Evaluation of the e ect of anisotropic consolidation and...

Scientia Iranica A (2013) 20(6), 1637{1653

Sharif University of TechnologyScientia Iranica

Transactions A: Civil Engineeringwww.scientiairanica.com

Evaluation of the e�ect of anisotropic consolidation andprinciple stress rotation on undrained behavior of siltysands

R. Keyhani and S.M. Haeri*

School of Civil Engineering, Sharif University of Technology, Tehran, Iran.

Received 16 September 2012; received in revised form 6 January 2013; accepted 12 March 2013

KEYWORDSHollow cylinder test;Anisotropic behavior;Silty sand;Pore water pressure;Undrained behavior.

Abstract. The dependence of undrained behavior of silty sand on initial state of stressand direction of principal stresses with respect to vertical (�) is assessed under generalizedloading paths using hollow cylinder apparatus. During applying shear load, value ofintermediate principal stress parameter (b) is held constant and � value is increased fromzero to the aimed value and held constant. Specimens are consolidated, both, isotropicallyand anisotropically to evaluate the e�ect anisotropic consolidation on the behavior of thesesoils. The wet tamping method was selected to prepare specimen. Shear loading was carriedout under strain-controlled condition to capture post-peak strain-softening response. Theresults of this study reveal that the principal stress direction and initial anisotropy instress condition have considerable e�ects on the behavior of silty sands. By increasing �,susceptibility of silty sand to instability increases. In addition, increase in silt content ofsilty sand mixtures presents higher tendency to ow compared to pure sand. For specimenswith high silt content, it is observed that stress-strain response has a sudden reduction inshear strength after a peak. This study reveals that shear strength and steady state frictionangle of the silty sands are a�ected by � and the amount of �nes present in the sand.c 2013 Sharif University of Technology. All rights reserved.

1. Introduction

Initial direction of major principle stress in natural hor-izontal layers of soils is usually vertical. However apply-ing shear load by excavation, embankment, foundationof structures and wave load in sea bed layer causesrotation of principal stress direction. The directions ofprincipal stresses in triaxial tests are �xed and can onlyrotate at 90�. However the Hollow Cylinder Apparatus(HCA) provides a convenient way of assessing in uenceof rotation of principal stress direction on the behaviorof soils including silty sands [1].

The role of non-plastic silt on stress-strain be-havior of loose sand has been under discussion for

*. Corresponding author. Fax: +98 21 66014828E-mail address: [email protected] (S.M. Haeri)

decades. Terzaghi [2] hypothesized that silt particlescould create a \metastable" structure that could ex-plain the static liquefaction observed during failureof large submarine slopes. Recent laboratory studieson susceptibility of liquefaction appear to be dividedregarding the e�ect of non-plastic silt content. Kuerbiset al. [3] observed that increasing silt content up to 20%resulted in more dilative behavior of sand in undrainedtriaxial tests when the tests were performed at the sameskeleton void ratio. Pitman et al. [4] also concludedthat when silt was added to Ottawa sand, it becameless collapsible in undrained triaxial compression tests.Ishihara [5] and Verdugo and Ishihara [6] have foundthat non-plastic silt may increase the potential of liq-uefaction. They concluded that increasing silt contentcauses a contractive behavior that can induce thepossibility of ow failure or liquefaction. Amini and

1638 R. Keyhani and S.M. Haeri/Scientia Iranica, Transactions A: Civil Engineering 20 (2013) 1637{1653

Qi [7] reported that �ne content increased resistanceto liquefaction of sand during cyclic tests. Lade andYamamuro [8] and Yamamuro and Lade [9], observedthat increasing non-plastic silt content in Nevada sandincreased the contractive behavior of a specimen inboth drained and undrained triaxial tests, even whendensity was increased. Thevanayagam [10] found thatthe presence of non-plastic silt may either increase ordecrease undrained shear strength depending on theintergranular void ratio [11,12].

The experimental data for specimens at the samevoid ratio indicate that steady-state shear strengthdecreases initially by increasing �nes content, but when�nes content increase beyond about 30%, steady-stateshear strength starts to increase [5,4,13].

The overall response of the mixed soils at di�er-ent percentages of �nes is investigated by Yang andWei [14]. One of the signi�cant �ndings is that thecritical state friction angle of a mixed soil is a�ectednot only by the shape of coarse particles but also by theshape of �ne particles, and this shape e�ect is coupledwith �nes content.

Many tests by HCA have been performed to provethe e�ect of anisotropy on the behavior of sands [15-17]. The inherent anisotropy e�ect in Toyoura sandhas been studied by Yoshimine et al. [15] for di�erentdirections of major principal stress. When directionof major principal stress with respect to vertical (�)becomes larger, the behavior of material clearly softensand shows to be more contractive. As reported byYoshimine et al. [15], under loading in the case of � =15�, a hardening behavior with only 20% excess porewater pressure ratio was developed. Whereas, in caseof � = 75�, pore water pressure ratio was developed upto nearly 90%, and there was a strong strain softeningin behavior. Similar results have been reported bySivathayalan and Vaid [16] and Uthayakumar andVaid [17]. Di�erence in the results of conventionaltriaxial compression and extension tests on sands also,to some extent, reveal the inherent anisotropy in sands.Although the compression tests have been generallyused for undrained monotonic loading in large defor-mation (e.g. [5,6]), a few researchers have pointed outthat the undrained shear behavior of sand in extensiontests is far more contractive than that in compressiontests [15]. This fact proves the e�ect of anisotropy insand using triaxial apparatus.

