Geological and Physical Factors Affecting the Friction Angle of ...

Geological and Physical Factors Affecting the Friction Angle of 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 from Wisconsin that are used as granular backfill for mechanically stabilized earth walls and reinforced soil slopes. Physical properties and shear strength were determined for 30 compacted sands collected from a broad range of geological deposits. Relationships between strength/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, and poorly 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 共␾⬘兲 of compacted sands from comparable geological origins based on effective particle size 共D10兲, maximum dry unit weight 共␥dmax兲, and Krumbein roundness 共Rs兲. DOI: 10.1061/共ASCE兲1090-0241共2008兲134:10共1476兲 CE Database subject headings: Sand; Friction; Displacement; Mineralogy; Backfills; Slopes.

Introduction Design of mechanically stabilized earth 共MSE兲 walls and reinforced soil 共RS兲 slopes by many agencies, including the Wisconsin Department of Transportation 共WisDOT兲, is generally conducted following the guidelines developed by Elias et al. 共2001兲 for the Federal Highway Administration 共FHWA兲. These guidelines indicate that properly compacted backfill can be assumed to have an internal angle of friction 共␾⬘兲 of 34° provided that specified criteria for particle size distribution and plasticity index are satisfied. In Wisconsin, natural sands meeting the criteria in Elias et al. 共2001兲 generally are used for MSE wall backfill and for RS slopes. However, testing conducted by WisDOT in 2002–03 indicated that some compacted natural sands meeting the criteria in Elias et al. 共2001兲 could have friction angles less than 34°. Sands having lower friction angles had similar geologic history, suggesting that geological factors should be considered when evaluating the suitability of sands for backfill. Accordingly, a statewide examination was undertaken to assess how geologic origin and physical properties influence the friction angle of naturally occurring sands in Wisconsin. 1

Graduate Research Assistant, Geological Engineering, Univ. of Wisconsin-Madison, Madison, WI 53706. E-mail: [email protected] 2 Professor, Geological Engineering, Univ. of Wisconsin-Madison, Madison, WI 53706. E-mail: [email protected] 3 Wisconsin Distinguished Professor and Chairman, Geological Engineering, Univ. of Wisconsin-Madison, Madison, WI 53706. E-mail: [email protected] 4 Professor Emeritus, Geology and Geophysics, Univ. of WisconsinMadison, Madison, WI 53706. E-mail: [email protected] Note. Discussion open until March 1, 2009. Separate discussions must be submitted for individual papers. The manuscript for this paper was submitted for review and possible publication on January 17, 2007; approved on February 6, 2008. This paper is part of the Journal of Geotechnical and Geoenvironmental Engineering, Vol. 134, No. 10, October 1, 2008. ©ASCE, ISSN 1090-0241/2008/10-1476–1489/$25.00.

Thirty sands throughout Wisconsin were sampled to obtain a representative assortment of potential granular backfill materials. Although all of the samples were collected in Wisconsin, they represent a reasonably wide range of geological origins and physical characteristics, and, therefore, are likely to be representative of the northern Midwest and other geographic regions where glaciation has occurred. Physical properties and geological origin of each sand were studied, and the friction angle of each sand was measured in direct shear test as is commonly done by WisDOT and other transportation agencies when evaluating the shear strength of compacted backfill materials for MSE walls and RS slopes 共Bareither et al. 2008b兲. Interface friction angles 共i.e., friction angles between backfill and reinforcing members兲 are also needed in the design and construction of MSE walls and RS slopes. However, this study focused only on the internal friction of granular materials; interface friction and its relationship to internal friction was beyond the scope of the study. Relationships between shear strength, physical properties, and regional geology were established. Additionally, a regression model was developed that can be used to estimate ␾⬘ based on commonly measured physical characteristics.

Sources of Sands Thirty samples were collected from the locations shown in Fig. 1. These sources represent the sand deposits typically found in Wisconsin 共weathered sandstone, fluvial, glacial outwash, ice-contact stratified deposits, and other deposits of glacial origin兲. Sampling was conducted at greater density near major metropolitan areas, where there is a greater need for granular backfill materials. When possible, samples were selected from an in situ layer at each site so that a precise geologic origin could be established. At three locations, however, samples were collected from a stockpile of sieved and washed backfill material. For these sands, the geologic origin was generalized for the entire location. Approximately 0.1 m3 of material was collected at each site. Each sample was

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Wisconsin Glaciation. Thus, sands derived from fluvial deposits contain particles having a broader distribution of size, shape, and mineralogy compared to the sands derived solely from weathered sandstone. Glacial Outwash Deposits Ten samples were obtained from glacial outwash deposits 共Fig. 1兲 formed during the Wisconsin Glaciation from glaciers overlying nonsandstone bedrock. These deposits were sampled at the highest frequency because of their abundance and broad geographic availability. Sediments contained in the glacial outwash samples were deposited closer to the glacier margin compared to those of the fluvial deposits. Outwash sediment near the glacier margin is often deposited rapidly during flood events, resulting in very well-graded sands and gravels that are more angular and coarser grained compared to fluvial deposits 共Church and Gilbert 1975; Werritty 1992; Bennett and Glasser 1996; Maizels 2002兲. Ice Contact Stratified Deposits

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

blended together thoroughly and allowed to air dry. After air drying, each sample was blended again and placed uniformly in a large 共0.12 m3兲 sealed container. Weathered Sandstone Deposits Four samples were obtained from deposits derived from eolian and fluvial weathering of underlying Cambrian and St. Peter sandstones 共Fig. 1兲. The sand particles in these sandstones had been exposed to more than 100 million years of eolian and fluvial abrasion before consolidation into sandstone 共Dott and Attig 2004兲. These weathering processes resulted in sandstones comprised of well-rounded medium-to-fine sand-size particles. These particles are comprised predominantly of quartz because of its resistance to disintegration and decomposition 共Prothero and Schwab 2004兲. The sand deposits derived from fluvial and eolian weathering of the Cambrian and St. Peter sandstones have the same characteristics as the sand particles in the parent rocks 共Dott and Attig 2004兲. These sand deposits are also free from direct glacial activity, which is unusual in Wisconsin and many other northern states in the US. The majority of Wisconsin was glaciated during the past 2.5 million years, and more significantly during the Wisconsin Glaciation 共25,000 and 10,000 bp兲共Clayton et al. 1991兲.

