Refined True Triaxial Apparatus for Testing Unsaturated Soils under Suction-Controlled Stress Paths

Refined True Triaxial Apparatus for Testing UnsaturatedSoils under Suction-Controlled Stress Paths

Laureano R. Hoyos1; Diego D. Pérez-Ruiz2; and Anand J. Puppala3

Abstract: This paper introduces a servocontrolled true triaxial apparatus that has been developed to test cubical specimens [with 7.62 cm(3 in.) sides] of unsaturated soil under controlled-suction states and for a wide range of stress paths not readily achievable in a cylindrical cell.The apparatus is a mixed-boundary-type device, with the specimen seated on top of a 5-bar high-air-entry-value (HAEV) ceramic disk andbetween five flexible membranes on the remaining sides of the cube. The new cell is an upgraded, more elaborate version of one previouslyreported by the authors, featuring two independent pore-air and pore-water pressure control systems, as well as a fully computer-driven stressapplication/control system. Suction states are induced in the specimens via the axis-translation technique. The paper outlines the full develop-ment of the apparatus, including its main components; assembling process; and selection of appropriate compaction method, dry unit weight,and constant-suction loading rate for clayey sand. The suitability of the apparatus is demonstrated by repeatable results from twotriaxial compression tests performed on identically prepared samples of compacted clayey sand under constant 200-kPa matric suction.DOI: 10.1061/(ASCE)GM.1943-5622.0000138. © 2012 American Society of Civil Engineers.

CE Database subject headings: Unsaturated soils; Soil suction; Triaxial tests; Stress.

Author keywords: Unsaturated soil; Suction-controlled testing; Axis-translation technique; True triaxial testing; Stress paths.

Introduction

Background and Importance

Over the previous few decades, the description of the stress-strain-strength behavior of unsaturated soils has been closely linkedwith efforts to isolate the relevant effective stress fields governingtheir mechanical response. The adoption of matric suction,s ¼ ðua � uwÞ, and the excess of total stress over air pressure,(σ � ua), as the relevant stress state variables, have facilitatedthe modeling of key features of unsaturated soil behavior viasuction-controlled oedometer, triaxial, and direct shear testing(Alonso et al. 1990; Fredlund and Rahardjo 1993; Wheeler andSivakumar 1995). Most of these devices allow for the applicationof loads along limited paths and modes of deformation, such asone-dimensional, hydrostatic, or axisymmetric loading. In nature,pavement subgrades and shallow foundation soils well above thegroundwater table may be subject to three-dimensional stressgradients attributable to changes in the stress-state variables(σij � uaδij) and (ua � uw)δij, as illustrated in Fig. 1. Therefore,accurate predictions of the stress-strain response of geosystemsresting on unsaturated ground require that the constitutive relationsbe valid for all principal stress paths that are likely to be experi-enced in the field. In this context, a true triaxial (cubical) cell,

capable of inducing in the test soil a wide range of simple to com-plex multiaxial stress paths under controlled-suction states, plays afundamental role in a thorough stress-strain-strength characteriza-tion of this type of material.

This paper describes a servocontrolled true triaxial apparatusthat has been developed to test cubical specimens [with 7.62 cm(3 in.) sides] of unsaturated soil under controlled-suction statesfor a wide range of stress paths that are not readily achievablein a conventional cylindrical cell. The apparatus is a mixed-boundary-type device, with the specimen seated on top of ahigh-air-entry-value (HAEV) ceramic disk and between fiveflexible membranes on the remaining sides of the cube. Thenew cell is an upgraded, more elaborate version of the one previ-ously introduced by Hoyos et al. (2005, 2008), featuring twoindependent pore-air and pore-water pressure control systems,and a fully computer-driven stress application/control system.Matric suction states, s ¼ ðua � uwÞ, are induced in the specimensvia the axis-translation technique, which is implemented by usingthe s ¼ ua testing concept (i.e., uw ¼ 0).

Previous Work

Hoyos and Macari (2001) reported a first attempt to test unsatu-rated soil samples under constant-suction multiaxial loading.However, the mixed-boundary-type cell presented some impor-tant limitations, such as a highly corrosive steel frame, whichcaused occasional clogging of the HAEV disk; the use of hy-draulic oil to pressurize the cubical latex membranes in contactwith the sample, which resulted in their occasional damage whenexposed to hydraulic oil for extended periods of time; andsignificant delays in the required pore-fluid equalization timebecause of the high pore-water temperatures generated by thehydraulic oil.

