INTRODUCTION



Barriers with a low hydraulic conductivity are used

as part of waste containment systems to prevent

groundwater contamination by liquids from the

waste. Commonly barriers are either a geomembrane

(usually an HDPE sheet), a mineral layer or

a combination of the two. Recently there has been

increasing interest in the use of bentonite±sand

mixtures as the mineral layer, in both land®ll liners

and vertical cut-off walls, partly because they are

less susceptible to frost damage and desiccation

cracking than compacted clay (Dixon et al., 1985;

Kraus et al., 1997). Currently there is uncertainty

about the strength and bearing capacity of these

materials. This note reports drained strength data

for bentonite±sand mixtures and proposes that

trends in these data are mainly the result of variations

in the relative density of the sand

Cousens, T.W.

Mollins, L.H.

Stewart, D.I.

English

White Rose Research Online

This is a repository copy of The Drained Strength of Bentonite Enhanced Sand.White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/1324/Article:Mollins, L.H., Stewart, D.I. and Cousens, T.W. (1999) The Drained Strength of Bentonite Enhanced Sand. Geotechnique, 49 (4). pp. 523-528. ISSN 0016-8505 eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse See Attached Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. TECHNICAL NOTEDrained strength of bentonite-enhanced sandL. H. MOLLINS, D. I . STEWART{ and T. W. COUSENS{KEYWORDS: clays; laboratory tests; sands; shearstrength.INTRODUCTIONBarriers with a low hydraulic conductivity are usedas part of waste containment systems to preventgroundwater contamination by liquids from thewaste. Commonly barriers are either a geomem-brane (usually an HDPE sheet), a mineral layer ora combination of the two. Recently there has beenincreasing interest in the use of bentonite±sandmixtures as the mineral layer, in both land®ll linersand vertical cut-off walls, partly because they areless susceptible to frost damage and desiccationcracking than compacted clay (Dixon et al., 1985;Kraus et al., 1997). Currently there is uncertaintyabout the strength and bearing capacity of thesematerials. This note reports drained strength datafor bentonite±sand mixtures and proposes thattrends in these data are mainly the result of varia-tions in the relative density of the sand.MATERIALSThe materials used in the study were Conquestgrade Wyoming bentonite supplied by Colin Stew-art MinChem, and Knapton Quarry sand. Conquestgrade Wyoming bentonite originates from New-castle, Wyoming, and is ground, dried and airclassi®ed during processing. X-ray diffraction spec-troscopy and chemical analysis (Mollins et al.,1996) indicate that it is predominantly a sodiummontmorillonite with some quartz and trace cristo-balite. Knapton Quarry sand is a slightly silty, ®ne,angular quartz sand (containing some iron oxidesand silicate minerals). It was sieved to removeparticles greater than 2 mm (the fraction removedrepresented less than 1% by weight). Other proper-ties of these materials are given in Table 1.TEST PROCEDURETriaxial specimens of Knapton Quarry sandmeasuring approximately 76 mm3 38 mm in dia-meter were prepared by tamping dry sand into amould. Once the specimens were con®ned in thetriaxial cell, the pore air was displaced by theupward ¯ow of de-aired water.Mixtures containing 5, 10 and 20% bentonite bydry weight were compacted into a Proctor mouldby the modi®ed Proctor method at optimum moist-ure content, and 76 mm3 38 mm diameter speci-mens were cored. These were saturated in a triaxialcell by a back pressure of 300 kPa, with radial andend drainage. Atkinson et al. (1985) have shownthat radial drains can cause non-uniformities inclay specimens subjected to either undrained load-ing followed by consolidation, or rapid drainedloading, but as such conditions were avoided, theuse of radial drains was considered satisfactory.Specimens were kept under back pressure until thepore pressure parameter B indicated a high degreeof saturation (Black & Lee, 1973). Typically thistook 2 months.Mixtures containing 10 and 20% bentonite bydry weight were tested in a standard WykehamFarrance 38 mm triaxial cell equipped with a 3 kNsubmersible load cell and an `Imperial Collegetype' volume change unit. Mixtures containing 5%bentonite by dry weight were tested in a 38 mmBishop-Wesley `stress-path' triaxial cell equippedwith a 5 kN submersible load cell and a rolling-diaphragm type volume change unit. Sand speci-mens were tested in both apparatuses.All specimens were subjected to a consolidateddrained triaxial compression test. A back pressureof 300 kPa was used in all tests except CD-05-2and CD-05-3, where 200 kPa was used, and CD-05-1, which was tested without back pressure sothat the specimens could be failed without exceed-ing the capability of the Bishop-Wesley cell. Mix-tures tested in the standard cell were compressedaxially at a rate of 1:53 10ÿ4 mm=min, and mix-tures in the stress-path cell were tested at variablerates of stress increase to achieve approximatelythe same compression rate. Typical rates were ofthe order of 0:02 kPa=min once the axial compres-sion had exceeded 3 mm. The average degree ofMollins, L. H., Stewart, D. I. & Cousens, T. W. (1999). GeÂotechnique 49, No. 4, 523±528523Manuscript received 3 April 1998; revised manuscriptaccepted 10 November 1998.Discussion on this technical note closes 5 November1999; for further details see p. ii. Douglas Partners, Australia.{ University of Leeds.consolidation at failure was typically 98%(Mollins, 1996). Sand specimens were compressedaxially at a rate of approximately 0:3 mm=min. Allspecimens were compressed until either the peakstrength or 20% axial strain were exceeded, andthe data were corrected for the membrane andradial drains following the recommendations ofBishop & Henkel (1962).RESULTSThe angle of repose of Knapton Quarry sandmeasured by the method recommended byCornforth (1973) was 348. Cornforth suggested thatthis angle is roughly equal to öcrit (for quartz sand,318 < öcrit < 358; Bolton, 1986). Table 2 showsthe results from drained triaxial compression testson Knapton Quarry sand. On average, KnaptonQuarry sand at an initial void ratio of 0´69 mobi-lized a öpeak of 38´28 at åa  7:2% and dilated atfailure.Table 3 and Fig. 1 show the results from con-solidated drained triaxial tests on 5, 10, and 20%bentonite±sand mixtures. Two different void ratiosare reported for each mixture, the clay void ratioec ( volume of water/volume of clay particles),which characterizes the state of the bentonite (i.e.re¯ects the stress required to con®ne the bento-nite), and the sand void ratio es (for a saturatedmixture, es  volume of clay and water/volume ofsand), which is a measure of the packing of thesand particles.The 5% mixtures had an average öpeak of 46´78at an average åa of 4´3% and dilated strongly atfailure. The average initial sand void ratio es ofthe 5% mixtures was 0´48. The 10% mixtures hadan average öpeak of 43´58 at an average åa of 5´2%.All the 10% mixtures dilated at failure, althoughthere was an overall volume decrease in testCD-10-4, where the initial es was 0´67 (the other10% mixtures had an initial es around 0´55). The20% mixtures had an average öpeak of 29´88 at anaverage åa of 13´3%. Specimens CD-20-1 and CD-20-2, with an initial es of 0´81 and 0´86, re-spectively, dilated at failure, whereas specimensCD-20-3 and CD-20-4, with an initial es of 1´01and 1´23, respectively, compressed until theysheared at roughly constant volume.In summary, the strength of bentonite±sand mix-tures decreases with increasing initial es, whichcorresponds to increasing bentonite content. Theaxial strain to failure increases with increasingTable 1. Properties of Wyoming bentonite and Knapton Quarry sandWyoming bentonite Knapton Quarry sandLiquid limit  407% Percentage ®nes  7%Plastic limit  48% Effective size (D10)  0:07 mmSpeci®c gravity  2´76 Speci®c gravity  2´67Moisture content{  13´5%(as supplied)Moisture content  4´5%(as supplied)Maximum void ratio  0´978Minimum void ratio  0´451 Determined by the small-pyknometer method on clay oven-dried at 1058C.