Four samples were obtained from ice-contact stratified 共ICS兲 deposits 共Fig. 1兲 that formed during the Wisconsin glaciation. ICS deposits are water-laid sediments formed in contact with glacial ice that consist of more angular particles due to short transport distances. They vary in particle size and gradation due to fluctuations in meltwater discharge and sediment concentration. Miscellaneous Glacial Deposits Five samples were obtained from miscellaneous glacial deposits, including drumlin, esker, and glaciolacustrine 共lake兲 sand deposits 共Fig. 1兲. The composition and physical properties of drumlins depend on the material present during glacial advance 共Bennett and Glasser 1996兲. The drumlin that was sampled contained outwash sands and gravels deposited during an earlier glacial advance. Eskers can be composed of sediments ranging from sorted silt to broadly graded and matrix-supported gravel 共Benn and Evans 1998兲 that typically have traveled less than 15 km from the outcrop source 共Lee 1965; Price 1973兲. The esker deposit in this study varied from poorly graded fine sand to well-graded gravel. The sample collected was from a poorly graded medium-fine sand layer. Glaciolacustrine sands were obtained from deposits related to Glacial Lake Oshkosh and Glacial Lake Wisconsin that consist of poorly-graded fine sands characteristic of selective deposition in waters having low turbulence. Sample P2-S3 may have been reworked postglaciation due to fluvial and eolian weathering.

Physical Characteristics

Fluvial Deposits

Index Properties

Fluvial deposits 共Fig. 1兲 were sampled at six locations. The fluvial deposits consist of poorly graded stratified sand with layers of fine sediment deposited during periods of decreased flow in the Wisconsin, Mississippi, Black, and Chippewa Rivers. All of the fluvial deposits lie in regions underlain by Cambrian Sandstone, which is a primary source of sediment. However, all of these fluvial deposits also contain glacial outwash sediments from large river systems that acted as outlets for glacial meltwater during the

Index properties of the samples are summarized in Table 1 and the particle size distribution curves are shown in Fig. 2. The samples vary from uniformly to broadly graded, with median particle size 共D50兲 ranging from 0.15 to 3.50 mm, coefficient of uniformity 共Cu兲 ranging from 1.8 to 34.1, and fines content ranging from 0.1 to 14.4%. The gravel content of the samples ranges from 0 to 47.8%. All of the samples classify as sands in the Unified Soil Classification System in ASTM D 2487, with the majority

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Table 1. Index Properties of the Sands Sample

D50a 共mm兲

D10a 共mm兲

C ub

C cb

Fines 共%兲

Gravel 共%兲

G sc

USCSb

P1-S2 0.38 0.20 2.18 1.03 0.4 2.0 2.63 SP P1-S4 0.30 0.15 2.67 0.95 1.0 5.7 2.65 SP P1-S5 0.44 0.19 2.63 1.01 0.2 1.8 2.65 SP P1-S6 0.34 0.17 2.35 1.15 0.8 1.8 2.63 SP P1-S1 0.31 0.18 1.86 1.12 0.8 0.0 2.64 SP P1-S3 0.31 0.15 2.33 0.92 0.8 0.0 2.66 SP P1-S7 0.29 0.15 2.03 0.96 0.7 0.0 2.66 SP P2-S3 0.16 0.08 2.27 0.86 12.6 10.2 2.68 SM P3-S3 0.54 0.25 2.48 0.92 0.6 0.3 2.66 SP P3-S5 0.48 0.19 3.00 0.89 0.8 4.9 2.65 SP P3-S6 0.29 0.15 2.07 1.04 0.8 0.0 2.65 SP P3-S7 0.22 0.15 1.79 0.96 0.6 0.0 2.66 SP P2-S1 0.30 0.17 1.88 0.97 1.1 1.0 2.68 SP P2-S2 0.20 0.10 2.10 1.20 0.9 0.0 2.67 SP P2-S4 0.32 0.08 5.30 1.92 9.8 17.8 2.68 SP-SC P2-S9 0.50 0.19 4.16 0.68 0.5 22.1 2.67 SP P2-S10 0.20 0.09 2.33 1.35 5.0 0.7 2.7 SP P2-S11 3.50 0.27 34.07 0.14 0.8 47.8 2.71 SW P3-S1 0.63 0.25 3.20 0.82 1.1 10.0 2.72 SP P3-S2 0.48 0.13 4.77 1.04 5.7 12.1 2.72 SP-SM P4-S1 0.58 0.31 2.00 1.10 0.1 3.3 2.69 SP P5-S1 0.69 0.18 5.28 0.76 5.2 16.6 2.67 SP-SM P2-S5 0.64 0.28 2.82 0.84 0.5 8.3 2.76 SP P2-S6 0.27 0.11 2.82 1.06 3.5 0.4 2.75 SP P2-S7 0.15 0.054 3.15 1.32 14.4 0.0 2.75 SM P2-S8 0.50 0.21 3.05 0.81 1.2 6.7 2.71 SP P2-S12 0.42 0.18 3.06 0.85 1.6 2.2 2.7 SP P3-S4 0.70 0.29 2.86 1.00 0.4 4.3 2.69 SP P4-S2 0.48 0.21 2.86 0.81 2.3 3.3 2.71 SP P4-S3 0.77 0.20 6.50 0.59 1.7 13.2 2.74 SP a Particle size determined by ASTM D 422: D50 = particle diameter at 50% finer; D10 = particle diameter at 10% finer. b USCS= Unified Soil Classification System 共ASTM D 2487兲; Cu = coefficient of uniformity; Cc = coefficient of curvature. c Specific gravity 共Gs兲 determined by ASTM C 127 and ASTM D 854. d AASHTO= American Association of Highway and Transportation Officials 共M 145-91兲.

共24 of 30兲 classifying as poorly graded sand 共SP兲. All of the sands classify as A-1, A-2, or A-3, i.e., “granular” according to the AASHTO soil classification system. The variations of D50 and Cu with respect to geologic deposit type are shown in Figs. 3共a and b兲. Sands derived from weathered sandstone are all poorly graded 共2.35艋 Cu 艋 3.00兲 medium to fine clean sands with similar specific gravity of solids 共2.63-2.66兲. Sands from fluvial deposits are more uniformly graded 共1.86艋 Cu 艋 2.86兲 compared to weathered sandstone, but have a broader range of median particle size 共0.29 mm艋 D50 艋 0.70 mm兲. Sands from glacial outwash contain the coarsest particles and sands from glacial outwash and ICS deposits represent the broadest distributions in particle size 共Fig. 3兲. The glaciolacustrine sands are poorly graded with the smallest median particle size 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 narrow range for naturally occurring sands 共Zelasko 1966; Edil et al. 1975兲 and surface texture is a second order feature that is cum-

