strain localization in solid cylindrical clay

67

i) Postdoctoral Fellow, IIT Kanpur, India (ajantas＠iitk.ac.in).ii) Professor, Dept. of Civil and Environmental Engineering, University of Tennessee, Knoxville, TN, USA (dpenumad＠utk.edu).

The manuscript for this paper was received for review on July 11, 2005; approved on September 25, 2006.Written discussions on this paper should be submitted before September 1, 2007 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.

Fig. 1. Deformation of a soil element under external loading condi-tions

67

SOILS AND FOUNDATIONS Vol. 47, No. 1, 67–78, Feb. 2007Japanese Geotechnical Society

STRAIN LOCALIZATION IN SOLID CYLINDRICAL CLAY SPECIMENSUSING DIGITAL IMAGE ANALYSIS (DIA) TECHNIQUE

AJANTA SACHANi) and DAYAKAR PENUMADUii)

ABSTRACT

The strain non-uniformity due to the end restraint for a deforming specimen during triaxial testing of clay specimenswas minimized in this study using lubricated end platens. This research presents the evidence of the occurrence ofstrain localization due to shear banding within the clay specimen by using DIA (Digital Image Analysis) technique. Thevariation in strain localization patterns of soil specimen is also studied for evaluating the in‰uence of conˆning stress,loading conditions, stress history, drainage conditions, and soil's microfabric (geometric arrangement of clay plate-lets) by performing a series of lubricated-end triaxial tests on solid cylindrical specimens of Kaolin clay. This paperpresents a comparative study based on the observed orientation of shear band formation, and the intensity of strainlocalization (by estimating the maximum local strain) within the specimen during its shear deformation process.

Key words: compression, digital image analysis, extension, Kaolin clay, localized deformation, lubricated ends, strainlocalization, triaxial (IGC: D6)

INTRODUCTION

When a macroscopically homogeneous material ele-ment is subjected to a su‹ciently low homogeneous stressapplied to its boundary, homogeneous deformationoccurs. As the deformation becomes larger, concentra-tion of strain at a local zone within the element can occurbecause of the actual non-uniformity of mass density andstiŠness of the material, as shown in Fig. 1. Failure ofmany engineering materials is characterized by theformation and propagation of zones of localized sheardeformation. The most typical localized deformationobserved in geo-materials is linear shear banding. Strainlocalization is caused by the imperfections inherent inthe soil specimen, the boundary constraints, and non-uniform loading conditions (Hvorslev, 1960; Hill, 1962;Rudnicki and Rice, 1975; Rice, 1976; Rice and Rudnicki,1980; Vardoulakis, 1980; Desrues et al., 1985; Tokimatsuand Seed, 1987; Peters et al., 1988; Bardet, 1990; Bigoniand Heueckel, 1991; Finno et al., 1997; Szabo, 2000;Lade and Wang, 2001; Yimsiri and Soga, 2002). There-fore, strain localization is considered to be a majorfactor, which controls the overall observed mechanicalresponse of the specimen, at or near failure. Strainlocalization manifests in the form of a shear band, anarrow zone of intense straining (Jirasek, 2002; Lai et al.,2003; Lade, 2003). Although, shear banding is one of thepossible deformation modes, it is usually a precursor tocatastrophic failure. The initial thickness of the localiza-tion band depends on the material's micro-structure. The

transmission of micro-defects in the localization bandleads to the formation of displacement discontinuity andstress-free crack at macro level. Although the localizationtheory is considered to be well established mathematical-ly, very limited experimental data on geo-materials havebeen reported (Vardoulakis, 1980; Desrues et al., 1985;Finno et al., 1997; Lade and Wang, 2001), mainly be-cause of the lack of experimental facilities to monitor theformation of the shear band and its orientation.

Previous investigations reported that the non-uni-formity of stress state and deformation mode along theheight of a specimen due to testing conditions can beavoided by the use of lubricated end platens in triaxialtesting system (Rowe and Barden, 1964; Barden andMcDermott, 1965; Sarsby et al., 1982). It is now wellknown that the strain non-uniformity due to the endrestraint and the strain localization due to shear bandingare essentially diŠerent in mechanism, but confusion still

6868 SACHAN AND PENUMADU

exists on the role of end-restraint on the initiation andpropagation of shear banding. In the past literature, itwas common to assume that triaxial experiments withlubricated ends on the specimens with slenderness ratio 1(heightWdiameter＝1) provide a more stable geometry andmuch greater uniformity of stress and deformationthroughout the test, and allow the specimen to retain itscylindrical shape even at large strains. In the currentresearch, all the experiments were performed on soilspecimen with slenderness ratio 1 using a triaxial testingsetup with lubricated ends; thus non-uniform deforma-tions due to end restraints was assumed negligiblethroughout the study. The focus of this study is toevaluate the strain localization within specimen of ˆnegrained cohesive soil (clay) due to the actual non-uni-formity of soil mass and stiŠness of the material (not dueto the end restraints) at diŠerent testing conditions.

