A Modified Triaxial Apparatus for Measuring the Stress Path Dependent Water Retention-A

TECHNICAL NOTE

Charles W. W. Ng,1 C. H. Lai,2 and C. F. Chiu3

A Modified Triaxial Apparatus for Measuring theStress Path-Dependent Water Retention Curve

ABSTRACT: This article reports a modied triaxial apparatus for measuring the stress path-dependent water retention curve (SDWRC) ofunsaturated soils under isotropic and deviatoric stress conditions. In this modied triaxial apparatus, an open-ended, bottle-shaped inner cell isinstalled together with a differential pressure transducer to measure the total volume change of a specimen accurately for the correct determinationof the degree of saturation of an SDWRC. Details of the calibration and test procedures are described and discussed. Some test results fromcompacted samples of a completely decomposed tuff, i.e., silt of low plasticity, are also presented in order to demonstrate the key features of themodied apparatus.

KEYWORDS: unsaturated soil, water retention curve, laboratory test

Introduction

The water storage capacity of a soil at different matric suctionscan be represented by a water retention curve (WRC). The waterstorage capacity is generally quantied in terms of the gravimetricwater content, the volumetric water content, or the degree of satu-ration. As experimental studies on unsaturated soil are time-consuming and costly, many studies in the past have developedempirical relationships between the WRC and the mechanical/hy-draulic properties of unsaturated soil (Fredlund et al. 1994,1996;Vanapalli et al. 1996).

A change in matric suction can cause the volume of unsatu-rated soil to change. Normally, soil (except collapsible soil) swellsas the matric suction decreases (a process known as wetting) andshrinks as the matric suction increases (known as drying). How-ever, the volume is often assumed to be constant when evaluatingthe conventional WRC. Furthermore, the WRC is usually obtainedfrom tests under zero stress, even though soil can be, and often is,subject to various stress paths in the eld.

Recently, the focus has been shifted onto the effects of stresson the WRC (Ng and Pang 1999,2000a,2000b; Vanapalli et al.

1999; Romero and Vaunat 2000). Ng and Pang (2000a) used amodied volumetric pressure plate extractor to study the effects ofstress and volume changes on the WRC during a wetting and dry-ing cycle. However, the modied volumetric pressure plate extrac-tor measures the WRC only under the K0 condition. The effects ofa broader range of stress paths, such as isotropic and deviatoricstress paths, on the WRC have rarely been reported in the litera-ture. This article presents a modied double cell triaxial apparatusfor measuring the stress path-dependent water retention curve(SDWRC) under isotropic and deviatoric stress conditions. Thedesign of the inner cell and the calibration of a novel device formonitoring the volume change of a specimen are also discussed.Finally, the preliminary test results of a compacted soil are used todemonstrate the key features of the equipment.

Modified Triaxial Apparatus

Control of Matric Suction and Stress

The schematic layout of the modied triaxial apparatus is illus-trated in Fig. 1. The axis translation technique (Hilf 1956) is usedto control the matric suction (the difference between pore-air pres-sure ua and pore-water pressure uw) in the soil specimen. Thepore-air pressure is applied at the top of the specimen through acoarse porous lter. The pore-water pressure is applied and meas-ured at the base of the specimen through a 5-bar high air-entry ce-ramic disk. In the study, the base pedestal is left open; thus thepore-water pressure equals the atmospheric pressure. An open-ended and bottle-shaped inner cell is used inside a conventionaltriaxial cell. The same cell pressure is applied to both the innerand outer cells. An axial force can be exerted on the test specimenthrough a loading ram. An internal load cell is attached to the

Manuscript received July 12, 2011; ; accepted for publication October 19,2011; published online March 2012.

1Cheung Kong Scholar Chair Professor, Key Laboratory ofGeomechanics and Embankment Engineering of Ministry of Education, HohaiUniv., 1 Xikang Rd., Nanjing 210098, China; and Chair Professor, Dept. ofCivil and Environmental Engineering, the Hong Kong Univ. of Science andTechnology, Clear Water Bay, Kowloon, Hong Kong, e-mail:[email protected]

2Former Student, Dept. of Civil and Environmental Engineering, the HongKong Univ. of Science and Technology, Clear Water Bay, Kowloon, HongKong.

