ARTICLE

Discrete-continuum analysis of monotonic pile penetration incrushable sandsJianfeng Wang and Budi Zhao

Abstract: This paper presents numerical results from a two-dimensional discrete element method (DEM) simulation study onthe monotonic pile installation in crushable sands. The particle breakage was included in the model by setting a crushable zonearound a pile that was filled with parallel-bonded agglomerates. In the other part of the model, rigid, unbreakable particles areused to minimize the computational cost. Parametric studies were carried out to examine the effects of initial in situ verticalstress, soil void ratio, and particle crushability on the penetration resistance behavior. The validity of the DEM model wasexamined by comparing the simulation data with published results from laboratory centrifuge and calibration chamber tests onmodel pile installation. A variety of DEM analysis techniques were employed to make a detailed discrete-continuum study on thepile penetration mechanisms, particularly on the particle breakage-related soil mechanics incurred during the penetrationprocess. Simulation results show that the in situ stress and particle breakage are the two competing factors dominating the tipresistance behavior. The underlying mechanism was elucidated through the analysis of stress and strain paths derived frompre-assigned sampling windows and their full-field distributions.

Key words: pile penetration, particle breakage, DEM simulation, discrete-continuum analysis, strain path.

Résumé : Cet article présente des résultats numériques d’une simulation a l’aide de la méthode par éléments discrets (MED) entrois dimensions (3D) réalisée sur l’installation d’un pieu monotonique dans des sables écrasables. Le bris des particules a étéinclus dans le modèle en considérant une zone écrasable autour du pieu qui est remplie d’agglomérats liés de façon parallèle.Dans l’autre partie du modèle, des particules rigides et incassables sont utilisées pour minimiser les difficultés de calcul. Desétudes paramétriques ont été réalisées pour examiner les effets de la contrainte verticale initiale in situ, de l’indice des vides dusol et de la broyabilité des particules sur le comportement en résistance a la pénétration. La validité du modèle MED a étéexaminée en comparant les données simulées aux résultats publiés provenant d’essais de laboratoire en centrifugeuse et enchambre de calibrage sur l’installation de pieux. Plusieurs techniques d’analyse MED ont été utilisé pour réaliser une étudediscrète-continue détaillée sur les mécanismes de pénétration des pieux, particulièrement sur la mécanique du bris des parti-cules versus le sol qui se produit durant le processus de pénétration. Les résultats des simulations indiquent que la contrainte insitu et le bris des particules sont les deux facteurs en compétition qui dominent le comportement en résistance a la pointe. Lemécanisme sous-jacent a été élucidé grâce a l’analyse des trajectoires des contraintes et déformations dérivées de fenêtresd’échantillonnages pré-assignées et de leur distribution sur le champ entier. [Traduit par la Rédaction]

Mots-clés : pénétration de pieux, bris de particules, simulation MED, analyse discrète-continue, trajectoire des contraintes.

IntroductionDespite being a subject under wide investigation over the last

50 years, the axial capacity of displacement piles in sand remainshaving large uncertainty in geotechnical engineering (Randolphet al. 1994). The complexity of the problem is created by manyhighly variable factors associated with the mechanical and geo-metrical properties of foundation soil and pile, and the engineer-ing process of pile installation. Substantial research work hasbeen dedicated to the exploration of fundamental mechanismsgoverning the pile–sand interaction during the pile-installationand pile-loading procedures, which is key to the development ofmore scientific, reliable, and economic methods for pile design(e.g., Randolph et al. 1994; Jardine and Chow 1996; Klotz and Coop2001). However, many basic facets of the pile–sand interactionproblem are still not clearly understood.

Apart from the possible high degree of inhomogeneity of foun-dation soil conditions, the primary technical difficulty associatedwith the formulation of pile penetration mechanism stems fromthe accurate and comprehensive account of the soil mechanics

occurring in a special semi-infinite, boundaryless type of problem.A very relevant and important issue in the laboratory chambertest or centrifuge test of model piles, therefore, is to determinethe minimum acceptable size of the testing apparatus that canreasonably reproduce the far field ground condition (e.g., Salgadoet al. 1998). When the soil micromechanics is considered, theproblem becomes much more convoluted as many scale-relatedgeometrical (e.g., relative pile to sand grain size) and mechanical(e.g., soil density and particle breakage) factors emerge into thepicture.

Being aware of the above problems, a number of authors (e.g.,Klotz and Coop 2001; White and Bolton 2004; White and Lehane2004; Yang et al. 2010; Jardine et al. 2013) recently reported find-ings from a variety of high-quality centrifuge or calibration cham-ber tests of instrumented model pile installation, which greatlyimproved our understanding of the pile penetration problem.Advances were made in revealing the lateral stress distributionalong the pile shaft and its evolution during the pile penetrationprocess, as well as their variations as a function of initial soil state,

Received 18 July 2013. Accepted 9 April 2014.

J. Wang and B. Zhao. Department of Civil and Architectural Engineering, City University of Hong Kong, Hong Kong.Corresponding author: Jianfeng Wang (e-mail: jefwang@cityu.edu.hk).

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Can. Geotech. J. 51: 1095–1110 (2014) dx.doi.org/10.1139/cgj-2013-0263 Published at www.nrcresearchpress.com/cgj on 21 April 2014.

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soil crushability, and pile installation method (Klotz and Coop2001; White and Lehane 2004; Lehane and White 2005; Yang et al.2006; Jardine et al. 2013). This information has led to the elucida-tion of several critical aspects of pile shaft resistance behavior,such as interface shearing, particle crushing, and friction fatigue,etc. (White and Lehane 2004; Yang et al. 2010). In addition, Whiteand Bolton (2004), by employing particle image velocimetry (PIV)and a close-range photogrammetry, reported full-field displace-ment, strain fields and their evolutions from a plane-strain modelpile installation study. The experimental evidence based onparticle-scale kinematics provided new insights into the pile pen-etration mechanism.

