Volume changes in undrained triaxial tests onsands

Vinod K. Garga and Huiming Zhang

Abstract: The error in dimension measurement and the volume changes during saturation, consolidation, and undrainedloading were investigated in the conventional triaxial tests on a Unimin sand. A Hall effect radial displacement transducer(HRDT) was developed. With the help of the HRDT and the linear varying displacement transducer (LVDT), the volumechange during saturation and the membrane penetration during consolidation can be easily determined by directly measuringradial and axial dimensional changes of a triaxial sample. The test results show that for a Unimin sand sample with nominaldimensions of 50 100 mm, the volume change due to saturation increased with a decrease in the initial density of thesample, varying from 2.79 cm3 at Dr = 1.9% to 0.87 cm3 at Dr = 54.7%. The volume change during undrained loadingresulted mainly from the variation of membrane penetration due to the buildup of pore-water pressure, increasing with theeffective stress at consolidation. The steady-state lines with volume correction at the onset of collapse and at phasetransformation were much lower than that without volume correction.

Key words: liquefaction, sand, steady-state strength, triaxial, undrained, volume.

Rsum : Lerreur commise sur la mesure des dimensions et sur les changements de volume des prouvettes pendant lasaturation, pendant la consolidation et pendant le chargement non drain a t tudie lors dessais triaxiaux conventionnelssur un sable Unimin. On a fabriqu un capteur de dplacement radial bas sur leffet Hall (HRDT). Grce ce capteur et uncapteur de dplacement linaire (LVDT), le changement de volume pendant la saturation ainsi que la pntration de lamembrane lors de la consolidation peuvent facilement tre dtermins par la mesure des changements des dimensions radialeet axiale de lchantillon triaxial. Les rsultats dessais montrent que pour une prouvette de sable Unimin de dimensionnominale 50 100 mm, le changement de volume d la saturation augmente lorsque la densit initiale de lchantillondcrot, passant de 2,79 cm3 pour un indice de densit de 1,9 % 0,87 cm3 pour un indice de densit de 54,7 %. Lechangement de volume pendant le chargement non drain rsulte principalement de la variation de pntration de lamembrane suite laccroissement de pression interstitielle, phnomne qui augmente avec la pression effective deconsolidation. Les lignes dtat stationnaire dtermines en dbut de rupture et au stade du changement de phase sont situesbien au-dessous de celles que lon calcule sans correction de volume.

Mots cls : liqufaction, sable, rsistance ltat stationnaire, triaxial, non drain, volume.[Traduit par la rdaction]

Introduction

The steady-state line relates the void ratio and the effectivestresses at the steady state (as defined by Poulos 1981) in un-drained triaxial tests or other shear tests on sands (Castro 1969;Casagrande 1975). This steady-state line is unique for a givensand under an undrained triaxial compression condition, re-gardless of the initial conditions of the sand samples (Castroet al. 1982; Poulos et al. 1985; Vaid and Chern 1985; Vaidet al. 1990; Sladen et al. 1985; Been et al. 1991; McRobertsand Sladen 1992; Negussey and Islam 1994; etc.). However,the steady-state line is often so flat within the normal range ofin situ stresses that a small change in the void ratio can resultin a large change in the steady-state strength. This may be oneof the reasons why often the steady state, in practice, is notlocated along a unique line, but on a wide band for a given sand(e.g., Konrad 1990a, 1990b). As an important factor affecting

the undrained behaviour of sands, the void ratio may be alteredsubstantially due to sample volume changes that occur intriaxial tests. Hence, it is of interest to investigate the potentialvolume changes of a sand sample in conventional undrainedtriaxial tests on saturated sands.

In laboratory tests, uncertainties of sample volumes canresult from errors in the initial dimension measurement, samplesaturation, membrane penetration, and the loading procedure.The error in initial void ratio of a sample may be caused byerrors in dimension measurement and weight measurement.The error in weight measurement, usually less than 0.01%, isnegligible. Castro et al. (1982) considered that the error in thedimension measurement should be less than 0.001 in termsof void ratio. However, this was only the error estimated fromthe resolution of the measurement tools. Observer error in voidratio determination may be much larger than the resolution error.

It is often necessary to prepare a loose sand triaxial samplewith strain-softening behaviour in unsaturated state, for exam-ple by using the moist tamping method (Castro et al. 1982), inwhich the surface tension between soil particles is employedto maintain a very loose sand structure. This type of structurecan result in sample volume change during saturation. However,

Received January 23, 1997. Accepted May 9, 1997.

V.K. Garga and H. Zhang. Department of CivilEngineering, University of Ottawa, 161 Louis Pasteur,Ottawa, ON K1N 6N5, Canada.

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a correction for the volume change occurring during saturationis difficult to make without measuring the radial deformationof the sample. Sladen and Handford (1987) found that a veryloose sample may be densified significantly during back-pressuresaturation. The potential error resulting from ignoring this den-sification was reported to be as much as 0.15 in terms of voidratio for the Syncrude tailings sand. Also, the volume changeof a sand sample during saturation, which occurs after the di-mension measurement, may be different for different satura-tion procedures.

