TECHBRIEF Friction Angles of OpenGraded Aggregates From

Large-Scale Direct Shear

Testing 

FHWA Publication No.: FHWA-HRT-13-068

FHWA Contact: Jennifer Nicks, HRDI-40, (202) 493-3075, 

jennifer.nicks@dot.gov

Introduction

State and local transportation agencies frequently use opengraded aggregates for wall, roadway, and bridge construction. 

The primary advantages of using this type of material in wall 

and abutment applications are ease of constructability, lighter 

in-place density than well-graded materials, very low fine 

content, free-draining characteristics, and simpler quality 

assurance testing, using a method specification for field density. 

The American Association of State Highway and Transportation 

Officials (AASHTO) classifies open-graded aggregates 

according to the M43 gradation based on standard sizes for 

processed aggregates.(1) Despite common use of these 

aggregates, their strength characteristics have not been 

systematically measured or used in design. Instead, engineers 

frequently use a default friction angle of 34,o leading to potential 

conservatism in retaining wall and foundation design. The primary purpose of this TechBrief is to present research results on 

the strength properties of standard open aggregates tested in 

a large-scale direct shear (LSDS) device to improve the state of 

practice for the design of structures using these materials.

Background

The most commonly used laboratory devices available to measure 

the strength of aggregates are the direct shear (DS) and triaxial 

(TX) tests, with DS being the simplest and most regularly used 

test. Based on the American Association of Testing Materials 

(ASTM) standards, the maximum particle sizes for DS and TX 

testing are 1/10th and 1/6th of the width or diameter of the 

device, respectively. Standard DS devices are typically either 

circular, with a 2.5-inch diameter, or square, with 4-inch sides; 

therefore, the largest aggregates that can be tested are 0.25 or 

0.4 inches, respectively. Similarly, standard TX devices are made 

for samples that are smaller than 2 inches in size; therefore, the 

maximum aggregate size that can be tested is about 0.3 inches. 

Because the AASHTO M43 aggregates are relatively large, 

with maximum aggregate sizes ranging from 0.375 to 4 inches, 

standard DS and TX devices are often not suitable.

Research, Development, and 

Technology

Turner-Fairbank Highway 

Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

www.fhwa.dot.gov/research

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One option in current practice is to test these 

aggregates in standard test devices with a 

scalped sample from which the larger particles 

have been removed by passing the aggregate 

sample through the appropriate sieves to meet 

the ASTM standards. Considering the opengraded nature of these materials, scalping 

may significantly alter the characteristics and 

not produce a representative sample. Another 

option is to perform parallel gradation in a standard shear device.(2) Parallel gradation involves 

scaling down a material to the desired size while 

ensuring the grain size distribution is parallel to the original sample. The accuracy of this 

method depends on several factors related to the 

particle shape and composition, fine content, and 

aggregate strength.(3) Because of the caveats 

associated with scalping and parallel gradation, 

the best option is to use large-scale devices 

for the accurate measurement of the strength 

properties for a representative sample; 

however, the use of LSDS devices is not a 

common practice at this time.

Test Program

At the Turner-Fairbank Highway Research Center 

(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 (see figure 1). 

This device was used to measure the strength of 

12 classifications of AASHTO aggregates, from 

No. 10 up to No. 5 (see table 1), under both 

dry and saturated conditions. The manufactured 

aggregates came from a variety of sources 

at locations across the country. In addition, 

four different No. 8 samples were tested from 

various quarries to determine the repeatability 

of the test based simply on the AASHTO gradation. Figure 2 illustrates the results of a sieve 

analysis that was also performed on each sample to ensure it met the gradation specifications. 

Figure 1. Photo. Large-scale DS device at TFHRC.

Sieve No.

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

Percent Passing Through Sieve

Table 1. Selected AASHTO M43-05 (ASTM D448) aggregate designations.

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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 

standard DS testing, which designated the gap 

size as 0.025 inch.(4) Because the LSDS device 

and the aggregates tested in this research are 

considerably larger, the gap size was instead set 

to D85, or the aggregate size in which 85 percent 

of the material is smaller, for each sample based 

on the sieve analysis. This was determined from 

review of test methods outlined in ASTM D5321 

and to avoid frictional interference from either 

the two shear boxes or larger particles within 

the gap during testing.(5)

The shear strain displacement rate was set at 

0.015 inch/min for the open-graded aggregates 

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.(6) Each aggregate 

was tested at normal stresses of 5, 10, 20, and 

30 psi, which is a typical stress range for wall 

and bridge applications, to determine the friction angle. Note that before testing, the LSDS 

device was calibrated for displacement and 

shear resistance; the load cells measuring 

normal and shear force were also calibrated. 

