Strength Characterization of

Open-Graded Aggregates for 

Structural Backfills

PUBLICATION NO. FHWA-HRT-15-034 JUNE 2015

Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296
FOREWORD

State and local transportation agencies frequently use crushed, manufactured open-graded 

aggregates (OGA) as structural backfill material for retaining walls, bridge foundations, and 

other ground improvement applications, yet their strength characteristics are not fully understood 

or applied. The friction angle is required to efficiently design for lateral earth pressures and 

bearing capacity, but because of the large size of the standard American Association of State 

Highway and Transportation Officials (AASHTO) OGAs, this parameter cannot be measured 

with standard testing equipment. Instead, current practice is to select a low, default friction angle,

which can lead to over-conservative, less cost-effective designs. To address this gap, research 

was initiated by the Federal Highway Administration’s Turner-Fairbank Highway Research 

Center (TFHRC) to establish a knowledge base on the most commonly used AASHTO OGAs. 

The study included a systematic approach to fully characterize the strength parameters utilizing 

the large scale direct shear and triaxial devices in the TFHRC geotechnical laboratory. 

Relationships between other important soil parameters on the friction angle, as well as the impact 

of different automated testing devices and data interpretation methods, were also investigated. 

This report presents the results of this research and will assist State and local transportation 

agencies, researchers, and design consultants in gaining confidence on the use of higher friction 

angles for structural backfills to optimize the design of geotechnical features.

Jorge E. Pagán-Ortiz

Director, Office of Infrastructure

Research and Development

Notice

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

in the interest of information exchange. The U.S. Government assumes no liability for the use 

of the information contained in this document. This report does not constitute a standard, 

specification, or regulation.

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

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

objective of the document.

Quality Assurance Statement

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

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

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

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

ensure continuous quality improvement.
TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.

FHWA-HRT-15-034

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

4. Title and Subtitle

Strength Characterization of Open-Graded Aggregates for 

Structural Backfills

5. Report Date

June 2015

6. Performing Organization Code: 

HRDI-40

7. Author(s)

Nicks, J.E., Gebrenegus, T., Adams, M.T. 

8. Performing Organization Report No. 

9. Performing Organization Name and Address

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101

10. Work Unit No.

11. Contract or Grant No.

N/A

12. Sponsoring Agency Name and Address

Office of Infrastructure R&D

FHWA Research, Development and Technology

6300 Georgetown Pike

McLean, VA 22101

13. Type of Report and Period Covered

Technical

14. Sponsoring Agency Code

15. Supplementary Notes

None. 

16. Abstract

Open-graded aggregates are common in road and bridge construction because they are easy to place, and they 

have the advantages of very low fine content, free-draining characteristics, low frost heave potential, and simple 

quality assurance testing. They are a suitable alternative to well-graded aggregate blends in many applications. 

Another key benefit is their strength, but this attribute it is often not accounted for in design. This report presents 

strength characteristics of 16 open-graded aggregates commonly selected as structural backfills and discusses the 

impact of different test and data interpretation methods. Results of large-scale direct shear and large diameter 

triaxial tests indicate higher strengths for these materials than typical default values typically assumed in design.

It was also observed that the mean grain size, sphericity, angularity, and void ratio play a role in the measured 

friction angles. This information will help designers better understand these backfills and aid in the cost-effective 

design of retaining walls and bridge foundations. 

17. Key Words

Friction angle, strength, open-graded aggregate, structural 

backfill, retaining wall, bridge foundation

18. Distribution Statement

No restrictions. The report will be available 

to the public at FHWA: 

www.fhwa.dot.gov/research or NTIS: 

www.ntis.gov.

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

149

22. Price

N/A

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol 

LENGTH

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2 square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m2

yd2 square yard 0.836 square meters m2

ac acres 0.405 hectares ha

mi2 square miles 2.59 square kilometers km2

VOLUME 

fl oz fluid ounces 29.57 milliliters mL 

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m3 

yd3 cubic yards 0.765 cubic meters m3 

NOTE: volumes greater than 1000 L shall be shown in m3

MASS oz ounces 28.35 grams g

lb pounds 0.454 kilograms kg

T short tons (2000 lb) 0.907 megagrams (or "metric ton") Mg (or "t") 

TEMPERATURE (exact degrees) o

F Fahrenheit 5 (F-32)/9 Celsius oC 

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2 poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA mm2 square millimeters 0.0016 square inches in2 

m2 square meters 10.764 square feet ft2 

m2 square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac

km2 square kilometers 0.386 square miles mi2 

VOLUME 

mL milliliters 0.034 fluid ounces fl oz 

L liters 0.264 gallons gal 

m3 cubic meters 35.314 cubic feet ft3 

m3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T 

TEMPERATURE (exact degrees) o

C Celsius 1.8C+32 Fahrenheit oF 

ILLUMINATION 

lx lux 0.0929 foot-candles fc 

cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2

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

(Revised March 2003)

ii
TABLE OF CONTENTS

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

1.1 PROBLEM STATEMENT................................................................................................ 1

1.2 OBJECTIVES..................................................................................................................... 1

1.3 REPORT OUTLINE .......................................................................................................... 1

CHAPTER 2. BACKGROUND................................................................................................... 3

2.1 USE OF OGAS.................................................................................................................... 3

2.2 STRENGTH PROPERTIES OF GRANULAR MATERIALS...................................... 3

Laboratory Testing.................................................................................................................. 5

Data Interpretation .................................................................................................................. 7

Design Practices.................................................................................................................... 10

2.3 DESIGN IMPLICATIONS.............................................................................................. 13

CHAPTER 3. TEST PROGRAM AND RESULTS................................................................. 17

3.1 MATERIALS .................................................................................................................... 17

3.2 LABORATORY TESTING AND RESULTS ................................................................ 19

Gradation............................................................................................................................... 19

Density .................................................................................................................................. 20

Repose Angle ........................................................................................................................ 23

Angularity, Texture, and Sphericity...................................................................................... 25

Strength ................................................................................................................................. 32

CHAPTER 4. ANALYSIS OF RESULTS................................................................................ 61

4.1 DETERMINATION OF STRENGTH PROPERTIES................................................. 61

4.2 TESTING DEVICE.......................................................................................................... 61

Scale Effects.......................................................................................................................... 66

Data Interpretation ................................................................................................................ 71

Effect of Saturation ............................................................................................................... 72

4.3 STRENGTH CORRELATIONS..................................................................................... 75

Gradation............................................................................................................................... 75

Maximum Unit Weight......................................................................................................... 79

Repose Angle ........................................................................................................................ 80

Angularity, Texture, and Sphericity...................................................................................... 81

CHAPTER 5. CONCLUSIONS................................................................................................. 87

5.1 FRICTION ANGLE ......................................................................................................... 87

5.2 TEST METHOD............................................................................................................... 88

5.3 STRENGTH CORRELATIONS..................................................................................... 89

5.4 FUTURE RESEARCH..................................................................................................... 90

APPENDIX A. RAW DATA...................................................................................................... 91

NO. 5 ........................................................................................................................................ 91

NO. 56 ...................................................................................................................................... 94

NO. 57 ...................................................................................................................................... 96

NO. 6 ........................................................................................................................................ 98

NO. 67 .................................................................................................................................... 100

NO. 68 .................................................................................................................................... 103

iii
NO. 7 ...................................................................................................................................... 105

NO. 78 .................................................................................................................................... 107

NO. 8A (DEFIANCE)........................................................................................................... 110

NO. 8B (STAUNTON LIME) .............................................................................................. 112

NO. 8C (FRAZIER).............................................................................................................. 113

NO. 8D (VULCAN MATERIALS)...................................................................................... 115

NO. 8E (LUCK STONE)...................................................................................................... 116

NO. 89 .................................................................................................................................... 118

NO. 9 ...................................................................................................................................... 121

NO. 10 .................................................................................................................................... 123

ACKNOWLEDGEMENTS ..................................................................................................... 127

REFERENCES.......................................................................................................................... 129

iv
LIST OF FIGURES

Figure 1. Chart. Effect of porosity and compaction on the shear strength of granular 

materials (modified from Rowe, 1962)..................................................................................... 4

Figure 2. Chart. The theoretical determination of the drained shear strength for sands based 

on the three components that comprise the mobilized friction angle (after Lee and Seed, 

1967) ......................................................................................................................................... 5

Figure 3. Chart. Secant ( 's) and tangent ( 't) friction angle illustration for DS testing................ 7

Figure 4. Graph. Sieve analysis results of tested aggregates........................................................ 20

Figure 5. Photo. Mold (0.1 ft3) for funnel and vibratory table tests ............................................. 22

Figure 6. Photo. LVDT and mold set-up for vibratory table tests................................................ 23

Figure 7. Photo. Repose angle cylinder test.................................................................................. 23

Figure 8. Photo. Aggregate pile to determine repose angle.......................................................... 24

Figure 9. Chart. Relationship between repose angle and mean aggregate size ............................ 25

Figure 10. Diagram. AIMS angularity index classification ranges .............................................. 26

Figure 11. Diagram. AIMS texture classification ranges ............................................................. 27

Figure 12. Diagram. AIMS sphericity index classification ranges............................................... 28

Figure 13. Chart. Angularity results from AIMS2........................................................................ 29

Figure 14. Chart. Texture results from AIMS2............................................................................. 30

Figure 15. Chart. Sphericity results from AIMS2......................................................................... 31

Figure 16. Photo. SDS test device at TFHRC............................................................................... 33

Figure 17. Chart. Shear stress versus horizontal displacement for No. 57 from SDS tests.......... 34

Figure 18. Chart. Shear stress versus horizontal displacement for No. 5 from SDS tests............ 35

Figure 19. Chart. Shear versus normal stress for No. 57 using SDS ............................................ 36

Figure 20. Chart. Deformation behavior of No. 57 during SDS testing ....................................... 38

Figure 21. Chart. Friction angle versus dilation angle for No. 57 using SDS .............................. 39

Figure 22. Chart. Relationship between friction and dilation angles in SDS testing.................... 40

Figure 23. Chart. Summary of SDS testing .................................................................................. 41

Figure 24. Photo. LSDS device at TFHRC................................................................................... 41

Figure 25. Chart. Vertical displacement calibration for LSDS device ......................................... 42

Figure 26. Chart. Global MC envelope for all AASHTO OGAs tested under both dry and 

saturated conditions ................................................................................................................ 45

Figure 27. Chart. Relationship between friction and dilation angles in LSDS testing ................. 47

Figure 28. Chart. Summary of LSDS testing under dry conditions.............................................. 48

Figure 29. Chart. Summary of LSDS testing under saturated conditions..................................... 48

Figure 30. Chart. Comparison of the effective tangent and secant friction angles for LSDS 

testing...................................................................................................................................... 49

Figure 31. Diagram. Overview of the adopted procedure for LDTX testing ............................... 50

Figure 32. Chart. The effective deviator stress versus axial strain for No. 57 from LDTX 

testing...................................................................................................................................... 52

Figure 33. Chart. Volumetric strain versus axial strain for No. 57 from LDTX testing............... 52

Figure 34. Chart. Graphical method to determine membrane penetration correction and the 

effect of aggregate size on volume reduction during LDTX testing ...................................... 55

Figure 35. Chart. Effect of confining stress on volume reduction for AASHTO No. 68 sample 

during LDTX testing............................................................................................................... 56

Figure 36. Chart. Relationship between p' and q values in LDTX testing series......................... 57

Figure 37. Chart. Relationship between friction and dilation angles in LDTX testing ................ 59

φ φ

v
Figure 38. Chart. Summary of LDTX testing............................................................................... 60

Figure 39. Chart. Comparison of the effective tangent and secant friction angles for LDTX 

testing...................................................................................................................................... 60

Figure 40. Chart. Difference between LSDS and LDTX as a function of mean aggregate 

size .......................................................................................................................................... 64

Figure 41. Chart. Relationship between LSDS and LDTX friction angles .................................. 64

Figure 42. Chart. Relationship between LSDS and LDTX effective secant friction angles ........ 65

Figure 43. Chart. Relationship between LDTX and LSDS measured dilation angles.................. 66

Figure 44. Chart. Relationship between LSDS and SDS measured friction angles ..................... 67

Figure 45. Chart. Relationship between LSDS and SDS measured dilation angles..................... 68

Figure 46. Chart. Relationship between measured tangent and CV friction angles..................... 72

Figure 47. Chart. Measured friction angles under dry and saturated LSDS testing using the 

MC approach........................................................................................................................... 73

Figure 48. Chart. Measured friction angles under dry and saturated LSDS testing using the 

ZDA approach......................................................................................................................... 74

Figure 49. Chart. Relationship between measured friction angles under dry and saturated 

conditions in the LSDS device................................................................................................ 75

Figure 50. Chart. Relationship between tangent friction angle and median grain size ................ 76

Figure 51. Chart. Relationship between CV friction angle and median grain size....................... 76

Figure 52. Chart. Relationship between secant friction angle and median grain size for 

LDTX testing .......................................................................................................................... 77

Figure 53. Chart. Relationship between tangent friction angle and Cu......................................... 78

Figure 54. Chart. Relationship between CV friction angle and Cu ............................................... 78

Figure 55. Chart. Relationship between tangent friction angle and maximum unit weight ......... 79

Figure 56. Chart. Relationship between CV friction angle and maximum unit weight................ 80

Figure 57. Chart. Relationship between CV friction angle and repose angle............................... 81

Figure 58. Chart. Relationship between tangent friction angle and angularity ............................ 82

Figure 59. Chart. Relationship between CV friction angle and angularity................................... 82

Figure 60. Relationship between initial void ratio and tangent friction angle.............................. 83

Figure 61. Chart. Relationship between CV friction angle and texture........................................ 83

Figure 62. Chart. Relationship between tangent friction angle and sphericity............................. 84

Figure 63. Chart. Relationship between CV friction angle and sphericity ................................... 85

Figure 64. Chart. Relationship between tangent friction angle and angularity in LSDS testing 

for AASHTO No. 8 aggregates............................................................................................... 85

Figure 65. Chart. Relationship between CV friction angle and angularity in LSDS testing for 

AASHTO No. 8 aggregates .................................................................................................... 86

Figure 66. Chart. Relationship between tangent friction angle and sphericity in LSDS testing 

for AASHTO No. 8 aggregates............................................................................................... 86

Figure 67. ZDA Approach for LDTX and LSDS testing.............................................................. 88

Figure 68. Photo. No. 5 aggregate sample .................................................................................... 91

Figure 69. Photo. No. 56 aggregate sample .................................................................................. 94

Figure 70. Photo. No. 57 aggregate sample .................................................................................. 96

Figure 71. Photo. No. 6 aggregate sample .................................................................................... 98

Figure 72. Photo. No. 67 aggregate sample ................................................................................ 100

Figure 73. Photo. No. 68 aggregate sample ................................................................................ 103

Figure 74. Photo. No. 7 aggregate sample .................................................................................. 105

vi
Figure 75. Photo. No. 78 aggregate sample ................................................................................ 107

Figure 76. Photo. No. 8A aggregate sample ............................................................................... 110

Figure 77. Photo. No. 8B aggregate sample ............................................................................... 112

Figure 78. Photo. No. 8C aggregate sample ............................................................................... 113

Figure 79. Photo. No. 8D aggregate sample ............................................................................... 115

Figure 80. Photo. No. 8E aggregate sample................................................................................ 116

Figure 81. Photo. No. 89 aggregate sample ................................................................................ 118

Figure 82. Photo. No. 9 aggregate sample .................................................................................. 121

Figure 83. Photo. No. 10 aggregate sample ................................................................................ 123

vii
LIST OF TABLES

Table 1. Reported friction angles from DS and TX testing .......................................................... 12

Table 2. Bearing capacity factors.................................................................................................. 14

Table 3. Impact of friction angle on geotechnical constants in design......................................... 15

Table 4. Selected AASHTO M43-05 (ASTM D448) aggregate designations.............................. 18

Table 5. OGAs tested.................................................................................................................... 19

Table 6. Aggregate gradation and classification........................................................................... 21

Table 7. Unit weight of aggregates............................................................................................... 22

Table 8. Repose angle of aggregates............................................................................................. 24

Table 9. Summary of AIMS2 average results for angularity, texture, and sphericity .................. 32

Table 10. Ottawa test results using SDS device and MC approach.............................................. 34

Table 11. SDS test results using MC approach............................................................................. 37

Table 12. SDS test results using the ZDA approach..................................................................... 39

Table 13. LSDS resistance calibration values............................................................................... 43

Table 14. LSDS Test results using MC approach......................................................................... 44

Table 15. LSDS test results using ZDA approach ........................................................................ 46

Table 16. LDTX test results for Ottawa sand and AASHTO No. 68 ........................................... 53

Table 17. LDTX test results using MC approach ......................................................................... 57

Table 18. LDTX test results using ZDA approach ....................................................................... 58

Table 19. LSDS versus LDTX measured friction angles using MC approach............................. 62

Table 20. LSDS versus LDTX measured friction angles using ZDA approach........................... 63

Table 21. SDS versus LSDS friction angles using MC approach................................................. 69

Table 22. SDS versus LSDS friction angles using ZDA approach............................................... 70

Table 23. Summary of LSDS and LDTX testing.......................................................................... 87

Table 24. No. 5 gradation ............................................................................................................. 92

Table 25. No. 5 density................................................................................................................. 92

Table 26. No. 5 repose angle ........................................................................................................ 92

Table 27. No. 5 standard DS results ............................................................................................. 92

Table 28. No. 5 LSDS results—dry.............................................................................................. 93

Table 29. No. 5 LSDS results—saturated..................................................................................... 93

Table 30. No. 5 LDTX results ...................................................................................................... 93

Table 31. No. 56 gradation ........................................................................................................... 94

Table 32. No. 56 density............................................................................................................... 95

Table 33. No. 56 repose angle ...................................................................................................... 95

Table 34. No. 56 standard DS results ........................................................................................... 95

Table 35. No. 56 LSDS results—dry............................................................................................ 95

Table 36. No. 56 LSDS results—saturated................................................................................... 95

Table 37. No. 57 LDTX results .................................................................................................... 96

Table 38. No. 57 gradation ........................................................................................................... 97

Table 39. No. 57 density............................................................................................................... 97

Table 40. No. 57 repose angle ...................................................................................................... 97

Table 41. No. 57 standard DS results ........................................................................................... 97

Table 42. No. 57 LSDS results—dry............................................................................................ 97

Table 43. No. 57 LSDS results—saturated................................................................................... 98

Table 44. No. 57 LDTX results .................................................................................................... 98

Table 45. No. 6 gradation ............................................................................................................. 99

viii
Table 46. No. 6 density................................................................................................................. 99

Table 47. No. 6 repose angle ........................................................................................................ 99

Table 48. No. 6 standard DS results ............................................................................................. 99

Table 49. No. 6 LSDS results—dry.............................................................................................. 99

Table 50. No. 6 LSDS results—saturated................................................................................... 100

Table 51. No. 6 LDTX results .................................................................................................... 100

Table 52. No. 67 gradation ......................................................................................................... 101

Table 53. No. 67 density............................................................................................................. 101

Table 54. No. 67 repose angle .................................................................................................... 101

Table 55. No. 67 standard DS results ......................................................................................... 101

Table 56. No. 67 LSDS results—dry.......................................................................................... 102

Table 57. No. 67 LSDS results—saturated................................................................................. 102

Table 58. No. 67 LDTX results .................................................................................................. 102

Table 59. No. 68 gradation ......................................................................................................... 103

Table 60. No. 68 density............................................................................................................. 104

Table 61. No. 68 repose angle .................................................................................................... 104

Table 62. No. 68 standard DS results ......................................................................................... 104

Table 63. No. 68 LSDS results—dry.......................................................................................... 104

Table 64. No. 68 LSDS results—saturated................................................................................. 104

Table 65. No. 68 LDTX results .................................................................................................. 105

Table 66. No. 7 gradation ........................................................................................................... 106

Table 67. No. 7 density............................................................................................................... 106

Table 68. No. 7 repose angle ...................................................................................................... 106

Table 69. No. 7 standard DS results ........................................................................................... 106

Table 70. No. 7 LSDS results—dry............................................................................................ 106

Table 71. No. 7 LSDS results—saturated................................................................................... 107

Table 72. No. 7 LDTX results .................................................................................................... 107

Table 73. No. 78 gradation ......................................................................................................... 108

Table 74. No. 78 density............................................................................................................. 108

Table 75. No. 78 repose angle .................................................................................................... 108

Table 76. No. 78 standard DS results ......................................................................................... 108

Table 77. No. 78 LSDS results—dry.......................................................................................... 109

Table 78. No. 78 LSDS results—saturated................................................................................. 109

Table 79. No. 78 LDTX results .................................................................................................. 109

Table 80. No. 8A gradation......................................................................................................... 110

Table 81. No. 8A density ............................................................................................................ 111

Table 82. No. 8A repose angle.................................................................................................... 111

Table 83. No. 8A standard DS results......................................................................................... 111

Table 84. No. 8A LSDS results—dry ......................................................................................... 111

Table 85. No. 8A LSDS results—saturated................................................................................ 111

Table 86. No. 8B gradation......................................................................................................... 112

Table 87. No. 8B LSDS results—dry ......................................................................................... 113

Table 88. No. 8B LSDS results—saturated ................................................................................ 113

Table 89. No. 8C gradation......................................................................................................... 114

Table 90. No. 8C LSDS results—dry ......................................................................................... 114

Table 91. No. 8C LSDS results—saturated ................................................................................ 114

ix
Table 92. No. 8D gradation......................................................................................................... 115

Table 93. No. 8D LSDS results—dry ......................................................................................... 116

Table 94. No. 8D LSDS results—saturated................................................................................ 116

Table 95. No. 8E gradation......................................................................................................... 117

Table 96. No. 8E density............................................................................................................. 117

Table 97. No. 8E LSDS results—dry.......................................................................................... 117

Table 98. No. 8E LSDS results—saturated ................................................................................ 117

Table 99. No. 8E LDTX results.................................................................................................. 118

Table 100. No. 89 gradation ....................................................................................................... 119

Table 101. No. 89 density........................................................................................................... 119

Table 102. No. 89 repose angle .................................................................................................. 119

Table 103. No. 89 standard DS results ....................................................................................... 119

Table 104. No. 89 LSDS results—dry........................................................................................ 120

Table 105. No. 89 LSDS results—saturated............................................................................... 120

Table 106. No. 89 LDTX results ................................................................................................ 120