The discrete element method (DEM), which allows full access tothe particle-scale kinetic and kinematic information, provides analternative tool for the investigation of pile–soil interaction prob-lem. Huang and Ma (1994) perhaps were the first to apply DEM tothe pile penetration study and showed that the penetration be-havior was affected by the loading history. Jiang et al. (2006, 2008)made detailed two-dimensional (2D) DEM analyses on the full-field kinematic variables of the granular ground due to the pene-tration of cone penetration testing (CPT). Recently, advances havealso been made in three-dimensional (3D) DEM simulations ofCPT. Using a virtual calibration chamber filled with a scaled gran-ular equivalent of real sand, Arroyo et al. (2011) investigated therelative cone–chamber size effect on the cone resistance. A similarstudy was carried out by Lin and Wu (2012) on the dependence ofpenetration resistance on the penetrometer diameter. An effortthat is in line with the size and scale problem of CPT was recentlymade by McDowell et al. (2012) to capture the realistic cone toparticle size effect via a particle refinement method. However, inall the above DEM studies, particle breakage was not considered,therefore largely limiting the level of micromechanical insightsobtained. A 2D DEM work that included particle breakage wasreported by Lobo-Guerrero and Vallejo (2005), who modeled par-ticle breakage by replacing a particle that meets the prescribedstress criterion with a few sub-particles and applied this methodto the investigation of pile tip shape effects on the penetrationbehavior (Lobo-Guerrero and Vallejo 2007). However, in their stud-ies, no effort was made to measure local stress and strain aroundthe pile based on discrete data during the penetration process andlimited discussion was given on the particle breakage-related mi-cromechanics underlying the penetration behavior. As an alterna-tive to DEM, Zhang et al. (2013) recently presented a rigorousapproach to incorporate the effects of particle breakage into theformulation of the end-bearing capacity of piles based on thebreakage mechanics theory (Einav 2007a, 2007b).

Based on the above relevant DEM studies, this paper seeks tofurther exploit the potential of DEM in tackling the pile–sandinteraction problem. The major thrust of this paper lies in anin-depth discrete-continuum analysis that reveals the stress andstrain fields around and away from the pile during the penetra-tion process, and thus provides a comprehensive picture of thepenetration mechanism in crushable sands.

Numerical model

2D DEM model of pile–sand interactionThe DEM model is made up of a rectangular container filled

with a well-compacted, poly-dispersed assembly of round parti-cles and a CPT-shaped model pile pushed gradually into the gran-ular foundation at the middle of the box. Taking advantage of themodel symmetry, only the right half of the model with a dimen-sion of 15B (W) × 30B (H) is used (Fig. 1a), where B is the pilediameter and is equal to 8 mm. Both the bottom and right walls ofthe model are fixed. The bottom wall is set to be frictionless butthe right wall is assigned a high friction coefficient of 0.9 to min-imize any relative slip between the particles and the wall. Theratio of model to pile width is equal to 30 in our study, which

agrees with the dimension ratios used in many experimental stud-ies (e.g., Salgado et al. 1998; Bolton et al. 1999; White and Bolton2004). It will be shown later that this dimension ratio is enough toeliminate the far-field boundary effects.

The granular material is composed of rigid disks with diametersuniformly varying between 0.6 mm and 1.2 mm. To accommodateparticle breakage in this study, we define a crushable zone witha size of 2B (W) × 27B (H) surrounding the pile (Fig. 1a). In thiscrushable zone, particle breakage is allowed by the disintegrationof agglomerates that are made of parallel-bonded particle clus-ters. The agglomerates used in this study are composed of 24–30 elementary balls with diameters between 0.069 and 0.278 mm(Fig. 1b). The particle cluster technique was frequently used byDEM researchers in the study of particle breakage behavior (e.g.,Robertson 2000; McDowell and Harireche 2002; Cheng et al. 2004;Wang and Yan 2012, 2013) and has been demonstrated to be aneffective and convenient tool for the investigation of microme-chanics of crushable soils. Although in these previous studies thistechnique was used in 3D simulations, it would work equally wellin 2D simulations as long as there is a large enough number ofelementary balls in any agglomerate for breakage to occur. Thephysical parameters of rigid disks and crushable agglomeratesused in the current study are shown in Table 1.

It needs to be mentioned that no intention exists in the currentstudy to accurately simulate the breakage behavior of real sand par-ticles using the above simplified technique, and the major purposefor including such a particle breakage behavior is to allow the inves-tigation of the particle breakage effects on the pile penetration be-havior that are mainly reflected through the material fabric change.

To create a relatively uniform granular foundation, the multi-layer under-compaction method (UCM) proposed by Jiang et al.(2003) was used to generate and compact the granular material.Specifically, five equal layers of granular materials are sequen-tially deposited and compacted to intermediate void ratios thatare slightly lower than the target void ratio (Jiang et al. 2003). Thecompaction was carried out by moving downwards the top wall toattain a specific intermediate void ratio and after five times of

Fig. 1. DEM model of pile penetration: (a) model geometry;(b) typical agglomerate composed of parallel-bonded disks; (c) layoutof column and row sampling windows.

15B (120 mm)

30B

(240

mm

)

B/2 (4 mm)

0.6-1.2 mm

Crushable Zone

0.6-1.2 mm

27B

(216

mm

)

2B (16 mm)

(a)

(b)

C-2

R-1

R-2

C-1

Strain pathretrievalwindows

0(2 2)x B =C-3C-4

x

y 0( 5)y B =

0( 10)y B =

(c)

0 12y B =

0(2 0.5)x B =

0(2 4)x B =0(2 10)x B =

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such compaction the overall void ratio of the specimen will reachthe target value. After the initial foundation is created, the crush-able zone is introduced into the model by replacing all the rigiddisks within this zone with agglomerates, each having the samediameter as the disk it replaces and is generated following theprocedure described above. Then the whole foundation is recon-solidated under gravity until a complete equilibrium is achieved.

Apparently, an important issue in the above foundation gener-ation process is the selection of the size of the crushable zone. Asimple principle for this is that the size should be large enough toallow all the breakage-related physics that will affect the penetra-tion behavior to be captured. However, a practical limitation forselecting a larger size of the crushable zone is the very high com-putational cost caused by a very large number of particles. For thecurrently adopted size of 2B × 27B, the number of particles in thecrushable zone is approximately 140 000, and approximately170 000 in the whole sample. It will be shown that this size issufficient for accommodating the vast majority of particle break-age events induced by pile penetration and can avoid any artifi-cial, undesired effects along the interface between the crushableand uncrushable zones.

The model pile is made up of two rigid wall segments, and at thebottom they formed a small cone making an angle of 60° withthe horizontal. The wall friction coefficient is set to be 0.5 for thewhole pile, simulating a rough pile–soil interface. After the gran-ular foundation is prepared, the model pile is pushed monotoni-cally into the foundation at a constant rate of 0.1 mm/s. Themaximum penetration depth for the simulations in this studyreached 25B.