AASHTO classificationd A-3共0兲 A-3共0兲 A-1-b共0兲 A-3共0兲 A-3共0兲 A-3共0兲 A-3共0兲 A-2-4共0兲 A-1-b共0兲 A-1-b共0兲 A-3共0兲 A-3共0兲 A-3共0兲 A-3共0兲 A-3共0兲 A-1-b共0兲 A-3共0兲 A-1-a共0兲 A-1-b共0兲 A-1-b共0兲 A-1-b共0兲 A-1-b共0兲 A-1-b共0兲 A-3共0兲 A-2-4共0兲 A-1-b共0兲 A-3共0兲 A-1-b共0兲 A-1-b共0兲 A-1-b共0兲

bersome to measure and highly variable 共Cho et al. 2006兲. Hence, for this study, particle shape was characterized by roundness using a visual procedure conducted with an optical microscope and charts developed by Krumbein 共1941兲. Digital image analysis techniques are currently available for determination of particle shape 共Janoo 1998; Jensen et al. 2001; Cho et al. 2006兲. However, the Krumbein method was adopted based on access to readily available equipment and its established use in previous research 共Edil et al. 1975; Zelasko et al. 1975兲. The Krumbein method can also be implemented by laboratories with little specialized equipment. Particles from each sample were partitioned into four size fractions: gravel 共⬍76.2 and ⬎4.75 mm兲, coarse sand 共⬍4.75 and ⬎2.0 mm兲, medium sand 共⬍2.0 and ⬎0.425 mm兲, and fine sand 共⬍0.425 and ⬎0.075 mm兲. Roundness was determined for each size fraction constituting at least 5% by weight of the total sample. Edil et al. 共1975兲 determined roundness for sand particles based on charts in Krumbein 共1941兲 and reported that viewing at least 25 particles yielded a reliable mean roundness. For this study, 50 particles were analyzed from each size fraction and a weighted whole sample roundness was calculated for each sand


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

based on the average roundness and percentage 共by weight兲 of the sample in each size fraction. The Krumbein roundness chart was kept at a constant scale and the particular size fraction was viewed at a similar scale as the particles on the roundness chart. The roundness measurements are summarized in Table 2. The roundness varies between a minimum of 0.22 共angular兲 to a maximum of 0.62 共rounded兲. The variation of roundness with respect to geologic deposit type is shown schematically in Fig. 3共c兲. Roundness is highest and most uniform for weathered sandstone deposits due to the uniformity of rounded particles in the parent sandstones. Roundness decreases from fluvial to glacial outwash to ICS deposits corresponding to a decrease in distance from the glacier margin 共i.e., abrasion causing roundness increases with transport distance兲. The roundness for the glaciolacustrine sands is typically low, but varies with distance and method of transport prior to deposition. Minimum and Maximum Void Ratios Three minimum void ratio 共emin兲 and three maximum void ratio 共emax兲 tests were performed on each sand. The minimum or maximum void ratio reported for each sand is the minimum or maximum void ratio obtained from the three tests. Maximum void ratio was determined according to Method B of ASTM D 4254 using a tremie tube and a 2.83 L mold. Minimum void ratio was measured according to ASTM D 4253 共Method 2A兲 using airdried soil in a 2.83 L mold. The mold was vertically vibrated for 12 min at a frequency of 50 Hz with a 25.6 kg surcharge.

Fig. 3. Influence of geologic deposit type on physical characteristics of sands: 共a兲 median particle size; 共b兲 coefficient of uniformity; and 共c兲 particle roundness; the box represents the middle 50% of the data; the central line in the box represents the median; the outer boundaries represent the interquartile range 共i.e., 25th and 75th percentiles兲; and the upper and lower whiskers extending from the box constitute the 5th and 95th percentiles of the data; for weathered sandstone, the upper whisker in 共c兲 is coincident with the 75th percentile

The minimum and maximum void ratios are summarized in Table 2. The relationship between emax and emin for the clean sands 共⬍5% fines兲 and the sands with 5–15% fines is shown in Fig. 4. The relationship between emax and emin compares well with the trend line reported by Cubrinovski and Ishihara 共2002兲 for natural clean sands 共⬍5% fines兲. The emin and emax also depend modestly on median grain size 共D50兲关Fig. 5共a兲兴 and roundness 关Fig 5共b兲兴. Cubrinovski and Ishihara 共2002兲 also report that emax decreases with increasing D50 for clean sands and sands with some fines 共5–15% fines兲, and Edil et al. 共1975兲 report that emax and emin decrease with increasing roundness. Standard Proctor Compaction The FHWA guidelines for MSE walls and RS slopes indicate that the backfill should be compacted to at least 95% of the maximum dry unit weight corresponding to standard Proctor compactive


Table 2. Physical Properties and Geological Origins of the Sands Sample

Roundness

emaxa

emina

␥d-maxb 共kN/ m3兲

␥d-maxCb 共kN/ m3兲

e␥dmb

␾⬘

Deposit type

Strength group

P1-S2 0.61 0.67 0.42 17.92 – 0.44 32.9 Fluvial 1 P1-S4 0.59 0.70 0.40 18.30 18.66 0.39 33.4 Weathered sandstone 1 P1-S5 0.62 0.76 0.43 18.15 – 0.43 32.3 Weathered sandstone 1 P1-S6 0.62 0.69 0.43 17.59 – 0.48 32.5 Weathered sandstone 1 P1-S1 0.50 0.76 0.48 17.36 – 0.49 35.8 Fluvial 2 P1-S3 0.40 0.83 0.50 17.08 – 0.53 34.3 Fluvial 2 P1-S7 0.42 0.81 0.52 16.88 – 0.55 34.8 Fluvial 2 P2-S3 0.24 0.96 0.58 16.02 16.92 0.55 35.1 Glaciolacustrine sand 2 P3-S3 0.59 0.64 0.37 18.39 – 0.41 35.4 Fluvial 2 P3-S5 0.56 0.62 0.38 18.54 – 0.38 36.4 Weathered sandstone 2 P3-S6 0.36 0.77 0.5 17.12 – 0.52 34.5 Fluvial 2 P3-S7 0.46 0.80 0.51 16.98 – 0.54 35.4 Glaciolacustrine sand 2 P2-S1 0.31 0.80 0.51 16.98 – 0.54 36.6 Ice contact stratified 3 P2-S2 0.29 0.83 0.56 16.51 – 0.59 37.8 Glaciolacustrine sand 3 P2-S4 0.40 0.68 0.39 18.46 19.21 0.37 36.5 Glacial outwash 3 P2-S9 0.43 0.56 0.33 18.11 19.58 0.34 38.5 Glacial outwash 3 P2-S10 0.31 0.75 0.46 17.51 – 0.50 36.4 Esker 3 P2-S11 0.52 0.43 0.26 18.58 21.62 0.23 38.7 Glacial outwash 3 P3-S1 0.50 0.58 0.35 18.68 19.59 0.36 39.2 Glacial outwash 3 P3-S2 0.48 0.7 0.39 19.08 20.35 0.31 36.9 Glacial outwash 3 P4-S1 0.42 0.84 0.56 16.67 – 0.58 36.7 Glacial outwash 3 P5-S1 0.38 0.55 0.31 18.84 19.83 0.33 39.1 Ice contact stratified 3 P2-S5 0.33 0.69 0.44 18.02 18.80 0.44 40.9 Glacial outwash 4 P2-S6 0.25 0.76 0.46 17.86 – 0.47 40.5 Drumlin 4 P2-S7 0.22 0.86 0.52 17.69 – 0.48 39.6 Ice contact stratified 4 P2-S8 0.37 0.64 0.4 18.30 18.69 0.42 41.5 Glacial outwash 4 P2-S12 0.42 0.64 0.39 18.64 – 0.42 42.5 Glacial outwash 4 P3-S4 0.52 0.60 0.37 18.77 19.06 0.38 40.3 Fluvial 4 P4-S2 0.31 0.72 0.44 17.52 17.86 0.49 40.7 Ice contact stratified 4 P4-S3 0.35 0.62 0.33 18.97 19.73 0.37 42.4 Glacial outwash 4 Note: emin determined by ASTM D 4253, emax determined by ASTM D 4254, ␥dmax determined by ASTM D 698 共standard Proctor兲, and ␥dmaxC calculated according to ASTM D 4718. a emax = maximum void ratio; emin = minimum void ratio. b ␥d-max = maximum dry unit weight of P4 material; ␥d-maxC = maximum dry unit weight including R4 material; e␥dm = void ratio at ␥d-maxC.

