Comparison of shear strength of sand backfills measured …Comparison of shear strength of sand backfills measured in small-scale and large-scale direct shear tests Christopher A

Comparison of shear strength of sand backfillsmeasured in small-scale and large-scale directshear tests

Christopher A. Bareither, Craig H. Benson, and Tuncer B. Edil

Abstract: Direct shear tests were conducted on 30 sand backfill materials having gravel contents ranging from 0% to 30%in a 64 mm square small-scale direct shear (SSDS) box and a 305 mm square large-scale direct shear (LSDS) box. The ob-jectives were to compare the shearing behavior of a broad range of natural sand backfill materials tested in SSDS andLSDS and to determine if the same friction angle (f’) is obtained in SSDS and LSDS when the natural backfill materialcontains gravel. Triaxial compression (TC) tests were also conducted on four of the backfill materials for comparison withthe SSDS and LSDS tests. Specimens tested in SSDS and TC included only material passing the No. 4 sieve (P4). Testspecimens in LSDS included the P4 material as well as material retained on the No. 4 sieve (R4), to a maximum particlediameter of 25.4 mm. Friction angles corresponding to peak strength (f’) measured in SSDS and LSDS differed by nomore than 48 for a given sand backfill, and in most cases were within 28. The friction angles also were unaffected by re-moval of the R4 material. Repeatability tests showed that statistically similar failure envelopes (p-value = 0.98) are ob-tained in SSDS and LSDS, and that highly repeatable friction angles (f’) are obtained using the SSDS (f’ ± 0.258) and theLSDS (f’ ± 0.458) methods. No statistically significant difference was found among the failure envelopes measured inSSDS, LSDS, and TC, suggesting that f’ for clean sand backfill with less than 30% gravel can be measured with similaraccuracy using any of the three test methods.

Key words: : direct shear box test, angle of internal friction, sand, triaxial compression, shear strength, backfill, gravel,mechanically stabilized earth.

Resume : Des essais de cisaillement direct ont ete realises sur 30 materiaux de remblai ayant des teneurs en graviers’etendant de 0 % a 30 % dans une boıte de cisaillement direct « SSDS » de petite echelle de 64 mm carree et une boıte acisaillement direct a grande echelle « LSDS » de 305 mm carree. Les sableux objectifs etaient de comparer le comporte-ment en cisaillement d’une large plage de materiaux sableux naturels de remblai testes dans des boıtes SSDS et LSDS.etde determiner si le meme angle de frottement (f’) est obtenu dans un SSDS et un LSDS lorsque le materiau de remblainaturel contient du gravier. On a aussi realise des essais de compression triaxiale « TC » sur quatre des materiaux de rem-blai pour com paraison avec les essais SSDS et LSDS. Les specimens testes dans le SSDS et le TC incluaient seulementdu materiau passant le No. 4 tamis (R4), jusqu’a une diametre maximum de particule de 25.4 mm. Les angles de frotte-ment correspondant a la resistance de pic (f’) mesures dans le SSDS et le LSDS ne differaient de pas plus que 48 pour unsable de remblai donne, et dans la plupart des cas ils etaient a l’interieur de 28. Les angles de frottement n’etaient aussipas affectes par l’elimination du materiau R4. Les essais de repetitivite ont montre qu’on obtient des enveloppes de rupturestatistiquement similaires (valeur de p = 0.98) dans le SSDS et le LSDS, et que des angles de frottement (f’) fortement re-petitifs sont obtenus en utilisant la methode SSDS (f’ ± 0.258) et la methode LSDS (f’ ± 0.458). On n’a pas trouve de dif-ferences statistiquement significatives entre les enveloppes de rupture mesurees dans le SSDS, le LSDS, et le TC, ce quisuggere que f’ pour le remblai de sable propre avec moins de 30 % de gravier peut etre mesure avec une precision simi-laire en utilisant n’importe laquelle des trois methodes d’essai.

Mots-cles : essai a la boıte de cisaillement direct, angle de frottement interne, sable, compression triaxiale, resistance aucisaillement, remblai, gravier, sol stabilise mecaniquement.

[Traduit par la Redaction]

Introduction

The direct shear (DS) test is commonly used in commer-cial geotechnical laboratories in North America for testinggranular materials used as backfill for mechanically stabi-

lized earth (MSE) walls and reinforced soil (RS) slopes.Most tests are conducted following the procedures describedin the American Association of State Highway and Trans-portation Officials (AASHTO) standard T 236-92 (AASHTO2001) or the American Society for Testing and Materials

Received 6 October 2006. Accepted 21 May 2008. Published on the NRC Research Press Web site at cgj.nrc.ca on 14 August 2008.

C.A. Bareither, C.H. Benson,1 and T.B. Edil. Geological Engineering, University of Wisconsin-Madison, 2214 Engineering Hall,1415 Engineering Drive, Madison, WI 53706, USA.

1Corresponding author (e-mail: [email protected]).

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Can. Geotech. J. 45: 1224–1236 (2008) doi:10.1139/T08-058 # 2008 NRC Canada

(ASTM) standard D 3080 (ASTM 2004a) in a small-scaledirect shear (SSDS) box that is square or circular. Both testmethods require that the width (or diameter) of the shearbox must be at least 50 mm, the specimen thickness mustbe at least 13 mm, and the specimen width-to-thickness ratiobe at least 2:1. The test methods also require that the width(or diameter) of the shear box be at least 10 times the max-imum particle diameter and that the initial specimen thick-ness be at least 6 times the maximum particle diameter. Fortypical SSDS boxes, which typically have a width or diame-ter of 64–73 mm (Bareither et al. 2008), the maximum par-ticle size is approximately 5 mm. Therefore, when granularbackfill materials contain gravel (i.e., particles > 4.75 mm),the gravel-sized particles are removed (scalped) if tests areconducted in SSDS. Alternatively, a large-scale direct shear(LSDS) box that accommodates larger particles is used.