The role of initial static shear stress in liquefactionresistance is studied by Yang and Sze [18]. Thepresence of initial static shear stress is bene�cial to theliquefaction resistance of loose sand at low initial shearstress ratio, but it becomes detrimental at high � levels.The initial static shear stress is an important factorin the softening behavior during the shear loading ofloose sand. Sivathayalan and Vaid [16] showed that theminimum undrained strength of the strain-softening

sand is found to be highly in uenced by the initialstress state, even though the friction angle mobilized atthe instant of minimum strength is unique. Also Katoet al. [19] speci�ed that the relation between void ratioand con�ning stress at steady state and quasi-steadystate are independent of the extent of anisotropicconsolidation. However di�erent states of consolidationstress were shown to a�ect the stress-strain behavior ofsand and the development of excess pore water pressureup to an axial strain of 5%. Additionally, Sladenet al. [20] indicated that anisotropically consolidatedsamples often failed in undrained triaxial monotonictests, when the stress state reached the collapse surfaceobtained from isotropic tests.

This paper presents an experimental study ofthe static undrained response of silty sand specimenreconstituted by wet tamping in a Hollow CylinderApparatus under di�erent directions of major principlestress (�). The main objective of this study is toassess the dependence of the behavior of silty sandson initial anisotropic stress state, in addition to thedirection of major principle stress. The tests wereconducted on sand samples containing 0, 10, 30 and40% silt content (fc). Similar preparation method,e�ective consolidation stress, and laboratory procedurewere used for each specimen. The results of the testson specimens with almost similar relative density arecompared and discussed.

2. Tested material

The tests in this experimental program were onBabolsar sand which is an standard sand in Iranand is classi�ed as SP according to the Uni�ed SoilClassi�cation System [21]. The non-plastic silt wasobtained by grinding local natural alluvium depositsof sand and gravel. This paper studies four mixturesof Babolsar sand with 0%, 10%, 30% and 40% byweight of non-plastic silt. The grain size distributioncurves of the mixtures are shown in Figure 1. Theuniformity coe�cient Cu and the mean grain size D50

Figure 1. Grain size distribution curves.

R. Keyhani and S.M. Haeri/Scientia Iranica, Transactions A: Civil Engineering 20 (2013) 1637{1653 1639

Table 1. Speci�c gravity and minimum and maximumvoid ratios for sand-silt mixtures.

Silt content(%)

Gs emax emin

0 2.75 0.790 0.53010 2.74 0.768 0.51030 2.73 0.720 0.46240 2.73 0.810 0.499

of sand were found to be equal to 2.00 and 0.23 mmrespectively. The maximum and minimum void ratiosand the speci�c gravity of soil solids (Gs) of the sand-silt mixtures respectively are provided in Table 1. Thespeci�c gravity of silt material is also 2.68.

3. Hollow cylinder apparatus

The tests were performed using the HCA at Ad-vanced Soil Mechanic Laboratory of Sharif Universityof Technology. The device is capable of subjectingan axial load (Wn), a torque (MT ) about the centralvertical axis, and di�erent external pressure (Po) andinternal pressure (Pi) to a hollow cylindrical specimenof soil (see Figure 2). These surface tractions areindependently controlled using automatic stress pathloading, thus enabling the loading of a specimen ofsoil along a prescribed stress path in the general four-dimensional e�ective stress space described by verticalnormal stress (�z), circumferential normal stress (�#),radial normal stress (�r) and shear stress (�z#) (seeFigure 2). Alternatively, the same stress state canbe represented in terms of magnitudes and directionsof three principal e�ective stresses �01, �02, �03 andangle of major principal e�ective stress with respectto vertical (�). The initial stress ratio kc = (�03=�01),e�ective mean normal stress P 0 = (�01 + �02 + �03)=3and intermediate principal stress parameter b = (�02 ��03)=(�01 � �03) are also frequently used as they are

Figure 2. Element component and principle stresses.

believed to be key stress variables that in uence onthe behavior of sand and silty sand.

Stress and strain gradients exist across the wallof a hollow cylinder specimen due to its shape andend restraint. Tests were controlled and interpretedin terms of average stresses and strains induced inspecimen during loading [22]. The average stresses arede�ned as:

�z =Wn

�(r2o � r2

i )+P0:r2

o � Pi:r2i

(r2o � r2

i ); (1)

�r =P0:ro + Pi:ri

(ro + ri); (2)

�� =P0:ro � Pi:ri

(ro � ri) ; (3)

�z� =3:MT

2�(r3o � r3

i ); (4)

in which ro and ri are the external and internalspecimen radii respectively.

Principle stress components can be calculated byusing Mohr's circle based on values of average stresses.Radial normal stress is equal to intermediate principlestress. So, the maximum and minimum principlestresses and � can be derived by the following formulas:

�1;3 =�z + ��

2�s�

�z � ��2

�2

+ �2z�; (5)

q = �1 � �3 = 2

s��z � ��

2

�2

+ �2z�; (6)

� =12

tan�1�

2�z��z � ��

�: (7)

4. Specimen preparation and testing procedure

4.1. Specimen preparationThe specimens tested had outer diameter of 100 mm,inner diameter of 60 mm and a height of approximately200 mm. These dimensions ensure a middle height zonein the specimen that remains una�ected by boundaryconditions [23].

In this study, the wet tamping method wasimplemented for specimen preparation using under-compaction procedure proposed by Ladd [24]. Theselected method was the most suitable method toobtain a very loose state of soil packing and a goodprocedure for building fairly uniform reconstitutedspecimens [5]. Initial water contents range from 5%to 8% for di�erent silt contents in order to obtainspecimens with allocated relative density.