Matsuoka et al. (2002) introduced a rigid boundary system inwhich suction states were induced in the specimens via negativepore-water pressure. This system also presented some limitations,including undesirable boundary effects attributable to stress

1Associate Professor, Dept. of Civil Engineering, Univ. of Texas atArlington, Arlington, TX 76019 (corresponding author). E-mail: [email protected]

2Associate Professor, Dept. de Ingeniería Civil e Industrial, PontificiaUniv. Javeriana, Cali, Colombia. E-mail: [email protected]

3Professor, Dept. of Civil Engineering, Univ. of Texas at Arlington,Arlington, TX 76019. E-mail: [email protected]

Note. This manuscript was submitted on November 19, 2010; approvedon April 29, 2011; published online on May 2, 2011. Discussion periodopen until November 1, 2012; separate discussions must be submittedfor individual papers. This paper is part of the International Journal ofGeomechanics, Vol. 12, No. 3, June 1, 2012. ©ASCE, ISSN 1532-3641/2012/3-281–291/$25.00.

INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / MAY/JUNE 2012 / 281

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http://dx.doi.org/10.1061/(ASCE)GM.1943-5622.0000138




application with rigid loading platens, reducing the capability of thecell to achieve a wide range of stress paths in the octahedral plane;and the very use of negative pore-water pressure to control suctionvia HAEV ceramics, which limits suction application up to 100 kPa(14.5 psi) to prevent cavitation of the water phase.

More recently, Hoyos et al. (2005; 2008) developed a newmixed-boundary-type cell similar in concept to that reportedby Hoyos and Macari (2001), with a few enhanced features, in-cluding the use of distilled water instead of hydraulic oil to pres-surize the membranes. However, the system still presented someimportant limitations, including the relatively low resolution ofthe pressure transducers, which restricted the external load incre-ments to a minimum of 6.9 kPa (1 psi); manual application ofload increments, which prevented a continuous, ramped loadingscheme from being carried out; no real-time monitoring of soildeformation from LVDTs between two consecutive load incre-ments; and occasional corrosion of the springs attached to theLVDTs extension rods when exposed to water over an extendedperiod of time.

The present true triaxial apparatus is aimed at overcoming allof the preceding limitations, yielding considerably enhancedperformance. The following sections outline the full develop-ment of the apparatus, including details of its main components;assembling process; and selection of appropriate compactionmethod, dry unit weight, and constant-suction loading/shearingrates for clayey sand soil. Finally, the suitability of the newlydeveloped cell is demonstrated by assessing the repeatabilityof results from two triaxial compression tests performed on iden-tically prepared samples of clayey sand under constant matricsuction, s ¼ 200 kPa.

Refined Suction-Controlled True Triaxial Apparatus:Main Features

Bottom Assembly

In general, true triaxial devices can be classified into three majorcategories: rigid boundary, flexible boundary, and mixed boundarycells (Sture 1979; Arthur 1988). The apparatus introduced in thispaper is a mixed-boundary-type cell, with the specimen seated ontop of a HAEV disk and between five flexible membranes on theremaining sides of the cube. The core frame was machined from asolid aluminum billet, and it featured six pressure cavities to ac-commodate a top and four lateral membranes, as well as a cubicalbase aluminum piece at the bottom assembly to house a 5-barceramic disk and four symmetrically spaced coarse porous stones,as shown in Fig. 2. The outside of the frame and its inner cavitywere machined to exact dimensions of 19 cm (7.5 in.) and 8.15 cm(3.2 in.) per side, respectively.

A round cavity with depth of 0.76 cm (0.3 in.) and a diameter of6.05 cm (2.38 in.) was machined at the top surface of the cubicalbase piece to accommodate the HAEV disk. This cavity had agrooved water compartment that allowed for uniform distributionof water pressure underneath the disk and appropriate flushing ofdiffused air bubbles during testing (Fig. 2). Water was suppliedfrom and drained to the exterior via 0.3 cm (1∕8 in:) diameterholes located at both ends of the grooved channel. In addition, fourcavities with depth of 0.65 cm (1∕4 in:) and a diameter of 1.9 cm(3∕4 in:) were machined on each corner of the cubical base piece toaccommodate an equal number of coarse porous stones to supplythe pore-air pressure. Air was also supplied from the exteriorthrough a 0.3 cm (1∕8 in:) diameter hole underneath each porousstone.

The 5.4 cm (2.125 in.) diameter, 0.72 cm (0.3 in.) thick, 5-barceramic disk (Soilmoisture Equipment Corp.) was sealed into asintered stainless steel ring using water-proof silicon resin alongits perimeter (Fig. 2). The ring also featured an outer 70 mm(2.8 in.) diameter O-ring to prevent air leaking from the soil poresinto the water compartment. Each porous stone was sealed onto thecubical base piece with a slight amount of silicon resin along itsperimeter. The entire bottom wall assembly was then tightly fas-tened onto the bottom cavity of the core frame via a full set ofsix stainless steel studs mounted on each face of the frame (Fig. 2).

