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    A particulate-scale investigation of cemented

    sand behavior

    Y.-H. Wang and S.-C. Leung

    Abstract: In this paper, triaxial tests and numerical simulations using the discrete element method (DEM) are combined

    to explore the underlying mechanisms of the unique behavior of artificially cemented sands. The experimental results

    show that strength enhancement, volumetric dilation, and the shear banding associated failure mode are observed in Port-

    land cement sand; these features become more pronounced with increasing cement content. Different responses are found

    in gypsum-cemented sand even though both types of cemented sand specimens were prepared under very similar void ra-

    tios before shearing. The DEM simulations on the Portland cement sand were carried out under two particular arrange-

    ments (i.e., the use of small cementing particles and flexible membrane boundaries). The simulation results reveal that

    particles in the bonding network jointly share the loading and many micro force-chains associated with cementation are

    created. Compared with uncemented sand, a more stable and stronger forcechain complex subjected to smaller force con-centration is formed in cemented sand, which gives rise to higher strength. Intensive bond breakage, concentrated relative

    particle movement, column-like force chains, great particle rotation, and high local porosity are found inside the shear

    band. The bonded clusters remain at large strains to help stabilize the particle arch and therefore to maintain the volumet-

    ric dilation.

    Key words: discrete element method, forcechain distribution, shear banding, volumetric dilation, bonded cluster.

    Resume : Dans cet article, des essais triaxiaux et des simulations numeriques utilisant la methode des elements discrets

    (DEM) sont combines pour explorer les mecanismes sous-jacents du comportement unique dans les sables cimentes artifi-

    ciellement. Les resultats experimentaux montrent quon observe une bonification de la resistance, une dilatation volume-

    trique, et un mode de rupture associes aux bandes de cisaillement dans le sable-ciment Portland; ces caracteristiques

    deviennent plus prononcees avec laugmentation de ciment. On trouve des reponses differentes dans le sable cimente au

    gypse meme si les deux specimens ont ete prepares avec des indices des vides tres similaires avant le cisaillement. Les si-

    mulations en DEM sur le sable-ciment Portland ont ete realisees dans deux arrangements particuliers (c.-a-d., lutilisation

    de petites particules de cimentation et des frontieres de membranes flexibles). Les resultats de la simulation revelent queles particules dans le reseau de bandes partagent conjointement la charge, et plusieurs cha nettes de microforces associees

    a la cimentation sont creees. En comparaison avec le sable non cimente, un complexe plus fort et plus stable de cha nettes

    de forces assujetti a une concentration de forces plus petites se forme dans le sable cimente, ce qui donne naissance a une

    resistance plus elevee. A linterieur des bandes de cisaillement, on trouve des bris intenses de liens, un mouvement relatif

    des particules, des chanettes de forces sous forme de colonnes, de fortes rotations de particules, et une forte porosite lo-

    cale. Les agglomerats lies survivent a de grandes deformations pour aider a stabilizer larche de particules et ainsi mainte-

    nir la dilatation volumetrique.

    Mots-cles : methode delements discrets, distribution de chanettes de forces, bandes de cisaillement, dilatation volume-

    trique, agregat lie.

    [Traduit par la Redaction]

    IntroductionCemented sands are widely found in nature, for example

    in aged sedimentary deposits. As a matter of fact, cementa-tion is often observed during the early diagenesis process(Pettijohn et al. 1987). Natural cementation originates fromdifferent sources, for example, from the precipitation of cal-cite, silica, iron oxides, and even clays (Santamarina et al.

    2001; Mitchell and Soga 2005). Apart from natural cementedsoils, artificially produced cemented soils are often encoun-tered in projects where soil is improved by mixing it withcement or chemicals. Although the formation of cementedsoils is complicated, general features regarding the cementa-tion effects on soil properties can still be observed in a col-lective way based on the experimental findings: (i) thestrength (dynamic and static) and small-strain stiffness areenhanced (Dupas and Pecker 1979; Acar and El-Tahir 1986;Clough et al. 1981 and 1989; Saxena et al. 1988; Huang andAirey 1998); (ii) the stressstrain and volumetric responsebecome relatively brittle and more dilative, respectively(Clough et al. 1981; Lade and Overton 1989; Abdulla andKiousis 1997; Schnaid et al. 2001); and (iii) quasiprecon-

    solidation pressure or yield stress can be observed in re-sponse to loading (Leroueil and Vaughan 1990; Airey

    Received 13 December 2006. Accepted 8 August 2007.Published on the NRC Research Press Web site at cgj.nrc.ca on8 February 2008.

