geological and physical factors affecting the …davem/abstracts/08-6.pdfgeological and physical...

Geological and Physical Factors Affecting the Friction Angleof Compacted Sands

Christopher A. Bareither1; Tuncer B. Edil2; Craig H. Benson3; and David M. Mickelson4

Abstract: This study evaluated the effects of physical characteristics and geologic factors on the shear strength of compacted sands fromWisconsin that are used as granular backfill for mechanically stabilized earth walls and reinforced soil slopes. Physical properties andshear strength were determined for 30 compacted sands collected from a broad range of geological deposits. Relationships betweenstrength/deformation behavior, geologic origin, and physical properties were used to categorize the sands into four friction angle groups.Sands with the lowest friction angle are derived from weathering of underlying sandstones, and tend to be medium-fine, well-rounded, andpoorly graded sands. Sands with the highest friction angle are from recent glacial activity and tend to be coarser grained, well-graded,and/or angular sands. A multivariate regression model was developed that can be used to predict friction angle �� of compacted sandsfrom comparable geological origins based on effective particle size �D10�, maximum dry unit weight ��dmax�, and Krumbein roundness�Rs�.

DOI: 10.1061/�ASCE�1090-0241�2008�134:10�1476�

CE Database subject headings: Sand; Friction; Displacement; Mineralogy; Backfills; Slopes.

Introduction

Design of mechanically stabilized earth �MSE� walls and rein-forced soil �RS� slopes by many agencies, including the Wiscon-sin Department of Transportation �WisDOT�, is generallyconducted following the guidelines developed by Elias et al.�2001� for the Federal Highway Administration �FHWA�. Theseguidelines indicate that properly compacted backfill can be as-sumed to have an internal angle of friction �� of 34° providedthat specified criteria for particle size distribution and plasticityindex are satisfied.

In Wisconsin, natural sands meeting the criteria in Elias et al.�2001� generally are used for MSE wall backfill and for RSslopes. However, testing conducted by WisDOT in 2002–03 indi-cated that some compacted natural sands meeting the criteria inElias et al. �2001� could have friction angles less than 34°. Sandshaving lower friction angles had similar geologic history, suggest-ing that geological factors should be considered when evaluatingthe suitability of sands for backfill. Accordingly, a statewide ex-amination was undertaken to assess how geologic origin andphysical properties influence the friction angle of naturally occur-ring sands in Wisconsin.

1Graduate Research Assistant, Geological Engineering, Univ. ofWisconsin-Madison, Madison, WI 53706. E-mail: [email protected]

2Professor, Geological Engineering, Univ. of Wisconsin-Madison,Madison, WI 53706. E-mail: [email protected]

3Wisconsin Distinguished Professor and Chairman, GeologicalEngineering, Univ. of Wisconsin-Madison, Madison, WI 53706. E-mail:[email protected]

4Professor Emeritus, Geology and Geophysics, Univ. of Wisconsin-Madison, Madison, WI 53706. E-mail: [email protected]

Note. Discussion open until March 1, 2009. Separate discussions mustbe submitted for individual papers. The manuscript for this paper wassubmitted for review and possible publication on January 17, 2007; ap-proved on February 6, 2008. This paper is part of the Journal of Geo-technical and Geoenvironmental Engineering, Vol. 134, No. 10,
October 1, 2008. ©ASCE, ISSN 1090-0241/2008/10-1476–1489/$25.00.
1476 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGIN

Thirty sands throughout Wisconsin were sampled to obtain arepresentative assortment of potential granular backfill materials.Although all of the samples were collected in Wisconsin, theyrepresent a reasonably wide range of geological origins andphysical characteristics, and, therefore, are likely to be represen-tative of the northern Midwest and other geographic regionswhere glaciation has occurred. Physical properties and geologicalorigin of each sand were studied, and the friction angle of eachsand was measured in direct shear test as is commonly done byWisDOT and other transportation agencies when evaluating theshear strength of compacted backfill materials for MSE walls andRS slopes �Bareither et al. 2008b�. Interface friction angles �i.e.,friction angles between backfill and reinforcing members� arealso needed in the design and construction of MSE walls and RSslopes. However, this study focused only on the internal frictionof granular materials; interface friction and its relationship to in-ternal friction was beyond the scope of the study. Relationshipsbetween shear strength, physical properties, and regional geologywere established. Additionally, a regression model was developedthat can be used to estimate �� based on commonly measuredphysical characteristics.

Sources of Sands

Thirty samples were collected from the locations shown in Fig. 1.These sources represent the sand deposits typically found in Wis-consin �weathered sandstone, fluvial, glacial outwash, ice-contactstratified deposits, and other deposits of glacial origin�. Samplingwas conducted at greater density near major metropolitan areas,where there is a greater need for granular backfill materials. Whenpossible, samples were selected from an in situ layer at each siteso that a precise geologic origin could be established. At threelocations, however, samples were collected from a stockpile ofsieved and washed backfill material. For these sands, the geologicorigin was generalized for the entire location. Approximately

3
0.1 m of material was collected at each site. Each sample was
EERING © ASCE / OCTOBER 2008

blended together thoroughly and allowed to air dry. After air dry-ing, each sample was blended again and placed uniformly in alarge �0.12 m3� sealed container.

Weathered Sandstone Deposits

Four samples were obtained from deposits derived from eolianand fluvial weathering of underlying Cambrian and St. Petersandstones �Fig. 1�. The sand particles in these sandstones hadbeen exposed to more than 100 million years of eolian and fluvialabrasion before consolidation into sandstone �Dott and Attig2004�. These weathering processes resulted in sandstones com-prised of well-rounded medium-to-fine sand-size particles. Theseparticles are comprised predominantly of quartz because of itsresistance to disintegration and decomposition �Prothero andSchwab 2004�.

The sand deposits derived from fluvial and eolian weatheringof the Cambrian and St. Peter sandstones have the same charac-teristics as the sand particles in the parent rocks �Dott and Attig2004�. These sand deposits are also free from direct glacial activ-ity, which is unusual in Wisconsin and many other northern statesin the US. The majority of Wisconsin was glaciated during thepast 2.5 million years, and more significantly during the Wiscon-sin Glaciation �25,000 and 10,000 bp� �Clayton et al. 1991�.

Fluvial Deposits

Fluvial deposits �Fig. 1� were sampled at six locations. The fluvialdeposits consist of poorly graded stratified sand with layers offine sediment deposited during periods of decreased flow in theWisconsin, Mississippi, Black, and Chippewa Rivers. All of thefluvial deposits lie in regions underlain by Cambrian Sandstone,which is a primary source of sediment. However, all of thesefluvial deposits also contain glacial outwash sediments from large

Fig. 1. Sample location and geologic origin of the sands

river systems that acted as outlets for glacial meltwater during the

JOURNAL OF GEOTECHNICAL AND GEO

Wisconsin Glaciation. Thus, sands derived from fluvial depositscontain particles having a broader distribution of size, shape, andmineralogy compared to the sands derived solely from weatheredsandstone.