Previous studies have shown that similar shear strengthcan be obtained in direct shear using shear boxes of differ-ent sizes (Taylor and Leps 1938; Bishop 1948; Palmeira andMilligan 1989), although variations in shear behavior mayexist (Wu et al. 2008). However, the previous studies havebeen limited to uniformly graded sands, and each study fo-cused on a single sand. The influence of gravel content onthe shear strength and shear behavior of sands has also beenstudied (Fragaszy et al. 1992, Simoni and Houlsby 2006),but these studies have focused on a single sand matrixblended with one or two gravels. To the authors’ knowledge,no studies have been conducted to evaluate the significanceof test size or gravel content for a broad variety of naturallyoccurring sand backfill materials.

This study had two objectives. One objective was to com-pare the shearing behavior of a broad range of natural sandbackfill materials measured in SSDS and LSDS. The otherobjective was to determine if the same friction angle (f’) isobtained in SSDS and LSDS when the natural backfill mate-rial contains or excludes gravel. Tests were conducted on 30naturally occurring sand backfill materials from Wisconsinin a LSDS box (305 mm square) that accommodates a max-imum particle diameter of 25.4 mm (based on the criterionin AASHTO T 236-92 (AASHTO 2001) and an SSDS box(64 mm square) that accommodates a maximum particle di-ameter of 4.75 mm. The backfill materials contained gravelcontents ranging from 0% to 30% in LSDS, of which 12backfill materials required different amounts of scalping tomeet the maximum particle size criteria in SSDS.Consolidated-drained triaxial compression (TC) tests werealso conducted on four of the backfill materials for compar-ison with the SSDS and LSDS tests.

BackgroundTaylor and Leps (1938) performed comparative tests on

oven-dried Ottawa sand in small (76 mm) and large(305 mm) square direct shear boxes to assess the influenceof specimen size on f’. They report that f’ measured in thelarge shear box was 0.58 smaller, on average, than f’ meas-ured in the small box.

Bishop (1948) also conducted direct shear tests on a drysand in small (60 mm) and large (305 mm) shear boxes.For porosities ranging from 0.36 to 0.46, f’ from the smallshear box was within ±28 of f’ measured with the large

shear box. Bishop also tested various well-graded gravelswith a maximum particle diameter of 38 mm in the largeshear box to investigate the influence of gradation on shearbehavior. Bishop concluded that the larger particles did notcontrol the shear behavior of well-graded gravels.

Palmeira and Milligan (1989) performed direct shear testson dry Leighton Buzzard sand in a 1 m cubic box, a252 mm � 152 mm box (thickness = 152 mm), and a tradi-tional 60 mm square box (thickness = 32 mm) to analyzescale effects. The sand had particles ranging in size from0.6 to 1.2 mm. They report f’ between 498 and 508 for testsconducted in all three boxes.

Cerato and Lutenegger (2006) performed direct shear testson five sands at varying densities in 60 mm (thickness =26.4 mm), 102 mm (thickness = 40.6 mm), and 305 mm(thickness = 177.8 mm) square shear boxes. A consistent re-lationship was not found between friction angle and speci-men size for the five sands. However, friction angles forOttawa sand were similar for the three varying-sized shearboxes at three different densities. The authors report thelargest ratios of box length to median particle diameter (L/D50) for Ottawa sand. Jewell and Wroth (1987) indicate thatL/D50 can be used as a measure of scale in direct shear tests.They report that tests conducted with L/D50 ‡ 50 have suffi-cient particles in the test specimen to allow local rupture anddiscontinuities to form, thereby limiting the influence of theshear box boundaries on the strength–deformation behavior.

Wu et al. (2008) conducted direct shear tests on Toyourasand in four square shear boxes: small (40 mm � 40 mm �20 mm thick), semi-medium (120 mm � 120 mm �120 mm thick), medium (300 mm � 300 mm � 300 mmthick), and large (800 mm � 500 mm � 600 mm thick).They report similar friction angles measured in the semi-medium, medium, and large direct shear boxes at compara-ble densities. The friction angle was 28–38 larger whenmeasured in the small shear box than in the larger shearboxes, and was attributed to mechanical boundary restraint.Wu et al. (2008) further concluded that the mechanicalboundary effect is mitigated as the shear box size increases(i.e., as the ratio of L/D50 increases), allowing developmentof multiple shear bands into a shear zone.

Fragaszy et al. (1992) conducted consolidated-drained andconsolidated-undrained triaxial tests on mixtures of‘‘oversize’’ particles (12.7 to 25.4 mm) and sandy gravel(particles < 12.7 mm) to evaluate how the oversize particlesaffected shear strength. Tests were conducted on the sandygravel matrix alone, the oversize particles alone, and on mix-tures of the sandy gravel blended with oversize particles(10%–90%, by weight). They conclude that the peak strengthand deformation behavior of soils containing < 40% sub-rounded to rounded oversize particles in a finer-grained ma-trix can be determined by testing the matrix material aloneprovided that the density of the matrix material is the same.

Simoni and Houlsby (2006) performed shear box tests ina large apparatus (254 mm � 152 mm, specimen thickness =150 mm) on poorly graded silica sand blended with 10%–60% gravel, defined as particles larger than 2 mm andsmaller than 20 mm. They report similar peak friction anglesfor pure sand and sand and gravel mixtures with up to 20%gravel tested at similar sand matrix densities. For sand andgravel mixtures with gravel ‡30%, they report an increase

Bareither et al. 1225

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in the peak-strength friction angle for specimens tested atsimilar sand matrix densities.

Materials and methods

SandsShear tests were conducted on 30 naturally occurring

sands from Wisconsin having different geologic origins.The sands were obtained from borrow pits used for granularbackfill by the Wisconsin Department of Transportation(WisDOT). Approximately 0.1 m3 of material was collectedat each borrow pit. Each sample was blended together thor-oughly and allowed to air dry. After air drying, each samplewas blended again and placed uniformly in a large (0.12 m3)sealed container. Additional details on the homogenizationprocedure can be found in Bareither et al. (2008).

