 100 100 — — 

1 inch 1.0 100 100 100 100 100 100 100 100 100 100 100 100 100

3/4 inch 0.75 90-100 96.0 95.0 94.1 95.5 98.1 94.4 95.0 93.0 93.9 95.5 95.0 94.5

1/2 inch 0.5 — 59.0 57.0 56.1 64.7 72.2 67.2 55.0 60.0 63.1 62.0 — — 

3/8 inch 0.375 30–65 41.0 37.0 35.9 51.2 54.8 51.9 36.0 41.0 44.9 42.3 44.4 45.2

No. 4 0.187 5–25 9.0 6.0 6.1 11.3 11.4 12.7 6.0 9.0 10.0 8.3 8.8 9.9

No. 8 0.0937 0–10 2.0 1.0 1.1 2.3 1.8 3.2 1.0 1.0 1.6 1.0 1.2 1.7

No. 16 0.0469 0–5 1.0 1.0 1.0 1.4 1.2 2.1 1.0 1.0 1.0 0.7 0.9 1.7

No. 30 0.0234 — 1.0 1.0 1.0 1.0 1.0 1.5 1.0 1.0 — — — — 

No. 50 0.0117 — 1.0 1.0 1.0 0.9 0.8 0.8 1.0 1.0 — — — — 

No. 100 0.0059 — 1.0 1.0 0.9 0.7 0.4 0.2 1.0 1.0 — — — — 

No. 200 0.0029 — 0.3 0.1 0.9 0.7 0.1 0.0 0.5 0.2 0.4 0.4 0.7 0.9

—No data.
130 

NO. 8

The pre- and post-shear sieving data for the No. 8 OGAs are presented in table 47 through table 51. 

Table 47. Pre- and post-shear sieving data for No. 8-BA.

Sieve 

No.

Sieve 

Size 

(inches)

No. 8 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 100 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 100 100 100 100 100 100 100 100 100

1.5 inch 1.5 — 100 100 100 100 100 100 100 100 100 100 — — 

1 inch 1.0 — 100 100 100 100 100 100 100 100 100 100 — — 

3/4 inch 0.75 — 100 100 100 100 100 100 100 100 100 100 — — 

1/2 inch 0.5 100 100 100 100 100 100 100 100 100 100 100 99.9 99.9

3/8 inch 0.375 85-100 86.0 84.0 91.2 88.3 72.4 89.7 89.0 93.0 89.9 89.1 88.4 89.3

No. 4 0.187 10–30 20.0 10.0 23.4 19.2 15.6 17.3 19.0 31.0 21.7 22.6 19.8 23.3

No. 8 0.0937 0–10 4.0 1.0 2.2 2.6 3.4 2.3 2.0 7.0 1.4 3.0 1.8 2.9

No. 16 0.0469 0–5 2.0 0.1 0.8 0.8 2.0 1.1 2.0 3.0 0.4 1.3 0.6 2.9

No. 30 0.0234 — 1.0 0.1 0.8 0.6 1.6 0.9 2.0 2.0 — — — — 

No. 50 0.0117 — 1.0 0.1 0.8 0.6 1.5 0.8 2.0 1.0 — — — — 

No. 100 0.0059 — 1.0 0.1 0.8 0.6 1.4 0.7 2.0 1.0 — — — — 

No. 200 0.0029 — 0.8 0.1 0.8 0.5 1.3 0.7 0.3 1.0 0.3 0.8 0.5 0.5

—No data.
131 

Table 48. Pre- and post-shear sieving data for No. 8-DI.

Sieve 

No.

Sieve 

Size 

(inches)

No. 8 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 — 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 — 100 100 100 100 100 100 100 100

1.5 inch 1.5 — 100 100 100 — 100 100 100 100 100 100 — — 

1 inch 1.0 — 100 100 100 — 100 100 100 100 100 100 — — 

3/4 inch 0.75 — 100 100 100 — 100 100 100 100 100 100 — — 

1/2 inch 0.5 100 100 100 100 — 100 100 100 100 100 100 100 100

3/8 inch 0.375 85-100 90.0 89.0 93.1 — 94.4 90.8 93.0 94.0 91.7 93.1 92.3 92.9

No. 4 0.187 10–30 14.0 14.0 15.2 — 21.0 13.6 16.0 20.0 12.0 16.9 18.3 18.2

No. 8 0.0937 0–10 1.0 2.0 1.0 — 5.4 2.5 2.0 1.0 0.7 0.6 2.5 1.8

No. 16 0.0469 0–5 1.0 1.0 0.8 — 4.6 2.1 1.0 1.0 0.6 0.3 1.8 1.2

No. 30 0.0234 — 0.0 0.0 0.7 — 4.1 2.1 1.0 1.0 — — — — 

No. 50 0.0117 — 0.0 0.0 0.7 — 3.6 2.0 1.0 1.0 — — — — 

No. 100 0.0059 — 0.0 0.0 0.6 — 2.5 2.0 1.0 1.0 — — — — 

No. 200 0.0029 — 0.0 0.0 0.5 — 0.8 1.8 0.7 0.6 0.0 0.0 0.0 0.8

—No data.
132 

Table 49. Pre- and post-shear sieving data for No. 8-GG.

Sieve No.

Sieve Size 

(inches)

No. 8 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 100 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 100 100 100 100 100 100 100 100 100

1.5 inch 1.5 — 100 100 100 100 100 100 100 100 100 100 — — 

1 inch 1.0 — 100 100 100 100 100 100 100 100 100 100 — — 

3/4 inch 0.75 — 100 100 100 100 100 100 100 100 100 100 — — 

1/2 inch 0.5 100 100 100 99.6 100 100 100 100 100 100 100 100 100

3/8 inch 0.375 85-100 86.0 83.0 87.4 84.9 80.8 83.7 79.0 90.0 86.0 88.6 85.0 89.0

No. 4 0.187 10–30 12.0 9.0 6.4 5.3 4.0 6.8 6.0 16.0 11.5 5.9 9.9 3.1

No. 8 0.0937 0–10 7.0 5.0 1.4 0.7 1.4 2.5 3.0 8.0 4.2 0.4 4.3 2.6

No. 16 0.0469 0–5 5.0 4.0 1.2 0.6 1.2 1.5 2.0 5.0 2.9 0.2 3.5 1.0

No. 30 0.0234 — 4.0 3.0 1.2 0.6 1.1 1.3 2.0 3.0 — — — — 

No. 50 0.0117 — 3.0 2.0 1.1 0.5 1.1 1.2 1.0 2.0 — — — — 

No. 100 0.0059 — 2.0 1.0 1.0 0.5 0.9 1.1 1.0 1.0 — — — — 

No. 200 0.0029 — 0.5 0.7 0.9 0.4 0.5 0.7 0.5 0.7 0.7 0.1 0.8 0.9

—No data.
133 

Table 50. Pre- and post-shear sieving data for No. 8-LI.

Sieve 

No.

Sieve 

Size 

(inches)

No. 8 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 100 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 100 100 100 100 100 100 100 100 100

1.5 inch 1.5 — 100 100 100 100 100 100 100 100 100 100 — — 

1 inch 1.0 — 100 100 100 100 100 100 100 100 100 100 — — 

3/4 inch 0.75 — 100 100 100 100 100 100 100 100 100 100 — — 

1/2 inch 0.5 100 100 100 100 99.7 100 100 100 100 100 100 100 100

3/8 inch 0.375 85–100 95.0 97.0 95.8 94.1 92.0 95.1 95.0 97.0 93.2 95.1 91.8 91.7

No. 4 0.187 10–30 29.0 35.0 32.0 31.4 18.8 27.9 29.0 39.0 25.3 28.1 22.3 27.0

No. 8 0.0937 0–10 4.0 6.0 6.2 4.0 2.0 3.8 3.0 6.0 2.3 3.3 3.3 5.5

No. 16 0.0469 0–5 2.0 2.0 2.9 1.2 1.1 1.6 1.0 1.0 0.7 1.2 1.6 2.4

No. 30 0.0234 — 1.0 2.0 2.1 1.1 0.9 1.1 1.0 1.0 — — — — 

No. 50 0.0117 — 1.0 1.0 1.8 1.0 0.8 1.0 1.0 1.0 — — — — 

No. 100 0.0059 — 1.0 1.0 1.6 1.0 0.5 0.6 1.0 1.0 — — — — 

No. 200 0.0029 — 0.4 0.6 1.5 1.0 0.2 0.4 0.8 0.3 0.3 0.5 0.0 0.7

—No data.
134 

Table 51. Pre- and post-shear sieving data for No. 8-SI.

Sieve 

No.

Sieve 

Size 

(inches)

No. 8 

Gradation 

Specification

Percent Passing for Each Participant Laboratory

L01 L02 L03 L04 L05 L06

PreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShearPreShearPostShear

3 inch 3 — 100 100 100 100 100 100 100 100 100 100 100 100

2 inch 2 — 100 100 100 100 100 100 100 100 100 100 100 100

1.5 inch 1.5 — 100 100 100 100 100 100 100 100 100 100 — —

1 inch 1.0 — 100 100 100 100 100 100 100 100 100 100 — —

3/4 inch 0.75 — 100 100 100 100 99.8 100 100 100 100 99.6 — —

1/2 inch 0.5 100 99.0 100 98.9 99.5 97.1 97.7 99.0 99.0 98.9 98.3 99.2 98.1

3/8 inch 0.375 85-100 86.0 86.0 93.7 93.0 88.0 88.8 90.0 91.0 88.9 87.6 87.9 84.3

No. 4 0.187 10–30 20.0 20.0 26.1 30.6 23.5 24.0 25.0 32.0 25.8 23.4 24.0 23.7

No. 8 0.0937 0–10 4.0 2.0 5.6 2.7 2.5 5.8 2.0 7.0 1.9 1.7 2.3 3.2

No. 16 0.0469 0–5 2.0 2.0 1.9 1.2 1.5 3.5 1.0 6.0 1.2 1.0 1.4 1.8

No. 30 0.0234 — 1.0 1.0 1.3 1.0 1.3 2.2 1.0 6.0 — — — —

No. 50 0.0117 — 1.0 1.0 1.1 0.8 1.1 1.0 1.0 5.0 — — — —

No. 100 0.0059 — 1.0 1.0 1.0 0.7 0.6 0.2 1.0 5.0 — — — —

No. 200 0.0029 — 0.8 0.2 1.0 0.6 0.1 0.1 0.5 5.0 0.7 0.7 0.9 0.9

—No data.
135 

APPENDIX C. AIMS2 PARTICLE CHARACTERISTIC RESULTS

This appendix contains the main results of AIMS2 digital image analyses conducted by FHWA, 

including angularity (GA) index, TX index, SP index, and flat and elongated (F&E) values. The 

plots shown in this appendix have the same x-axis scale for ease of visual comparison and are 

followed by summary tables containing the weighted average values for GA, TX, SP, and F&E 

results. Weighted averages were calculated for each parameter by summing the per-sieve results 

multiplied by the percentage of material retained on that sieve. Classifications per AASHTO R 

91-18 are included for the weighted average angularity, TX, and SP indexes (AASHTO 2018b). 