Newland and Allely (1957) first observed that membranepenetration into the interstices of the soil grains at a sampleboundary under cell pressure can lead to erroneous volumemeasurement. Since then, many investigators have studied themeasurement of and correction due to the membrane penetra-tion (e.g., Roscoe et al. 1963; Raju and Sadasivan 1974; Vaidand Negussey 1984; Ohara and Yamamoto 1991; Tanaka et al.1991; Nicholson et al. 1993a, etc.). However, membrane pene-tration can be affected by many factors including the effectiveconfining pressure; grain size, shape, gradation, and density ofthe sample; characteristics of the rubber membrane such asthickness and extension modulii; and the surface area of thesample in contact with the rubber membrane (Raju and Sadasivan1974). Hence, no single approach can consider all the factorsand can be used to accurately estimate membrane penetrationfor different sands

The volume of a saturated sand sample is not constant dur-ing undrained shear due to membrane penetration (Newlandand Allely 1959). This undrained volume change may signifi-cantly affect the undrained behaviour of sands. Thus, the cor-rection of the membrane penetration effect, or its elimination,have drawn much attention (e.g., Pickering 1973; Kiekbuschand Schuppener 1977; Lade 1977; Martin et al. 1978;

Molenkamp and Luger 1981; Ramana and Raju 1981; Baldiand Nova 1984; Tokimatsu and Nakamura 1986; Seed et al.1989; Evans et al. 1992; Nicholson et al. 1993b; Ansal andErken 1996; etc.). Seed et al. (1989) and Nicholson et al. (1993b)used a technique of injectionremoval compensation to inves-tigate the undrained behaviour of a sand. Their results showedthat a partly strain-softening response without the injectioncompensation could become a strain-hardening response withthe compensation. The use of their compensation scheme mayoverestimate the undrained strength of the sand samples withpartly strain-softening behaviour.

A potential problem, which has been ignored to date, iswhether the pore-water volume can be changed during un-drained loading on a saturated sand sample. It is a generallyaccepted assumption that the pore water within the sample isincompressible, because of the low compressibility of deairedwater. However, the sample may not be completely saturatedwith water, particularly in the case of moist tamped samples.The compressibility of pore water in such a sand sample may notbe negligible and may affect the undrained behaviour of sands.

The objective of this paper is to investigate the errors insample dimension measurements, the membrane penetrationduring consolidation, and in the sample volume changes dur-ing saturation and during undrained triaxial tests on sand sam-ples. Further, the limitation of constant volume triaxial tests isalso explored.

Laboratory investigation

The experiments in this study consisted of sample dimensionmeasurement, saturation tests, consolidation tests, B valuetests, undrained triaxial compression tests, deaired water com-pression tests, and air dissolution tests. A height gauge wasdeveloped, borrowed from the idea of a reference dial indicator(Sasitharan 1994; Vaid and Sivathayalan 1996), to measure theheight of a triaxial sample (Fig. 1). A calibration curve can beobtained by using the height gauge to measure several alumi-num dummy samples with known heights. Then the height ofa sample can be easily measured to 0.01 mm with this heightgauge. A Hall effect radial displacement transducer (HRDT)was improved, from the concept described by Clayton et al.(1989), to measure the radial deformation of a triaxial sampleduring saturation and consolidation (Fig. 2). The HRDT hasan effective linear range of about 2 mm, with a resolution of0.01 mm. Two bellofram-type volume gauges with a resolu-tion of 0.02 cm3 were also used in the triaxial apparatus system(Fig. 3). One was connected to base of the sample in the usualmanner, while the other was connected to the triaxial cell tomeasure the volume change of the cell water. The volumemeasurement from the later volume gauge together with themovement of the ram into the cell was used to estimate thevolume change of sample pore fluid during undrained loadingunder constant cell pressure.

The main material tested was the Unimin sand, an angularmedium crushed quartz sand obtained from St-Canut, Quebec.Ottawa sand (C190) was also used in some tests. Their indexproperties and grain size distributions are given in Table 1 andFig. 4, respectively. The minimum and maximum void ratioswere determined according to the ASTM test methodsD425393 (method 1A) and D425491 (method A), respec-tively. Triaxial specimens, 50 mm in diameter 100 mm in

Fig. 1. Schematic diagram of height gauge.

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height, were prepared by water pluviation (Vaid and Negussey1988) and moist tamping methods (Castro et al. 1982). Un-drained stress-controlled triaxial shear tests were employed,since the rapid collapse, which is relevant to liquefaction failure,occurs in stress-controlled tests and not in strain-controlledtests (Casagrande 1975). Also, it is not very clear how strainrate affects the steady-state strength of a loose sand sample(Zhang 1997).