Particle-size distribution curves for the 30 sands areshown in Fig. 1, and physical characteristics of the sandsare summarized in Table 1. The maximum dry unit weight(gd-max) in Table 1 was determined for the material passingthe No. 4 sieve using a standard Proctor compaction test.

Compaction testing was conducted because gd-max is com-monly used in practice for controlling compaction of granu-lar backfills.

Twenty-four of the sands classify as poorly graded sand(SP), four classify as poorly graded sands with fines and(or) gravel (SP-SM or SP-SC), two classify as silty sands(SM), and one classifies as well-graded sand with gravel(SW). Although the majority of the sands share a commondesignation (SP), the gradations vary considerably (Fig. 1)with coefficients of uniformity (Cu) ranging from 1.79 to6.50. The other physical properties also exhibit considerablevariation (Gs = 2.63 to 2.76, emax = 0.43 to 0.96, emin = 0.26to 0.58, gd-max = 16.02 to 19.08 kN/m3, and roundness =0.22 to 0.62).

Small-scale direct shear testsThe SSDS tests were conducted following the procedure

in AASHTO T 236-92 (AASHTO 2001) using a squareshear box 64 mm wide containing a specimen 31 mm thick.Tests were conducted for normal stresses between 26 and184 kPa. The maximum stress is comparable to the stress

Fig. 1. Particle-size distribution curves for backfill materials used in study.

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expected at the bottom of a 10 m high MSE wall backfilledwith dense granular fill having a unit weight of approxi-mately 18 kN/m3.

Sands tested in SSDS were air dried and sieved past aNo. 4 sieve (4.75 mm). Material passing the No. 4 sieve(P4) was used to ensure that the ratio of box length to max-imum particle diameter was at least 10 and that the ratio ofbox thickness to maximum particle diameter was at least 6,as stipulated in AASHTO T 236-92 (AASHTO 2001). Thesand was compacted in the shear box in three lifts of equalthickness by tamping the top of each lift with a wood tam-per. The number of tamps per layer was adjusted to achievethe target density for each specimen (95% of maximum drydensity determined by standard Proctor compaction, whichis the backfill compaction criterion recommended by theUnited States Federal Highway Administration, Elias et al.2001).

Inundation of the specimen followed immediately after thenormal stress was applied. Drainage was permitted through9 mm thick perforated PVC plates placed on the top and bot-tom of the specimen. Separation was provided by a thin non-woven heat-bonded calendered geotextile placed between the

sand and the plates. Compression of the PVC and geotextilewas measured at each normal stress. Volume change meas-urements on initial normal loading were corrected for com-pression of the PVC plate and geotextile.

All tests were conducted at a constant rate of horizontaldisplacement of 0.24 mm/min to a maximum horizontal dis-placement of 7 mm. Measurements of horizontal displace-ment, vertical displacement, and shear force were recordedusing a personal computer equipped with a Validyne dataacquisition card (UPC601-U) and LabVIEW software (Na-tional Instruments, Austin, Tex.). Two linear variable dis-placement transducers (LVDTs) (Schlumberger Industriesmodel AG/5, 5 ± 0.003 mm) were used to measure horizon-tal and vertical displacements and a load cell (Revere trans-ducer model 363-D3-500-20P1, 2.2 ± 0.00015 kN) was usedto measure shear force. Sixty data points were recorded dur-ing each test. Normal and shear stresses were computedfrom the loads using a displacement-corrected area of theshear plane.

Large-scale direct shear testsThe LSDS tests were also performed following the proce-

Table 1. Physical properties of sands used for shear strength testing.

Sample Cu Cc % fines % gravel Gs emax* emin* gd-max (kN/m3) Roundness USCS symbolP1-S1 1.86 1.12 0.78 0.0 2.64 0.76 0.48 17.36 0.50 SPP1-S2 2.18 1.03 0.41 2.0 2.63 0.67 0.42 17.92 0.61 SPP1-S3 2.33 0.92 0.84 0.0 2.66 0.83 0.50 17.08 0.40 SPP1-S4 2.67 0.95 1.03 5.7 2.65 0.70 (0.70) 0.40 (0.40) 18.30 0.59 SPP1-S5 2.63 1.01 0.15 1.8 2.65 0.76 0.43 18.15 0.62 SPP1-S6 2.35 1.15 0.79 1.8 2.63 0.69 0.43 17.59 0.62 SPP1-S7 2.03 0.96 0.65 0.0 2.66 0.81 0.52 16.88 0.42 SPP2-S1 1.88 0.97 1.12 1.0 2.68 0.80 0.51 16.98 0.31 SPP2-S2 2.10 1.20 0.85 0.0 2.67 0.83 0.56 16.51 0.29 SPP2-S3 2.27 0.86 12.63 10.2 2.68 0.96 (1.03) 0.58 (0.64) 16.02 0.24 SMP2-S4 5.30 1.92 9.75 17.8 2.68 0.68 (0.95) 0.39 (0.60) 18.46 0.40 SP-SCP2-S5 2.82 0.84 0.46 8.3 2.76 0.69 (0.75) 0.44 (0.50) 18.02 0.33 SPP2-S6 2.82 1.06 3.52 0.4 2.75 0.76 0.46 17.86 0.25 SPP2-S7 3.15 1.32 14.44 0.0 2.75 0.86 0.52 17.69 0.22 SMP2-S8 3.05 0.81 1.24 6.7 2.71 0.64 (0.68) 0.4 (0.43) 18.30 0.37 SPP2-S9 4.16 0.68 0.53 22.1 2.67 0.56 (0.64) 0.33 (0.40) 18.11 0.43 SPP2-S10 2.33 1.35 4.98 0.7 2.7 0.75 0.46 17.51 0.31 SPP2-S11 34.07 0.14 0.75 47.8 2.71 0.43 (0.61) 0.26 (0.37) 18.58 0.52 SWTS 3.06 0.85 1.55 2.2 2.7 0.64 0.39 18.64 0.42 SPP3-S1 3.20 0.82 1.11 10.0 2.72 0.58 (0.63) 0.35 (0.37) 18.68 0.50 SPP3-S2 4.77 1.04 5.70 12.1 2.72 0.70 (0.84) 0.39 (0.41) 19.08 0.48 SP-SMP3-S3 2.48 0.92 0.55 0.3 2.66 0.64 0.37 18.39 0.59 SPP3-S4 2.86 1.00 0.40 4.3 2.69 0.60 0.37 18.77 0.52 SPP3-S5 3.00 0.89 0.77 4.9 2.65 0.62 0.38 18.54 0.56 SPP3-S6 2.07 1.04 0.79 0.0 2.65 0.77 0.5 17.12 0.36 SPP3-S7 1.79 0.96 0.61 0.0 2.66 0.80 0.51 16.98 0.46 SPP4-S1 2.00 1.10 0.14 3.3 2.69 0.84 0.56 16.67 0.42 SPP4-S2 2.86 0.81 2.32 3.3 2.71 0.72 0.44 17.52 0.31 SPP4-S3 6.50 0.59 1.74 13.2 2.74 0.62 (0.68) 0.33 (0.38) 18.97 0.35 SPP5-S1 5.28 0.76 5.17 16.6 2.67 0.55 (0.66) 0.31 (0.38) 18.84 0.38 SP-SM