OS-20-30 

Figure 57 shows the cumulative angularity results for OS-20-30; the weighted GA index is 674, 

which classifies OS-20-30 as having low angularity. 

Source: FHWA.

Figure 57. Chart. AIMS2 cumulative angularity distributions for OS-20-30. 

NO. 57 OGAS

The cumulative angularity, TX, and SP results are presented for No. 57-BA (figure 58), 

No. 57-DI (figure 59), No. 57-GG (figure 60), No. 57-LI (figure 61), and No. 57-SI (figure 62). 

 

 

 

 
136 

Source: FHWA.

A. Angularity. 

Source: FHWA.

B. TX. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
137 

Source: FHWA.

C. SP. 

Figure 58. Charts. AIMS2 cumulative distributions for No. 57-BA.

Source: FHWA.

A. Angularity. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
138 

Source: FHWA.

B. TX. 

Source: FHWA.

C. SP. 

Figure 59. Charts. AIMS2 cumulative distributions for No. 57-DI.

 

 

 

 

 

 

 

 

 

 

 

 
139 

Source: FHWA.

A. Angularity. 

Source: FHWA.

B. TX. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
140 

Source: FHWA.

C. SP. 

Figure 60. Charts. AIMS2 cumulative distributions for No. 57-GG.

Source: FHWA.

A. Angularity. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
141 

Source: FHWA.

B. TX. 

Source: FHWA.

C. SP. 

Figure 61. Charts. AIMS2 cumulative distributions for No. 57-LI.

 

 

 

 

 

 

 

 

 

 

 

 
142 

Source: FHWA.

A. Angularity. 

Source: FHWA.

B. TX. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
143 

Source: FHWA.

C. SP. 

Figure 62. Charts. AIMS2 cumulative distributions for No. 57-SI.

Summary tables with the weighted averages and F&E values are provided in table 52 and 

table 53, respectively.

Table 52. Summary of AIMS2 weighted averages for No. 57 OGAs. 

Sample ID

Avg. 

GA 

Index

GA

Classification

Avg. 

TX 

Index

TX 

Classification

Avg. 

SP 

Index

SP

Classification

No. 57-BA 2948 Low 335 Medium 0.568 Medium 

No. 57-DI 2957 Low 523 Medium 0.588 Medium 

No. 57-GG 2934 Low 633 High 0.607 Medium 

No. 57-LI 3177 Low 479 Medium 0.541 Medium 

No. 57-SI 3031 Low 261 Medium 0.595 Medium 

No. 57-Avg. 3009 Low 446 Medium 0.580 Medium 

 

 

 

 

 

 
144 

Table 53. Summary of AIMS2 weighted average F&E values for No. 57 OGAs. 

Sample ID

F&E Distribution (Percent)

L/S ≥ 1:1 L/S > 2:1 L/S > 3:1 L/S > 4:1 L/S > 5:1 

No. 57-BA 98.0 73.3 33.6 13.8 7.7 

No. 57-DI 96.8 79.6 42.3 16.9 3.6 

No. 57-GG 99.4 68.5 23.8 10.8 2.0 

No. 57-LI 96.9 80.9 38.6 16.6 7.2 

No. 57-SI 93.8 81.6 43.1 20.4 8.8 

No. 57-Avg. 97.0 76.8 36.3 15.7 5.9 

NO. 68 OGAS

The cumulative angularity, TX, and SP results are presented for No. 68-BA (figure 63), 

No. 68-DI (figure 64), No. 68-GG (figure 65), No. 68-LI (figure 66), and No. 68-SI (figure 67).

Source: FHWA.

A. Angularity.

 

 

 

 

 

 

 

 

 

 
145 

Source: FHWA.

B. TX. 

Source: FHWA.

C. SP. 

Figure 63. Charts. AIMS2 cumulative distributions for No. 68-BA.

 

 

 

 

 

 

 

 

 

 

 

 
146 

Source: FHWA.

A. Angularity. 

Source: FHWA.

B. TX. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
147 

Source: FHWA.

C. SP. 

Figure 64. Charts. AIMS2 cumulative distributions for No. 68-DI.

Source: FHWA.

A. Angularity. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
148 

Source: FHWA.

B. TX. 

Source: FHWA.

C. SP. 

Figure 65. Charts. AIMS2 cumulative distributions for No. 68-GG.

 

 

 

 

 

 

 

 

 

 

 

 
149 

Source: FHWA.

A. Angularity. 

Source: FHWA.

B. TX. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
150 

Source: FHWA.

C. SP. 

Figure 66. Charts. AIMS2 cumulative distributions for No. 68-LI.

Source: FHWA.

A. Angularity. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
151 

Source: FHWA.

B. TX. 

Source: FHWA.

C. SP. 

Figure 67. Charts. AIMS2 cumulative distributions for No. 68-SI.

 

 

 

 

 

 

 

 

 

 

 

 
152 

Summary tables with the weighted averages and F&E values are provided in table 54 and 

table 55, respectively.

Table 54. Summary of AIMS2 weighted averages for No. 68 OGAs. 

Sample ID

Avg.

GA 

Index

GA 

Classification

Avg.

TX 

Index

TX 

Classification

Avg.

SP 

Index

SP

Classification

No. 68-BA 2956 Low 483 Medium 0.626 Medium

No. 68-DI 2936 Low 571 High 0.614 Medium

No. 68-GG 3158 Low 628 High 0.577 Medium

No. 68-LI 3185 Low 552 High 0.527 Medium

No. 68-SI 3147 Low 336 Medium 0.612 Medium

No. 68-avg. 3076 Low 514 Medium 0.591 Medium

Table 55. Summary of AIMS2 weighted average F&E values for No. 68 OGAs. 

Sample ID

F&E Distribution (Percent)

L/S ≥ 1:1 L/S > 2:1 L/S > 3:1 L/S > 4:1 L/S > 5:1

No. 68-BA 86.4 67.8 30.1 12.0 6.3

No. 68-DI 94.2 85.6 43.8 16.8 4.7

No. 68-GG 95.9 81.5 46.0 18.1 7.5

No. 68-LI 90.1 87.6 66.5 32.9 11.6

No. 68-SI 92.0 82.6 45.7 20.3 9.4

No. 68-Avg. 91.7 81.0 46.4 20.0 7.9

NO. 8 OGAS

The cumulative angularity, TX, and SP results are presented for No. 8-BA (figure 68), No. 8-DI 

(figure 69), No. 8-GG (figure 70), No. 8-LI (figure 71), and No. 8-SI (figure 72).
153 

Source: FHWA.

A. Angularity. 

Source: FHWA.

B. TX. 

 

 

 

 

 

 

 

 

 

 

 

 

 
154 

Source: FHWA.

C. SP. 

Figure 68. Charts. AIMS2 cumulative distributions for No. 8-BA

Source: FHWA.

A. Angularity. 

 

 

 

 

 

 

 

 

 

 

 

 

 
155 

Source: FHWA.

B. TX. 

Source: FHWA.

C. SP. 

Figure 69. Charts. AIMS2 cumulative distributions for No. 8-DI.

 

 

 

 

 

 

 

 

 

 
156 

Source: FHWA.

A. Angularity. 

Source: FHWA.

B. TX. 

 

 

 

 

 

 

 

 

 

 

 

 

 
157 

Source: FHWA.

C. SP. 

Figure 70. Charts. AIMS2 cumulative distributions for No. 8-GG.

Source: FHWA.

A. Angularity. 

 

 

 

 

 

 

 

 

 

 

 

 
158 

Source: FHWA.

B. TX. 

Source: FHWA.

C. SP. 

Figure 71. Charts. AIMS2 cumulative distributions for No. 8-LI.

 

 

 

 

 

 

 

 
159 

Source: FHWA.

A. Angularity. 

Source: FHWA.

B. TX. 

 

 

 

 

 

 

 

 

 

 

 

 

 
160 

Source: FHWA.

C. SP. 

Figure 72. Charts. AIMS2 cumulative distributions for No. 8-SI.

Summary tables with the weighted averages and F&E values are provided in table 56 and 

table 57, respectively.

Table 56. Summary of AIMS2 weighted averages for No. 8 OGAs. 

Sample ID

Avg. 

GA 

Index

GA 

Classification

Avg. 

TX 

Index

TX 

Classification

Avg. 

SP 

Index

SP 

Classification

No. 8-BA 3131 Low 518 Medium 0.556 Medium 

No. 8-DI 2922 Low 582 High 0.567 Medium 

No. 8-GG 3147 Low 630 High 0.576 Medium 

No. 8-LI 3209 Low 366 Medium 0.547 Medium 

No. 8-SI 3192 Low 372 Medium 0.580 Medium 

No. 8-Avg. 3120 Low 494 Medium 0.565 Medium 

 

 

 

 
161 

Table 57. Summary of AIMS2 weighted average F&E values for No. 8 OGAs. 