Dimension measurements

To investigate the measurement error, four dummy aluminumsamples, whose dimensions (D = 48.86 ~ 50.76 mm, H =100.54 ~ 111.25 mm) were previously measured by a caliperwith a resolution of 0.01 mm, were fully installed on thetriaxial base, in a manner similar to a sand sample. Theirheights were again measured by two different methods: calipermethod (as used by Castro et al. 1982) and the height gaugemethod. In the caliper method, four readings of a sample heightin different directions were taken, and their average was usedas the measured height of the sample. In the height gaugemethod, only one reading was taken. The caliper method (asused by Castro et al. 1982) and perimeter tape method (as used

by Sasitharan 1994; Verdugo and Ishihara 1996) were alsoused to measure the diameters of the aluminum samples. In thecaliper method, the diameters at the top, middle and bottom ofa sample were measured over a membrane in two orthogonaldirections. The average of the six readings, after deductingtwice the thickness of the membrane, was used as the measureddiameter. The perimeter of the sample was also measured by aperimeter tape with a resolution of 0.5 mm. However, the cor-responding accuracy, equal to 0.5 /pi = 0.15 mm, was too poorto be acceptable for the measurement of the sample diameter(D = 50 mm) used in this study. Instead, the perimeter readingswere taken by marking the circumferential connecting pointson the tape with a fine pencil and measuring the linear distancebetween the connection points with a caliper. In this way, theperimeter readings at the top, middle, and bottom of the samplewere taken; and their average, divided by pi and then deductingtwice the thicknesses of the membrane and the perimeter tape,was taken as the measured diameter of the sample.

The errors in measurement are shown in Table 2. The errorin height measurement by using the caliper method was large,from 0.09 to 0.23 mm. This error results mainly from the cali-per inclination and the observers error to distinguish theboundaries between a sample and the end platens. A two de-gree inclination of the caliper can make the measured length0.06 mm longer than the nominal vertical length of 100 mm.The sample boundaries are usually not very distinct, particu-larly when observed from outside of a membrane. The heightgauge method provided better results, with no insignificantobservation error. Its average relative error was only 0.02%,much less than that in the caliper method.

Fig. 2. Schematic diagram of HRDT. Fig. 3. Schematic diagram of triaxial apparatus.

Gs D50 (mm) Cu emin emaxUnimin sand 2.665 0.61 2.00 0.655 1.037Ottawa sand (C190) 2.670 0.72 1.25 0.496 0.674

Table 1. Index properties of the tested materials.

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The error in diameter measurement using a caliper was from0.01 to 0.03 mm, less than that incurred using the perimeter tape.The average relative errors were 0.04% and 0.11% for thecaliper method and the perimeter method, respectively. Thelimitations of the perimeter method are the low resolution ofthe perimeter tape and the difficulty in determining the contactpoints of the tape. The potential error in void ratio of a nominal50 100 mm Unimin sand sample with Dr = 30% would be0.006 and 0.003 by using a caliper to measure both the diame-ter and height of the sample, and by using a caliper to measurethe diameter and using a height gauge to measure the height,respectively.

It should be noted that the measured volumetric error maybe much higher in sand samples than in the aluminum dummysamples. The primary problem lies in the diameter measure-ment: how to place a caliper or a perimeter tape on the surfaceof a sand sample accurately? A 0.1 mm or higher error in di-ameter measurement is possible; the corresponding error invoid ratio for a 50 100 mm sand sample is over 0.008. Thelooser the sand sample, the higher the potential error. Unfor-tunately, the sand samples for the determination of the steady-state line are often very loose. A better measurement device orapproach appears to be necessary to increase the accuracy ofthe diameter measurement.

Volume change during saturation

Saturation of moist tamped samples is usually undertaken intwo stages: water flushing and back-pressure saturation. Twowater flushing methods are commonly used. In the first method(e.g., Sladen and Handford 1987), carbon dioxide gas followedby deaired water is flushed through the sample; then the sample

top cap is seated and the membrane is secured with O-rings. Atthis step, the sample dimensions are measured after applying alow suction on the sample and removing the mold. In the sec-ond method (e.g., Sasitharan 1994), the sample dimension isfirst measured under a low suction (about 20 kPa in this study)before carbon dioxide gas and water is flushed through thesample. In conventional triaxial tests, the volume change dur-ing back-pressure saturation in the first method or during waterflushing and back-pressure saturation in the second method isoften ignored.

In the first method, in which the sample dimension is meas-ured after water flushing, no suction is applied during waterflushing, and so soil grains can move to a state approximatingthat in a water-pluviated sample. Thus a loose sample preparedby the moist tamping method will be formed close to the loos-est density that can be reached in the water-pluviation method.For example, two Unimin sand samples with initial relativedensities of 7% and 19% were densified to relative densitiesof 25% and 26%, respectively (the loosest relative density forUnimin sand in water pluviation method is about 30%). There-fore, in order to obtain a larger density range, all other moisttamped samples in this study were flushed by using the secondmethod only.