effort. Maximum dry unit weights obtained from compaction tests are also commonly used by transportation departments to control placement of coarse and fine-grained soils, even though some coarse-grained soils do not exhibit a conventional compaction curve. Therefore, standard Proctor compaction tests were conducted on each sand following ASTM D 698-Method A using the sample fraction passing the No. 4 sieve 共4.75 mm兲. Method A was used for all sands for consistency, even though two sands had greater than 20% material retained on the No. 4 sieve 共R4兲. Maximum dry unit weights 共␥dmax兲 and the void ratios corresponding to the maximum dry unit weight 共e␥dm兲 are summarized in Table 2. For samples containing ⬎5% R4 material, a unit weight correction was applied following ASTM D 4718 to adjust ␥dmax and e␥dm to account for the removed material. For a majority of the sands 共22 of 30兲, ␥dmax was obtained at zero water content 共addition of water consistently resulted in lower ␥dmax兲. Arcement and Wright 共2001兲, who studied granular backfills in Texas, also indicate that ␥dmax for poorly graded sands typically occurs at zero water content. Of the remaining eight sands, four had greater than 6% fines and exhibited a conventional bellshaped compaction curve, whereas four had negligible fines and

exhibited an increase in dry unit weight near saturation. Compaction tests performed by Arcement and Wright 共2001兲 on silty sands and poorly graded sands with silt showed conventional bellshaped compaction curves. A graph of e␥dm 共compaction test兲 versus emin 共vibratory table兲 is shown in Fig. 6共a兲. Good correspondence exists between both measures of maximum density, although the vibratory table typically resulted in a slightly denser packing 共emin = 99% of e␥dm, on average兲. The variation of ␥dmax with respect to geologic deposit type is shown in Fig. 6共b兲. The maximum dry unit weight of a given granular material represents its packing efficiency for a specific packing energy and depends on particle characteristics, such as size, shape, and gradation. The variation in particle characteristics between sands of differing geologic deposit type 共Fig. 3兲 results in a different median and range of ␥dmax for each geologic deposit type 关Fig. 6共b兲兴. For example, the coarser particles and broader particle distributions of glacial outwash deposits produce sands that achieve a greater ␥dmax for given compactive effort. However, for a given type of deposit, ␥dmax varies within a relatively narrow range 共⬇2 kN/ m3兲, as has been shown by others 共Peck et al. 1974兲.


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

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

Mineralogy and Chemical Properties

Fig. 5. Relationships between minimum and maximum void ratio and 共a兲 median particle size 共D50兲; 共b兲 roundness; sand P2-S-11 is not included in the relationships due to the high gravel content of the sample

Mineralogy was determined for 15 samples by X-ray diffraction 共Table 3兲. Quartz constitutes the majority of each sand 共Table 3兲, except for P2-S5 共25% quartz兲. Plagioclase, dolomite, potassiumfeldspar, and phyllosilicates 共includes illite, mica, kaolinite, and chlorite兲 are the other dominant minerals present along with quartz. The average mineralogical fractions of quartz, nonquartz, and phyllosilicates for weathered sandstone, fluvial, glacial outwash, and ice contact stratified type deposits are shown in Fig. 7 共X-ray diffraction was not performed on any miscellaneous glacial deposits兲. The large fraction of quartz in the sands from weathered sandstone and fluvial deposits reflects that these sands are derived from the Cambrian and St. Peter Sandstones. Although quartz is the dominant mineral in all deposit types, there is an increase in nonquartz material for glacial outwash and ICS sands, which primarily originate from regions of nonsandstone bedrock. The pH, chloride content, sulfate content, and resistivity of each sand were measured as indicated in Elias et al. 共2001兲. pH was measured in accordance with AASHTO T 289-91 using a single electrode pH meter, chloride content was measured following AASHTO T 291-94, sulfate content was measured following T 290-95, and resistivity was measured following AASHTO T 288-91. All of the sands meet the electrochemical requirements


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

Strength group

Quartz

Potassiumfeldspar

P1-S2 1 97.0 P1-S6 1 99.0 P1-S1 2 91.0 P1-S3 2 69.0 P3-S3 2 93.0 P3-S5 2 95.0 P2-S1 3 73.0 P3-S1 3 72.0 P3-S2 3 70.0 P4-S1 3 88.0 P5-S1 3 74.0 P2-S5 4 25.0 P2-S12 4 58.0 P3-S4 4 83.0 P4-S2 4 60.0 a Includes illite, mica, kaolinite, and chlorite.

1.3 0.6 3.0 5.3 2.7 3.0 6.0 3.8 0.5 1.1 9.3 2.6 2.2 4.7 5.6

Plagioclase

Calcite

Hematite

Dolomite

Pyrite

Total phyllosilicatea

0.2 0.1 5.6 21.0 1.6 1.3 2.8 2.3 6.7 8.7 12.0 7.9 5.5 8.9 25.0

0.1 0.0 0.4 0.0 0.9 0.0 2.5 0.3 1.80 0.3 0.7 0.3 0.0 0.0 0.4

0.0 0.0 0.4 1.2 0.0 0.0 0.0 0.0 0.0 1.2 1.0 0.0 2.6 0.0 2.5

0.4 0.0 0.0 1.8 0.0 0.0 15.0 21.0 20.0 0.0 0.0 62.0 31.0 0.0 0.0

0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.9 0.0

1.0 0.7 0.0 2.3 1.3 0.8 0.2 1.0 1.1 1.2 2.6 2.0 1.1 1.8 6.4

for steel and geosynthetic reinforcing elements, except for P1-S4, which has a pH of 4.6 共Bareither 2006兲. Elias et al. 共2001兲 also specifies a limiting organic content of 1% when using steel reinforcements. Visual inspection of the samples indicated that the organic content was negligible.