Table 107. No. 9 gradation ......................................................................................................... 121

Table 108. No. 9 density............................................................................................................. 122

Table 109. No. 9 repose angle .................................................................................................... 122

Table 110. No. 9 standard DS results ......................................................................................... 122

Table 111. No. 9 LSDS results—dry.......................................................................................... 122

Table 112. No. 9 LSDS results—saturated................................................................................. 122

Table 113. No. 9 LDTX results .................................................................................................. 123

Table 114. No. 10 gradation ....................................................................................................... 124

Table 115. No. 10 density........................................................................................................... 124

Table 116. No. 10 repose angle .................................................................................................. 124

Table 117. No. 10 standard DS results ...................................................................................... 124

Table 118. No. 10 LSDS results—dry........................................................................................ 124

Table 119. No. 10 LSDS results—saturated............................................................................... 125

Table 120. No. 10 LDTX results ................................................................................................ 125

x
LIST OF ABBREVIATIONS

AASHTO American Association of State Highway and Transportation Officials

AIMS Aggregate imaging measurement system

AIMS2 Second generation aggregate imaging measurement system

CC Consolidation curve

COV Coefficient of variation

CV Constant volume

DS Direct shear

FHWA Federal Highway Administration

FM Fineness modulus

LDTX Large diameter triaxial

LSDS Large-scale direct shear

LVDT Linear variable differential transformer

MC Mohr-Coulomb

MSE Mechanically stabilized earth

NAVFAC Naval Facilities Engineering Command

OG Open-graded

OGA Open-graded aggregate

PS Plane strain

SDS Standard direct shear

TFHRC Turner-Fairbank Highway Research Center

TX Triaxial

ZDA Zero dilation angle

xi
LIST OF SYMBOLS

Angle of the modified (stress-path) failure envelope

( ′

1- ′3) Change in effective deviator stress due to the membrane correction

h Change in horizontal displacement

v Change in vertical displacement

1 Axial strain

V Volumetric strain

′1 Effective major principal stress

′3 Effective minor principal stress

′c Effective confining stress

′c,1 Low-range effective confining stress

′c,2 Mid-range effective confining stress

′c,3 High-range effective confining stress

′d Deviator stress

′n Effective normal stress

Shear strength

f Shear stress at failure

Friction angle

DS Friction angle measured from direct shear testing

TX Friction angle measured from triaxial testing

′ Effective friction angle

′ True friction angle

′cv Constant volume effective friction angle

′cv,dry Constant volume effective friction angle under dry conditions

′cv,LDTX Constant volume effective friction angle from LDTX testing

′cv,LSDS,dry Constant volume effective friction angle from LSDS testing under dry 

conditions

α

∆ σ σ

∆

∆

ε

ε

σ

σ

σ

σ

σ

σ

σ

σ

τ

τ

φ

φ

φ

φ

φ μ

φ

φ

φ

φ

xii
′cv,sat Constant volume effective friction angle under saturated conditions

′cv,SDS Constant volume effective friction angle from SDS testing

′Dense Friction angle for aggregates tested at a dense state

′f Dilation corrected friction angle 

′Loose Friction angle for aggregates tested at a loose state

′Medium Friction angle for aggregates tested at a medium dense state

′s Secant, or peak effective friction angle

′s,LDTX Effective secant friction angle from LDTX testing 

′s,LSDS,sat Effective secant friction angle from LDTX testing 

′t,LDTX Effective tangent friction angle from LDTX testing 

′t,LSDS,dry Effective tangent friction angle from LSDS testing under dry conditions

′t,LSDS,sat Effective tangent friction angle from LSDS testing under saturated conditions

′t,SDS Effective tangent friction angle from SDS testing

′t Tangent effective friction angle

Dilation angle

max Maximum dilation angle

A Nonlinear material constant (Charles and Watts 1980)

Ac Corrected area

Ao Original sample area

a Experimental constant

b Nonlinear material constant (Charles and Watts 1980)

c Cohesion

c′ Effective cohesion determined from the Mohr-Coulomb approach

c′SDS Effective cohesion from standard direct shear testing

Cc Coefficient of curvature

Cu Coefficient of uniformity

φ

φ

φ

φ

φ

φ

φ

φ

φ

φ

φ

φ

φ

φ

ψψ

ψψ

xiii
d10 Particle diameter at which 10 percent of the sample is finer, by mass

d30 Particle diameter at which 30 percent of the sample is finer, by mass

d50 Median grain size; particle diameter at which 60 percent of the sample is finer, 

by mass

d60 Particle diameter at which 60 percent of the sample is finer, by mass

d85 Particle diameter at which 85 percent of the sample is finer, by mass

d 1 Incremental axial strain

d 3 Incremental lateral strain

dmax Maximum diameter of the aggregate sample

D Sample diameter

Dc Specimen diameter at the end of the consolidation phase

Em Young’s modulus for the membrane material

F Area correction actor

h horizontal displacement

Ka Active earth pressure coefficient

L Distance from intersection of bisector line and consolidation curve for the 

membrane penetration correction

n Porosity

N Bearing capacity factor 

Nc Bearing capacity factor

Nq Bearing capacity factor 

p′ Effective mean stress path

q Shear stress path

t90 Time needed to achieve 90 percent of the total consolidation

tm Thickness of the membrane

ε

ε

γ

xiv
CHAPTER 1. INTRODUCTION

1.1 PROBLEM STATEMENT

Open-graded aggregates (OGA), or poorly graded aggregates, are defined by their gradation,

with most particles being uniform in size. They can be rounded or angular and classified as either 

sand or gravel. OGAs are used in concrete and asphalt mixes as well as for transportation 

structures, where requirements often specify the use of angular open-graded (OG) gravels. The 

primary advantages of using this type of material are ease of constructability, very low fine 

content, free-draining characteristics, low frost heave potential, and simple quality assurance 

testing, with a method specification for compaction. Angular OGAs also have the added benefit 

of increased strength compared with rounded aggregates. Because of these qualities, State and 

local transportation agencies are more routinely specifying crushed, manufactured OGAs for 

wall, roadway, and bridge construction. The American Association of State Highway and 

Transportation Officials (AASHTO) classifies manufactured OGAs according to the M43 

gradation based on standard sizes for processed aggregates; the equivalent ASTM standard is 

D448.

(1,2)

In the design of retaining walls and foundation systems, the friction angle and cohesion are 

important parameters to define the strength of the backfill, commonly described by the MohrCoulomb (MC) failure envelope. The AASHTO OGAs are cohesionless, and the friction angle 

can be measured using laboratory testing devices, including plane strain (PS), direct shear (DS), 

and triaxial (TX) devices, although DS and TX are the most common. Oftentimes, however, 

designers will either have scalped samples tested or simply use a default friction angle of 34

degrees in lieu of testing. These measures are considered conservative; however, the actual 

strength properties of OGAs have not been systematically measured nor have the influences of 

various testing devices on the results been studied. 

1.2 OBJECTIVES

The Federal Highway Administration (FHWA) initiated a research program to conduct 

laboratory testing of common AASHTO OGAs. The primary objectives of this program are to 

quantify the strength parameters, determine the influence of various factors on strength, and 

evaluate different testing devices. As a starting point, testing commenced using a large-scale 

direct shear (LSDS) device to measure the friction angle of uncompacted, common AASHTO 

OG aggregates.(3) In addition, standard DS and large-diameter triaxial (LDTX) devices were used 

in this study. The study also looked at whether strength (i.e., friction angle) could be correlated 

to other properties of the backfill.

1.3 REPORT OUTLINE

This research report will detail the results of the testing program and is organized as follows:

• Chapter 2 provides background information on the use and design of OGAs in the 

transportation sector, the various testing and data interpretation methods available,

and the associated implications.

1
• Chapter 3 details the laboratory testing program and presents the results. Beyond 

strength, the gradation, density, repose angle, angularity, and texture were measured 

using appropriate devices and standards.

• Chapter 4 describes the data analysis for different testing devices and data reduction 

methods. In addition, correlations between various soil properties and strength 

parameters were examined.

• Chapter 5 presents a summary of the testing and provides conclusions that 

transportation agencies can consider when designing with AASHTO OGAs. 

Additional research gaps and future research plans within FHWA are also discussed. 

2
CHAPTER 2. BACKGROUND

2.1 USE OF OGAs

Manufactured OGAs are used in a variety of transportation applications, including retaining wall 

backfill, concrete, asphalt, pavement structures, and foundation support. These materials are 

selected primarily because of their strength, excellent drainage properties, and speed of 

placement in the field. The first known attempt by AASHTO to standardize gradations for 

processed aggregates was in 1988, which followed ASTM standard D448 (published in 1986). 

The standard included 19 gradations, ranging from 4 inches minus material to 0.375 inch minus 

material. While six additional versions have since come out, the same gradations and 

nomenclature is used; the biggest difference is the elimination of metric units.

For some projects, contractors and designers have the flexibility to select backfills that meet 

certain requirements; in other projects, the backfill type is specified by the owner. Many State 

transportation departments and other transportation agencies have specifications related to the 

use of AASHTO M 43, but these guidelines are primarily focused on concrete and pavement 

design requirements.(See references 4 through 7.) For structural backfills, the specifications are 

typically more open where OG or well-graded aggregates meeting the broad gradation and 

durability requirements can be used. 

2.2 STRENGTH PROPERTIES OF GRANULAR MATERIALS

The shear strength ( ) of granular materials is the measure of their resistance to mass 

deformation developed from a combination of particle rolling, sliding, and crushing.(8) The 

interparticle attraction or cohesion (c) and the angle of internal friction ( ) are the two 

commonly used parameters employed to quantify the shear strength. The values of these strength 

parameters are not constant, varying as a function of the loading condition, stress history,

compaction, relative density, confining pressure, grain shape, hardness, and mineralogy, among 

other factors. 

The peak friction angle at a given applied confinement is one of the measured parameters during 

shear testing that is widely adopted to characterize the shear strength of granular materials. Rowe

(1962) proposed that the mobilized peak friction angle can be represented as the sum of the 

resistance to the interparticle sliding, or true friction angle ( 'u), the resistance to crushing and 

rearrangement, and resistance due to dilation of the material (figure 1).

(9) It should be noted that 

figure 1 displays a general trend, and the magnitude and exact shape of the components within 

the sketch could change slightly at extreme levels of confining stress or for samples with 

heterogeneous mineral composition and shape.

τ

φ

φ

3
Figure 1. Chart. Effect of porosity and compaction on the shear strength of granular 

materials (modified from Rowe, 1962).

(9)

As shown in figure 1, the rate of dilation is higher under denser states. The reason is that in a 

dense medium, rearrangement is limited, forcing particles to climb over each other during 

shearing and resulting in volume expansion and higher measured friction angles. With the 

increase in void ratio, the contribution from the dilation component diminishes gradually, and the 

particles shear primarily by rearrangement of adjacent particles, which results in more 

contraction and less dilation of the granular material during shear.

(10) The general observation is 

that there is a net increase of the mobilized friction angle with the decrease in initial porosity

because the rate of increase of the dilatancy component is higher than the rate of decrease of the 

rearrangement. The critical state is defined at the density state where the granular materials shear 

at a constant volume and stress state. At this state, the dilatancy rate diminishes and approaches 

zero; hence, the friction angle at this critical state is termed the constant volume (CV) friction 

angle ( 'cv).

Visualizing the shear strength as a function of varying confining stress for a given density state, 

similar components comprise the mobilized peak friction angle (figure 2). At high effective 

confining stresses, the relative movement of the particles via dilation will reduce significantly. In 

addition, a high breakage rate through crushing will result in contraction, shifting the phase from 

the initially achieved true friction angle to a new phase of non-constant volume.

(11)

φ

4
Figure 2. Chart. The theoretical determination of the drained shear strength for sands 

based on the three components that comprise the mobilized friction angle (after Lee and 

Seed, 1967).(11)

Knowledge about the contributing factors and the various laboratory shear strength tests, data 

interpretation, and the application of the strength parameters for designing geotechnical 

applications with OGAs is therefore important. In-situ tests are available to quantify or correlate 

with in-place shear strength; however, this study focuses on the laboratory analysis.

Laboratory Testing

The state of in-situ shearing deformations—which can eventually lead to failure—is oftentimes 

best approximated as a PS problem. For instance, the failures in several geotechnical applications 

such as landslide problems, retaining walls, earth dams, long foundations, culverts, pipe lines, 

tunnels, and beam foundations, for the most part, are all cases of PS; however, there is 

considerable difficulty in designing and conducting PS shear tests. Such tests require the 

fabrication of a special fixture, membrane, accessories, and preparation of a prismatic soil 

specimen.(12) The complexity of the PS shear test leads geotechnical engineering researchers and 

practitioners to the simpler DS or TX tests to characterize the shear strength of geomaterials. 

Both DS and TX methods have been widely accepted for design and research to determine shear 

strength. The wide popularity of TX compression tests is partially because of the numerous 

structures designed and constructed based on the strength data from TX that perform well after 

many years, the ability of TX tests to combine simplicity with versatility, the ability to allow 

drainage control, the reproduction of the effects of most common field loading conditions, and 

the application of the desired major and minor principal stresses.(13) The wide application of DS 

tests in characterizing the strength parameters of granular materials is attributed to their 

5
simplicity, requirement of shorter experimental run times, and ability to predetermine the 

orientation of the failure surface as desired and allow determination of the residual strength.(14) 

However, the inability to control the drainage and the non-uniformity of stress and strain in DS 

tests relative to PS and TX tests inhibits the suitability of DS apparatuses in studies that involve 

the stress-strain behavior of granular materials.

Note that there are several drawbacks associated with TX and DS tests relative to tests using a 

PS apparatus. One of the major differences between TX and PS is that in TX-based tests, the 

applied stresses are axisymmetric, leading to the absence of intermediate principle stresses. The 

DS tests are closer to the PS condition, but the geometry and boundary conditions of the DS test 

predetermine the localized region of high strains through which failure is forced to happen; 

failure is not allowed to occur along its natural plane.

(15) The PS tests are better suited to help us 

understand the in-situ strain localization problems and shear band formations.(16) Several studies 

have reported the formation of shear bands along a well-defined shear failure plane in PS 

compression tests, whereas samples sheared in a TX apparatus rarely developed a distinct shear 

plane.(17,18,19) Instead, some microscale observations using advanced imaging techniques proved 

the prevalence of complex fan-shaped patterns in samples subjected to TX-based compression 

tests.(20,21)

The other difference among the different laboratory shear tests is the imposed lateral boundary 

conditions.(22)Both PS and DS tests have a rigid boundary condition that significantly reduces 

the grain movements during shearing. The flexible membrane boundary in TX tests allows lateral

movement of the particles, which inhibits mobilization of the friction angles. The other marked 

difference of the testing methods is their effect on post peak strain behavior. For sand, Sterpi

(2000) indicated that TX-based tests suggest a perfectly plastic behavior, whereas the PS results 

showed marked strain softening effects, in particular for the denser samples or for high values of 

confining stress levels.

(23) In general, the measured shear strength from PS testing is greater than 

that measured from DS testing, which is greater than that measured from TX testing.

Regardless of test device, the determination of strength and deformation parameters for granular 

materials that contain particles of larger sizes such as rockfill materials and OGAs requires 

equipment of unconventional dimensions.(24) To be characterized by the conventional DS and TX 

apparatuses, which require smaller-sized specimens, the sizes of particles are reduced based on 

various modeling techniques. As cited by Honkanadavar and Sharma (2013), four modeling 

techniques are used to reduce the size of the prototype material: the scalping technique, the 

parallel gradation technique, the generation of a quadratic grain size distribution curve, and the 

replacement technique. (See references 25 through 29.) Following the findings of Ramamurthy 

and Gupta, which indicated that the parallel gradation was the best method, several other 

researchers have conducted shear tests on modeled materials based on the parallel gradation 

technique. (See references 30, 29, 24, and 31.) The results from these modeled materials could 

potentially lead to inaccurate deformation behavior and failure modes because of the inevitable 

size-dependent dilation and different mechanisms of particle crushing.(32) Therefore, the use of 

large-scale triaxial and direct shear apparatus is imperative for a realistic depiction of the 

strength and deformation characteristics of aggregates with large-size grains such OGAs.

6
Data Interpretation

The shear strength of granular materials is usually characterized by the angle of internal friction 

( ) and cohesion (c). Because of the high drainage rate in OGAs, shear studies for OGAs should 

be conducted under drained condition, and for this reason, the stresses and strength parameters 

will be presented in their effective stress forms (e.g., ', c', '

1, '3). There are three concepts of 

presenting the values of friction angles for any shear test. First, a secant or peak friction angle 

( 's) can be determined for a given test subjected to a specific effective consolidation stress and

assuming a zero c-value due to the absence of cohesion in OGAs (figure 3). Secondly, a 

combined or tangent friction angle ( 't) can also computed for the same aggregate type 

(examined as the best-fit across a series of stress levels) to form the MC failure envelope (figure 

3). Lastly, a CV friction angle can be computed as the friction angle in which there is zero 

dilation, termed the zero dilation angle (ZDA) approach.(3)

Figure 3. Chart. Secant ( 's) and tangent ( 't) friction angle illustration for DS testing.

The MC failure criterion is the most commonly adopted approach to determine 't (equation 1).

φ

φ σ σ

φ

φ

φ φ

φ

7
(1)

Where:

f = Shear stress at failure.

c' = Effective cohesion.

'

n = Effective normal stress. ' = Effective angle of internal friction.

For OGAs that are cohesionless, the cohesive term is zero. This approach assumes that shear 

failure starts at a point in a mass of soil when, on some surface passing through the point, a 

critical combination of shearing and normal stresses is reached.(10) The TX and DS equipment are 

developed to determine and investigate these critical combinations; the results are then used to 

compute the strength parameters.

In TX compression tests, it is assumed that only principal stresses are applied to the boundaries 

of the specimen, with the strength parameters extracted from the measured major ( ′

1) and minor 

( '

3) principal stresses at failure. The shear stress path (q) and mean stress path (p’

) 

representations are computed for a series of tests according to equation 2 and equation 3, 

respectively.(33) 

 (2)

(3)

When looking at stress paths, a modified failure envelope based on the p and q values was 

developed, commonly called the Kf line.(34) The envelope is defined by equation 4.

(4)

Where:

= Angle that the modified (stress-path) failure envelope makes with the horizontal. 

The relationship between the tangent effective friction angle ( '

t) and is shown in equation 5.

(5)

For TX tests, the value of the secant or peak friction angle ( '

s) for each specific test is computed 

using equation 6, which is developed from Mohr’s circles by applying trigonometric 

relationships.

(34)

ττff = cc′ + σσnn

′ tanφφ′

τ

σ

φ

σ

σ

qq = σσ1

′ − σσ3′

2

pp′ = σσ1

′ + σσ3′

2

qq = pp′ × tan αα

α

φ α

φφtt

′ = sin−1(tan αα)

φ

8
(6)

Unlike in TX tests, the major and minor principal stresses in DS tests are not measured. Hence, 

the applied normal stress and measured shear stress at failure are used to compute these strength 

parameters. Similar to TX test, the individual pairs of f and '

n from a series of tests of the same 

aggregate type as a function of various confining stress are plotted, and the MC linear failure 

envelope is developed as the best fit line of the peak shear and normal stress values at these 

different stress points (figure 3). The value of '

t is then computed as the arctangent of the slope 

of the linear fit. The '

s value for each specific shear test is determined according to equation 7.

(7)

The linear MC failure criterion is the linear representation of the otherwise nonlinear failure 

envelope of the strength behavior. Several approaches have been developed to describe this 

nonlinear increase in peak shear strength of granular materials as a function of the increasing 

confining stress. The power strength function (equation 8) that was developed by Charles and 

Watts has been also adopted by other several other researchers with some modifications to the 

original equation. (See references 35 through 38.)

(8)

Where:

A and b = nonlinear material constants that are determined by curve fitting of the experimental 

data. This power curve strength model can be used to interpret data from both TX and DS tests. 

Other models, such as the Hoek-Brown model, have been established to characterize strength of 

rock materials in terms of major and minor principal stresses. Therefore, they are more valid to 

TX data.(39,40,41) This model also has material constants that need to be estimated from the 

geological data and additional tests like uniaxial compressive strength. Nicks and Adams (2013)

employed a ZDA that is based on the linear relationship between the friction angles and the 

dilation angles as a function of varying consolidation stresses for the same aggregate.(3)

According to Bolton (1986), the y-intercept of the best-fit linear envelope in this approach 

corresponds to the constant volume or critical state friction angle ( '

cv).(42) The advantage of this 

technique is that the effect of dilation is negated and a conservative shear strength value results 

without relying on an apparent cohesion value as in the linear MC approach. 

This study focuses on the simple approaches that are used to determine common shear strength 

parameters (e.g. '

s, '

t,and 'cv) applicable for both TX and DS tests to have an unbiased 

comparison and an approach that does not require any additional strength tests. The MC linear 

relationship is widely used and accepted because of its reasonable tolerance for the majority of 

geotechnical applications.(36) This approach also does not require any other strength test or 

geological data and can be used to extract '

s and 't for both TX and DS tests. The ZDA is 

another simple method to compute '

cv. Therefore, these two approaches are adopted and 

φφss

′ = sin−1 �

σσ1

′ − σσ3′

σσ1

′ + σσ3′ �

τ σ

φ

φ

φφss

′ = tan �

ττff

σσnn

′ �

ττ = AAσσnn

bb

φ

φ φ φ

φ φ

φ

9
compared in this study to characterize the strength parameters of the OGAs based on the TX and 

DS apparatuses.

Design Practices

The design practices in problems involving the application of stresses to soils may be divided 

into (a) deformation-controlled design (e.g., settlement), and (b) failure-controlled design (e.g.,

bearing resistance).(43) In other terms, the service and strength limit states must be satisfied in 

design. For applications involving relatively rigid structures such as bridge foundations and 

retaining walls, where deformations are expected to be low, the strength limit of the backfill or 

underlying soil is especially important. The shear strength of the backfill is therefore a key 

parameter in design.