    Y.-H. Wang1 and S.-C. Leung. Department of CivilEngineering, The Hong Kong University of Science and

    Technology, Hong Kong, China.1Corresponding author (e-mail: [email protected]).

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    Can. Geotech. J. 45: 2944 (2008) doi:10.1139/T07-070 # 2008 NRC Canada

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    1993). In addition, the mechanical responses of cementedsoils are found to depend on the amount and nature of thecementing agents (Ismail 2000; Ismail et al. 2002). However,in these studies, only the macroscale responses are empha-

    sized, and the associated underlying mechanisms often re-main hypothesized, vague, or even undescribed. The mainobjective of this study is to reveal these puzzles in explainingcemented sand behavior with a focus on strength enhance-ment and volumetric dilation due to cementation. Experimen-tal characterizations by drained triaxial compression tests andnumerical simulations by the discrete element method(DEM) will be used in parallel to achieve this purpose.

    Experimental details

    Artificially cemented sand samples

    Obtaining high-quality samples of natural cemented sandsfrom the field is difficult because cementation can some-

    times be destroyed during sampling. In addition, identicalsamples of natural cemented sand cannot be replicated forparametric studies. Hence, artificially cemented sands areused in this study. The properties of the cementing agentsare essential in determining the behavior of cemented sands,therefore two very different cementing agents were pur-posely selected (i.e., Portland cement and gypsum). One rep-resents strong and stiff cementation whereas the otherrepresents weak and soft cementing bonds.

    Ottawa 2030 sand is chosen as the sand matrix simply be-cause its grains are uniformly sized and have a round shape.This characteristic can be easily modeled using DEM in nu-merical simulations. The grain-size distribution is shown in

    Fig. 1. The maximum and minimum void ratios were deter-mined according to the BS 13774 (1990) standard. Theyare 0.749 and 0.481, respectively.

    Sample preparations and testing procedures

    Natural cemented sands exhibit a wide range of densities;however, to eliminate the density effects on the mechanicalresponses, the samples used in this study were purposely pre-pared in a loose state. All the samples also had a similar ini-tial void ratio, e&0.72, or a relative density of ~11% beforeshearing in the drained triaxial compression tests. The artifi-cially cemented sands were produced by mixing cementslurry with Ottawa sand particles. The sand particles werethoroughly washed and oven dried at 100 8C for 24 h before

    use. The slurry was prepared by mixing water with Portlandcement or gypsum powder in a ratio of 1:1 by weight. Themixture of cement slurry and sand particles was then putinto a cylindrical sample mold. A specimen with a height of140 mm and a diameter of 70 mm was prepared by 10 layercompaction following the method suggested by Ladd (1978)to ensure homogeneity. The compacted specimens weresealed into a plastic bag under a constant temperature of~20 8C to minimize moisture loss during the curing processand cracking caused by temperature variations. The curingtimes for the Portland cement and gypsum-cemented speci-mens were 7 and 3 d, respectively. The cement content wasdetermined by the ratio of the cement weight to the dryweight of the sand particles.

    The drained triaxial compression tests were performed us-ing a CKC triaxial system (Li et al. 1988). Lubricated end

    platens were used to reduce the friction between the endplaten and the specimen. Carbon dioxide gas was circulatedthrough the specimens for 45 min first to facilitate the satu-ration. However, this process was not used for the Portlandcement specimens because carbon dioxide was expected toreact with Portland cement through an acidalkali reaction,which could have affected the bonding strength. Deairedwater was then circulated to saturate the specimen througha small pressure difference (5~10 kPa). Back-pressure satu-ration (200 kPa) was implemented in the last stage to ensurethat the B-value was greater than 0.95. The designated con-fining pressure was applied to the specimen, and shearingwas carried out with an axial-strain rate of 6%/h. To make

    the cementation effects more pronounced and to prevent se-vere bond breakage, a low confining pressure was used. Themaximum values of 100 and 50 kPa were selected for thePortland cement and the gypsum-cemented samples, respec-tively.