Sample ID

F&E Distribution (Percent) 

L/S ≥ 1:1 L/S > 2:1 L/S > 3:1 L/S > 4:1 L/S > 5:1 

No. 8-BA 80.6 73.4 57.1 38.9 21.8 

No. 8-DI 82.6 78.3 49.1 22.0 9.3 

No. 8-GG 92.0 83.6 50.8 31.1 11.4 

No. 8-LI 74.2 67.8 50.1 31.8 19.9 

No. 8-SI 76.8 72.2 46.9 23.8 16.4 

No. 8-Avg. 81.2 75.1 50.8 29.5 15.8 

163 

APPENDIX D. LSDS TEST RESULTS

This appendix contains the main results of LSDS testing by each laboratory for all tested 

materials, including shear stress versus horizontal strain, vertical strain versus horizontal strain, 

and linear Mohr-Coulomb failure envelopes. The plots shown in this appendix are followed by 

summary tables containing the initial shear stress before zeroing reported in each laboratory’s 

raw data, normal stress at peak shear, peak and residual shear stresses, secant friction angles at 

peak and residual shear, and maximum dilation angle for each applied nominal normal stress 

alongside the tangent friction angle at peak, ca, tangent friction angle at residual shear stress, and 

constant volume friction angle from each four‐point test series.

OS-20-30 

The shear stress versus horizontal strain curves for OS-20-30 are shown in figure 73. The vertical 

strain versus horizontal strain curves for OS-20-20 are shown in figure 74, with the linear 

Mohr-Coulomb failure envelopes shown in figure 75. A full summary of results can be found in 

table 58. 

Source: FHWA.

Figure 73. Charts. Shear stress versus horizontal strain for OS-20-30. 

 

 

 
164 

Source: FHWA.

Figure 74. Charts. Vertical strain versus horizontal strain for OS-20-30. 

 

 

 
165 

Source: FHWA.

Figure 75. Chart. Linear Mohr-Coulomb failure envelopes for OS-20-30. 

 

 

 

 

 

 

 

 
166 

Table 58. Summary of LSDS results for OS-20-30. 

Lab 

ID 

Target 

σn (psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.2 5.2 4.1 3.1 39.4 32.0 9.6

34.5 0.9 29.2 32.4 10 0.1 10.1 7.5 6.1 36.9 31.3 5.9

15 0.1 15.1 10.8 8.7 35.8 30.0 8.7

30 0.1 30.1 20.6 16.4 34.5 28.7 7.7

L02

5 0.0 5.0 5.0 5.0 45.3 45.2 10.6

40.0 0.5 36.5 48.4 10 0.0 10.0 8.4 8.1 40.0 39.1 14.3

15 0.0 15.0 13.3 11.6 41.5 37.6 14.3

30 0.0 30.0 25.9 21.6 40.8 35.7 19.6

L03

5 0.1 5.0 3.7 2.4 36.8 25.2 14.4

37.1 0.4 26.2 34.3 10 0.2 10.0 7.3 4.7 36.0 25.0 15.6

15 0.0 14.9 10.7 7.5 35.6 26.7 9.6

30 0.1 30.0 21.0 14.7 35.0 26.2 4.9

L04

5 0.0 5.0 4.2 2.5 39.8 26.2 5.7

36.7 0.5 29.7 41.1 10 0.0 10.0 7.2 4.5 35.8 24.0 21.8

15 0.0 15.0 10.8 8.7 35.7 30.1 24.2

30 0.0 30.0 21.2 17.5 35.3 30.3 24.2

L05

5 0.6 5.1 5.6 3.7 48.3 36.8 15.2

3.0 1.6 28.4 44.7 10 0.1 10.0 10.1 4.8 45.4 25.5 18.4

15 0.1 15.1 14.2 8.1 43.5 28.5 16.9

30 1.2 30.2 26.7 16.2 41.6 28.4 15.3

L06

5 0.0 5.1 7.3 4.4 55.8 41.1 19.3

8.2 3.7 31.1 −0.7 10 −0.2 10.1 12.1 8.3 50.3 39.7 16.4

15 2.1 15.1 14.3 9.9 43.6 33.4 14.7

30 3.4 30.1 26.6 16.7 41.5 29.2 15.0

NO. 57 OGAS

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 57-BA are shown in figure 76, figure 77, and figure 78, 

respectively. The full summary of LSDS results is presented in table 59. 
167 

Source: FHWA.

Figure 76. Charts. Shear stress versus horizontal strain for No. 57-BA.

 

 

 
168 

Source: FHWA.

Figure 77. Charts. Vertical strain versus horizontal strain for No. 57-BA.

 

 

 
169 

Source: FHWA.

Figure 78. Chart. Linear Mohr-Coulomb failure envelopes for No. 57-BA. 

 

 

 

 

 

 

 

 
170 

Table 59. Summary of LSDS results for No. 57-BA.

Lab ID

Target 

σn (psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.1 5.1 7.3 4.0 55.7 39.0 18.9

51.5 1.9 38.5 49.3 10 0.1 10.3 14.5 7.9 55.5 38.4 23.3

15 −0.2 15.2 22.3 11.8 56.0 38.2 17.8

30 0.2 30.1 39.1 24.0 52.5 38.6 15.1

L02

5 0.0 5.0 7.0 4.1 54.3 39.5 25.6

62.1 −2.5 59.9 61.3 10 0.0 10.0 16.1 14.6 58.1 55.6 3.5

15 0.0 15.0 26.4 26.4 60.4 60.4 9.7

30 0.0 30.0 54.1 53.2 61.0 60.6 8.4

L03

5 0.2 5.0 10.0 5.8 63.4 49.2 28.5

51.2 3.3 47.2 61.6 10 0.2 10.0 15.3 11.6 56.9 49.3 28.5

15 0.2 15.1 21.5 16.5 55.1 47.8 38.3

30 0.2 30.0 40.7 31.8 53.6 46.7 26.1

L04

5 0.0 5.0 7.0 4.9 54.4 44.3 32.6

49.2 1.1 32.3 37.7 10 0.0 10.0 12.3 6.3 50.8 32.3 28.8

15 0.0 15.0 18.8 7.4 51.3 26.3 31.0

30 0.0 30.0 35.7 19.7 50.0 33.3 24.7

L05

5 0.0 5.0 34.0 16.7 81.6 73.3 25.9

59.9 26.9 61.7 57.0 10 0.0 10.1 44.5 19.7 77.3 63.1 25.0

15 0.0 15.0 55.0 25.6 74.7 59.7 17.0

30 0.0 30.1 77.7 55.3 68.9 61.5 15.6

L06

5 0.1 5.1 15.3 11.9 71.9 67.2 25.1

63.1 8.9 59.2 56.8 10 −1.6 10.1 30.2 15.3 71.7 56.8 20.8

15 −0.7 15.0 42.2 31.6 70.4 64.6 20.2

30 −3.0 30.0 66.2 47.0 65.6 57.5 15.0
171 

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 57-DI are shown in figure 79, figure 80, and figure 81, 

respectively. The full summary of LSDS results is presented in table 60. 

Source: FHWA.

Figure 79. Charts. Shear stress versus horizontal strain for No. 57-DI.

 

 

 
172 

Source: FHWA.

Figure 80. Charts. Vertical strain versus horizontal strain for No. 57-DI.

 

 

 
173 

Source: FHWA.

Figure 81. Chart. Linear Mohr-Coulomb failure envelopes for No. 57-DI.

 

 

 

 

 

 

 

 
174 

Table 60. Summary of LSDS results for No. 57-DI.

Lab ID

Target 

σn (psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.1 5.2 9.7 4.8 62.7 43.6 26.7

51.9 3.8 41.3 38.2 10 0.1 10.3 16.9 9.2 59.5 42.5 24.6

15 0.1 15.3 23.0 14.2 56.9 43.4 23.2

30 0.0 30.1 41.9 25.7 54.4 40.6 17.7

L02

5 0.0 5.0 16.1 11.6 72.7 66.6 —

61.5 6.9 64.5 — 10 0.0 10.0 24.3 21.2 67.7 64.8 —

15 0.0 15.0 35.8 35.8 67.3 67.3 —

30 0.0 30.0 61.8 60.3 64.1 63.5 —

L03

5 0.3 5.0 7.4 4.9 55.8 44.7 19.4

50.7 2.4 46.2 65.8 10 0.2 10.0 15.5 11.1 57.2 47.9 22.4

15 0.2 14.9 21.6 17.5 55.3 49.4 23.8

30 0.2 29.7 38.6 30.1 52.1 45.1 24.0

L04

5 0.0 5.0 5.8 3.7 49.4 36.3 35.8

44.5 1.5 30.4 44.2 10 0.0 10.0 11.5 5.6 49.1 29.4 25.6

15 0.0 15.0 16.7 8.8 48.1 30.4 19.3

30 0.0 30.0 30.7 17.6 45.6 30.4 20.8

L05

5 0.6 5.0 19.9 4.0 75.9 38.7 24.4

56.3 16.8 56.5 54.8 10 −0.1 10.1 37.6 21.0 75.1 64.6 20.7

15 0.3 15.0 38.9 25.0 68.9 59.1 15.5

30 0.2 30.0 60.7 42.7 63.7 54.9 10.2

L06

5 −1.4 5.1 13.7 7.7 69.9 56.9 21.2

63.1 5.4 55.7 55.0 10 −3.1 10.1 28.4 17.6 70.6 60.3 19.8

15 −1.8 15.0 33.5 19.3 65.9 52.2 16.5

30 −5.5 30.0 64.6 44.4 65.1 55.9 13.2

—Not measured/evaluated.
175 

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 57-GG are shown in figure 82, figure 83, and 

figure 84, respectively. The full summary of LSDS results is presented in table 61. 

Source: FHWA.

Figure 82. Charts. Shear stress versus horizontal strain for No. 57-GG.

 

 

 
176 

Source: FHWA.

Figure 83. Charts. Vertical strain versus horizontal strain for No. 57-GG.

 

 

 
177 

Source: FHWA.

Figure 84. Chart. Linear Mohr-Coulomb failure envelopes for No. 57-GG.