Glacial Outwash Deposits

Ten samples were obtained from glacial outwash deposits �Fig. 1�formed during the Wisconsin Glaciation from glaciers overlyingnonsandstone bedrock. These deposits were sampled at the high-est frequency because of their abundance and broad geographicavailability. Sediments contained in the glacial outwash sampleswere deposited closer to the glacier margin compared to those ofthe fluvial deposits. Outwash sediment near the glacier margin isoften deposited rapidly during flood events, resulting in verywell-graded sands and gravels that are more angular and coarsergrained compared to fluvial deposits �Church and Gilbert 1975;Werritty 1992; Bennett and Glasser 1996; Maizels 2002�.

Ice Contact Stratified Deposits

Four samples were obtained from ice-contact stratified �ICS� de-posits �Fig. 1� that formed during the Wisconsin glaciation. ICSdeposits are water-laid sediments formed in contact with glacialice that consist of more angular particles due to short transportdistances. They vary in particle size and gradation due to fluctua-tions in meltwater discharge and sediment concentration.

Miscellaneous Glacial Deposits

Five samples were obtained from miscellaneous glacial deposits,including drumlin, esker, and glaciolacustrine �lake� sand deposits�Fig. 1�. The composition and physical properties of drumlinsdepend on the material present during glacial advance �Bennettand Glasser 1996�. The drumlin that was sampled contained out-wash sands and gravels deposited during an earlier glacial ad-vance. Eskers can be composed of sediments ranging from sortedsilt to broadly graded and matrix-supported gravel �Benn andEvans 1998� that typically have traveled less than 15 km from theoutcrop source �Lee 1965; Price 1973�. The esker deposit in thisstudy varied from poorly graded fine sand to well-graded gravel.The sample collected was from a poorly graded medium-fine sandlayer. Glaciolacustrine sands were obtained from deposits relatedto Glacial Lake Oshkosh and Glacial Lake Wisconsin that consistof poorly-graded fine sands characteristic of selective depositionin waters having low turbulence. Sample P2-S3 may have beenreworked postglaciation due to fluvial and eolian weathering.

Physical Characteristics

Index Properties

Index properties of the samples are summarized in Table 1 andthe particle size distribution curves are shown in Fig. 2. Thesamples vary from uniformly to broadly graded, with median par-ticle size �D50� ranging from 0.15 to 3.50 mm, coefficient of uni-formity �Cu� ranging from 1.8 to 34.1, and fines content rangingfrom 0.1 to 14.4%. The gravel content of the samples ranges from0 to 47.8%. All of the samples classify as sands in the Unified
Soil Classification System in ASTM D 2487, with the majority
ENVIRONMENTAL ENGINEERING © ASCE / OCTOBER 2008 / 1477

als �M

�24 of 30� classifying as poorly graded sand �SP�. All of the sandsclassify as A-1, A-2, or A-3, i.e., “granular” according to theAASHTO soil classification system.

The variations of D50 and Cu with respect to geologic de-posit type are shown in Figs. 3�a and b�. Sands derived fromweathered sandstone are all poorly graded �2.35�Cu�3.00�medium to fine clean sands with similar specific gravity ofsolids �2.63-2.66�. Sands from fluvial deposits are more uniformlygraded �1.86�Cu�2.86� compared to weathered sandstone, buthave a broader range of median particle size �0.29 mm�D50

�0.70 mm�. Sands from glacial outwash contain the coarsest par-ticles and sands from glacial outwash and ICS deposits representthe broadest distributions in particle size �Fig. 3�. The glaciola-custrine sands are poorly graded with the smallest median particlesize compared to all other materials.

Particle Roundness

Particle shape can be described in terms of roundness, sphericity,and surface texture. Sphericity generally falls within a narrowrange for naturally occurring sands �Zelasko 1966; Edil et al.

Table 1. Index Properties of the Sands

SampleD50

a

�mm�D10

a

�mm� Cub Cc

b

P1-S2 0.38 0.20 2.18 1.03

P1-S4 0.30 0.15 2.67 0.95

P1-S5 0.44 0.19 2.63 1.01

P1-S6 0.34 0.17 2.35 1.15

P1-S1 0.31 0.18 1.86 1.12

P1-S3 0.31 0.15 2.33 0.92

P1-S7 0.29 0.15 2.03 0.96

P2-S3 0.16 0.08 2.27 0.86

P3-S3 0.54 0.25 2.48 0.92

P3-S5 0.48 0.19 3.00 0.89

P3-S6 0.29 0.15 2.07 1.04

P3-S7 0.22 0.15 1.79 0.96

P2-S1 0.30 0.17 1.88 0.97

P2-S2 0.20 0.10 2.10 1.20

P2-S4 0.32 0.08 5.30 1.92

P2-S9 0.50 0.19 4.16 0.68

P2-S10 0.20 0.09 2.33 1.35

P2-S11 3.50 0.27 34.07 0.14

P3-S1 0.63 0.25 3.20 0.82

P3-S2 0.48 0.13 4.77 1.04

P4-S1 0.58 0.31 2.00 1.10

P5-S1 0.69 0.18 5.28 0.76

P2-S5 0.64 0.28 2.82 0.84

P2-S6 0.27 0.11 2.82 1.06

P2-S7 0.15 0.054 3.15 1.32

P2-S8 0.50 0.21 3.05 0.81

P2-S12 0.42 0.18 3.06 0.85

P3-S4 0.70 0.29 2.86 1.00

P4-S2 0.48 0.21 2.86 0.81

P4-S3 0.77 0.20 6.50 0.59aParticle size determined by ASTM D 422: D50=particle diameter at 50%bUSCS=Unified Soil Classification System �ASTM D 2487�; Cu=coefficcSpecific gravity �Gs� determined by ASTM C 127 and ASTM D 854.dAASHTO=American Association of Highway and Transportation Offici

1975� and surface texture is a second order feature that is cum-


bersome to measure and highly variable �Cho et al. 2006�. Hence,for this study, particle shape was characterized by roundnessusing a visual procedure conducted with an optical microscopeand charts developed by Krumbein �1941�. Digital image analysistechniques are currently available for determination of particleshape �Janoo 1998; Jensen et al. 2001; Cho et al. 2006�. However,the Krumbein method was adopted based on access to readilyavailable equipment and its established use in previous research�Edil et al. 1975; Zelasko et al. 1975�. The Krumbein methodcan also be implemented by laboratories with little specializedequipment.