    Experimental results

    Strength and failure mode

    Figures 2 and 3 demonstrate the stressstrain response ofthe Portland cement samples under the drained triaxial com-pression tests with different cement contents (1%, 2%, and3%) and confining pressures (50 and 100 kPa). For compar-

    isons, the responses of the uncemented sample are also pre-sented. In the cemented samples, the peak strength and theassociated strain-softening response become more distinct asthe cement content increases or the confining pressure de-creases. The uncemented samples, however, always followa strain-hardening process. Adding cementation can mark-edly increase the strength and alter the stressstrain behav-ior. These findings are in accordance with previouslypublished results, for example, Clough et al. (1981), Abdullaand Kiousis (1997), Schnaid et al. (2001), and Ismail et al.(2002), although the void ratio (before shearing) is not acontrol factor in these earlier tests. As shown in the imagescaptured during testing, shear banding occurs with thestrain-softening response (see picture B in Fig. 2). Also, the

    appearance of shear banding becomes more visible with in-creasing cement content, and it cannot be observed in the

    Fig. 1. The grain-size distribution of Ottawa 2030 sand.

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    uncemented sample, which exhibits only a bulging type offailure (see picture D in Fig. 2).

    As demonstrated in Fig. 4, the influence on the stressstrain behavior due to gypsum cementation is less whencompared with the Portland cement samples under the sameconfining pressure of 50 kPa. This may be because gypsumbonding is naturally weaker and some cementation is de-stroyed during the stage of isotropic consolidation. The pro-nounced strength and stiffness enhancement can be foundonly under a lower confining pressure of 25 kPa (Fig. 5).All the gypsum-cemented samples are prone to exhibit astrain-hardening response or, more precisely, the differencebetween the peak and ultimate strength is very small, andstrain localization is not observed (see Fig. 4, picture E).

    Volumetric response

    Figures 6 and 7 present the volumetric responses of thePortland cement samples. All the Portland cement samples

    exhibit volumetric dilation upon shearing even with 1% ce-ment content, whereas the uncemented sample shows volu-metric contraction. As noted, all of the samples are preparedwith very similar void ratios and are in a loose state. There-fore, the volumetric dilation is completely due to the cemen-

    tation effect and not to the density effect. This dilativefeature has been hypothetically attributed to cemented par-ticles forming highly interlocked clusters (Saxena et al. 1988;Lade and Overton 1989); however, such a general explana-tion requires further elaboration (to be discussed later). Thedilative response, as expected, is suppressed by confinement.

    Figures 8 and 9 present the volumetric responses of thegypsum-cemented samples; they are completely differentfrom the response of the Portland cement samples. The volu-metric contraction is higher than the amount measured in theuncemented specimens. This extra contraction increases withthe gypsum cement content and may be attributed to crush-ing of the gypsum cementation. Gypsum cement is light (thespecific gravity, Gs, is 2.3). A 3% or 5% cement content,

    which is determined by weight, implies that an appreciablevolume of the sample is occupied by the gypsum cementingagent. To maintain a similar initial void ratio of the sample(i.e., e&0.72), the sand particles themselves have to forman even looser packing compared with the uncemented sam-ple. If the cementing agent of gypsum is easily crushable,greater contraction should result. Similar comments on thefeatures of crushable gypsum cementation can also be foundin Ismail (2000).

    Details of the numerical simulations

    Experimental results showed that cementation by Portlandcement has a more pronounced influence on soil properties

    (i.e., increasing strength and changing the volumetric re-sponse from contraction to dilation). Numerical simulations

    Fig. 2. Stressstrain relationships of Portland cement sand samples under 50 kPa confining pressure. Note that the deformation characteris-

    tics are also demonstrated in the images captured during testing.