 

 

 

 

 

 

 

 
178 

Table 61. Summary of LSDS results for No. 57-GG.

Lab ID

Target 

σn (psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.2 5.3 6.9 3.9 54.2 38.1 18.4

47.9 2.4 38.4 41.3 10 0.2 10.2 13.7 8.4 53.8 40.0 16.4

15 −0.2 15.1 20.6 10.9 53.9 35.9 18.4

30 0.2 30.1 35.0 24.1 49.4 38.8 11.8

L02

5 0.0 5.0 12.3 10.9 67.9 65.4 19.6

59.1 5.2 59.5 52.1 10 0.0 10.0 23.9 22.9 67.3 66.4 18.4

15 0.0 15.0 29.6 24.7 63.1 58.7 13.8

30 0.0 30.0 55.2 49.1 61.5 58.6 11.4

L03

5 0.1 5.0 7.4 5.5 56.1 47.6 23.7

49.5 2.7 46.0 50.4 10 0.2 10.0 14.9 10.2 56.2 45.5 36.2

15 0.2 14.9 21.3 16.4 54.9 47.6 18.0

30 0.2 29.7 37.2 30.6 51.1 45.6 12.7

L04

5 0.0 5.0 5.5 3.1 47.8 31.9 43.5

45.0 0.1 34.7 43.1 10 0.0 10.0 10.3 6.5 45.7 32.9 24.7

15 0.0 15.0 14.4 9.2 43.8 31.4 19.8

30 0.0 30.0 30.5 21.6 45.4 35.7 13.5

L05

5 −0.1 4.9 15.8 7.6 72.4 56.7 18.7

54.0 9.8 49.0 48.5 10 1.0 10.0 24.5 11.8 67.8 49.7 15.9

15 1.2 15.0 30.7 19.4 63.9 52.3 15.1

30 1.9 30.0 50.8 33.0 59.5 47.7 8.4

L06

5 −1.6 5.1 18.6 9.7 74.9 62.6 23.2

54.7 10.6 58.2 52.3 10 0.0 10.1 21.9 14.9 65.5 56.2 17.2

15 −2.9 15.1 34.1 28.0 66.2 61.8 15.0

30 −9.9 30.0 52.6 46.5 60.3 57.2 7.8
179 

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 57-LI are shown in figure 85, figure 86, and figure 87, 

respectively. The full summary of LSDS results is presented in table 62. 

Source: FHWA.

Figure 85. Charts. Shear stress versus horizontal strain for No. 57-LI.

 

 

 
180 

Source: FHWA.

Figure 86. Charts. Vertical strain versus horizontal strain for No. 57-LI.

 

 

 
181 

Source: FHWA.

Figure 87. Chart. Linear Mohr-Coulomb failure envelopes for No. 57-LI.

 

 

 

 

 

 

 

 
182 

Table 62. Summary of LSDS results for No. 57-LI.

Lab ID

Target 

σn (psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.1 5.2 9.3 5.8 61.6 42.3 20.5 

51.6 3.4 47.9 20.7 10 0.0 10.1 16.1 10.2 58.1 38.6 19.7 

15 0.0 15.1 22.9 16.6 56.8 38.2 19.3 

30 −0.1 30.2 41.0 33.4 53.8 36.3 16.8 

L02

5 0.0 5.0 16.1 12.6 72.8 72.3 18.0 

63.6 4.8 65.2 65.9 10 0.0 10.0 23.4 18.7 66.8 62.4 15.3 

15 0.0 15.0 34.9 34.9 66.7 68.2 0.0 

30 0.0 30.0 65.6 64.6 65.4 60.2 0.0 

L03

5 0.0 5.0 7.8 5.6 57.4 46.9 21.1 

49.4 3.1 46.6 46.8 10 0.1 10.0 15.3 11.0 56.8 48.2 24.5 

15 0.4 15.0 22.0 17.4 55.7 47.4 22.6 

30 0.2 30.3 37.5 30.7 51.4 47.0 11.3 

L04

5 0.0 5.0 6.9 3.0 54.0 35.3 20.7 

46.4 0.4 39.8 47.0 10 0.0 10.0 10.8 5.9 47.1 23.6 30.1 

15 0.0 15.0 14.4 9.8 43.8 24.8 17.7 

30 0.0 30.0 32.6 27.4 47.4 36.9 11.3 

L05

5 0.0 5.0 19.6 16.3 75.7 62.4 19.4 

51.2 16.1 56.9 47.0 10 0.0 10.0 29.0 19.5 71.0 70.3 17.2 

15 0.0 15.0 38.8 30.7 68.8 64.7 15.1 

30 0.0 30.0 51.7 39.3 59.9 64.0 8.8 

L06

5 −2.0 5.1 18.2 13.5 74.7 70.3 20.0 

53.5 12.3 59.0 51.7 10 0.2 10.1 28.3 20.2 70.5 64.9 17.1 

15 −3.3 15.0 30.8 29.1 64.0 58.2 10.8 

30 −5.2 30.0 53.1 45.8 60.5 58.3 7.8 
183 

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 57-SI are shown in figure 88, figure 89, and figure 90, 

respectively. The full summary of LSDS results is presented in table 63. 

Source: FHWA.

Figure 88. Charts. Shear stress versus horizontal strain for No. 57-SI.

 

 

 
184 

Source: FHWA.

Figure 89. Charts. Vertical strain versus horizontal strain for No. 57-SI.

 

 

 
185 

Source: FHWA.

Figure 90. Chart. Linear Mohr-Coulomb failure envelopes for No. 57-SI. 

 

 

 

 

 

 

 

 
186 

Table 63. Summary of LSDS results for No. 57-SI.

Lab ID

Target σn

(psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.2 5.2 7.8 4.5 57.3 38.4 16.1

48.4 2.1 40.6 37.7 10 0.1 10.1 13.5 8.0 53.4 38.2 15.2

15 0.0 15.1 18.7 11.8 51.3 38.6 12.3

30 −0.1 30.2 35.9 22.0 50.1 0.0 10.1

L02

5 0.0 5.0 16.3 15.7 72.9 55.6 13.0

58.6 7.6 62.3 61.3 10 0.0 10.0 19.4 19.1 62.8 60.4 15.2

15 0.0 15.0 37.7 37.6 68.3 60.6 12.5

30 0.0 30.0 55.6 52.4 61.7 0.0 11.0

L03

5 0.0 5.0 7.5 5.4 56.4 49.3 28.3

49.8 2.2 46.6 55.1 10 0.0 10.0 14.3 11.2 55.0 47.8 28.3

15 −0.1 14.8 20.6 16.3 53.9 46.7 39.2

30 −0.1 30.1 37.4 32.2 51.3 0.0 20.7

L04

5 0.0 5.0 5.9 3.5 49.5 32.3 33.0

47.2 0.1 34.2 42.8 10 0.0 10.0 10.7 4.4 46.9 26.3 29.2

15 0.0 15.0 15.8 6.9 46.6 33.3 24.7

30 0.0 30.0 32.7 22.5 47.5 0.0 22.8

L05

5 0.0 5.0 22.3 9.6 77.4 63.1 20.3

63.0 14.4 57.8 52.3 10 0.0 10.0 34.0 27.9 73.6 59.7 16.4

15 0.0 15.0 46.8 31.7 72.2 61.5 16.7

30 0.0 30.0 71.9 61.6 67.4 0.0 11.6

L06

5 −2.6 5.1 20.0 14.0 76.0 56.8 21.3

50.0 14.0 58.3 53.3 10 −1.9 10.0 27.5 21.4 70.0 64.6 13.4

15 −2.1 15.1 29.4 24.2 63.0 57.5 11.1

30 −4.6 30.0 50.3 48.5 59.2 0.0 7.4
187 

NO. 68 OGAS

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 68-BA are shown in figure 91, figure 92, and figure 93, 

respectively. The full summary of LSDS results is presented in table 64. 

Source: FHWA.

Figure 91. Charts. Shear stress versus horizontal strain for No. 68-BA.

 

 

 
188 

Source: FHWA.

Figure 92. Charts. Vertical strain versus horizontal strain for No. 68-BA.

 

 

 
189 

Source: FHWA.

Figure 93. Chart. Linear Mohr-Coulomb failure envelopes for No. 68-BA.

 

 

 

 

 

 

 

 
190 

Table 64. Summary of LSDS results for No. 68-BA.

Lab ID

Target σn

(psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.1 5.1 7.6 4.4 56.8 41.6 17.6

49.3 2.4 38.0 43.8 10 0.1 10.2 13.8 7.7 54.0 37.7 15.1

15 −0.1 15.3 21.3 11.3 54.8 37.0 16.6

30 0.2 30.2 36.8 23.5 50.8 38.1 9.8

L02

5 0.0 5.0 6.8 6.3 53.6 51.7 22.8

61.8 −3.5 58.8 60.0 10 0.0 10.0 14.1 11.2 54.6 48.1 9.5

15 0.0 15.0 24.3 22.7 58.3 56.6 5.3

30 0.0 30.0 52.8 52.6 60.4 60.3 4.2

L03

5 0.2 5.0 9.1 5.4 61.1 47.4 23.0

48.9 3.4 45.5 43.1 10 0.6 10.0 14.2 11.1 54.8 47.9 23.6

15 0.2 15.1 21.6 16.4 55.2 47.5 16.6

30 0.3 30.5 37.6 29.6 51.4 44.6 15.4

L04

5 0.0 5.0 7.5 5.8 56.2 49.2 30.1

47.7 1.2 34.6 50.8 10 0.0 10.0 10.6 5.8 46.6 30.0 33.0

15 0.0 15.0 18.5 10.8 50.9 35.6 20.8

30 0.0 30.0 34.2 20.5 48.7 34.3 22.8

L05

5 0.0 5.0 39.5 11.8 82.8 67.0 31.0

68.1 26.8 61.8 63.2 10 0.0 10.0 51.2 15.0 78.9 56.3 26.5

15 0.0 15.0 64.2 27.9 76.8 61.7 22.0

30 0.0 30.0 101.3 56.7 73.5 62.1 16.4

L06

5 −0.4 5.2 26.8 11.0 79.4 65.5 26.1

59.6 18.4 58.0 50.2 10 1.1 10.0 33.6 14.1 73.4 54.7 23.6

15 −2.7 15.1 46.7 30.1 72.2 63.5 19.9

30 −0.3 30.1 68.9 45.1 66.5 56.3 15.1
191 

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 68-DI are shown in figure 94, figure 95, and figure 96, 

respectively. The full summary of LSDS results is presented in table 65. 