{Measured by oven drying at 1058C.Table 2. Details of the drained triaxial compression tests on Knapton Quarry sandTest ó 93:kPae0 (ó 91 ÿ ó 93)peak:kPaöpeak:degreesåa, peakstrength: %åv, peakstrength: %ÿdåvdå1 maxCD-S-1 51 0´74 169 38´6 8´0 ÿ1´6 0´404CD-S-2{ 51 0´68 170 38´7 8´0 ÿ0´9 0´359CD-S-3{ 51 0´68 176 39´3 7´5 ÿ1´9 0´446CD-S-4 52 0´74 197 40´9 5´2 ÿ2´0 0´576CD-S-5{ 87 0´66 264 37´1 6´6 ÿ1´3 0´495CD-S-6 101 0´73 343 39´0 6´6 ÿ1´9 0´425CD-S-7 101 0´71 350 39´4 6´7 ÿ2´0 0´516CD-S-8{ 200 0´66 588 36´5 9´3 ÿ0´5 0´347CD-S-9{ 200 0´65 602 36´9 7´3 ÿ0´8 0´374CD-S-10{ 201 0´66 602 36´8 7´1 ÿ0´9 0´392CD-S-11{ 201 0´67 617 37´3 8´3 ÿ1´0 0´426CD-S-12 203 0´72 697 39´2 5´8 ÿ1´1 0´407 Bishop-Wesley `stress-path' cell.{ Standard Wykeham Farrance cell.524 MOLLINS, STEWART AND COUSENSTable 3. Details of the consolidated drained triaxial compression tests on bentonite±sand mixturesTest Bentonite content:% by dry weightó 93:kPaes ec (ó 91 ÿ ó 93)peak: kPa öpeak:degreesåa, peakstrength: %åv, peakstrength: % ÿdåvdå1 maxCD-05-1 5 187 0´49 8´35 983 46´4 4´2 ÿ1´9 1´17CD-05-2 5 103 0´48 8´16 473 44´2 4´0 ÿ1´8 0´90CD-05-3 5 103 0´50 8´46 558 46´9 4´0 ÿ2´5 0´94CD-05-4 5 51 0´45 7´61 253 45´5 5´4 ÿ3´0 1´07CD-05-5 5 25 0´48 8´06 156 49´2 4´6 ÿ3´1 1´22CD-05-6 5 25 0´46 7´65 143 47´8 3´8 ÿ2´6 1´24CD-10-1{ 10 197 0´52 3´68 807 42´2 4´7 ÿ0´8 0´71CD-10-2{ 10 98 0´57 4´11 460 44´5 2´3 ÿ0´9 0´90CD-10-3{ 10 50 0´55 3´96 269 46´8 4´8 ÿ2´9 1´02CD-10-4{ 10 24 0´67 5´00 89 40´5 8´8 1´9 0´49CD-20-1{ 20 195 0´81 2´22 373 29´3 8´8 ÿ4´3 0´54CD-20-2{ 20 99 0´86 2´44 208 30´8 10´1 ÿ3´0 0´42CD-20-3{ 20 47 1´01 3´03 80 27´4 19´0 2´9 ÿ0´06CD-20-4{ 20 21 1´23 3´90 46 31´5 15´4 3´8 0´01 Bishop-Wesley `stress-path' cell.{ Standard Wykeham Farrance cell.DRAINEDSTRENGTHOFBENTONITE-ENHANCEDSAND525initial es. These trends are illustrated by Fig. 1.The drained strength of Knapton Quarry sand pre-pared at an initial void ratio of about 0´69 wasintermediate between the drained strengths of the10% mixtures (average es 0:58) and the 20% mix-tures (average es 0:98).DISCUSSIONThe stress±dilatancy relationship of Rowe(1962) relates the maximum effective stress ratiosupported by an assembly of irregular rigid parti-cles in contact to the friction between the particlesand the rate of dilatancy. When written in terms oföpeak, this equation istan2(458 öpeak=2)  tan2(458 öf=2)3 1ÿdåvdå1 max(1)where öf depends on the mechanism of energydissipation, that is, either particle sliding associatedwith the average angle of shearing resistance be-tween particle surfaces öì or turbulent shear asso-ciated with the critical-state angle of shearingresistance öcrit (Rowe, 1972). Substitution of thedrained triaxial compression data for KnaptonQuarry sand (Table 2) into equation (1) yieldsöf  30:08. Data presented by Rowe (1962) sug-gest that öì  298 for ®ne quartz sand shearingacross a quartz block, whereas for Knapton Quarrysand, öcrit  348, so a value of öf  30:08 indicatesa predominantly sliding mode of shearing at peakstrength. Such behaviour is characteristic of amedium dense sand (Rowe, 1972).Figure 2 shows the variation in peak strength ofthe bentonite±sand mixtures with the maximumrate of dilation. Also shown in Fig. 2 are the sanddata and a line representing equation (1) withöf  30:08. The data for mixtures containing 5 and10% bentonite fall close to the line representingRowe's stress±dilatancy relationship, suggestingthat it is the interaction of the sand particles inthese mixtures that controls the behaviour (i.e.minimal work is done on, or released by, the clayduring shearing). Rowe's stress±dilatancy theorycannot be used predictively, as it does not specifythe relationship between the peak rate of dilationand the initial state of a soil. Bolton (1986) re-viewed extensive data on the strength and dilatancyof numerous types of sand at a range of densitiesand con®ning stresses. Bolton reported that the rateof dilation of sand during shearing is a function ofrelative density and mean effective stress, andproposed a relative dilatancy index IR that corre-lates with the dilatant component of strength:Fig. 1. (a) Peak angle of shearing resistance and (b)axial strain to failure against void ratio of the sand forKnapton Quarry sand and Wyoming bentonite/Knap-ton Quarry sand mixtures0 0.2 0.4 0.6 0.8 1.0 1.2(a)05101520253035404550φpeak: degreesSand 5% mixture 10% mixture 20% mixture0 0.2 0.4 0.6 0.8 1.0 1.2(b)Sand void ratio es02468101214161820εa: %emin emaxSand5% mixture10% mixture20% mixtureEquation (1)0 0.2 0.4 0.6 0.8 1.0 1.2Rate of dilation05101520253035404550φpeak: degreesFig. 