Cubical Membranes

The cubical custom-made membranes were prepared in the labo-ratory using Silastic J-RTV-type silicon rubber (Dow CorningCompany), which yielded membranes with high tear strengthand relatively low stiffness. The membranes formed a pressure sealbetween each wall assembly and the reaction frame, acting as theactual fluid barrier for the distilled water pressurizing the top andlateral faces of the cubical specimen. A sequence of the membranefabrication process is shown in Fig. 3. The J-RTV curing agent wasfirst mixed with the silicon base material in a proportion of 10 partssilicon base to one part curing agent by weight. The mixture wasthen poured into a custom-made bottom mold having the exact di-mensions of the required membranes. Entrapped air bubbles wereremoved by subjecting the mixture in the mold to a 28–30 psivacuum for at least 1 h (Fig. 3), after which the bottom moldwas taken out of the vacuum chamber and a matching top moldwas carefully bolted into place. The mixture was then allowedto cure for at least 2 days. Upon curing, the top mold was gentlytaken off and the cubical membrane was removed from the bottommold. Once the excess rubber was cut out, the average membraneweight was approximately 85 g (Fig. 3).

Traffic load

(ua – uw)(σ1 – ua)

(ua – uw)

(σ2 – ua)

(σ3 – ua) (ua – uw)

Pavement

Foundation load

(ua – uw)(σ1 – ua)

(ua – uw)

(σ2 – ua)

(σ3 – ua) (ua – uw)

(ua – uw)(σ1 – ua)

(ua – uw)

(σ2 – ua)

(σ3 – ua) (ua – uw)

Pavement

(ua – uw)(σ1 – ua)

(ua – uw)

(σ2 – ua)

(σ3 – ua) (ua – uw)

(a)

(b)

Fig. 1. Unsaturated soil systems: (a) multiaxial stress states;(b) idealized cubical soil sample

282 / INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / MAY/JUNE 2012

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To assess the suitability of the membranes to withstand unusu-ally large deformations without tearing, a loose sample of clayeysand was monotonically loaded to about 40% vertical strain under aconstant 34.5 kPa (5 psi) confinement. The vertical pressure wasthen maintained constant and one of the lateral assemblies carefullyremoved to expose the membrane, as shown in Fig. 4. The over-stretched membrane was fully exposed after partial removal of thefailed soil. The membranes showed adequate performance in twosimilar trial tests (Pérez-Ruiz 2009). Moreover, the Silastic J-RTV-type membrane used in this work has long been proved to yield thebest performance, especially in terms of minimal levels of stressconcentration at each corner (Sture 1979; Sture and Desai 1979;Janoo 1986). Hence, further studies on this specific subject arebeyond the scope of the present work.

Top and Lateral Wall Assemblies

The wall assemblies were also machined from solid aluminum andtightly fastened onto the core frame via stainless steel studs. Typicalside and top views of the lateral wall assemblies are shown in Fig. 5.Each wall assembly consisted of a cover plate, two external pres-sure inlet/outlet connections, and optional stainless steel housingsto receive up to three LVDTs per face. (The present cell did notrequire the use of LVDTs in direct contact with the membranesfor soil deformation monitoring.) When the membranes weremounted and the walls were bolted onto the frame, each assemblyprovided an effective seal against leakage of the pressurized fluid(distilled water) to the atmosphere.

External Stress Application/Control System

A panoramic view of the entire suction-controlled true triaxialtest layout is shown in Fig. 6. This section includes only essentialdescriptions—and the respective capabilities—of the pressurecontrol panel (PCP-5000-UNSAT), pressure volume control(PVC-100-UNSAT) panel, and data acquisition/process control

system (DA/PCS) (shown in Fig. 6). A detailed description ofeach, including specifications, sensor calibration, schematic func-tioning, and software programming, has been documented byPérez-Ruiz (2009).

The external hydraulic pressure, applied by rubber membranesto the top and lateral sides of the specimen using pressurized dis-tilled water, was supplied by both PCP-5000 and PVC-100 panels(GCTS Testing Systems). The PCP-5000 unit was used to controlthe major and minor principal stresses in the vertical (Z) and hori-zontal (X) directions of the cube, respectively; while the PVC-100unit was used to control the intermediate principal stress in the re-maining horizontal (Y) direction. Each unit featured a full set ofindependent servovalves to control the displacement of an equalnumber of hydraulic pistons; hence, controlling the external pres-sure being supplied to the soil in any principal direction. Any prin-cipal stress combination path in the first octant could then beachieved by simultaneous and independent control over the threeservovalves.

The output line from each servovalve was split into two lines tosupply the same pressure to the positive and negative faces of thecube in any principal direction; namely, XðþÞ, Xð�Þ, YðþÞ, Yð�Þ,and ZðþÞ. These lines consisted of flexible nylon tubing rated at2,000 kPa (290 psi) burst strength and were connected to thepressure inlet/outlet connections of each wall assembly viaquick-disconnect couplings. The system allowed for both stress-controlled and strain-controlled testing schemes (Pérez-Ruiz 2009).