The density of soil after consolidation is a veryimportant parameter in the behavior of soils. Soilswith higher density show more dilative response. Itis common to use void ratio for clean sands. In mixedsoils, like silty sand, the controlling density conditiondi�ers from clean sands. As reported in Table 1, theminimum and maximum void ratios are not constantfor di�erent silt contents. So it is not appropriateto compare the behavior of a silty soil with that ofa clean sand using global void ratio (e) or any othersolid density parameter. Sand and sand-silt mixesare expected to show similar mechanical behavior, ifcompared at the same contact density index. A soilclassi�cation system, based on contact density, hasbeen developed by Thevanayagam et al. [25] and The-vanayagam [26]. The relevant equivalent intergranularec(eq) and relevant equivalent inter�ne ef(eq) contactdensity indices have been introduced as:

ec(eq) =e+ (1� bi)fc1� (1� bi)fc ; (8)

ef(eq) =e

fc + 1�fcRmd

: (9)

Both bi and m are empirical values. Parameter bidenotes the portion of the �ne grains that contributesto the active intergrain contacts and statistically isabout 0.25. Parameter m is reinforcement factor andaccording to the reported studies by Thevanayagam etal. [25], it is about 0.65. Also parameter Rd is particlesize disparity ratio (D50(sand)=d50(silt)) and in our caseis equal 26.

As mentioned, the specimens with di�erent siltcontents should have the same contact density indexto show similar behavior. However preparing sampleswith the same ec(eq) for soils with silt contents is verydi�cult and somehow impossible. So in this study,because of the wide variation of the tested sand-siltmixtures, the intergranular and inter�ne void ratiocannot be �xed for di�erent silt contents and cannotbe adopted as controlling density indices despite apossible better interpretation of the problem (Table 2).Relative density (Dr) is a more common and suitableindex property for comparing undrained behavior ofspecimens with di�erent silt percentages [11,12].

During and after saturation and consolidationstages, the volume of the specimens decrease consid-erably [12]. Therefore preparing hollow specimensof high silt content with low relative density is verydi�cult. Practically, it seems that it is not possible toprepare mixed soils with a broad range of silt contentwith equal relative densities after consolidation. Inthis study, specimens with di�erent silt contents areprepared with similar preparation method in the lowestpossible relative densities. Thus, for example, when the

relative density of the pure sand is about 40% afterconsolidation, the relative density of less than 50%cannot be obtained for silty sand with 40% silt andthe same specimen preparation method.

4.2. SaturationAfter the specimen was prepared by wet tampingmethod, a hydrostatic pressure of 20 kPa applied onthe specimen and vacuum was removed from aroundthe specimen and carbon dioxide gas was circulatedfrom the bottom to the top of the specimen for 30minutes. Test specimens were initially saturated by ushing deaired water from the base of the specimen.Then a back pressure was applied to ensure watersaturation with Skempton's B value exceeding 0.95. Asmall amount of silt migration was noted in sampleswith large �ne contents.

4.3. ConsolidationIsotropic consolidation was attained by increasing bothaxial and lateral stresses with the same amount simul-taneously. In contrast, anisotropic consolidation withinitial stress ratio kc = �03c=�01c other than unity wasachieved by raising both axial stress (�01c) and lateralstress (�03c) simultaneously, while maintaining kc equalto the desired value during consolidation stage. Inanisotropic consolidation, the intermediate principalstress parameter (b) and mean e�ective stress (p0)should be controlled, as well, to be able to de�neappropriate stress path. In the present study thespecimens are consolidated with kc equal 0.33, 0.5 and1 to study the e�ect of anisotropic consolidation on thebehavior of sands and silty sands.

4.4. Stress pathAfter completed consolidation, undrained loading wasapplied in a strain-controlled manner with an axialstrain rate of 0.5% per minute. In order to study theanisotropic consolidation e�ect, b is planned to be heldconstant during each test. In the end of consolidationstage, � is equal zero except for isotropic consolidationcondition. So, � should be increased from zero tothe aimed value during shear loading. However it isincreased fast during the initial stage of shear loadingand then it is held constant.

According to Verdugo and Ishihara [6], estima-tion of void ratio of specimen in consolidation stagebased on water content is more accurate and has lessstatistical scatter than that estimated based on initialspecimen dimensions and measured volume changesduring consolidation.

Membrane penetration was not taken into accountsince the sand and silty sand used in this experimentwere �ne to medium sand and silty sand. In addition,visual observation of the specimens throughout thetests indicated that membranes were smooth with novisual indication of penetration.


Table 2. Summery of test result.

No.Silt

content(%)

�(deg.)

Kc

e(void ratio at the

end of consolidation)

Relativedensity

(%)ec(eq) ef(eq)

qpeak

(kPa)qmin

(kPa)

1 0 20 1 0.683 41 0.683 5.54 - -2 0 40 1 0.686 40 0.686 5.56 - -3 0 60 1 0.681 42 0.681 5.52 - -4 0 80 1 0.681 42 0.681 5.52 128.0 96.25 10 20 1 0.660 42 0.794 3.13 - -6 10 40 1 0.652 45 0.786 3.09 - -7 10 60 1 0.657 43 0.791 3.11 130.0 85.08 10 80 1 0.657 43 0.791 3.11 118.0 65.09 30 20 1 0.596 48 1.060 1.54 130.0 85.810 30 40 1 0.591 50 1.053 1.53 120.0 70.111 30 60 1 0.591 50 1.053 1.53 108.0 45.112 30 80 1 0.594 49 1.056 1.54 102.0 37.913 40 20 1 0.651 51 1.359 1.37 142.8 103.914 40 40 1 0.648 52 1.355 1.37 127.8 81.215 40 60 1 0.655 50 1.364 1.38 114.9 60.516 40 80 1 0.642 54 1.346 1.35 108.2 44.717 0 20 0.5 0.681 42 0.681 5.52 - -18 0 40 0.5 0.683 41 0.683 5.54 - -19 0 60 0.5 0.686 40 0.686 5.56 - -20 0 80 0.5 0.681 42 0.681 5.52 180.0 143.521 10 20 0.5 0.657 43 0.791 3.11 - -22 10 40 0.5 0.660 42 0.794 3.13 - -23 10 60 0.5 0.665 40 0.800 3.15 174.0 119.924 10 80 0.5 0.652 45 0.786 3.09 170.0 101.825 30 20 0.5 0.591 50 1.053 1.53 170.0 112.926 30 40 0.5 0.596 48 1.060 1.54 160.0 95.927 30 60 0.5 0.591 50 1.053 1.53 148.0 66.228 30 80 0.5 0.599 47 1.063 1.55 143.0 54.329 40 20 0.5 0.651 51 1.359 1.37 181.2 128.030 40 40 0.5 0.639 55 1.341 1.35 167.0 110.531 40 60 0.5 0.658 49 1.368 1.39 153.6 79.132 40 80 0.5 0.645 53 1.350 1.36 150.0 67.233 0 20 0.33 0.683 41 0.683 5.54 - -34 0 40 0.33 0.683 41 0.683 5.54 - -35 0 60 0.33 0.681 42 0.681 5.52 - -36 0 80 0.33 0.678 43 0.678 5.50 232.0 181.837 10 20 0.33 0.657 43 0.791 3.11 - -38 10 40 0.33 0.657 43 0.791 3.11 - -39 10 60 0.33 0.662 41 0.797 3.14 226.0 151.640 10 80 0.33 0.660 42 0.794 3.13 222.0 128.541 30 20 0.33 0.594 49 1.056 1.54 222.0 144.942 30 40 0.33 0.594 49 1.056 1.54 216.0 122.443 30 60 0.33 0.588 51 1.050 1.52 212.0 94.544 30 80 0.33 0.596 48 1.060 1.54 210.0 74.745 40 20 0.33 0.655 50 1.364 1.38 225.3 165.146 40 40 0.33 0.645 53 1.350 1.36 218.8 141.547 40 60 0.33 0.642 54 1.346 1.35 214.7 110.048 40 80 0.33 0.648 52 1.355 1.37 211.5 94.0