Failure-controlled design for geotechnical applications involves the determination of the internal 

angle of friction ( ), which is one of the fundamental engineering parameters. The friction angle 

is critical because it is used to compute lateral pressures and bearing resistance. For 

transportation applications, the AASHTO Load and Resistance Factor Design Bridge Design and 

Constructions Specifications are primarily employed.(44,45,46) For mechanically stabilized earth 

(MSE) walls, the design specifications note that a value of 34 degrees may be assumed for the 

friction angle, with a limit of 40 degrees if tested. The construction specifications require 

verification of the design assumption that the material exhibits a friction angle of at least 34 

degrees on the portion passing the No. 10 (0.08-inch) sieve, as determined by the standard direct 

shear (SDS) test.(45) No testing is required for backfills where 80 percent of the sizes are greater 

than 0.75 inch. While the AASHTO specifications do not prohibit the use of OGAs, FHWA 

guidelines for MSE walls, which are adopted by many transportation agencies, recommend the 

use of well-graded materials.(47,48) For geosynthetic reinforced soil walls and abutments, both 

OGAs and well-graded aggregates meeting a minimum friction angle of 38 degrees can be used 

in construction. No maximum limitation is imposed if appropriately tested in the laboratory.

Based on a survey of State transportation departments, approximately 74 percent responded that 

they use assumed strength parameters for backfills in retaining wall design, with 65 percent of 

the respondents assuming a friction angles of 34 degrees or less.(49) When testing is performed, 

60 percent and 70 percent stated that they use direct shear and triaxial devices, respectively. A 

review of the literature found reported friction angles for poorly graded granular materials tested

using DS and TX devices (table 1). Despite the availability of vast strength data that demonstrate

friction angles higher than the default of 34 degrees for various granular materials conducted 

using all kinds of shearing tests devices, there is very limited data on large-sized aggregates with 

a narrow gradation, such as the AASHTO M43 aggregates (e.g., OGAs). Three studies were 

found that examined materials close to the No. 7, No. 56, and No. 57 aggregates.(50,51,52)

For the approximate No. 7 aggregate, the difference between standard DS and TX tests was 

about 7 degrees; the TX results were 15 percent less than the DS results (table 1). For the 

approximate No. 56 aggregate, the difference was significantly larger between the two types of 

tests, with the TX 25 degrees, or 33 percent, lower than the DS. The researcher acknowledged 

that in most reported works in literature, the difference in friction angles are much lower, but the 

researcher concluded that such reports are not valid for the tested Bremanger sandstone.(51)

φ

10
Two researchers reported friction angles for the No. 57 aggregate; however, both focused on 

either TX or DS testing, with no comparison. 

Limited studies do show the comparison of ' values from both TX and DS tests for OGAs. 

From table 1, the maximum reported is 33 percent, with TX values being lower than DS; while 

high, this finding is consistent with other research findings showing that TX friction angles are 

lower than DS, which are lower than PS. (See references 53 through 56.) Based on a compilation 

of various studies on sand, Kulhawy and Mayne (1990) presented the relationship for DS and TX 

compression testing, also as a function of the CV friction angle (equation 9).(57) 

(9)

This relationship is based on sands and standard testing devices. Because of the lack of a 

sufficient database of the strength and stress-strain properties of the AASHTO M 43 designated 

aggregates, there is an absence of any established relationships of strength data between PS

condition (as well as DS test) and the axisymmetric loading condition of TX tests. Therefore, the 

scarcity of such data is one of the major motivations of this work.

φ

φφDDDD = tan−1{tan(1.12φφTTTT) cos(φφcccc )}

11
Table 1. Reported friction angles from DS and TX testing.

Sample 

No. Backfill Soil Description

dmax

(inches)

Test 

Method ' (degrees)1 Reference

1 Uniform subrounded fine 

to medium sand 0.187 DS 43

58 2 Uniformly graded fine to 

medium sand 0.630 DS 41

3

Clean uniform-size 

washed sand with some 

gravel

0.315 DS 46–53

4 Poorly graded sand with 

gravel — TX 38

59

5 Non-plastic poorly graded 

sand — TX 38

6 Poorly graded sand — DS 36.4

48

7 Poorly graded sand — DS 38.5

8 Poorly graded sand — DS 39.2

9 Poorly graded sand — DS 40.9

10 Poorly graded sand — DS 41.5

11 Poorly graded sand — DS 42.4

12

Durable sandstone

12.00

DS 43

60

(square, 

5 ft)

(32 psi 

confinement)

0.75

DS 52.5

(circular, 

0.5 ft)

(32 psi 

confinement)

Non-durable silty shale 

rock

12.00

DS 44

(square, 

5 ft)

(32 psi 

confinement)

0.75

DS 52.2

(circular, 

0.5 ft)

(39 psi 

confinement)

13

Manufactured granular 

material 0.787

DS

44–45 (eo = 0.68–

0.69)

61

36–38 (eo = 0.8–

0.83)

TX 42–45 (eo = 0.68–

0.69)

Rockfill material 1.969

DS

51–55 (eo = 0.37)

37–38 (eo = 0.56)

TX 52–55 (eo = 0.37)

φ

12
Sample 

No. Backfill Soil Description

dmax

(inches)

Test 

Method ' (degrees)1 Reference

48–49 (eo = 0.42)

Rockfill material 3.937 DS

50–54 (eo = 0.42)

38–39 (eo = 0.56)

14

Dacite rock material (close 

to a No. 7) 1.476

TX 41

50 DS 48.3

Crushed stone and crushed 

sandstone 1.476

TX 50.1

DS 56

15 Andesite rockfill material 1.969 TX 39.9–57.8 24

16 Poorly graded sandstone 

rockfill (close to a No. 56) — TX 49.9 51 DS 74.9

17

No. 57 (Limestone)—Low 

density

— TX

53.5 ( '3 = 4 psi)

52

42.8 ( '3 = 

30.3 psi)

No. 57 (Limestone)—High 

density

53.1 ( '3 = 

3.7 psi)

44.1 ( '3 = 30 psi)

No. 57 (Phyllite)—Low 

density

— TX

54.6 ( '3 = 

3.9 psi)

51 ( '3 = 9.7 psi)

No. 57 (Phyllite)—High 

density

56.1 ( '3 = 4 psi)

52.8 ( '3 = 

9.8 psi)

18 Densified No. 57 crushed 

stone — DS 49 62

1

Unless specified for a single confining pressure, ' refers to the tangent friction angle obtained from the MohrCoulomb failure envelope.

DS = Direct shear.

TX = Triaxial.

— = Information not provided

2.3 DESIGN IMPLICATIONS

As previously discussed, the strength of these materials is an important design consideration. For 

OGAs, the strength is primarily defined by the internal friction angle ( ). The selection of 

friction angle, therefore, has significant impacts on the design of geotechnical features. It plays a 

role in the earth pressure coefficients, used in the determination of lateral earth pressures. In 

retaining wall design, the active earth pressure coefficient (Ka) is often used for failure 

conditions (equation 10). The higher the friction angle, the lower the coefficient, and thus the 

lower the lateral pressures that need to be resisted in design.

φ

σ

σ

σ

σ

σ

σ

σ

σ

φ

φ

13
(10)

The internal friction angle is also important in determining bearing capacity factors (table 2) used 

in the conventional equation to estimate nominal bearing resistance, described by Munfakh et al.

(2001).

(44,45) As the bearing factors increase in value, the bearing resistance also increases, thus 

reducing the required size of the foundation. Table 3 illustrates the impact of using higher 

friction angles on Ka and the bearing capacity factors, Nc, Nq, and N . The difference in Ka

between 34 degrees and 45 degrees is a factor of 1.6; the differences in bearing resistance are 

even higher. By utilizing the actual strength properties of OGAs rather than defaulting to 

34 degrees, more cost-effective designs can be realized.

Table 2. Bearing capacity factors.(44)

Nc Nq Nγ Nc Nq Nγ

0 5.14 1.0 0.0 23 18.1 8.7 8.2

1 5.4 1.1 0.1 24 19.3 9.6 9.4

2 5.6 1.2 0.2 25 20.7 10.7 10.9

3 5.9 1.3 0.2 26 22.3 11.9 12.5

4 6.2 1.4 0.3 27 23.9 13.2 14.5

5 6.5 1.6 0.5 28 25.8 14.7 16.7

6 6.8 1.7 0.6 29 27.9 16.4 19.3

7 7.2 1.9 0.7 30 30.1 18.4 22.4

8 7.5 2.1 0.9 31 32.7 20.6 26.0

9 7.9 2.3 1.0 32 35.5 23.2 30.2

10 8.4 2.5 1.2 33 38.6 26.1 35.2

11 8.8 2.7 1.4 34 42.2 29.4 41.1

12 9.3 3.0 1.7 35 46.1 33.3 48.0

13 9.8 3.3 2.0 36 50.6 37.8 56.3

14 10.4 3.6 2.3 37 55.6 42.9 66.2

15 11.0 3.9 2.7 38 61.4 48.9 78.0

16 11.6 4.3 3.1 39 67.9 56.0 92.3

17 12.3 4.8 3.5 40 75.3 64.2 109.4

18 13.1 5.3 4.1 41 83.9 73.9 130.2

19 13.9 5.8 4.7 42 93.7 85.4 155.6

20 14.8 6.4 5.4 43 105.1 99.0 186.5

21 15.8 7.1 6.2 44 118.4 115.3 224.6

22 16.9 7.8 7.1 45 133.9 134.9 271.8

KKaa = tan2 �45oo − φφ

2

�

γ

φ φ

14
Table 3. Impact of friction angle on geotechnical constants in design.

Ka Nc N

q N

34 0.282 42.2 29.4 41.1

40 0.217 75.3 64.2 109.4

45 0.171 133.9 134.9 271.8

φ γ

15

CHAPTER 3. TEST PROGRAM AND RESULTS

3.1 MATERIALS

In this study, 12 of the 19 AASHTO M43 gradations are tested and selected because of their 

common use in geotechnical applications as well as the limitations of the testing equipment 

available (table 4). The 12 unique samples ranged from an AASHTO No. 10 to an AASHTO 

No. 5. For the No. 8 aggregate, five different samples were tested to investigate the effect of 

source; four were from various quarries around the Commonwealth of Virginia, and one was 

from Defiance County, OH. In total, 16 aggregates were tested in this study.

17
Table 4. Selected AASHTO M43-05 (ASTM D448) aggregate designations.

Sieve No.

Percent Passing Through Sieve

No. 5 No. 56 No. 57 No. 6 No. 67 No. 68 No. 7 No. 78 No. 8 No. 89 No. 9 No. 10

1.5 inches 100 100 100

1 inch 90–100 90–100 95–100 100 100 100

0.75 inches 20–55 40–85 90–100 90–100 90–100 100 100

0.50 inches 0–10 10–40 25–60 20–55 90–100 90–100 100 100

0.375 inches 0–5 0–15 0–15 20–55 30–65 40–70 40–75 85–100 90–100 100 100

4 0–5 0–10 0–5 0–10 5–25 0–15 5–25 10–30 20–55 85–100 85–100

8 0–5 0–5 0–10 0–5 0–10 0–10 5–30 10–40

16 0–5 0–5 0–5 0–10 0–10

50 0–5 0–5

100 10–30

18
There are two geologic materials for the series of aggregates tested in this study: diabase and 

limestone (table 5). All of the aggregates tested are diabase except for the No. 89 and various 

No. 8 samples, which are limestone (Nos. 8A, 8B, 8C, and 8D). Diabase is an igneous rock,

whereas limestone is a sedimentary rock. Typically, igneous rocks will be harder/stronger than 

sedimentary rocks. The limestone in Defiance County, OH, is from the Devonian period, while 

the limestone found in Virginia is from the Triassic period.

(63, 64) Pictures of each sample tested 

are shown in appendix A.

Table 5. OGAs tested.

AASHTO Gradation Rock Source Location

No. 5 Diabase Ashburn, VA

No. 56 Diabase Ashburn, VA

No. 57 Diabase Sterling, VA

No. 6 Diabase Ashburn, VA

No. 67 Diabase Ashburn, VA

No. 68 Diabase Sterling, VA

No. 7 Diabase Ashburn, VA

No. 78 Diabase Sterling, VA

No. 8A Limestone (Devonian) Defiance County, OH

No. 8B Limestone (Triassic) Staunton, VA

No. 8C Limestone (Triassic) Harrisonburg, VA

No. 8D Limestone (Triassic) Stafford, VA

No. 8E Diabase Ashburn, VA

No. 89 Limestone (Devonian) Defiance County, OH

No. 9 Diabase Sterling, VA

No. 10 Diabase Ashburn, VA

3.2 LABORATORY TESTING AND RESULTS

Because the AASHTO manufactured OG aggregates had not been fully characterized, a suite of 

tests was conducted, including gradation, minimum and maximum density, repose angle, 

angularity, texture, and strength.

Gradation

The first step with each aggregate was to perform a sieve analysis on oven-dried samples to 

ensure that the gradation of the sample met the appropriate AASHTO M43 specifications 

(figure 4). The sieve analysis was conducted according to the AASHTO T27 test method.(65)

Particle sizes of interest, the coefficient of uniformity (Cu) and coefficient of curvature (Cc), and 

the Unified Soil Classification System classification are presented in table 6. The fine content for 

the aggregates (percent passing the No. 200 sieve) is less than 3 percent, except for the No. 10 

aggregate, which has about 11 percent (appendix A). Aggregates larger than a No. 9 are 

classified as poorly graded gravels; No. 9 and No. 10 are both poorly graded sands. 

19
Figure 4. Graph. Sieve analysis results of tested aggregates.

In addition, the fineness modulus (FM) was estimated for each aggregate. The FM is typically 

used in pavement and concrete materials. According to the manual for concrete practice, the FM 

is a factor obtained by adding the total percentages by weight of an aggregate sample retained on 

each of a specified series of sieves and dividing the sum by 100; in the United States, the 

standard sieve sizes are No. 100, No. 50, No. 30, No. 16, No.8, No.4, 0.375 inches, 0.75 inches,

and 1.5 inches.

(66) The FM was shown analytically to be proportional to the average of the 

logarithmic particle size distribution (the higher the value, the more coarse the aggregate). In the 

standard specification for concrete aggregates (ASTM C33), the FM for fine aggregate must be 

between 2.3 and 3.1.

(67)

Density

The minimum and maximum dry unit weight for the aggregates were determined using the 

funnel (Method A of ASTM D4254) and vibratory table (Method 1A of ASTM D4253) methods, 

respectively.(68,69) This information is useful in calculating the weight of the material for 

geotechnical applications and in determining relative compaction and relative density for 

laboratory testing requirements. In the field, compaction control for OGAs is typically a methodbased specification, such as compact to non-movement or no appreciable displacement and 

20
assess with visual inspection.(70) Other methods of compaction control have included the use of a 

nuclear density gauge and soil stiffness gauge.

(71)

 Table 6. Aggregate gradation and classification.

Sample

dmax

(inches)

d85

(inches)

d60

(inches)

d50

(inches)

d30

(inches)

d10

(inches) Cu Cc FM USCS

No. 5 1.5 0.992 0.888 0.847 0.764 0.582 1.53 1.13 7.71 GP

No. 56 1.5 0.748 0.61 0.555 0.45 0.299 2.04 1.11 6.95 GP

No. 57 1 0.736 0.616 0.569 0.467 0.301 2.05 1.18 6.88 GP

No. 6 1 0.692 0.563 0.511 0.436 0.315 1.79 1.07 6.78 GP

No. 67 1 0.653 0.466 0.41 0.311 0.216 2.16 0.96 6.51 GP

No. 68 0.75 0.631 0.434 0.421 0.32 0.202 2.15 1.17 6.46 GP

No. 7 0.75 0.469 0.389 0.352 0.269 0.184 2.11 1.01 6.23 GP

No. 78 0.75 0.423 0.332 0.305 0.251 0.197 1.69 0.96 6.15 GP

No. 8A 0.5 0.343 0.276 0.250 0.196 0.117 2.36 1.19 5.68 GP

No. 8B 0.5 0.38 0.31 0.283 0.23 0.16 1.78 1.18 5.96 GP

No. 8C 0.5 0.36 0.31 0.29 0.24 0.20 1.57 0.96 5.99 GP

No. 8D 0.5 0.35 0.29 0.268 0.22 0.14 1.86 1.24 5.85 GP

No. 8E 0.5 0.438 0.345 0.315 0.254 0.194 1.78 0.96 6.19 GP

No. 89 0.5 0.33 0.236 0.198 0.143 0.087 2.71 1.00 6.35 GP

No. 9 0.375 0.174 0.139 0.125 0.097 0.05 2.78 1.35 4.64 SP

No. 10 0.375 0.1045 0.0433 0.031 0.0102 0.0029 14.93 0.83 2.98 SP

FM = Fineness modulus.

GP = Poorly graded gravel.

SP = Poorly graded sand.

USCS = Unified Soil Classification System.

Because of the wide range of aggregate sizes tested, two cylindrical molds were used: a 

0.1-ft3 mold for aggregates with a maximum diameter less than or equal to 0.75 inches, and a 

0.5-ft3 mold for aggregates larger than 0.75 inch (figure 5). For the minimum density test, a 

scoop was used to place all aggregates, except the No. 9 and No. 10 aggregates, for which a 

pouring device with a 1-inch diameter spout was used for placement. Three sets of tests were 

performed for each aggregate, and the average minimum index density is reported in table 7. 

For the maximum density tests, double amplitude of vertical vibration of 0.013 inch at 60 Hz was 

set. A digital linear variable differential transformer (LVDT) was used to measure the sample 

displacement during vibratory testing (figure 6). Two tests were performed on each aggregate,

and the average maximum index density was reported (table 7). The No. 10 aggregate was the 

heaviest, weighing as much as a conventional well-graded aggregate, but it also has the highest 

coefficient of uniformity (Cu).

21
Figure 5. Photo. Mold (0.1 ft3) for funnel and vibratory table tests.

Table 7. Unit weight of aggregates.

Sample Minimum (pcf) Maximum (pcf)

No. 5 94.9 109.6

No. 56 100.6 103.8

No. 57 95.4 108.7

No. 6 101.0 110.3

No. 67 106.2 124.10

No. 68 96.9 115.9

No. 7 103.3 120.9

No. 78 92.3 109.6

No. 8A 85.7 101.3

No. 8B — —

No. 8C — —

No. 8D — —

No. 8E 97.9 112.8

No. 89 88.4 108.2

No. 9 92.3 110.7

No. 10 115.8 146.3

— = Not measured.

22
Figure 6. Photo. LVDT and mold set-up for vibratory table tests.

Repose Angle

The angle of repose is the maximum angle relative to the horizontal direction that a material can 

naturally sustain. Various methods are available to measure the repose angle; the one adopted by 

the authors consists of scooping the aggregate into a 6-inch diameter hollow cylinder resting 

vertically on a level platform and then slowly raising the cylinder to allow the aggregate to 

naturally fall into a conical pile (figure 7 and figure 8). The repose angle was then measured 

using an average of two methods: (1) protractor device tilted to match the slope of the pile in 

five locations, and (2) string method whereby the circumference of the stockpile was measured 

three times and compared with the volume of the aggregate to determine the height and 

corresponding angle (table 8). 

The full set of results is provided in appendix A. Because the No. 8 aggregate study was started 

after initiation of the strength characterization, the repose angle was not tested for the various 

source locations because the results indicated no correlation. In any case, a general trend is found 

where the repose angle increases with increasing mean grain size, as expected (figure 9).(72) 

Figure 7. Photo. Repose angle cylinder test.

23
Figure 8. Photo. Aggregate pile to determine repose angle.

Table 8. Repose angle of aggregates.

Sample

Repose Angle

Angle Finder String Method Average

No. 5 30.1 31.5 30.8

No. 56 31.4 29.6 30.5

No. 57 29.7 30.8 30.2

No. 6 31.2 29.7 30.4

No. 67 27.6 28.4 28.0

No. 68 32.3 29.5 30.4

No. 7 29.3 27.9 28.6

No. 78 33.6 32.6 33.1

No. 8A 31.1 30.8 31.0

No. 8B — — —

No. 8C — — —

No. 8D — — —

No. 8E — — —

No. 89 29.9 31.6 30.7

No. 9 26.8 27.8 27.3

No. 10 27.4 25.3 26.4

— = Not measured.

24
Figure 9. Chart. Relationship between repose angle and mean aggregate size.

Angularity, Texture, and Sphericity

The aggregate imaging measurement system (AIMS) is a device that combines hardware that can 

capture real-time digital images of fine and course aggregates with software that can process 

those images and analyze the distribution of particle angularity, texture, and sphericity for the 

sample.

(73) The second-generation AIMS device (AIMS2) is primarily used in the pavement 

industry for asphalt and concrete design; however, its applicability for structural backfill was

investigated in this study. The procedure involves placing aggregates within an indented slot on a 

circular tray; the plate is then rotated slowly with a backlight, illuminating it as a digital camera 

takes images of the aggregates. Algorithms within the companion software convert the images to 

a graphical output describing the aggregates’ angularity, texture, sphericity, and other 

parameters.

Angularity describes variations at the edges of the aggregates; in AIMS, it was defined as an 

index in terms of rounded, sub-rounded, sub-angular, or angular (figure 10), but in AIMS2, this 

index was changed to low, moderate, high, and extreme, although the relative range of the 

categories did not change.

(74,73) To better relate angularity (as well as texture and sphericity) for 

geotechnical applications, the initial AIMS classifications are used herein. The surface texture of 

aggregates is also important; the index is defined in terms of polished or smooth, or low, 

moderate and high roughness (figure 11). Sphericity describes the degree of cubicalness of an 

aggregate; it is defined in terms of high sphericity (e.g., the aggregate is roughly the same 

dimension in all axes), moderate sphericity (i.e., semi-circular), low sphericity (i.e., semielongated), and flat/elongated (figure 12).

25
 

Figure 10. Diagram. AIMS angularity index classification ranges.(74)

26
Figure 11. Diagram. AIMS texture classification ranges.(74)

27
Figure 12. Diagram. AIMS sphericity index classification ranges.(74)

AIMS2 measures angularity by the gradient method, texture by wavelet analysis, and sphericity 

by three-dimensional measurements taken from the microscope (for depth) and the image from 

the camera (using eigenvector analysis).

(73) After performing the analysis, the cumulative 

28
distribution of angularity, texture, and sphericity indexes for all particles making up the 

aggregate sample tested was then plotted (figure 13, figure 14, and figure 15, respectively). The 

averages for each aggregate are presented in table 9.

Figure 13. Chart. Angularity results from AIMS2.