It is important to note that clay specimens used in thecurrent research were macroscopically homogeneousmaterial before their shear deformation. If the stress andstrain states were interpreted at the stage of shear bandformation ignoring the fact that the strain localizationwould have already taken place, the interpreted stressand strain would be inaccurate. Lin and Penumadu(2005) studied the strain localization patterns of hollowcylindrical specimens sheared under combined axial-torsional loading conditions using digital image analysis(DIA) technique. They developed an experimental setupfor DIA technique, a procedure for digital data proc-essing, and a program for data interpolation; which wasused in this study to produce the strain contour plots andstudy the initiation and propagation of strain localizationwithin the specimen. This DIA technique was used in thecurrent research for evaluating the impact of conˆningpressure, loading conditions, stress history, drainageconditions, and soil's microfabric on the strain localiza-tion aspect for solid cylindrical specimens of Kaolin clay.

PREVIOUS INVESTIGATION

The localization theory is recognized to be a mathemat-ically well established concept for many years; however,only a few experimental studies including Rice andRudnicki (1980), Vardoulakis (1980), Desrues et al.(1985), Finno et al. (1997), Lade and Wang (2001), havebeen performed using geo-materials. Hvorslev (1960)observed shear bands andWor post failure bulging in aseries of unconˆned compression tests on clay specimens,and reported that the degree of non-uniformity at largestrains was much larger than theoretically expected non-uniformity due to the in‰uence of frictional end restraint.Hill (1962) gave a general formulation for shear bands inelasto-plastic material using the concept of accelerationwave in the context of a boundary value problem.Rudnicki and Rice (1975), and Rice (1976) proposedcriterion for formation of shear band and critical orienta-tion of shear band, considering a non-associated ‰owrule. Based on Rice's work, the general principles oflocalization of deformation into shear strain band were

well established, and they were applied to investigate thethin shear band type localization (Peters et al., 1988;Bardet, 1990; Bigoni and Heueckel, 1991; Szabo, 2000;Lade and Wang, 2001; Heueckel, 2002). The most typicallocalized deformation observed in geo-materials is linearshear banding.

Most of the previous experimental studies on strainlocalization were dependent on the visual observationsfrom the deformation proˆle of the specimens.During previous investigation using triaxial testing, thisphenomenon was not studied in depth due to the lack ofproper techniques for quantifying the local strains with areasonable degree of accuracy. Recent developments indigital image analysis (DIA), to some extent, allows forthe capturing and studying local deformations within thespecimen as a function of global deformations. In thisstudy, many triaxial tests were performed to study thevariation in strain localization and pattern of shearbanding within the clay specimens with respect to thechange in stress history of clay (normally consolidatedand heavily overconsolidated), microfabric of clay speci-mens (dispersed and ‰occulated), drainage conditionsduring shearing (drained and undrained), the type ofdeviatoric loading (compression and extension), and forvarying levels of eŠective conˆning stress. Particleassociation in clay suspensions can be described in theform of dispersed and ‰occulated microfabric. Flocculat-ed microfabric refers to the platelets (or particles) thatare oriented in all possible directions; whereas, dispersedmicrofabric refers to the platelets that are aligned in apreferential direction (Sachan and Penumadu, 2006a).

During the deformation process, a digital imageanalysis (DIA) was used to monitor the overall specimenuniformity, potential initiation of localization, and toquantify the specimen dimensions. Digitized data wereobtained from digital images to perform the calculationsfor local deformation and strain proˆle, which alsofacilitated the analysis for strain localization. Digitalimaging technique was used in this research for all triaxialexperiments to study the evolution of shear bands withrespect to the specimen and loadingWboundary condi-tions, which is important for evaluating constitutivebehavior of cohesive soil.