Shear Strength Testing Direct Shear Tests The friction angle of each sand was measured in direct shear following the procedure in AASHTO T 236-92. Tests were conducted in a 64 mm-wide square shear box that contained a 31 mm-thick specimen. Small-scale direct shear tests were used in lieu of other methods because direct shear testing is more common in practice when evaluating backfill materials for MSE walls and RS slopes. Prior to testing, the sands were air dried and sieved on a No. 4 sieve 共4.75 mm兲. The fraction passing No. 4 sieve was compacted

Fig. 7. Percentages of mineralogical components in sands for different geologic deposits

air dried in the shear box in three lifts of equal thickness by tamping the top of each lift with a wooden tamper. The number of tamps per layer was adjusted to achieve the target density for each specimen 共95% of maximum dry density determined by standard Proctor compaction, which is the compaction criterion in Wisconsin for MSE backfill兲. Inundation of the specimen followed immediately after applying the normal stress. Drainage was permitted through 9 mm-thick perforated PVC plates placed on the top and bottom of the specimen. Separation was provided by a thin nonwoven heat-bonded calendered geotextile placed between the sand and the plates. Compression of the PVC and geotextile was measured at each normal stress and volume change measurements on initial normal loading were corrected. All tests were conducted using a constant rate of displacement of 0.24 mm/ min. Normal stresses between 26 and 184 kPa were applied. The maximum stress is comparable to the stress expected at the bottom of a 10 m high MSE wall backfilled with dense granular fill having a unit weight of approximately 18 kN/ m3. Measurements of horizontal displacement, vertical displacement, and shear force were recorded using a personal computer equipped with a Validyne data acquisition card 共UPC601-U兲 and LABView software. Two linear variable displacement transducers 共LVDTs兲共Schlumberger Industries Model AG/5, 5 ⫾ 0.003 mm兲 were used to measure horizontal and vertical displacements, and a load cell 共Revere Transducer Model 363-D3-500-20P1, 2.2⫾ 0.00015 kN兲 was used to measure shear force. Failure was defined at the peak shear stress for all sands exhibiting a peak stress. For sands exhibiting only an ultimate stress, failure was defined as the shear stress corresponding to the initial horizontal tangent to the shear stress-displacement curve. Mohr-Coulomb failure envelopes were obtained by linear leastsquares regression with a nonnegative intercept. The failure envelopes exhibited a high degree of linearity within the range of normal stresses employed, with coefficients of determination 共R2兲 ranging from 0.997 to 1.000. Intercepts at the origin were small 共⬍8 kPa, and in most cases ⬍4 kPa兲, and were largely due to machine friction rather than nonlinearity of the failure envelope 共Bareither et al. 2008b兲. To be consistent with common practice for MSE walls and RS slopes, the friction angles were defined from the slope of the


Fig. 9. Relationship between ␾⬘ and roundness for fine sand 共D50 ⬍ 0.425 mm兲 and medium/coarse sand 共D50 ⬎ 0.425 mm兲

Fig. 8. Comparison of ␾⬘ and dilatancy factor 共a兲; comparison of ␾⬘ and relative horizontal displacement at failure 共%兲共b兲 for the shear box used in this study, RHD= 1% corresponds to a horizontal displacement of 0.64 mm

linear regressions. Friction angles were also computed from the shear strength at each normal stress assuming no intercept at the origin. Friction angles determined by both methods differed by only 1.5°, on average. Comparison Tests Comparative tests were conducted on four of the sands using consolidated-drained triaxial compression tests. Triaxial tests were performed on the fraction passing the No. 4 sieve 共⬍4.75 mm兲 compacted in a similar manner and to the same density as specimens in direct shear. Effective confining pressures ranging from 21 to 83 kPa were used so that normal and shear stresses at failure on the estimated failure plane fell within the range of those used in the DS tests 共Bareither et al. 2008a兲. Friction angles obtained from the direct shear and the triaxial tests fell within ⫾1.7°, indicating that the friction angles obtained from the direct shear test are representative. To assess the effect of gravel fraction on friction angle, largescale direct shear tests were conducted on the sands containing ⬎5% gravel. Large-scale direct shear tests were conducted in a 305 mm square box 共152 mm thick兲 on the fraction passing a 25.4 mm sieve. Test specimens were prepared so that the density of the fraction passing a No. 4 sieve was consistent with specimen densities in small-scale direct shear. Large-scale direct shear tests were performed at similar normal stresses and at a similar rate of

horizontal displacement as the small-scale direct shear tests 共Bareither et al. 2008b兲. Friction angles obtained form the large-scale tests typically were within ⫾2.0° of the small-scale direct shear tests in which material retained on a No. 4 sieve was removed. Thus, for sands containing 5–30% gravel, the friction angles from the small-scale direct shear test are representative of the bulk sample. The direct shear test procedure used in this study was also evaluated for repeatability 共Bareither et al. 2008a兲. Comparison of five 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 the direct shear testing procedure are highly repeatable when the test is conducted by a single operator.

Shear Strength Behavior The 30 sands tested in direct shear exhibited a wide range of shear strength behavior and a strong correspondence between ␾⬘ and propensity for dilation. This correspondence is shown in Fig. 8共a兲, where ␾⬘ is graphed versus the dilatancy factor 共␺兲, which is defined at failure as ␺=

共⌬H/Ho兲 f 共⌬L/Lo兲 f

共1兲

where ⌬H = change in thickness of the specimen; Ho = initial thickness after normal stress application and inundation; ⌬L = change in horizontal displacement; and Lo = initial specimen length. A strong correspondence also exists between ␾⬘ and relative horizontal displacement 关RHD= 共horizontal displacement/ specimen length兲 ⫻ 100兴 at failure 关Fig. 8共b兲兴. Sands with the larger ␾⬘ typically have large dilatancy factors 关Fig. 8共a兲兴 and reach failure at smaller RHD 关Fig. 8共b兲兴. Friction angle is also affected by particle roundness and particle size as shown in Fig. 9. The data in Fig. 9 are grouped into fine sands and medium/coarse sands based on median particle size 共D50 ⬍ or⬎ 0.425 mm兲. Lower roundness or larger median particle size results in larger ␾⬘. Hennes 共1951兲, Koerner 共1970兲,