    Fig. 3. Stressstrain relationships of Portland cement sand samples

    under 100 kPa confining pressure.

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    Fig. 4. Stressstrain relationships of gypsum-cemented sand samples under 50 kPa confining pressure. Note that the deformation character-

    istics are also demonstrated in the images captured during testing.

    Fig. 5. Stressstrain relationships of gypsum-cemented sand sam-

    ples under 25 kPa confining pressure.

    Fig. 6. Void-ratio variations of Portland cement sand samples in

    response to shearing (50 kPa confining pressure).

    Fig. 7. Void-ratio variations of Portland cement sand samples in

    response to shearing (100 kPa confining pressure).

    Fig. 8. Void-ratio variations of gypsum cemented sand samples in

    response to shearing (25 kPa confining pressure).

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    were carried out to understand the associated underlying me-

    chanisms of this behavior. The commercial DEM software,Particle Flow Code 2-Dimensional, PFC2D (Itasca Consult-ing Group Inc., Minneapolis, Minn. ) was used. The inputparameters, such as the stiffness and bond strength in thenormal and shear directions (i.e., the contact model), particlesize and density, and friction between particles, are inti-mately coupled with the constitutive relations that governthe overall responses of cemented sand. Table 1 summarizesthe parameters of the three kinds of particles used in the si-mulations (i.e., sand particles, cementing particles, andmembrane particles). By combining these three kinds of par-ticles, the numerical specimen can be formed, as illustratedin Fig. 10. The size of the numerical specimen is 140 mmin height and 70 mm in width. The simulations of eachkind of particle are described in detail in the following sec-tions.

    Simulations of sand particles

    The sizes of sand particles are generated according to thegrain-size distribution of Ottawa 2030 sand. For the pur-pose of reducing the calculation time, the radii were scaledup 1.25 times to reduce the total particle numbers used inthe simulations, which were about 2000 in total. The normalstiffness was set on the order of 1 107, which was inferredfrom the forcedisplacement relationship of quartz sand par-ticles (Nakata et al. 1999) and from the relationship pro-posed by Potyondy and Cundall (2004). According to Bass

    (1995), the ratio between the bulk modulus and the shearmodulus of quartzose material is close to 1, and, therefore,the same normal and shear stiffness were selected for thesand particles in the simulations. The input parameters wereadjusted by comparing the simulation results with the meas-ured responses of the intended physical specimen until simi-lar behavior could be reproduced as suggested in Hazzard etal. (2000). The same method was also implemented in find-ing suitable input parameters for cementing and membraneparticles.

    Simulations of cementing particles and associatedbonding

    The interactions between the cementing agents and the

    soil grains are essential in reproducing true soil behavior inthe simulations. A special arrangement between the cement-

    ing particles and the sand grains was adopted, and it is

    shown in detail in Fig. 10a. The cementing particles aremodeled with tiny particles deposited around the contactsof the large soil grains. This arrangement is similar to thereal formation process of cementation as shown in Fig. 11:a strong capillary suction keeps pulling the cementingagents towards the particle contacts during the drying proc-ess until the cementation precipitates or crystallizes aroundthe contacts. The interaction between sand grains and ce-menting particles is simulated better, and the amount of ce-ment contents is controlled better with this arrangement. Inthe experiments, the cement content was quantified by theweight ratio. The same practice was also used in the simu-lations. The weight ratio was converted to a volume ratio or

    area ratio by relating it to the specific gravity (Gs) of thecementing agent. This area ratio was then used to regulatethe number of cementing particles in the simulations fordifferent cement-content specimens. For instance, the 3%Portland cement specimens require ~6000 cementing par-ticles. The specific gravity used in the calculations is 2.65for quartz (i.e., for the sand particles) and 3.15 for Portlandcement.

    As indicated in Fig. 10b, the parallel-bond model wasadopted in the simulations to regulate the contact model be-tween the cementing particles and the sand grains. The par-allel-bond model can be envisaged as a set of constantnormal and shear stiffness uniformly distributed over a con-tact area (details are given in the users manual for PFC2D).