EXPERIMENTAL PROGRAM

In this study, solid cylindrical specimens of Kaolin clay(LL＝62z, PI＝30z, Gs＝2.63) were prepared by usingthe 1-D slurry consolidation method, which allowed onlyvertical drainage at top and bottom of the specimen(Penumadu et al., 1998). Specimens with ‰occulatedmicrofabric were obtained by mixing powdered Kaolinclay with de-aired and de-ionized water at a water contentof 155z, and then consolidating the slurry under K0

condition at 207 kPa vertical stress in a slurry con-solidometer (207 kPa pressure was applied in one step).The dispersed microfabric specimens were obtained byusing the same procedure and by adding 2z dispersant(Calgon) in the clay slurry of 155z water content. Clay

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Fig. 2. Experimental data for triaxial tests (as listed in Table 1) performed on solid cylindrical specimens of Kaolin clay: (a) Normalized stress-strain curves for Tests 1 to 3, (b) Normalized stress-strain curve for Tests 4 to 7, (c) Stress paths for Tests 1 to 3 and (d) Stress paths for Tests 4to 7

69STRAIN LOCALIZATION IN CLAY SPECIMENS

specimen with ‰occulated microfabric was obtainedafter 24 hours of consolidation; whereas, the dispersedspecimen was obtained after 330 hours of consolidation(Sachan and Penumadu, 2006a). The diameter (D ) andheight (H ) of all the slurry consolidated specimens(dispersed, ‰occulated) was obtained to be 102 mm (H＝D＝102 mm; slenderness ratio＝1). Initially these speci-mens were isotropically consolidated under 207 kPaW276kPaW345 kPa of eŠective conˆning pressure. Afterisotropic consolidation, the specimens were shearedunder compression and extension loading conditionsusing lubricated end triaxial testing device developed forthis study, and the measured data were recorded on acomputer using a data acquisition system. The stress-strain relationships and stress paths for Kaolin clay for allthe tests are presented in Fig. 2. The Lubricated end triax-ial testing setup used in this study had a strain controlledloading frame, which was capable of applying compres-sionWextension loads on soil specimen at desired axialstrain rate under diŠerent loadingWboundary conditions;thus the global axial strain (eg) was directly obtainedusing global displacements measured from LVDT datafor the entire height of the specimen. The other informa-tion about this lubricated end triaxial setup and itstesting procedure could be obtained from Sachan andPenumadu (2006b).

Lubricated ends require smooth and polished endplatens containing radial drainage ports at their outer

surface. Porous plastic strip is extended circumferentiallycovering all radial drainage ports completely for achiev-ing ``good'' drainage conditions within the testing system(Sachan and Penumadu, 2006b). In order to prepare thelubricated end platens for testing the clay specimens, theend platens are cleaned thoroughly, a thin layer of highvacuum grease is spread uniformly over each platen, anda circular piece of latex membrane is then laid on to thegrease and pressed in such a way as to minimize theamount of entrapped air. A circular piece of ˆlter paper,with much larger diameter than the platen is placed ontop of the latex membrane in a way that the ˆlter papercompletely covers the porous plastic strip on the sides ofthe platens. If excess pore pressure generation is achievedto be zero during drained testing, drainage conditions ofthat lubricated end triaxial system are considered to be``good'' drainage conditions. The other informationrelated to all drained and undrained triaxial testsperformed in this study are summarized in Table 1; whichincludes axial strain rate for diŠerent tests, void ratiobefore shear deformation (ebs), specimen size beforeshear deformation (Hbs, Dbs), peak shear stress (sp) andfailure location (ep) of each test.

DIGITAL IMAGE ANALYSIS (DIA)

To address the strain localization and its impact on theinterpretation of test results, the deformation and strain

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Fig. 3. Strain localization using digital image analysis: (a) Digital imaging setup, (b) Prepared Kaolin clay specimen for digital imaging setup and(c) Calibration factor using ‰at plate analysis


components at various locations of a deforming specimenare needed. However, direct measurement of deforma-tion at various locations along the height of a specimen isa di‹cult experimental task. In the present study, digitalimage analysis (DIA) was used to evaluate the strainlocalization in the solid cylindrical Kaolin clay specimenssheared by using lubricated end triaxial testing setup, asshown in Fig. 3. Digital imaging technique in this studyuses a latex membrane (thickness 0.3 mm) with dotsmarked in a grid pattern. Grid points were spacedapproximately 10 mm apart, as shown in Fig. 3(a). Thelatex membrane was placed over the cylindrical specimen

used for triaxial testing, which was conˆned in acast-acrylic cylinder ˆlled with water. The dots on thespecimen were tracked using high resolution digitalimages. To obtain the digital images of triaxial speci-mens, a Digital camera (Kodak DC 290}) with approxi-mately 2.1-million pixel resolution (1792 H: 1200V) wasplaced at 562 mm distance from the outer wall of cell, asshown in Fig. 3(a). The digital camera was mounted on atwo-axis controller, which allowed for precisely adjustingcamera position in two directions. Images were thendownloaded in to a personal computer, and Image-Pro-Plus 4.1 software was used to measure the co-ordinates of