Parametric studyWe performed a total number of five simulations in this study

to examine the influence of three model parameters, namely,initial vertical stress field, initial void ratio, and soil crushability.In particular, the initial vertical stress field was varied by em-ploying an artificially raised gravity acceleration (e.g., 100g) thatwas similar to the physical effects attained in a centrifuge test,and the soil crushability was varied by setting different parallelbond strength values (pb_s). The simulation program is shownin Table 2.

Observation and analysis methodTo make a detailed discrete-continuum analysis of the soil me-

chanics occurring due to the pile installation, window-based andfull-field stress and strain calculation techniques were employedto provide a comprehensive picture of the pile penetration mech-anism. These techniques are briefly described below.

Full-field stress and strain distributionsThe full-field shear and volumetric strain distributions will be

generated using the meshless strain calculation method proposedand used by the first author in his previous studies (Wang et al.2007a, 2007b; Wang and Gutierrez 2010; Wang and Yan 2013). Thefull-field stress distributions can be calculated using a grid-basedmethod similar to the strain-calculation method. First, the iden-

tical procedure of grid generation and mapping of grid nodes toindividual DEM particles will be followed. Then, the stress tensorat any grid node can be calculated based on its associated particle.Simply repeating the same calculation for all the grid nodes willgive the full-field distribution of any stress component desired. Toavoid the possible stress discontinuities or fluctuations due to theexistence of floating particles (i.e., particles not carrying any con-tact force), the mean stress tensor of a grid element is calculatedby averaging the stress tensors of its four grid nodes and used inthe plotting of full-field stress distributions.

Sampling window observationIt would be extremely computationally expensive to track the

continuous evolution of the full-field stress and strain during thepile penetration process. A much more convenient and efficientway is to monitor the stress and strain evolutions within thepre-assigned sampling windows. To obtain a full picture of thisinformation over the entire model domain, two rows and fourcolumns of sampling windows are placed underneath and besidethe pile, as shown in Fig. 1c. The sampling windows in the firstcolumn are sized as 0.5B × 0.5B and all other sampling windowsare sized as 1B × 1B. Each sampling window is denoted using a codeof “C-a-b” or “R-a-b”, where C denotes column, R denotes row, a isthe column or row number, and b is the window number in thatcolumn or row.

Results and discussion

Stress–strain data of crushable sandsIt is necessary to show the shear strength of the DEM materials

from a typical element test before we present the pile simulationresults. Figure 2 compares the stress ratio – strain data from thedirect shear simulations on the crushable sands with two differ-

Table 1. DEM parameters of rigid disks and crushable agglomerates.

Parameters Values

Diameters of agglomerate (mm) 0.6–1.2Diameters of elemental ball (mm) 0.069–0.278Density of ball in crushable zone (kg/m3) 2650Density of ball in uncrushable zone (kg/m3) 2492Normal and shear stiffnesses of ball (N/m) 4×108

Friction coefficient of ball 0.5Normal and shear parallel bond strengths (N/m2) 2×107

Normal and shear parallel bond stiffnesses (N/m3) 1.5×1012

Ratio of parallel bond radius to ball radius 0.5

Table 2. Simulation program of parametric study.

Simulation No. Gravity level (g) Void ratioBond strength,pb_s (N/m)

Test 1 50 0.2 2×107

Test 2 100 0.2 2×107

Test 3 150 0.2 2×107

Test 4 100 0.17 2×107

Test 5 100 0.2 1×107

Fig. 2. Comparison of stress ratio – strain curves from DEMsimulations and experiments of direct shear tests (from Tarantinoand Hyde 2005).

v/τ

0 5 10 15

0.0

0.2

0.4

0.6

0.8

1.0

1.2 1 MPa, pb_s = 2x107 N/m 1 MPa, pb_s = 1x107 N/m 3 MPa, pb_s = 2x107 N/m 3 MPa, pb_s = 1x107 N/m 1 MPa, DBS 1.4 MPa, DBS

Stre

ss ra

tio,

Shear strain (%)

' σ

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ent levels of crushability and experimental data from direct sheartests on Dog’s Bay sand (DBS) by Tarantino and Hyde (2005). Thedirect shear simulations were conducted using the DEM modelpreviously developed by the first author (Wang et al. 2007a; Wangand Gutierrez 2010). It can be seen in Fig. 2 that under the same orsimilar confining pressure of 1 MPa, the overall stress ratio – straincurves from the DEM simulations lie below those from the directshear tests. The critical-state friction angles given by the simula-tions for the low-crushability (i.e., with parallel bond strengthvalue 2 × 107 N/m) sand and high-crushability (i.e., with parallelbond strength value 1 × 107 N/m) sand are about 24° and 22°,respectively, which are lower than the critical-state friction angleof about 33° given by the experiment for DBS. When the confiningpressure is raised to 3 MPa, which is close to the maximum con-finement level encountered in our pile simulations, the frictionangles of the two kinds of materials are further reduced to about21° and 16°, respectively. Although the shear strengths of the DEMmaterials are lower than that of a real crushable sand, the effectsof different levels of DEM particle crushability on the pile pene-tration mechanism can be fully captured and demonstrated, aswill be shown below. The simulated shear strengths of crushablesands are close to those obtained by Jiang et al. (2006) from biaxialsimulations and used also in the 2D simulations of pile penetra-tion in uncrushable sands.

Tip and shaft resistance curvesFigures 3 and 4 show the average pile tip resistance qb and shaft

resistance qs, respectively, throughout the penetration processfrom all the simulations. The results are categorized to show theeffects of the three model variables on the penetration resistancein three sub figures. To demonstrate the validity of our simulationresults, some measured data of model pile resistance from thecentrifuge tests by Klotz and Coop (2001) are also included in Fig. 3and Fig. 4 for comparison. It needs to be mentioned that thesimulation data has been plotted using the equivalent prototypedepth due to the employment of artificial gravitation fields thatare intended to emulate the centrifuge test effects. It is seen inFig. 3a that the three gravity levels used in the simulations, withall the other variables being the same, produce a unique qb curveagainst the prototype depth. The feature is also evident from thetwo selected sets of centrifuge test data on Leighton Buzzard sand(LBS) included in Fig. 3a, whose overall distribution is in goodagreement with the simulation data although lower magnitudesof qb are found in the latter. However, when replotted against theactual model penetration depth, the simulation data are decom-posed into three distinct curves, as shown in the inset diagram ofFig. 3a.