    The model is characterized by five parameters: normal andshear strength, linear normal and shear stiffness, and the

    Fig. 9. Void-ratio variations of gypsum cemented sand samples in

    response to shearing (50 kPa confining pressure).

    Table 1. Parameters of the three kinds of particles used in the

    DEM simulations.

    For soil particles

    Soil particle density (kg/m3) 2650Initial porosity 0.20

    Radii of particles (m) 0.375103 1.475103

    Interparticle friction angle 0.55

    Particle/cap friction angle 0.00

    Normal contact stiffness (N/m) 5107

    Shear contact stiffness (N/m) 5107

    Contact stiffness between soil andmembrane particles (N/m)

    5106

    For membrane particles

    Radius of membrane particle (m) 0.5104

    Particle density (kg/m3) 1800

    Normal bond strength (Pa) 110300

    Shear bond strength (Pa) 110300

    Normal contact stiffness (N/m) 5106

    Shear contact stiffness (N/m) 5106

    For cementing particles (Portland cement)

    Particle density (kg/m3) 3150

    Radius of cementing particle (m) 6.66105

    Bond radius 1

    Normal contact stiffness (N/m) 5107

    Shear contact stiffness (N/m) 5107

    Normal bond strength (Pa) 3106

    Shear bond strength (Pa) 3106

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    bond radius as given in Table 1. The cementation bond wasconsidered broken when the normal force or shear force ex-ceeded the maximum resistance strength.

    Simulations of the membrane particles and applying aconfining pressure

    Kuhn (1995), Corriveau et al. (1997), and Iwashita andOda (1998) adopted the membrane particles in their DEM

    simulations and suggested that using a flexible membraneboundary can capture the deformation characteristics partic-ularly well in the development of shear banding. A similarsimulation method is used here but further modified as illus-trated in Fig. 10d. The flexible membrane is modeled by astring of small same-sized particles. These particles are

    linked by a strong but flexible contact bond so that the mo-ment cannot be transmitted. The membrane-particle string

    Fig. 10. Characteristics of the numerical specimen: (a) special arrangements of the cementing particles; (b) parallel bonds between cement-

    ing particles and sand grains; (c) specimen used in the biaxial tests; (d) membrane particles.

    Fig. 11. Features of Portland cement sand samples: (a) physical specimen used in the triaxial test; (b) loosely cemented sand particles; (c)

    cementation linking the sand particles together; (d) cementation formed at particle contacts. The sand image was taken through a micro-

    scope (Olympus SZH10 Research Stereo Microscope, Mellville, N.Y.).

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    therefore behaves like the rubber membrane used in the tri-axial tests, which is strong enough not to be torn apart butcan be stretched to deform freely.

    Figure 12 illustrates how the target confining pressure canbe achieved by adjusting the forces directly applied onto thestress-controlled membrane particles. The Fc represents theequivalent force on the membrane segment, AB, which ren-ders the required confining pressure on the soil particles. Its

    x- and y-direction components, Fx and Fy, can be calculatedbased on a geometrical relationship, that is,

    1 Fx Fcy1 y2ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

    y1 y22 x1 x22p

    2 Fy Fcx1 x2ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

    y1 y22 x1 x22p

    where (x1, y1) and (x2, y2) are the coordinates of particles Aand B. The forces, Fx and Fy, are then equally shared by the

    two membrane particles, A and B that constitute the segment,that is,

    Fig. 12. Confining pressure applied to the flexible membrane boundary: (a) the equivalent force applied on the membrane segment; (b) the

    force shared by the individual membrane particles. Note that the size of the membrane particles is enlarged for better presentation.

    Fig. 13. Flow chart of the numerical simulations.

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    3

    Fx

    2 Fxa

    Fxb

    4Fy

    2 Fya Fyb

    Simulations of biaxial tests

    Figure 13 presents the flow chart of the biaxial test simu-lations and the important details are described in the follow-ing sections.