3Associate Professor, Key Laboratory of Geomechanics and EmbankmentEngineering of Ministry of Education, Hohai Univ., 1 Xikang Rd., Nanjing210098, China (Corresponding author), e-mail: [email protected]

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loading ram inside the cell in order to measure the axial forceapplied on the specimen directly. A dial gauge is mounted on theloading ram to measure the axial displacement of the soilspecimen.

Measurement of Total and Water Volume Change

The volume change of the specimen is monitored by the volumechange of the water in the inner cell. The change in volume of theinner cell can be minimized by the open-ended design, as both theinner and the outer cells are subjected to the same cell pressure.During a test, changes in the water level in the inner cell takeplace only within the neck of the bottle. The inner diameter of thebottle neck is 20 mm, which is larger than the diameter of theloading ram (10 mm). Thus, the net cross-sectional area excludingthe diameter of the loading ram at the bottle neck is used in calcu-lations. As a result, the measurement of the change in water levelinside the inner cell due to a change in the volume of the specimenis quite sensitive because of the small cross-sectional area of theneck of the bottle. A special device for measuring volumechanges, previously developed by Ng et al. (2002), was used tomonitor the volume change of the soil specimen in this study. Thebasic aim of the measuring device is to monitor the changes in thedifferential pressure between the water level inside the inner celland that in the reference tube with a differential pressure trans-ducer (DPT). The model of the DPT is Druck LPM9381. Bronzeconnecting tubes are used to minimize the potential pressure-induced expansion/compression of the drainage lines. Deairedwater is used inside the inner cell and reference tube. In order tominimize the evaporation of water and slow down the rate of airdiffusion into the water, a thin layer of parafn is added on thesurface of both the inner cell and the reference tube, as suggestedby Sivakumar (1993). The material used to manufacture the innercell is acrylic. It is understood that an apparent volume change

due to water absorption by an acrylic inner cell wall should betaken into account during a test (Sivakumar 1993). In this study,the inner cell was soaked in deaired water between each test inorder to minimize the effect of water absorption. Detailed calibra-tion procedures and accuracy evaluation of this type of inner cellhave been presented by Ng et al. (2002).

The ow of water into or out of the specimen is monitored bya burette together with an air trap and a ballast tube (see Fig. 1).This system functions as a buffer, storing the water owing out ofthe specimen during the drying process and allowing the backowof water from the ballast tube into the specimen during the wettingprocess. An air trap connected by the rubber connecting tubes tothe base of the triaxial cell is used to collect any air bubbles thatdiffuse through the high air entry disk. There is a level mark onthe stem of the air trap to measure the volume of water. There isanother level mark on the ballast tube, and a ruler attachedbeneath it, with which the equilibrium condition of the specimenfor a given matric suction can be monitored. In this study, theequilibrium condition is assumed to be attained when the waterow rate is less than 0.1 g/day.

Flushing System

The pore air cannot ow through the high air-entry ceramic disk ifthe matric suction of the soil specimen is lower than the air-entryvalue (AEV) of the ceramic disk. However, the pore air can stilldissolve into the water and diffuse through the ceramic disk dur-ing a test. This can affect the measurement of the water volumechange. Therefore, the apparatus is equipped with a ushing sys-tem to remove the diffused air. The schematic layout of the basepedestal is shown in Fig. 2. The water compartment beneath thehigh air-entry ceramic disk is a spiral groove 2 mm wide and1 mm deep. The spiral channel is more efcient than the conven-tional rectangular channel in ushing the accumulated air bubblesresulting from the air diffusion. The diffused air bubbles in thewater compartment are removed by running a roller over therubber connecting tube and are then collected in the air trap (seeFig. 1). The air collected in the air trap is removed by opening thestopcock and readjusting the water level to the level mark. Duringa test, the diffused air bubbles are removed at regular 12-hourintervals. In this study, the averaged air diffusion rate was notconsidered when evaluating the total measured water ow rate.This is because diffused air was ushed regularly at 12-hour inter-vals, and thus the inuence of diffused air may be consideredinsignicant.

Calibration for Apparent Volume Change

The double cell system is calibrated for compliance errors, includ-ing the movement of the loading ram, the deformation of the innercell and drainage lines due to the variation in cell pressure, andcreep. The calibration for the effects of cell pressure and creep onthe deformation of the inner cell and drainage lines was conductedon a rigid dummy specimen. The cell pressure was rst increasedquickly by a prescribed amount and then maintained for about aweek or longer. During the entire process, the output of the DPTwas monitored regularly.