Note: Particle-size analysis conducted following ASTM D 422 (ASTM 2004b) (fines < 0.75 mm); Gs, determined by ASTM D 854 (ASTM 2004c) forparticles < 4.75 mm and by ASTM C 127 (ASTM 2004d) for particles > 4.75 mm; emin determined by ASTM D 4253 (ASTM 2004e), emax determined byASTM D 4254 (ASTM 2004f); gd-max, determined by ASTM D 698 (ASTM 2004g) (standard Proctor); roundness determined by procedures in Krumbein(1941); and the Unified Soil Classification (USCS) is determined by ASTM D 2487 (ASTM 2004h). Cu, coefficient of uniformity; Cc, coefficient of curva-ture; Gs, specific gravity; emax, maximum void ratio; emin, minimum void ratio; gd-max, maximum dry unit weight.*Parentheses represent maximum and minimum void ratios for P4 material.


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dures in AASHTO T 236-92 (AASHTO 2001). A schematicof the LSDS box is shown in Fig. 2. The LSDS box is305 mm square, contains a 152 mm thick specimen, and isconstructed from stainless steel plate (13 mm for the sides,19 mm for the front and back). A rear platform (19 mmthick aluminum plate) (Fig. 2) was included to allow dis-placement of the upper and lower boxes without loss ofsoil. A Teflon sheet was glued to the inner walls of the boxto reduce side-wall friction. The Teflon lining was inspectedprior to each test and replaced periodically as needed. Theshear box was contained within an external box that acts asa reservoir for inundation of the specimen.

Shear displacement was controlled by a stepper motor thatdrives the external box on a slide track (the lower half of theshear box is bolted to the external box). Movement of theupper portion of the shear box is prevented by a horizontalarm affixed to the frame of the machine. A load cellmounted between the arm and the frame is used to measurethe shear force. Normal force is applied through a rubberbladder filled with compressed air that is overlain by twosteel plates. A vertical arm mounted to the frame acts onthe steel plates to provide the reaction for the rubber blad-der. A load cell mounted on the arm monitors the normalforce. Normal forces are maintained by a feedback-controlled pressure regulator attached to the rubber bladderand the load cell attached to the vertical arm.

Measurements of horizontal displacement, vertical dis-placement, normal force, and shear force were recorded us-ing a personal computer equipped with a Validyne dataacquisition card (UPC601-U) and LabVIEW software. TwoLVDTs were used for measuring vertical displacements (So-

lartron model M9200000721–02, 30 ± 0.02 mm; SchaevitzEngineering series 1000 HR, 50 ± 0.025 mm), and oneLVDT was used to measure horizontal displacement (Solar-tron model M920002A721–01, 100 ± 0.01 mm). Vertical de-formations of the soil specimen were measured via LVDTscontacting a steel plate placed on top of the soil specimenand below the rubber bladder. Load cells were used to meas-ure shear force (Sensotec model 41/0573–05, 89 ± 0.15 kN)and normal force (Sensotec model 41/0573–05, 133 ±0.22 kN).

Sand used in the LSDS tests was sieved past a 25.4 mmsieve to meet the criterion on maximum particle diameterstipulated in AASHTO T 236-92 (AASHTO 2001). To en-sure that shear strengths measured in SSDS and LSDS couldbe compared directly, the density of P4 material (i.e., thefraction used in the SSDS tests) was maintained the same inthe SSDS and LSDS tests, as suggested by Fragaszy et al.(1992). Specimens for LSDS testing were prepared follow-ing the same procedure used for the SSDS tests and wereplaced between perforated PVC plates (13 mm thick) over-lain with nonwoven heat-bonded calendered geotextiles forseparation. Each sand was tested in LSDS at five normalstresses (26, 69, 105, 148, and 184 kPa), with inundationimmediately following application of the normal stress.Compression of the specimen was monitored during normalstress application and inundation. All specimens weresheared at a rate of 0.24 mm/min to a maximum horizontaldisplacement of 38 mm. Approximately 300 data pointswere recorded during each test.

The LSDS data were corrected to account for box frictionat the shear box interface. Similar corrections were not ap-

Fig. 2. Schematic of large-scale direct shear machine. LVDT, linear variable displacement transducer.