29
Figure 14. Chart. Texture results from AIMS2.

Although visual analysis suggests the aggregates are angular, the average of the measured 

distributions using AIMS2 is between 2,100 and 4,000, indicating that the aggregates are subrounded based on the AIMS classification (table 9). The texture and sphericity of the aggregates 

were slightly more scattered. Characterizing the aggregates based on AIMS results in six sample 

groups: (1) No. 5, No. 56, No. 68, No. 8C, and No. 8E all have sub-rounded angularity, moderate 

roughness, and low sphericity; (2) No. 57, No. 8A, No. 89, and No. 9 all have sub-rounded 

angularity, polished texture, and low sphericity; (3) No. 6, No. 67, and No. 7 all have subrounded angularity, moderate roughness, and moderate sphericity; (4) No. 8B and No. 8D both 

have sub-rounded angularity, low roughness, and flat/elongated particles; (5) No. 10 is similar to 

Nos. 8B and 8D, except it has flat/elongated particles; and (6) No. 78 is the only aggregate with a 

smooth texture and low sphericity. Note that these properties are specific to the aggregates tested 

in this study, as evidenced by the various No. 8 aggregates. The use of AIMS in the classification 

of aggregates for structural backfill will be further investigated.

30
Figure 15. Chart. Sphericity results from AIMS2.

31
Table 9. Summary of AIMS2 average results for angularity, texture, and sphericity.

Sample

Angularity Texture Sphericity

Average

Index Classification

Average

Index Classification

Average

Index Classification

No. 5 2915.2 Sub-Rounded 375.6 Moderate 

Roughness 0.688 Low

No. 56 2774.7 Sub-Rounded 447.4 Moderate 

Roughness 0.644 Low

No. 57 3083.1 Sub-Rounded 161.2 Polished 0.662 Low

No. 6 2577.2 Sub-Rounded 360.1 Moderate 

Roughness 0.74 Moderate

No. 67 2643.1 Sub-Rounded 361.1 Moderate 

Roughness 0.741 Moderate

No. 68 2985.8 Sub-Rounded 373.5 Moderate 

Roughness 0.64 Low

No. 7 2770.5 Sub-Rounded 370.2 Moderate 

Roughness 0.714 Moderate

No. 78 2869.6 Sub-Rounded 232.5 Smooth 0.654 Low

No. 8A 2714.6 Sub-Rounded 154.2 Polished 0.682 Low

No. 8B 3202.1 Sub-Rounded 295.9 Low Roughness 0.565 Flat/Elongated

No. 8C 2984.3 Sub-Rounded 379.3 Moderate 

Roughness 0.629 Low

No. 8D 3269.3 Sub-Rounded 298.1 Low Roughness 0.567 Flat/Elongated

No. 8E 2834.2 Sub-Rounded 419.8 Moderate 

Roughness 0.699 Low

No. 89 2742.1 Sub-Rounded 152.1 Polished 0.641 Low

No. 9 2726.2 Sub-Rounded 149.8 Polished 0.675 Low

No. 10 3295.5 Sub-Rounded 418.4 Moderate 

Roughness 0.581 Flat/Elongated

Strength

The strength of the aggregates was determined using three different devices: SDS, LSDS, and 

LDTX. In each test, samples were placed in the devices uncompacted with a relative density 

around 30 percent based on the vibratory table tests (table 7).

Standard Direct Shear Tests

Oftentimes, soil samples will be sent for DS testing to determine the strength parameters (friction 

angle and cohesion) of the material. The most common DS devices are either 2.5 inches in

diameter or 4 inches square. According to ASTM D3080, the maximum particle size of the 

sample tested must be less than 1/10th the width or diameter of the device; for a 2.5-inch

diameter device, the maximum particle size is limited to 0.25 inch, and for the 4-inch square 

device, the maximum particle size is limited to 0.4 inch.

(75) For this reason, samples are often 

scalped, which neglects the effect the larger aggregate particles may have on strength.

32
From table 6, only two of the smaller AASHTO M43 aggregates could be tested in a standard 

4-inch DS device: the No. 9 and No. 10. For most geotechnical applications utilizing OGAs, 

where a minimum of 0.5-inch maximum particle size is typically specified, standard DS testing 

cannot be performed. This limitation requires either (a) scalping the sample, whereby material 

greater than that which can be tested according to ASTM is removed; (b) generating a parallel 

gradation with the material, whereby the maximum gradation is 1/10th the DS device size with 

the remaining gradation curve parallel to that of the actual sample; or (c) testing in a larger DS 

device, whereby nothing special needs to be done to the sample.

Test Setup: To evaluate the impact of scalping the sample, SDS tests were performed according 

to ASTM D3080 using a 2.5-inch circular device in the geotechnical laboratory at FHWA’s 

Turner-Fairbank Highway Research Center (TFHRC) (figure 16); material larger than the No. 4 

sieve (opening size of 0.187 inches) was removed prior to testing. The shear rate was set at 

0.002 inches/min based on the maximum measured time for 90 percent consolidation (t90) using 

the square root of time method (Taylor’s method); the gap size was 0.025 inches.

(75) 

Figure 16. Photo. SDS test device at TFHRC.

Prior to testing the aggregates, three sets of tests were performed using Ottawa 20/30 sand to 

ensure appropriate and repeatable results with the SDS device. The resulting measured peak 

friction angles for each test (dry and uncompacted), using the conventional MC criteria, are 

33
shown in table 10. The values are all less than 3 percent of the average, or 33 degrees for the 

tangent friction angle, which is consistent for Ottawa sand and demonstrates the repeatability of 

the test method.

(76,77)

Table 10. Ottawa test results using SDS device and MC approach.

Test Tangent Friction Angle (degree) Secant Friction Angle at 5 psi (degree)

1 34 34

2 32 31

3 33 32

After verification of the test apparatus and procedures using Ottawa sand, four tests were 

performed for each AASTHO aggregate tested, at different applied normal stresses: 5, 10, 20, 

and 30 psi. This range of stresses was selected based on typical loads a retaining wall or 

foundation utilizing these aggregates may experience, with 30 psi equivalent to most in-service,

bridge-bearing pressures. The samples were tested in a dry condition.

For each initial applied normal stress, the shear stress and horizontal displacement were 

measured during shear using a load cell and LVDT, respectively. An example for the No. 57 

aggregate is shown in figure 17.

Figure 17. Chart. Shear stress versus horizontal displacement for No. 57 from SDS tests.

The peak shear stress ( f) is equal to the maximum measured during testing. In some cases, the 

peak shear stress was not always reached. (See figure 18 as an example.) The peak was therefore 

determined to equal the shear stress measured at a lateral strain of 20 percent (or 0.5 inches for a 

2.5-inch device).(75)

τ

34
Figure 18. Chart. Shear stress versus horizontal displacement for No. 5 from SDS tests.

MC Approach: Using the MC approach, the peak shear stress is then compared with the 

corresponding applied normal stress. Note that the applied normal stress must be corrected 

during the shear phase because the contact area is constantly changing. For a circular sample, 

the area correction factor (F) is found using equation 11.

(11)

Where:

h = Horizontal displacement.

D = Sample diameter.

The correction factor is then applied to the original sample area (Ao) to determine the corrected 

area (Ac); see equation 12. 

(12)

This post-processing procedure was performed on each set of results to determine the normal 

pressure at the point of peak shear stress. No correction is needed for the recorded shear stress. 

The peak, or secant, friction angle ( 's) at each corresponding applied normal stress ( 'n) is 

calculated according to equation 13.

FF = 2

ππ �cos−1 �

h

DD� − ∆h

DD �1 − �

h

DD�

2

��

AAcc = FFAAoo

φ σ

35
(13)

If a known applied load is given, then the corresponding peak friction angle can be directly 

selected (termed the secant angle of friction); however, oftentimes the stresses will be variable so 

a tangent internal angle of friction ( 't) is determined over a range of stresses. The best-fit linear 

regression through the four points represents the MC failure envelope. (See figure 19 as an 

example.) The tangent of the slope is equal to the internal friction angle, and the shear stress 

intercept is equal to the (apparent) cohesion. 

The results of standard DS testing using the linear MC approach for all of the aggregates are 

presented in table 11. Note that aggregates 8B, 8C, 8D, and 8E were not scalped and tested using 

the standard DS device. Appendix A provides the standard DS test results (peak shear and 

corresponding normal stress) leading to the resulting friction angle and measured cohesion in 

table 11.

The measured friction angles range between 43 and 57 degrees, with an average of 52 degrees. 

The results are generally within 10 percent of the average. The scalped samples indicate high 

strength, but the accuracy is unknown because the majority of the particles were removed. Eight 

of the samples removed about 90 percent of the sample or more during scalping, but two of the 

samples (No. 9 and No. 10) did not need much scalping, so their results may be more reliable. 

Comparison to large-scale testing will help in the analysis.

Figure 19. Chart. Shear versus normal stress for No. 57 using SDS.

φ′

s = tan−1 � τf

σ′

n

�

φ

36
Table 11. SDS test results using MC approach.

Sample

Percent Passing

No. 4 Sieve

(figure 4)

't,SDS

(degree)

c'SDS

(psi)

No. 5 0.46 50.1 1.7

No. 56 2.58 51.7 6.5

No. 57 3.67 56.5 1.9

No. 6 3.72 51.7 4.2

No. 67 3.96 57.3 7.1

No. 68 7.40 42.8 9.5

No. 7 10.26 54.6 7.8

No. 78 6.18 51.3 9.7

No. 8A 26.50 53.0 5.2

No. 8B — — —

No. 8C — — —

No. 8D — — —

No. 8E — — —

No. 89 47.01 54.0 6.1

No. 9 94.22 50.2 3.5

No. 10 98.96 50.6 3.3 '

t,SDS = The friction angle using the Mohr-Coulomb (MC) approach.

c'

SDS = The shear stress intercept from the best-fit linear MC failure 

envelope.

— = Not measured.

Note that using a linear MC interpretation results in a cohesion value for each test because the 

y-intercept of the best-fit approximation is not zero (figure 19, for example); however, these 

aggregates are cohesionless. This inconsistency is attributed to the fact that the failure envelope 

is actually nonlinear; there is also aggregate interlocking and dilation that occurs during shearing, 

depending on the applied normal stress.(54) In reality, the friction angle decreases with increased 

applied normal stress in a logarithmic function. For the range of stresses tested, the secant 

friction angle corresponding to the peak for each applied normal stress was larger than that 

approximated from the MC approach. Because of these issues, the use of an alternative ZDA 

method is proposed to determine the design friction angle, which is based on the critical state or 

constant volume concept.(3)

ZDA Approach: The ZDA method requires knowledge about the dilation behavior of the 

sample. The vertical displacement during the consolidation and shearing phases was measured 

using an LVDT. Comparing the vertical displacement to the horizontal displacement during 

shear provides an indication of the dilation behavior of the aggregates. An example for the No. 

57 aggregate is shown in figure 20. Positive vertical displacement indicates compression of the 

sample, whereas negative displacement indicates dilation. The dilation angle ( ) is found 

according to equation 14.

φ

φ

ψψ

37
(14)

Where:

v = The change in vertical displacement.

h = The change in horizontal displacement. 

Figure 20. Chart. Deformation behavior of No. 57 during SDS testing.

Data for the DS testing is provided at every 0.01 inch of horizontal displacement, so h is 

constant. As the sample is sheared, v will change for each horizontal displacement increment. 

The maximum dilation angle for the aggregate is therefore found when the maximum change in 

vertical displacement occurs. A three-point moving average of the change in vertical 

displacement was taken to smooth the data and eliminate any misleading sharp peaks.

There is generally a linear relationship between the measured dilation angles and the peak 

friction angles. The intercept at zero dilation is the constant volume friction angle ( 'cv) found 

using the ZDA approach. For example, 'cv is equal to 49 degrees for the No. 57 aggregate 

(figure 21). The resulting friction angle for each aggregate is shown in table 12; however, when 

combining the aggregates together (figure 22), there is no clear relationship. It was observed that 

the dilation angles measured during testing were sporadic and not as expected, likely a result of 

the considerable scalping performed on the aggregates, which changes its dilative behavior. 

tanψ = Δv

Δh

∆

∆

∆

∆

φ

φ

38
Figure 21. Chart. Friction angle versus dilation angle for No. 57 using SDS.

Table 12. SDS test results using the ZDA approach.

Sample 'cv,SDS (degree)

No. 5 50.6*

No. 56 37.7

No. 57 49.0

No. 6 53.9

No. 67 49.1

No. 68 36.9

No. 7 51.3

No. 78 44.2

No. 8A 37.3

No. 8B —

No. 8C —

No. 8D —

No. 8E —

No. 89 42.3

No. 9 52.0

No. 10 39.0

*Modified zero dilation angle approach whereby the 

stress-strain curves were used to determine constant 

volume friction angle.

— = Not measured.

φ

39
Figure 22. Chart. Relationship between friction and dilation angles in SDS testing.

Summary: The results from the standard direct shear testing on the scalped samples are shown 

in figure 23. The scalped samples all had friction angles higher than 34 degrees. Using the MC 

approach, friction angles ranged from 43 to 57 degrees, with a mean across all different sample 

aggregates of 52 degrees, a standard deviation of about 4 degrees, and a coefficient of variation 

(COV) of 7.2 percent. Using the ZDA approach, friction angles ranged from 38 to 54 degrees, 

with an overall mean of 45 degrees, a standard deviation of 6 degrees, and a COV of 

13.6 percent.

40
Figure 23. Chart. Summary of SDS testing.

LSDS Tests

To evaluate the strength properties of the AASTHO OG aggregates, a DS test is needed that is 

large enough to avoid scalping. At TFHRC, a 12- by 12- by 8-inch DS box is available to 

perform LSDS testing on aggregates of up to 1.2-inch maximum particle size (figure 24). This 

device was used to measure the strength of the 12 classifications of AASHTO aggregates (table 

4) under both dry and saturated conditions. Note that the SDS tests were only tested under dry 

conditions.

Figure 24. Photo. LSDS device at TFHRC.

41
Test Setup: The ASTM D3080 test method was followed for LSDS testing with the exception of 

the gap size between the top and bottom shear boxes. ASTM D3080 was originally developed for 

SDS testing, which designated the gap size as 0.025 inches.(75) Because the LSDS device and the 

aggregates tested in this research are considerably larger, the gap size was instead set to d85 (the 

aggregate size in which 85 percent of the material is smaller) for each sample based on the sieve 

analysis (table 6). This setting was determined from review of test methods outlined in ASTM 

D5321 and trial runs at various gap sizes, and to it was used to avoid frictional interference from 

either the two shear boxes or larger particles that may fall within the gap during testing.(78,79)

The shear strain displacement rate was set at 0.015 inches/min for the OGAs based on the results 

obtained during the compression phase of testing. The samples were sheared to a maximum of 

20 percent of the device length for a total shear displacement of 2.4 inches. Because the friction 

angle increases with relative density for sands and gravels, an assumed worst-case condition was 

used by placing the samples with no compactive effort into the shear box.(79) Similar to the SDS 

tests, each aggregate was tested at normal stresses of 5, 10, 20, and 30 psi to determine the 

internal friction angle, which is a typical stress range for most wall and bridge applications. 

Note that before testing, the load cells and LVDTs were calibrated. In addition, the LSDS device 

was also calibrated for displacement and shear resistance. With no sample in the shear box and 

no shear deformation occurring, the vertical displacement during loading and unloading was 

measured to account for box compression. The resulting calibration equation (figure 25) is then 

subtracted from the raw data to obtain a true displacement of the sample itself.

Figure 25. Chart. Vertical displacement calibration for LSDS device.

42
Similarly, the shear resistance of the rollers to movement must be subtracted from the measured 

shear stress. To do this, dead load was put in the shear box to equal the normal stresses tested in 

the program (5, 10, 20, and 30 psi), and the average shear stress was computed (table 13). 

Table 13. LSDS resistance calibration values.

Normal Stress (psi) Average Shear Stress (psi)

5 0.0307

10 0.0287

20 0.0481

30 0.0303

The area correction factor (F) for the applied normal load during testing is found in a different 

manner from that in equation 11 because the device is square, instead of circular like the SDS 

tests performed (equation 15). 

(15)

Where:

h = horizontal displacement.

B = Sample side dimension. 

The correction factor is then applied to the original sample area (Ao) to determine the corrected 

area (Ac) (equation 12).

Similar to the verification of the SDS device, tests were performed using the LSDS device on 

Ottawa sand to demonstrate the repeatability and validity of the device. This material was 

evaluated at 5 psi; the average secant friction angle across two sets of tests is 30.4 degrees. (Each 

test was about 1 percent from the average.) The results of the LSDS test are approximately 

2 degrees less than the SDS tests at the same applied pressure. These results are consistent with 

results showing that LSDS devices produce a lower friction angle than SDS devices for the same 

material.(54)

MC Approach: After taking into account the calibrations and corrections, the results of LSDS 

testing using the linear MC approach for all of the aggregates are presented in table 14. The 

cohesion values are omitted because the materials are cohesionless; however, the entire set of 

results can be found in appendix A and are visualized in figure 26. While there is a large amount 

of scatter across the entire series of AASHTO OGAs tested, a linear fit can be made to determine 

a global tangent friction angle: 49 and 48 degrees for dry and saturated conditions, respectively.

FF = 1 − h

BB

43
Table 14. LSDS Test results using MC approach.

AASHTO 

Gradation

Dry Saturated

't,LSDS,dry

(degree)

't,LSDS,sat

(degree)

No. 5 47.6 55.3

No. 56 56.0 54.4

No. 57 48.9 52.1

No. 6 56.4 57.5

No. 67 53.2 57.3

No. 68 47.3 48.7

No. 7 54.0 48.9

No. 78 50.6 44.9

No. 8A 52.3 46.9

No. 8B 43.4 41.6

No. 8C 48.3 41.9

No. 8D 37.8 37.5

No. 8E 52.2 46.8

No. 89 44.8 41.2

No. 9 50.5 42.9

No. 10 42.9 37.1

AASHTO = American Association of State Highway and 

Transportation Officials.

φ φ

44
Figure 26. Chart. Global MC envelope for all AASHTO OGAs tested under both dry and 

saturated conditions.

ZDA Approach: Using the ZDA approach, the CV friction angle from LSDS testing was found 

for each aggregate (table 15).

45
Table 15. LSDS test results using ZDA approach.

AASHTO 

Gradation

Dry Saturated

’cv,LSDS, dry

(degree)

’cv,LSDS, sat 

(degree)

No. 5 48.1 44.6

No. 56 50.3 52.9

No. 57 43.2 52.9

No. 6 45.2 51.7

No. 67 49.9 53.7

No. 68 47.0 47.9

No. 7 50.9 49.0

No. 78 49.2 45.5

No. 8A 51.8 50.3

No. 8B 45.7 45.5

No. 8C 46.6 45.8

No. 8D 44.4 42.1

No. 8E 50.4 45.6

No. 89 45.6 45.8

No. 9 49.8 45.5

No. 10 43.0 42.0

AASHTO = American Association of State Highway and Transportation 

Officials.

Comparing the relationship between peak friction angle and maximum dilation angle for all of 

the aggregates yields a reasonable linear trend for the entire AASHTO OGA dataset evaluated in 

this study (figure 27). This relationship is better than that found from SDS testing (figure 22) and 

is considered more accurate because no scalping was necessary.

φ φ

46
Figure 27. Chart. Relationship between friction and dilation angles in LSDS testing.

Summary: The results from the LSDS testing on the unscalped samples are shown in figure 28

for dry conditions and figure 29 for saturated conditions. The samples all had friction angles 

higher than 34 degrees. Using the MC approach, friction angles ranged from 37.1 to 

57.5 degrees, with a mean across all different sample aggregates of 48.2 degrees, a standard 

deviation of 5.9 degrees, and a COV of 12.3 percent. The average friction angle under dry and 

saturated conditions is 49.1 and 47.2 degrees, respectively, so there is little impact resulting from 

saturation.

Using the ZDA approach, friction angles ranged from 42.0 to 53.7 degrees, with an overall mean 

of 47.6 degrees, a standard deviation of 3.3 degrees, and a COV of 6.9 percent. Saturation had no

impact on the mean overall. It is interesting to note that the secant friction angles ( 's) for the 

range of confining stresses tested are all higher than the tangent friction angle ( 't). 

By comparing the COV for the secant friction angles ( 's) over the range of confining stresses 

tested with the variation between the average 's and the corresponding 't under dry and 

saturated conditions, a general linear relationship is observed (figure 39). The scatter in saturated 

conditions is larger, but the general trend is the same. No relationship was found between 's 

values and 'cv values; however, using the ZDA approach across all samples tested, the peak 

friction angle is 46.1 degrees (figure 27).

φ

φ

φ

φ φ

φ

φ

47
Figure 28. Chart. Summary of LSDS testing under dry conditions.

Figure 29. Chart. Summary of LSDS testing under saturated conditions.

48
Figure 30. Chart. Comparison of the effective tangent and secant friction angles for LSDS 

testing.

LDTX Tests

At TFHRC, a 6-inch diameter TX unit is available to conduct large-scale consolidated 

drained/undrained compression testing on aggregates of up to 1-inch maximum particle size. A 

consolidated drained TX compression test was conducted according to ASTM D7181 to 

determine the strength of the 12 primary AASHTO aggregates.(800) The same series of aggregates 

tested in the LSDS device were tested with the LDTX device; however, only No. 8E was 

examined from the five types of No. 8 aggregates (table 5).

Test Setup: All of the tests were conducted at loose compaction with relative density of 

30 percent to simulate the worse-case scenario for strength characterization of granular materials. 

The dry mass needed for each test to achieve the target value of compaction was determined 

based on the performed funnel and vibratory table tests according to ASTM D4254 and 

ASTM D4253, respectively.

(68,69) The overall steps starting from sample preparation to the end of 

the LDTX test are illustrated in figure 31. 

Sample preparation for the loose condition consisted of pouring a known mass of OGAs through 

a funnel into the split mold from nearly zero drop height. The nominal diameter and height of the 

prepared sample was 6 inches and 12 inches, respectively; the height-to-diameter ratio is 2, as 

recommended by ASTM.(800) The stability of the samples throughout the sample preparation 

phase, prior to mounting into the load frame, was maintained by applying partial suction to the 

specimen through one of the drainage valves located on the base of the pedestal. 

49
Figure 31. Diagram. Overview of the adopted procedure for LDTX testing.

To minimize the risk of membrane puncture during shearing by the coarse aggregates, two 

0.025-inch-thick membranes were used; the inner membrane was used as a sacrificial membrane 

during compaction, and the second membrane was placed once compaction was completed. The 

stiffness of the individual and double membranes was measured to determine the appropriate 

membrane correction for the test results. The results yielded a Young’s modulus for the double 

membrane of 11.1 kip/ft2.