FIG. 1Schematic layout of the modied triaxial apparatus.

NG ETAL. ON TRIAXIAL APPARATUS FOR STRESS PATH-DEPENDENT WATER RETENTION CURVE 491


Figure 3(a) depicts a typical calibration result for a cell pres-sure of 80 kPa. The gure shows that the total apparent volumechange can be divided into two components: (i) immediate vol-ume change due to the elastic deformation of the double cell sys-tem, and (ii) volume change with time due to the creep of thedouble cell system. The immediate volume change might resultfrom the compression of any possible trapped air, the compressi-bility of the water and the membrane surrounding the specimen,and the slight expansion of the connecting tubes and valves. Thegure shows that the apparent volume change due to creep isabout 0.13 cm3 under a cell pressure of 80 kPa, which is equiva-lent to 0.18 % volumetric strain for a soil specimen 70 mm indiameter and 19 mm in height. Figure 3(b) shows the relationshipbetween the immediate volume change and the cell pressure,which is nonlinear and fairly reversible. A relatively greatervolume change is observed for a cell pressure below 100 kPa.The relationship is approximated by a second-order polynomialequation.

The following two developments have been noted for thenewly modied equipment presented in this paper in comparisonwith the apparatus presented by Ng et al. (2002). Firstly, the origi-nal inner cell could accommodate a specimen of only 38 mm indiameter and 76 mm in height. In order to reduce the time for suc-tion equalization and test duration, the equipment has been modi-ed to accommodate specimens that are 70 mm in diameter and

19 mm in height. Secondly, the net cross-sectional area at the bot-tle neck of this new equipment has been reduced to 236 mm2 (thatof the original one was 314 mm2). As a result, the estimated accu-racy of the newly modied equipment is improved, i.e., compar-ing 23.6 mm3, equivalent to 0.03 % of volumetric strain in thismodied equipment versus 0.04 % in the previous apparatus.

Test Study

Basic Soil Properties

The tested soil used in this laboratory study is a completelydecomposed tuff (CDT) taken from an excavation site in Fanling,Hong Kong. Block samples were excavated at a depth of around9.25 m below ground level. The color of the soil is a yellowishbrown. The basic physical properties of the soil were determinedin accordance with the procedures given in BS1377-2 (BritishStandards Institution 1990) and are presented in Ng et al. (2004).It should be noted that all index properties presented here wereobtained from soil samples with particles smaller than 2 mm,except for the Atterberg limits, which were obtained from the soilsamples with particles smaller than 425 lm. The specic gravityof the CDT is found to be 2.73. The fractions of sand, silt, and

FIG. 2Layout of the base pedestal: (a) plan view; (b) section view. FIG. 3Calibration of apparent volume change: (a) relationship betweenapparent volume change and time under a cell pressure of 80 kPa; (b) rela-tionship between immediate volume change and cell pressure.

492 GEOTECHNICALTESTING JOURNAL


clay are 24 %, 71 %, and 5 %, respectively. The plastic and liquidlimits are 29 % and 43 %, respectively. The shrinkage limit is4.3 %. It should be noted that the shrinkage limit was determinedfrom the SDWRC test under zero net stress. According to theUnied Soil Classication System, the CDT can be described assilt of low plasticity (ML). The maximum dry density and opti-mum water content determined from the standard Proctor test are1760 kg/m3 and 16.3 %, respectively.