The result adequately verifies the effectiveness of the model toreproduce and reflect the in situ vertical stress field effects on the

Fig. 3. Unit base resistance qb versus prototype depth under the influence of (a) gravity level, (b) parallel bond strength, (c) void ratio, and(d) normalized curves by qb

f at final depth (from Klotz and Coop 2001).

200150100500

0 2 4 6Unit base resistance, : MPa

Mod

el p

enet

ratio

nde

pth

(mm

)

bq

bq

bq

(a) (b)

(c)

20

15

10

5

00.0 0.4 0.8 1.2

Normalized base resistance,

pb_s = 1x107 N/m pb_s = 2x107 N/m DBS (b) LBS (200g)

Prot

otyp

e de

pth

(m)

bfbq(d)

201510

50

0 1 2 3Unit base resistance, : MPa

Mod

el p

enet

ratio

nde

pth

(mm

)

bq

bq

30

25

20

15

10

5

00 5 10 15 20

50g 100g 150g LBS (100g) LBS (200g)

Unit base resistance, (MPa)

Prot

otyp

e de

pth

(m)

20

15

10

5

00 2 4 6 8

Unit base resistance, (MPa)

Loose Dense DBS (L) DBS (D)

Prot

otyp

e de

pth

(m)

20

15

10

5

00 2 4 6 8 10

pb_s = 2x107 N/m pb_s = 1x107 N/m DBS (a) DBS (b)

Unit base resistance, (MPa)

Prot

otyp

e de

pth

(m)

q

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penetration behavior. This element of the model's capability isessential, because the in situ stress field is one of the crucialfactors dominating the pile resistance behavior (Klotz and Coop2001) and will be closely examined together with the soil crush-ability in this paper.

The tip resistance curves in Fig. 3a exhibit a nearly linear profilewith little sign of a limiting tip resistance value at the end of thepenetration process. Note these results are obtained in the low-crushability sand adopting the higher parallel bond strength of2 × 107 N/m. Clear effects of the other two variables on the pene-tration resistance are illustrated in Figs. 3b–3c and 4b–4c. Prototypedepth is again used in these plots, but it should be noted that nodifference will arise if the actual model penetration depth is usedbecause the same gravity level of 100g is used in these cases. Theincrease of soil crushability via the decrease of parallel bondstrength results in an appreciable reduction of the tip resistance,especially at larger penetration depths. Interestingly, the nonlin-ear profile of the higher-crushability sands exhibits a trend of aconstant value after about 8 m (see inset diagram of Fig. 3b). Thisfeature can also be identified in the centrifuge test data of DBSincluded in Fig. 3b although the turning point marking the limit-ing tip resistance value may occur at a smaller depth.

To facilitate the comparison between the degrees of non-linearity of the DEM data and centrifuge data of the tip resistancehaving different magnitudes, the data in Figs. 3a and 3b are replot-

Fig. 4. Unit shaft resistance qs versus prototype depth under theinfluence of (a) gravity level, (b) parallel bond strength, and (c) voidratio (from Klotz and Coop 2001).

sq

sq

sq

sq

200150100

500

0.00 0.04 0.08

Average unit shaft resistance, (MPa)

Mod

el p

enet

ratio

nde

pth

(mm

)

(a)

(b)

(c)

20

15

10

5

00.00 0.02 0.04 0.06 0.08Average unit shaft friction, (MPa)

Prot

otyp

e de

pth

(m)

pb_s = 1x107 N/m pb_s = 2x107 N/m DBS LBS

30

25

20

15

10

5

00.00 0.03 0.06 0.09 0.12

Average unit shaft friction, (MPa)

Prot

otyp

e de

pth

(m)

50g 100g 150g LBS (100g) LBS (200g)

20

15

10

5

00.00 0.04 0.08 0.12 0.16 0.20

Loose Dense LBS (L) LBS (D)

Average unit shaft friction, (MPa)

Prot

otyp

e de

pth

(m)

Fig. 5. Initial average (a) vertical and (b) horizontal stressdistributions in tests 2 and 4.

30

25

20

15

10

5

00 200 400 600 800 1000

Initial vertical stress, (kPa)

Test 2 Test 4

v0'σ

h0'σ

0yB

0yB

(a)

(b)

30

25

20

15

10

5

00 200 400 600 800 1000

Initial horizontal stress,

(kPa)

Test 2 Test 4

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ted in Fig. 3d by normalizing each curve to its value at the finaldriven depth. It is clear that the data of high-crushability sandsfrom both DEM simulation and centrifuge test (i.e., DBS) exhibitmuch higher degrees of nonlinearity than those of low-crushabilitysands. Apparently the linear distribution of the tip resistance sug-gests a consistent penetration mechanism independent of thepenetration depth that is dominated by the in situ stress field.

This reconfirms the fallacy of adopting a limiting value of tipresistance for low-crushability sands in many design codes (Klotzand Coop 2001). In contrast, the higher nonlinearity with a trendtowards a limiting value observed in a high-crushability sand islargely attributed to the massive amount of particle breakagecaused by the pile penetration overriding the in situ stress effects.Detailed micromechanical evidences supporting the above state-ment will be presented later.

Fig. 6. Typical sampling window-based stress distributionsthroughout the penetration process from test 2: (a) vertical stressdistributions from C-1 windows; (b) horizontal stress distributionsfrom C-2 windows; (c) shear stress distributions from C-2 windows(counterclockwise is positive).

C-1

v'σ

h'σ

0yB

C-2

C-2

(a)

(b)

(c)

30

25

20

15

10

5

00 600 1200 1800 2400 3000

Vertical stress, (kPa)

D = 0 D = 5B D = 10B D = 15B D = 20B D = 25B

30

25

20

15

10

5

00 400 800 1200

D = 0 D = 5B D = 10B D = 15B D = 20B D = 25B

Horizontal stress, (kPa)

30

25

20

15

10

5

0-200 0 200 400

D = 0 D = 5B D = 10B D = 15B D = 20B D = 25B

Shear stress, (kPa)

0yB

0yB

τ

Fig. 7. Normalized vertical stress distributions from C-1 windowsthroughout the penetration process: (a) test 2; (b) test 4; (c) test 5.