The compacted sample housed under the properly tightened chamber was mounted on the load 

frame, and the test chamber was filled with tap water. The sample was gravity presaturated 

through the tube connected to the bottom of the drainage valve prior to the initiation of the test. 

The water was also allowed to run through the drainage lines and the two tubes that connect 

these lines to remove the trapped air bubbles within the system. These steps helped reduce the 

back pressure required for saturation, and, as a result, the saturation period decreased. 

Furthermore, the pumps connected to the cell and the sample have a limited capacity; without the 

50
presaturation procedure, the pumps have to be filled multiple times while the test is running,

which interrupts the experiment and further increases the duration of the experiment. 

The next step was to connect the cell and pore pressure pumps to the base of the TX setup and

open a new file for each new test with the right values of dry mass of the aggregates and the

diameter and height of the specimen. To achieve the acceptable minimum Skempton’s B-value 

of 0.95 during the saturation phase, a back-pressure saturation in the range of 4.2 to 7.5 kip/ft2

was employed. 

Following saturation, the specimen was subjected to isotropic consolidation to the desired 

effective confining stress (5, 10, 20, or 30 psi) before the onset of the strain-controlled shear 

stage. The strain rate used for the shear phase was computed based on the estimated time needed 

to achieve 90 percent of the total consolidation (t90).(800) The shear tests terminated when 

15 percent axial strain was reached.

At the end of each test, the provided outputs include: axial ( 1) and volumetric ( V) strain, major 

( ′

1) and minor ( ′3) effective principal stresses, and pore pressure. The difference between the 

major and minor principal stresses is termed the deviator stress ( ′

d). This parameter is then 

plotted against the axial strain; an example for the No. 57 aggregate is shown in figure 32 for 

each of the four effective confining pressures. The deformation behavior is shown in the 

relationship between volumetric strain and axial strain; an example for the No. 57 aggregate is 

shown in figure 33. 

The secant, or peak, friction angle for each test was computed from the measured ′

1 and ′3

values corresponding to the maximum ′d for each test (equation 6). The maximum dilation 

angle ( max) is computed using equation 16 based on the measured volumetric and axial 

deformation behavior.(81)

(16)

Where:

d 1 = The incremental axial strain.

d 3 = the incremental lateral strain (equation 17).

ε ε

σ σ

σ

σ σ

σ

ψψ

ψψmm mm = sin−1 �

(ddεε1 + 2 × ddεε3)

(ddεε1 − 2 × ddεε3)

�

mm mm

ε

ε

51
(17)

Figure 32. Chart. The effective deviator stress versus axial strain for No. 57 from LDTX 

testing.

Figure 33. Chart. Volumetric strain versus axial strain for No. 57 from LDTX testing.

εε3 = (εεVV − εε1)

2

52
The reliability and repeatability of the TX apparatus was verified by conducting a drained 

consolidated test for Ottawa 20/30 sand and a AASHTO No. 68 sample, respectively. The 

Ottawa sands were subjected to various stress levels, and the resulting secant friction angles and 

the tangent angle are shown in table 1. The resulting 't is very close to the well-recorded friction 

angle values of the uniform Ottawa sands. In addition, three replicates of fresh No. 68 OGAs 

with the same compaction state were subjected to the same stress level (5 psi) to verify the 

repeatability of the test; the measured peak friction angles has a standard deviation of 0.5, and all 

values are within less than 1.3 percent of the average (50.5 degrees).

Table 16. LDTX test results for Ottawa sand and AASHTO No. 68.

Sample Type

Effective Confining 

Stress (psi)

's 

(degree)

't

(degree)

Ottawa

5 33.7

32.7 10 33.9

20 31.8

30 33.1

AASHTO #68

5 49.9

5 50.7 —

5 50.9

AASHTO = American Association of State Highway and Transportation 

Officials.

— = Not measured.

Prior to determining the strength parameters, correction procedures were performed on the raw 

data collected from the LDTX software. The corrections are conducted to minimize the errors 

that could be incurred because of (1) the changing cross-sectional area during the consolidation 

and shearing phase, (2) the membrane stiffness, and (3) the considerable change of volume due 

to membrane penetration during the consolidation phase. 

A bulging type area correction (equation 18) method was implemented to determine the 

corrected cross-sectional area of the specimen as the sample deformed during the shearing 

process.(82)

(18)

Where:

Ac = Corrected area.

Ao = Initial area before correction.

εV = Volumetric strain.

a = Experimental constant normally between 1 and 2.

1 = Axial strain. 

For the experimental constant, a value of 1.67 was used.

(83)

φ

φ φ

AAcc = AAoo × � 1 − εε

1 − (aa × εε1)

�

ε

53
The extra radial stress added to the effective confining stress due to the membrane stiffness was 

also corrected according to equation 19.

(80) The computed value from equation 19 was then 

subtracted from the measured deviator stress.

(19)

Where:

( 1- 3) = Change in effective deviator stress due to the membrane correction.

Em = Young’s modulus for the membrane material (11.1 kip/ft2).

tm = Thickness of the membrane (0.025 inches).

1 = Axial strain.

Dc = The specimen’s diameter at the end of the consolidation phase.

The other potential error during the shear test is the significant volume reduction due to 

membrane penetration, which could be wrongly assumed as sample volume reduction. This 

phenomenon is more pronounced in samples with coarse grain sizes during the isotropic 

consolidation stage, especially after the application of high confining pressures. A graphical 

method proposed by Noor et al. was adopted to correct these potential errors in sample volume 

changes.(84) The approach assumes that the occurrence of membrane penetration and specimen 

compression is a consecutive process because the compression is only triggered after the 

membrane penetration has been fully mobilized. As a result, the initial sharp decrease in volume

that is measured could be attributed to the membrane penetration (figure 32). 

As demonstrated in figure 34, two straight (dashed) lines are drawn to best fit the initial and tail 

parts of the consolidation curve (CC).

(84) A bisector line originating from the intersection of these

lines is then made to connect to the CC; the distance from the intersection to the curve is found 

(L). A line with an equal distance of L is drawn away from the CC along the bisector line; from 

there, a perpendicular line is drawn until it intersects the initial part of the CC. This point marks 

the volume of the membrane reduction, which is deducted from the total reduced volume to 

determine the correct value of sample volume at the end of the consolidation phase. It is clear 

from figure 34 that the volume reduction due to membrane penetration increased significantly 

with the increase in grain size (AASHTO No. 5 > No. 8 > No. 10). Similarly, the correction 

increases with the increase of effective confining stress, the highest being for 30 psi (figure 35).

∆(σσ1 − σσ3) = 4 × EEmm × ttmm × εε1

DDcc

∆ σ σ

ε

54
Figure 34. Chart. Graphical method to determine membrane penetration correction and 

the effect of aggregate size on volume reduction during LDTX testing.

55
Figure 35. Chart. Effect of confining stress on volume reduction for AASHTO No. 68 

sample during LDTX testing.

MC Approach: The linear MC approach presented in equation 5 for LDTX testing was used to 

compute 't for the 12 tested OGAs. The summarized results are displayed in table 17. The full 

results displaying the individual 's, max, and corresponding shear and normal stresses at failure 

for each test can be found in appendix A. The individual p' and q stress path values for the entire 

database tested were plotted together, and a good correlation is found for the entire series of 

OGAs tested with the LDTX device (figure 36). Using a linear regression, the overall computed 

friction angle is 39.1 degrees. An apparent cohesion is still observed because of the limitation of 

the MC approach for OGAs; however, if the linear regression is force-fit to zero, then q would 

equal about two-thirds p', with the friction angle slightly higher at 41.5 degrees. 

φ

φ ψψ

56
Table 17. LDTX test results using MC approach.

AASHTO 

Gradation 't,LDTX (degree)

No. 5 36.5

No. 56 39.5

No. 57 40.5

No. 6 36.4

No. 67 39.0

No. 68 38.1

No. 7 38.4

No. 78 34.9

No. 8A —

No. 8B —

No. 8C —

No. 8D —

No. 8E 39.3

No. 89 38.3

No. 9 38.4

No. 10 40.1

AASHTO = American Association of State 

Highway and Transportation Officials.

— = Not measured.

Figure 36. Chart. Relationship between p' and q values in LDTX testing series.

φ

57
ZDA Approach: The constant volume friction angle ( 'cv), which corresponds to the friction 

angle at which the dilation angle is zero, is determined using the ZDA approach. The results for 

each tested aggregate are presented in table 18. Similar to the LSDS results, the relationship 

between peak friction angle and maximum dilation angle for all of the aggregates yields a 

reasonable linear trend for the entire AASHTO OGA dataset evaluated in this study (figure 37). 

The resulting friction angle is 38.9, which is close to the value computed from the MC approach 

above. 

Table 18. LDTX test results using ZDA approach.

AASHTO 

Gradation 'cv,LDTX (degree)

No. 5 39.7

No. 56 39.4

No. 57 38.4

No. 6 36.8

No. 67 36.6

No. 68 38.7

No. 7 36.9

No. 78 38.3

No. 8A —

No. 8B —

No. 8C —

No. 8D —

No. 8E 37.5

No. 89 40.3

No. 9 39.4

No. 10 34.8

AASHTO = American Association of State 

Highway and Transportation Officials.

— = Not measured.

φ

φ

58
Figure 37. Chart. Relationship between friction and dilation angles in LDTX testing.

Summary: The results for both the tangent and CV friction angles for all conducted LDTX tests 

were marginally higher than the commonly adopted design value of 34 degrees (figure 38). The 

average and COV values for 't for the entire series tested are 38.4 degrees and 4.6 percent, 

respectively; similarly for 'cv, they are 38.1 degrees and 4.2 percent, respectively. It is 

interesting to note that the secant friction angles ( 's) for the range of confining stresses tested 

are typically higher than the tangent friction angle ( 't).

By comparing the COV for the secant friction angles ( 's) over the range of confining stresses 

tested with the variation between the average 's and the corresponding 't, a linear relationship 

is again observed (figure 39). The highest COV (11 percent) corresponds to the largest sample 

(i.e., No. 5), while the lowest (2 percent) corresponds to the smallest sample (i.e., No. 10). 

Despite high values of individual 's for sample No. 5, the 't was the lowest (appendix A). This 

trend was not observed for the 'cv values using the ZDA approach.

φ

φ

φ

φ

φ

φ φ

φ φ

φ

59
Figure 38. Chart. Summary of LDTX testing.

Figure 39. Chart. Comparison of the effective tangent and secant friction angles for LDTX 

testing.

60
CHAPTER 4. ANALYSIS OF RESULTS

4.1 DETERMINATION OF STRENGTH PROPERTIES

A total of sixteen different OGAs were tested in this study. From these series of tests, the 

strength parameters were found (table 11 through table 18). The strength of the aggregates was 

determined using three different devices: (1) SDS, (2) LSDS, and (3) LDTX. The choice of 

testing device plays a major role in the measured strength parameters.

4.2 TESTING DEVICE

To compare the testing devices, the measured friction angles were first investigated. Because the 

LDTX testing is performed saturated, the comparison focused on the LSDS test results under 

saturated conditions. Findings show that testing with the LSDS device produces higher measured 

friction angles than when compared with the LDTX device, regardless of the method of data 

interpretation, the MC or the ZDA approach (table 19 and table 20, respectively). In general, 

LSDS test results are generally between 8 and 52 percent higher than the LDTX test results. One 

exception is the No. 10 aggregate when using the MC approach; however, further study is 

needed to determine the reason for this smallest and most uniform aggregate tested.

61
Table 19. LSDS versus LDTX measured friction angles using MC approach.

MC Tangent Friction Angle LSDS Relationship to LDTX

Sample

LSDS

(degree)

LDTX

(degree)

Total Difference

(LSDS-LDTX)

(degree)

Percent Difference

(LSDS/LDTX - 1)*100

(percent)

No. 5 55.3 36.5 18.8 51.5

No. 56 54.4 39.5 14.9 37.7

No. 57 52.1 40.5 11.6 28.6

No. 6 57.5 36.4 21.1 58.0

No. 67 57.3 39.0 18.3 46.9

No. 68 48.7 38.1 10.6 27.8

No. 7 48.9 38.4 10.5 27.3

No. 78 44.9 34.9 10.0 28.7

No. 8A 46.9 — — —

No. 8B 41.6 — — —

No. 8C 41.9 — — —

No. 8D 37.5 — — —

No. 8E 46.8 39.3 7.5 19.1

No. 89 41.2 38.3 2.9 7.6

No. 9 42.9 38.4 4.5 11.7

No. 10 37.1 40.1 -3.0 -7.5

LDTX = Large-diameter triaxial.

LSDS = Large-scale direct shear.

MC = Mohr-Coulomb

— = Not measured.

62
Table 20. LSDS versus LDTX measured friction angles using ZDA approach.

ZDA CV Friction Angle (degree) LSDS Relationship to LDTX

Sample LSDS LDTX

Total Difference

(LSDS-LDTX)

(degree)

Percent Difference

(LSDS/LDTX - 1)*100

(percent)

No. 5 44.6 39.7 4.9 12.3

No. 56 52.9 39.4 13.5 34.3

No. 57 52.9 38.4 14.5 37.8

No. 6 51.7 36.8 14.9 40.5

No. 67 53.7 36.6 17.1 46.7

No. 68 47.9 38.7 9.2 23.8

No. 7 49.0 36.9 12.1 32.8

No. 78 45.5 38.3 7.2 18.8

No. 8A 50.3 — — —

No. 8B 45.5 — — —

No. 8C 45.8 — — —

No. 8D 42.1 — — —

No. 8E 45.6 37.5 8.1 21.6

No. 89 45.8 40.3 5.5 13.6

No. 9 45.5 39.4 6.1 15.5

No. 10 42.0 34.8 7.2 20.7

LDTX = Large-diameter triaxial.

LSDS = Large-scale direct shear.

MC = Mohr-Coulomb

— = Not measured.

The mean size of the aggregate plays a role in the percent increase for LSDS test results as 

compared with LDTX test results (figure 40). As the aggregate gets larger, the percent difference 

typically increases. Overall, however, there is no observed relationship between friction angles 

measured using LDTX and LSDS testing for the range of OGAs tested (figure 41).

Looking at the range of aggregates tested, from the No. 5 to the No. 10, the mean tangent friction 

angle using the LSDS device under saturated conditions is 47.2 degrees, with a COV of 

14.2 percent. The tests using the LDTX device, however, resulted in a mean tangent friction of 

38.4 degrees and a COV of 4.6 percent. For the CV friction angle, the mean and COV using the 

LSDS device is 47.6 degrees, with a COV of about 7 percent; with the LDTX device, the values 

are 38.1 degrees and 4.2 percent, respectively. The aggregate type (i.e., size) had more of an 

impact with LSDS testing than with LDTX testing under loose compaction, likely as a result of 

the different boundaries conditions between the two tests. 

63
Figure 40. Chart. Difference between LSDS and LDTX as a function of mean aggregate 

size.

Figure 41. Chart. Relationship between LSDS and LDTX friction angles.

A similar observation is made for the measured secant friction angles; however, the difference 

between LDTX and LSDS testing tends to decrease with increasing confining stress (figure 42).

This observation again may be related to the reduced dilative behavior at higher confining 

64
stresses. The linear relationship found between the COV of the secant friction angles for a 

particular aggregate and the variation of the tangent friction angle from the average secant angle 

was found for both LSDS (figure 30) and LDTX testing (figure 39). The LDTX testing produces 

results that are considerably less scattered than the LSDS testing, thus reducing the variability

across all samples tested. 

Figure 42. Chart. Relationship between LSDS and LDTX effective secant friction angles.

When looking at the dilation angle, those measured with the LDTX device are also lower than 

those measured with the LSDS device (figure 43). This result is expected because of the forced 

failure plane that the aggregates must displace over in the LSDS device, causing more dilation.

There is a general trend observed for dilation angles measured with the different large-scale 

devices; the dilation angle measured with LDTX is approximately 60 percent of that measured 

with LSDS. This result also explains the lower friction angles measured with LDTX because

dilation behavior plays a big role in the strength of aggregates. Considering there is a trend with 

dilation but not with tangent or CV friction angles between LDTX and LSDS results, it is clear 

that more factors are contributing to the strength between the two test methods. 

65
Figure 43. Chart. Relationship between LDTX and LSDS measured dilation angles.

Scale Effects

One parameter investigated in this study was scale of the direct shear testing device used to 

measure the strength of the aggregates. A 2.5-inch-diameter SDS device and a 12-inch-square 

LSDS device were used in the comparison. To ensure that the ASTM standard was met for each 

test, the samples were scalped prior to testing in the SDS device; no scalping was needed for the 

LSDS tests.(75) Tests were performed uncompacted under dry conditions.

Some samples measured with the LSDS results show higher strength than the SDS results; 

however, the differences largely lie within 10 to 20 percent (figure 44). The difference in the 

measured tangent friction angle when conducting SDS tests on scalped samples versus LSDS 

tests on complete samples ranged from 0 to 9.2 degrees when evaluating the results using the 

MC approach (table 21). When using the ZDA approach, the difference is greater, up to 

14.5 degrees, and the LSDS results are about 40 percent higher than the SDS results (table 22).

The larger difference using the ZDA approach is explained by the variation and scatter in 

measured dilation angles between scalped and unscalped samples (see figure 22 and figure 27). 

The scalping process changes the dilation properties of the aggregates, with relative differences 

ranging from 15 to 65 percent; no trend was found (figure 45). The initial void ratio for testing is 

also changed, which has an impact on strength. Overall, scalped samples are unrepresentative of 

field behavior; results from strength testing cannot be relied upon. 

66
Figure 44. Chart. Relationship between LSDS and SDS measured friction angles.

67
Figure 45. Chart. Relationship between LSDS and SDS measured dilation angles.

68
Table 21. SDS versus LSDS friction angles using MC approach.

AASHTO 

Gradation

MC Friction Angle (degree) LSDS Relationship to SDS

SDS LSDS

Total Difference

(LSDS-SDS)

(degree)

Percent Difference

(LSDS/SDS - 1)*100

(percent)

No. 5 50.1 47.6 -2.5 -5.0

No. 56 51.7 56.0 4.3 8.3

No. 57 56.5 48.9 -7.6 -13.5

No. 6 51.7 56.4 4.7 9.1

No. 67 57.3 53.2 -4.1 -7.2

No. 68 42.8 47.3 4.5 10.5

No. 7 54.6 54.0 -0.6 -1.1

No. 78 51.3 50.6 -0.7 -1.4

No. 8A 53.0 52.3 -0.7 -1.3

No. 8B — 43.4 — —

No. 8C — 48.3 — —

No. 8D — 37.8 — —

No. 8E — 52.2 — —

No. 89 54.0 44.8 -9.2 -17.0

No. 9 50.2 50.5 0.3 0.6

No. 10 50.6 42.9 -7.7 -15.2

AASHTO = American Association of State Highway and Transportation Officials.

LSDS = Large-scale direct shear.

MC = Mohr-Coulomb.

SDS = Standard direct shear.

— = Not measured.

69
Table 22. SDS versus LSDS friction angles using ZDA approach.

AASHTO 

Gradation

ZDA Friction Angle (degree) LSDS Relationship to SDS

SDS LSDS

Total 

Difference

(LSDS-SDS)

(degree)

Percent Difference

(LSDS/SDS - 1)*100

(percent)

No. 5 50.6 48.1 -2.5 -4.9

No. 56 37.7 50.3 12.6 33.4

No. 57 49.0 43.2 -5.8 -11.8

No. 6 53.9 45.2 -8.7 -16.1

No. 67 49.1 49.9 0.8 1.6

No. 68 36.9 47.0 10.1 27.4

No. 7 51.3 50.9 -0.4 -0.8

No. 78 44.2 49.2 5 11.3

No. 8A 37.3 51.8 14.5 38.9

No. 8B — 45.7 — —

No. 8C — 46.6 — —

No. 8D — 44.4 — —

No. 8E — 50.4 — —

No. 89 42.3 45.6 3.3 7.8

No. 9 52.0 49.8 -2.2 -4.2

No. 10 39.0 43.0 4 10.3

AASHTO = American Association of State Highway and Transportation Officials.

LSDS = Large-scale direct shear.

SDS = Standard direct shear.

ZDA = Zero dilation angle.

— = Not measured.

The results of the Ottawa sand and the No. 10 aggregate tests can more directly be compared for 

scale effects because no or very little scalping was needed. The average secant friction angle 

from SDS testing of Ottawa sand at 5 psi was 32.2 degrees; from LSDS testing, it was 

30.4 degrees. For the No. 10 aggregates, the difference is larger, up to 15.2 percent, with the SDS 

results also higher than the LSDS results. These findings are relatively consistent with research 

on sands in which larger devices resulted in lower measured friction angles for the same 

material.(54)

In contrast, the difference for the CV friction angles measured from SDS and LSDS tests is 

approximately 4 degrees, with the LSDS device producing a higher friction angle than that 

measured with the SDS device. This difference is considered negligible, however, because it is 

about 10 percent.

(85) With dilation negated through the ZDA approach, it is expected that the 

aggregate would have similar strength regardless of the size of the device, assuming that all other 

aspects are constant.

70
Data Interpretation

The use of the traditional MC approach results in the peak, or secant, friction angle at each 

applied normal stress, which can provide the tangent friction angle over the range tested. The 

ZDA approach, however, results in the constant volume friction angle, which is a measure at the 

critical state. The tangent and constant volume friction angle are not equivalent parameters. A 

comparison between the friction angles resulting from the MC and ZDA approaches indicates 

that the difference between the two is within 20 percent regardless of testing device (figure 46).

The choice of data interpretation method, unless specified, will often default to the MC approach 

because it is the most common. The linear MC interpretation, however, results in measured 

cohesion for each test because the y-intercept of the best-fit approximation is not zero. This 

inconsistency for these cohesionless materials is attributed to the fact that the failure envelope is 

actually nonlinear; there is also aggregate interlocking and dilation that occurs during shearing, 

depending on the applied normal stress. In reality, the friction angle decreases with increased 

applied normal stress in a logarithmic function. 

For the range of stresses tested, the secant friction angle corresponding to the peak for each 

applied normal stress was larger than that approximated from the MC approach. Because of these 

issues, an alternative ZDA method is proposed to determine the design friction angle. The ZDA 

approach reduces the friction angle to the critical state, thereby negating the effect of dilation 

from peak conditions. This approach helps reduce the amount of factors affecting the measured 

strength of aggregates and is theoretically the worst-case scenario.