the points (dots made on the latex membrane placed onthe clay specimen). The accuracy of measurement was0.2 mm in vertical direction and 0.3 mm in circumferen-tial direction. A soft light (Lowell Softlite 2}) was used toprovide uniform illumination of the triaxial specimen andsigniˆcantly reduced shadows in the digital images. Afterˆnding the co-ordinates of the points on the specimen byusing Image-Pro-Plus 4.1 software, the co-ordinates werethen used to get the shear band information by using acontour plot program made in programming languageMAPLE (Lin, 2003).

Using image analysis software (ImagePro Plus}), thedistance between the specimen edges and the image edgeswere measured in terms of pixels. If these distances werenot equal, then the camera was repositioned using thehorizontal adjustment. The process was repeated untilboth distances are equal. The vertical position adjust-ment was used to bring the entire specimen into the ˆeldof view. The second horizontal adjustment was perpen-dicular to the image plane. This adjustment was also usedto ensure that complete specimen was in view and also foraccurate camera calibration. The camera was calibratedto determine the true horizontal and vertical positions onthe specimen surface from digital images as a function ofdistance to image plane. A ‰at plate with grid pointsspaced exactly 10 mm apart was used to calibrate thecamera. This plate was ˆxed to the bottom end plateninside the triaxial cell, and images were obtained whilevarying the distance between the camera and the front ofthe ‰at plate using the horizontal controller of the cameranormal to the image plane. Using image analysissoftware, the observed distance between any two pointscan be measured in units of pixels. The camera calibra-tion factor was calculated from the observed distance, inpixels, and the known value, in mm. Average calibrationfactors, one for the horizontal and one for the verticaldirection, were calculated for each image based onrepeated observations. The average calibration factor asa function of the distance between the camera and theimage plane (corresponding to the front of the ‰at plate)was obtained, as shown in Fig. 3(c).

During the triaxial test, the specimen was conˆned in acast-acrylic cylinder ˆlled with water, as shown inFig. 3(b). The presence of conˆning cylinder and wateraround the specimen in a triaxial cell caused multiplerefractions of light rays to occur, which needed to beaccounted in the analysis of digital images. Light raysbend, or refract, as they travel through media of diŠeringindices of refraction, which can magnify or reduce theobserved size of the target object being analyzed. In triax-ial testing, the refraction of light will cause the specimento appear enlarged. Therefore, corrections must be ap-plied to the data obtained from digital images (Fig. 3(b))in order to determine true specimen dimensions and gridpoint positions. By incorporating Snell's law of refrac-tion, a 2-D correction model (Parker, 1987; Lin andPenumadu, 2005) was developed to describe the relation-ship between the observed and actual specimen measure-ments. This model was used in this study to obtain the

true position and displacement of tracking dots on thesurface of cylindrical specimens. Macari et al. (1997) alsoused a similar technique for measuring volume changes intriaxial testing.

EVOLUTION OF SHEAR BAND

Using the data from digital images, the strain compo-nents of a point on the soil specimen were calculatedbased on the formulation developed by Lin (2003). Thecontour plots were developed to illustrate the strain ˆeld,which facilitated the visualization of the potential for theoccurrence of strain localization. In a contour plot of soilspecimen, such as those shown in Fig. 4, the verticalstrain on the surface of the specimen is displayed and theintensity of color at certain point of the plot representsthe magnitude of corresponding axial strain. It shouldbe noted that the X-coordinate of a contour plot isessentially the circumferential coordinate, so that thecylindrical surface of the specimen can be visualized in aplanar manner. The contour lines connect the points thatshare the same value of strain. It is more meaningful toread the pattern of a whole contour plot rather thanfocusing on a single point in a contour plot. Figure 4shows the deformation proˆle of Kaolin clay specimensheared under triaxial compression loading conditionsat the conˆning pressure of 207 kPa, which includes theimages of specimen and corresponding local-strain-contour plots at diŠerent global axial strain values.Visual inspection of the images of specimen during sheardeformation can help in identifying non-uniformity ofdeformation within the specimen but only when the non-uniformities are large enough in magnitude. An advancedtechnique such as DIA used in this research is required tomeasure the variation of local strains more precisely andstudy small magnitude of deformation that could lead tothe development of shear band type formations withinthe specimen. As shown in Fig. 4, the images of clayspecimen at 6z, 11z and 14z global axial strain did notexhibit a signiˆcant variation in the local deformationpattern by visual inspection through naked eye. Afterprocessing these images using DIA technique, thecorresponding local strain contour plots indicated theformation of strong localized deformation zones at highstrain levels. It is important to note that the accuracy ofmeasuring displacements using DIA system was 0.2 mmin the vertical direction. The calculations of local strainswere based on an element with maximum vertical dimen-sion of approximately 10 mm; therefore, the accuracy ofmeasurement was ±2z for obtaining local axial strain.The contour plot at 6z global axial strain (Fig. 4(a))showed distribution of local vertical strains within theaccuracy range, which can be used to infer that within theconstraints of the measurement system, the deformationwas relatively uniform until the global axial strainreached 6z. Shear band with practically constant incli-nation emerged at 11z global axial strain and becamemore signiˆcant as the global axial strain increased. Theshear band was observed to be fully developed at 14z