2. Peak angle of shearing resistance againstmaximum rate of dilation for Wyoming bentonite/Knapton Quarry sand mixtures526 MOLLINS, STEWART AND COUSENSIR  ID(10ÿ ln p9)ÿ 1 (2)where ID is the relative density (ID  (emax ÿ e)=(emax ÿ emin)) and p9 is the mean effective normalstress in kN=m2.Bolton proposed a correlation between IR andthe peak rate of dilation,ÿdåvdå1 max 0:3IR8 (3)and another between IR and the dilatant componentof strength,ömax ÿ öcrit  3IR8 (4)which were validated in the range 0, IR , 4 for awide range of sands. Equations (2) and (3) predictthat a sand will dilate when ID > (10 ÿ ln p9)ÿ1.Figure 3 shows the maximum rates of dilationand öpeak of the sand and the 5 and 10% mixturesplotted against the value of IR based on (ID)s, therelative density calculated using es. Figs 3(a) and3(b) show clear trends of increasing dilation andincreasing öpeak, respectively, with increasing IR.Lines representing equations (3) and (4) (assumingöcrit  348) are shown on Figs 3(a) and 3(b),respectively, and are good ®ts to the experimentaldata.The mixtures containing 20% bentonite all gavea ömax of about 308, and therefore the data fromthose tests where there was signi®cant dilation atfailure (CD-20-1 and CD-20-2) fall signi®cantlybelow the line representing equation (1) in Fig. 2.The application of equation (1) to a bentonite±sandmixture implicitly assumes that the net work doneby the external forces is dissipated as friction be-tween the sand particles. The initial clay void ratiosof specimens CD-20-1 and CD-20-2 were lowerthan in the other tests (see Table 3) so the effectivestress con®ning the bentonite will have been signi®-cantly larger, and therefore ignoring the frictionalwork dissipated by the clay will be inappropriate forthese tests. As the effective stress required to con-®ne the clay at a particular void ratio is heavilydependent on stress history, no attempt has beenmade to correct the data for this effect.The two 20% bentonite mixtures con®ned bythe lowest effective cell pressure (CD-20-3 andCD-20-4) swelled signi®cantly during `consolida-tion' in the triaxial cell to reach initial sand voidratios of 1´01 and 1´23 (i.e. higher than the maxi-mum void ratio for the sand alone). These speci-mens had maximum angles of shearing resistanceof 27´48 and 31´58, respectively. Kenney (1977)measured the direct shear strength of clay±sandmixtures and observed that there was a transitionin the ultimate angle of shearing resistance of themixture ö from the critical-state angle of the sand(öcrit)s at a sand void ratio of around unity, to theresidual angle of the clay (ör)c, at large sand voidratios. Kenney used the relative residual strengthRö to describe this transition, whereRö tanöÿ tan(ör)ctan(öcrit)s ÿ tan(ör)cLupini et al. (1981) presented data for bentonite±sand mixtures where Rö varied from unity at a sandvoid ratio of about 0´9 to zero at a sand void ratioof about 4. They also reported that when Rö wasgreater than about 0´7, the mode of shearing wasturbulent (i.e. the mode of shearing exhibited bysand at the critical state). Mixtures CD-20-3 andCD-20-4 had residual strength ratios of 0´74 and0´90 (based on (ör)c  48) and would seem to havebeen in a state of turbulent shear, as suggested byLupini et al., and at, or near, a critical state.Fig. 3. Variation of (a) maximum rate of dilation and(b) peak strength with dilatancy index for the sand10% mixture5% mixtureSandEquation (3)0 1 2 3 4 