71
Figure 46. Chart. Relationship between measured tangent and CV friction angles.

Effect of Saturation

Saturation was investigated in the LSDS device by performing tests under both dry and saturated 

conditions. Tests with saturation are considered drained tests because the material is freedraining, the water is free to move into and out of the sample, and the strain rate is relatively low 

to prevent build-up of pore pressures during testing. The measured friction angle results are 

shown in table 14 and table 15. Generally, for the samples larger than the No. 7 aggregates 

(dmax > 0.75 inches), the friction angles measured from the saturated tests using the MC approach 

were higher than from the dry tests, up to 15 percent (figure 47). The reverse trend was found for 

No. 7 and smaller aggregates (dmax ≤ 0.75 inches), where saturated testing produced lower 

friction angles. The biggest difference was for the No. 9 and No. 10 aggregates, where 

differences were up to 16 percent. Similar results are seen using the ZDA approach (figure 48).

For two-thirds of the aggregates (10 out of 15), the difference in measured tangent friction angles 

is within 10 percent. The results are similar for a larger population, almost 90 percent of the 

samples (13 out of 15), when using the ZDA approach. It is thought that saturation affects the 

dilative behavior, which is why the ZDA approach shows more negligible results. Overall, 

however, the difference between friction angles under dry and saturated conditions is within 

20 percent for all samples regardless of test method (figure 49). While saturated tests take longer 

to perform than dry tests because of the time needed to achieve saturation and to drain the water 

72
after testing, the test should ideally mimic in-service conditions; however, the effect for OGAs 

appears to be minimal.

Figure 47. Chart. Measured friction angles under dry and saturated LSDS testing using the 

MC approach.

73
Figure 48. Chart. Measured friction angles under dry and saturated LSDS testing using the 

ZDA approach.

74
Figure 49. Chart. Relationship between measured friction angles under dry and saturated 

conditions in the LSDS device.

4.3 STRENGTH CORRELATIONS

In the absence of shear testing, designers will sometimes refer to correlations between other 

measured parameters and the friction angle of the material. The results were therefore compared 

with standard testing parameters to determine whether simple trends or correlations exist for 

OGAs.

Gradation

It was found that when comparing the measured tangent and CV friction angles with the mean

aggregate size (d50, see table 6), there is a general trend whereby as the mean size increases, the 

friction angle also increases under LSDS testing (figure 50 and figure 51, respectively). This 

result is not observed for LDTX testing in which the tangent friction angle is independent of 

mean aggregate size; however, when looking at the secant friction angles results from LDTX 

testing, a small positive relationship is observed that diminishes as confining stress increases 

(figure 52). This relationship may be the result of the low relative density under which testing 

occurred (about 30 percent). For the LSDS testing confined in a rigid box, the friction angle may 

not be affected as much for this reason as with LDTX testing, which has a more flexible 

boundary. Similar relationships are found with other gradation limits (e.g., d10, d30, d60, d85) and 

with the FM. 

75
Figure 50. Chart. Relationship between tangent friction angle and median grain size.

Figure 51. Chart. Relationship between CV friction angle and median grain size.

76
Figure 52. Chart. Relationship between secant friction angle and median grain size for 

LDTX testing.

The coefficient of uniformity (Cu) is another important parameter; it helps describe whether a 

material is OG or well-graded. Based on the findings of this study, a clear relationship was not

found between the measured friction angles and the Cu for the materials (figure 53 and figure 

54). For OGAs, this lack of a relationship indicates that aggregate size plays more of a role than 

the overall gradation; however, the range of Cu values examined is relatively narrow. 

77
Figure 53. Chart. Relationship between tangent friction angle and Cu.

Figure 54. Chart. Relationship between CV friction angle and Cu.

78
Maximum Unit Weight

The samples were tested uncompacted at about 30 percent relative density, which was 

determined using the minimum and maximum unit weight of the OGAs found through vibratory 

table testing, described previously (table 7). By comparing the results for both LSDS and LDTX 

testing, it is found that the tangent friction angle is independent of the maximum density of the 

material (figure 55). A similar result is found when comparing the CV friction angle determined 

using LSDS testing and maximum unit weight (figure 56); however, there is a trend for the TX

results whereby as maximum unit weight increases, the constant volume decreases.

These results are contrary to the Naval Facilities Engineering Command (NAVFAC) correlation 

that shows friction angle increasing with increasing dry unit weight for a given relative 

density.

(86) Also contrary is that the estimated friction angle for a poorly graded gravel classified 

soil at 30 percent relative density is shown by NAVFAC as about 32 degrees, which is on the 

low side based on the measured test results in this study. More testing is needed on OGAs to 

investigate this discrepancy. 

Figure 55. Chart. Relationship between tangent friction angle and maximum unit weight.

79
Figure 56. Chart. Relationship between CV friction angle and maximum unit weight.

Repose Angle

Others have postulated that the repose angle is equal to the constant volume friction angle; 

however, this theory is based on the behavior of soils.(10,87) For the OGAs tested, however, the 

CV friction angle is greater than the repose angle, with no clear relationship found between the 

measured repose angle and CV friction angle (figure 57).

80
Figure 57. Chart. Relationship between CV friction angle and repose angle.

Angularity, Texture, and Sphericity

Angularity, texture, and sphericity were all described in this study with AIMS2 (table 9). The 

tangent and CV friction angles measured with the LSDS device show an inverse relationship 

with the average angularity index (figure 58 and figure 59, respectively). While this result is 

contrary to expectations, it is postulated that as the aggregates get more angular, there is less 

contact area between the particles and a higher void ratio (i.e., less dense). Higher void ratios 

typically result in lower friction angles (figure 60).

81
Figure 58. Chart. Relationship between tangent friction angle and angularity.

Figure 59. Chart. Relationship between CV friction angle and angularity.

82
Figure 60. Relationship between initial void ratio and tangent friction angle.

Because all of the aggregates have the same classification for angularity, however, it is difficult 

to make a definitive conclusion. Texture was found to not influence the measured tangent 

friction angle (figure 61) or the CV friction angle.

Figure 61. Chart. Relationship between CV friction angle and texture.

83
Sphericity does play a role in LSDS test results; as the average sphericity index increases, the 

friction angle also increases (figure 62 and figure 63). As with many of the other parameters, the 

LDTX results are independent of the sphericity. With the forced failure plane in LSDS testing, 

sphericity (the general roundness of the aggregates) affects the amount of dilation that occurs. 

Assuming the same angularity, flat/elongated particles will more easily slide past one another 

than rounded particles. 

The measured angularity indexes help explain the variation between the various No. 8 aggregates 

tested, regardless of data interpretation (figure 64 and figure 65). To a lesser extent, sphericity 

influences the results as well (figure 66). Additional testing is needed to expand the database and 

develop design equations to correlate angularity with friction angle for all relevant AASHTO 

OGAs.

Figure 62. Chart. Relationship between tangent friction angle and sphericity.

84
Figure 63. Chart. Relationship between CV friction angle and sphericity.

Figure 64. Chart. Relationship between tangent friction angle and angularity in LSDS 

testing for AASHTO No. 8 aggregates.

85
Figure 65. Chart. Relationship between CV friction angle and angularity in LSDS testing 

for AASHTO No. 8 aggregates.

Figure 66. Chart. Relationship between tangent friction angle and sphericity in LSDS 

testing for AASHTO No. 8 aggregates.

86
CHAPTER 5. CONCLUSIONS

Sixteen AASHTO M43 gradations, ranging from an AASHTO No. 10 to an AASHTO No. 5 

aggregate, were characterized in this study, including their gradation, minimum and maximum 

density, repose angle, angularity, and texture. In addition, LSDS and LDTX tests were conducted 

on the samples, compacted at a relative density of approximately 30 percent, to evaluate the 

strength. The results provide insight into the strength behavior of manufactured OGAs.

5.1 FRICTION ANGLE

Transportation agencies use OGAs as structural backfill for road and bridge construction, yet 

their strength parameters are not fully understood. To address this need, a comprehensive study 

was initiated, with the primary objectives to quantify the strength parameters, evaluate different 

conventional testing devices, and determine the influence of various factors on strength. The 

results indicate that the typical default friction angle of 34 degrees is a conservative measure 

(table 23). It is important to note that the reported friction angles are from samples tested at 

30 percent relative density. In the field, compaction would result in added strength; therefore, the 

friction angles reported herein are considered conservative.

Table 23. Summary of LSDS and LDTX testing.

Sample

MC Tangent Friction Angle ZDA CV Friction Angle (degree)

LSDS

(degree)

LDTX

(degree) LSDS LDTX

No. 5 55.3 36.5 44.6 39.7

No. 56 54.4 39.5 52.9 39.4

No. 57 52.1 40.5 52.9 38.4

No. 6 57.5 36.4 51.7 36.8

No. 67 57.3 39.0 53.7 36.6

No. 68 48.7 38.1 47.9 38.7

No. 7 48.9 38.4 49.0 36.9

No. 78 44.9 34.9 45.5 38.3

No. 8A 46.9 — 50.3 —

No. 8B 41.6 — 45.5 —

No. 8C 41.9 — 45.8 —

No. 8D 37.5 — 42.1 —

No. 8E 46.8 39.3 45.6 37.5

No. 89 41.2 38.3 45.8 40.3

No. 9 42.9 38.4 45.5 39.4

No. 10 37.1 40.1 42.0 34.8

CV = Constant volume.

LDTX = Large-diameter triaxial.

LSDS = Large-scale direct shear.

MC = Mohr-Coulomb.

ZDA = Zero dilation angle.

— = Not measured.

87
Two methods for determining the friction angle were investigated for comparison: (1) the slope 

of the best-fit linear MC failure envelope as in current practice, and (2) the ZDA approach. When 

combining all the results from every aggregate, the tangent friction angle was 48.2 and 

38.4 degrees for LSDS and LDTX testing, respectively. Similarly, the CV friction angle from the 

ZDA method was 46.1 and 38.9 degrees for LSDS and LDTX testing, respectively (figure 67). 

Based on a typical COV of 5 to 10 percent for lab testing, and using the ZDA method for LSDS 

testing, the recommended default friction angle for AASHTO OGAs is 41 degrees.(85)

Figure 67. ZDA Approach for LDTX and LSDS testing.

Regardless of the approach, the results are similar; however, the ZDA method offers more 

confidence as a conservative estimate for strength. The linear MC method resulted in more data 

scatter and produces a measured cohesion value for a cohesionless material. The ZDA method 

also provides a consistent basis for obtaining the friction angle at the critical state but requires an 

extra step in the analysis to determine the dilation angle. Other methods such as measuring the 

secant friction angle at a given confining stress are available but rely on a design assumption that 

confining stress will remain constant throughout the life of the structure.

5.2 TEST METHOD

The selection of the test device to measure strength plays an important role. The LDTX device 

resulted in strengths that were considerably lower than those measured in the LSDS device. The 

difference in results generally increases with increasing aggregate size. The dilation angles 

88
determined from the LDTX device are also lower than those measured with the LSDS device 

(about 60 percent) because there is a forced failure plane during the LSDS test, causing more 

dilation. The difference in dilatancy from each test device helps explain the lower friction angles 

measured with LDTX because dilation is a component in the strength of aggregates. Because the

contribution of dilation is different depending on whether the LDTX or LSDS test is employed 

(which suggests that there is a trend with dilation but not with tangent or CV friction angles 

between LDTX and LSDS results), it is clear that more factors are contributing to the strength 

between the two devices.

The SDS device was also investigated to evaluate a common practice of scalping the sample. To 

use a 2.5-inch-diameter SDS device, aggregates larger than 0.25 inches must be removed from 

each test sample. The SDS results of the scalped samples indicated friction angles that were still 

considerably greater than the default of 34 degrees. There was no clear relationship between the

scalped and unscalped results determined from SDS and LSDS testing, respectively, with friction 

angles largely between 10 and 20 percent different. While the overall strength values were 

similar, the scalping process changes the dilation properties of the aggregates, with relative 

differences ranging from 15 to 65 percent; no trend was found. In addition, the initial void ratio 

also changed, which has an impact on strength. Overall, scalped samples are unrepresentative of 

field behavior and lead to uncertainty in the results. 

The effect of saturation was evaluated in the LSDS device. For two-thirds of the aggregates (10 

out of 15), the difference in the tangent friction angles between saturated and dry conditions was 

within 10 percent. The results were similar for a larger population—almost 90 percent of the 

samples (13 out of 15)—when using the ZDA method. It is thought that saturation reduces the 

dilative behavior, which is why the ZDA approach shows more negligible results. Overall, the 

difference between friction angles under dry and saturated conditions was within 20 percent for 

all samples regardless of test method. While the test should ideally mimic in-service conditions,

the effect of saturation for OGAs appears minimal.

To take advantage of the strength of these engineered aggregates for more cost-effective designs, 

large-scale testing is recommended. The selection of LSDS versus LDTX testing depends on the 

use of the results and other factors. For example, if the friction angle is the only parameter 

needed, then the LSDS device is quicker and simpler to perform. The LDTX test can offer more 

information about the deformation behavior but is more complex, time consuming, and costly to 

perform. 

Both the LSDS and LDTX devices produce friction angles that are theoretically less than PS

conditions. The result from either device is appropriate in design; however, in most cases, the 

LSDS results would produce more cost-effective structures. In typical applications utilizing 

OGAs, such as in reinforced soil retaining walls and bridge foundations, the aggregates will be 

confined in a PS condition, which the LSDS device would more adequately mimic as compared 

with the LDTX device

5.3 STRENGTH CORRELATIONS

Correlations between various soil properties and parameters were investigated, but no direct 

relationship was found that designers can use in the absence of strength testing. LDTX results 

89
were independent of the various parameters; however, there were general trends found for LSDS 

testing. The strongest relationships were observed when comparing the aggregate size, 

angularity, void ratio, and sphericity to strength. There was no relationship between the 

measured friction angle and the coefficient of uniformity, maximum unit weight, repose angle, 

and aggregate texture; however, these poor correlations could potentially be the result of the 

relatively small differences between the physical parameters for the aggregates tested in this 

study.

As the mean aggregate size increased, the friction angle also increased. The tangent and CV 

friction angles measured with the LSDS device show an inverse relationship with the average 

angularity index. While this result is contrary to expectations, it is postulated that as the 

aggregates gets more angular, there is less contact area between the particles and a higher void 

ratio (i.e., less dense), and higher void ratios typically result in lower friction angles. There is a 

positive trend with sphericity, however, whereby as the average sphericity index increases, the 

friction angle also increases. With the forced failure plane in LSDS testing, sphericity affects the 

amount of dilation that occurs. 

5.4 FUTURE RESEARCH

This study was the first to systematically test and characterize AASHTO OGAs. While many 

insightful results were produced, additional research is needed before concrete design 

recommendations can be proposed. A database of multiple sources of each OGA is needed to 

quantify the material variability to determine appropriate confidence intervals. The impact of 

relative density on the strength will also be investigated. In addition, the results presented 

utilized material that was retested for each confining stress; the influence and practicality of 

using virgin material for each test will be studied. Until this range of research is conducted, 

readers are encouraged to understand and take advantage of the strength of these OGAs in 

design. Testing can then be used to facilitate the use of higher than 34-degree default values

90
APPENDIX A. RAW DATA 

NO. 5

Figure 68. Photo. No. 5 aggregate sample.

91
Table 24. No. 5 gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan 

(kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

1.5 1.5 1,476 1,476 0 0.00 100.00

1 1 2,443.8 1,453 990.8 13.06 86.94

0.75 0.75 5,974.3 1,393.2 4,581.1 60.36 26.58

0.50 0.5 2,955.3 1,087.8 1,867.5 24.61 1.98

0.375 0.375 1,208.3 1,102.6 105.7 1.39 0.58

4 0.187 1,524.3 1,515 9.3 0.12 0.46

8 0.0937 1,129.2 1,129.2 0 0.00 0.46

16 0.0469 910.1 909.8 0.3 0.00 0.46

200 0.0029 930.7 916.4 14.3 0.19 0.27

Pan — 690.2 669.8 20.4 0.27 0.00

Table 25. No. 5 density.

Sample

Minimum Density (pfc) ASTM D4254 Maximum Density (pcf) ASTM D4253

Test 1

Test 

2

Test 

3 Average

Standard

Deviation Test 1 Test 2 Average

Standard

Deviation

No. 5 94.7 95.6 94.5 94.9 0.6 109.8 109.3 109.6 0.4

Table 26. No. 5 repose angle.

Angle Finder String Method Average

Repose 

Test 1 2 3 4 5 Average Angle

Circumference 

(inches) Angle Average

1 30 30 35 32 32

30.13

50 32.74

2 30 31 28 30 32 51.375 30.65 31.53 30.83

3 28 30 26 29 29 51 31.21

Table 27. No. 5 standard DS results.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Max Dilation Angle

(degree)

5.13 8.74 59.61 8.37

10.05 18.62 61.64 9.82

20.02 31.04 57.18 9.55

30.07 49.57 58.76 9.28

92
Table 28. No. 5 LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Max Dilation Angle

(degree)

5.59 17.30 72.10 21.48

11.27 30.53 69.74 16.58

22.72 40.45 60.68 10.42

34.17 50.55 55.94 7.41

Table 29. No. 5 LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Max Dilation Angle

(degree)

5.69 12.17 64.93 15.86

11.10 24.91 65.99 14.75

22.36 34.62 57.15 10.92

34.24 56.10 58.60 9.46

Table 30. No. 5 LDTX results.

'1 (psi) '3 (psi) 's (degree) max (degree)

5.22 42.32 51.31 12.23

10.12 63.25 46.42 9.99

20.05 103.81 42.55 3.88

30.01 139.98 40.25 0.00

σ σ φ ψψ

93
NO. 56

Figure 69. Photo. No. 56 aggregate sample.

Table 31. No. 56 gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan 

(kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

1.5 1.5 1,475.9 1,475.9 0 0.00 100.00

1 1 1,421 1,127.1 293.9 4.27 95.73

0.75 0.75 2,109.9 1,393.21 716.69 10.42 85.31

0.50 0.5 4,203.1 1,087.95 3,115.15 45.27 40.04

0.375 0.375 2,821.4 1,102.79 1,718.61 24.98 15.07

4 0.187 2,374.5 1,514.98 859.52 12.49 2.58

8 0.0937 1,253.2 1,129.04 124.16 1.80 0.77

16 0.0469 922.5 909.95 12.55 0.18 0.59

50 0.0117 749.9 741.69 8.21 0.12 0.47

200 0.0029 928.4 916.46 11.94 0.17 0.30

Pan — 620.9 600.56 20.34 0.30 0.00

94
Table 32. No. 56 density.

Sample

Minimum Density (pfc) ASTM D4254 Maximum Density (pcf) ASTM D4253

Test 

1

Test 

2

Test 

3 Average

Standard 

Deviation

Test 

1

Test 

2 Average

Standard

Deviation

No. 56 100.4 100.4 101.8 100.9 0.8 108.5 99.1 103.8 6.6

Table 33. No. 56 repose angle.

Test Angle Finder String Method

Average Repose 

Angle

1 35 35 32 28 33

31.4

52.75 28.70

2 32 30 27 25 30 53 28.36 29.55 30.48

3 33 30 33 34 34 50.75 31.59

Table 34. No. 56 standard DS results.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.43 12.81 67.03 19.94

10.05 22.17 65.61 17.10

20.24 34.26 59.43 12.85

30.14 50.04 58.94 13.28

Table 35. No. 56 LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.54 9.97 60.94 14.96

10.72 17.91 59.10 12.05

22.03 35.91 58.47 10.49

33.04 50.52 56.82 9.94

Table 36. No. 56 LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.66 11.34 63.47 15.15

11.05 22.98 64.32 14.46

22.36 38.18 59.65 7.14

32.98 50.44 56.82 7.44

95
Table 37. No. 57 LDTX results.

'1 (psi) '3 (psi) 's (degree) max (degree)

34.59 5.21 47.58 11.73

65.42 10.23 46.85 9.95

110.50 20.05 43.86 6.46

146.86 30.12 41.27 2.63

NO. 57 

Figure 70. Photo. No. 57 aggregate sample.

σ σ φ ψψ

96
Table 38. No. 57 gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan 

(kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

1 1 1,127.1 1,127.1 0 0.00 100.00

0.75 0.75 2,311 1,393.4 917.6 12.09 87.91

0.50 0.5 5,052.1 1,087.8 3,964.3 52.22 35.69

0.375 0.375 2,739.5 1,102.7 1,636.8 21.56 14.13

4 0.187 2,308.8 1,514.8 794 10.46 3.67

8 0.0937 1,224.5 1,128.9 95.6 1.26 2.41

16 0.0469 981.1 909.8 71.3 0.94 1.47

200 0.0029 974.5 916.7 57.8 0.76 0.71

Pan — 723.3 669.7 53.6 0.71 0.00

Table 39. No. 57 density.

Sample

Minimum Density (pfc) ASTM D4254 Maximum Density (pcf) ASTM D4253

Test 

1

Test 

2

Test 

3 Average

Standard 

Deviation

Test 

1

Test 

2 Average

Standard

Deviation

No. 57 95.1 96.0 95.1 95.4 0.5 108.1 109.3 108.7 0.8

Table 40. No. 57 repose angle.

Test Angle Finder String Method

Average Repose 

Angle

1 30 30 30 32 30

29.67

50.75 31.59

2 31 30 27 30 26 52 29.75 30.79 30.23

3 27 29 29 34 30 51.125 31.02

Table 41. No. 57 standard DS results.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.74 12.59 65.48 28.11

10.29 16.88 58.64 16.79

20.51 37.50 61.33 18.10

29.73 52.45 60.45 13.06

Table 42. No. 57 LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.49 17.55 72.62 15.36

10.81 21.19 62.96 13.15

22.23 40.21 61.07 9.93

33.22 47.19 54.85 6.28

97
Table 43. No. 57 LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.52 13.23 67.35 15.66

11.14 23.01 64.16 10.58

22.63 37.33 58.77 5.94

33.97 50.37 56.00 3.28

Table 44. No. 57 LDTX results.

'1 (psi) '3 (psi) 's (degree) max (degree)

37.09 5.11 49.28 12.15

61.16 10.21 45.55 10.17

114.64 20.15 44.51 7.03

152.52 30.12 42.08 4.35

NO. 6

Figure 71. Photo. No. 6 aggregate sample.