Soil Deformation Control/Monitoring System

The present cell, as previously mentioned, did not require the use ofLVDTs with their extension rods thrust into contact with the mem-branes for soil deformation measurements. Instead, soil deforma-tions along each principal direction were determined by measuringthe change in volume experienced by each membrane, which, inturn, was dictated by the volume of pressurized water displaced

Fig. 2. Bottom wall assembly with sealed 5-bar HAEV ceramic and four coarse stones


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by each hydraulic piston in the stress application/control systemsummarized above.

Fig. 6 shows a DC-750-5000-model LVDT (Macro Sensors) at-tached to the hydraulic piston right behind the PVC-100 panel.(The PCP-5000 panel had two identical piston settings in its rearlayout.) Each LVDT featured a 45.5 cm (17.9 in.) long, 1.9 cm(3∕4 in:) diameter, stainless steel housing calibrated for volume

measurements of pressurized, piston-displaced water to a full-scalerange of 300 cc, allowing for sufficient contraction or expansion asthe specimen deformed in compression or extension, respectively,along the XðþÞ, Xð�Þ, YðþÞ, Yð�Þ, or ZðþÞ direction. The outputsfrom the LVDTs, as well as those from the built-in pressure sensorsin each hydraulic piston, were instantly recorded and processed bythe DA/PCS.

Fig. 3. Custom-made mold and fabrication process for cubical membranes

Fig. 4. Stretchability of membranes: (a) typical failed sample; (b) exposed membrane after partial removal of soil stressed to 40% vertical strain


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Pore-Air and Pore-Water Pressure Control Systems

In this work, as mentioned in the Introduction, the axis-translationtechnique was implemented by using the s ¼ ua testing approach(i.e., uw ¼ 0). Pore-air pressure ua was supplied through the stoneslocated at each corner of the cubical base piece on which the sampleseats (Fig. 2). The external air pressure was supplied to the bottomassembly from a spare air-pressure outlet in the PCP-5000 unit, asshown in Fig. 7(a). The output line from this outlet, also made offlexible nylon tubing, was split into two separate T fittings, simul-taneously supplying the same pore-air pressure through all fourstones into the soil, as shown in Fig. 7(b). During suction-controlled testing, the PCP-5000 unit automatically adjusted theair supply to ensure a sustained and constant pore-air pressureua throughout the test.

A diffused-air flushing mechanism, consisting of two flush-inand flush-out outlets isolated from each other, is also shown inFig. 7(b). The flush-in line, made of flexible nylon tubing, was di-rectly connected to a spare water-pressure outlet in the PVC-100unit, which can be seen right behind the assembled cell inFig. 7(a). The flush-out line, also made of flexible nylon tubing,released the entrapped air underneath the five-bar disk to the atmos-phere. Before testing, the flushing lines and the water compartment

underneath the disk were thoroughly saturated by generating a con-stant flow of water from the PVC-100 unit. Flushing was performedevery 12 h during suction-controlled testing (Pérez-Ruiz 2009).The ceramic disk was saturated in place by following a proceduresimilar to that suggested by Bishop and Henkel (1962) andFredlund (1973) and adapted to the working conditions of the diskin the cubical cell. The procedure has been described by Hoyos andMacari (2001).

Data Acquisition/Process Control System

The external pressure applied in all principal directions and theresulting soil deformations were controlled, recorded, and/or proc-essed in real time by a fully automated DA/PCS, as shown inFig. 6. The system used a Keithley Metrabyte DAS-16 board todrive the servovalves in the stress application/control systemthrough a servoamplifier (GCTS 2004a; b). The analog inputsignals (volts) delivered by the LVDT and pressure sensor in eachhydraulic piston were converted into digital output signals bythe DAS-16 analog-to-digital converter. The following sectionsdescribe the processes used to select the most appropriate compac-tion method, dry unit weight, and constant-suction loading rate fora clayey sandy soil.

Fig. 5. Side and top views of lateral wall assemblies with cubical specimen inside

Fig. 6. Panoramic view of entire suction-controlled true triaxial test layout


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Selection of Appropriate Soil Compaction Method

Soil Material

The test soil in this work was classified as poorly graded sand withclay (SP-SC) according to the Unified Soil Classification System,containing 90% sand and 10% high-plasticity clay with a plasticityindex of 42%. The particle-size distribution curve and soil-watercharacteristic curve (SWCC) are shown in Fig. 8. Sieve Nos. 270and 400 were also included in the sieve analysis. The SWCC wasobtained via a pressure plate testing up to a suction value of 850 kPa(120 psi), which was the maximum house pressure in the labora-tory. Additional data points on the SWCC at higher suctionvalues were assessed through a filter paper technique. Best-fittingmodels for the experimental SWCC are also shown in Fig. 8(i.e., Brooks and Corey 1964; van Genuchten 1980; Fredlundand Xing 1994). Before preparation of specimens via tampingor static compaction, a standard Proctor compaction test wasconducted on SP-SC soil to assess the optimum moisture con-tent, wopt ¼ 11:6%, and maximum dry unit weight, γd�max ¼19:18 kN∕m3 (122:0 lb∕ft3), under the highest possible compac-tion energy that could be imparted to the soil.