Test 2

Test 4

Test 5

v'σ

0yB

(a)

(b)

(c)

30

25

20

15

10

5

00 5 10 15 20

D = 5B D = 10B D = 15B D = 20B D = 25B

Normalized vertical stress,

30

25

20

15

10

5

00 5 10 15 20

D = 5B D = 10B D = 15B D = 20B D = 25B

Normalized vertical stress,

0yB

0yB

30

25

20

15

10

5

00 5 10 15 20

D = 5B D = 10B D = 15B D = 20B D = 25B

Normalized vertical stress,

'σ/ v0

v'σ 'σ/ v0

v'σ 'σ/ v0

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Strong influence of the initial void ratio of the sand is alsoobserved in Figs. 3c and 4c, where a reduction of the void ratiofrom 0.2 to 0.17 leads to a nearly 100% increase of both tip andshaft resistance values at any depth. Similar effects of void ratioare found in the centrifuge test data included in Figs. 3c and 4c. Itis worth pointing out that this significant effect of soil relativedensity cannot be fully explained by the in situ stress field (i.e.,local confinement). As shown in Fig. 5, the initial vertical and

horizontal stress distributions from tests 2 and 4 are found to bevery close. It is also unlikely to be caused by the model boundaryeffects, which will be demonstrated later. Indeed, the source ofthe relative density effect lies in the dense granular packingwhich could support the development of higher deviatoric stress.

Window-based stress distributionsFigure 6 shows the typical distribution of the average stress

components from the column sampling windows at different pile

Fig. 8. Normalized horizontal stress distributions from C-2 windowsthroughout the penetration process: (a) test 2; (b) test 4; (c) test 5.

Test 2

Test 4

Test 5

0yB

(a)

(b)

(c)

0yB

0yB

30

25

20

15

10

5

00 2 4 6 8

D = 5B D = 10B D = 15B D = 20B D = 25B

Normalized horizontal stress,

30

25

20

15

10

5

00 2 4 6 8

D = 5B D = 10B D = 15B D = 20B D = 25B

Normalized horizontal stress,

30

25

20

15

10

5

00 2 4 6 8

D = 5B D = 10B D = 15B D = 20B D = 25B

Normalized horizontal stress,

'σ 'σ/h v0

'σ 'σ/h v0

'σ 'σ/h v0

Fig. 9. Normalized shear stress distributions from C-2 windowsthroughout the penetration process: (a) test 2; (b) test 4; (c) test 5(counterclockwise is positive).

Test 2

Test 4

Test 5

0yB

(a)

(b)

(c)

τ

0yB

0yB

30

25

20

15

10

5

0-1.0 -0.5 0.0 0.5 1.0

D = 5B D = 10B D = 15B D = 20B D = 25B

Normalized shear stress,

30

25

20

15

10

5

0-1.0 -0.5 0.0 0.5 1.0

D = 5B D = 10B D = 15B D = 20B D = 25B

Normalized shear stress,

30

25

20

15

10

5

0-1.0 -0.5 0.0 0.5 1.0

D = 5B D = 10B D = 15B D = 20B D = 25B

Normalized shear stress,

'σ/ v0

τ 'σ/ v0

τ 'σ/ v0

Wang and Zhao 1101

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driven depths from test 2. Only selected data of the average verti-cal stress in C-1 windows and average horizontal stress and shearstress in C-2 windows are presented because they are most closelyrelated to the pile resistance behavior. For every stress distribu-tion curve shown in Fig. 6, the peak value occurs approximately asthe pile tip levels with the window centre. For the data in C-1windows, each curve starts from the window immediately belowthe pile tip since the soil in all the windows above has been dis-placed (Fig. 6a). A very large stress gradient is found to exist withina zone about 4�6B beneath the pile tip, followed by a nearlyconstant profile extending close to the model bottom. Further-more, the stress gradient and the subsequent constant value in-crease with the pile driven depth, with the latter reaching about5 times the initial in situ vertical stress at a driven depth of 20B(Fig. 6a). The envelope connecting all the peak points at variousdriven depths in Fig. 6a represents a close approximation of the qbcurve, although the envelope has slightly lower magnitudes due

to the homogenization of the stress and strain made within thesampling windows. For the data in C-2 windows representing thevery-near field adjacent to the pile shaft, the primary influencezone is found to extend 2�4B above and below the pile tip, withthe values beyond the primary influence zone being much closerto the in situ values (Figs. 6b and 6c). No clear evidence of thedegradation of radial effective stress or shaft resistance with theincreasing penetration depth is spotted, as has been widely re-ported in field and centrifuge tests on instrumented piles (e.g.,White and Lehane 2004) and attributed to the large number ofload cycles imposed by pile driving or jacking, a factor that wasnot considered in this study.

To better demonstrate the effects of the variables of concern onthe penetration mechanism, we show the stress distributions,which are normalized with respect to the corresponding initial insitu vertical stress at any depth in Figs. 7–9. Simulation data fromtests 2, 4, and 5 are selected to allow an investigation into the

Fig. 10. Survival rate distribution (SRD) of agglomerates at the end of simulation and evolution of particle size distribution (PSD) within thecrushable zone: (a) SRD in test 2; (b) SRD in test 5; (c) experimental result reproduced from Yang et al. (2010); (d) PSD evolution in test 2; (e) PSDevolution in test 5.

0 5 10

-25

-20

-15

-10

-5

0

0.0

0.2

0.4

0.6

0.8

1.00 1 2-27

-26

-25

-24

-23

-22

-21

-20

0 1 2-27

-26

-25

-24

-23

-22

-21

-20

0 5 10

-25

-20

-15

-10

-5

0

Zone 1: highcrushing

Zone 2: significantcrushing

Zone 3: moderatecrushing

yB

x B

(a) (b) (c)

Zone 1

Zone 2

Zone 3

Zone 4

(d) (e)

yB

yB yB

x B x B

x B

0.4 0.8 1.2

1

10

100

Perc

enta

ge fi

ner b

y w

eigh

t

Particle diameter (mm)

D = 0 D = 5B D = 10B D = 15B D = 20B D = 25B

0.4 0.8 1.2

1

10

100

Perc

enta

ge fi

ner b

y w

eigh

t

Particle diameter (mm)

D = 0 D = 5B D = 10B D = 15B D = 20B D = 25B

1102 Can. Geotech. J. Vol. 51, 2014

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influence of void ratio and soil crushability by comparing test 2 tothe other two tests respectively.