All of the tests were performed along the stresspaths shown in Figure 3 by controlling the internal andexternal pressures, the vertical load and the torque, asexplained previously. Figure 3 shows the normalizedshear stress (�z#=P 0c) against the normalized deviatorstress ((�z � �#)=P 0c), where P 0c is the initial con�ningpressure. As shown in Figure 3(a) to (c), stress pathsof specimens with di�erent anisotropic consolidationconditions are the same and only the initial stress stateof shear loading is di�erent.

Figure 3. Stress paths employed on silty sand specimenswith isotropic and anisotropic consolidation.

5. Type of tests performed and results

Forty eight undrained shear tests were conducted withconstant value of b during shear stage of each test asdepicted in Table 2. The tests were carried out on sandand silty sand consolidated to almost identical relativedensities. The tests were carried out to study the e�ectof initial stress states characterized by kc and � andvarious silt percentages on the behavior of sility sands.A constant e�ective mean normal consolidation stress(p0c) of 200 kPa and b = 0:5 was used in all tests.

5.1. Test resultsFor a systematic quanti�cation of undrained behaviorof the studied silty soil, following three states were dis-tinguished: the steady state, the quasi-steady state andthe phase transformation state [27,28]. These states arediscussed next for the test results of this study.

The steady state is the state at which the soil de-forms at constant e�ective stresses (i.e. zero change in qand p) and constant void ratio in drained tests and con-stant pore water pressure in undrained tests. However,in experiments, there are small deviations from theseideal conditions. The steady state usually happens forsand with high silt content when it is sheared in a high� value. The quasi-steady state (QSS) is de�ned as thestate at which the Deviatoric Stress q reaches a localminimum in undrained shearing. Experimental resultsshow that the QSS constitutes a distinct soil state. Thephase transformation is the state at which contractivebehavior changes to dilative one and usually occurswithout losing the strength at that state. In pure sandsamples especially in small � value a distinct phasetransformation could be observed.

The results of the tests on sand and silty sandmaterials are shown in Figures 4 to 15 for kc = 0:33,0.5 and 1 and � = 20�, 40�, 60� and 80�. Figures 4to 6 include the results of a package of tests on cleansand. The relative densities (Dr) of the samples werein a range of 41% to 42% after consolidation and theinitial con�ning stress was 200 kPa. It can be noticedfrom Figures 4 to 6 that, by increasing �, the behaviorbecomes clearly softer and more contractive and porewater pressure increases during undrained shear. Inthe tests with � = 20� the behavior was completelydilative and softening behavior did not occur, whereasin the tests with � = 80� Quasi Steady State wasobvious. The stress path and stress-strain curves ofthe tests with � = 40� and � = 60� also have dilativebehavior. Such a systematic softening (with �) hasbeen attributed to change in loading condition fromcompression (� = 20�) to extension (� = 80�).

The comparative behavior of sand consolidatedwith identical � and di�erent kc values can be observedfrom Figures 4 to 6. As can be observed, the sandmaterial does not exhibit strain softening at � = 20�


Figure 4. E�ect of � on the behavior of Babolsar sand in P 0c = 200 kPa and kc = 0:33.

Figure 5. E�ect of � on the behavior of Babolsar sand in P 0c = 200 kPa and kc = 0:5.

Figure 6. E�ect of � on the behavior of Babolsar sand in P 0c = 200 kPa and kc = 1.

and 40� for all kc values. But it appears for shearloading with � = 60� and 80�that the behavior ofspecimens become marginally less strain softening byincreasing anisotropy in consolidation (decreasing kc);although the di�erence is relatively minor.

As mentioned before and shown in Figures 4 to6, the behavior of sand specimen changes from strain,hardening to strain softening when � increases. Alsodeviatoric stresses increase by increasing shear strain,so it seems there is no tendency to reach a steady statefor the sand specimens. Consolidating specimen withlower kc (higher anisotropy) causes the sand samplesto behave more dilative in contrast to the specimenconsolidated isotropically.

The stress path of shear stress for specimens with10% silt is shown in Figures 7 to 9. The relativedensities of specimens were in the range of 40% to45% and the initial mean e�ective stress was 200 kPa.By increasing �, the behaviors of specimens changefrom dilative to strain-softening. The specimens havedilative behavior at � = 20� and 40�. But for � =60�, the specimen exhibits a dilative behavior in theinitial stage of shear, and the shear strength of thespecimen decreased and reached to a local minimumvalue (QSS), however the shear strength increasedagain by increasing the shear strain indicating a phase-transformation. The strength of specimens with 10%silt decreases from that of the sand specimens.