Particles from each sample were partitioned into four sizefractions: gravel ��76.2 and �4.75 mm�, coarse sand ��4.75 and�2.0 mm�, medium sand ��2.0 and �0.425 mm�, and fine sand��0.425 and �0.075 mm�. Roundness was determined for eachsize fraction constituting at least 5% by weight of the totalsample. Edil et al. �1975� determined roundness for sand particlesbased on charts in Krumbein �1941� and reported that viewing atleast 25 particles yielded a reliable mean roundness. For thisstudy, 50 particles were analyzed from each size fraction and a

es�

Gravel�%� Gs

c USCSbAASHTO

classificationd

.4 2.0 2.63 SP A-3�0�

.0 5.7 2.65 SP A-3�0�

.2 1.8 2.65 SP A-1-b�0�

.8 1.8 2.63 SP A-3�0�

.8 0.0 2.64 SP A-3�0�

.8 0.0 2.66 SP A-3�0�

.7 0.0 2.66 SP A-3�0�

.6 10.2 2.68 SM A-2-4�0�

.6 0.3 2.66 SP A-1-b�0�

.8 4.9 2.65 SP A-1-b�0�

.8 0.0 2.65 SP A-3�0�

.6 0.0 2.66 SP A-3�0�

.1 1.0 2.68 SP A-3�0�

.9 0.0 2.67 SP A-3�0�

.8 17.8 2.68 SP-SC A-3�0�

.5 22.1 2.67 SP A-1-b�0�

.0 0.7 2.7 SP A-3�0�

.8 47.8 2.71 SW A-1-a�0�

.1 10.0 2.72 SP A-1-b�0�

.7 12.1 2.72 SP-SM A-1-b�0�

.1 3.3 2.69 SP A-1-b�0�

.2 16.6 2.67 SP-SM A-1-b�0�

.5 8.3 2.76 SP A-1-b�0�

.5 0.4 2.75 SP A-3�0�

.4 0.0 2.75 SM A-2-4�0�

.2 6.7 2.71 SP A-1-b�0�

.6 2.2 2.7 SP A-3�0�

.4 4.3 2.69 SP A-1-b�0�

.3 3.3 2.71 SP A-1-b�0�

.7 13.2 2.74 SP A-1-b�0�

D10=particle diameter at 10% finer.

uniformity; Cc=coefficient of curvature.

145-91�.

Fin�%

0

1

0

0

0

0

0

12

0

0

0

0

1

0

9

0

5

0

1

5

0

5

0

3

14

1

1

0

2

1

finer;

ient of

weighted whole sample roundness was calculated for each sand


based on the average roundness and percentage �by weight� of thesample in each size fraction. The Krumbein roundness chart waskept at a constant scale and the particular size fraction wasviewed at a similar scale as the particles on the roundness chart.

The roundness measurements are summarized in Table 2. Theroundness varies between a minimum of 0.22 �angular� to a maxi-mum of 0.62 �rounded�. The variation of roundness with respectto geologic deposit type is shown schematically in Fig. 3�c�.Roundness is highest and most uniform for weathered sandstonedeposits due to the uniformity of rounded particles in the parentsandstones. Roundness decreases from fluvial to glacial outwashto ICS deposits corresponding to a decrease in distance from theglacier margin �i.e., abrasion causing roundness increases withtransport distance�. The roundness for the glaciolacustrine sandsis typically low, but varies with distance and method of transportprior to deposition.

Minimum and Maximum Void Ratios

Three minimum void ratio �emin� and three maximum void ratio�emax� tests were performed on each sand. The minimum or maxi-mum void ratio reported for each sand is the minimum or maxi-mum void ratio obtained from the three tests. Maximum voidratio was determined according to Method B of ASTM D 4254using a tremie tube and a 2.83 L mold. Minimum void ratio wasmeasured according to ASTM D 4253 �Method 2A� using air-dried soil in a 2.83 L mold. The mold was vertically vibrated for

Fig. 2. Particle-size distribution curves: �a� P1-S1 through P2-S8; �b�P2-S9 through P5-S1

12 min at a frequency of 50 Hz with a 25.6 kg surcharge.


The minimum and maximum void ratios are summarized inTable 2. The relationship between emax and emin for the cleansands ��5% fines� and the sands with 5–15% fines is shown inFig. 4. The relationship between emax and emin compares well withthe trend line reported by Cubrinovski and Ishihara �2002� fornatural clean sands ��5% fines�. The emin and emax also dependmodestly on median grain size �D50� �Fig. 5�a�� and roundness�Fig 5�b��. Cubrinovski and Ishihara �2002� also report that emax

decreases with increasing D50 for clean sands and sands withsome fines �5–15% fines�, and Edil et al. �1975� report that emax

and emin decrease with increasing roundness.

Standard Proctor Compaction

The FHWA guidelines for MSE walls and RS slopes indicate thatthe backfill should be compacted to at least 95% of the maximum

Fig. 3. Influence of geologic deposit type on physical characteristicsof sands: �a� median particle size; �b� coefficient of uniformity; and�c� particle roundness; the box represents the middle 50% of the data;the central line in the box represents the median; the outer boundariesrepresent the interquartile range �i.e., 25th and 75th percentiles�; andthe upper and lower whiskers extending from the box constitute the5th and 95th percentiles of the data; for weathered sandstone, theupper whisker in �c� is coincident with the 75th percentile

dry unit weight corresponding to standard Proctor compactive


y unit

effort. Maximum dry unit weights obtained from compactiontests are also commonly used by transportation departments tocontrol placement of coarse and fine-grained soils, even thoughsome coarse-grained soils do not exhibit a conventional com-paction curve. Therefore, standard Proctor compaction testswere conducted on each sand following ASTM D 698-Method Ausing the sample fraction passing the No. 4 sieve �4.75 mm�.Method A was used for all sands for consistency, even though twosands had greater than 20% material retained on the No. 4 sieve�R4�.

Maximum dry unit weights ��dmax� and the void ratios corre-sponding to the maximum dry unit weight �e�dm� are summarizedin Table 2. For samples containing �5% R4 material, a unitweight correction was applied following ASTM D 4718 to adjust�dmax and e�dm to account for the removed material. For a major-ity of the sands �22 of 30�, �dmax was obtained at zero watercontent �addition of water consistently resulted in lower �dmax�.Arcement and Wright �2001�, who studied granular backfills inTexas, also indicate that �dmax for poorly graded sands typicallyoccurs at zero water content. Of the remaining eight sands, fourhad greater than 6% fines and exhibited a conventional bell-

Table 2. Physical Properties and Geological Origins of the Sands

Sample Roundness emaxa emin

a�d-max

b

�kN /m3�

P1-S2 0.61 0.67 0.42 17.92

P1-S4 0.59 0.70 0.40 18.30

P1-S5 0.62 0.76 0.43 18.15

P1-S6 0.62 0.69 0.43 17.59

P1-S1 0.50 0.76 0.48 17.36

P1-S3 0.40 0.83 0.50 17.08

P1-S7 0.42 0.81 0.52 16.88

P2-S3 0.24 0.96 0.58 16.02

P3-S3 0.59 0.64 0.37 18.39

P3-S5 0.56 0.62 0.38 18.54

P3-S6 0.36 0.77 0.5 17.12

P3-S7 0.46 0.80 0.51 16.98

P2-S1 0.31 0.80 0.51 16.98

P2-S2 0.29 0.83 0.56 16.51

P2-S4 0.40 0.68 0.39 18.46

P2-S9 0.43 0.56 0.33 18.11

P2-S10 0.31 0.75 0.46 17.51

P2-S11 0.52 0.43 0.26 18.58

P3-S1 0.50 0.58 0.35 18.68

P3-S2 0.48 0.7 0.39 19.08

P4-S1 0.42 0.84 0.56 16.67

P5-S1 0.38 0.55 0.31 18.84

P2-S5 0.33 0.69 0.44 18.02

P2-S6 0.25 0.76 0.46 17.86

P2-S7 0.22 0.86 0.52 17.69

P2-S8 0.37 0.64 0.4 18.30

P2-S12 0.42 0.64 0.39 18.64

P3-S4 0.52 0.60 0.37 18.77

P4-S2 0.31 0.72 0.44 17.52

P4-S3 0.35 0.62 0.33 18.97

Note: emin determined by ASTM D 4253, emax determined by ASTM D 42according to ASTM D 4718.aemax=maximum void ratio; emin=minimum void ratio.b�d-max=maximum dry unit weight of P4 material; �d-maxC=maximum dr

shaped compaction curve, whereas four had negligible fines and


exhibited an increase in dry unit weight near saturation. Compac-tion tests performed by Arcement and Wright �2001� on siltysands and poorly graded sands with silt showed conventional bell-shaped compaction curves.