It can be found that the general profiles of the normalized stressratios are similar to their corresponding stress profiles but thepeak magnitudes of the normalized curves show much less varia-tions throughout the penetration process, with the peak values of�v

′ /�v0′ varying between 5 and 14, those of �h

′ /�v0′ between 2 and 5,

and those of �/�v0′ between 0.4 and 0.8. The small variations of the

peak normalized stress ratios suggest the dominant control of thein situ vertical stress on the penetration resistance behavior, withthe void ratio and soil crushability being the interfering factors ofthis mechanism. Strong effects of the void ratio are again mani-fested in the overall much higher peak magnitudes of all the threegroups of the normalized curves by comparing tests 2 and 4. Sucha result can be well predicted using the normalized in situ stressratio (with respect to the mean stress at the critical state) sug-gested by Klotz and Coop (2001).

The soil crushability effects can also be discerned from the over-all much lower and gently decreasing peak values of �v

′ /�v0′ with

the increasing penetration depth from test 5 (Fig. 7c), which isconsistent with the trend of a limiting tip resistance observedpreviously. Given the identical initial vertical stress distributionfor tests 2 and 5, the attenuation of the in situ vertical stress effectis apparent and microscopically caused by a significant amount ofparticle crushing which hinders the development of local dila-tancy and shear-induced anisotropy. This mechanism has beenfully demonstrated in the fundamental studies on the mechanicalbehavior of crushable sands conducted previously by the firstauthor (Wang and Yan 2012, 2013). Little work in the literature,however, is known to the authors that attempt to explain thelinkage between soil crushing and pile tip resistance from themicroscopic point of view.

More direct information of particle crushing from the simula-tions is given in Fig. 10, in which the survival rate distribution ofagglomerates and the evolution of particle size distribution (PSD)within the crushable zone from tests 2 and 5 are shown. Thesurvival rate is calculated as the ratio of the number of existingparallel bonds to the total number of ball contacts per unit area. Itis interesting to find in Figs. 10a and 10b that three or four zoneswith increasing values of survival rate are developed from the pileshaft towards the radial direction. This distribution is very similarto the one described by Yang et al. (2010) inferred from the exper-imental observations, where the three zones with differentintensity levels of shearing are distinguished using the visual ob-servation and the capillary suction-adherence criterion, the latterbeing a direct reflection of the change of the average inter-grainpore size as a consequence of significant particle breakage. It isnoted that all the crushing zones start from beneath the pile tipand extend over the entire pile shaft. The particle crushing mostlytook place in front of the pile tip then the fragments migrated tothe side and coated the pile shaft, which is identical to the resultsobtained by Lobo-Guerrero and Vallejo (2005). However there is atrend of decreasing thickness of the high crushing zone (i.e., zone 1)away from the tip, which is opposite to the experimental trend(Yang et al 2010). This is probably again due to the absence ofintensive cyclic shearing along the shaft in our simulations, re-flecting only the particle crushing induced by the pile tip com-pression.

Figures 10d and 10e show the evolutions of PSD within the entirecrushable zone from tests 2 and 5. It is seen that the PSD curvesstay concave upwards and rotate around the maximum particlesize. Due to the higher particle crushability, the PSD in test 5approaches closer to the linear distribution in the double logarith-mic graph, suggesting a trend towards the fractal distribution(McDowell and Bolton 1998). However, the PSD does not seem toconverge towards a stable grading in either case. It should benoted that, although the current numerical study is conducted in

2D, the particle-cluster technique employed for the breakage sim-ulation is fully effective in producing a meaningful result of PSDevolution that is comparable to that from a previous 3D DEMstudy employing the same technique (Wang and Yan 2013).

Window-based strain pathsNext, we present simulation data of strain path from the sam-

pling windows. Figure 11 shows the typical evolutions of totalnatural horizontal and vertical strains calculated within C-2 win-dows from test 2. It needs to be mentioned that the natural strainwas particularly used in this and the next three figures to permita direct comparison with the PIV results of White and Bolton(2004). The procedure to calculate the natural strain and rotationtensors is identical to that of White and Bolton (2004).

It is evident in Fig. 11 that similar patterns hold for the strainprofiles from windows at various elevations: the horizontal strainpaths are featured with an initial extension followed by a sharpreversal into a strong compression and then a quasi-constant re-gime; whereas the vertical strain paths are featured with an initialcompression followed by a sharp reversal into a strong extensionand then a quasi-constant regime too. Both strain reversals occurwhen the pile tip levels with the window centre, echoing thesharp unloading event of the soil element from that moment. The

Fig. 11. Natural (a) horizontal and (b) vertical strain paths from C-2windows throughout the penetration process from test 2.

(a)

(b)

xxεyyε

0 5 10 15 20 25

-0.1

0.0

0.1

0.2

0.3

Hor

izon

tal s

train

,

Normalized driven depth, D/B

C-2-14 C-2-16 C-2-18 C-2-20 C-2-22 C-2-24

C-2-2 C-2-4 C-2-6 C-2-8 C-2-10 C-2-12

0 5 10 15 20 25

-0.2

-0.1

0.0

0.1

0.2

0.3 C-2-14 C-2-16 C-2-18 C-2-20 C-2-22 C-2-24

C-2-2 C-2-4 C-2-6 C-2-8 C-2-10 C-2-12

Ver

tical

stra

in,

Normalized driven depth, D/B

Wang and Zhao 1103

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final constant strain values after the passing of the pile tip are alsofound not to vary much, agreeing with the experimental observa-tions of White and Bolton (2004). The above results imply again aconsistent penetration mechanism from the soil deformationpoint of view and verify the kinematic constraint condition (i.e.,zero strain increment) beside the pile shaft. They also serve as thebasis of the strain path analysis approach taken by White andBolton (2004), in which the penetration process is treated as theflow of a soil element located at any elevation towards the tip of astationary pile.

Figures 12–14 illustrate the strain paths from selected simula-tions obtained using the same approach of White and Bolton(2004). Specifically, three strain path retrieval windows at thesame depth of 12B were chosen to produce all the strain path data(Fig. 1c). Comparisons to their typical measured data on LeightonBuzzard sand and Dog’s Bay sand are also included in Figs. 12 and13, respectively. In each figure, data of soil elements in the verynear field, near field, and far field are presented with the corre-sponding ratios of the distance between the soil element and thepile centreline to the pile radius, 2x0/B, equal to 2, 4, and 10,respectively, from our simulations, and the corresponding ratiosfrom White and Bolton (2004) are labeled in Figs. 12 and 13; and2h/B denotes the normalized vertical distance between the soilelement and the pile tip.