Figure 7. E�ect of � on the behavior of Babolsar sand with 10% silt in P 0c = 200 kPa and kc = 0:33.


Figure 9. E�ect of � on the behavior of Babolsar sand with 10% silt in P 0c = 200 kPa and kc = 1.

Figures 10 to 12 show the test results for siltysand material with 30% silt. As shown in these �gures,the behavior of the material becomes more contractiveand shear strength decrease by adding silt content inthe specimens. Adding non-plastic silt to the host sandmade it much more susceptible to strain softening. Itcan be observed in the Figures 10 to 12 that all of thespecimens have a similar strain softening behavior forall � and kc value and for silt content of 30%.

The test results for specimens with 40% silt areshown in Figures 13 to 15. The relative densitiesof tested specimens are 49% to 55%. As depicted,the shear strength of these specimens decreases withrespect to that of sand specimen but they increase with

respect to the shear strength of sand with 30% silt.That is, adding silt to sand material initially decreasesshear strength and then increases it when silt contentsare beyond a threshold value. As mentioned byMurthy et al. [29], this phenomenon is very importantbecause it seems that bearing skeleton of sand is beingchanged to silt skeleton. In this condition, silt skeletondominates and the sand grains are in silty skeletonwithout any contact of sand grain. In the lower amountof silt content, the silt material does not have a separateskeleton and only �lls the voids of the sand skeleton.It seems that the particles of silty material lubricatemoving the sand grains and reduce the strength ofinterparticle contacts. As a result, the strength of silty




sand decreases by the increase in silt up the point ofseparation of sand particle where it starts to increase.

As shown in Figures 6, 9, 12 and 15, by in-creasing silt content of the material for the specimensconsolidated isotropically, the behavior of the materialbecomes more contractive and usually reaches to thesteady state condition without any phase transforma-tion (e.g. Figure 15). Also the same trends can beobserved for anisotropically consolidated material withkc = 0:33 and kc = 0:5 as shown in Figures 5, 8, 11and 14. On the other hand, referring to Table 2, onecan observe that increasing silt content in the mixturedecrease the strength of the specimen (qpeak) andincrease the susceptibility to strain softening behavior(qpeak � qini). The previous studies by Yamamuro andCovert [30] and Bahadori et al. [12] show that addingsilt material to host sand reduces shear strength ofthe sand. The current study approves this statement.Shear strength of a material decreases by adding siltcontents up to 30% silt and then starts to increase byadding more silt to the material for all values of kc.

The minimum undrained strength at kc = 0:33is about double of that at kc = 1 when � � 60� forsand with di�erent silt contents (e.g. Figures 7 and9). However for � � 40�, the ratio of the minimumundrained strengths at kc = 0:33 and kc = 1 is less than2 (e.g. Figures 10 and 12). This demonstrates thatthe in uence of initial kc on the minimum undrained

strength of sands is more prominent for higher valuesof �.

By decreasing kc, the stress state at the end ofconsolidation becomes closer to failure line as shown inFigures 7, 10 and 13. So with a slight increase in shearstress for kc = 0:33, stress state reaches to failure lineand steady state condition. As a result, the behaviorsof highly anisotropic silty sand materials are alike andvariation of � has little e�ect on undrained behaviorof highly anisotropically consolidated material. Asshown in Figures 4 to 15, for specimens with thesame silt contents, decreasing kc (higher anisotropy)causes the total peak shear strength of sand and siltysand material to increase; however the deviatoric stressrequired after anisotropic consolidation stress decreasesby decrease in kc as shown in Figure 16.

6. Analysis of the results and discussion

6.1. Initiation of contractive deformationThe degree of strain softening is often characterized bythe brittleness index IB [31], de�ned as:

IB =qpeak � qmin

qpeak; (10)

in which qpeak and qmin are the peak and minimumundrained deviatoric stress, respectively. IB is re-garded as an indicator of ow potential for strain-


Figure 16. Variation of qpeak � qini with kc and � for sand and silty sand.

Figure 17. Variation of brittleness index with kc and � for sand and silty sand.

softening behavior of sands. A considerable increase inIB was reported by Bahadori et al. [12] and Sivatahanand Vaid [16] with increasing � in sands and silty sands.

As shown in Figures 4 to 9, for sand, and sandwith 10% silt, respectively, under loading conditionsat � � 60� and � � 40�, the reduction in the strengthdoes not occur and IB in these cases is equal to zero. Inother cases, either the quasi steady state or the steadystate condition is determined as the minimum strengthand the peak points are determined as peak strengths.

Figure 17 shows the variation of IB against kc forsand and silty sand material. Increasing anisotropicconsolidation or initial shear stress (decreasing kc) does

not appear to in uence IB signi�cantly and it is almostconstant for selected value of �. The variation ofaverage of IB against � for silty material is shownin Figure 18. An absolute increase in brittlenessindex can be noted with increasing � especially byincreasing silt content of the material up to 30%silt content. Similar results have been reported forsand under compression, extension, shear and principlestress rotation loading [16,27].

The anisotropic consolidated sand and siltyspecimens with low values of kc may experience strainsoftening behavior at high values of �. The steadystate strength can be much lower than the initial shear


Figure 18. Variation of average brittleness index with silt content and �.

Figure 19. Variation of modi�ed brittleness index with kc and � for sand and silty sand.

stress. Such a behavior can represent a potential fora ow slide.

Keeping kc constant and increasing � and thesilt content, brittleness index increases but this trendstops at 30% silt. At 40% silty sand, brittleness indexdecreases with respect to that of 30% silt as shown inFigure 18.