A graph of e�dm �compaction test� versus emin �vibratory table�is shown in Fig. 6�a�. Good correspondence exists between bothmeasures of maximum density, although the vibratory table typi-cally resulted in a slightly denser packing �emin=99% of e�dm,on average�. The variation of �dmax with respect to geologic de-posit type is shown in Fig. 6�b�. The maximum dry unit weight ofa given granular material represents its packing efficiency for aspecific packing energy and depends on particle characteristics,such as size, shape, and gradation. The variation in particlecharacteristics between sands of differing geologic deposit type�Fig. 3� results in a different median and range of �dmax for eachgeologic deposit type �Fig. 6�b��. For example, the coarserparticles and broader particle distributions of glacial outwash de-posits produce sands that achieve a greater �dmax for given com-pactive effort. However, for a given type of deposit, �dmax varieswithin a relatively narrow range ��2 kN /m3�, as has been shown

xCb

3� e�dmb �� Deposit type

Strengthgroup

0.44 32.9 Fluvial 1

6 0.39 33.4 Weathered sandstone 1

0.43 32.3 Weathered sandstone 1


0.49 35.8 Fluvial 2

0.53 34.3 Fluvial 2

0.55 34.8 Fluvial 2

2 0.55 35.1 Glaciolacustrine sand 2

0.41 35.4 Fluvial 2


0.52 34.5 Fluvial 2

0.54 35.4 Glaciolacustrine sand 2

0.54 36.6 Ice contact stratified 3

0.59 37.8 Glaciolacustrine sand 3

1 0.37 36.5 Glacial outwash 3


0.50 36.4 Esker 3




0.58 36.7 Glacial outwash 3

3 0.33 39.1 Ice contact stratified 3


0.47 40.5 Drumlin 4

0.48 39.6 Ice contact stratified 4


0.42 42.5 Glacial outwash 4

6 0.38 40.3 Fluvial 4

6 0.49 40.7 Ice contact stratified 4


ax determined by ASTM D 698 �standard Proctor�, and �dmaxC calculated

weight including R4 material; e�dm=void ratio at �d-maxC.

�d-ma

�kN /m

–

18.6

–

–

–

–

–

16.9

–

–

–

–

–

–

19.2

19.5

–

21.6

19.5

20.3

–

19.8

18.8

–

–

18.6

–

19.0

17.8

19.7

54, �dm

by others �Peck et al. 1974�.



Mineralogy and Chemical Properties

Mineralogy was determined for 15 samples by X-ray diffraction�Table 3�. Quartz constitutes the majority of each sand �Table 3�,except for P2-S5 �25% quartz�. Plagioclase, dolomite, potassium-feldspar, and phyllosilicates �includes illite, mica, kaolinite, andchlorite� are the other dominant minerals present along withquartz. The average mineralogical fractions of quartz, nonquartz,and phyllosilicates for weathered sandstone, fluvial, glacial out-wash, and ice contact stratified type deposits are shown in Fig. 7�X-ray diffraction was not performed on any miscellaneous gla-cial deposits�. The large fraction of quartz in the sands fromweathered sandstone and fluvial deposits reflects that these sandsare derived from the Cambrian and St. Peter Sandstones. Al-though quartz is the dominant mineral in all deposit types, there isan increase in nonquartz material for glacial outwash and ICSsands, which primarily originate from regions of nonsandstonebedrock.

The pH, chloride content, sulfate content, and resistivity ofeach sand were measured as indicated in Elias et al. �2001�. pHwas measured in accordance with AASHTO T 289-91 using asingle electrode pH meter, chloride content was measured follow-ing AASHTO T 291-94, sulfate content was measured followingT 290-95, and resistivity was measured following AASHTO T

Fig. 6. Minimum void ratio at maximum dry density from standardcompaction versus minimum void ratio from vibratory table �a�;influence of geologic origin on maximum dry unit weight �b�

Fig. 4. Relationship between maximum void ratio and minimumvoid ratio and comparison to trend line for clean sands ��5% fines�reported by Cubrinovski and Ishihara �2002�

Fig. 5. Relationships between minimum and maximum void ratioand �a� median particle size �D50�; �b� roundness; sand P2-S-11 is notincluded in the relationships due to the high gravel content of thesample
288-91. All of the sands meet the electrochemical requirements

for steel and geosynthetic reinforcing elements, except for P1-S4,which has a pH of 4.6 �Bareither 2006�. Elias et al. �2001� alsospecifies a limiting organic content of 1% when using steel rein-forcements. Visual inspection of the samples indicated that theorganic content was negligible.

Shear Strength Testing

Direct Shear Tests

The friction angle of each sand was measured in direct shearfollowing the procedure in AASHTO T 236-92. Tests were con-ducted in a 64 mm-wide square shear box that contained a31 mm-thick specimen. Small-scale direct shear tests were usedin lieu of other methods because direct shear testing is more com-mon in practice when evaluating backfill materials for MSE wallsand RS slopes.

Prior to testing, the sands were air dried and sieved on a No. 4sieve �4.75 mm�. The fraction passing No. 4 sieve was compacted

Table 3. Mineralogical Percentages of Select Sands from X-Ray Diffrac

SampleStrength

group QuartzPotassium-

feldspar Plagioclase

P1-S2 1 97.0 1.3 0.2

P1-S6 1 99.0 0.6 0.1

P1-S1 2 91.0 3.0 5.6

P1-S3 2 69.0 5.3 21.0

P3-S3 2 93.0 2.7 1.6

P3-S5 2 95.0 3.0 1.3

P2-S1 3 73.0 6.0 2.8

P3-S1 3 72.0 3.8 2.3

P3-S2 3 70.0 0.5 6.7

P4-S1 3 88.0 1.1 8.7

P5-S1 3 74.0 9.3 12.0

P2-S5 4 25.0 2.6 7.9

P2-S12 4 58.0 2.2 5.5

P3-S4 4 83.0 4.7 8.9

P4-S2 4 60.0 5.6 25.0aIncludes illite, mica, kaolinite, and chlorite.