The procedure to prepare a saturated sand sample in thisstudy was carried out in the following steps: (1) tamp a samplein five layers; (2) apply a suction (20 kPa) on the sample andmeasure its dimensions; (3) install the HRDT, the triaxial cellcover, and the external linear varying displacement transducer(LVDT); (4) fill the cell with water and apply a low cell pres-sure (25 kPa) on the sample; (5) remove suction and flushcarbon dioxide gas and deaired water through the sample;(6) apply the desired back pressure and cell pressure. All dis-placements after the initial dimension measurement, except thevertical deformation during the installation of the triaxial cell,were monitored with the HRDT and the LVDT.

The test results of sample volume changes occurring insteps (4) to (6) are shown in Table 3 and Fig. 5. The resultsindicate that for the Unimin sand, the volume changes undera cell pressure increase of 25 kPa were small and did not varysignificantly with relative density. During water flushing, thevolume change was large at low densities (as high as 1.78 cm3for the sample with initial Dr = 1.9%); but decreased rapidlyup to a relative density of 30%. During back-pressure satura-tion, the volume change ranged from 0.27 to 0.92 cm3. Theentire saturation procedure resulted in a volume change of0.026 to 0.008 in terms of void ratio; the looser the sample, thelarger the volume change. This indicates that the error in voidratio due to ignoring the volume change during saturation canbe over 0.020 for the loose Unimin sand samples. The steady-state line is often very flat for many sands (Castro et al. 1982)and is usually determined based on undrained tests on veryloose samples. Thus, the high void ratio error in loose sand

Fig. 4. Grain size distribution curves.

Error in height Error in diameterHeight gauge method Caliper method Perimeter method Caliper method

Error range (mm) 0.02 to 0.03 0.09 to 0.23 0.07 to 0.06 0.01 to 0.02Avg. relative error (%) 0.02 0.14 0.11 0.04

Note: Avg. relative error = {measured dimension - known dimension}/ {known dimension}.

Table 2. Error in dimension measurement.

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samples may significantly overestimate the undrained steady-state strength for a given sand. For example, this research hasindicated that for a Drc = 30% Unimin sand sample, an errorin void ratio of 0.02 may overestimate its steady-state strengthfrom 101 to 183 kPa.

Sladen and Handford (1987) showed that a very high errorof 0.15 in terms of void ratio occurred in Syncrude tailing sandas a result of ignoring sample densification during back-pres-sure saturation. Compared with the maximum void ratiochanges of 0.026 during the entire saturation procedure and0.009 during the back-pressure saturation for the Unimin sandsamples, the above-mentioned 0.15 void ratio error appears tohave been overestimated, since both Syncrude and Uniminsands have the same (emax emin) difference value of 0.38. Avoid ratio change of 0.15 would make a loose Unimin sandsample become very dense. In the reported tests on the Syn-crude sand, the final volumes of the samples were determinedindirectly by measuring the moisture content of these samplessubsequent to undrained shear. Thus the high estimated vol-ume change reported by Sladen and Handford (1987) may re-sult not only from the back-pressure saturation, but also from

the volume change during undrained shearing and lack of100% saturation of the samples.

Volume change due to membranepenetration

Volume change due to membrane penetration occurs when a latexmembrane penetrates into the surface irregularities of a sand sam-ple when applying effective confining stress to the sample duringconsolidation. It is equal to the difference between the total watervolume expelled out of the sample and the volume change of thesoil skeleton. In this study, only the effect of the membrane thick-ness on the penetration was investigated. The expelled water vol-ume was measured by a precise volume gauge, and the skeletonvolume change was determined from the vertical and radial de-formations of the sample measured by the LVDT and the HRDT,respectively. Thus, the membrane penetration could be directlydetermined for each sample.

Water-pluviated Unimin sand and Ottawa sand sampleswere used to determine membrane penetrations with thin(0.33 mm) and thick (0.62 mm) membranes. The initial rela-tive densities of the Unimin sand and the Ottawa sand sampleswere about 33% and 17%, respectively. The test results areshown in Fig. 6. Clearly, the membrane thickness () significantly

Fig. 5. Volume change during saturation (Unimin sand).

InitialDr(%)

VCP(cm3)

Vwater(cm3)

VBP(cm3)

Total V(cm3)

Totale

Bvalue

1.9 0.34 1.78 0.50 2.79 0.026 1.0144.3 0.25 1.68 0.27 2.18 0.023 1.0066.9 0.31 1.33 0.35 1.99 0.020 1.004

14.7 0.24 0.78 0.89 1.90 0.019 1.01117.0 0.34 0.34 0.92 1.60 0.016 1.01828.1 0.26 0.12 0.43 0.81 0.008 0.99733.4 0.12 0.16 0.71 0.99 0.00945.1 0.24 0.22 0.43 0.89 0.00954.7 0.12 0.08 0.67 0.87 0.008Note: VCP, Vwater, and VBP are the volume changes due to application of 25 kPa cell pressure, flushing water

through sample, and back-pressure saturation (BP = 500 kPa), respectively.

Table 3. Volume changes during saturation (Unimin sand).

Fig. 6. Membrane penetration.