The original de�nition of brittleness index byBishop [31] was intended to characterize ow potentialof initially hydrostatically consolidated soils. It cannotfully describe ow potential for initially anisotropicallyconsolidated sands. Sivathayalan and Vaid [16] sug-gested an alternative expression for ow potential ofsands at di�erent � and kc values by considering thepeak and the minimum strength values with referenceto the initial level of deviatoric stress (qini) at consol-idation stage. This modi�ed brittleness index IB(mod)was de�ned as:

IB(mod) =qpeak � qmin

qpeak � qini: (11)

A better characterization is expected for ow potentialof anisotropically consolidated sands using modi�edde�nition for brittleness index. Figure 19 shows thevariation of modi�ed brittleness index against kc forvarious amount of � for sand and silty sand materialtested in this study. IB(mod) = 0 corresponds to nostrain softening, and IB(mod) = 1 represents minimumundrained strength, which is equals to the initial staticshear stress. IB(mod) values larger than 1 imply min-imum undrained strength lower than the initial staticshear stress, and hence the triggering of a ow slide,if equilibrium is disturbed by a small undrained per-turbation. As indicated in Figure 19, the potential of ow increases at high levels of initial shear stress by in-creasing �. Also adding more silt to host sand increasethe rate of increase in IB(mod), that is, the potential of ow of silty sand specimen increases by increasing thesilt content up to 30% silt and decrease afterwards.

6.2. Steady-State Friction angle �ssUndrained tests on sand and silty sand have shown


Figure 20. E�ective stress conditions at quasi steady state and steady state for Babolsar sand with silt.

that steady state friction angle (or slope of q � p0curve at steady state condition) is a unique parameterfor a given sandy soil. This parameter is said tobe independent of initial fabric, kc and � [5]. Thecondition of steady state at large strains is achievedafter complete rearrangement of the sand particles. Itshould be noted that (for sands) this rearrangementtakes place at the shear zone and not at other parts ofthe specimen. The initial fabric is completely destroyedand due to large strains at constant volume, a newfabric is formed at steady-state. The steady statefriction angle (�0ss), mobilized at large strains, is amaterial characteristic which depends only on physicalproperties such as mineralogy, gradation and the shapeof coarse and �ne grains of the soil [5]. Steady statefriction angle (�0ss) may be calculated using Mohr-Columb failure criteria (Eq. (12)).

�01�03

=1 + sin�0ss1� sin�0ss

: (12)

The principle stresses (�01, �03) can be replaced ac-cording to mean e�ective pressure (P 0) and induceddeviator stress (q). So Eq. (12) can be rewritten as:

sin�0ss =�

3q6p0 + q � 2bq

�ss; (13)

sin�0ss=

0@ 3�qp0�

6+�qp0��2b

�qp0�1A

ss

=�

3Mss

6+Mss�2bMss

�;

(14)

where MSS is the slope of q�p0 curve in q�p0 space inthe steady state condition and p0 = (�01 + �2 + �03)=3,q = (�1 � �03). As indicated in Eq. (14), steady statefriction angle depends on b. The value of MSS for eachtype of material is obtained from q � p0 curve and thevalue of steady state friction angle is calculated usingEq. (13). Figure 20 show data from undrained testsplotted in q � p0 space. This �gure shows that thedata associated with di�erent value of � for specimenswith 30% and 40% silt contents lie along a straightline passing through the origin, regardless of the initialvalue of �, kc, or the mechanism of deformation.However, the steady state happens for 10% silt andclear sand only for high � values. This implies theuniqueness of the steady state in the e�ective stressspace. The value for �tting parameter derived throughleast squares regression, MSS , and associated steadystate friction angle are summarized in Table 3.

As shown in Table 3, the steady state frictionangle of the sand decreases with increasing silt content

Table 3. The value of MSS and �0ss for di�erent mixturesof Babolsar sand with silt

Silt content(%)

MSS �0ss

0 0.654 40.810 0.625 38.730 0.564 34.440 0.572 34.9


to reach a minimum value at sand with 30% silt. Thenthe steady state friction angle starts to increase forsilty sand material with 40% silt. The present resultssuggest that the addition of silt in the sand leads toa decrease in �0ss. The maximum reduction of �0ss isabout 16% which happens for sand with 30% silt.

The angularities of the silt particles play animportant role on the behavior of silty sand material.Both silt and Babolsar sand which are used in thisstudy were obtained from natural alluvial deposits. Al-luvial deposits have usually been eroded and reshapedby water, so their particles have usually rounded andsemi-rounded shape with a few semi-angular particlesas shown in Figure 21. When shear loading was appliedto silty sand specimen, because of shape of silt andsand particles, they can move easily against each otherand decrease �0ss of the mixture. In contrast, data byMurthy et al. [24] and Sladen et al. [20] showed thatthe addition of non-plastic crushed silica silt to angularparticles increased the average value of �0ss. The di�er-ent angularities of silt and host sand lead to increase the

e�ect of silt on the �0ss. In addition to the angularitiesof the particles, the method of preparation of specimenhas direct e�ect on the fabric of silty sand mixtures andit should be considered in interpretation of the results.

Decreasing �0ss with increasing silt content canphysically be explained. When small amount of non-plastic silt �nes is added to sand grains, most of thesilt particles �ll in the voids of sand material. In thiscondition, the sand skeleton bearing the applied shearload and the sand behavior is dominant. The presenceof relatively small amounts of silt between the sandgrains makes a sort of smoothing the contacting surfaceof sands and reduces the shear strength of the fabricof the silty sand. In other words, when the silty sandwith small amount of silt is sheared, the weak contactsbetween sand grains dominate and the shear strengthdecreases.

6.3. Minimum undrained strengthFigure 22 illustrates the dependence of minimumundrained strength �min (qmin=2) on � and kc for sand

Figure 21. Subrounded Particle of Babolsar sand and subangualr particle of silt.