Source: FHWA.

Figure 94. Charts. Shear stress versus horizontal strain for No. 68-DI.

 

 

 
192 

Source: FHWA.

Figure 95. Charts. Vertical strain versus horizontal strain for No. 68-DI.

 

 

 
193 

Source: FHWA.

Figure 96. Chart. Linear Mohr-Coulomb failure envelopes for No. 68-DI.

 

 

 

 

 

 

 

 
194 

Table 65. Summary of LSDS results for No. 68-DI.

Lab ID

Target σn

(psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.1 5.1 8.5 4.9 59.6 44.2 24.3

51.5 3.2 43.0 44.2 10 0.1 10.1 16.6 9.8 58.9 44.5 25.3

15 0.1 15.3 22.8 12.7 56.7 40.2 21.9

30 0.0 30.3 40.6 28.4 53.5 43.5 15.4

L02

5 0.0 5.0 13.8 10.7 70.0 64.9 —

53.7 9.1 58.9 — 10 0.0 10.0 23.4 18.2 66.9 61.1 —

15 0.0 15.0 32.0 28.2 64.9 62.0 —

30 0.0 30.0 48.8 47.2 58.4 57.6 —

L03

5 0.2 5.0 6.7 4.7 53.1 43.0 22.1

49.1 2.2 45.7 48.8 10 0.2 10.0 14.1 10.2 54.7 45.4 20.0

15 0.2 15.1 21.3 17.3 54.8 49.1 32.3

30 0.2 30.3 36.0 29.9 50.2 44.9 11.7

L04

5 0.0 5.0 6.1 3.0 50.6 30.9 26.6

40.2 2.1 28.1 38.9 10 0.0 10.0 10.9 4.8 47.4 25.8 30.1

15 0.0 15.0 14.6 7.7 44.2 27.1 15.6

30 0.0 30.0 27.4 16.3 42.4 28.5 11.3

L05

5 −0.1 5.0 24.7 8.5 78.6 59.7 22.4

57.2 17.3 53.7 51.1 10 0.0 10.0 33.8 16.5 73.5 58.8 18.2

15 1.1 15.0 39.8 28.8 69.3 62.5 15.0

30 0.6 30.0 63.9 35.3 64.9 49.7 11.2

L06

5 −3.6 5.1 22.9 13.4 77.7 69.5 24.3

60.3 14.7 59.6 51.8 10 −4.4 10.1 30.6 21.7 71.9 65.2 19.4

15 −2.7 15.0 44.2 26.6 71.2 60.6 17.9

30 −7.6 30.1 66.4 48.4 65.7 58.2 13.1

—Not measured/evaluated.
195 

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 68-GG are shown in figure 97, figure 98, and 

figure 99, respectively. The full summary of LSDS results is presented in table 66. 

Source: FHWA.

Figure 97. Charts. Shear stress versus horizontal strain for No. 68-GG.

 

 

 
196 

Source: FHWA.

Figure 98. Charts. Vertical strain versus horizontal strain for No. 68-GG.

 

 

 
197 

Source: FHWA.

Figure 99. Chart. Linear Mohr-Coulomb failure envelopes for No. 68-GG.

 

 

 

 

 

 

 

 
198 

Table 66. Summary of LSDS results for No. 68-GG.

Lab ID

Target 

σn (psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.0 5.2 7.7 3.9 56.8 38.1 18.6

48.3 1.9 37.2 37.3 10 −0.1 10.1 13.2 8.0 53.0 38.8 16.1

15 0.0 15.2 18.3 10.8 50.6 35.8 12.5

30 0.1 30.1 35.7 22.9 50.0 37.4 12.5

L02

5 0.0 5.0 11.8 10.1 67.0 63.7 21.6

52.5 5.1 56.3 49.6 10 0.0 10.0 18.7 17.7 61.8 60.5 14.1

15 0.0 15.0 23.6 22.6 57.5 56.4 9.3

30 0.0 30.0 44.4 43.5 56.0 55.4 8.6

L03

5 0.2 5.0 6.4 4.6 52.0 42.7 19.9

48.7 1.7 44.1 45.8 10 0.2 10.0 13.7 10.2 53.8 45.6 23.1

15 0.3 15.1 19.5 14.8 52.4 44.7 17.3

30 0.0 30.4 35.4 28.9 49.7 43.9 19.6

L04

5 0.0 5.0 6.2 2.9 51.1 30.0 33.0

40.6 1.7 31.1 39.8 10 0.0 10.0 9.5 4.3 43.6 23.2 23.7

15 0.0 15.0 15.3 9.7 45.5 32.8 12.7

30 0.0 30.0 27.3 18.4 42.3 31.5 10.2

L05

5 1.0 5.0 16.8 5.2 73.4 46.3 22.1

57.9 14.0 53.7 51.9 10 0.0 9.9 34.8 17.5 74.0 60.2 21.2

15 0.0 15.0 40.0 20.9 69.4 54.3 16.8

30 0.0 30.0 60.1 39.6 63.5 52.9 11.8

L06

5 −2.3 5.1 14.9 9.2 71.4 61.6 20.4

42.1 10.6 45.0 43.9 10 −1.3 10.0 19.3 14.7 62.6 55.7 14.5

15 −0.2 15.1 25.0 15.9 59.1 46.6 12.0

30 2.2 30.0 37.4 27.3 51.3 42.3 5.1
199 

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 68-LI are shown in figure 100, figure 101, and 

figure 102, respectively. The full summary of LSDS results is presented in table 67. 

Source: FHWA.

Figure 100. Charts. Shear stress versus horizontal strain for No. 68-LI.

 

 

 
200 

Source: FHWA.

Figure 101. Charts. Vertical strain versus horizontal strain for No. 68-LI.

 

 

 
201 

Source: FHWA.

Figure 102. Chart. Linear Mohr-Coulomb failure envelopes for No. 68-LI.

 

 

 

 

 

 

 

 
202 

Table 67. Summary of LSDS results for No. 68-LI.

Lab ID

Target σn

(psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.0 5.2 8.0 5.1 58.0 38.6 19.8

48.9 3.1 42.3 42.4 10 0.0 10.2 14.9 9.3 56.1 36.8 16.3

15 −0.1 15.2 21.0 13.9 54.5 38.6 18.5

30 0.0 30.2 37.0 27.0 51.0 37.9 11.8

L02

5 0.0 5.0 10.1 8.9 63.6 69.3 10.7

55.9 3.8 58.1 45.9 10 0.0 10.0 18.4 17.7 61.5 65.1 10.0

15 0.0 15.0 28.1 26.7 61.9 65.8 11.8

30 0.0 30.0 47.4 46.2 57.6 61.5 8.5

L03

5 0.1 5.0 6.6 4.6 52.8 43.6 25.5

49.4 1.5 45.9 50.2 10 0.1 10.0 13.8 10.5 54.1 49.0 23.2

15 0.2 15.0 19.3 16.8 52.2 47.0 10.4

30 0.3 30.4 36.2 30.4 50.3 45.0 5.6

L04

5 0.0 5.0 5.6 3.2 48.2 33.4 35.0

41.5 1.1 31.8 38.7 10 0.0 10.0 9.5 6.1 43.5 29.5 21.8

15 0.0 15.0 14.8 8.5 44.5 30.8 26.6

30 0.0 30.0 27.5 19.0 42.5 34.5 12.7

L05

5 0.0 5.0 22.3 12.2 77.4 66.0 23.3

55.4 15.5 56.7 50.8 10 −0.1 10.0 29.6 17.4 71.3 64.6 16.9

15 0.0 15.0 38.6 25.6 68.8 62.0 15.3

30 0.3 30.0 58.6 42.8 62.9 61.6 10.9

L06

5 −2.1 5.0 19.8 13.9 75.8 69.3 20.8

55.2 17.0 59.0 54.1 10 −4.0 10.1 33.8 26.3 73.5 72.8 18.2

15 −3.6 15.0 42.5 28.1 70.6 61.1 14.8

30 −6.2 30.1 58.0 44.3 62.7 62.4 8.4
203 

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 68-SI are shown in figure 103, figure 104, and 

figure 105, respectively. The full summary of LSDS results is presented in table 68. 

Source: FHWA.

Figure 103. Charts. Shear stress versus horizontal strain for No. 68-SI.

 

 

 
204 

Source: FHWA.

Figure 104. Charts. Vertical strain versus horizontal strain for No. 68-SI.

 

 

 
205 

Source: FHWA.

Figure 105. Chart. Linear Mohr-Coulomb failure envelopes for No. 68-SI.

 

 

 

 

 

 

 

 
206 

Table 68. Summary of LSDS results for No. 68-SI.