    Specimen generation

    The numerical specimens were generated from ten equal

    layers, and in each layer the sand particle number and thevoid ratio are identical. Uniform packing with a consistentdistribution of local void ratios can be obtained with thismethod. After the sand particle packing was formed, the ce-menting particles were positioned following the procedureillustrated in Fig. 14. The specimen was formed withoutlarge overlapping and high locked-in forces between par-ticles before the biaxial test was conducted.

    Biaxial tests

    The experimental conditions applied to the physical speci-men were reproduced in the simulations. The top and bottomcaps were modeled with a rigid frictionless plate (or wall).The bottom plate was fixed, and the axial loading was ap-

    plied only from the top plate. The stress, strain, and overallvoid ratio were monitored during the test by three major

    measurement circles at representative locations in the speci-men. Apart from that, thousands of small measurementcircles were set to monitor the evolution of local void ratios.The simulations of the biaxial compression tests were div-ided into two stages: consolidation and shearing. The consol-idation was accomplished by applying loading onto the topcap and the membrane particles. The confining pressure wasconstantly checked and the target value was maintainedthroughout the test. The shearing stage was strain-controlledso that the top plate moved down at a constant velocity.

    Static equilibrium was achieved in each strain increment byallowing a very low ratio of unbalanced forces. The total

    Fig. 14. Procedures for positioning the cementing particles. Note that the size of the cementing particles is enlarged for better presentation.

    Fig. 15. Stressstrain relationships of Portland cement sand ob-

    tained from the biaxial-test simulations under 50 kPa confiningpressure.

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    forces acting on the top and bottom plates were kept at asimilar magnitude to ensure equilibrium throughout thespecimen.

    Particulate-scale behavior of cemented sand

    Enhanced strength

    As demonstrated in Fig. 15, similar stressstrain relation-ships, compared with experimental observations, were repro-duced for the Portland cement sand in the simulations. Thestrength enhancement, peak strength, and strain-softening re-sponse became more distinct when the cement content washigher.

    Oda (1972) and Oda et al. (1982) carried out biaxial com-

    pression tests on a packing of photoelastic disks. The resultsdemonstrated that the external loading was not evenlyshared and only concentrated in the main force-carryingchains. These chains were prone to align with the directionof the major principal stress. Particles outside the mainforce-carrying chains served as a complementary network toprevent them from buckling upon loading (Radjai et al.1998; Santamarina et al. 2001; Mitchell and Soga 2005).The buckling events of the main force-carrying chains areresponsible for the strength evolution, and, therefore, theydetail the failure process (Iwashita and Oda 1998; Radjai etal. 1998; Santamarina et al. 2001; Mitchell and Soga 2005).In this context, the associated underlying mechanisms of thestrength enhancement due to cementation can be revealed

    based on the characteristics of force-chain distributions (i.e.,the distribution of contact normal forces). As shown in

    Figs. 16a and 16b, the force-chain distributions of the unce-mented and cemented sands at an axial strain ("a) of 1.76%are compared. The comparison suggests that all particles inthe bonding network jointly share the load and many microforce-chains associated with cementation are generated. Theforce-chain distribution is relatively uniform and exhibits awebbed pattern in the cemented sand. In addition, thecementation provides an additional support to minimize par-ticle rotation and sliding away from the force chains. Thus,extra energy is required to break the cement bonding to give

    rise to force-chain buckling. These features lead to a morestable and stronger force-chain complex subjected to smaller

    Fig. 16. Force-chain distribution of the Portland cement sample under the confining pressure of 50 kPa and axial strain of 1.76%: (a) un-

    cemented sample; (b) 2% cement content sample. Note that the force chain thickness represents the magnitude of contact normal forces.

    Fig. 17. Volumetric responses of biaxial-test simulations on Port-land cement sand under 50 kPa confining pressure.

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    force concentrations so that higher strength is rendered inthe cemented sand.

    Volumetric dilation

    As shown in Fig. 17, similar to the experimental observa-tions, simulations revealed that cementation can effectivelyalter the volumetric response from contraction to dilation,and such a change is enhanced with increasing cement con-tent. The simulation results of the 2% cement content speci-men are further analyzed to explore the associated underlyingmechanism.