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affects the membrane penetration in both sands. The thinner themembrane, the higher the volume change due to the membranepenetration. The membrane penetration for the 0.33 mm mem-brane was 23 times that for the 0.62 mm membrane.

These results, as well as published data, indicate that it isquestionable practice to apply a constant membrane penetra-tion correction for different membranes and test conditions.

Compressibility of airwater mixture andthe B value

The compressibility of a fully deaired, i.e., pure water isequal to 4.58 107 (kPa1) (Fredlund and Rahardjo 1993).When water pressure increases from 0 to 500 kPa, the volumechange of the pore water in a fully saturated sand sample withtypical dimensions of 50 100 mm is very small, equal toabout 0.02 cm3. However, the pore water in a saturated sandsample often contains some dissolved air and possibly evenfree air in some cases. The compressibility of water with dis-solved air is approximately two orders of magnitude greaterthan that of pure water, and the inclusion of even 1% free airin the voids is sufficient to significantly increase the pore fluidcompressibility (Fredlund and Rahardjo 1993). Hence, thepore fluid volume change in a saturated sand sample may belarge enough to affect the undrained behaviour of sands, andtherefore merits further examination.

Compressibility of airwater mixtureThe water compression tests were conducted in a hydraulicconsolidation cell (Garga and Khan 1991). The compressibil-ity of deaired water was obtained from the difference betweenthe total volume changes of two deaired water samples with

different volumes subjected to the same pressure. Then, thesystem volume change was calibrated by deducting the volumechange of the deaired water from the total volume change ofeach of the two deaired water samples. Next, the compressibil-ity of three water samples with different but known free aircontent was determined. The known free air content was intro-duced by using a syringe to draw the desired volume of waterfrom the cell, which was initially full of freshly deaired water.

The test results are shown in Fig. 7 and Table 4. It can beseen that the volume change of the fresh deaired water samplewas very small, its volumetric strain was less than 0.1% evenat a pressure of 1500 kPa (Fig. 7). Its compressibility wasequal to 13.7 107 to 3.4 107 kPa1 in a pressure range of01500 kPa (Table 4), close to that of pure water. However,the volumetric strain increased rapidly with an increase in theinitial free air content, changing from 0.03% at a pressure of400 kPa for the freshly deaired water to 1.48%, 3.35%, and7.41% for initial air contents of 1.8%, 4.2%, 9.3%, respectively(Fig. 7). The compressibility of the airwater mixture was, atlow pressure, two orders of magnitude greater than that of thedeaired water and decreased with water pressure. Even at awater pressure of 500 kPa, the airwater mixture still exhibitedhigh compressibility, 1.19 105 kPa1, for an initial air con-tent of 4.2% (Table 4). This indicates that even using a highback pressure, the volume change of the pore fluid in a satu-rated sand sample may not be negligible during undrainedloading, particularly in the case of moist tamped samples.

Solution of air in deaired waterIt was noted during the set up of sand samples that when asuction was adjusted before it was applied to a sample, numerousair bubbles appeared in the water in the tubing, which wasdeaired only 3 hours before. This indicated that air could rap-idly dissolve in the deaired water. To investigate the rate of air

Pressure (100 kPa)Initial air content (%) 01 12 24 46 68 810 1013 1315

0 13.7 8.9 6.9 5.6 4.7 4.0 3.4 3.41.8 867 334 140 58 38 21 21 214.2 2027 703 311 119 79 48 34 219.3 4413 1671 665 280 157 119 59 48

Table 4. Compressibility of water (107 kPa1).

Fig. 7. Compression of airwater mixture. Fig. 8. Air dissolution test results.

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dissolution in deaired water, an oxygen meter (model 860,manufactured by Orion Research Incorporated, Germany) wasemployed. In these tests, distilled water was filled into the tankof a Nold DeAeriator and was deaired under a suction of97 kPa for 40 min. Next, the deaired water was drained into a300 mL beaker after flushing the drainage line. The oxygencontent in the deaired water was then measured at differenttimes. The test results are shown in Fig. 8. It can be seen thatthe oxygen content in the fresh deaired water was 2.2 mg/L,and it increased rapidly to 4.4 mg/L in 10 min. Two hours later,the deaired water had regained its original air content of6.3 mg/L. This implies that, if assuming that air dissolves intothe deaired water at the same rate as oxygen and if the deairedwater is used 2 hours after being exposed to air in a smallcontainer, the deairing effect may be eliminated. One day later,the deaired water had an oxygen content of 9.0 mg/L, almostthe same as that of tap water after waiting for 10 hours. Theoxygen content of the deaired water, kept in the Nold reservoirbut exposed to air, increased to 4.4 mg/L in 12 hours, a muchlower value than that of the deaired water contained in abeaker. It was also noted that the water deaired under highsuction remains at an oxygen content of 2.2 mg/L. Thus, eventhe fresh deaired water is not fully deaired, and the compressi-bility of deaired water is larger than that of pure water.