σ σ φ ψψ

98
Table 45. No. 6 gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (kg)

Mass of 

Pan 

(kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

1 1 1,127.1 1,127.1 0 0.00 100.00

0.75 0.75 1,640.8 1,393.3 2,47.5 3.83 96.17

0.50 0.5 4,210.5 1,087.8 3,122.7 48.27 47.91

0.375 0.375 3,365 1,102.5 2,262.5 34.97 12.94

4 0.187 2,110.7 1,514.6 596.1 9.21 3.72

8 0.0937 1,207.1 1,129.1 78 1.21 2.52

200 0.0029 990.9 916.5 74.4 1.15 1.37

Pan — 758 669.6 88.4 1.37 1.15

Table 46. No. 6 density.

Sample

Minimum Density (pfc) ASTM D4254 Maximum Density (pcf) ASTM D4253

Test 

1

Test 

2

Test 

3 Average

Standard 

Deviation

Test 

1

Test 

2 Average

Standard

Deviation

No. 6 100.8 100.8 101.3 101.0 0.3 116.3 104.2 110.3 8.6

Table 47. No. 6 repose angle.

Test Angle Finder String Method

Average Repose 

Angle

1 33 33 31 33 32

31.2

52.175 29.50

2 32 31 28 29 30 52 29.75 29.67 30.43

3 31 35 36 25 29 52 29.75

Table 48. No. 6 standard DS results.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.134 11.86186 66.60 7.00

10.13 20.50297 63.71 7.20

20.14 38.43 62.34 10.68

30.13 53.4429 60.59 9.22

Table 49. No. 6 LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.36 13.16 67.83 19.30

11.13 21.42 62.54 14.28

21.18 40.18 62.21 15.57

33.10 53.92 58.45 11.45

99
Table 50. No. 6 LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.35 15.00 70.36 17.30

10.78 20.17 61.88 15.83

21.58 38.40 60.67 11.26

32.57 56.84 60.19 8.28

Table 51. No. 6 LDTX results.

'1 (psi) '3 (psi) 's (degree) max (degree)

29.43 5.13 44.66 9.74

51.71 10.09 42.33 9.12

90.16 20.04 39.52 3.71

127.48 30.05 38.21 1.97

NO. 67

Figure 72. Photo. No. 67 aggregate sample.

σ σ φ ψψ

100
Table 52. No. 67 gradation.

Sieve 

No.

Sieve

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan 

(kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

1 1 1,127.1 1,127.1 0 0.00 100.00

0.75 0.75 1,622.1 1,393.3 228.8 3.09 96.91

0.50 0.5 3,356.9 1,087.8 2269.1 30.67 66.24

0.375 0.375 2,783.2 1,102.7 1680.5 22.71 43.52

4 0.187 4,442.4 1,514.9 2927.5 39.57 3.96

8 0.0937 1,345.1 1,128.9 216.2 2.92 1.03

16 0.0469 914.2 909.9 4.3 0.06 0.98

50 0.0117 745 741.6 3.4 0.05 0.93

200 0.0029 928.6 916.7 11.9 0.16 0.77

Pan — 726.6 669.7 56.9 0.77 0.00

Table 53. No. 67 density.

Sample

Minimum Density (pfc) ASTM D4254 Maximum Density (pcf) ASTM D4253

Test 

1

Test 

2

Test 

3 Average

Standard 

Deviation

Test 

1

Test 

2 Average

Standard

Deviation

No. 67 105.8 107.7 105.1 106.2 1.3 122.9 125.2 124.1 1.6

Table 54. No. 67 repose angle.

Test Angle Finder String Method

Average Repose 

Angle

1 28 27 28 29 29

27.6

52.25 29.40

2 29 27 29 30 26 52.75 28.70 28.38 27.99

3 27 27 25 26 27 54 27.04

Table 55. No. 67 standard DS results.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.311 15.2042 70.75 14.72

10.25 28.5173 70.23 16.62

20.04 49.13 67.81 11.65

30.25 65.2277 65.12 10.30

101
Table 56. No. 67 LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.34 10.93 63.94 17.39

10.73 20.05 61.84 11.90

21.97 34.77 57.71 9.15

32.41 47.48 55.68 8.03

Table 57. No. 67 LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.41 11.03 63.89 15.34

10.89 22.87 64.55 12.69

21.84 37.99 60.10 11.11

33.29 55.53 59.06 7.41

Table 58. No. 67 LDTX results.

'1 (psi) '3 (psi) 's (degree) max (degree)

32.13 5.13 46.42 11.02

57.28 10.28 44.09 8.50

100.00 20.05 41.76 5.70

142.31 30.05 40.64 4.61

σ σ φ ψψ

102
NO. 68 

Figure 73. Photo. No. 68 aggregate sample.

Table 59. No. 68 gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan 

(kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

0.75 0.75 1,393.4 1,393.4 0 0.00 100.00

0.50 0.5 2,943.3 1,088 1,855.3 31.56 68.44

0.375 0.375 2,818.9 1,102.7 1,716.2 29.19 39.25

4 0.187 3,387.1 1,514.8 1,872.3 31.85 7.40

8 0.0937 1,446.8 1,128.9 317.9 5.41 2.00

16 0.0469 938.5 909.8 28.7 0.49 1.51

50 0.0117 741.6 741.6 0 0.00 1.51

200 0.0029 949.7 918.2 31.5 0.54 0.97

Pan — 727.1 670 57.1 0.97 0.00

103
Table 60. No. 68 density.

Sample

Minimum Density (pfc) ASTM D4254 Maximum Density (pcf) ASTM D4253

Test 

1

Test 

2

Test 

3 Average

Standard 

Deviation

Test 

1

Test 

2 Average

Standard

Deviation

No. 68 98.1 96.2 96.4 96.9 1.0 116.6 115.1 115.9 1.1

Table 61. No. 68 repose angle.

Test Angle Finder String Method

Average Repose 

Angle

1 31 36 30 32 32

31.27

52.125 29.57

2 33 30 33 29 33 52 29.75 29.46 30.36

3 29 32 31 28 30 52.5 29.05

Table 62. No. 68 standard DS results.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.456 13.60408 68.15 19.20

10.2 22.662 65.77 13.91

20.04 32.53 58.36 9.67

30.3 44.2085 55.57 9.52

Table 63. No. 68 LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.48 9.85 60.90 13.05

10.95 19.70 60.92 10.19

22.90 27.71 50.42 3.51

32.98 41.90 51.79 4.04

Table 64. No. 68 LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.39 8.82 58.56 13.82

11.08 15.59 54.59 7.37

22.55 24.78 47.69 1.44

32.92 41.37 51.49 3.05

104
Table 65. No. 68 LDTX results.

'1 (psi) '3 (psi) 's (degree) max (degree)

29.73 5.20 44.61 8.64

52.60 10.16 42.54 5.95

90.90 20.04 39.70 1.34

135.42 30.01 39.58 1.25

NO. 7

Figure 74. Photo. No. 7 aggregate sample.

σ σ φ ψψ

105
Table 66. No. 7 gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (kg)

Mass of 

Pan 

(kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

0.75 0.75 1,393.3 1,393.3 0 0.00 100.00

0.50 0.5 1,398.8 1,087.8 311 5.28 94.72

0.375 0.375 3,408.1 1,102.6 2,305.5 39.17 55.55

4 0.187 4,180.3 1,514.7 2,665.6 45.28 10.26

8 0.0937 1,545.1 1,128.9 416.2 7.07 3.19

200 0.0029 1,014.3 916.4 97.9 1.66 1.53

Pan — 759.9 669.8 90.1 1.53 1.66

Table 67. No. 7 density.

Sample

Minimum Density (pfc) ASTM D4254 Maximum Density (pcf) ASTM D4253

Test 

1

Test 

2

Test 

3 Average

Standard 

Deviation

Test 

1

Test 

2 Average

Standard

Deviation

No. 7 102.6 103.6 103.7 103.3 0.6 120.4 121.3 120.9 0.6

Table 68. No. 7 repose angle.

Test Angle Finder String Method

Average Repose 

Angle

1 29 28 28 32 25

29.3333

53.5 27.69

2 30 27 30 29 30 54.25 26.72 27.94 28.63

3 33 31 31 29 28 52.25 29.40

Table 69. No. 7 standard DS results.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.81 15.9929 70.03 30.05

10.33 28.7211 70.22 18.61

20.26 39.15 62.64 17.03

30.63 60.6459 63.20 21.99

Table 70. No. 7 LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.36 10.63 63.25 18.21

10.74 20.47 62.32 14.72

21.70 36.67 59.39 11.22

32.85 48.62 55.95 7.88

106
Table 71. No. 7 LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.30 10.03 62.15 16.88

10.62 18.37 59.98 12.80

21.41 33.41 57.34 8.48

32.98 41.58 51.58 4.39

Table 72. No. 7 LDTX results.

'1 (psi) '3 (psi) 's (degree) max (degree)

33.09 5.23 46.65 13.58

55.98 10.17 43.82 10.12

101.23 20.25 41.80 6.73

139.31 30.19 40.08 4.45

NO. 78

Figure 75. Photo. No. 78 aggregate sample.

σ σ φ ψψ

107
Table 73. No. 78 gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan (kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

0.75 0.75 0 1,393.3 0 0.00 100.00

0.50 0.5 1,096.3 1,087.9 8.4 0.12 99.88

0.375 0.375 2,791.8 1,102.7 1,689.1 24.07 75.81

4 0.187 6,401.5 1,515 4,886.5 69.63 6.18

8 0.0937 1,503.8 1,129 374.8 5.34 0.84

16 0.0469 929.6 910.2 19.4 0.28 0.57

50 0.0117 747.6 741.5 6.1 0.09 0.48

100 0.0059 814.6 809.4 5.2 0.07 0.41

200 0.0029 923.1 916.4 6.7 0.10 0.31

Pan — 691.6 669.8 21.8 0.31 0.00

Table 74. No. 78 density.

Sample

Minimum Density (pfc) ASTM D4254 Maximum Density (pcf) ASTM D4253

Test 

1

Test 

2

Test 

3 Average

Standard 

Deviation

Test 

1

Test 

2 Average

Standard

Deviation

No. 78 93.2 92.5 91.2 92.3 1.0 110.1 109.1 109.6 0.7

Table 75. No. 78 repose angle.

Test Angle Finder String Method

Average Repose 

Angle

1 33 33 30 35 31

33.6

50.75 31.59

2 34 34 35 30 33 50 32.74 32.62 33.11

3 36 34 35 36 35 49.5 33.53

Table 76. No. 78 standard DS results.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.608 16.1631 70.87 21.60

10.53 26.6066 68.41 17.87

20.37 42.82 64.56 11.81

30.26 56.4644 61.81 10.87

108
Table 77. No. 78 LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.48 8.77 58.00 12.38

10.78 17.36 58.17 8.49

21.49 30.29 54.65 6.77

32.62 42.35 52.39 7.41

Table 78. No. 78 LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.40 8.43 57.32 9.42

10.98 15.81 55.22 6.07

21.99 24.90 48.56 3.02

32.77 36.55 48.12 1.93

Table 79. No. 78 LDTX results.

'1 (psi) '3 (psi) 's (degree) max (degree)

32.44 5.16 46.49 8.31

54.01 10.15 43.13 5.38

92.61 20.02 40.13 0.84

123.08 29.94 37.49 0.00

σ σ φ ψψ

109
NO. 8A (DEFIANCE)

Figure 76. Photo. No. 8A aggregate sample.

Table 80. No. 8A gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan (kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

0.50 0.5 0 1,087.9 0 0.00 100.00

0.375 0.375 1,314.4 1,102.7 211.7 3.01 96.99

4 0.187 6,469.6 1515 4,954.6 70.49 26.50

8 0.0937 2,666.2 1129 1,537.2 21.87 4.63

16 0.0469 1,105.3 910.2 195.1 2.78 1.85

50 0.0117 807.6 741.5 66.1 0.94 0.91

100 0.0059 820.1 809.4 10.7 0.15 0.76

200 0.0029 924.1 916.4 7.7 0.11 0.65

Pan — 715.4 669.8 45.6 0.65 0.00

110
Table 81. No. 8A density.

Sample

Minimum Density (pfc) ASTM D4254 Maximum Density (pcf) ASTM D4253

Test 

1

Test 

2

Test 

3 Average

Standard 

Deviation

Test 

1

Test 

2 Average

Standard

Deviation

No. 8A 86.2 85.3 85.7 85.7 0.5 101.3 101.3 101.3 0.0

Table 82. No. 8A repose angle.

Test Angle Finder String Method

Average Repose 

Angle

1 30 32 30 30 32

31.1333

51.5 30.47

2 32 34 31 32 33 51.25 30.84 30.78 30.96

3 30 30 30 31 30 51.125 31.02

Table 83. No. 8A standard DS results.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.41 10.77703 63.34 17.97

10.50 21.74814 64.23 20.87

20.56 38.72 62.03 19.89

30.4 47.9136 57.61 15.47

Table 84. No. 8A LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.31 9.51 60.84 12.96

10.76 19.06 60.57 11.65

21.40 30.53 54.97 6.35

32.40 45.65 54.64 5.63

Table 85. No. 8A LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.36 10.08 61.98 11.06

10.89 14.32 52.74 5.58

21.71 26.68 50.87 1.70

33.16 39.28 49.83 1.93

111
NO. 8B (STAUNTON LIME)

Figure 77. Photo. No. 8B aggregate sample.

Table 86. No. 8B gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan (g)

Mass of Soil 

(g)

Percent

Retained

Percent

Passing

0.75 0.75 1,189.4 1,189.4 0 0.00 100.00

0.50 0.5 1,398.1 1,386.4 11.7 0.19 99.81

0.375 0.375 2,101.9 1,171.1 930.8 14.93 84.88

4 0.187 5,961.1 1,514.5 4,446.6 71.32 13.56

8 0.0937 1,774.1 1,041.7 732.4 11.75 1.82

16 0.0469 945.9 910.6 35.3 0.57 1.25

50 0.0117 811.9 799 12.9 0.21 1.04

100 0.0059 747.5 743 4.5 0.07 0.97

200 0.0029 745.6 737.4 8.2 0.13 0.84

Pan — 739.9 687.6 52.3 0.84 0.00

112
Table 87. No. 8B LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.55 7.73 54.35 8.50

11.18 13.84 51.06 4.20

22.15 26.53 50.14 2.53

34.09 34.26 45.14 1.08

Table 88. No. 8B LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.55 8.63 57.26 8.99

11.08 15.25 54.00 4.80

22.86 23.60 45.91 1.00

34.02 34.78 45.64 0.00

NO. 8C (FRAZIER)

Figure 78. Photo. No. 8C aggregate sample.

113
Table 89. No. 8C gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan (kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

0.75 0.75 1,189.4 1,189.4 0 0.00 100.00

0.50 0.5 1,386.4 1,386.4 0 0.00 100.00

0.375 0.375 1,783.6 1,171.1 612.5 9.70 90.30

4 0.187 6,838 1,514.5 5,323.5 84.32 5.98

8 0.0937 1,355.2 1,041.7 313.5 4.97 1.02

16 0.0469 919.4 910.6 8.8 0.14 0.88

50 0.0117 801.9 799 2.9 0.05 0.83

100 0.0059 745.2 743 2.2 0.03 0.80

200 0.0029 743.5 737.5 6 0.10 0.70

Pan — 750.4 669.8 80.6 0.88 0.00

Table 90. No. 8C LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.45 10.16 61.77 12.35

10.94 17.93 58.60 9.90

22.07 33.96 56.98 7.29

34.30 42.03 50.79 3.85

Table 91. No. 8C LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.43 9.38 59.93 11.19

11.11 13.75 51.06 3.83

22.78 25.91 48.68 1.91

34.06 34.42 45.30 0.00

114
NO. 8D (VULCAN MATERIALS)

Figure 79. Photo. No. 8D aggregate sample.

Table 92. No. 8D gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan (g)

Mass of Soil 

(g)

Percent

Retained

Percent

Passing

0.50 0.5 1,386.4 1,386.4 0 0.00 100.00

0.375 0.375 1,550 1,171.1 378.9 5.97 94.03

4 0.187 6,416.4 1,514.5 4,901.9 77.18 16.86

8 0.0937 1,989.2 1,041.8 947.4 14.92 1.94

16 0.0469 973.6 910.6 63 0.99 0.95

50 0.0117 817.7 798.9 18.8 0.30 0.65

100 0.0059 747.3 742.9 4.4 0.07 0.58

200 0.0029 750.4 737.6 12.8 0.20 0.38

Pan — 711.8 687.6 24.2 0.38 0.00

115
Table 93. No. 8D LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.46 10.22 61.87 10.51

11.43 15.43 53.48 6.23

23.03 25.72 48.16 1.20

35.28 33.10 43.17 0.00

Table 94. No. 8D LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.57 8.28 56.08 7.33

12.37 13.99 48.51 3.81

23.99 22.48 43.15 0.00

36.24 31.96 41.41 0.00

NO. 8E (LUCK STONE)

Figure 80. Photo. No. 8E aggregate sample.

116
Table 95. No. 8E gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan (kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

1 1 1,127.1 1,127.1 0 0.00 100.00

0.50 0.5 1,116.5 1,087.7 28.8 0.31 99.69

0.375 0.375 3,832 1,102.6 2,729.4 29.83 69.86

4 0.187 6,694.3 1,013.8 5,680.5 62.08 7.78

8 0.0937 1,688.5 1,128.7 559.8 6.12 1.66

10 0.079 1,398.7 1,374 24.7 0.27 1.39

16 0.0469 935 909.7 25.3 0.28 1.11

40 0.0165 810 793.1 16.9 0.18 0.93

50 0.0117 746.2 741.8 4.4 0.05 0.88

Pan — 750.4 669.8 80.6 0.88 0.00

Table 96. No. 8E density.

Sample

Minimum Density (pfc) ASTM D4254 Maximum Density (pcf) ASTM D4253

Test 

1

Test 

2

Test 

3 Average

Standard. 

Deviation.

Test 

1

Test 

2 Average

Standard

Deviation

No. 8E 97.3 98.4 97.9 97.9 0.6 111.1 114.5 112.8 2.4

Table 97. No. 8E LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.38 15.22 70.53 17.80

10.86 26.73 67.90 12.40

21.62 39.89 61.55 10.04

33.51 52.55 57.47 6.51

Table 98. No. 8E LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.46 11.00 63.59 16.46

10.89 18.57 59.60 12.66

22.07 35.24 57.94 9.89

33.38 39.74 49.97 4.47

117
Table 99. No. 8E LDTX results.

'1 (psi) '3 (psi) 's (degree) max (degree)

40.70 5.43 49.86 15.89

69.68 10.44 47.68 13.24

121.65 20.30 45.56 9.28

154.29 30.20 42.27 5.20

NO. 89

Figure 81. Photo. No. 89 aggregate sample.

σ σ φ ψψ

118
Table 100. No. 89 gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan (kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

0.75 0.75 0 1,393.2 0 0.00 100.00

0.50 0.5 1,092.6 1,087.8 4.8 0.08 99.92

0.375 0.375 1,280.5 1,102.7 177.8 2.93 96.99

4 0.187 4,543.2 1,514.7 3,028.5 49.98 47.01

8 0.0937 3,313.7 1,128.8 2,184.9 36.06 10.95

16 0.0469 1,312.3 909.7 402.6 6.64 4.31

50 0.0117 882 741.5 140.5 2.32 1.99

200 0.0029 937.9 916.4 21.5 0.35 1.63

Pan — 768.7 669.8 98.9 1.63 0.00

Table 101. No. 89 density.

Sample

Minimum Density (pfc) ASTM D4254 Maximum Density (pcf) ASTM D4253

Test 

1

Test 

2

Test 

3 Average

Standard 

Deviation

Test 

1

Test 

2 Average

Standard

Deviation

No. 89 88.9 89.5 86.8 88.4 1.4 107.0 109.4 108.2 1.7

Table 102. No. 89 repose angle.

Test Angle Finder String Method

Average Repose 

Angle

1 32 30 29 30 31

29.87

51 31.21

2 27 29 30 30 30 50 32.74 31.60 30.73

3 29 31 30 29 31 51.25 30.84

Table 103. No. 89 standard DS results.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.57 16.6604 71.51 20.87

10.4 19.9907 62.51 13.52

20.24 36.06 60.69 15.63

30.13 53.6784 60.69 11.91

119
Table 104. No. 89 LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.35 11.20 64.46 17.62

10.78 15.51 55.21 8.95

21.42 28.76 53.32 6.11

32.68 37.40 48.86 3.85

Table 105. No. 89 LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.35 11.83 65.69 13.19

10.74 15.13 54.62 6.30

21.73 27.74 51.92 3.66

33.43 35.40 46.64 0.62

Table 106. No. 89 LDTX results.

'1 (psi) '3 (psi) 's (degree) max (degree)

36.41 5.32 48.17 13.39

64.16 10.29 46.34 10.24

107.05 20.05 43.19 4.45

141.61 30.00 40.57 0.67

σ σ φ ψψ

120
NO. 9

Figure 82. Photo. No. 9 aggregate sample.

Table 107. No. 9 gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan (kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

0.375 0.375 0 1,102.79 0 0.00 100.00

4 0.187 1,785.33 1,514.98 270.35 5.78 94.22

8 0.0937 4,236.2 1,129.04 3,107.16 66.47 27.75

16 0.0469 1,791.1 909.95 881.15 18.85 8.90

50 0.0117 986.6 741.69 2,44.91 5.24 3.66

100 0.0059 830 809.4 20.6 0.44 3.22

200 0.0029 934.9 916.46 18.44 0.39 2.82

Pan — 732.6 600.56 132.04 2.82 0.00

121
Table 108. No. 9 density.

Sample

Minimum Density (pfc) ASTM D4254 Maximum Density (pcf) ASTM D4253

Test 

1

Test 

2

Test 

3 Average

Standard 

Deviation

Test 

1

Test 

2 Average

Standard

Deviation

No. 9 93.4 90.9 92.6 92.3 1.3 113.0 108.3 110.7 3.3

Table 109. No. 9 repose angle.