Lab ID

Target σn

(psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.0 5.2 7.3 4.0 55.8 37.7 16.8

48.3 2.4 39.7 40.0 10 −0.1 10.1 13.4 7.5 53.2 37.0 16.0

15 −0.1 15.2 20.6 12.0 53.9 38.1 14.6

30 −0.1 30.1 35.5 23.4 49.8 0.0 13.2

L02

5 0.0 5.0 14.4 13.2 70.9 48.1 12.5

59.7 6.3 59.0 53.0 10 0.0 10.0 21.5 21.5 65.1 56.6 13.0

15 0.0 15.0 35.5 33.4 67.1 60.3 11.0

30 0.0 30.0 56.8 55.3 62.2 0.0 11.7

L03

5 −0.1 5.0 7.4 4.8 56.0 47.9 30.8

48.9 2.5 45.4 47.9 10 −0.1 10.0 14.5 11.5 55.5 47.5 33.9

15 −0.1 15.1 20.2 16.1 53.4 44.6 45.6

30 −0.1 30.3 36.5 30.0 50.6 0.0 26.6

L04

5 0.0 5.0 5.8 3.3 49.0 30.0 31.8

42.8 1.9 31.8 38.9 10 0.0 10.0 12.4 5.7 51.2 35.6 33.4

15 0.0 15.0 15.2 8.9 45.4 34.3 26.6

30 0.0 30.0 29.6 20.6 44.6 0.0 24.7

L05

5 0.0 4.9 27.9 11.2 79.8 56.3 28.3

67.2 18.0 57.6 55.9 10 0.0 10.0 44.7 21.1 77.4 61.7 23.4

15 0.0 15.0 53.3 28.3 74.3 62.1 19.2

30 0.0 30.0 89.0 55.4 71.4 0.0 14.5

L06

5 −1.0 5.2 23.4 13.2 77.9 54.7 24.6

62.6 14.0 57.0 50.8 10 −4.6 10.0 32.6 32.3 72.9 63.5 18.2

15 −4.1 15.1 44.3 27.2 71.3 56.3 17.7

30 −3.9 30.1 71.4 57.3 67.2 0.0 13.7
207 

NO. 8 OGAS 

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 8-BA are shown in figure 106, figure 107, and 

figure 108, respectively. The full summary of LSDS results is presented in table 69. 

Source: FHWA.

Figure 106. Charts. Shear stress versus horizontal strain for No. 8-BA.

 

 

 
208 

Source: FHWA.

Figure 107. Charts. Vertical strain versus horizontal strain for No. 8-BA.

 

 

 
209 

Source: FHWA.

Figure 108. Chart. Linear Mohr-Coulomb failure envelopes for No. 8-BA.

 

 

 

 

 

 

 

 
210 

Table 69. Summary of LSDS results for No. 8-BA.

Lab ID

Target σn

(psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.0 5.2 7.4 4.8 55.9 43.9 19.2

49.7 1.9 37.1 37.0 10 0.0 10.1 13.5 8.1 53.4 38.9 16.6

15 −0.1 15.2 20.6 10.8 54.0 35.9 18.3

30 −0.1 30.2 36.9 22.6 50.9 36.9 14.5

L02

5 0.0 5.0 5.3 5.2 46.6 46.3 35.7

51.4 0.9 52.0 59.1 10 0.0 10.0 14.4 14.4 55.2 55.2 9.1

15 0.0 15.0 21.8 21.1 55.4 54.5 23.6

30 0.0 30.0 37.6 37.2 51.4 51.1 21.0

L03

5 0.1 5.0 5.1 4.0 45.5 38.8 15.4

40.8 1.1 38.5 39.8 10 0.1 10.0 9.7 8.3 44.3 39.6 18.3

15 0.1 14.9 14.5 12.5 44.1 39.9 18.8

30 0.2 30.0 26.7 23.4 41.7 38.0 14.9

L04

5 0.0 5.0 5.8 3.5 49.3 35.3 25.6

42.9 1.9 33.4 34.3 10 0.0 10.0 12.0 6.4 50.2 32.7 30.1

15 0.0 15.0 16.1 7.8 47.1 27.3 26.6

30 0.0 30.0 29.6 20.9 44.6 34.9 19.8

L05

5 0.0 5.0 24.4 7.9 78.4 57.8 26.9

64.0 16.6 52.3 58.2 10 0.0 10.0 37.3 15.0 75.0 56.3 21.9

15 0.0 15.1 51.4 22.9 73.7 56.8 19.4

30 0.0 30.0 76.6 36.2 68.6 50.4 14.3

L06

5 −3.8 5.0 29.0 12.4 80.2 68.0 26.7

51.8 22.7 51.1 35.3 10 −0.4 10.1 33.1 13.2 73.2 52.9 22.4

15 −1.6 15.2 44.6 22.4 71.4 56.2 20.8

30 2.2 30.1 60.1 34.1 63.5 48.6 16.9
211 

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 8-DI are shown in figure 109, figure 110, and 

figure 111, respectively. The full summary of LSDS results is presented in table 70. 

Source: FHWA.

Figure 109. Charts. Shear stress versus horizontal strain for No. 8-DI.

 

 

 
212 

Source: FHWA.

Figure 110. Charts. Vertical strain versus horizontal strain for No. 8-DI.

 

 

 
213 

Source: FHWA.

Figure 111. Chart. Linear Mohr-Coulomb failure envelopes for No. 8-DI.

 

 

 

 

 

 

 

 
214 

Table 70. Summary of LSDS results for No. 8-DI.

Lab ID

Target σn

(psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.1 5.1 7.2 4.8 55.3 43.6 21.8

44.4 3.1 39.5 37.9 10 0.0 10.2 13.8 7.9 54.0 38.5 19.8

15 0.0 15.1 17.9 11.9 50.0 38.5 17.1

30 0.2 30.0 32.2 24.9 47.1 39.7 11.1

L02

5 0.0 5.0 7.2 6.3 55.4 51.7 —

55.8 2.5 55.9 — 10 0.0 10.0 18.4 15.3 61.5 56.7 —

15 0.0 15.0 27.0 24.5 61.0 58.5 —

30 0.0 30.0 45.3 43.2 56.5 55.2 —

L03

5 0.3 5.0 5.8 4.6 49.4 42.7 16.0

42.8 1.5 39.5 41.2 10 0.0 10.0 10.5 7.9 46.3 38.3 17.5

15 0.0 15.0 16.3 12.9 47.5 40.8 13.6

30 0.0 30.1 29.0 24.5 44.0 39.3 8.7

L04

5 0.0 5.0 5.9 3.0 49.7 30.8 45.0

39.4 2.1 30.2 40.4 10 0.0 10.0 10.2 5.6 45.7 29.4 24.5

15 0.0 15.0 15.0 7.7 45.0 27.3 15.3

30 0.0 30.0 26.5 18.0 41.5 30.9 11.3

L05

5 0.0 5.0 16.5 7.4 73.1 55.8 22.6

50.7 13.9 49.8 51.2 10 −0.1 10.0 26.9 15.5 69.6 57.2 15.3

15 0.0 15.0 37.0 22.6 68.0 56.4 13.8

30 0.0 30.0 48.5 31.6 58.3 46.5 9.4

L06

5 −2.1 5.1 16.4 9.2 73.0 61.6 22.6

59.6 9.2 54.7 52.4 10 −2.9 10.1 25.3 16.1 68.4 58.1 18.1

15 −4.5 15.1 38.5 26.6 68.7 60.6 15.5

30 −5.4 30.1 59.2 38.6 63.1 52.1 13.0

—Not measured/evaluated.
215 

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 8-GG are shown in figure 112, figure 113, and 

figure 114, respectively; the full summary of LSDS results is presented in table 71. 

Source: FHWA.

Figure 112. Charts. Shear stress versus horizontal strain for No. 8-GG.

 

 

 
216 

Source: FHWA.

Figure 113. Charts. Vertical strain versus horizontal strain for No. 8-GG.

 

 

 
217 

Source: FHWA.

Figure 114. Chart. Linear Mohr-Coulomb failure envelopes for No. 8-GG.

 

 

 

 

 

 

 

 
218 

Table 71. Summary of LSDS results for No. 8-GG.

Lab ID

Target 

σn (psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr 

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca 

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.0 5.3 6.4 3.6 51.8 35.8 15.9

42.6 2.2 36.3 38.1 10 −0.1 10.1 11.7 7.8 49.4 37.9 14.7

15 0.2 15.1 16.2 10.6 47.2 35.4 9.8

30 0.0 30.1 29.6 22.1 44.6 36.4 8.7

L02

5 0.0 5.0 9.1 7.9 61.3 57.7 12.5

48.9 3.2 49.8 45.3 10 0.0 10.0 13.5 12.4 53.5 51.2 12.5

15 0.0 15.0 21.5 18.1 55.1 50.3 10.8

30 0.0 30.0 37.3 34.9 51.2 49.3 6.0

L03

5 0.1 5.0 5.5 4.3 47.8 40.9 17.1

41.0 1.4 38.8 44.3 10 0.1 10.0 10.0 8.2 44.9 39.4 31.5

15 0.1 14.9 15.0 12.7 45.0 40.2 8.7

30 0.1 29.7 27.3 23.7 42.3 38.3 11.7

L04

5 0.0 5.0 5.0 2.9 44.9 30.2 31.0

34.5 1.7 27.8 35.4 10 0.0 10.0 8.3 4.5 39.8 24.3 12.4

15 0.0 15.0 12.7 8.1 40.2 28.3 11.6

30 0.0 30.0 22.1 15.9 36.4 27.9 6.8

L05

5 2.3 5.1 11.8 3.4 67.0 34.4 18.3

53.4 8.8 47.2 50.1 10 0.0 10.0 22.4 13.0 65.9 52.4 17.1

15 0.0 15.0 35.3 17.3 67.0 49.0 13.9

30 0.0 30.1 46.8 31.5 57.3 46.4 8.8

L06

5 −0.2 5.1 15.5 7.3 72.2 55.5 22.3

48.5 10.1 44.6 49.4 10 1.8 10.1 17.9 9.5 60.8 43.5 16.4

15 −3.1 15.1 32.2 22.2 65.0 55.9 10.5

30 2.3 30.0 42.7 25.6 54.9 40.5 9.3
219 

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 8-LI are shown in figure 115, figure 116, and 

figure 117, respectively; the full summary of LSDS results is presented in table 72. 

Source: FHWA.

Figure 115. Charts. Shear stress versus horizontal strain for No. 8-LI.
220 

Source: FHWA.

Figure 116. Charts. Vertical strain versus horizontal strain for No. 8-LI. 

 

 

 
221 

Source: FHWA.

Figure 117. Chart. Linear Mohr-Coulomb failure envelopes for No. 8-LI.

 

 

 

 

 

 

 

 
222 

Table 72. Summary of LSDS results for No. 8-LI.