Fig. 10. Influence of quartz content 共%兲 on ␾⬘ 共a兲; roundness 共b兲

Zelasko et al. 共1975兲, and Cho et al. 共2006兲 report similar correspondence between ␾⬘ and particle size and roundness for laboratory mixtures of granular materials. Friction angle is also affected by quartz content, as shown in Fig. 10共a兲. The sands with less quartz contained greater amounts of potassium-feldspar, plagioclase, calcite, and/or dolomite 共Table 3兲 and these minerals generally have higher sliding frictional resistance compared to that of quartz 共Horn and Deere 1962; Ohnaka 1975兲. Equally important, however, is that the predominantly quartz sands also have greater roundness 关Fig. 10共b兲兴, which results in a lower friction angle 共Fig. 9兲. Sands with a greater fraction of quartz particles tend to have undergone more cycles of transport, and, therefore, tend to be more rounded 共Pettijohn et al. 1965; Prothero and Schwab 2004兲. The well-rounded quartz sands of Wisconsin that have low ␾⬘ are primarily derived from the Cambrian and St. Peter sandstones, and the particles in these sandstones are some of the most physically weathered sand particles in Wisconsin 共Dott and Attig 2004兲. Friction Angle Groups Friction angles of the sands are summarized in Table 2. The data are presented in four groups 共1–4兲 corresponding to sands having similar friction angles 共increasing group number corresponds to increasing friction angle兲. Sands in each group generally have similar stress-displacement behavior. Representative relationships of shear stress versus relative horizontal displacement 共RHD兲 and vertical displacement versus RHD for each group are shown in

Fig. 11. Representative behavior of sands: 共a兲 shear stress versus relative horizontal displacement 共RHD兲; 共b兲 vertical displacement versus RHD in each strength group at normal stress of 99 kPa; Group 1 共P1-S4兲, Group 2 共P3-S7兲, Group 3 共P5-S1兲, and Group 4 共P2-S5兲

Fig. 11 at a normal stress of 99 kPa. Sands in Group 1 typically exhibit contractive behavior and an ultimate strength, whereas sands in the other three groups exhibit dilatant behavior with a distinct peak shear stress and postpeak loss in strength. Exceptions from the generalized stress-displacement behavior include P2-S3 共Group 2兲 and P2-S4 and P3-S2 共Group 3兲, which showed contractive behavior and an ultimate shear stress 共Fig. 12兲. These sands also are the outlier points in Fig. 8共b兲共␾⬘ versus RHD兲. Group 1 includes three weathered sandstone deposits and one fluvial deposit that have friction angles between 32° and 33°. Each of these sands consists predominantly of well-rounded medium to fine grained quartz particles 共Table 2兲 from the Cambrian and St. Peter sandstones. The rounded grain shape and the uniformity in grain size 共Fig. 3兲 limit interlocking between neighboring particles, resulting in very little dilation 共Figs. 8 and 11兲 and an ultimate shearing strength that is attained primarily from particle frictional resistance and rearrangement 共Terzaghi et al. 1996兲. Group 2 includes eight sands that have friction angles ranging from 34° to 36°. Five of the sands are from fluvial deposits. Two glaciolacustrine sands and a weathered sandstone comprise the rest of Group 2. The sands in Group 2 have larger particle size or lower roundness compared to the sands in Group 1, resulting in higher friction angles. The larger particle size and lower roundness of the fluvial materials 共Fig. 3兲 are attributed to the influx of


Fig. 12. Relationships between shear stress and relative horizontal displacement 共RHD兲共a兲; vertical displacement and RHD 共b兲 at normal stress of 99 kPa for sands P2-S3, P2-S4, and P3-S2

sediments from recent glaciations. The fluvial deposits in Group 2 were obtained from gravel pits of major river systems in Wisconsin, which accommodated glacial meltwater as recently as the Wisconsin Glaciation. The influx of glacial sediments provides particles to the fluvial systems that are less rounded and coarser, compared to particles eroded from the underlying sandstones. The glaciolacustrine sands have low roundness due to glacial sediments that are deposited in a lake setting where there is no further particle shape modification. The weathered sandstone in Group 2 has a lower roundness compared to the weathered sandstones of Group 1. These differences in physical properties are likely due to differences of the sediments contained in the parent sandstone. Sand P2-S3, the only sand in Group 2 not exhibiting dilatant shearing behavior 关Fig. 6共b兲兴, is angular and predominantly fine sand from a glaciolacustrine sand deposit, and contains more than 12% fines. The larger percentage of fines distinguishes P2-S3 from the other sands in Group 2, all of which have less than 1% fines 共Table 1兲. Group 3 includes 10 sands that have friction angles ranging from 37° to 39°. Six of the sands in Group 3 consist of glacial outwash sediments deposited in the medial and proximal glacial zones. Group 3 also includes two sands from ICS deposits, one sand from an esker deposit, and one glaciolacustrine sand deposit. The glacial outwash sands are more broadly graded 共P4-S1 is an exception兲, contain a larger fraction of coarse particles, and consist of more angular particles compared to those in Groups 1 and 2, which combine to produce a denser packing, more dilation,

and higher ␾⬘ 共Kolbuszewski and Frederick 1963; Youd 1973; Edil et al. 1975兲. Each of the physical characteristics of the glacial outwash sands 共particle size, gradation, and shape兲 is directly influenced by glacial processes. The glacial outwash sands are more broadly graded 关Fig. 3共b兲兴 due to varying sized particles contained in the glacial meltwater that are often deposited rapidly near the glacier margin. The glacial outwash sands are also deposited at a shorter distance to the glacier margin compared to fluvial deposits, which results in coarser 关Fig. 3共a兲兴 and more angular 关Fig. 3共c兲兴 particles. The higher ␾⬘ associated with the nonglacial outwash materials is also due to more angular particles, larger particle size, and/or broader particle gradation compared to sands in Groups 1 and 2. The low roundness of the ICS deposits and the esker deposit is due to the short transport distance of the particles. The low roundness of the glaciolacustrine sand is due to similar processes as for the glaciolacustrine sands in Group 2. The particle size and gradation of the nonglacial outwash sands depends on the sediment contained in the glacial meltwater, and can be highly variable. All of the sands in Group 3 also contain a greater fraction of nonquartz material 共potassium-feldspar, plagioclase, calcite, and/or dolomite兲, compared to the sands in Groups 1 and 2 共Table 3兲, which may also contribute to the higher ␾⬘ of the sands in Group 3 compared to the sands in Groups 1 and 2. As depicted in Fig. 7, these glacial outwash and ICS deposits have a greater fraction of nonquartz material, primarily from the formation of these types of deposits in regions of nonsandstone bedrock. As mentioned previously, samples P2-S4 and P3-S2 do not exhibit the dilative strength-deformation behavior characteristic of the other sands in Group 3. The reason for this difference is not apparent. The eight sands in Group 4 have friction angles ranging between 40° and 42°. They are glacial outwash and ICS deposits 共the exception is Sand P3-S4, which is fluvial兲. The sands in Group 4 are not necessarily as well graded as the sands in Group 3, but they are more angular and/or coarser grained, which combine to produce a higher ␾⬘. The sands in Group 4 also have the highest fraction of nonquartz material 共Table 3兲. The lower roundness, larger particle size, and/or broader gradation, combined with minerals exhibiting higher friction, result in the largest ␾⬘ of the sands that were studied. Glacial processes impact the physical characteristics of the glacial outwash and ICS sands in a similar manner as described for Group 3. The fluvial sand in Group 4 contains particles with a higher roundness compared to other sands in Group 4 共Table 2兲; however, this sand contains coarser particles relative to other fluvial deposits, which contributes to higher ␾⬘. Additionally, this fluvial sand was deposited in closer proximity to the glacial margin, and is more similar to the glacial outwash sands in Group 4 than the other fluvial sands, which are in Group 2.