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Fig. 4. Contour plots (X axis: circumferential coordinate in cm, Z axis: vertical coordinate in cm) and the digital images for Test 1: (a) Uniformdeformation (relatively), (b) Initiation of shear banding and (c) Shear band formation


global axial strain, as shown by the contours of two localzones (Zone A and Zone B) in Fig. 4(c). Zone A shows amuch smaller values of local axial strains (8–10z) incomparison to Zone B (14–16z). The contour lines arevery dense in the Zone B as compared to Zone A, whichimplies a dramatic transition of the axial strain values.Therefore, the zone of intense straining (such as Zone B)can be regarded as a shear band with an approximatelyconstant inclination. It should be noted that the localstrains in the shear bands could be much higher than whatis depicted by the contour plots. This is because the shearbands were much thinner than the distance betweennodes of measurements (approximately 10 mm grid)

causing an averaging eŠect in deforming local strainvalues.

In Fig. 4(c), the Zone C represents a part of anothershear band, which is approximately parallel to the shearband in Zone B. For local strain analysis, the imagestaken during shear deformation covered approximately1W3 of the perimeter of specimen. At the end of shearing,the specimens were extruded from the triaxial cell andthen visually inspected to evaluate the continuity andinclination of shear bands around the specimen. Figure 5shows images of the specimens extruded after shearingunder triaxial compression and extension stress paths.These images were taken from four orthogonal directions

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Fig. 5. Shear banding in Kaolin clay specimens using lubricated endtriaxial setup: (a) Compression shearing (Test 2) and (b) Extensionshearing (Test 4)

Fig. 6. Interpretation of shear band inclination (c)


to completely observe the outer surface of specimen(front, rear, right, and left views). As shown in Fig. 5, theinclinations of all the thin shear band formations in asheared specimen were observed to be identical, and itwas true for both compression and extension tests. Thespecimens were also observed to have additional zones oflocalized deformations as can be seen in Fig. 5.

The stress-strain relationship for triaxial compressiontest on Kaolin clay specimen with ‰occulated microfabricexhibited the peak shear stress location at approximately11z axial strain (ep), as shown in Fig. 2(a). It is im-portant to note that small amount of localized deforma-tions were observed before 11z axial strain, and thedegree of localization increased as the shearing processcontinued. However, a clear shear band type formationwas observed starting at a global axial strain of 11z.It could be reasonable to interpret that strain localizationinitiated at peak shear stress location, and the failureplanes in the form of signiˆcant shear bands weredeveloped in the post-peak response. Peak shear stress(sp) is the maximum value of deviator stress experiencedby the soil specimen during its shear deformation. Theaxial strain (global) at peak shear stress location (ep) istermed as the ``failure'' of specimen in the current study.Stress paths (Figs. 2(c) and 2(d)) showed clearly thefailure point of each test, which represents the peak shearstress level. In the current research, formation of shearbanding was explained as the stage where the diŠerence inmaximum local axial strain (em) experienced by the soil

specimen and global axial strain (eg) applied on the speci-men by loading frame was more than 4z. For example;the diŠerence in em and eg for Test 1 was 1z in Fig. 4(b)(initiation of shear banding; eg＝11z, em＝12z) and 4zin Fig. 4(c) (formation of shear banding; eg＝14z, em＝18z). Thus, the global axial strain at the stage of shearband formation (eSB) was observed to be 14z for Test 1.