Fig. 7. Percentages of mineralogical components in sands for differ-ent geologic deposits


air dried in the shear box in three lifts of equal thickness bytamping the top of each lift with a wooden tamper. The number oftamps per layer was adjusted to achieve the target density for eachspecimen �95% of maximum dry density determined by standardProctor compaction, which is the compaction criterion in Wiscon-sin for MSE backfill�.

Inundation of the specimen followed immediately after apply-ing the normal stress. Drainage was permitted through9 mm-thick perforated PVC plates placed on the top and bottomof the specimen. Separation was provided by a thin nonwovenheat-bonded calendered geotextile placed between the sand andthe plates. Compression of the PVC and geotextile was measuredat each normal stress and volume change measurements on initialnormal loading were corrected.

All tests were conducted using a constant rate of displacementof 0.24 mm /min. Normal stresses between 26 and 184 kPa wereapplied. The maximum stress is comparable to the stress expectedat the bottom of a 10 m high MSE wall backfilled with densegranular fill having a unit weight of approximately 18 kN /m3.Measurements of horizontal displacement, vertical displacement,and shear force were recorded using a personal computerequipped with a Validyne data acquisition card �UPC601-U� andLABView software. Two linear variable displacement transducers�LVDTs� �Schlumberger Industries Model AG/5, 5�0.003 mm�were used to measure horizontal and vertical displacements, and aload cell �Revere Transducer Model 363-D3-500-20P1,2.2�0.00015 kN� was used to measure shear force.

Failure was defined at the peak shear stress for all sands ex-hibiting a peak stress. For sands exhibiting only an ultimatestress, failure was defined as the shear stress corresponding to theinitial horizontal tangent to the shear stress-displacement curve.Mohr-Coulomb failure envelopes were obtained by linear least-squares regression with a nonnegative intercept. The failure en-velopes exhibited a high degree of linearity within the range ofnormal stresses employed, with coefficients of determination �R2�ranging from 0.997 to 1.000. Intercepts at the origin were small��8 kPa, and in most cases �4 kPa�, and were largely due tomachine friction rather than nonlinearity of the failure envelope�Bareither et al. 2008b�.

To be consistent with common practice for MSE walls and RS

alcite Hematite Dolomite PyriteTotal

phyllosilicatea

0.1 0.0 0.4 0.4 1.0

0.0 0.0 0.0 0.0 0.7

0.4 0.4 0.0 0.0 0.0

0.0 1.2 1.8 0.0 2.3

0.9 0.0 0.0 0.0 1.3

0.0 0.0 0.0 0.0 0.8

2.5 0.0 15.0 0.0 0.2

0.3 0.0 21.0 0.0 1.0

1.80 0.0 20.0 0.0 1.1

0.3 1.2 0.0 0.0 1.2

0.7 1.0 0.0 0.0 2.6

0.3 0.0 62.0 0.0 2.0

0.0 2.6 31.0 0.0 1.1

0.0 0.0 0.0 1.9 1.8

0.4 2.5 0.0 0.0 6.4

tion

C

slopes, the friction angles were defined from the slope of the


linear regressions. Friction angles were also computed from theshear strength at each normal stress assuming no intercept at theorigin. Friction angles determined by both methods differed byonly 1.5°, on average.

Comparison Tests

Comparative tests were conducted on four of the sands usingconsolidated-drained triaxial compression tests. Triaxial testswere performed on the fraction passing the No. 4 sieve��4.75 mm� compacted in a similar manner and to the same den-sity as specimens in direct shear. Effective confining pressuresranging from 21 to 83 kPa were used so that normal and shearstresses at failure on the estimated failure plane fell within therange of those used in the DS tests �Bareither et al. 2008a�. Fric-tion angles obtained from the direct shear and the triaxial tests fellwithin �1.7°, indicating that the friction angles obtained from thedirect shear test are representative.

To assess the effect of gravel fraction on friction angle, large-scale direct shear tests were conducted on the sands containing�5% gravel. Large-scale direct shear tests were conducted in a305 mm square box �152 mm thick� on the fraction passing a25.4 mm sieve. Test specimens were prepared so that the densityof the fraction passing a No. 4 sieve was consistent with specimendensities in small-scale direct shear. Large-scale direct shear tests

Fig. 8. Comparison of �� and dilatancy factor �a�; comparison of ��and relative horizontal displacement at failure �%� �b� for the shearbox used in this study, RHD=1% corresponds to a horizontal dis-placement of 0.64 mm

were performed at similar normal stresses and at a similar rate of


horizontal displacement as the small-scale direct shear tests �Ba-reither et al. 2008b�. Friction angles obtained form the large-scaletests typically were within �2.0° of the small-scale direct sheartests in which material retained on a No. 4 sieve was removed.Thus, for sands containing 5–30% gravel, the friction angles fromthe small-scale direct shear test are representative of the bulksample.

The direct shear test procedure used in this study was alsoevaluated for repeatability �Bareither et al. 2008a�. Comparison offive replicate tests on a single sand yielded �� ranging from 41.5°to 41.8°, with an average of 41.6° and standard deviation of 0.12°.Thus, the failure envelopes and friction angles obtained with thedirect shear testing procedure are highly repeatable when the testis conducted by a single operator.

Shear Strength Behavior

The 30 sands tested in direct shear exhibited a wide range ofshear strength behavior and a strong correspondence between ��and propensity for dilation. This correspondence is shown in Fig.8�a�, where �� is graphed versus the dilatancy factor ��, which isdefined at failure as

� =��H/Ho� f

��L/Lo� f�1�

where �H=change in thickness of the specimen; Ho=initialthickness after normal stress application and inundation;�L=change in horizontal displacement; and Lo=initial speci-men length. A strong correspondence also exists between ��and relative horizontal displacement �RHD= �horizontaldisplacement /specimen length�100� at failure �Fig. 8�b��.Sands with the larger �� typically have large dilatancy factors�Fig. 8�a�� and reach failure at smaller RHD �Fig. 8�b��.

Friction angle is also affected by particle roundness andparticle size as shown in Fig. 9. The data in Fig. 9 are groupedinto fine sands and medium/coarse sands based on median particlesize �D50�or�0.425 mm�. Lower roundness or larger median

Fig. 9. Relationship between �� and roundness for fine sand �D50

�0.425 mm� and medium/coarse sand �D50�0.425 mm�

particle size results in larger ��. Hennes �1951�, Koerner �1970�,


Zelasko et al. �1975�, and Cho et al. �2006� report similar corre-spondence between �� and particle size and roundness for labo-ratory mixtures of granular materials.

Friction angle is also affected by quartz content, as shownin Fig. 10�a�. The sands with less quartz contained greateramounts of potassium-feldspar, plagioclase, calcite, and/or dolo-mite �Table 3� and these minerals generally have higher slidingfrictional resistance compared to that of quartz �Horn and Deere1962; Ohnaka 1975�. Equally important, however, is that the pre-dominantly quartz sands also have greater roundness �Fig. 10�b��,which results in a lower friction angle �Fig. 9�. Sands with agreater fraction of quartz particles tend to have undergone morecycles of transport, and, therefore, tend to be more rounded �Pet-tijohn et al. 1965; Prothero and Schwab 2004�. The well-roundedquartz sands of Wisconsin that have low �� are primarily derivedfrom the Cambrian and St. Peter sandstones, and the particles inthese sandstones are some of the most physically weathered sandparticles in Wisconsin �Dott and Attig 2004�.