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plied to the SSDS data because testing showed that box fric-tion in SSDS was negligible (Bareither 2006). Shear resist-ance due to box friction (tB) was determined by thefollowing equation:

½1� �B ¼FNð1� �Þ þW 0B

ACB

� ��B

where FN is the applied normal force, a is the fraction ofthe applied normal force transmitted to the shear plane andaccounts for load transfer into the box walls, W 0B is thebuoyant weight of the upper box, ACB is the contact area ofthe shear box interface, and mB is the coefficient of frictionof the shear box interface. Details of the LSDS box frictioncorrection are included in Bareither (2006). Preliminarytests showed that a ranges between 0.907 and 0.936; theaverage a (= 0.9203) was used to compute the applied nor-mal stress and the box friction in each test (details providedin Bareither 2006).

Repeatability of direct shear methodsRepeatability of the testing method was evaluated by con-

ducting five replicate tests on TS sand in SSDS and LSDS.Failure envelopes from the replicate tests are shown inFig. 3. All tests exhibited strain-softening behavior, withfailure defined at peak strength. The failure envelopes inSSDS (Fig. 3a) are nearly identical, with the shear strengthat a given normal stress varying within ±4.0 kPa. The failureenvelopes in LSDS (Fig. 3b) show slightly greater variationwith shear strength at a given normal stress, varyingwithin ±8.0 kPa. Shear strength parameters and coefficientsof determination (R2) for the SSDS and LSDS envelopes arein Table 2. The range in f’ for SSDS is from 42.58 to 42.88,with an average of 42.68 and standard deviation of 0.258.For LSDS, f’ ranges from 40.18 to 41.18, with an averageof 40.58 and standard deviation of 0.458.

To confirm that the replicate failure envelopes obtained ineach test were the same, analysis of covariance (ANCOVA)was conducted at a significance level of 0.05 on both sets offailure envelopes by testing for homogeneity of slopes. Theanalysis evaluates the similarity of slopes of regression lines(in this case tan f’) under the null hypothesis that the slopesare identical, and returns a p-value corresponding to theprobability of falsely rejecting the null hypothesis (Lowry2006). One test compared the five failure envelopes ob-tained in SSDS to each other, another compared the fivefailure envelopes in LSDS to each other, and a third testcompared the five failure envelopes from SSDS to the fivefailure envelopes from LSDS. The ANCOVA yielded a p-value of 0.99 for the SSDS envelopes, a p-value of 0.80 forthe LSDS envelopes, and a p-value of 0.98 when comparingthe SSDS and LSDS envelopes. Thus, for all three analyses,no statistically significant difference was observed betweenthe failure envelopes (i.e., p >> 0.05 in each case).

Triaxial compression testsThe TC tests were conducted on P1-S1, P1-S6, P2-S9,

and TS sands for comparison with shear strengths obtained

Fig. 3. Failure envelopes for repeatability tests: (a) small-scale di-rect shear and (b) large-scale direct shear. All tests conducted withTS sand while inundated using a displacement rate of 0.24 mm/min.

Table 2. Shear strength parameters for repeatability testsconducted on TS sand using small-scale (SS) and large-scale(LS) direct shear (DS) tests.

Envelope f’ Intercept (kPa) R2

Small boxSS-1 42.5 2.27 0.999SS-2 42.8 1.12 0.998SS-3 42.5 1.80 0.999SS-4 42.5 1.79 0.999SS-5 42.6 2.19 0.997Average 42.6 1.83 0.998Standard deviation 0.2 0.46 0.001

Large boxLS-1 40.3 14.10 0.991LS-2 40.8 8.21 0.997LS-3 40.1 13.47 0.986LS-4 40.1 13.05 0.993LS-5 41.1 13.32 0.993Average 40.5 12.43 0.992Standard deviation 0.5 2.39 0.004


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in direct shear. These sands were selected to provide a rangeof f’ and shear behavior, as illustrated subsequently. Thesesands also have negligible fines, thereby precluding issuesregarding drainage. No standard method exists for perform-ing consolidated drained TC tests on granular soils. Thus,the triaxial testing procedure simulated, as closely as possi-ble, conditions imposed in the direct shear tests.

Specimens for the TC tests were prepared in a split mold(74 mm diameter, 147 mm tall) lined with a latex mem-brane. Air-dried sand passing the No. 4 sieve was used forall specimens. Compaction was performed in three layers ofequal thickness by tamping the top of each layer with a tam-per, with the number of tamps per layer adjusted to achievethe target density for each specimen. The specimens wereprepared to the same density used in the SSDS tests.

A cell pressure of 34 kPa was initially applied and water

was circulated through the specimen from the bottom up us-ing a small head difference (<0.6 m). Elevated backpressurewas not used and B-checks were not performed so as to sim-ulate the inundation condition used for the DS tests. Eachsand was tested at effective confining pressures of 21, 41,62, and 83 kPa. The effective confining pressures werechosen by superimposing Mohr circles on the DS failure en-velopes, so that the normal and shear stresses at failure fellwithin a range similar to the stresses in the SSDS tests.

An axial strain rate of 0.11 mm/min was used to provide asimilar displacement rate along the failure plane as was ap-plied in the direct shear tests. Measurements of axial dis-placement, axial force, and volume change were recordedusing a personal computer equipped with a National Instru-ments data acquisition card (model SC-2345) and LabVIEWsoftware. An external LVDT was used to measure vertical

Fig. 4. Shear stress versus relative horizontal displacement mea-sured in small-scale direct shear with failure stress defined by(a) peak stress (P2-S6 sand) and (b) initial horizontal tangent (P3-S2 sand).

Fig. 5. Shear-displacement curves for large-scale direct shear(LSDS) tests showing failure stress for cases with (a) initial hori-zontal tangent followed by plowing (P3-S1 sand) and (b) shearstress increasing at the same rate with additional horizontal displa-cement (P3-S2 sand).