Estimating Shear Strength Based on Physical Properties Multivariate Regression Modeling A multivariate regression analysis was used to develop a model to predict ␾⬘ based on relevant physical characteristics. Regression was preferred relative to other prediction methods because of the simplicity 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 the dependent and independent variables can be evaluated. Stepwise regression was used because the method only incorporates independent variables that are statistically significant. Forward and backward stepwise regressions were performed with ␾⬘ as the dependent variable and the following as independent variables: D60, D50, D10, Cu, Cc, % fines, Gs, emax, emin, ␥d-max, and Rs. A forward stepwise regression begins with no independent variables and sequentially adds variables to a model in order of their significance in predicting the dependent variable. A backward stepwise regression begins with all independent variables and sequentially removes variables from a model that are least significant in predicting the dependent variable. Independent variables are added 共forward regression兲 or removed 共backward regression兲 until only those variables that are statistically significant 共as measured by an F-test兲 are included in the model 共Ramsey and Schafer 2002兲. A significance level 共␣兲 of 0.05 was used to evaluate statistical significance of each independent variable. Forward and backward stepwise regression results were analyzed to obtain the best overall model 共i.e., highest coefficient of determination R2兲. Variables included in the model were required to have statistical and physical significance and to be readily measured in conventional laboratories. The following model was obtained: ␾⬘ = 1.89 + 20.56 ⫻ D10 + 2.35 ⫻ ␥d max − 24.10 ⫻ Rs

共2兲

where D10 is in mm, Rs = weighted average Krumbein roundness for the bulk sample 共dimensionless兲, and ␥d max is in kN/ m3 as determined by ASTM D 698-Method A using the sample fraction passing the No. 4 sieve. The model has an R2 = 0.83 and all three independent variables have p-values ⬍0.0001 共i.e., Ⰶ0.05兲. The coefficients also have physical significance. The positive coefficient on D10 infers that ␾⬘ increases with increasing particle size 关i.e., as reported by Hennes 共1951兲 and as shown in Fig. 9兴 and the negative coefficient on Rs infers that ␾⬘ decreases with increasing roundness 关i.e., as reported by Koerner 共1970兲, Zelasko et al. 共1975兲, and Cho et al. 共2006兲 and shown in Fig. 9兴. The variable ␥d max reflects the packing characteristics of a sand for a specific packing energy, and is influenced by the size, gradation, and shape of the particles 共Youd 1973; Edil et al. 1975兲. Materials that pack more efficiently have higher ␾⬘, when all other factors are equal 共Kolbuszewski and Frederick 1963; Zelasko et al. 1975兲. Thus, the coefficient for ␥d max should be positive. A positive relationship between ␾⬘ and ␥d max is also reported in NAVFAC 共1986兲. A graph of ␾⬘ predicted using Eq. 共2兲 versus the measured ␾⬘ is shown in Fig. 13共a兲. The regression model predicts ␾⬘ within ⫾2° 共shown by dashed lines兲 of the measured ␾⬘ for nearly all sands in this study. An additional comparison was made between the average friction angle in each strength group and friction angles computed using Eq. 共2兲 and the average D10, ␥d max, and Rs for each group 共Table 4兲. This comparison is shown as the solid symbols in Fig. 13共a兲. The difference between the average measured ␾⬘ in each group and ␾⬘ computed using the average properties in each group is less than 1° for each group. Of the three independent variables in Eq. 共2兲, roundness is measured least frequently in practice. Thus, an analysis was conducted to evaluate the efficacy of Eq. 共2兲 for cases where roundness was determined by a simple visual inspection. The Krumbein roundness scale 共0.1 to 0.9兲 was partitioned into five roundness categories 共angular, subangular, subrounded, rounded, and well rounded兲, with each category assigned a range and average roundness as tabulated in Table 5. Each sand was categorized as well

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

rounded 共Rs = 0.82兲, rounded 共Rs = 0.66兲, subrounded 共Rs = 0.50兲, subangular 共Rs = 0.34兲, or angular 共Rs = 0.18兲. For this analysis, the average roundness in each roundness category was assigned to each of the 30 sands based on the determined weighted roundness for each sand 共Table 2兲 falling within the range of roundness measurements for the five roundness categories 共Table 5兲. The actual D10 and ␥d max for each sand along with the average roundness were used to calculate ␾⬘ based on Eq. 共2兲. Even with roundness defined using the five general categories, the multiple regression model predicts ␾⬘ within ⫾2° for nearly all of the sands. Comparison of Prediction Methods Methods to predict the friction angle of granular materials from physical and engineering properties have also been presented in NAVFAC 共1986兲, Schmertmann 共1977兲, and Terzaghi et al. 共1996兲. NAVFAC 共1986兲 presents one of the most widely referenced correlations, where ␾⬘ is estimated with respect to USCS classification and dry unit weight or relative density. The correla-


Table 4. Average and Standard Deviation of Independent Variables in Eq. 共2兲 for Strength Groups, ␾⬘ Predicted with Eq. 共2兲 Using Average Independent Variables, and Range of ␾⬘ Predicted with Eq. 共2兲 Using Independent Variables Unique to Each Sand Group 1 2 3 4 a Standard deviation.