Specimen Preparation

The soil samples were rst oven-dried at 45C for 48 h. After thesoil was removed from the oven, soil particles larger than 2 mmwere separated out via dry sieving and discarded. Then, the drysamples were thoroughly mixed with water at a water content of16.3 %. Homogeneity of the samples was achieved by breakingdown large soil lumps using a pestle and sieving through a 2 mmaperture sieve. This process was repeated until only a smallamount of the soil was retained on the sieve. In order to avoid theloss of moisture, the process of sieving and grinding was done asquickly as possible. About 30 min were generally needed in orderto prepare 500 g of dry soil, and the water content lost during theprocess was found to be approximately 1 %. Afterward, the soilsamples were transferred to a plastic bag, which was then sealedand kept in a temperature- and moisture-controlled room for oneweek for moisture equalization. Then, the soil was compacted to adry density of 1510 kg/m3, which is equivalent to 86 % of themaximum dry density determined by the standard Proctor method.The corresponding initial void ratio is 0.795. The specimen wasprepared using the moist-tamping method (or dynamic compac-tion). The required amount of soil was placed in an oedometerring 19 mm high and 70 mm in diameter. A sliding hammermounted on a supporting frame was dropped through a roll bear-ing to compact the soil. The compaction was carried out in twolayers, with scarication between each layer, to ensure that thecompacted specimen was uniform. Thereafter, the compacted soilspecimen and the oedometer ring were clamped between two po-rous stones and submerged in the deaired water inside a desicca-tor. A small vacuum was applied to the desiccator for 48 h tosaturate the specimen. Before each specimen was assembled onthe testing apparatus, its mass was measured before and after thesaturation process, so that the initial degree of saturation of eachspecimen could be evaluated.

Test Procedures

A total of three SDWRC tests were conducted under (i) zero netstress, (ii) 40 kPa isotropic stress, and (iii) 80 kPa isotropic stress.The SDWRC test consists of three stages: (1) suction equalization,(2) loading, and (3) a cycle of drying and wetting. An initialmatric suction of 0.1 kPa was applied to the specimen. This wasachieved by placing outlet tubing located at an elevation 10 mmbelow the middle of the soil specimen. The water ow rate wasmonitored at intervals of 2 h for the rst 12 h, followed by inter-vals of 24 h. The suction equalization was terminated when thewater ow rate was smaller than 0.1 cm3/day, which is equivalentto a rate of change of 0.09 %/day in water content. After reaching

an initial suction of 0.1 kPa, specimens I-40 and I-80 were iso-tropically compressed to a mean net stress of 40 kPa and 80 kPa,respectively. The volume changes of the specimens were moni-tored during the loading stage. After isotropic compression, bothspecimens were normally compressed, and the correspondingvoid ratios (or before drying) are 0.736 and 0.717 for specimens I-40 and I-80, respectively. Subsequently, the SDWRC was meas-ured by increasing the matric suction in steps. For a given suction,equilibrium was reached when the rate of change in the water con-tent was smaller than 0.09 %/day. Typically, 2 to 7 days wererequired in order to achieve the equilibrium condition for a givensuction for both drying and wetting stages. The drying test wasconducted until a maximum suction of 500 kPa was reached, andthis was followed by the wetting test by reducing the matric suc-tion in steps until a value of 0.1 kPa was reached. Throughout thedrying and wetting tests, the volume change and water volumechange of the specimens were continuously monitored.

Test Results

Figures 4(a) and 4(b) show the SDWRC of specimens I-40 andI-80 presented in terms of the gravimetric water content and thedegree of saturation, respectively. The WRC of the specimen sub-jected to zero net stress (I-0) is also shown in the gure for com-parison. It should be noted that the volume change of thespecimen is not taken into account when the SDWRC is repre-sented by the gravimetric water content. The AEV of each dryingcurve (the suction beyond which the specimen commences todesaturate) is estimated using the method suggested by Fredlundand Xing (1994). The AEV of the three WRCs ranges from 62kPa to 70 kPa. Signicant hysteresis between the drying and wet-ting curves is also observed for the three specimens. Furthermore,the degree of saturation on the wetting curve at zero suction is notequal to 1 due to the presence of entrapped air. It is found that forisotropically and normally compressed specimens, the AEV, theentrapped air content, and the hysteresis are inuenced by themean net stress. The AEV increases with increasing mean netstress, but the entrapped air content and the hysteresis loopdecrease with increasing mean net stress. The test results are con-sistent with those of an Indian Head Till (Vanapalli et al. 1999)and a compacted silt (Ng and Pang 2000b). As the WRC dependson the porosity of the soil, the differences observed in the WRC atdifferent stress states may be attributed to the volume changescaused by the applied stress. The effects of applied stress on thevoid ratio with changes to the soil fabric and structure are furtherdiscussed in the subsequent paragraph.