Back pressure, B value, and degree of saturationSkemptons pore pressure coefficient B is usually used to ver-ify the degree of saturation of a sample. In the 1980s, thesample was assumed to be saturated if the B value was equalto or larger than 0.95 (e.g., Castro et al. 1982); currently, ahigher B value (0.99) is targeted (e.g., Sasitharan 1994).

The B value tests on water-pluviated samples were con-ducted to investigate the volume change of the pore water ina saturated sample. The samples were prepared by pluviatingboiled sands under freshly deaired water. The volume changein the measuring system due to pressure change was calibratedprior to the application of the back pressure. The water volumeintroduced into the samples due to back pressure change couldthen be obtained from the volume and deformation measure-ments. The test results shown in Fig. 9 indicate that the B valuesat zero back pressure were low, equal to 0.68 for Unimin sandand 0.72 for Ottawa sand. In order to reach a high B value ofover 0.99, the required back pressures were 600 and 500 kPa

and the water volumes introduced in the soil were 1.06 and0.98 cm3 for Unimin sand and Ottawa sand samples, respec-tively. The compressibility of the pore water in the sampleswas equal to about 1.9 105 (kPa1), 21 times that of thefreshly deaired water. This higher compressibility in the porewater may result from some tiny air bubbles which could havebeen caught between the membrane and the sample cap orbase, or from the compression of the pore water.

The B value tests on moist tamped Unimin sand sampleswere also carried out to investigate the relationships betweenthe back pressure and B value or the degree of saturation. Thesamples were flushed with or without carbon dioxide gas be-fore flushing water. The final degree of saturation of the sam-ples was obtained from the final dimensions and the final watercontent of the sample. Then, the degree of saturation could bedetermined based on the deformations, introduced water volume,and the final degree of saturation. The test results are shownin Fig. 10. For the CO2 flushed sample, the degree of saturationwas equal to 94% at zero back pressure, and its B value wasas high as 0.934 under a back pressure of 100 kPa. When thedegree of saturation was increased to 99.7%, a B value of 1.011was obtained. In the sample without CO2 flushing, the degreeof saturation was equal to 74% at zero back pressure, muchless than that for the CO2 flushed sample, and could attain avalue of only 98% under a back pressure of 700 kPa. Its B valueswere low, equal to 0.502 and 0.98 under back pressures of 100and 700 kPa, respectively. Therefore, in order to obtain ahighly saturated sand sample, it is necessary to flush carbondioxide gas through the sample before flushing deaired water.

Even a high B value, over 0.99, may not indicate a sandsample to be fully saturated in some cases. Skempton (1954)derived the pore pressure coefficient, B, as a function of theporosity n, the compressibility of pore fluid Cv, and the com-pressibility of soil skeleton Cc:

B =u3

=1

1 + nCv /CcThis expression indicates that the B value would be always lessthan unity. When the voids in a soil sample are fully saturatedwith water, the void fluid compressibility nCv is equal to thewater compressibility nCw, which is much less than that of the

Fig. 9. Relationship between back pressure and B value. Fig. 10. Relationship between back pressure, B value, and degree ofsaturation.

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soil skeleton. Thus the B value is close to, but less than, unity.It is in fact assumed in the derivation of the formula that thevolume change of the soil skeleton could be caused only by thevariation in effective confining stress. However, in the case ofsandy soils, the skeleton volume change can occur under con-stant effective confining stress due to the application of backpressure (Sladen and Handford 1987 and previous section inthis paper). If under undrained condition, the skeleton volumechange is close to or larger than that of the pore fluid due toapplication of the cell pressure, the B value can be close to orover unity, even though the sample may not be completelysaturated.

Volume change during undrained loading

Consideration of sample volume changeThe volume change of a soil sample results from its void vol-ume change, which consists of two components. The first com-ponent is due to the fluid drainage out of or into the soilskeleton, which also includes the variation of membrane pene-tration, and the second component is due to the compression ofthe pore fluid. No pore fluid is drained out of the sample underundrained loading conditions. Since membrane penetrationvaries with the change in effective confining stress, the porefluid can migrate into or out of the sample peripheral bound-ary. This migration can result in a change of the sample skele-ton volume (Newland and Allely 1959). The application of avertical stress may also cause a further compression of the porefluid. Therefore, the volume change of a saturated sand sampleduring undrained loading can be expressed as follows:

[1] V = Vm + Vwwhere V is the volume change of a sample (compression aspositive); Vm is the volume change due to membrane penetra-tion; and Vw is the volume change of pore fluid.