Tamping Compaction

To assess the feasibility of tamping compaction to produce samplesthat would yield repeatable results in the newly developed cell,constant-suction conventional triaxial compression (CTC) testswere conducted on two identically prepared specimens of SP-SC soil using in-place tamping. The initial moisture in the soil-water mix was kept at 10–11% while the target dry unit weightwas fixed at 15:34 kN∕m3 (97:6 lb∕ft3), which corresponded to80% of the standard Proctor’s maximum. The initial moisture cor-responded to a suction value of about 50 kPa according to theSWCC (Fig. 8), which reduced the time required for pore-fluidequalization for the 50–200 kPa suction range considered inthis work.

The soil-water mix was compacted into a custom-made, 1.5 mm(0.06 in.) thick, stainless steel shaft that conformed to the innercavity of the core frame, as shown in Fig. 9. Specimens wereprepared in approximately eight lifts, with the amount of materialin each lift controlled by weight: 61.5 g for the first lift and100 g for each subsequent lift. A photograph of a typicalsample prepared by tamping is also shown in Fig. 9. The observedlayered structure is indicative of a potentially high degree ofanisotropy. As was expected, tamping was heavily operator-dependent and delivered a compactive effort considerably lower

than that of the standard Proctor, which made it quite challengingto reproduce identical specimens.

These observations were further substantiated by the resultsshown in Fig. 10. Once the specimen was compacted by tampingto the target density, the shaft was gently removed and the topassembly was set into place. CTC trial tests were performed atconstant matric suction, s ¼ ua ¼ 50 kPa, and initial net mean

0

5

10

15

20

25

30

0.01 0.1 1 10 100 1000 10000 100000 1000000

Matric suction, ua - uw (kPa)

Gra

vim

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wat

er c

onte

nt, w

(%

)

Experimental

Van Genuchten (1980)

Brooks & Corey (1964)

Fredlund & Xing (1994)

0

10

20

30

40

50

60

70

80

90

100

0.010.1110Particle size (mm)

Per

cent

fine

r (%

)

Fig. 8. Particle-size distribution and soil–water characteristic curves ofSP-SC test soil

Fig. 7. Axis-translation implementation: (a) cell interacting with pressure panels; (b) pore-air pressure and flushing lines


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stress, p ¼ ð1∕3Þðσ1 þ σ2 þ σ3Þ � ua ¼ 20 kPa, on two speci-mens of SP-SC soil prepared by the previously described tampingprocedure. The soil was sheared under a monotonic deviatoric-stress application rate of 10 kPa∕h (about 1:5 psi∕h), which hasbeen proved to be reasonably adequate for constant-suction testingof sandy soils (Macari and Hoyos 2001). Further investigations onthe loading rate effects are presented subsequently. The results in

Fig. 10 are presented in terms of deviatoric stress versus principalstrain response, in which the deviatoric stress is defined by Eq. (1)as follows:

q ¼ 1ffiffiffi2

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðσ1 � σ2Þ2 þ ðσ2 � σ3Þ2 þ ðσ1 � σ3Þ2

qð1Þ

The results show considerably inconsistent responses from thetwo samples.

Static Compaction

In light of the results observed in Fig. 10, cubical specimens ofSP-SC soil were also prepared by static compaction. As withthe samples prepared by tamping, the initial water content was keptat 10–11% while the target dry unit weight remained at approxi-mately 15:34 kN∕m3 (97:6 lb∕ft3). However, in this case a triaxialload frame was used to apply a quasi-static axial load to the loosesoil-water mix until achieving the desired volume. Samples werecompacted into a custom-made stainless steel mold, as shownin Fig. 11.

The mold was first filled with 761.5 g of SP-SC soil mixed withwater to the target 10–11% moisture. The loose mixture was thencompressed in one single lift by the loading ram at a constant rate of1:0 mm∕min via a custom-made aluminum loading ramp that con-formed exactly to the inner cross section of the compaction mold.Immediately after compaction, the specimen was gently extrudedfrom the mold and transferred to the test cell. A photograph ofa typical statically compacted sample is also shown in Fig. 11.A manifestly more homogenous structure was achieved by this

Fig. 9. In-place tamping compaction process and typical layered specimen

0

50

100

150

200

250

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-30 -20 -10 0 10 20 30Principal strain (%)

Dev

iato

ric s

tres

s, q

(kP

a)

Trial 1

Trial 2

ε1ε3

1

3 2

11

33 22

Fig. 10. Response from two CTC trial tests at s ¼ 50 kPa on SP-SCspecimens prepared by tamping

Fig. 11. Static compaction process and typical statically compacted specimen


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method, compared with that rendered by tamping compac-tion (Fig. 9).