Friction Angle Groups

Friction angles of the sands are summarized in Table 2. The dataare presented in four groups �1–4� corresponding to sands havingsimilar friction angles �increasing group number corresponds toincreasing friction angle�. Sands in each group generally havesimilar stress-displacement behavior. Representative relationshipsof shear stress versus relative horizontal displacement �RHD� and

Fig. 10. Influence of quartz content �%� on �� a�; roundness �b�

vertical displacement versus RHD for each group are shown in


Fig. 11 at a normal stress of 99 kPa. Sands in Group 1 typicallyexhibit contractive behavior and an ultimate strength, whereassands in the other three groups exhibit dilatant behavior with adistinct peak shear stress and postpeak loss in strength. Excep-tions from the generalized stress-displacement behavior includeP2-S3 �Group 2� and P2-S4 and P3-S2 �Group 3�, which showedcontractive behavior and an ultimate shear stress �Fig. 12�. Thesesands also are the outlier points in Fig. 8�b� �� versus RHD�.

Group 1 includes three weathered sandstone deposits and onefluvial deposit that have friction angles between 32° and 33°.Each of these sands consists predominantly of well-rounded me-dium to fine grained quartz particles �Table 2� from the Cambrianand St. Peter sandstones. The rounded grain shape and the unifor-mity in grain size �Fig. 3� limit interlocking between neighboringparticles, resulting in very little dilation �Figs. 8 and 11� and anultimate shearing strength that is attained primarily from particlefrictional resistance and rearrangement �Terzaghi et al. 1996�.

Group 2 includes eight sands that have friction angles rangingfrom 34° to 36°. Five of the sands are from fluvial deposits. Twoglaciolacustrine sands and a weathered sandstone comprise therest of Group 2. The sands in Group 2 have larger particle size orlower roundness compared to the sands in Group 1, resulting inhigher friction angles. The larger particle size and lower round-

Fig. 11. Representative behavior of sands: �a� shear stress versusrelative horizontal displacement �RHD�; �b� vertical displacementversus RHD in each strength group at normal stress of 99 kPa; Group1 �P1-S4�, Group 2 �P3-S7�, Group 3 �P5-S1�, and Group 4 �P2-S5�

ness of the fluvial materials �Fig. 3� are attributed to the influx of


sediments from recent glaciations. The fluvial deposits in Group 2were obtained from gravel pits of major river systems in Wiscon-sin, which accommodated glacial meltwater as recently as theWisconsin Glaciation. The influx of glacial sediments providesparticles to the fluvial systems that are less rounded and coarser,compared to particles eroded from the underlying sandstones. Theglaciolacustrine sands have low roundness due to glacial sedi-ments that are deposited in a lake setting where there is no furtherparticle shape modification. The weathered sandstone in Group 2has a lower roundness compared to the weathered sandstones ofGroup 1. These differences in physical properties are likely due todifferences of the sediments contained in the parent sandstone.

Sand P2-S3, the only sand in Group 2 not exhibiting dilatantshearing behavior �Fig. 6�b��, is angular and predominantly finesand from a glaciolacustrine sand deposit, and contains more than12% fines. The larger percentage of fines distinguishes P2-S3from the other sands in Group 2, all of which have less than 1%fines �Table 1�.

Group 3 includes 10 sands that have friction angles rangingfrom 37° to 39°. Six of the sands in Group 3 consist of glacialoutwash sediments deposited in the medial and proximal glacialzones. Group 3 also includes two sands from ICS deposits, onesand from an esker deposit, and one glaciolacustrine sand deposit.The glacial outwash sands are more broadly graded �P4-S1 isan exception�, contain a larger fraction of coarse particles, andconsist of more angular particles compared to those in Groups 1

Fig. 12. Relationships between shear stress and relative horizontaldisplacement �RHD� �a�; vertical displacement and RHD �b� at nor-mal stress of 99 kPa for sands P2-S3, P2-S4, and P3-S2

and 2, which combine to produce a denser packing, more dilation,


and higher �� Kolbuszewski and Frederick 1963; Youd 1973;Edil et al. 1975�. Each of the physical characteristics of the glacialoutwash sands �particle size, gradation, and shape� is directly in-fluenced by glacial processes. The glacial outwash sands are morebroadly graded �Fig. 3�b�� due to varying sized particles con-tained in the glacial meltwater that are often deposited rapidlynear the glacier margin. The glacial outwash sands are also de-posited at a shorter distance to the glacier margin compared tofluvial deposits, which results in coarser �Fig. 3�a�� and moreangular �Fig. 3�c�� particles.

The higher �� associated with the nonglacial outwash materi-als is also due to more angular particles, larger particle size,and/or broader particle gradation compared to sands in Groups 1and 2. The low roundness of the ICS deposits and the esker de-posit is due to the short transport distance of the particles. Thelow roundness of the glaciolacustrine sand is due to similar pro-cesses as for the glaciolacustrine sands in Group 2. The particlesize and gradation of the nonglacial outwash sands depends onthe sediment contained in the glacial meltwater, and can be highlyvariable. All of the sands in Group 3 also contain a greater frac-tion of nonquartz material �potassium-feldspar, plagioclase, cal-cite, and/or dolomite�, compared to the sands in Groups 1 and 2�Table 3�, which may also contribute to the higher �� of the sandsin Group 3 compared to the sands in Groups 1 and 2. As depictedin Fig. 7, these glacial outwash and ICS deposits have a greaterfraction of nonquartz material, primarily from the formation ofthese types of deposits in regions of nonsandstone bedrock.

As mentioned previously, samples P2-S4 and P3-S2 do notexhibit the dilative strength-deformation behavior characteristicof the other sands in Group 3. The reason for this difference is notapparent.

The eight sands in Group 4 have friction angles ranging be-tween 40° and 42°. They are glacial outwash and ICS deposits�the exception is Sand P3-S4, which is fluvial�. The sands inGroup 4 are not necessarily as well graded as the sands in Group3, but they are more angular and/or coarser grained, which com-bine to produce a higher ��. The sands in Group 4 also have thehighest fraction of nonquartz material �Table 3�. The lower round-ness, larger particle size, and/or broader gradation, combined withminerals exhibiting higher friction, result in the largest �� of thesands that were studied. Glacial processes impact the physicalcharacteristics of the glacial outwash and ICS sands in a similarmanner as described for Group 3. The fluvial sand in Group 4contains particles with a higher roundness compared to othersands in Group 4 �Table 2�; however, this sand contains coarserparticles relative to other fluvial deposits, which contributes tohigher ��. Additionally, this fluvial sand was deposited in closerproximity to the glacial margin, and is more similar to the glacialoutwash sands in Group 4 than the other fluvial sands, which arein Group 2.