If the effective confining stress varies from the consolidationstress 3c to some value 3 because of the buildup of the porepressure in the sample during undrained loading, the volumechange due to membrane penetration is given by the following:

[2] Vm = Amc (3c) Am (3)where, () is the unit membrane penetration, dependent onthe effective confining stress for a given sample. It can bepredetermined at the consolidation stage for each sample. Amcand Am are the sample peripheral areas corresponding to 3cand 3, respectively. Based on the relationship between thediameter and height of a triaxial sand sample at axial strain aand volumetric strain v during loading (Zhang 1997), the pe-ripheral area, Am, can be expressed as follows:

[3] Am =16 Amc (1 a)

30(1 v)

(1 a) 5

1/2

+ 1

The volumetric strain v is usually less than 0.01 under un-drained loading and may be negligible. Therefore,

[4] AmAmc=

16 { [5(5 + a) (1 a)]

1/2 + (1 a)}

The volume change of the pore fluid, Vw can be determined bymeasuring the cell water volume change during undrained loading:

[5] Vw = Vt Vc Vcrp + Vpwhere Vt is the total volume change of the cell water, meas-ured by a volume gauge connected to the triaxial cell; Vc isthe volume change of the triaxial cell, equal to zero when cellpressure is constant; Vp is the volume change of the cell waterdue to the movement of the loading piston, equal to the verticaldeformation times the area of the piston; and Vcrp is the vol-ume change due to the creep deformation of the triaxial celland the cell water. It is usually negligible if the undrained testis conducted after 40 min or longer subsequent to the applica-tion of the cell pressure in the system used in this investigation.

Test results of sample volume change during undrainedloading

The results of conventional undrained triaxial tests on Uniminsand are showed in Figs. 11 to 13 and in Table 5. For the looseUnimin sand sample, its deviator stress and induced pore pres-sure gradually increased up to a small strain (less than 1%),then a sudden collapse occurred with a significant decrease inthe deviator stress and a large increase in the induced porepressure. Following this collapse, with further axial strain, thedeviator stress continuously increased accompanied by a de-crease in the pore presure (Fig. 11). It is noted that the postcol-lapse behaviour was observed for all loose Unimin sandsamples. The medium-dense Unimin sand sample exhibited atypical strain hardening behaviour, as shown in Fig. 12.

The tests on samples with dilative behaviour show that thepore fluid compression increased with strain at the initial stageof undrained loading, reaching a peak at about the phase trans-formation (Ishihara et al. 1975), and then slightly decreased

Fig. 11. Undrained volume change (loose sand).

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or remained constant (Fig. 12). In a loose sample with contrac-tive behaviour, the volume of the pore fluid decreased duringinitial straining and collapse, and then slowly increased or re-mained essentially constant with further strain (Fig. 11).

The membrane penetration volume change was estimatedfrom the pore pressure, hence its tendency was similar to thatof the pore pressure (Figs. 11, 12). The penetration volumechange during undrained loading is mainly dependent on thechange of the effective confining stress. The higher the con-solidation stress of a sand sample, the larger its penetrationvolume change at the onset of collapse and at the phase trans-formation (Table 5). The results in Fig. 11 show that prior tothe collapse, the effective confining stress decreased from theconsolidation stress of 200 kPa to 76 kPa, and caused a totalvolume change of 0.57 cm3. During collapse, the effectivestress dropped rapidly to 10 kPa and the membrane penetrationvolume change increased to 1.41 cm3. The membrane penetra-tion volume change continued to decrease with further straindue to a subsequent decrease in pore pressure.

Table 5 and Fig. 13 show a summary of the volume changesduring undrained loading in 12 samples of the Unimin sandtested at different relative densities. The volume change dueto pore fluid compression during undrained loading variedfrom 0.05 to 0.23 cm3 at the onset of collapse and from 0.08to 0.39 cm3 at the phase transformation. The compressibilityof the pore fluid in these samples varied between 3 106 and14 106 (kPa1), which is within the range of compressibilityof the deaired water as shown in Table 4. The membrane pene-tration volume change was large, about six times the pore fluidvolume change. It resulted in a change of 0.003 to 0.020 invoid ratio at the onset of collapse and from 0.009 to 0.027 atthe phase transformation stage (Fig. 13).

Effect of undrained volume change on steady-statestrength

Seed et al. (1989) and Nicholson et al. (1993b) found that thevariation of membrane penetration during undrained shear in aconventional undrained triaxial test may significantly affectthe steady-state line of a sand. They further stated that thiseffect on the steady-state line may be eliminated by conductingconstant volume triaxial tests or undrained triaxial tests on

large samples, or by deducting the variation of membranepenetration from the consolidation volume of a sample in aconventional undrained triaxial test.