5Dilatancy index (IR)s(a)00.20.40.60.81.01.21.41.6Rate of dilation010% mixture5% mixtureSandEquation (4)0 1 2 3 4 5Dilatancy index (IR)s(b)5101520253035404550φpeak: degreesDRAINED STRENGTH OF BENTONITE-ENHANCED SAND 527In summary, the drained strength of bentonite±sand mixtures can be idealized by three modes ofbehaviour, as shown in Fig. 4, over the range ofsand relative densities that may be encountered inland®ll liners and environmental barriers. Above asand relative density of (10ÿ ln p9)ÿ1, bentonite±sand mixtures will exhibit a peak strength anddilate at failure in a manner indistinguishable fromsand alone, except when the bentonite in the mix-ture supports an appreciable proportion of thestress. The strength of such mixtures can be esti-mated using the dilatancy index proposed byBolton (1986). When 0 < (ID)s < (10ÿ ln p9)ÿ1,the strength of a bentonite±sand mixture will beequal to the critical state strength of the sand. As(ID)s reduces below zero (i.e. the sand void ratioexceeds the maximum for sand alone), the strengthof the mixture reduces from the critical-statestrength of the sand alone towards the residualstrength of the clay.CONCLUSIONSThe ultimate shear strength of a bentonite±sandmixture depends primarily on the relative densityand critical-state friction angle of the sand withinthe mixture. Over the range of bentonite contentsused for environmental barriers, the bentonite hasvery little in¯uence on drained strength unless itsupports a signi®cant proportion of the stress (in-dicated by a low clay void ratio). However, at veryhigh bentonite contents (and consequently highsand void ratios) the strength of the mixture willtend towards the strength of the clay.REFERENCESAtkinson, J. H., Evans, J. S. & Ho, E. W. L. (1985). Non-uniformity of triaxial samples due to consolidationwith radial drainage. GeÂotechnique 35, No. 3,353±355:Bishop, A. W. & Henkel, D. J. (1962). The measurementof soil properties in the triaxial test, 2nd edn. Lon-don: Edward Arnold.Black, D. K. & Lee, K. L. (1973). Saturating laboratorysamples by back pressure. J. Soil Mech. Found. Div.,ASCE 99, No. SM1, 75±93.Bolton, M. D. (1986). The strength and dilatancy ofsands. GeÂotechnique 36, No. 1, 65±78.Cornforth, D. H. (1973). Prediction of the drainedstrength of sands from relative density measurements,Special Technical Publication 523, pp. 281±303. Phi-ladelphia: American Society for Testing and Ma-terials.Dixon, D. A., Gray, M. N. & Thomas, A. W. (1985). Astudy of the compaction properties of potential clay±sand buffer mixtures for use in nuclear fuel wastedisposal. Engng Geol. 21, 247±255.Kenney, T. C. (1977). Residual strengths of mineral mix-tures. Proc. 9th Int. Conf. Soil Mech. 1, 155±160.Kraus, J. F., Benson, C. H., Erickson, A. E. & Chamber-lain, E. J. (1997). Freeze±thaw cycling and hydraulicconductivity of bentonite barriers. J. Geotech. EngngDiv., ASCE 123, No. 3, 229±238.Lupini, J. F., Skinner, A. E. & Vaughan, P. R. (1981). Thedrained residual strength of cohesive soils. GeÂotech-nique 31, No. 2, 181±213.Mollins, L. H. (1996). The design of bentonite±sandmixtures. PhD thesis, University of Leeds.Mollins, L. H., Stewart, D. I. & Cousens, T. W. (1996).Predicting the properties of bentonite±sand mixtures.Clay Minerals 31, 243±252.Rowe, P. W. (1962). The stress±dilatancy relation forstatic equilibrium of an assembly of particles incontact. Proc. Roy. Soc. 269A, 1962, 500±527.Rowe, P. W. (1972). Theoretical meaning and observedvalues of deformation parameters for soil. In Stress±strain behaviour of soils (ed. R. H. G. Parry),pp. 143±194. London: Foulis.Relative density (ID)s(10 2 ln p ′)21φ(φcrit)sTending to φcFig. 4. Schematic graph showing the variation in thedrained strength ö of bentonite±sand mixtures withthe initial relative density of the sand in the mixture(ID)s528 MOLLINS, STEWART AND COUSENS

The Drained Strength of Bentonite Enhanced Sand

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The Drained Strength of Bentonite Enhanced Sand

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