D10 共mm兲

␥d-max 共kN/ m3兲

Rs

Measured ␾⬘

Predicted average ␾⬘

Predicted range ␾⬘

0.192⫾ 0.079a 0.177⫾ 0.08 0.161⫾ 0.049 0.178⫾ 0.022

18.22⫾ 0.53 17.94⫾ 0.95 17.30⫾ 0.82 17.99⫾ 0.31

0.35⫾ 0.10 0.40⫾ 0.08 0.44⫾ 0.11 0.61⫾ 0.01

41.0⫾ 1.0 37.6⫾ 1.2 35.2⫾ 0.7 32.8⫾ 0.5

40.3 38.1 35.3 33.2

42.2–39.3 40.7–35.8 36.6–33.7 33.8–31.8

tion presented in Schmertmann 共1977兲 provides an estimate of ␾⬘ based on relative density and generalized material descriptions. The method in Terzaghi et al. 共1996兲 uses a secant definition for the friction angle that is a function of effective normal stress as well as generalized material descriptions and porosity. A compilation of friction angles measured in direct shear and triaxial compression by others is in Table 6. This collection of friction angles was created to represent a broad range of sands, but is not intended to be inclusive of all friction angles for sands reported in the literature. The data sources in Table 6 also include sufficient information to assess whether each of the four prediction methods was applicable, as well as the input data required for each method. Comparisons between friction angles predicted by the methods in NAVFAC 共1986兲, Schmertmann 共1977兲, Terzaghi et al. 共1996兲, Eq. 共2兲, and the measured friction angles reported in Table 6 are shown in Fig. 13共b兲. On average, the NAVFAC 共1986兲 Table 5. Roundness Categories Including Krumbein Images, Range of Roundness, and Average Roundness

method underestimates ␾⬘ by 2.4°, Eq. 共2兲 underestimates ␾⬘ by 2.0°, the Schmertmann 共1977兲 method overestimates ␾⬘ by 0.8°, and the method in Terzaghi et al. 共1996兲 overestimates ␾⬘ by 6.6°. The standard deviation of all four correlation techniques is similar, ranging from 2.8° to 3.5°. Therefore, each of the four prediction methods is capable of predicting ␾⬘ with similar precision; however, the bias varies between methods. The secant definition in the Terzaghi et al. 共1996兲 method may have contributed to the greater bias associated with this method in Fig. 13共b兲. Given that NAVFAC and Eq. 共2兲 have negative bias, ␾⬘ estimated with these methods tends to be conservative, on average. Eq. 共2兲 has the advantage that all of the independent variables can be measured directly using conventional methods and a prediction can be made using a simple equation rather than a chart. Eq. 共2兲 can be used to estimate ␾⬘ for preliminary geotechnical design or to provide a reasonableness check for ␾⬘ measured in a direct shear test. However, Eq. 共2兲 should only be applied to the range of physical parameters of the sands used in this study 共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兲. Moreover, Eq. 共2兲 was developed using data from sands from Wisconsin compacted at 95% of maximum dry unit weight, most of which were poorly graded. The applicability of Eq. 共2兲 to other sands, sands with greater fines or coarse fraction, sands prepared at other densities, and to stresses outside the range used in this study 共26 to 184 kPa兲, is not known and needs greater evaluation.

Conclusions This paper presents the findings of a study conducted to determine how geologic processes and physical properties affect the shear strength of compacted natural sands from Wisconsin used as granular backfill material. Thirty naturally occurring sands were sampled representing the regional variation throughout Wisconsin. Shear strength of each sand was measured in direct shear for a range of normal stresses characteristic of MSE wall and RS slope backfills. Friction angles 共␾⬘兲 obtained from the direct shear tests were related to the geologic origins and physical characteristics of the sands. The 30 sands were differentiated into four strength groups based on shear strength and deformation behavior. Sands comprising each strength group share similar geologic origin and/or physical characteristics that contribute to similarity in the shear strength and deformation behavior. The lowest strength sands are comprised of quartz particles that have undergone extensive transport and physical weathering. These particles are mechanically weathered from the underlying Cambrian and St. Peter sandstones and are well rounded, medium to fine in size, and uniformly graded. The highest strength sands, derived primarily from outwash of the Wisconsin glaciation, have undergone less transport and physical weathering, have lower quartz content, are more JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / OCTOBER 2008 / 1487

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

Reference

Material

Nash 共1953兲 Kirkpatrick 共1965兲

Test methoda

Closely graded river sand Leighton buzzard sand Glass beads Grading No. 3 Lee and Seed 共1967兲 Sacramento river sand Koerner 共1970兲 Crushed Ottawa sand Ottawa sand Holubec and D’Appolonia 共1973兲 Ottawa sand Southport sand Zelasko et al. 共1975兲 Ottawa 35–45 Ottawa 50–70 Ottawa 70–100 Ottawa 100–140 Evanston beach 35–45 Evanston beach 50–70 Evanston beach 70–100 Franklin Falls 30–45 Franklin Falls 50–70 Mix A 20–70 Mix B 20–70 Mix F 20–45 Salgado et al. 共2000兲 Ottawa sand 共ASTM C 778兲 Simoni and Houlsby 共2006兲 Leighton buzzard sand Cerato and Lutenegger 共2006兲 Brown mortar Ottawa a DS= Direct shear and TC= triaxial compression. b Krumbein roundness approximated from material descriptions and averages in

angular, are larger in size, and have broader gradation compared to the other sands. Sands with higher ␾⬘ also have higher dilatancy factor, confirming that the shear strength of compacted sands 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. Variables included in the regression model were required to be statistically significant 共p-value ⬍0.05兲, to have physical significance regarding effect on ␾⬘, and to be readily measured in the laboratory. The multivariate regression model can be used to estimate ␾⬘ for preliminary geotechnical design or to provide a reasonableness check on ␾⬘ for granular backfill materials measured in direct shear.

Acknowledgments Financial support for this study was provided by the Wisconsin Department of Transportation 共WisDOT兲 through the Wisconsin Highway Research Program. The assistance of Daniel Reid, Dennis Althaus, and Bruce Pfister of WisDOT is greatly appreciated. Xiaodong Wang, geotechnical laboratory manager at University of Wisconsin-Madison, assisted with the laboratory testing. X-ray diffraction analyses were conducted by K/T Geoservices, Inc. of Argyle, Texas. The findings and inferences that have been reported are solely those of the writers. This paper has not been

DS TC

TC TC TC TC

TC DS DS

D10 共mm兲

Krumbein roundnessb

Maximum dry unit weight 共kN/ m3兲

0.14 0.37 0.31 0.36 0.14 0.25 0.25 0.15 0.25 0.37 0.22 0.16 0.11 0.37 0.22 0.16 0.38 0.22 0.23 0.23 0.39 0.28 0.21 0.30 0.30

0.34 0.50 0.82 0.50 0.34 0.34 0.50 0.66 0.34 0.60 0.52 0.50 0.50 0.43 0.41 0.42 0.35 0.34 0.35 0.59 0.36 0.50 0.34 0.34 0.66

16.1 17.5 17.9 17.9 16.3 16.3 17.0 17.6 17.2 17.7 17.1 17.0 17.0 17.3 16.9 17.2 16.1 16.0 17.0 18.4 16.6 17.6 18.8 16.7 17.7

Reported friction angle 36.5 40.5 27.0 37.0 39.0 40.3 36.9 35.0 40.0 39.1 38.5 38.9 37.9 37.2 37.7 39.3 40.4 40.0 41.7 39.0 41.3 35.9 45.0 48.3 35.6

Table 5 if not provided directly.

reviewed by WisDOT. Endorsement by WisDOT is not implied and should not be assumed.

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