The steady-state lines for the Unimin sand both with andwithout volume correction are shown in Fig. 14. The steady-state line (SSL1) at which the total volume change at the onsetof collapse is corrected is much lower than the steady-state line

At onset of collapse At phase transformationDrc(%)

3c(kPa)

3(kPa)

vw(cm3)

vm(cm3)

V(cm3)

3(kPa)

vw(cm3)

vm(cm3)

V(cm3)

13.9 100 62 0.05 0.30 0.33 5 0.08 0.77 0.8515.5 200 71 0.13 0.53 0.66 7 0.22 1.08 1.3017.4 200 76 0.10 0.57 0.67 10 0.17 1.41 1.5821.1 200 94 0.17 0.95 1.12 15 0.24 1.31 1.5525.2 399 163 0.14 0.94 1.08 34 0.24 1.43 1.6726.7 200 93 0.07 0.32 0.39 15 0.12 1.00 1.1228.5 500 187 0.07 0.98 1.06 36 0.13 1.65 1.7829.3 398 166 0.11 0.52 0.63 39 0.19 1.42 1.6137.5 601 211 0.18 1.35 1.68 84 0.33 1.88 2.2139.6 806 354 0.15 1.25 1.40 118 0.26 2.05 2.3141.4 997 349 0.19 0.92 1.11 155 0.32 1.53 1.8545.1 1092 380 0.23 1.73 1.96 195 0.39 2.20 2.59

Table 5. Undrained volume changes of loose Unimin sand samples.

Fig. 12. Undrained volume change (medium-dense sand).

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(SSL) without any volume correction. For the Unimin sand,the difference in mean effective stress between SSL and SSL1is 5 kPa for very loose samples and over 100 kPa for medium-dense samples. If the total volume change at phase transfor-mation (PT) is corrected, the steady-state line of the sand(SSL2) is even lower. For a given void ratio, the steady-statestress p determined from SSL2 is only approximately 76% ofthat determined from the steady-state line without volumechange. Therefore, the steady-state strength of a sand may besignificantly overestimated in conventional undrained triaxialtesting due to the variation of membrane penetration duringundrained shear.

The induced pore pressure during undrained shear reflectsthe global volume change tendency of a sample, which maybe also affected by the sample end restraint (Zhang 1997) andthe formation of a shear band (Finno et al. 1996). Thus, careshould be exercised to correct the induced pore pressure or tocarry out the constant volume tests. For example, in somecases, the corrected pore pressure could be larger than the cellpressure in a conventional undrained triaxial test (Ansal andErken 1996). Also, for a sand sample with quasi-steady-statebehaviour, its undrained strength under constant volume con-dition could be much larger than that under a conventionalundrained triaxial shear condition (Seed et al. 1989; Nicholsonet al. 1993b). Furthermore, if the constant volume tests arestress- or strain-controlled by utilizing a servo loading system,the volume change of a loose sand sample resulting duringrapid collapse may not be eliminated. The increase in porepressure during the collapse of the sample is faster than theresponse of most servo-activated systems.

Further evidence is necessary to determine whether themembrane penetration correction should be applied at the on-set of collapse or at the phase transformation for obtaining thereal steady-state line.

Conclusions

The following conclusions may be drawn from experimentaldata on clear Unimin and Ottawa sands:(1) Volume change during saturation and membrane penetra-

tion during consolidation can be easily determined by di-rectly measuring axial and radial dimensional changes ofa sample.

(2) The volume changes due to flushing water through a moisttamped sand sample (nominally 50 mm in diameter and100 mm in height) and due to back-pressure saturation canreach 1.78 and 0.92 cm3, respectively; and the total volumechange during the entire saturation procedure can be2.79 cm3 for the Unimin sand.

(3) A high B value may not necessarily imply that the sampleis completely saturated. Evaluating the void ratio from thefinal water content after shear may result in a large errorin the void ratio.

(4) Air can dissolve in deaired water rapidly. The compressi-bility of pore water in a saturated sample is much largerthan that of pure water. For the water-pluviated sand sam-ples, the average compressibility of pore water was about20 106 (kPa1) in the pressures range of 0500 kPa. Thecompressibility of the pore water in moist tamped sampleswas from 3 106 to 14 106 (kPa1) during undrainedloading.

(5) The volume change of a sand sample during undrainedloading consists of two components: the compression ofpore fluid and the penetration volume change. The porefluid volume change varied from 0.08 to 0.39 cm3 at thephase transformation, mainly depending on the pore pres-sure and density of the samples. It reached a peak at aboutthe phase transformation. The penetration volume changevaried from 0.30 to 1.73 cm3 at the onset of collapse andfrom 0.77 to 2.20 cm3 at the phase transformation, depend-ing on the induced pore pressure.

(6) Different steady-state lines were obtained from volumecorrections applied at the onset of collapse and at phasetransformation. The difference between the uncorrectedand corrected steady-state lines becomes important asthe mean effective stress increases.

Acknowledgment

The authors gratefully acknowledge the financial support fromthe Natural Sciences and Engineering Research Council ofCanada (NSERC).

Fig. 13. Volume change during undrained loading (Unimin sand). Fig. 14. Effect of undrained volume change on steady-state line.

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AbstractRsumIntroductionLaboratory investigationDimension measurementsVolume change during saturationVolume change due to membrane penetrationCompressibility of airwater mixture and the B valueVolume change during undrained loadingConclusionsAcknowledgmentReferencesTablesTable 1Table 2Table 3Table 4Table 5

FiguresFig. 1Fig. 2Fig. 3Fig. 4Fig. 5Fig. 6Fig. 7Fig. 8Fig. 9Fig. 10Fig. 11Fig. 12Fig. 13Fig. 14