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displacement (RDP ELECTRONICS model ACTL000A,50 ± 0.09 mm), an external load cell was used for axialforce measurements (Revere transducer model 363-D3–500–20P1, 2.2 ± 0.00015 kN), and a burette equipped with pres-sure transducer was used to monitor the volume expelled orimbibed by the specimen (Validyne model DP15–26 con-nected to a Valydine model CD379 digital transducer indica-tor). The water level in the burette used for monitoringvolume change during shear was positioned near the centerof the specimen. Approximately 250 data points were col-lected during each test. Failure was defined at the peakstress and the friction angle was obtained from the p’–q rela-tionship.

Shear behavior in direct shear testing

Definition of failureTypical curves relating shear stress and relative horizontal

displacement (RHD = (horizontal displacement/specimenlength) � 100) for the SSDS tests are shown in Fig. 4. Twoshear stress versus RHD relationships were observed:(i) shear stress increasing to a peak stress and then decreas-ing to a large-displacement stress (i.e., strain-softening,Fig. 4a) and (ii) shear stress increasing to an ultimate stressand remaining essentially constant thereafter (Fig. 4b). Fail-ure was defined as the peak shear stress for all sands exhib-iting peak stress behavior. For sands exhibiting only anultimate stress, the failure stress was defined by the initialhorizontal tangent to the shear stress – RHD curve. Periodi-cally, a small increase in shear stress was observed after theinitial horizontal tangent. This increase in shear stress wasalways less then 5 kPa and is believed to be a test artifact(see subsequent discussion of particle–box interactions in

LSDS tests). For consistency, these small increases in shearstress were disregarded.

Three shapes were observed for the shear stress – RHDcurves for the LSDS tests: (i) a peak stress similar to thatobserved in SSDS and then decreasing to a large-displacement stress (not shown); (ii) shear stress increasingto an ultimate stress similar to that observed in SSDS, butfollowed by a gradual increase in shear stress at a constantrate at larger horizontal displacement (Fig. 5a); and(iii) shear stress increasing until the slope of the shearstress – RHD curve reached a minimum, after which theshear stress increased at a constant rate with additional hori-zontal displacement (Fig. 5b). The gradual increase in shearstress (Fig. 5a) and the constant rate of increasing shearstress (Fig. 5b) observed at large displacements are believedto be due to particle–box interactions, as described subse-quently.

Failure was defined as the peak shear stress for the testsexhibiting a distinct peak and as the shear stress at the initialhorizontal tangent when a horizontal tangent was evident(Fig. 5a). For the tests where the shear stress increased mo-notonically with horizontal displacement (Fig. 5b), the fail-ure stress was defined as the shear stress at the same RHDat failure identified in SSDS. This definition was selectedbecause failure occurred at essentially the same RHD inSSDS and LSDS when a distinct peak shear stress was ob-served in both tests (Fig. 6). A two-sided paired t test wasconducted at the 5% significance level on the 28 observa-tions in Fig. 6 to confirm that the RHD at failure for theSSDS and LSDS tests was essentially the same. The testyield a two-sided p-value of 0.35 (>>0.05), indicating thatthere is no statistically significant difference in the relative

Fig. 6. Relative horizontal displacement at failure in large-scale di-rect shear (LSDS) versus relative horizontal displacement at failurein small-scale direct shear (SSDS) for sands exhibiting a peakstress.

Fig. 7. Vertical displacement at front and rear of the large-scale di-rect shear (LSDS) box versus relative horizontal displacement forP2-S4 sand, which exhibited ‘‘plowing’’ behavior for normal stres-ses between 62 and 184 kPa inclusive.


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horizontal displacements at failure for these SSDS andLSDS tests.

Particle–box interactionsThe increases in shear stress at larger displacements that

were observed in the LSDS tests (Fig. 5), and occasionallyin the SSDS tests, may be due to interactions between gran-ular particles and the shear box. Vertical displacements atthe front and back of the LSDS box (see box schematic inFig. 2) were compared for those tests without a distinctpeak shear stress, as illustrated in Fig. 7 for P2-S4 sand.Vertical displacements at a normal stress of 26 kPa wereomitted from Fig. 7 because monotonic increases in shearstress were not observed at this normal stress for any of thetests.

In Fig. 7, dilation is occurring at the front of the box andcontraction at the back of the box. Particle movementswithin the LSDS box corresponding to these volumechanges are shown schematically in Fig. 8. Simulations ofdirect shear tests on sand by Liu (2006) with a discrete ele-ment model (DEM) have shown particle movements similarto those illustrated in Fig. 8. Additionally, DEM studies con-ducted by Cui and O’Sullivan (2006) and Zhang and Thorn-ton (2007) as well as photoelastic studies conducted by Dyerand Milligan (1984) on direct shear tests identified particle-to-particle force concentrations at the front of the uppershear box and back of the lower shear box during shearing.Thus, particle movements may create particle-to-particleforce concentrations that are transferred to the particle–boxinterface, increasing the measured shear resistance.

The particle–box interaction was far less significant in theSSDS test than in the LSDS test. The exaggerated particle–box interaction in LSDS probably is due to a greater numberof particles moving within the shear band in the larger scaletest. For example, Palmeira and Milligan (1989) and Wu etal. (2008) measured the shear band thickness in differentsize direct shear box tests and report an increase in shear

band thickness with increase in specimen thickness. Also,Jewell (1989) has shown that rotation occurs in direct sheartests with free top platens (as used in the SSDS and LSDS),and that rotation is more significant when the normal stressis applied by a pressure bag (as in the LSDS) than with arigid top platen (as in the SSDS).