It should be noted that the observed inclination of theshear band in the contour plots (Fig. 6) was not the trueinclination of the shear band in the 3-D space. Figure 6illustrates the conversion from the observed inclination tothe true inclination of shear band with the 3-D view(Fig. 6(a)), front view (Fig. 6(b)) and top view (Fig. 6(c)).Assuming a shear band (an ellipse containing points i, j,k, and l ) cut through the cylindrical specimen during atest, the true inclination should be the angle c (Fig. 6(a)),which is the angle between the vertical direction (majorprincipal stress direction) and the shear band plane.Angle c can be calculated by using Eq. (1):

c＝tan－1 (dWH ) (1)

where d is the outer diameter of the specimen and H is thevertical distance between point i and m (or l ). Sincepoints i, j, k, and l are in the plane of the shear band, thefollowing relationship holds:

H＝(pdW2Ajk)･h (2)

where h is the vertical distance between points j and k,and Ajk is the arc length between points j and k inFig. 6(c). The contour plots in Fig. 4 shows essentially theinner dashed rectangle in Fig. 6(b). Therefore, both h andAjk can be read from the contour plots. Equation (1) canbe rewritten as Eq. (3), which is independent of thespecimen diameter:

c＝tan－1 Ø2Ajk

ph » (3)

The value of true inclination angle (c) for diŠerent triaxi-al tests performed on cylindrical specimens of Kaolin clayare given in Table 1.

DISCUSSION ON LOCAL STRAIN ANALYSIS

Table 1 summarizes the information related toorientation of shear band formation within the specimensduring a series of triaxial tests performed under diŠerentloadingWboundary conditions. The contour plots of local

74

j Table 1. EŠect of various factors on the strain localization patterns and the orientation of shear bands observed in the patterns

Test No.a) Testing conditionsb) Conˆning stressc) Specimen typed) Dbs and Hbs (Di＝Hi＝102 mm)e) ebs, Axial strain rate

Triaxial shear test Strain localization analysis

Peakshear

q? ep eSB em cstress,

(deg) (z) (z) (z) (deg)sp?

(kPa)

Test 1a) Undrained, Compressionb) po?＝sc?＝207 kPac) NC, Flocculated microfabric 127 31.7 11.0 14.0 18.0 31d) Dbs＝99.1 mm, Hbs＝100.5 mme) ebs＝1.03(ei＝1.18), Rate＝0.05zWmin



Test 4a) Undrained, Extensionb) po?＝sc?＝276 kPac) NC, Flocculated microfabric 147 35.2 11.0 13.0 26.0 31d) Dbs＝98.8 mm, Hbs＝99.7 mme) ebs＝1.00(ei＝1.18), Rate＝0.05zWmin

Test 5a) Undrained, Compressionb) po?＝276 kPa, sc?＝28 kPac) HOC, Flocculated microfabric 106 21.8 12.5 14.0 19.0 32d) Dbs＝99.9 mm, Hbs＝101.0 mme) ebs＝1.07(ei＝1.18), Rate＝0.05zWmin

Test 6a) Drained, Compressionb) po?＝sc?＝276 kPac) NC, Flocculated microfabric 448 26.6 26.0 26.0 29.0 NAd) Dbs＝98.8 mm, Hbs＝99.6 mme) ebs＝1.00(ei＝1.18), Rate＝0.005zWmin

Test 7a) Undrained, Compressionb) po?＝sc?＝276 kPac) NC, Dispersed microfabric 251 27.7 10.9 11.0 17.0 33d) Dbs＝100.2 mm, Hbs＝99.6 mme) ebs＝0.69(ei＝0.79), Rate＝0.008zWmin


deformations on the surface of solid cylindrical Kaolinclay specimens were analyzed with respect to the variationin following factors: Conˆning pressure, External load-ing conditions, Stress History, Drainage conditions, andMicrofabric.

Strain Localization Patterns of Clay Specimens Shearedunder Undrained Conditions

The undrained triaxial compression tests were per-formed on NC clay specimens with ‰occulated micro-fabric at the conˆning pressures sc? of 207, 276 and 345

kPa to study the impact of conˆning pressure on strainlocalization patterns of Kaolin clay. The eŠect ofanisotropic loading conditions and specimen's stresshistory were also studied by performing an undrainedtriaxial extension test on NC clay specimen at sc?＝276kPa and compression test on HOC clay specimen(OCR＝10) at sc?＝28 kPa. The contour plots of localstrain measurements during triaxial compression test atsc?＝207 kPa were discussed earlier, as shown in Fig. 4.Similar contour plots for the other individual tests areshown in the Fig. 7 to 10.