    Figure 18 presents the relationships between the bond-breakage events and the volumetric and stressstrain re-sponses. The volumetric dilation commences after the sam-ple passes over the initial yield point (i.e., around point F),and the occurrence of bond breakage accelerates afterwards.

    After the peak strength (i.e., after point G is reached), theparticle movement becomes concentrated along the shear

    banding direction, which can be seen from the record ofthe displacement field shown in the same figure. It is worth

    noting that the severe bond-breakage events occurring be-tween points G and H coincide with great volumetric dila-tion. This observation implies that the bonded clustersdetached from the bonding network assist the volumetric di-lation.

    A further analysis is presented in Fig. 19 where the bond-ing network, displacement field, force-chain distribution, andcontours of particle rotation and local porosity at a strain of"a = 7.15% (i.e., point I in Fig. 18) are jointly considered. Aclose correlation among these five properties can be estab-lished. Intensive bond breakage, concentrated relative par-ticle movement, column-like force chains (instead of awebbed pattern) with force concentrations, great particle ro-tation, and, most importantly, a high local porosity can be

    found at similar locations of the sample, especially insidethe shear band. In the region outside the shear band, the

    Fig. 18. Results of the biaxial-test simulation on 2% Portland cement sand under 50 kPa confining pressure. Note that the deformation

    characteristics at different strains are also presented by the record of the displacement field.

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    bonding network is still preserved and, therefore, the particle

    rotation and volumetric dilation are prohibited. These find-ings suggest that monitoring the evolution of these five prop-erties inside the shear band may reveal the underlyingmechanism of volumetric dilation in Portland cement sand.The series of illustrations shown in Figs. 2024 and the fol-lowing discussions are aimed at this revelation.

    As indicated in Fig. 20, a large void with an elongatedshape, void V, was established at "a = 7.15%. Four differenttypes of particles or bonded clusters are involved to formthe particle arch that contains this void:

    . Particle A: this is a sand particle without any cementationcoating

    . Particle B: this is a sand particle coated with cementing

    particles and serves as a key element to lock the left sideof the particle arch

    . Particle C: this is a sand particle coated with cementing

    particles and functions as a roller to facilitate the slidingof cluster D when void V is formed.. Cluster D: this is a properly sized cluster located at the

    right side of the particle arch.

    The formation process of this particle arch and associatedvoid V is described as follows according to the evolution ofeach participating particle or cluster:

    (1) Particle A, as shown in Figs. 2124, was originally freeto move or rotate and did not participate in the force-carrying chains at "a = 1.43%. This particle is finally in-terlocked with particle B to join the left side of the parti-cle arch at "a = 7.15%. Note that particle A is tightlylocked by the two cementing particles attached on the

    surface of particle B, which can be seen in the bondingnetwork and the enlargement at "a = 7.15% (Fig. 24).

    Fig. 19. Features recorded in the biaxial-test simulation on the 2% Portland cement sand under the confining pressure of 50 kPa and the

    axial strain of 7.15%: (a) bonding network; (b) displacement field; (c) force-chain distribution; (d) particle rotation; (e) local porosity (the

    initial porosity is 0.2).

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    Fig. 20. Descriptions of particles or clusters involved to form void V inside the shear band II at "a = 7.15%.

    Fig. 21. Records of displacement field around the region of shear band II.

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    (2) Particle B originally belonged to a bonded cluster (i.e.,the one that contained cluster D), which can be seenfrom the bonding network at "a = 1.43% (Fig. 24). Thisparticle was then released and became mobile after thecementation bond was broken at "a = 5.72%. The bondwas broken by tensile failure when particle B rotated ina counter direction with respect to its parent cluster.Such a detaching process can be seen by comparing theparticle rotation (Fig. 22) and the bonding network(Fig. 24) at "a = 5.01% and "a = 5.72%. This finding ex-

    plains why the intensive bond breakage and greater par-ticle rotation can be observed at similar locations, aspresented in Fig. 19.