Figure 22. Variation of minimum undrained strength with kc and � for sand and silty sand.


and sitly sand material. The minimum undrainedstrengths correspond to minimum values of either quasisteady state or steady state conditions for each loadingcondition on each material. At a given kc, as de-picted in Figure 22, a systematic decrease in minimumundrained strength can be seen with an increase in �,regardless of the type of the material. For a given �, therate of increase of qmin with decrease of kc (increaseinginitial static shear stress) is essentially constant forall soils in question (Figure 22). As explained, theminimum undrained strengths are selected accordingto either quasi steady state or steady state conditions.But both of the quasi-steady state and the steady stateare located on one curve and the relationship between�min and kc is not dependent on the state of the soil atminimum strength.

In other words, the specimens are initially indrained equilibrium under an anisotropic consolidationstress qini. Then, the specimen is loaded underundrained conditions, the shearing resistance buildsup to a peak value (Figure 16). At that point thespecimen becomes unstable and strains rapidly towardthe minimum shear strength (�min) that is smaller thanthe initial shear stress.

The data shown in Figure 23 is normalized valueof Figure 22 by major principal stress at consolidation.As shown in Figure 23, the normalized minimumundrained strength is essentially independent of kc orinitial diavetoric stresses (qini); however it depends on�. Similar normalized data from previous studies [16]on sand material in triaxial extension and simple shearloading also support this contention. Adding siltcontent to the host sand does not in uence too muchthe behavior of the host sand in this respect. Therelationship between normalized minimum undrainedstrength and � is linear (the normalized minimumundrained strength decreases with increase in �).

According to the tests results and Figure 23,the location of the lines associated with normalizedminimum undrained strength changes for sand withdi�erent silt contents, and the minimum values of nor-malized minimum undrained strength occur for sandwith 30% silt content for any �. This fact indicatesthe dependency of normalized minimum undrainedstrength on the silt content.

7. Conclusions

A series of undrained tests with using hollow cylinderapparatus were performed on clean and silty sandswith nonplastic silt contents ranging from 10% to 40%.Specimens were prepared using wet tamping methods.The main focus of this paper is on the evaluation ofthe behavior of anisotropic silty sand under a varietyof stress path with constant value b during shearstage.

Figure 23. Variation of normalized minimum undrainedstrength with � for silty sand.

Di�erent states of consolidation stress producedi�erent stress-strain behavior during shearing andhence di�erent excess pore water pressure. Inanisotropic consolidation, the stress state at consoli-dation with kc = 0:33 becomes closer to the failureline and for the same material decreasing kc causes theminimum shear strength of the material to increase.

Adding silt up to 30% by weight to the sand hostreduces the shear strength of the material and thenthe shear strength increases for sand with 40% silt. Inaddition adding silt to the sand makes the materialweaker and more susceptible to ow.

Applying load with higher � can change behaviorof specimen from dilative to contractive and increases


susceptibility to ow. Also silt contents and � havemore in uence on brittleness index compared to kc.

The steady state friction angle (�0ss) for siltysand with 30% and 40% silt contents is essentiallyconstant and the data associated with di�erent valueof � lie along a straight line passing through the origin,regardless of the initial value of �, kc, or the mechanismof deformation. This implies uniqueness of the steadystate in the e�ective stress space. Also the normal-ized minimum undrained strength by major principalstress at consolidation appears to be dependent on theloading path and independent from the kc.

Acknowledgment

Hollow cylinder tests were conducted in the AdvancedGeotechnical Engineering Laboratory of Civil Engi-neering Department of Sharif University of Technology.

References

1. Symes, M.J., Gens, A. and Hight, D.W. \Drained prin-cipal stress rotation in saturated sand", Geotechnique,38(1), pp. 59-81 (1988).

2. Terzaghi, K. \Varieties of submarine slope failures",Proc., 8th Texas Conf. on Soil Mech. and Found.Engrg., Univ. of Texas, Austin, Texas, pp. 29-41(1956).

3. Kuerbis, R., Negussey, D. and Vaid, Y.P. \E�ect ofgradation and �ne content on the undrained responseof sand", Hydraulic Fill Structure, Geotechnical SpecialPunlication, 21, New York, pp. 330-345 (1988).

4. Pitman, T.D., Robertson, P.K. and Sego, D.C. \In u-ence of �nes on the collapse of loose sands", CanadianGeotechnical Journal, 31, pp. 728-739 (1994).

5. Ishihara, K. \Liquefaction and ow failure duringearthquake", Geotechnique, 43(3), pp. 351-415 (1993).

6. Verdugo, R. and Ishihara, K. \The steady state ofsandy soils", Soil and Foundation, 36(2), pp. 81-91(1996).

7. Amini, F. and Qi, G.Z. \Liquefaction testing of strat-i�ed silty sands", J. Geotech. and Geoenviron. Engrg.,ASCE, 126(3), pp. 208-217 (2000).

8. Lade, P.V. and Yamamuro, J.A. \E�ects of nonplastic�nes on static liquefaction sands", Canadian Geotech-nical Journal, 34, pp. 918-928 (1997).

9. Yamamuro, J.A. and Lade, P.V. \Steady-state conceptsand static liquefaction of silty sands", J. Geotech.and Geoenviron. Engrg., ASCE, 124(9), pp. 868-877(1998).

10. Thevanayagam, S. \E�ect of �nes and con�ning stresson undrained shear strength of silty sands", J. Geotech.and Geoenviron. Engrg., ASCE, 124(6), pp. 479-491(1998).

11. Haeri, S.M. and Yasrebi, S.S. \E�ect of amount andangularity of particles on undrained behavior of silty

sands", Scientia Iranica, 6(3&4), pp. 188-195 (1999).

12. Bahadori, H., Ghalandarzadeh. A. and Towhata, I.\E�ect of non plastic silt on the anisotropic behaviorof sand", Soils and Foundation, 48(4), pp. 531-545(2008).