Small-scale versus large-scale shearstrength

The SSDS and LSDS tests were performed on the 30sands described in Table 1. A Mohr–Coulomb failure enve-lope for each test was defined by linear least-squares regres-sion with a non-negative intercept. Strength parameters forthe envelopes are summarized in Table 3. The envelopeswere linear for all practical purposes, with R2 ranging from0.997 to 1.000 for SSDS and from 0.991 to 1.000 for LSDS.The intercepts represent friction in the shear box not ac-counted for by the box friction correction and possibly non-linearity of the failure envelopes near the origin. However,in all cases, the apparent cohesion was small, typically 3.0–4.0 kPa in SSDS and 6.0–7.0 kPa in LSDS.

A comparison of friction angles obtained from the LSDStests (f’LSDS) and those obtained form the SSDS tests(f’SSDS) is shown in Fig. 9. The data are segregated intotwo sets corresponding to sands with less than 5% R4 mate-rial and more than 5% R4 material. For both data sets,f’LSDS & f’SSDS, although scatter exists in the data. Thelargest difference between f’LSDS and f’SSDS is 4.08, corre-sponding to P2-S11 sand, which contained 30% R4 materialin LSDS (the largest R4 for the sands that were tested). Forthe other 29 sands, f’LSDS and f’SSDS differ by less than 4.08,with most of the friction angles differing by less than 28.

Two-sided paired t tests were performed at the 5% signif-icance level on the <5% R4 data and >5% R4 data to deter-mine if the friction angles obtained from LSDS and SSDSwere statistically similar. The t test on sands with <5% R4

Fig. 8. Schematic of particle movements during shearing in large-scale direct shear (LSDS).


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(18 sands) yielded a p-value of 0.65, whereas the p-valuewas 0.70 for the sands with >5% R4. Thus, for both datasets, there is no statistically significant difference in f’ ob-tained with LSDS and SSDS (i.e., p >> 0.05).

The ratio of box length to median particle diameter (L/D50) for the SSDS and LSDS tests is listed in Table 3. Theminimum L/D50 for SSDS is 93 and the average is 197,whereas the minimum L/D50 for LSDS is 359 and the aver-age is 888. An L/D50 ‡ 50 was proposed by Jewell andWroth (1987) and ‡ 66 was experimentally evaluatedthrough DEM simulations by Jacobson et al. (2007) to bean approximate threshold ratio where there are sufficientparticles in the specimen to mitigate any scale effects in di-rect shear. Variations in friction angles similar to this studyhave also been reported by Taylor and Leps (1938), Bishop(1948), Palmeira and Milligan (1989), and Cerato and Lute-negger (2006) for dense granular materials with L/D50 ‡ 66in various-sized direct shear boxes. Thus, shear strength pa-rameters determined in direct shear with L/D50 ‡ 66 may beregarded as an accurate estimate; however, physical tests areneeded to more precisely identify the threshold L/D50 ratio.

Additionally, the findings from this study suggest thatconclusions reported by Fragaszy et al. (1992) and Simoni

and Houlsby (2006) for laboratory prepared mixtures ofsand and gravel also apply to a broad range of natural gran-ular backfills having R4 < 30%. In particular, for naturalgranular backfills with R4 < 30%, the shear strength can bedetermined by performing shear tests on the P4 (i.e., matrix)material alone provided the P4 material is tested at the samedensity as the P4 matrix in backfill containing R4 material.A threshold gravel content may exist beyond which the R4material does affect f’. Fragaszy et al. (1992) suggest thatthis threshold corresponds to 40%–50% gravel, whereas Si-moni and Houlsby (2006) indicate that the threshold is be-tween 20%–40% gravel. Conclusively identifying thisthreshold was not a focal point of this study and is a topicin need of further research. However, the data from thisstudy suggest that the threshold on gravel content for naturalsand backfills is near 30%.

Comparison of triaxial compression, small-scale direct shear, and large-scale directshear

Friction angles obtained from the TC tests are tabulated inTable 4 along with the friction angles from the SSDS and

Table 3. Shear strength parameters, specimen void ratio, and ratio of box length to median particle dia-meter (L/D50) for small-scale direct shear (SSDS) and large-scale direct shear (LSDS) tests.

SSDS LSDS

SampleIntercept(kPa) f’ R2

Voidratio L/D50

Intercept(kPa) f’ R2

Voidratio L/D50

P1-S1 5.1 35.8 0.998 0.57 206 0.0 38.1 0.991 0.57 984P1-S2 4.5 32.9 0.999 0.52 168 4.2 31.7 0.997 0.52 803P1-S3 5.3 34.3 0.999 0.61 206 3.1 35.7 0.999 0.61 984P1-S4 3.5 33.4 1.000 0.50 213 7.1 32.8 0.997 0.48 1017P1-S5 5.1 32.3 0.999 0.51 145 3.8 32.0 0.996 0.51 693P1-S6 6.0 32.5 0.999 0.54 188 9.3 31.8 0.997 0.54 897P1-S7 4.3 34.8 1.000 0.63 221 11.2 38.0 0.996 0.63 1052P2-S1 2.2 36.6 0.999 0.63 213 7.1 36.1 0.999 0.63 1017P2-S2 1.3 37.8 0.999 0.67 320 6.3 35.3 0.995 0.67 1525P2-S3 4.6 35.1 0.999 0.71 533 6.2 37.0 0.999 0.66 1906P2-S4 4.6 36.5 1.000 0.65 213 5.3 37.0 1.000 0.47 953P2-S5 5.6 40.9 1.000 0.58 107 12.1 41.3 0.998 0.55 477P2-S6 0.8 40.5 1.000 0.59 237 6.0 41.7 0.993 0.59 1130P2-S7 0.0 39.6 1.000 0.61 427 13.0 38.9 0.992 0.61 2033P2-S8 0.6 41.5 0.998 0.53 139 8.4 40.1 0.998 0.50 610P2-S9 8.0 38.5 0.998 0.53 168 13.4 36.6 0.991 0.45 709P2-S10 4.1 36.4 0.999 0.59 320 5.2 37.7 0.994 0.59 1525P2-S11 5.6 38.7 0.998 0.50 133 24.4 42.8 0.990 0.36 359TS* 1.8 42.6 0.998 0.50 156 12.4 40.5 0.992 0.50 726P3-S1 4.1 39.2 0.997 0.49 107 6.6 37.6 0.999 0.46 484P3-S2 0.6 36.9 0.998 0.46 152 0.3 35.0 0.997 0.42 635P3-S3 6.7 35.4 0.998 0.49 119 3.2 34.7 0.992 0.49 565P3-S4 2.9 40.3 0.998 0.48 93 5.9 40.9 1.000 0.48 436P3-S5 2.6 36.4 0.998 0.48 139 7.0 35.0 0.997 0.47 635P3-S6 4.3 34.5 0.999 0.60 221 5.1 35.2 0.999 0.60 1052P3-S7 2.8 35.4 0.999 0.62 291 2.6 36.4 0.995 0.62 1386P4-S1 2.0 36.7 0.999 0.67 114 1.6 35.3 0.998 0.67 526P4-S2 2.6 40.7 0.998 0.60 136 0.0 43.7 0.993 0.60 635P4-S3 3.8 42.4 0.999 0.50 107 7.2 41.9 0.994 0.44 396P5-S1 2.9 39.1 1.000 0.47 125 5.0 39.3 0.999 0.41 477