Results

For each applied normal stress, the shear stress 

was measured as a function of shear displacement. The peak shear stress typically occurred at 

a lateral strain of 5 to 10 percent of the sample 

length. The resulting friction angle was then 

determined based on (1) a best-fit linear MohrCoulomb (MC) envelope, which is the current 

standard of practice, and (2) a Zero Dilation 

Angle (ZDA) approach proposed by the authors 

(see table 2). The MC and ZDA methods of 

determining the friction angle are illustrated in 

figure 3 and figure 4, respectively, for the No. 8A 

sample as an example.

Figure 2. Graph. Sieve analysis results of tested aggregates.

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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 3, for example); however, these aggregates are cohesionless. This inconsistency is 

attributed to the fact that the failure envelope 

is actually nonlinear (figure 5); 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, the authors propose

the use of an alternative ZDA method to 

determine the design friction angle, which is

based on the critical state or constant 

volume concept.(7)

In the case of the LSDS, the dilation angle (Ψ) is 

the ratio of the incremental vertical displacement

of the sample (∆y) to the incremental horizontal 

displacement (∆x) measured during testing, 

where tan(Ψ) = ∆y/∆x.

(7) At a dilation angle of 

zero, the change in incremental vertical height of 

Note: For the MC approach, the peak friction angle reported 

is with the corresponding cohesion values omitted; for 

the ZDA approach, the critical state, or constant volume, 

friction angle is reported.

Figure 3. Graph. Linear MC failure envelopes for No. 8A.

Table 2. Friction angle results using the linear MC 

envelope and ZDA approaches.

AASHTO 

Gradation

Friction Angle (o)

Mohr-Coulomb 

(MC)

Zero Dilation Angle 

(ZDA)

Dry Saturated Dry Saturated

5 51 59 52 49

56 59 57 53 56

57 52 56 47 56

6 59 60 50 54

67 55 60 53 57

68 50 52 51 51

7 57 52 54 52

78 53 48 51 49

8A 54 50 52 50

8B 47 45 50 50

8C 43 43 50 48

8D 52 46 53 50

89 47 45 48 49

9 53 45 52 48

10 46 41 46 44

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the sample during shearing is zero. As with the 

friction angle, the dilation angle decreases 

with increasing applied normal stress in a 

logarithmic function. The relationship between friction angle and dilation angle 

is linear (figure 4, for example).(8) The 

y-intercept of the best-fit linear envelope 

in the ZDA approach is the proposed design friction angle at peak conditions for a 

particular aggregate (table 2), which corresponds to the constant volume or critical 

state friction angle. 

Figure 6 shows a general trend of the friction 

angle decreasing with smaller aggregate 

size, regardless of the method used to deterFigure 5. Graph. Nonlinear MC failure envelopes for No. 8A.

Figure 4. Graph. ZDA approach for No. 8A.

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mine strength. Although there is scatter in the 

results, there is no significant difference 

in the results between dry and saturated 

conditions for the open-graded aggregates 

tested. The scatter is largely attributed to 

variations and uncertainties inherent in laboratory testing; typical coefficients of variation 

for friction angles measured in laboratory tests 

are up to 10 percent.(9)

The difference in friction angles for the AASHTO 

No. 8 aggregates was apparent when using a 

linear MC failure envelope, with the highest and 

lowest peak friction angle measured at 55o and 

43,o respectively, for dry conditions. Although 

both are angular, the weakest No. 8 aggregate 

had flat, elongated particles while the strongest 

No. 8 aggregate was not flat. Therefore, the 

resulting dilation angles were different, with the 

weakest No. 8 having lower dilation angles than 

the strongest, as expected based on the visual 

observations of the aggregate shape. Based on 

the ZDA approach, however, the friction angles 

were more similar for the No. 8 aggregates. This 

is because the ZDA approach reduces the friction angle to the critical state, thereby negating 

the effect of dilation from peak conditions.