This observation was further substantiated by the results shownin Fig. 12. The results from two CTC trial tests performed at con-stant matric suction, s ¼ 50 kPa, and initial net mean stress,p ¼ 20 kPa, on two specimens of SP-SC soil prepared by thepreviously described static compaction procedure are shown inFig. 12(a). The results from two CTC trial tests performed at con-stant matric suction, s ¼ 100 kPa, and initial net mean stress,p ¼ 20 kPa, on two additional statically compacted specimensare shown in Fig. 12(b). Soil samples in all four tests were shearedat the same deviatoric-stress application rate of 10 kPa∕h. The re-sults show consistent responses from both statically compactedsamples. In addition, the virtually identical response of the minorand intermediate principal strains is indicative of a minimal degreeof soil anisotropy in the horizontal directions. Hence, the staticcompaction procedure, as previously described, was adopted forall further suction-controlled testing.

Influence of Compaction Dry Unit Weight

Four hydrostatic compression (HC) tests were conducted at con-stant matric suction, s ¼ ua ¼ 100 kPa, to experimentally deter-mine the adequate dry unit weight for statically compacted

samples of SP-SC soil. The main intent was to reproduce identicalsamples with a relatively small preconsolidation pressure so that itwas feasible to bring the soil to a full virgin state—thereby inducingelastoplastic deformations large enough to identify the loading-collapse curve postulated by the Barcelona model (Alonso et al.1990). Although all samples were compacted with the same initialwater content, 10–11%, each sample had enough solid mass to at-tain a different dry unit weight for the same total volume (Fig. 11).The selected dry unit weights, γd ¼ 19:18, 17.26, 16.30, and15:34 kN∕m3, correspond to 100, 90, 85, and 80% of maximumdry unit weight γd�max, respectively.

Fig. 13 shows the variation of specific volume, v ¼ 1þ e, withnet mean stress from all four suction-controlled HC tests. Each testwas carried out from an initial net mean stress, p ¼ 20 kPa, to afinal net mean stress, p ¼ 600� 700 kPa. A dry unit weight of15:34 kN∕m3, which corresponds to 80% of γd�max, was foundto yield the lowest preconsolidation pressure (about 110 kPa)and, therefore, was adopted as the target density for all subsequentsamples to be tested in this work. The initial (elastic) portion of allcurves showed a reasonably similar slope, including the reboundportion of the curve for γd ¼ 15:34 kN∕m3 ¼ 80% of γd�max.

Statically compacted samples yielded an average specificvolume, v ¼ 1:72, and an average degree of saturation, S ¼37:5%. Fig. 13 also shows that the loosest sample, compacted at80% of γd�max, experienced the highest decrease in volume duringthe initial equalization stage under a sustained suction, s ¼ ua ¼100 kPa; that is, before suction-controlled ramped consolidation.The opposite was observed in the densest sample compacted at100% of γd�max. [Assessment of the appropriate pore-fluid equali-zation time and a detailed description of the experimental proce-dures are documented in a companion paper (Hoyos et al. 2012).]

Strain-Controlled versus Stress-Controlled TestingScheme

The typical strain rates suggested for testing low-plasticity soilsunder suction-controlled conditions in conventional triaxial anddirect shear systems are in the order of 0.001–0.004% strain/min. For high-plasticity soils the rates could be considerably slower(Bishop and Gibson 1963; Ho and Fredlund 1982; Fredlund andRahardjo 1993). The amount of time required for the pore fluidsto come to equilibrium under a sustained suction state orsuction/stress increment is governed by the hydraulic impedance

0

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300

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tres

s, q

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a)

Trial 1

Trial 2

ε1ε2ε3

(b)

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300



Dev

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ric s

tres

s, q

(kP

a)

Trial 1

Trial 2

ε1ε1ε2ε2ε3ε3

(a)

Fig. 12. Response from CTC trial tests on statically compacted SP-SCspecimens: (a) s ¼ 50 kPa; (b) s ¼ 100 kPa

1.35

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100010010Net mean stress, p (kPa)

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e

γd = γd-max

γd = 0.90 γd-max

γd-max = 19.18 kN/m3

γd = 0.85 γd-max

γd = 0.80 γd-max

Fig. 13. Response from HC tests at s ¼ 100 kPa on staticallycompacted SP-SC specimens prepared at four different dry densities


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and the corresponding drainage rate through the soil-ceramic sys-tem (Lu and Likos 2004). The cubical cell developed in this workallows for both stress-controlled and strain-controlled tests. TheDA/PCS allows for a stress-controlled loading rate as low as2 kPa∕h (0:28 psi∕h); however, it only allows for a minimumstrain-controlled deformation rate of 0:1 mm∕min, which corre-sponds to about 0.131% strain/min in a typical 7.62 cm (3 in.) sidecubical sample—a significantly larger rate than that recommendedfor low-plasticity soils such as SP-SC soil.