Figure 5 depicts the drying and wetting induced volumechanges for the two isotropically compressed specimens (I-40 andI-80) and the control specimen (I-0). As expected, the specimenspossess different void ratios (e) after isotropic compression beforethe drying and wetting tests, which range from 0.717 to 0.795. Itcan be seen from the shrinkage curves (i.e., along the dryingpaths) that a yield point exists, beyond which a substantialincrease in the volumetric deformation with respect to the changein suction is observed. After yielding, the gradient of the post-yield shrinkage curve (ks) depends on the stress level. It is found



that ks decreases with increasing mean net stress. As the suctionincreases further beyond the AEV, desaturation occurs and ksdecreases with increasing suction (or a decreasing degree of satu-ration) and should approach zero when the shrinkage limit isreached, i.e., the gravitational water content beyond which no vol-umetric change is observed. The gure shows that the shrinkage

limit occurs at a value of suction between 140 and 220 kPa. It isfound that the suction corresponding to the shrinkage limitincreases with increasing mean net stress, but the limiting void ra-tio decreases with increasing mean net stress. During the wettingprocess, no wetting-induced collapse compression is observed forthe three specimens, but swelling is observed. The gradient of theswelling curve (i.e., the wetting path) is close to that of the pre-yield shrinkage curve (i.e., the drying path). A prominent irrevers-ible compression is observed at the end of a cycle of the dryingand wetting process. It seems that the amount of irreversible com-pression is inuenced by the stress state of the soil.

Based on the experimental data reported by Romero (1999),Vanapalli et al. (1999), and Sugii et al. (2002), Nuth and Laloui(2008) proposed the concept of an intrinsic shape of the WRC fornon-deformable soil and demonstrated that the shape is similar foreach initial void ratio within the range of study. They further sug-gested that the AEV depends on the initial void ratio, and that theshifting of the WRC from one intrinsic curve to another is gov-erned by the volume changes during drying and wetting. The testresults reported in this study are consistent with those presentedby Nuth and Laloui (2008); e.g., the AEV increases, but the sizeof a hysteresis loop decreases, with an increasing stress level fornormally compressed specimens, because the soil is deformableunder an applied stress. In other words, an applied stress canreduce the initial void ratio and cause the redistribution of poresizes, and it might change the soil fabric/structure before drying,resulting in the differences observed in the SDWRC. Under anapplied stress, it can also be seen that the specimen exhibits a sub-stantial amount of volumetric compression before reaching theAEV (see Fig. 5). Thus, this additional amount of volumetricstrain and the corresponding changes in the pore size distributionshould be considered when evaluating the shape of the SDWRC.

Summary and Conclusions

A modied triaxial apparatus for measuring the stress path-dependent water retention curve under isotropic and deviatoricstress paths is presented. By installing an open-ended, bottle-shaped inner cell together with a differential pressure transducer,the total volume change of a specimen can be measured accuratelyfor the correct determination of the degree of saturation of anSDWRC. This open-ended double cell system is adopted in orderto minimize possible compliance errors, and the precision of thevolume change measurement is improved via the use of a bottle-shaped inner cell. Any change of the total volume of a specimenis monitored by a high precision differential pressure transducer.The test results for compacted samples of a completely decom-posed tuff showed that for isotropically and normally compressedspecimens, the SDWRC and shrinkage curve are inuenced bythe stress level. For the SDWRC, the AEV increases, but theentrapped air content and the size of a hysteresis loop decrease,with increasing mean net stress. Regarding the shrinkage curve,the gradient of its post-yield part (ks) depends on the stress level.It is found that ks decreases with increasing mean net stress. Thespecimen exhibits a substantial amount of volumetric compressionbefore reaching the AEV during a drying test. Furthermore, it is

FIG. 4SDWRC in terms of (a) gravimetric water content and (b) degree ofsaturation.

FIG. 5Shrinkage and swelling curves.

494 GEOTECHNICALTESTING JOURNAL


apparent that the suction corresponding to the shrinkage limitincreases, but the limiting void ratio and the amount of irreversiblevolumetric compression decrease, with increasing mean net stress.

Acknowledgments

This study was sponsored by the National Natural Science Foun-dation of China through Grant No. 50878076 and supported byHKUST9/CRF/09 from the Research Grants Council of HKSAR.

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A Modified Triaxial Apparatus for Measuring the Stress Path-Dependent Water Retention CurveIntroductionModified Triaxial ApparatusTest StudyTest ResultsSummary and ConclusionsReferences

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A Modified Triaxial Apparatus for Measuring the Stress Path Dependent Water Retention-A