It is seen in Figs. 12 and 13 that all the profiles of horizontalstrain, vertical strain, and rotation have overall good agreementwith the experimental data of White and Bolton (2004). The maindivergence appears to be the much later development of the soilstrain in the very near and near fields in our simulations. Theauthors assume that the smaller stress influence zone ahead ofthe pile tip (Figs. 7 and 8) is caused by the large gravity fieldsimplemented in the simulations. However, the reproduction ofthe stress and rotation paths on the qualitative level, particularlythe marked strain reversal behavior, attests to the model’s capa-bility to simulate the critical soil deformation behavior before andafter the passing of the pile tip.

The soil mechanics at various distances from the pile shaft arefound to be affected strongly by soil crushability and initial voidratio by comparing Figs. 13 and 14 to Fig. 12. In test 2 with the highvoid ratio and low particle crushability, an initial very slight vol-umetric compression followed by a strong dilation when the piletip is within a distance of 5 pile radii, and then a stronger com-pression after the passing of the tip is observed in the very nearfield (Fig. 12a). When the particle crushability is high, there is anabsence of dilation before the passing of the tip, followed by anabrupt, severe turn into the compression due to a massive amountof particle breakage (Fig. 13a). These results also agree with theobservation by White and Bolton (2004) on the less crushable

Fig. 12. Strain and rotation paths from strain path retrieval windows in test 2; for all strain components, compression is positive; forrotation, counterclockwise is positive (from White and Bolton 2004).

Very near field

Near field

Far field Rotation

xxεyyεvε

xxεyyε

(LBS)(LBS)

0(2 / 2)x B =0(2 / 2)x B =0(2 / 2)x B =

0(2 / 1.99)x B =0(2 / 1.99)x B =

vε (LBS) 0(2 / 1.99)x B =

xxεyyεvε

0(2 / 4)x B =0(2 / 4)x B =0(2 / 4)x B =

xxεyyε

(LBS)(LBS)

0(2 / 3.92)x B =0(2 / 3.92)x B =

vε (LBS) 0(2 / 3.92)x B =

xxεyyεvε

0(2 / 10)x B =

0(2 / 10)x B =0(2 / 10)x B =

xxεyyε

(DBS)(DBS)

0(2 / 10.03)x B =0(2 / 10.03)x B =

vε (DBS) 0(2 / 10.03)x B =

-25 -20 -15 -10 -5 0 5

-0.3

-0.2

-0.1

0.0

0.1

0.2

Stra

in

Position relative to pile tip, 2h/B

-25 -20 -15 -10 -5 0 5

-0.2

-0.1

0.0

0.1

0.2

Stra

in

Position relative to pile tip, 2h/B

-25 -20 -15 -10 -5 0 5

-0.2

-0.1

0.0

0.1

0.2

Stra

in

Position relative to pile tip, 2h/B

-25 -20 -15 -10 -5 0 5

-5

5

15

25 Very near field Near field Far field LBS (Very near field) LBS (Near field) LBS (Far field)

Rot

atio

n: d

egre

es

Position relative to pile tip, 2h/B

1104 Can. Geotech. J. Vol. 51, 2014

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Leighton Buzzard sand and highly crushable Dog’s Bay sand. It isworth pointing out that the volumetric strain reversal seen in test 2is indeed caused by the rotation of the principal stress (i.e., fromvertical to horizontal) as the soil element passes the tip. The sub-sequent unloading event continues in both processes of thevolumetric compression and principal stress rotation until thecritical state with constant volume is reached. For test 4 withthe low void ratio, the strain reversal is much less pronounced,making the entire volumetric strain path a roughly constantprofile. This implies that the soil element does not deviatesignificantly from the critical state throughout the process dueto the combined effects of initial higher confinement and moresignificant particle breakage (Fig. 14a).

The overall pattern of the volumetric strain behavior in thenear field is similar to that of the very near field but less pro-nounced due to the reduced stress field (Figs. 12b, 13b, and 14b). Inthe far field, the strain reversal phenomenon almost disappears ineach test (Figs. 12c, 13c, and 14c).

Model boundary effectsIt is necessary to demonstrate the model boundary effects in

our study. From Figs. 12c, 13c, and 14c, it is already seen that thestrains are reduced to a very low level at 2x0/B = 10. Since soils are

uncrushable in this region, the initial void ratio dominates thevolumetric strain behavior, with slight compression and dilationfound in tests 2 and 4, respectively. More information about theboundary effects is given by the distributions of normalized hor-izontal stress from the row windows up to the lateral boundary, asshown in Fig. 15. It should be mentioned that the normalization inFig. 15 is made with respect to the initial in situ horizontal stressto better depict any boundary effect. It is found that at the twoselected penetration depths of 5B and 10B, the normalized hori-zontal stress at the elevation of the pile tip decays rapidly to anearly constant value of 2 or less in a distance of approximately 7�8B.The stress distributions from the row windows above and belowthe pile tip have all constant profiles with values less than 2. Thisobservation indicates further that all the pile-induced soil me-chanics has been covered by the current model and no severelateral boundary effect is introduced.

Full-field stress and strain distributionsFinally, we present the full-field shear stress and incremental

shear strain and volumetric strain distributions, the typical exam-ples of which are shown in Figs. 16 and 17. The shear stress dataplotted were the deviatoric stress � of the plane-strain stress ten-sor, which was also normalized with respect to the initial in situ

Fig. 13. Strain and rotation paths from strain path retrieval windows in test 5; for all strain components, compression is positive; forrotation, counterclockwise is positive (from White and Bolton 2004).

Wang and Zhao 1105

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vertical stress �v0′ , as done in Fig. 9. Since the current problem

involves extremely large strain in soils near the pile shaft andaround the pile tip, the currently deformed ground, instead of theinitial ground configuration (before pile installation), was used asthe reference configuration for the calculation of incrementalshear strain (��xy) and volumetric strain (��v) incurred within thenext pile advancement of 1B to obtain a better picture of the localsoil deformation around the tip. It is first interesting to find thattwo inclined bands of shear stress localization emanate from thepile tip towards lower- and upper-right, respectively, both makingan angle of about 45° from the horizontal, especially at a largerpenetration depth. The direction of emanation apparently marksthe principal stress direction around and away from the pile tip.The opposite signs of the shear stress in the two bands areconsistent with the principal stress rotation across the tip, whichcauses the strain reversal phenomenon. The high stress zone isconcentrated around the tip and decays gradually along the direc-tion of emanation. As compared to test 2, the high crushable soilin test 5 results in less pronounced emanation bands of localizedstress, particularly below the pile tip (Figs, 17a and 17b), suggestingagain the attenuation of the in situ vertical stress effects due tomassive particle breakage.