Estimating Shear Strength Based on PhysicalProperties

Multivariate Regression Modeling

A multivariate regression analysis was used to develop a model topredict �� based on relevant physical characteristics. Regressionwas preferred relative to other prediction methods because of thesimplicity with which a regression equation can be applied, the
ability to ensure statistical significance of each independent vari-

able, and the clarity with which physical significance between thedependent and independent variables can be evaluated.

Stepwise regression was used because the method only incor-porates independent variables that are statistically significant. For-ward and backward stepwise regressions were performed with ��as the dependent variable and the following as independent vari-ables: D60, D50, D10, Cu, Cc, % fines, Gs, emax, emin, �d-max, and Rs.A forward stepwise regression begins with no independent vari-ables and sequentially adds variables to a model in order of theirsignificance in predicting the dependent variable. A backwardstepwise regression begins with all independent variables and se-quentially removes variables from a model that are least signifi-cant in predicting the dependent variable. Independent variablesare added �forward regression� or removed �backward regression�until only those variables that are statistically significant �as mea-sured by an F-test� are included in the model �Ramsey and Scha-fer 2002�. A significance level �� of 0.05 was used to evaluatestatistical significance of each independent variable.

Forward and backward stepwise regression results were ana-lyzed to obtain the best overall model �i.e., highest coefficientof determination R2�. Variables included in the model were re-quired to have statistical and physical significance and to bereadily measured in conventional laboratories. The followingmodel was obtained:

�� = 1.89 + 20.56 D10 + 2.35 �d max − 24.10 Rs �2�

where D10 is in mm, Rs=weighted average Krumbein roundnessfor the bulk sample �dimensionless�, and �d max is in kN /m3 asdetermined by ASTM D 698-Method A using the sample fractionpassing the No. 4 sieve. The model has an R2=0.83 and all threeindependent variables have p-values �0.0001 �i.e., �0.05�. Thecoefficients also have physical significance. The positive coeffi-cient on D10 infers that �� increases with increasing particle size�i.e., as reported by Hennes �1951� and as shown in Fig. 9� andthe negative coefficient on Rs infers that �� decreases with in-creasing roundness �i.e., as reported by Koerner �1970�, Zelaskoet al. �1975�, and Cho et al. �2006� and shown in Fig. 9�. Thevariable �d max reflects the packing characteristics of a sand for aspecific packing energy, and is influenced by the size, gradation,and shape of the particles �Youd 1973; Edil et al. 1975�. Materialsthat pack more efficiently have higher ��, when all other factorsare equal �Kolbuszewski and Frederick 1963; Zelasko et al.1975�. Thus, the coefficient for �d max should be positive. A posi-tive relationship between �� and �d max is also reported in NAV-FAC �1986�.

A graph of �� predicted using Eq. �2� versus the measured ��is shown in Fig. 13�a�. The regression model predicts �� within�2° �shown by dashed lines� of the measured �� for nearly allsands in this study. An additional comparison was made betweenthe average friction angle in each strength group and frictionangles computed using Eq. �2� and the average D10, �d max, and Rs

for each group �Table 4�. This comparison is shown as the solidsymbols in Fig. 13�a�. The difference between the average mea-sured �� in each group and �� computed using the average prop-erties in each group is less than 1° for each group.

Of the three independent variables in Eq. �2�, roundness ismeasured least frequently in practice. Thus, an analysis was con-ducted to evaluate the efficacy of Eq. �2� for cases where round-ness was determined by a simple visual inspection. The Krumbeinroundness scale �0.1 to 0.9� was partitioned into five roundnesscategories �angular, subangular, subrounded, rounded, and wellrounded�, with each category assigned a range and average round-
ness as tabulated in Table 5. Each sand was categorized as well

rounded �Rs=0.82�, rounded �Rs=0.66�, subrounded �Rs=0.50�,subangular �Rs=0.34�, or angular �Rs=0.18�. For this analysis, theaverage roundness in each roundness category was assigned toeach of the 30 sands based on the determined weighted roundnessfor each sand �Table 2� falling within the range of roundnessmeasurements for the five roundness categories �Table 5�. Theactual D10 and �d max for each sand along with the average round-ness were used to calculate �� based on Eq. �2�. Even with round-ness defined using the five general categories, the multipleregression model predicts �� within �2° for nearly all of thesands.

Comparison of Prediction Methods

Methods to predict the friction angle of granular materials fromphysical and engineering properties have also been presented inNAVFAC �1986�, Schmertmann �1977�, and Terzaghi et al.�1996�. NAVFAC �1986� presents one of the most widely refer-enced correlations, where �� is estimated with respect to USCS

Fig. 13. Comparison between �� predicted using regression modeland �� measured in direct shear for sands in this study �a� and ��predicted using regression model, NAVFAC �1986�, Schmertmann�1977�, Terzaghi et al. �1996�, and �� reported in Table 6

classification and dry unit weight or relative density. The correla-


tion presented in Schmertmann �1977� provides an estimate of ��based on relative density and generalized material descriptions.The method in Terzaghi et al. �1996� uses a secant definition forthe friction angle that is a function of effective normal stress aswell as generalized material descriptions and porosity.

A compilation of friction angles measured in direct shear andtriaxial compression by others is in Table 6. This collection offriction angles was created to represent a broad range of sands,but is not intended to be inclusive of all friction angles for sandsreported in the literature. The data sources in Table 6 also includesufficient information to assess whether each of the four predic-tion methods was applicable, as well as the input data required foreach method. Comparisons between friction angles predicted bythe methods in NAVFAC �1986�, Schmertmann �1977�, Terzaghiet al. �1996�, Eq. �2�, and the measured friction angles reported inTable 6 are shown in Fig. 13�b�. On average, the NAVFAC �1986�

Table 5. Roundness Categories Including Krumbein Images, Rangeof Roundness, and Average Roundness

Table 4. Average and Standard Deviation of Independent Variables in EqVariables, and Range of �� Predicted with Eq. �2� Using Independent Va

GroupD10

�mm��d-max

�kN /m3�

1 0.192�0.079a 18.22�0.53 0.3

2 0.177�0.08 17.94�0.95 0.4

3 0.161�0.049 17.30�0.82 0.4

4 0.178�0.022 17.99�0.31 0.6aStandard deviation.


method underestimates �� by 2.4°, Eq. �2� underestimates �� by2.0°, the Schmertmann �1977� method overestimates �� by 0.8°,and the method in Terzaghi et al. �1996� overestimates �� by 6.6°.The standard deviation of all four correlation techniques is simi-lar, ranging from 2.8° to 3.5°. Therefore, each of the four predic-tion methods is capable of predicting �� with similar precision;however, the bias varies between methods. The secant definitionin the Terzaghi et al. �1996� method may have contributed to thegreater bias associated with this method in Fig. 13�b�. Given thatNAVFAC and Eq. �2� have negative bias, �� estimated with thesemethods tends to be conservative, on average.