To experimentally assess the suitability of the strain-controlledtesting scheme for the SP-SC soil, suction-controlled CTC testswere performed under both stress-controlled and strain-controlledschemes at constant matric suction, s ¼ ua ¼ 50 kPa, and initialnet mean stress, p ¼ 50 kPa, on two specimens of SP-SC soil stati-cally compacted to the target dry unit weight of 15:34 kN∕m3. Theresults, shown in Fig. 14, are presented in terms of deviatoric stressversus principal strain response. The stress-controlled test, carriedout at a deviatoric-stress application rate of 10 kPa∕h (about1:5 psi∕h), induces an average soil deformation rate of0:0078 mm∕min, which corresponds to approximately 0.01% ver-tical strain/min. On the other hand, the strain-controlled test, carriedout at the minimum deformation rate of 0:1 mm∕min allowed bythe GCTS software, required an average deviatoric-stress applica-tion rate of 125 kPa∕h (about 18 psi∕h), more than tenfold the rateof the stress-controlled testing scheme (Pérez-Ruiz 2009).

Even though the overall soil behavior patterns observed fromboth testing schemes were reasonably similar, the significant scat-tering of strain-controlled test data suggested that the minimum de-formation rate of 0:1 mm∕min might not be suitable for testingSP-SC soil; that is, an average 125 kPa∕h loading rate may not al-low for sufficient pore-fluid equalization time under a sustained suc-tion of 50 kPa, still a relatively low value of suction, when a 5-barHAEV ceramic disk was used. These patterns were equally man-ifested when the results were plotted in terms of deviatoric stressversus total shear strain, and specific volume versus net mean stress,as shown in Fig. 15. In light of these observations, the stress-controlled scheme was adopted for all further testing on SP-SC soil.

Constant-Suction Loading Rate Effects

In the previous sections, the assessment of the appropriate soilcompaction method, dry unit weight, and testing scheme were

all accomplished via suction-controlled testing under a trial loadingrate of 10 kPa∕h, as recommended for sandy soils by Macari andHoyos (2001). In addition, the samples were prepared with a�10%tolerance with regard to the target dry unit weight. To further val-idate the suitability of the 10 kPa∕h loading rate for testing SP-SCsoil under suction-controlled conditions in the newly developedcell, a series of HC trial tests were performed at constant matricsuction, s ¼ ua ¼ 50 kPa, on four statically compacted specimensof SP-SC soil. The samples were compacted with 0% tolerance forthe target dry unit weight, 15:34 kN∕m3, to ensure an identicalspecific volume in all four samples before testing. Each test wascarried out from an initial net mean stress of p ¼ 50 kPa to a maxi-mum net mean stress of p ¼ 700 kPa.

The first trial HC test was performed under an isotropic loadingrate of 2 kPa∕h, which was the minimum rate allowed by theDA/PCS software. The other three tests were performed at10 kPa∕h each to assess the repeatability of the results under theseconditions. The test results, plotted in both arithmetic and semilog-arithmic scales, are shown in Fig. 16, which confirm the suitabilityof the 10 kPa∕h loading rate, with virtually no difference in soilresponse from all four HC tests. Again, the initial (elastic) portionof all curves, as well as the two rebound portions of the last trialtest, show reasonably identical slopes.

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-15 -10 -5 0 5 10 15 20 25Principal strain (%)

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s, q

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Strain-controlled: 0.1 mm/min

ε1ε2ε3

Fig. 14. Principal strain response from strain-controlled andstress-controlled CTC tests at s ¼ 50 kPa on compacted SP-SC soil

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0 5 10 15 20 25Total shear strain (%)

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Fig. 15. Stress-strain and volume change response from strain-controlled and stress-controlled CTC tests at s ¼ 50 kPa on compactedSP-SC soil


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With the operational apparatus, a comprehensive follow-up ex-perimental program was undertaken by the authors to calibrate andfurther validate two of the most popular constitutive models postu-lated to date for unsaturated soils. The results from this secondphase of the work are documented in Hoyos et al. (2012). In lightof the results documented in this and all previous sections, it wasdecided that an 8 kPa∕h loading rate would be appropriate for allfurther suction-controlled testing on SP-SC soil to accomplish theremaining research work within a time frame of 18 months.