From the plots of shear strain distribution, it is found that themajor zone of strain localization extends from the pile tip to adistance of approximately 5B�7B in the radial direction and up-wards along the pile shaft as well (Figs. 16c, 16d and 17c, 17d).Similar patterns of strain localization featured with a “nose cone”beneath the tip and several shear bands with opposite signs ofshear strain curving from below the pile tip around to theupward direction are observed at two different penetrationdepths (Figs. 16c and 16d). Such a pattern exhibits both features ofcavity expansion (Vesic 1972; Yu and Houlsby 1991; Salgado et al.1997) and bearing capacity-type failure, the latter failing to beobserved by White and Bolton (2004), probably because the incre-mental displacement and (or) strain was not used in their study.For the case of high-crushable soil (i.e., test 5), the feature ofbearing capacity failure is less pronounced because the significantparticle breakage greatly reduces the soil dilation (Figs. 17c and 17d).Such a trend, however, also exists in the case of low-crushable soil(i.e., test 2) as the penetration depth becomes larger, resulting inmore particle breakage as well. The volumetric strain fields fromboth tests exhibit similar patterns to those of the shear strainfields, with the high volumetric contraction zones fully coveredby the crushable zone (Figs. 16e, 16f and 7e, 17f). A smooth transi-

Fig. 14. Strain and rotation paths from strain path retrieval windows in test 4; for all strain components, compression is positive; forrotation, counterclockwise is positive.

1106 Can. Geotech. J. Vol. 51, 2014

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tion across the boundary between the crushable and uncrushablezones is found. This observation, together with the results shownin Figs. 10a and 10b, indicate the adequate effectiveness and valid-ity of the model setting of the crushable zone.

Concluding remarksThis paper reexamines the problem of close-ended pile installa-

tion in crushable sands using the discrete element simulationmethod. Through the careful construction of the pile–sand inter-action model and the application of a series of DEM analysis tech-niques, we presented a detailed and in-depth discrete-continuumstudy on the pile penetration mechanism, elucidating the effectsof and interplay between the in situ vertical stress field, soil crush-ability, and void ratio on the penetration behavior. By comparingthe simulation results with published experimental data of modelpile installation in centrifuge and calibration chamber tests, wedemonstrated the high capabilities of the model in reproducingmany facets of the soil mechanics during the installation processseen in the laboratory or field, particularly the dominant influ-ence of the in situ vertical stress on the tip resistance in a low-crushability sand, the competition between particle breakage andin situ stress in controlling the tip resistance as the soil crushabil-ity increases, as well as the essential strain reversal phenomenonin a soil element flowing past a “stationary” pile. It should bestressed that achieving the understanding of these mechanisms isnot affected by the quantitative disparities between the simula-

tion and experimental data, which is resulted from the simplifi-cation of the reality by the current model and the imperfectmodel validation process. No significant boundary effects due tothe current plane-strain model employing rigid disks, based onthe comparison with the plane-strain experimental results, werefound. This is probably because the current DEM materials exhib-ited an overall lower strength than the real sands.

Attributed to the unique capability of DEM in providing allparticle-scale data, this paper offers rich insights into the micro-mechanical processes and mechanisms underlying a range ofpenetration behavior that was known to be scientifically and prac-tically important but not fully understood yet. Notable examplesinclude the semi-constant tip resistance profile at larger penetra-tion depths in high-crushability sands, which is caused by signif-icant particle breakage prevailing against the in situ stress, andthe strain reversal behavior after the passing of the tip, which iscaused by the principal stress rotation. These and many othernovel insights have advanced our understanding of the pile mono-tonic penetration mechanism in crushable sand.

However, due to the absence of the cyclic loading along the pileshaft that commonly occurs in the dynamic pile driving processand the inclusion of soil creep behavior in our simulations, someimportant aspects of penetration behavior cannot be captured,including shaft friction fatigue, densification of an intensiveshearing zone along the shaft, pile aging, and radial relaxation.

Fig. 15. Normalized horizontal stress distributions in R-1 and R-2 windows at selected penetration depths: (a and c) test 2; (b and d) test 4.

Wang and Zhao 1107

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Fig. 16. Full-field stress and strain distributions from test 2: (a and b) normalized shear stress (�/�v0′ ) distributions at (a) D = 5B and (b) D = 15B;

(c and d) incremental shear strain (��xy) distributions at (c) D = 5B and (d) D = 15B; (e and f) incremental volumetric (��v) strain distributions at(e) D = 5B and (f) D = 15B (for shear stress and shear strain, counterclockwise is positive; for volumetric strain, contraction is positive).

0 5 10

-25

-20

-15

-10

-5

0

0 5 10

-25

-20

-15

-10

-5

0

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

0 5 10

-25

-20

-15

-10

-5

0

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0 5 10

-25

-20

-15

-10

-5

0

0 5 10

-25

-20

-15

-10

-5

0

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0 5 10

-25

-20

-15

-10

-5

0

(a) (b)

(c) (d)

x B

yB

(e) (f)

x B

yB

x B

yB

x B

yB

x B

yB

x ByB

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Fig. 17. Full-field stress and strain distributions from test 5: (a and b) normalized shear stress (�/�v0′ ) distributions at (a) D = 5B and (b) D = 15B;

(c and d) incremental shear strain (��xy) distributions at (c) D = 5B and (d) D = 15B; (e and f) incremental volumetric strain (��v) distributions at(e) D = 5B and (f) D = 15B (for shear stress and shear strain, counterclockwise is positive; for volumetric strain, contraction is positive).

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These issues are currently under investigation using an improvedmodel that incorporates soil creep and aging effects.

AcknowledgementsThe study presented in this article was supported by the

General Research Fund CityU No. 122813 from the Research GrantCouncil of the Hong Kong SAR and Research Grant No. 51109182and 51379180 from the National Science Foundation of China.

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1110 Can. Geotech. J. Vol. 51, 2014

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