*Averaged values from repeatability tests.


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LSDS tests on the same sands. Failure envelopes for the TC,SSDS, and LSDS tests are presented in Fig. 10. For the TCtests, the normal stress and shear stress on the failure plane(assumed to be at 45 + f’/2) were determined from Mohr’scircle so that the envelopes from direct shear and triaxialcompression could be compared directly.

For each of the four sands, good agreement exists be-tween the failure envelopes obtained for all three tests, andthe f’ differ by at most 3.38 (P1-S1 sand, Table 4). To con-firm that the failure envelopes from each test were statisti-cally similar, an ANCOVA was conducted at the 5%significance level on each set of envelopes. A summary ofthe p-values from the ANCOVA is in Table 4. In all cases,p > 0.05, indicating that there is no statistically significantdifference between the envelopes.

The friction angles obtained from the TC tests were alsocompared to those from the SSDS and LSDS tests to deter-mine if statistically significant differences existed betweenthe friction angles measured in triaxial compression and di-rect shear. The differences f’SSDS – f’TC and f’LSDS – f’TCwere evaluated using t tests at a significance level of 0.05.The tests yielded two-sided p-values of 0.61 (SSDS versusTC) and 0.55 (LSDS versus TC), indicating that there is nostatistically significant difference between the friction anglesmeasured in DS and TC (p >> 0.05). This finding suggeststhat the conclusions in Taylor (1939), Nash (1953), Rowe(1969), and Pells et al. (1973), which indicate that f’ meas-ured in triaxial compression and direct shear differs lessthan ±38 for medium–dense sands (i.e., relative density rang-ing between 60% and 75%), also apply to natural compactedsand backfills.

Summary and conclusionsThe shear strength of 30 compacted sand backfill materi-

als having a gravel content (particles greater than 4.75 mm)

ranging from 0% to 30% was measured in small-scale (SS)and large-scale (LS) direct shear (DS) tests. The SSDS testswere conducted in a 64 mm square box accommodating amaximum particle diameter of 4.75 mm, whereas the LSDStests were conducted in a 305 mm square box accommodat-ing a maximum particle diameter of 25.4 mm. Tests con-ducted in SSDS required removal of the gravel. Triaxialcompression (TC) tests were also conducted on four of thebackfill materials tested in SSDS and LSDS tests. Resultsof these tests were compared, from which the following con-clusions are drawn:

� Friction angles measured in SSDS and LSDS are essen-tially the same provided that the gravel fraction is lessthan 30%. Friction angles measured in this study differedby no more than 48, and in most cases differed by lessthan 28.

� Representative friction angles for sands containing gravelcan be determined in SSDS after removing the gravelfraction, provided that the gravel content is less than30% and the minimum box length to median particle dia-meter (L/D50) is at least 93.

� Replicate testing showed that the peak friction angle (f’)obtained with the SSDS and LSDS procedures is highly

Fig. 9. Friction angles obtained from large-scale direct shear (LSDS) tests versus friction angles obtained from small-scale direct shear(SSDS) tests.

Table 4. Friction angles and analysis of covariance (AN-COVA) statistics for P1-S1, P1-S6, P2-S9, and TS sandsfor small-scale direct shear (SSDS), large-scale directshear (LSDS), and triaxial compression (TC) tests.

Test type P1-S1 P1-S6 P2-S9 TSSSDS 35.8 32.5 38.5 42.6LSDS 38.1 31.8 36.6 40.5TC 34.8 34.2 39.5 41.3ANCOVA p-value 0.70 0.07 0.09 0.45


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repeatable (within f’ ± 0.258 in SSDS and ± 0.458 inLSDS).

� For sands exhibiting peak stress behavior in both SSDSand LSDS, relative horizontal displacements correspond-ing to peak stress are similar, differing by ±0.88%.

� A gradual increase in shear stress occurred at larger hor-izontal displacements in some of the LSDS tests. This in-crease in shear stress is attributed to particle movementsduring shearing that cause force concentrations to de-velop between particles and the front of the upper shearbox and back of the lower shear box, thereby increasingthe measured shear resistance. This is an artifact of LSDStesting and it should be ignored in determining the max-imum shearing resistance.

� The friction angle of compacted sand backfills can bemeasured in SSDS, LSDS, or TC with comparable accu-racy.

AcknowledgementsThis project was funded by the Wisconsin Department of

Transportation (WisDOT). The assistance of Dan Reid, Den-nis Althaus, and Bruce Pfister of WisDOT is greatly appre-ciated.

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Comparison of shear strength of sand backfills measured …Comparison of shear strength of sand backfills measured in small-scale and large-scale direct shear tests Christopher A