Repeatability of Suction-Controlled TriaxialCompression Test Results

In the previous sections, the dependability of the newly developedcell has been demonstrated through a series of suction-controlledHC and CTC tests performed on samples subject to a maximumsuction state of 100 kPa. As definitive evidence of the suitabilityof the apparatus, as well as the appropriateness of all previouslyselected variables, two additional triaxial compression (TC) trialtests were performed at constant matric suction, s ¼ ua ¼200 kPa, and initial net mean stress of p ¼ 100 kPa, on identicallyprepared specimens of SP-SC soil compacted to the target dry unitweight. The results are presented in Fig. 17, which shows

reasonably identical trends from both trial tests. It is also observedin Fig. 17 that the cell is capable of reproducing the compressivenature (+) of the major principal strain and the extensive nature (−)of the minor and intermediate principal strains, as dictated by theloading scheme of the TC stress path. Again, the virtually identicalresponse of the minor and intermediate principal strains is furtherindication of a minimal degree of soil anisotropy in the horizontalprincipal directions when samples are prepared via staticcompaction.

Concluding Remarks

A fully servocontrolled true triaxial apparatus has been developedto test cubical specimens with 7.62 cm (3 in.) sides of unsaturatedsoil under controlled-suction states and for a wide range of stresspaths that are not readily achievable in a conventional cylindricalcell. The apparatus is an upgraded, more elaborate version of theone previously introduced by Hoyos et al. (2005, 2008), featuringtwo independent pore-air and pore-water pressure control systemsand a fully computer-driven stress application/control system.

A total of 18 trial tests (eight CTC, eight HC, and two TC) wereaccomplished in approximately 26 months, with each suction-controlled test taking about 2.5 weeks to complete. Preliminarytesting on SP-SC soil for controlled suction states ranging from50 to 200 kPa has shown that the newly developed cell is suitablefor testing unsaturated soils under suction-controlled conditions viathe axis-translation technique. Reasonably consistent responseswere observed from samples prepared by static compaction.A dry unit weight, γd ¼ 15:34 kN∕m3 (97:6 lb∕ft3), which corre-sponds to 80% of the standard Proctor’s maximum, γd�max, wasfound to yield the lowest preconsolidation pressure. Finally, astress-controlled testing scheme, with a 10 kPa∕h loading rate(about 1:5 psi∕h), was found to be adequate for testing SP-SC soilunder suction-controlled conditions. An 8 kPa∕h loading rate(about 1:15 psi∕h) was then adopted for all further suction-controlled testing on SP-SC soil.

With the operational apparatus, a comprehensive experimentalprogram has been undertaken by the authors to calibrate and furthervalidate two of the most popular constitutive models postulated todate for unsaturated soils. The results are documented in acompanion paper (Hoyos et al. 2012), including suction-controlledsimple shear testing in the deviatoric plane. The developed cell will

1.30

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Trial 1: 2 kPa/h

Trial 2: 10 kPa/h

Trial 3: 10 kPa/h

Trial 4: 10 kPa/h

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Trial 2: 10 kPa/h

Trial 3: 10 kPa/h

Trial 4: 10 kPa/h

Fig. 16. Loading rate effects on volume change response of compactedSP-SC soil from stress-controlled HC tests at s ¼ 50 kPa (arithmeticand semilogarithmic scales)

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ε1ε1

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Fig. 17. Response from two TC trial tests at loading rate ¼ 8 kPa∕hand s ¼ 200 kPa on compacted SP-SC soil


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play a fundamental role in the thorough stress-strain-strengthcharacterization of unsaturated soil materials subjected to a widerange of multiaxial stress paths likely to be experienced in the field.

Acknowledgments

The true triaxial apparatus was developed under U.S. NationalScience Foundation Award No. CMS-0216545. This support isgratefully acknowledged. Any findings, conclusions or recommen-dations expressed in this material are those of the authors and donot necessarily reflect the views of the NSF. The authors also thankDr. Manuel Padilla of GCTS and Professor Stein Sture of the Uni-versity of Colorado at Boulder for all their technical assistance,especially in the manufacturing of the basic core system duringthe early stages of this research effort.

References

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Arthur, J. R. F. (1988). “Cubical devices: versatility and constraints.”Advanced triaxial testing of soil and rock (STP 977), R. T. Donaghe,R. C. Chaney and M. L. Silver, eds., ASTM, Philadelphia, 743–765.

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http://dx.doi.org/10.1680/geot.1990.40.3.405

http://dx.doi.org/10.1139/t94-061

http://dx.doi.org/10.1520/GTJ11277J




http://dx.doi.org/10.1139/t02-031


http://dx.doi.org/10.2136/sssaj1980.03615995004400050002x

http://dx.doi.org/10.2136/sssaj1980.03615995004400050002x

http://dx.doi.org/10.1680/geot.1995.45.1.35

Refined True Triaxial Apparatus for Testing Unsaturated Soils under Suction-Controlled Stress Paths

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Transcript of Refined True Triaxial Apparatus for Testing Unsaturated Soils under Suction-Controlled Stress Paths