Lab ID Target σn

(psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.0 5.2 6.8 4.8 53.8 40.0 14.1 

46.7 2.1 40.5 46.0 10 −0.1 10.1 12.9 9.1 52.3 39.3 13.8 

15 −0.2 15.2 18.6 13.1 51.2 36.9 9.5 

30 −0.1 30.1 33.6 25.2 48.2 36.7 4.7 

L02

5 0.0 5.0 9.8 9.4 62.9 57.7 14.5 

55.2 3.3 57.4 53.4 10 0.0 10.0 17.5 15.1 60.2 61.2 11.6 

15 0.0 15.0 26.2 25.3 60.2 59.7 8.9 

30 0.0 30.0 45.9 45.9 56.8 58.9 6.0 

L03

5 0.2 5.0 5.5 4.6 47.6 40.0 10.7 

41.8 1.5 38.9 45.9 10 0.2 10.0 10.4 7.9 46.2 43.2 12.4 

15 0.2 14.9 15.7 12.3 46.4 41.0 5.4 

30 0.2 29.7 28.0 24.1 43.0 39.3 10.0 

L04

5 0.0 5.0 5.5 4.3 47.9 26.6 21.8 

37.7 1.7 35.2 34.6 10 0.0 10.0 9.6 5.1 43.8 28.0 11.3 

15 0.0 15.0 13.3 9.4 41.6 26.7 13.5 

30 0.0 30.0 24.9 22.3 39.7 32.7 11.3 

L05

5 −0.1 5.0 18.6 9.6 75.0 58.4 20.6 

57.7 12.1 55.8 50.6 10 0.2 10.0 28.2 15.5 70.5 58.4 16.9 

15 0.0 15.1 37.7 23.5 68.3 55.4 15.3 

30 −0.1 30.0 58.7 42.8 62.9 50.7 10.4 

L06

5 −4.0 5.1 23.2 14.5 77.9 51.7 21.5 

60.8 17.3 63.7 58.8 10 −1.8 10.1 38.0 24.6 75.3 60.3 16.4 

15 1.2 15.1 45.2 30.6 71.7 60.6 14.2 

30 −8.0 30.1 69.9 58.5 66.8 58.8 9.2 
223 

The shear stress versus horizontal strain, vertical strain versus horizontal strain, and linear 

Mohr-Coulomb failure envelopes for No. 8-SI are shown in figure 118, figure 119, and 

figure 120, respectively. The full summary of LSDS results is presented in table 73. 

Source: FHWA.

Figure 118. Charts. Shear stress versus horizontal strain for No. 8-SI.

 

 

 
224 

Source: FHWA.

Figure 119. Charts. Vertical strain versus horizontal strain for No. 8-SI.

 

 

 
225 

Source: FHWA.

Figure 120. Chart. Linear Mohr-Coulomb failure envelopes for No. 8-SI.

 

 

 

 

 

 

 

 
226 

Table 73. Summary of LSDS results for No. 8-SI.

Lab ID Target 

σn (psi)

τinitial

(psi)

σn at τpeak

(psi)

τpeak

(psi)

τr

(psi)

φs

(deg)

φr

(deg)

ψmax

(deg)

φt 

(deg)

ca

(psi)

φt,r

(deg)

φcv

(deg)

L01

5 0.1 5.3 6.8 4.2 53.5 38.9 12.3

45.8 1.5 38.1 40.3 10 0.1 10.1 11.9 8.2 50.1 35.9 14.3

15 −0.2 15.1 16.7 11.3 48.0 36.9 9.8

30 0.0 30.1 32.5 22.4 47.3 0.0 7.7

L02

5 0.0 5.0 8.3 7.9 58.9 55.2 14.4

58.9 0.7 54.9 56.1 10 0.0 10.0 18.2 18.2 61.2 54.5 12.5

15 0.0 15.0 25.7 25.7 59.7 51.1 12.7

30 0.0 30.0 50.4 49.7 59.2 0.0 12.3

L03

5 0.0 5.0 5.8 4.2 49.4 39.6 17.4

40.9 2.4 39.1 42.9 10 0.0 10.0 11.7 9.4 49.4 39.9 40.0

15 0.0 14.8 16.1 13.1 47.0 38.0 23.5

30 −0.1 30.0 28.0 24.6 43.0 0.0 14.8

L04

5 0.0 5.0 6.0 2.5 50.3 32.7 30.6

41.5 1.0 31.6 35.3 10 0.0 10.0 9.7 5.3 44.0 27.3 22.8

15 0.0 15.0 13.7 7.6 42.4 34.9 19.8

30 0.0 30.0 27.9 19.3 42.9 0.0 16.7

L05

5 0.0 5.0 21.9 8.1 77.1 56.3 23.8

61.7 14.8 51.5 52.8 10 0.0 10.0 32.2 16.2 72.8 56.8 20.2

15 0.0 15.0 47.6 21.7 72.5 50.4 17.7

30 0.0 30.0 68.6 36.7 66.4 0.0 13.3

L06

5 1.7 5.1 14.2 6.3 70.6 52.9 21.1

61.7 7.6 54.6 50.5 10 −0.4 10.1 26.5 17.6 69.3 56.2 17.5

15 −4.3 15.1 39.8 26.6 69.3 48.6 16.4

30 −6.1 30.1 61.6 49.5 64.0 0.0 11.5
227 

APPENDIX E. AD TEST AND ANOVA ANALYSIS

The sections included within this appendix are related to the summarized steps for the 

Anderson‐Darling (AD) goodness-of-fit test and the two-way ANOVA analysis. The steps 

followed to evaluate the appropriate assumptions were satisfied for performing ANOVA analysis 

are also presented.

AD TEST

Besides computing mean, standard deviation, and COV, more advanced statistical analyses were 

performed to determine the frequency distribution types that would best suit the underlying data 

collected, namely dry unit weight and shear strength, as well as to determine the sensitivity of 

these data as a function of sample type and testing laboratory. Goodness-of-fit tests are methods 

used to evaluate how well a dataset fits a given distribution type (D’Agostino and Stephens 

1986). A wide range of goodness-of-fit tests are available in the literature. As reported in 

Jäntschi and Bolboacă (2018), the most frequently used tests are AD, Kolmogorov-Smirnov 

(KS), Pearson’s chi-square, Cramer-von Mises, Shapiro-Wilk, Jarque‐Bera, D’Agostino-Pearson, 

and Lilliefors. In a comparison between AD and K-S tests conducted by Engmann and 

Cousineau (2011), the AD test was found to be superior because it detects small variations 

between two distributions and differences at the extreme ends of distributions more reliably, 

even for small sample sizes. Thus, the AD test gives weight to the tails of the data, where such 

phenomena could be critical in engineering design. Hence, the AD method is used in this study 

to perform normality tests for the unit weight and shear strength data collected from the OGA 

round-robin study.

The null hypothesis (H0) of the AD test states that the data follow a specified distribution (e.g., 

normal distribution). Conversely, the alternative hypothesis (H1) would be that the data depart 

significantly from the specified, theoretical distribution. The functional form for the AD test is 

provided in equation 8 (Stephens 1986). 

 (8)

Where: 

n = sample size. 

F(xi) and F(xN-i+1) = the cumulative probability for the parameter value at the i

th order 

and N-i+1 order. 

AD = AD statistic. 

To perform an AD test for normality, the data were first sorted in ascending order and then the 

cumulative probability of each data point was estimated based on the mean and standard 

deviation of the entire dataset. Using equation 8, the AD statistic was computed. The OGAs used 

for this study were considered representative but not exhaustive samples of their corresponding 

rock sources; accordingly, instead of directly using the AD statistic, an adjusted AD statistic 

(AD*) for testing normality was computed using equation 9 (Stephens 1986).The computed AD* 

was then used to estimate the p-value for each normality test, as shown in table 74 (Stephens 

1986). The p-value is a statistical measure indicating the probability of producing results at least 
228 

as extreme as the observed outcome if the null hypothesis (H0) is correct. An alpha of 0.05 was 

selected in this study, meaning H0 would be accepted if the p-value were greater than 0.05 (i.e., a 

5 percent probability that random chance could have produced the observed results). 

Alternatively, H0 would be rejected if the p-value were less than 0.05. If normality was not found 

(i.e., H0 was rejected), then lognormality was tested. To test for lognormality, the data were

log‐transformed before the basic AD* normality test was repeated (Romeu 2003). Additional 

groupings of data were evaluated if neither normality nor lognormality was found for a given 

parameter.

 (9) 

Table 74. AD* p-values for normal distributions.

AD* p-value 

AD tests were performed based on the entire 90-point dataset, representing five rock types from 

each of the three stone sizes, with results from all six participating laboratories. Tests were 

performed for dry unit weight at 95RD and for strength (i.e., φs, φt, φt,r, and φcv) and dilatancy 

(ψmax) parameters. Data across the range of σn values (i.e., 5 to 30 psi) were combined for the φs

and ψmax AD tests. The analysis based on the entire dataset (table 75) showed that only φt and φcv

are normally distributed. The data for γd95, φs, φt,r and ψmax followed neither normal nor lognormal 

distributions. The descriptive statistics of φt,r (table 33) suggest that φt,r follows a uniform 

distribution. Further evaluation of γd95, φs, and ψmax (table 76) found that normality was present 

when the datasets were separated into groups based on OGA bulk dry specific gravity, LSDS 

device upper box fixity, and LSDS device data collection frequency and corresponding dilation 

data smoothing, respectively.

Table 75. AD test results for key parameters. 

Parameter n 

Normal Distribution Lognormal Distribution

p-value Data Fitted p-value Data Fitted

γd95 90 0.00 No 0.01 No

φs 360 0.00 No 0.00 No

φt 90 0.08 Yes 0.10 Yes

φt,r 90 0.00 No 0.00 No

φcv 86 0.70 Yes 0.04 No

ψmax 346 0.00 No 0.02 No
229 

Table 76. Grouped AD results for nonnormal key parameters.