Test Angle Finder String Method

Average Repose 

Angle

1 29 26 24 26 27

26.8

53.75 27.36

2 25 26 28 28 31 52.5 29.05 27.82 27.31

3 26 26 25 27 28 54 27.04

Table 110. No. 9 standard DS results.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.323 12.13962 66.32 1.53

10.08 17.8952 60.61 15.62

20.08 31.37 57.38 13.53

30.17 46.6205 57.09 11.82

Table 111. No. 9 LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.35 9.73 61.22 13.64

10.66 17.70 58.93 10.38

21.57 31.97 55.99 5.82

32.60 42.84 52.73 4.73

Table 112. No. 9 LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.26 8.39 57.93 12.08

10.76 13.05 50.49 5.58

21.54 25.38 49.69 2.71

32.53 32.98 45.40 0.61

122
Table 113. No. 9 LDTX results.

'1 (psi) '3 (psi) 's (degree) max (degree)

27.85 5.20 43.27 8.03

49.83 10.14 41.44 4.22

91.75 20.03 39.92 0.86

134.13 30.01 39.37 0

NO. 10

Figure 83. Photo. No. 10 aggregate sample.

σ σ φ ψψ

123
Table 114. No. 10 gradation.

Sieve 

No.

Sieve 

Size 

(inches)

Mass of Soil 

+ Pan (g)

Mass of 

Pan (kg)

Mass of Soil 

(kg)

Percent

Retained

Percent

Passing

0.375 0.375 0 1,102.6 0 0.00 100.00

4 0.187 1,560.7 1,514.9 45.8 1.04 98.96

8 0.0937 1,821.7 1,128.9 692.8 15.78 83.18

16 0.0469 1,798.3 909.8 888.5 20.23 62.95

50 0.0117 2,022.6 741.5 1,281.1 29.17 33.78

100 0.0059 1,464.5 809.4 655.1 14.92 18.86

200 0.0029 1,267.7 916.4 351.3 8.00 10.86

Pan — 1,146.6 669.8 476.8 10.86 0.00

Table 115. No. 10 density.

Sample

Minimum Density (pfc) ASTM D4254 Maximum Density (pcf) ASTM D4253

Test 

1

Test 

2

Test 

3 Average

Standard 

Deviation

Test 

1

Test 

2 Average

Standard

Deviation

No. 10 114.9 116.4 116.0 115.8 0.8 146.4 146.2 146.3 0.1

Table 116. No. 10 repose angle.

Test Angle Finder String Method

Average Repose 

Angle

1 32 30 28 28 31

27.4

54 27.04

2 28 25 28 26 25 55.625 25.03 25.32 26.36

3 26 24 28 27 25 56.625 23.88

Table 117. No. 10 standard DS results.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.399 10.24149 62.20 15.86

10.28 16.7196 58.41 14.18

20.4 30.12 55.89 14.15

30.14 42.6877 54.78 10.35

Table 118. No. 10 LSDS results—dry.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.32 7.89 56.01 10.29

10.50 13.79 52.70 9.33

21.63 23.32 47.15 4.43

32.88 33.93 45.90 1.87

124
Table 119. No. 10 LSDS results—saturated.

Normal Stress

(psi)

Max Shear

(psi)

Peak Friction Angle

(degree)

Peak Dilation Angle

(degree)

5.29 7.41 54.48 7.59

10.61 10.97 45.94 0.77

20.98 18.96 42.10 0.58

34.27 29.17 40.40 0.00

Table 120. No. 10 LDTX results.

'1 (psi) '3 (psi) 's (degree) max (degree)

24.14 5.03 42.79 2.50

47.60 10.04 41.76 2.58

99.31 20.02 41.78 2.30

143.19 30.05 40.91 2.34

σ σ φ ψψ

125

ACKNOWLEDGEMENTS

The authors thank Justice Maswoswe of the FHWA Resource Center and Khalid Mohamed of 

the FHWA Office of Bridges and Structures for their feedback and review of this study. The 

authors also recognize the contributions of Jan Li of ESC, INC., who performed many of the 

LSDS tests in this report. Tom Stabile of ESC, INC., and Phillip Ooi of the University of Hawaii 

at Manoa provided advice throughout the project; the authors gratefully acknowledge their 

insights. 

127

REFERENCES

1. AASHTO. (2005). M 43: Standard Specification for Sizes of Aggregate for Road and 

Bridge Construction, American Association of State Highway and Transportation 

Officials, Washington, DC.

2. ASTM D448. (2012). “Standard Classification for Sizes of Aggregate for Road and 

Bridge Construction,” Annual Book of ASTM Standards, ASTM International, West 

Conshohocken, PA.

3. Nicks, J.E. and Adams, M.T. (2013). TechBrief: Friction Angles of Open-Graded 

Aggregates from Large-Scale Direct Shear Testing, Publication No. FHWA-HRT-13-

068, Federal Highway Administration, McLean, VA.

4. FHWA. (2003). Standard Specifications for Construction of Roads and Bridges on 

Federal Highway Projects, FP-03, Federal Highway Administration, McLean, VA.

5. HDOT. (2005). Standard Specifications for Road and Bridge Construction, Hawaii 

Department of Transportation. 

6. ODOT. (2013). Construction and Material Specifications. Ohio Department of 

Transportation.

7. AKDOT. (2005). Standard Specifications for Highways. Alaska Department of 

Transportation, Juneau, AK.

8. Bowles, J.E. (1996). Foundation Analysis and Design, 5th Ed., The McGraw-Hill 

Companies, Inc., New York, NY.

9. Rowe, P.W. (1962). “The Stress Dilatancy Relation for Static Equilibrium of an 

Assembly of Particles in Contact,” Proceedings of the Royal Society, A 269, pp. 500–

527.

10. Terzaghi, K., Peck, R.B., and Mesri, G. (1996). Soil Mechanics in Engineering Practice,

3rd Ed., John Wiley and Sons, Inc., NY, 549 pp.

11. Lee, K.L. and Seed, H.B. (1967). “Drained Strength Characteristics of Sands,” Journal of 

the Soil Mechanics and Foundation Division, Proceedings of the American Society of 

Civil Engineers, 93, No. SM6, pp. 117–141.

12. Alabdullah, J. (2010). Testing Unsaturated Soil for Plane Strain Conditions: A New 

Double-Wall Biaxial Device, PhD Thesis, Bauhaus-University Weimar, Homs, Syria.

13. Lee, K.L. (1970). “Comparison of Plane Strain and Trixial Tests on Sand,” Journal of the 

Soil Mechanics and Foundations Division, 96:901–923.

129
14. Maccarini, M. (1993). “A Comparison of Direct Shear Box Tests with Triaxial 

Compression Tests for a Residual Soil,” Geotechnical and Geological Engineering,

11:69–80.

15. Evans, T.M. (2005). Microscale Physical and Numerical Investigations of Shear Banding 

in Granular Soils, PhD Thesis, Georgia Institute of Technology, Atlanta.

16. Wanatowski, D. (2005). Strain Softening and Instability of Sand Under Plane-Strain 

Conditions, PhD. Thesis, Nanyang Technological University, Singapore.

17. Peters, J., Lade, P., and Bro, A. (1988). “Shear Band Formation in Triaxial and Plane 

Stress Tests; Advanced Triaxial Testing of Soil and Rock,” ASTM STP 977, R. Donaghe, 

R. Chaney and M. Silver, Eds., ASTM, West Conshohocken, PA., 604–627.

18. Alshibli, K.A., Batiste, S., and Sture, S. (2003). “Strain Localization in Sand: Plane 

Strain Versus Triaxial Compression,” J. Geotech. Geoenviron. Eng., 129:483–494.

19. Sadrekarimi, A. (2009). Development of a New Ring Shear Apparatus for Investigating 

the Critical State of Sands, PhD Thesis. University of Illinois at Urbana-Champaign, 

Urbana.

20. Desures, J., Chambon, R., Mokni, M., and Mozerolle, F. (1996). “Void Ratio Evolution 

Inside Shear Bands in Triaxial Sand Specimens Studied by Computed Tomography,”

Geotechnique. 46:529–546.

21. Alshibli, K.A., Sture, S., Costes, N.C., Frank, M.L., Lankton, M.R., Batiste, S.N., and 

Swanson, R.A. (2000). “Assessment of Localized Deformations in Sand Using X-ray 

Computed Tomography,” Geotechnical Testing Journal, 23:274–299.

22. Sadrekarimi, A. and Olson, S.M. (2011). “Critical State Friction Angle of Sands,”

Geotechnique, 61:771–783.

23. Sterpi, D. (2000). “Influence of the Kinematic Testing Conditions on the Mechanical 

Response of a Sand,” Computers and Geotechnics, 26:23–41.

24. Araei, A.A., Soroush, A., and Rayhani, M. (2010). “Large-Scale Triaxial Testing and 

Numerical Modeling of Rounded and Angular Rockfill Materials,” Scientia Iranica,

Transaction A, Civil Engineering, 17(3), 169–183.

25. Zeller, J., and Wullimann. R. (1957). “The Shear Strength of the Shell Materials for the 

Goschenenalp Dam, Switzerland,” Proc., 4th Int. Conf. on Soil Mechanics and 

Foundation Engineering. 2:399–404.

26. Lowe, J. (1964). “Shear Strength of Coarse Embankment Dam Materials,” Proc., 8th Int. 

Congress on Large Dams, 3:745–761.

27. Fumagalli, E. (1969). “Tests on Cohesionless Materials for Rockfill Dams,” J. Soil Mech. 

And Found. Div., 95(1): 313–332.

130
28. Frost, R.J. (1973). “Some Testing Experiences and Characteristics of Boulder-Gravel 

Fills in Earth Dams; Evaluation of Relative Density and Its Role in Geotechnical Projects 

Involving Cohesionless Soils (STP523),” ASTM, West Conshohocken, PA, 207–252.

29. Honkanadavar, N.P. and Sharma, K.G. (2013). “Testing and Modeling the Behavior of 

Riverbed and Blasted Quarried Rockfill Materials,” Int. J. Geomech., 

10.1061/(ASCE)GM. 1943-5622.0000378, 04014028.

30. Ramamurthy, T., and Gupta, K.K. (1986). “Response Papers to How Ought One to 

Determine Soil Parameters to Be Used in the Design of Earth and Rockfill Dams,” Proc., 

Indian Geotechnical Conf., 2, Indian Geotechnical Society, New Delhi, India, 15–19.

31. Varadarajan, A., Sharma, K.G., Venkatachalam, K., and Gupta, A.K. (2003). “Testing 

and Modeling Two Rockfill Materials,” J. Geotech. Geoenviron. Eng., 

10.1061/(ASCE)1090-0241(2003)129:3(206), 206–218.

32. Indraratna, B., Ionescu, D., and Christie, H.D. (1998). “Shear Behavior of Railway 

Ballast Based on Large-Scale Triaxial Tests,” Journal of Geotechnical and 

Geoenvironmental Engineering, 124(5):439–449.

33. Lambe, T.W. (1964). “Methods of Estimating Settlement,” Journal of the Soil Mechanics 

and Foundations Division, ASCE, 90, No. SM5, 47–74.

34. Das, B.M. 2010. Principles of Geotechnical Engineering, 7th Ed., Cengage Learning, 

Stamford, CT.

35. Charles, A., and Watts, K.S. (1980). “The Influence of Confining Pressure on the Shear 

Strength of Compacted Rockfill,” Geotechnique, 30, 353–367.

36. Nusier, O.K., Almohd, I.M., and Jaradat, R.A. (2008). Nonlinearity of Shear Strength and 

Stress-Strength Behavior and Induced Stress Predictions, ICCBT 2008, June 16–20, 

Kuala Lumpar, Malaysia.

37. Ravi Sharma, M.S., Baxter C.D.P., Hoffmann, W., Moran, K., and Vaziri, H. (2010). 

“Characterization of Weakly Cemented Sands Using Nonlinear Failure Dnvelope, Int. J. 

Rock Mech. Mining Sci. doi:10.1016/j.ijrmms.2010.06.008.

38. Lade, P.V. (2010). “The Mechanics of Surficial Failure in Soil Slopes,” Engineering 

Geology. 114:57–64.

39. Hoek, E. & Brown, E.T. (1997). “Practical Estimates of Rock Mass Strength,”

International Journal of Rock Mechanics and Mining Sciences, 34(8):1165–86.

40. Eberhardt, E. (2012). “The Hoek-Brown Failure Criterion,” Rock Mech. Rock Eng. 

45:981–988.

41. Baker, R. (2004). “Nonlinear Mohr Envelopes Based on Triaxial Data,” Journal of 

Geotechnical and Geoenvironmental Engineering. 130:498–506.

131
42. Bolton, M.D. (1986). “The Strength and Dilatancy of Sands,” Géotechnique, 36(1), 

pp. 65–78.

43. Poulos, S.J. (1971). The Stress-Strain Curves of Soils, Geotechnical Engineers, Inc. 

Winchester, MA, pp. 1–80.

44. AASHTO. (2012). LRFD Bridge Design Specifications, 5th Ed., American Association 

of State Highway and Transportation Officials, Washington, DC.

45. Munfakh, G., A. Arman, J. G. Collin, J. C.-J. Hung, and R. P. Brouillette. (2001). 

Shallow Foundations Reference Manual, FHWA-NHI-01-023. Federal Highway 

Administration, U.S. Department of Transportation, Washington, DC.

46. AASHTO. (2010). LRFD Bridge Construction Specifications, 3rd Ed., American 

Association of State Highway and Transportation Officials, Washington, DC.

47. Berg, R., Christopher, B., and Samtani, N. (2009). Design of Mechanically Stabilized 

Earth Walls and Reinforced Soil Slopes—Volume 1, Report No. FHWA-NHI-10-024, 

National Highway Institute, Federal Highway Administration, Arlington, VA.

48. Bareither, C.A., Edil, T.B., Benson, C.H., Mickelson, D.M. 2008. “Geological and 

Physical Factors Affecting the Friction Angle of Compacted Sands,” Journal of 

Geotechnical and Geoenvironmental Engineering. DOI: 10.1061/(ASCE)1090-

0241(2008)134:10(1476).

49. Aksharadananda, T. and Wu, J.T.H. (2001). Strength Parameters of Backfills for Design 

and Construction of Retaining Walls, CDOT Report No. 2001-07, Colorado Department 

of Transportation Research Branch, Denver, CO.

50. Yamaguchi, Y., Satoh, H., Hayashi, N., Yoshinaga, H. (2009). Strength Evaluation of 

Rockfill Materials Considering Confining Pressure Dependency, 1st International 

Symposium on Rockfill Dams, 18–21 October 2009, Chengdu, China.

51. Fitsum, Y.E. (2011). Shear Strength of Bremanger Sandstone Rockfill at Low Stress,

MSc Thesis, Delft University of Technology, The Netherlands.

52. Duncan, J.M., Brandon, T., Jian, W., Park, Y., Griffith, T., Corton, J., and Ryan, E. 

(2007). Densities and Friction Angles of Granular Materials with Standard Gradations 

21b and #57, Report CPGR #45, Center for Geotechnical Practice and Research, Virginia 

Polytechnic Institute, Blacksburg, VA, 100 pp.

53. Rowe, P.W. (1969). “The Relation Between the Shear Strength of Sands in Triaxial 

Compression, Plane Strain and Direct Shear,” Geotechnique, 19, No. 1. pp. 75–86.

54. Cerato, A.B. (2005). Scale Effects of Shallow Foundation Bearing Capacity on Granular 

Material, PhD Dissertation, University of Massachusetts Amherst.

132
55. Pells, P.J.N., Maurenbrecher, P.M., and Elges, H.F.W.K. (1973). “Validity of Results 

from the Direct Shear Test,” Proceedings of the 8th International Conference on Soil 

Mechanics and Foundation Engineering, 1.2, pp. 333–339.

56. Ladd, R.S. (1977). “Specimen Preparation and Cyclic Stability of Sands,” ASCE Journal 

of the Geotechnical Engineering Division, 103, No. GT6, pp. 535–547.

57. Kulhawy, F.H. and Mayne, P.W. (1990). Manual on Estimating Soil Properties for 

Foundation Design, EL-6800, Electrical Power Research Institute (EPRI): Research 

Project 1493-6.

58. Allen, T.M. and Bathurst, R.J. (2003). Prediction of Reinforcement Loads in Reinforced 

Soil Walls, Report No. WA-RD 522.2, Washington State Department of Transportation,

363 pp.

59. Allen, T.M., Christopher, B.R., Elias, V., and DiMaggio, J.D. (2001). Development of the 

Simplified Method for Internal Stability Design of Mechanically Stabilized Earth (MSE) 

Walls, WSDOT Research Report WA-RD 513.1, 108 pp.

60. Hribar, J., Dougherty, M., Ventura, J., and Yavorskyu, P. (1986). “Large Scale Direct 

Tests on Surface Mine Spoil,” Proceedings of the International Symposium on 

Geotechnical Stability in Surface Mining, Calgary, AB, November 1986, pp. 295–303.

61. Matsuoka, H. and Liu, S.H. (1998). “Simplified Direct Box Shear Test on Granular 

Materials and Its Application to Rockfill Materials,” Soils and Foundations, 38(4):275–

284.

62. Fox, N.S. and Cowell, M.J. (1998). Geopier Foundation and Soil Reinforcement Manual,

Geopier Foundation Company, Inc., Scottsdale, AZ.

63. Stewart, G.A. (1955). “Age Relations of the Middle Devonian Limestones in Ohio,” Ohio 

Journal of Science, 55(3), pp. 147–181.

64. Toewe, E.C. (1966). Geology of the Leesburg Quadrangle Virginia, Report of 

Investigations 11, Virginia Division of Mineral Resources, Charlottesville, VA.

65. AASHTO. (2011). T27: Standard Method of Test for Sieve Analysis of Fine and Course 

Aggregates, American Association of State Highway and Transportation Officials,

Washington, DC. 

66. ACI. (1980). ACI Manual of Concrete Practice, Part I, American Concrete Institute,

Detroit, MI.

67. ASTM C33. (2003). “Standard Specification for Concrete Aggregates,” Annual Book of 

ASTM Standards, ASTM International, West Conshohocken, PA.

133
68. ASTM D4254. (2006e1). “Standard Test Methods for Minimum Index Density and Unit 

Weight of Soils and Calculation of Relative Density,” Annual Book of ASTM Standards, 

ASTM International, West Conshohocken, PA.

69. ASTM D4253. (2006). “Standard Test Methods for Maximum Index Density and Unit 

Weight of Soils Using a Vibratory Table,” Annual Book of ASTM Standards, ASTM 

International, West Conshohocken, PA.

70. Adams, M., Nicks, J., Stabile, T., Wu, J., Schlatter, W., and Hartmann, J. 2011. 

Geosynthetic Reinforced Soil Integrated Bridge System Interim Implementation Guide,

Report No. FHWA-HRT-11-026, Federal Highway Administration, McLean, VA.

71. Smith, D. R. (2007), “Construction of Bases for Permeable Interlocking Concrete 

Pavements- Part II,” Contractor Focus, Interlocking Concrete Pavement Magazine, 

November 2007.

72. Liu, J. and Zhou, J. (2008). “Numerical Study on Sandpile Formation of Granular 

Materials with Different Grain Size Distributions,” Geotechnical Engineering for 

Disaster Mitigation and Rehabilitations, Proceedings of the 2nd International 

Conference GEDMAR08, Nanjing, China.

73. Gates, L., Masad, E., Pyle, R. and Bushee, D. (2011). Aggregate Imaging Measurement 

System 2 (AIMS2): Final Report, Report No. FHWA-HIF-11-030, Federal Highway 

Administration, Washington, DC.

74. Masad. E.A. (2005). Aggregate Imaging System (AIMS): Basics and Applications, Report 

No. FHWA/TX-05-5-1707-01-1, Texas Transportation Institute, Texas Department of 

Transportation, Austin, TX.

75. ASTM D3080. (2004). “Standard Test Method for Direct Shear Test of Soils under 

Consolidated Drained Conditions,” Annual Book of ASTM Standards, ASTM 

International, West Conshohocken, PA.

76. Montoya, B.M. (2012). Bio-Mediated Soil Improvement and the Effect of Cementation on 

the Behavior, Improvement, and Performance of Sand, Doctoral Dissertation, University 

of California, Davis, pp. 238.

77. Olson, R.E. (2007). Direct Shear Testing, Lecture notes, Department of Civil, 

Architectural, and Environmental Engineering, University of Texas, Austin.

78. ASTM D5321. (2008). “Standard Test Method for Determining the Coefficient of Soil 

and Geosynthetic or Geosynthetic and Geosynthetic Friction by the Direct Shear 

Method,” Annual Book of ASTM Standards, ASTM International, West Conshohocken, 

PA.

79. Simoni, A. and Houlsby, G.T. (2006). “The Direct Shear Strength and Dilatancy of SandGravel Mixtures,” Journal of Geotechnical and Geological Engineering, 24, pp. 523–

549.

134
80. ASTM D7181. (2011). “Method for Consolidated Drained Triaxial Compression Test for 

Soils,” Annual Book of ASTM Standards, ASTM International, West Conshohocken, PA.

81. Chakraborty, T. and Salgado, R. (2010). “Dilatancy and Shear Strength of Sand at Low 

Confining Pressure,” Journal of Geotechnical and Geoenvironmental Engineering,

136(3):527–532.

82. Germaine, J.T. and Ladd, C.C. (1988). State-of-the-Art: Triaxial Testing of Saturated 

Cohesive Soils; Advanced Triaxial Testing of Soil and Rock, ASTM STP 977, Donaghe, 

R.T., Chaney, R.C., and Silver, M.L., Eds., American Society for Testing and Materials, 

Philadelphia, PA, pp. 421–459.

83. Triaxial User’s Manual. (2012). Control and Report Software for Fully Automated 

Triaxial UU, CU, CD and Stress Path Soil Tests on LoadTrac-II/FlowTrac-II Systems 

Using Windows®XP/Vista/7, Geocomp Corporation, Acton, MA.

84. Noor, M.J.M., Nyuin, J.D., and Derahman, A. (2012). “A Graphical Method for 

Membrane Penetration in Triaxial Tests on Granular Soils,” The Institution of Engineers, 

73(1):23–30, Malaysia.

85. Paikowsky, S.G. Canniff, M.C., Lesny, K., Kisse, A., Amatya, S. and Muganga, R. 

(2010). LRFD Design and Construction of Shallow Foundations for Highway Bridges,

NCHRP Report 651, Transportation Research Board, Washington, DC.

86. NAVFAC. (1986). Soil Mechanics Design Manual 7.01, Naval Facilities Engineering 

Command, Alexandria, VA, p. 7.1–149.

87. Sadrekarimi, A. and Olson, S.M. (2011). “Critical State Friction Angle of Sands,” 

Geotechnique, 61, No. 9, pp. 771–783.

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