Recommendations and Conclusions 

LSDS testing of the AASHTO open-graded 

aggregates resulted in measured friction angles 

well above the 34o default friction angle typically 

used in design. Two approaches were investigated: (1) measuring the friction angle as the 

slope of the conventional, best-fit linear MC 

failure envelope and (2) measuring the friction 

angle corresponding to a ZDA approach. The 

linear MC approach resulted in more scatter 

within the data and measured cohesion values, 

but the resulting peak friction angle is conservative for open-graded aggregates and familiar to 

designers. The ZDA approach resulted in less 

scatter and provided a more accurate basis for 

obtaining the critical state friction angle, but 

requires an extra step in the analysis of DS 

results. Based on the samples tested in this 

program to date, the lowest friction angle 

measured was for the No. 10 aggregates (the 

smallest aggregate tested) under saturated 

conditions—41o and 45o for the MC and ZDA 

approaches, respectively. 

LSDS testing is recommended to quantify the 

actual friction angle and take advantage of the 

strength of these engineered aggregates to 

Figure 6. Graph. Summary of peak friction angle results.

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produce more cost-effective designs. The 

authors propose the ZDA approach to define 

the friction angle for design when using 

AASHTO open-graded aggregates. If preliminary analysis is needed before testing, then a 

default friction angle of 39o is recommended. 

This recommendation is based on the relationship between friction angle and dilation angle 

for all aggregates tested in this program and 

assumes a 95-percent confidence interval; the 

proposed new default of 39o corresponds to 

the peak friction angle of 49o (see figure 7), less 

two standard deviations. Note that this default 

angle is still conservative with respect to the 

actual strength properties of the open-graded 

aggregates tested (see table 2).

Future Testing 

Additional laboratory testing is planned at TFHRC 

to further characterize the engineering properties of both open- and well-graded aggregates 

and develop a database of material variability. In 

addition to LSDS testing, large-diameter (6-inch) 

TX testing is underway for open-graded aggregates. The impact of compaction on strength 

and dilation will be investigated. Commonly 

used well-graded aggregates will also be tested 

in both the LSDS and TX devices. The primary 

objective of this research is to encourage designers to employ more realistic strength values in 

design when using these engineered fills. 

Acknowledgements

The authors would like to acknowledge the hard 

work of geotechnical technician, Jan Li, who prepared and tested many of the samples for this 

study. Special thanks also go to Dr. Phillip Ooi for 

his feedback throughout the project. Finally, the 

authors are grateful to Justice Maswoswe and 

Khalid Mohamed for their review of this testing 

program and report. 

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. 

2. Ooi, P.S.K. and Selvarajah, P. (2010). “Use of 

the Parallel Gradation Technique to Assess 

the Shear Strength of Reclaimed Asphalt 

Pavement in Direct Shear.” Proceedings, 

International Conference on Sustainable 

Built Environment, pp. 219–226. 

Figure 7. Graph. Relationship between friction and dilation angles.

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Researchers—This research was conducted at Turner-Fairbank Highway Research Center by Jennifer 

Nicks and Mike Adams of FHWA with the help of geotechnical technician Jan Li of ESC, Inc.

Distribution—This TechBrief is being distributed according to a standard distribution. Direct 

distribution is being made to the Divisions and Resource Center.

Availability—This TechBrief may be obtained from the FHWA Product Distribution Center by e-mail to 

report.center@dot.gov, fax to (814) 239-2156, phone to (814) 239-1160, or online at http://www.fhwa.dot.

gov/research.

Key Words—Aggregates, laboratory testing, large-scale direct shear, AASHTO, materials, friction 

angle, dilation angle 

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. 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 the Government, industry, and 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.

JULY 2013 FHWA-HRT-13-068

HRDI-40/07-13(200)E

3. Verdugo, R. and de la Hoz, Karem. (2006). 

“Strength and Stiffness of Coarse Granular 

Soils.” Geotechnical Symposium in Rome, 

March 16–17, 2006.

4. 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.

5. 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.

6. Simoni, A. and Houlsby, G.T. (2006). “The 

Direct Shear Strength and Dilatancy of SandGravel Mixtures.” Journal of Geotechnical 

and Geological Engineering, Vol. 24, 

pp. 523–549. 

7. Bolton, M.D. (1986). “The Strength and 

Dilatancy of Sands.” Géotechnique, Vol. 36(1), 

pp. 65–78.

8. Houlsby, G.T. (1991). “How the Dilatancy of 

Soils Affects Their Behavior.” Proceedings, 

Tenth European Conference on Soil 

Mechanics and Foundation Engineering, Soil 

Mechanics Report No. 121/91, Florence, Italy. 

9. Paikowsky, S.G. et al. (2010). LRFD Design 

and Construction of Shallow Foundations for Highway Bridges. NCHRP Report 

651, Transportation Research Board, 

Washington, DC.

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