Parameter Group n 

Normal Distribution Lognormal Distribution

p-Value Data Fitted p-Value Data Fitted

γd95

Low Specific Gravity 54 0.30 Yes 0.25 Yes

High Specific Gravity 36 0.40 Yes 0.37 Yes

φs

Fixed Box 180 0.16 Yes 0.01 No

Mobile Box 180 0.03 No 0.01 No

ψmax

Data Smoothing 226 0.62 Yes 0.00 No

No Data Smoothing 120 0.25 Yes 0.00 No

ANOVA

ANOVA is a common type of statistical analysis employed for comparing the means of groups 

of measurement data (Casella and Berger 2002). The ANOVA technique was used to evaluate 

the sensitivity of the physical properties and shear strength to inherent variability (e.g., stone size 

and mineralogy) and measurement variability (e.g., device type, operator). For example, the data 

collected for φt, considered the dependent variable, can be grouped according to two categorical, 

independent variables, represented by factor A (i.e., sample type) and factor B (i.e., laboratory), 

as shown in table 77. Each value of one independent variable is therefore found in combination 

with each value of the other independent variable. In this case, a two-factor ANOVA without 

replicates (Zaiontz 2020) was selected.

Two null hypotheses to test using the adopted two-factor ANOVA without replicates exist. 

Taking table 77 as an example, the two null hypotheses will be that there is no difference in the 

mean of φt among the 15 sample types for factor A, and there is no difference in the mean of φt

due to the laboratory for factor B. The approach to determine whether to accept or reject the null 

hypotheses is based on comparing a computed F-statistic to a critical value (i.e., F-critical). The 

F-statistic for factors A and B are computed using equations 10 and 11 (Zaiontz 2020). 
230 

Table 77. LSDS test results for tangent friction angle by factor.

Factor A—Sample Type

Factor B—Laboratory 

L01 L02 L03 L04 L05 L06

No. 57-BA 51.5 62.1 51.2 49.2 59.9 63.1 

No. 57-DI 51.9 61.5 50.7 44.5 56.3 63.1 

No. 57-GG 47.9 59.1 49.5 45.0 54.0 54.7 

No. 57-LI 51.6 63.6 49.4 46.4 51.2 53.5 

No. 57-SI 48.4 58.6 49.8 47.2 63.0 50.0 

No. 68-BA 49.3 61.8 48.9 47.7 68.1 59.6 

No. 68-DI 51.5 53.7 49.1 40.2 57.2 60.3 

No. 68-GG 48.3 52.5 48.7 40.6 57.9 42.1 

No. 68-LI 48.9 55.9 49.4 41.5 55.4 55.2 

No. 68-SI 48.3 59.7 48.9 42.8 67.2 62.6 

No. 8-BA 49.7 51.4 40.8 42.9 64.0 51.8 

No. 8-DI 44.4 55.8 42.8 39.4 50.7 59.6 

No. 8-GG 42.6 48.9 41.0 34.5 53.4 48.5 

No. 8-LI 46.7 55.2 41.8 37.7 57.7 60.8 

No. 8-SI 45.8 58.9 40.9 41.5 61.7 61.7 

 (10) 

 (11)

Where: 

i and j refer to the i

th row (i.e., level) of factor A and jth column (i.e., level) of factor B, 

respectively. 

a and b refer to the total number of levels for factors A and B. 

x̄i, x̄j, and x̄ are the mean of the i

th row of factor A, the jth column of factor B, and the grand 

mean of all data, respectively.

Step-by-step details for computing these values is provided by Zaiontz (2020). 

F-critical values for both target factors (sample type or testing laboratory) were selected from 

established F-distribution tables based on Kanji (2010) using an alpha value of 0.05, the degrees 

of freedom for the target factor of interest (equal to one less than the number of levels within the 

target factor), and the product of both factors’ degrees of freedom. The null hypotheses were 

accepted when the F-statistic was lower than F-critical, meaning that there was no statistically 

significant influence on the parameter due to the considered factor. Conversely, F-statistics 
231 

greater than the F-critical validate the alternative hypothesis, meaning the examined factor is 

significant enough to impact the parameter. 

The ANOVA analysis results for all parameters are summarized in table 78. The F-statistics for 

all tests, except for one case, were greater than their paired F-critical values. Thus, the null 

hypotheses are rejected. The interpretation of these results is that the measured parameters were 

significantly sensitive to sample type and laboratory. 

Table 78. Test results from the two-factor ANOVA without replicates analysis.

Parameter Factor

Two-Factor ANOVA

F-statistic F-critical Significant

γd95

Sample type 86.00 1.84 Yes

Laboratory 18.21 2.35 Yes

φs

Sample type 6.56 1.37 Yes

Laboratory 442.58 2.24 Yes

φt

Sample type 4.00 1.84 Yes

Laboratory 45.33 2.35 Yes

φt,r

Sample type 5.81 1.84 Yes

Laboratory 172.83 2.35 Yes

φcv

Sample type 1.94 2.03 No

Laboratory 18.79 2.40 Yes

ψmax Sample type 5.29 1.43 Yes

Laboratory 29.80 2.25 Yes

The major assumptions for two-factor ANOVA without replicates is that (a) the observations 

within each level are normally distributed, (b) the levels within each factor have equal variance 

and (c) there is no interaction between the factors (Zaiontz 2020). Since there were no replicates 

in this study, assumption (c) is valid for the entire dataset. To evaluate whether the assumptions 

for normality were satisfied (i.e., assumption (a)), AD tests were performed for each level (i.e., 

each individual testing laboratory and sample type) in the same manner discussed in the previous 

section. 

A summary of the AD tests performed for normality testing of the levels within each factor are 

presented in table 79. In general, most of the levels within both factors passed the normality test, 

meeting assumption (a) of the two-factor ANOVA. Overall, it seems that a higher percentage of 

the levels within factor A (i.e., sample type) passed the normality test compared to the levels 

within factor B (i.e., laboratory). 
232 

Table 79. Summary of AD normality test results for datasets within each factor.

Parameter

Factor A—Sample Type Factor B—Laboratory

No. of

Levels

No. of

Passing Levels

Percent

Passing

No. of

Levels

No. of

Passing Levels

Percent

Passing

γd95 15 14 93 6 5 83

φs 60 60 100 6 5 83

φt 15 15 100 6 5 83

φt,r 15 15 100 6 3 50

φcv 11 10 91 6 5 83

ψmax 46 38 83 6 5 83

Levene’s test were employed to test assumption (b), or the equality of variance among the levels 

(Levene 1960). This test uses the absolute value of residuals (i.e., the difference between a given 

measured parameter and the mean for a given level). For example, in examining φt (table 77) 

when sample type (i.e., factor A) is considered, the level is represented by the rows, so there are 

15 levels total each with a sample size of 6. The mean was calculated for each level, and the 

absolute value of the difference between φt and the mean of that level was found. 

A one-factor ANOVA analysis was then performed to evaluate the homogeneity of variance 

among the levels. The null hypothesis (H0) is that there is equality of variance among the 

columns. F-critical values were determined using an alpha of 0.05, the degrees of freedom of the 

factor (equal to the number of levels within the target factor minus one), and the remaining 

degrees of freedom within the dataset (equal to the number of samples minus the sample size of 

the tested factor). As before, H0 is accepted when the F-statistic is lower than the F-critical, 

meaning that there is equal variance along the target factor of the given parameter. 

The results from Levene’s tests for all key parameters are presented in table 80. Except for ψmax, 

a significant equality of variance was observed among the levels when sample type was the 

factor of interest, satisfying this assumption for ANOVA. However, only γd95, φt,r, and φcv passed 

Levene’s test when the considered factor was testing device.
233 

Table 80. Levene’s test for selected parameters by factor.

Parameter Factor

Equality of Variance Test

F-statistic F-critical Equal Variance

γd95

Sample type 0.65 1.83 Yes

Laboratory 0.08 2.32 Yes

φs

Sample type 0.80 1.37 Yes

Laboratory 4.74 2.24 No

φt

Sample type 1.29 1.83 Yes

Laboratory 3.11 2.32 No

φt,r

Sample type 0.76 1.83 Yes

Laboratory 1.70 2.32 Yes

φcv

Sample type 2.08 2.01 No

Laboratory 0.56 2.37 Yes

ψmax Sample type 1.78 1.42 No

Laboratory 8.39 2.25 No

In summary, the results from both the AD test and Levene’s test showed that most of the data 

satisfied the ANOVA assumptions for normality and equal variance, yet there were some 

departures, namely for φt where there were deviations from both assumptions for factor B. A lack 

of consensus exists regarding the robustness of using an ANOVA analysis when the main 

assumptions are violated. In these cases, a Type 1 error (NIST 2012) in ANOVA can occur 

whereby H0 is falsely rejected. However, many researchers have validated the method’s 

robustness against moderate departures from nonnormality (Glass et al. 1972; Lix et al. 1996; 

Schmider et al. 2010). Thus, the chance of Type I errors is likely minimal using the data 

considered in this report.

235 

ACKNOWLEDGMENTS

FHWA gratefully acknowledge the efforts and contributions of the following individuals:

• Rick Meininger (former Federal laboratory manager) and Mengesha Beyene (contract 

laboratory manager) of the FHWA Aggregate and Petrology Laboratory for performing 

petrographic analysis of the rock types to verify the mineralogy. 

• Silas Nichols (FHWA Principal Geotechnical Engineer) and Justice Maswoswe (FHWA 

Senior Geotechnical Engineer) for their technical review of this report.

• Timothy Barrett (FHWA Concrete Materials Engineer) for his technical review and 

statistical analysis verification of the goodness-of-fit and ANOVA approaches employed.

• The five participating laboratories in this round-robin study. While their identities are 

held confidential, their participation and feedback throughout the course of the study led 

to many valuable insights and a better understanding of LSDS testing.

237 

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Recyclable

Recommended citation: Federal Highway Administration, 

Variability in the Engineering Properties of Open-Graded Aggregate 

Backfills: A Large-Scale Direct Shear Round-Robin Study

(Washington, DC: 2023) https://doi.org/10.21949/1521990