13. Zlatovic, S. and Ishihara, K. \On the in uence ofnonplastic �nes on residual strength", 1st Int. Conf. onEarthquake Geotech. Engrg., Rotterdam, Netherlands,pp. 239-244 (1995).

14. Yang, J. and Wei, L.M. \Collapse of loose sand withthe addition of �nes: the role of particle shape",Geotechnique, 62(12), pp. 1111-1125 (2012).

15. Yoshimine, M., Ishihara, K. and Vargas, W. \E�ectsof principal stress direction and intermediate principalstress on undrained shear behavior of sand", Soils andFoundations, 38(3), pp. 179-188. (1998).

16. Sivathayalan, S. and Vaid, Y.P. \In uence of general-ized initial state and principal stress rotation on theundrained response of sands", Canadian GeotechnicalJournal, 39, pp. 63-76 (2002).

17. thayakumar, M. and Vaid, Y.P. \Static liquefaction ofsands under multiaxial loading", Canadian Geotechni-cal Journal, 35, pp. 273-283 (1998).

18. Yang, J. and Sze, H.Y. \Cyclic behaviour and resis-tance of saturated sand under non-symmetrical loadingconditions", Geotechnique, 61(1), pp. 59-73 (2011).

19. Kato, S., Ishihara, K. and Towhata, I. \Undrainedshear characteristic of saturated sand underAnisotropic consolidation", Soils and Foundations,41(1), pp. 1-11 (2001).

20. Sladen, J.A., D`ollander, R.D. and Krahn, J. \Theliquefaction of sands, a collapse surface approach",Canadian Geotechnical Journal, 22(4), pp. 564-578(1985).

21. Haeri, S.M., Noorzad, R. and Oskoorouchi, A.M.\E�ect of geotextile reinforcement on the mechanicalbehavior of sand", Geotextile and Geomembrane, 18,pp. 385-402 (2000).

22. Hight, D.W., Gens, A. and Symes, M.J. \The de-velopment of a new hollow cylinder apparatus forinvestigating the e�ects of principle stress rotation insoils", Geotechnique, 33(4), pp. 355-383 (1983).

23. Sayao, A. and Vaid, Y.P. \A critical assessment ofstress non uniformities in hollow cylinder test speci-mens", Soil and Foundation, 31(1), pp. 60-72 (1992).

24. Ladd, R.S. \Preparing test specimens using undercom-paction", Geotechnical Testing Journal, 1(1), pp. 16-23(1978).

25. Thevanayagam, S., Shenthan, T., Mohan, S. andLiang, J. \Undrained fragility of clean sands, siltysands and sandy silts", J. Geotech. and Geoenviron.Engrg., ASCE, 128(10), pp. 849-859 (2002).

26. Thevanayagam, S. \Intergrain contact density indicesfor granular mixes-I: Framework", J. Earthquake En-


gineering and Engineering Vibration, 6(2), pp. 123-134(2007).

27. Vaid, Y.P. and Sivathayalan, S. \Fundamental factorsa�ecting liquefaction susceptibility of sands", Cana-dian Geotechnical Journal, 37, pp. 592-606 (2000).

28. Yoshimine, M. and Ishihara, K. \Flow potential ofsand during liquefaction", Soils and Found, 38(3), pp.189-198 (1998).

29. Murthy, T.G., Loukidis, D., Carraro, J.A.H., Prezzi,M. and Salgado, R. \Undrained monotonic response ofclean and silty sands", Geotechnique, 57(3), pp. 273-288 (2007).

30. Yamamuro, J.A. and Covert, K.M. \Monotonic andcyclic liquefaction of very loose sands with high siltcontent", Journal of Geotechnical and Geoenvironmen-tal Engineering, ASCE, 127(4), pp. 314-324 (2001).

31. Bishop, A.W. \Shear strength parameters for undis-turbed and remoulded soil specimens", In Proceedingsof the Roscoe Memorial Symposium, Cambridge Uni-versity, Cambridge, Mass., pp. 3-58 (1971).

Biographies

Reza Keyhani received the B.Sc. Degree in CivilEngineering from the Amir Kabir University of Tech-nology, Tehran, Iran, in 1996 and the M.Sc. Degree inGeotechnical Engineering from the Sharif Universityof Technology (SUT), Tehran, Iran, in 1999. He iscurrently the PhD candidate in SUT.

He has the �rst place in Iranian Civil Engineeringchampionship in 1996. His research interests lie inanalytical and numerical analysis of earth and rock�lldams and laboratory investigation of soil characteri-zation. He has published 4 Journal and conference

papers. He also has valuable professional experiencesin designing large earth and rock�ll dam, deep ex-cavation and managing and leading di�erent stagesof engineering studies, site investigations and o�cejob.

Seyed Mohsen Haeri received an M.Sc. Degree inCivil Engineering form University of Tehran, Iran in1977, another M.Sc. Degree in Geotechnical Engineer-ing from University of Illinois at Urbana-Champaign,USA, in 1979, and the PhD degree from ImperialCollege of Science and Technology, London, UK in1988. He is Professor of Civil Engineering and currentlyis the Director of the GeotechnicalEngineering Studiedand Research Center of Sharif University of Technology(SUT), Tehran, Iran.

Previously he served as the Chairman of Civil En-gineering Department and the Director of EarthquakeEngineering Research Center of SUT. His researchinterests lie in the areas of earthquake geotechnical en-gineering, static and dynamic behavior and character-ization of earth and rock�ll dams, soil characterizationespecially for cemented gravelly sands and unsaturatedcollapsible soils, and implementation of neural networkand neuro-fuzzy in geotechnical engineering problemsand he has accomplished several national researchprojects. Prof. Haeri has supervised several PhDand MSc students and has published more than 30Journal and more than 90 conference papers. He hasalso published 6 books in Persian. Being consultant tomany important engineering projects especially largedams and deep excavations, he has been member ofseveral national committees on various civil engineeringissues as well.

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