Eq. �2� has the advantage that all of the independent variablescan be measured directly using conventional methods and a pre-diction can be made using a simple equation rather than a chart.Eq. �2� can be used to estimate �� for preliminary geotechnicaldesign or to provide a reasonableness check for �� measured in adirect shear test. However, Eq. �2� should only be applied to therange of physical parameters of the sands used in this study �i.e.,D10 from 0.05 to 0.31 mm, �d max from 16 to 19 kN /m3, and Rs

from 0.1 to 0.9�. Moreover, Eq. �2� was developed using datafrom sands from Wisconsin compacted at 95% of maximum dryunit weight, most of which were poorly graded. The applicabilityof Eq. �2� to other sands, sands with greater fines or coarse frac-tion, sands prepared at other densities, and to stresses outside therange used in this study �26 to 184 kPa�, is not known and needsgreater evaluation.

Conclusions

This paper presents the findings of a study conducted to deter-mine how geologic processes and physical properties affect theshear strength of compacted natural sands from Wisconsin used asgranular backfill material. Thirty naturally occurring sands weresampled representing the regional variation throughout Wiscon-sin. Shear strength of each sand was measured in direct shear fora range of normal stresses characteristic of MSE wall and RSslope backfills. Friction angles �� obtained from the direct sheartests were related to the geologic origins and physical character-istics of the sands.

The 30 sands were differentiated into four strength groupsbased on shear strength and deformation behavior. Sands com-prising each strength group share similar geologic origin and/orphysical characteristics that contribute to similarity in the shearstrength and deformation behavior. The lowest strength sands arecomprised of quartz particles that have undergone extensive trans-port and physical weathering. These particles are mechanicallyweathered from the underlying Cambrian and St. Peter sandstonesand are well rounded, medium to fine in size, and uniformlygraded. The highest strength sands, derived primarily from out-wash of the Wisconsin glaciation, have undergone less transport

r Strength Groups, �� Predicted with Eq. �2� Using Average IndependentUnique to Each Sand

Measured ��Predicted

average ��Predictedrange ��

0 41.0�1.0 40.3 42.2–39.3

8 37.6�1.2 38.1 40.7–35.8

1 35.2�0.7 35.3 36.6–33.7

1 32.8�0.5 33.2 33.8–31.8

. �2� foriables

Rs

5�0.1

0�0.0

4�0.1

1�0.0

and physical weathering, have lower quartz content, are more


angular, are larger in size, and have broader gradation comparedto the other sands. Sands with higher �� also have higher dila-tancy factor, confirming that the shear strength of compactedsands is directly related to the propensity for dilation.

A multivariate regression model was developed that predicts�� of compacted sands in Wisconsin. The model predicts ��based on D10, �d max, and Rs with reasonable accuracy. Variablesincluded in the regression model were required to be statisticallysignificant �p-value �0.05�, to have physical significance regard-ing effect on ��, and to be readily measured in the laboratory. Themultivariate regression model can be used to estimate �� for pre-liminary geotechnical design or to provide a reasonableness checkon �� for granular backfill materials measured in direct shear.

Acknowledgments

Financial support for this study was provided by the WisconsinDepartment of Transportation �WisDOT� through the WisconsinHighway Research Program. The assistance of Daniel Reid, Den-nis Althaus, and Bruce Pfister of WisDOT is greatly appreciated.Xiaodong Wang, geotechnical laboratory manager at Universityof Wisconsin-Madison, assisted with the laboratory testing. X-raydiffraction analyses were conducted by K/T Geoservices, Inc. ofArgyle, Texas. The findings and inferences that have been re-

Table 6. Properties of Other Granular Materials Used in Assessment of

Reference Material

Nash �1953� Closely graded river sand

Kirkpatrick �1965� Leighton buzzard sand

Glass beads

Grading No. 3

Lee and Seed �1967� Sacramento river sand

Koerner �1970� Crushed Ottawa sand

Ottawa sand

Holubec and D’Appolonia �1973� Ottawa sand

Southport sand

Zelasko et al. �1975� Ottawa 35–45

Ottawa 50–70

Ottawa 70–100

Ottawa 100–140

Evanston beach 35–45



Franklin Falls 30–45

Franklin Falls 50–70

Mix A 20–70

Mix B 20–70

Mix F 20–45

Salgado et al. �2000� Ottawa sand �ASTM C 778�

Simoni and Houlsby �2006� Leighton buzzard sand

Cerato and Lutenegger �2006� Brown mortar

OttawaaDS=Direct shear and TC=triaxial compression.bKrumbein roundness approximated from material descriptions and avera

ported are solely those of the writers. This paper has not been


reviewed by WisDOT. Endorsement by WisDOT is not impliedand should not be assumed.

References

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Bareither, C. A. �2006�. “Shear strength of backfill sands in Wisconsin.”MS thesis, Univ. of Wisconsin-Madison, Madison, Wis.

Bareither, C. A., Benson, C. H., and Edil, T. B. �2008a�. “Reproducibilityof direct shear tests conducted on granular backfill materials.” Geo-tech. Test. J., 31�1�, 84–94.

Bareither, C. A., Benson, C. H., and Edil, T. B. �2008b�. “Comparison ofshear strength of granular backfill measured in small-scale and large-scale direct shear tests.” Can. Geotech. J., in press.

Benn, D. I., and Evans, D. J. A. �1998�. Glaciers and glaciation, OxfordUniversity Press, New York.

Bennett, M. R., and Glasser, N. F. �1996�. Glacial geology: Ice sheets andlandforms, Wiley, Chichester, England.

Cerato, A. C., and Lutenegger, A. J. �2006� “Specimen size and scaleeffects of direct shear box tests on sands.” Geotech. Test. J., 29�6�,1–10.

Cho, G. C., Dodds, J., and Santamarina, J. C. �2006�. “Particle shapeeffects on packing density, stiffness, and strength: Natural and crushed

tion Methods

Testethoda

D10

�mm�Krumbeinroundnessb

Maximumdry unitweight

�kN /m3�

Reportedfrictionangle

DS 0.14 0.34 16.1 36.5

TC 0.37 0.50 17.5 40.5

0.31 0.82 17.9 27.0

0.36 0.50 17.9 37.0

TC 0.14 0.34 16.3 39.0

TC 0.25 0.34 16.3 40.3

0.25 0.50 17.0 36.9

TC 0.15 0.66 17.6 35.0

0.25 0.34 17.2 40.0

TC 0.37 0.60 17.7 39.1

0.22 0.52 17.1 38.5

0.16 0.50 17.0 38.9

0.11 0.50 17.0 37.9

0.37 0.43 17.3 37.2

0.22 0.41 16.9 37.7

0.16 0.42 17.2 39.3

0.38 0.35 16.1 40.4

0.22 0.34 16.0 40.0

0.23 0.35 17.0 41.7

0.23 0.59 18.4 39.0

0.39 0.36 16.6 41.3

TC 0.28 0.50 17.6 35.9

DS 0.21 0.34 18.8 45.0

DS 0.30 0.34 16.7 48.3

0.30 0.66 17.7 35.6

Table 5 if not provided directly.

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