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Fig. 7. Contour plots (X axis: circumferential coordinate in cm, Zaxis: vertical coordinate in cm) and the digital images for Test 2: (a)Uniform deformation (relatively) and (b) Shear band formation



EŠect of Conˆning PressureAs shown in Figs. 4, 7 and 8, the distribution of local

axial strain on the deforming triaxial specimens at thethree conˆning pressure values of 207, 276, and 345 kPawas observed to be uniform for global axial strain valuesup to 6z. The shear band emerged at 11z of global axialstrain and became more and more signiˆcant as the strainlevel increased. Shear banding was observed at 14zglobal axial strain for sc?＝207 and 276 kPa (Fig. 4(c) and7(b)), and at 14.8z global axial strain for sc?＝345 kPa(Fig. 8(b)). For all the three cases, strain localization wasobserved to be initiated for stress state corresponding tothe occurrence of peak shear stress in the stress-strain plot(Fig. 2). The intensity of strain localization was observedto be much stronger for higher conˆning stressesexhibiting an increase in the value of maximum local axialstrain (18–20z) experienced by the specimen with theincrease in conˆning pressure (207–345 kPa). A trend ofincreasing c angle was observed with the increase inconˆning pressure, which varied from c＝31 to 399forthe variation in conˆning pressure from 207 to 345 kPa,as listed in Table 1.

EŠect of External Loading ConditionsContour plots for compression and extension stress

paths (Figs. 7 and 9) showed that local deformation wasuniformly distributed up to 6z global axial strain forboth the loading conditions. Small zones of localizeddeformation were observed within the clay specimen after6z of global axial strain and were connected with eachother in the process of further shear deformation. Strainlocalizations in the form of shear bands were observed to

occur at the peak value of stress-strain curve, as shown inFig. 2. It is thus reasonable to interpret the state of stressand strain from measured external load and displacementassuming a uniform state of deformation up to an axialstrain value of 11z for compression stress path and of11.5z for extension. The shear band formation wasobserved to be fully developed at a global axial strain of14z for compression, and 13z for extension testing. Asigniˆcant diŠerence was noticed between the values ofmaximum local axial strain (em) for compression (19z)and extension tests (26z), which indicated that the strainlocalization was much stronger in the specimen subjectedto extension stress path. The orientation of shear band(c) was observed to be signiˆcantly higher for compres-sion loading (369) in comparison to extension loading(319), as listed in Table 1. The reason could be attributedto the rotation of major principal stress by 909fromvertical to horizontal direction. During extension shear-ing, the specimen tends to have a smaller cross-sectionalarea (necking) at the middle of the clay specimen com-pared to the area at top and bottom of the specimen(Fig. 9(b)). The necking of specimen induced by theextension loading conditions could also in‰uence theinclination of shear bands, which was not an issue forcompression loading.

EŠect of Stress History of Clay SpecimenFor the HOC specimen, the global axial strain (eg)

corresponding to uniform distribution of strains (eg＝6z), initiation of shear banding (eg＝11z), and fullydeveloped shear band (eg＝14z) were the same as thosefor NC specimen. They also shared the same value of

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Fig. 9. Contour plots (X axis: circumferential coordinate in cm, Z axis: vertical coordinate in cm) and the digital images for Test 4: (a) Uniformdeformation (relatively) and (b) Shear band formation



maximum local strain (em) when the shear band was fullydeveloped at eg＝14z, as shown in Figs. 7 and 10. Theorientation of shear banding for NC clay (369) wasobserved to be larger than that for HOC clay (329), aslisted in Table 1.

EŠect of Drainage ConditionsThe impact of drainage conditions on strain localiza-

tion behavior of clay specimens was studied by repeatingthe triaxial compression test on NC clay specimen ofKaolin clay with ‰occulated microfabric at the conˆningstress of 276 kPa, and by allowing free drainage duringthe shearing stage of repeated test. The contour plots oflocal strain measurements during drained compressiontest are shown in Fig. 11. The distribution of local axialstrain was observed to be uniform until 6z global axialstrain for undrained shearing and 13z for drainedshearing (Figs. 7 and 11). As discussed earlier, theundrained triaxial compression showed clear evidence ofshear bands within the specimen at 14z global axialstrain (eSB). During drained triaxial compression test, thespecimen did not show linear shear band type localizeddeformation mode as observed during undrained testing;however, it was observed to have many small zones ofhighly localized deformations at 26z of global axialstrain. The reason could be attributed to the diŠerentmodes of instability causing strain localization for

77




varying drainage conditions. During undrained shearing,the instability caused by pore pressure evolution couldplay an important role in the development of shear bandtype formations within the specimen, which apparentlydid not occur under free drainage conditions duringdrained testing.

EŠect of MicrofabricIn this research, two extreme microfabrics of Kaolin

clay were used to study the eŠect of microfabric on strainlocalization behavior of soil. The results of triaxialcompression test on Kaolin clay specimens with‰occulated microfabric at sc?＝276 kPa were discussedearlier (Fig. 7). The same test was repeated using theKaolin clay specimen with dispersed microfabric, and thecorresponding contour plots of local axial strainmeasurements are shown in Fig. 12. The distribution oflocal strains was observed to be uniform until 6z globalaxial strain for ‰occulated microfabric and 4z fordispersed microfabric. The initiation of shear bandingwas observed at 9 and 11z global strain for dispersedand ‰occulated microfabric respectively. The shear bandtype formation was observed at much lower strain levelsfor dispersed microfabric (eSB＝11z) in comparison to‰occulated microfabric (eSB＝14z), which indicated ahigher possibility of sudden failure in Kaolin clay withdispersed microfabric. As shown in Fig. 2, the peak shearstress was observed at a global axial strain of 11.5zfor ‰occulated microfabric and 10.9z for dispersedmicrofabric. Unlike the response of ‰occulatedmicrofabric specimen, the specimen with dispersed

microfabric showed a clear formation of shear band atpeak shear stress followed by a sudden failure response.A notable diŠerence in c value was observed for ‰occu-lated (369) and dispersed (339) microfabric, as listed inTable 1.

CONCLUSIONS

A series of triaxial tests were performed on solidcylindrical specimens of ˆne grained cohesive soils (clay),and a technique with digital image analysis (DIA) wasused to evaluate the initiation and propagation of strainlocalization within the clay specimen due to actual non-uniformity of soil mass density and stiŠness of thematerial at diŠerent testing conditions. In the currentstudy, lubricated end platens were used to performtriaxial tests, which signiˆcantly reduced the friction atspecimen's ends; thus non-uniform deformations due toend restraints were assumed to be negligible throughoutthis study. The impact of conˆning stress, loadingconditions, stress history, drainage conditions, and soil'smicrofabric on the strain localization patterns and shearband orientation was discussed with the following keyobservations.

1) Impact of Conˆning Stress: A clear formation ofshear banding was observed at the same strainlevels for all values of conˆning stresses. Muchstronger strain localization and a larger value ofthe orientation angle of shear band were observedfor higher value of conˆning stress.

2) Impact of Loading Conditions: Strain localizationwas observed to be much stronger for extensionloading conditions in comparison to compression.


The value of orientation angle of shear band wasestimated to be smaller for extension shearing thanthe compression shearing.

3) Impact of Stress History: Strain localization pat-tern, shear band formation, and the orientation ofshear band were observed to be the same for boththe NC and HOC specimens of the Kaolin clayindicating no signiˆcant impact of stress history.

4) Impact of Drainage Conditions: The drained test-ing did not show the linear shear band type forma-tions as observed for undrained testing.

5) Impact of Microfabric: Dispersed microfabricshowed the shear band formations at lower strainlevels in comparison to ‰occulated microfabric. Anotable diŠerence in the orientation angle of shearbands was obtained for both the microfabrics.

ACKNOWLEDGEMENTS

Financial Support from National Science Foundation(NSF) through grants CMS-9872618 and CMS-0296111is gratefully acknowledged. Any opinions, ˆndings, andconclusions or recommendations expressed in thismaterial are those of authors and do not necessarilyre‰ect the views of NSF.

NOTATION

Di＝Initial diameter of specimenDbs＝Diameter of specimen before shearing (bs)Hi＝Initial height of specimen

Hbs＝Height of specimen before shearing (bs)ei＝Initial void ratio of specimen

ebs＝Void ratio before shearing (bs) of specimeneg＝Global axial strain applied on the specimen by loading frameep＝Global axial strain at peak shear stress level

eSB＝Global axial strain at the formation of Shear Banding (SB)em＝Maximum ``Local'' axial strain experienced by the soil at its

local zones within the specimen during its shear deformationprocess

OCR＝Overconsolidation RatioHOC＝Heavily Overconsolidated

NC＝Normally Consolidatedpo?＝Pre-consolidation pressuresc?＝EŠective conˆning pressure before shearing (bs)sp?＝Peak shear stress which corresponds the maximum value of

shear stress experienced by the specimen during its sheardeformation process

q?＝EŠective friction angle at peak shear stress levelc＝Angle of Shear Band (SB) from vertical axis (Z axis)

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