    (3) Particle C was also originally connected to a cluster (i.e.,the one that contained cluster D), which, again, can beseen from the bonding network at "a = 1.43% (Fig. 24).The comparisons of the particle rotation (Fig. 22) andthe bonding network (Fig. 24) between "a = 3.14% and"a = 5.01% reveal that particle C experienced a similarfate to that of particle B. The cementation bond is sub-jected to tensile failure when particle C rotates at a dif-ferent rate with respect to its parent cluster, that is,differential rotation. This released particle later serves asa roller that facilitates the sliding of cluster D as void V

    is formed. This scenario can be viewed by comparing theparticle rotation shown in Fig. 22. Particle C rotates

    more than 908 in the clockwise direction when "a in-creases from 5.72% to 7.15%.

    (4) As presented in Fig. 24, the bonding network associatedwith cluster D is almost intact at "a = 1.43%. With in-creasing strain level, some particles are gradually de-tached from the bonding network due also to differentialrotation and cluster D is therefore formed. At "a =7.15%, the properly sized cluster D joins the right halfof the arch and void V is established.

    Apart from these scenarios, owing to the great stiffnessand strength of Portland cement bonding, the rigid-clusterrotation can also contribute to volumetric dilation, such asthat shown by cluster E in Figs. 2024. Note that cluster Eis also detached from a large bonding network, as shown inFig. 24.

    The last and most important question is how can void Vbe stabilized to maintain volumetric dilation. As shown inFig. 23, the force-chain distribution keeps changing with in-creasing strain. A sudden change in the force-chain distribu-tion takes place, especially in the shear band, when force-chain buckling or bond breakage occurs. These observations,on the one hand, suggest that the force chains establishedaround void V can be destabilized in response to larger

    strains, which in turn initiates the other life cycle of voidformations. On the other hand, these findings imply the im-

    Fig. 22. Records of particle rotation around the region of shear band II. Note that particle B and cluster D have an identical particle rotation

    at "a = 5.01% but different ones at "a = 5.72%.

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    portance of cluster D in stabilizing the arch to maintain thelarge void space for volumetric dilation. With reference tothe force-chain distribution at "a = 7.15% shown in Fig. 23,the force chains have a thick column shape on the left sideof the particle arch that establishes void V, which indicatesa greater force concentration and a higher chance of buck-ling. On the right side of the arch, the force chains exhibit awebbed pattern because each particle in cluster D jointlyshares the load. The risk of force-chain buckling is thereforeminimized and void V can be maintained for volumetric di-lation. As the experimental results in Fig. 2 demonstrate, thecemented specimens are still subjected to higher deviatoric

    stress, q, compared with the uncemented specimen at largerstrains, for example, at "a = 25%. If a cemented cluster suchas cluster D does not help to maintain the stability of theparticle arch, which contains open voids, the apparent differ-ence in the void ratios between the cemented and unce-mented specimens at this strain level will not be measured(see the volumetric response in Fig. 6). Following this logic,if the cemented cluster is not strong, such an arch with alarge void will not exist nor will the volumetric dilation.This partially explains the behavior of the gypsum-cementedspecimen, as shown in Figs. 8 and 9.

    Summary and conclusion

    The mechanical responses of cemented sands not only de-pend on the density and confining pressure, but they also in-

    timately rely on the amount and, in particular, the nature ofthe cementing agents. Although all of the samples for thetriaxial test were prepared in a loose state with very similarinitial void ratios (~0.72), the Portland cement (strongcementation) and gypsum-cemented (weak cementation) sandsamples exhibited different responses. Increasing theamount of cementation in the Portland cement sand canmarkedly augment the strength and enhance the associatedstrain-softening response. The shear banding associatedfailure mode is noticed. In addition, the Portland cementsand samples, regardless of the cement content, all areprone to exhibit volumetric dilation while the uncementedsample with the same void ratio tends to contract. In thegypsum-cemented sand, the strength enhancement by cemen-tation only prevails under low confining pressure. Thestrain-hardening behavior and a bulging type of failure areobserved and shear banding is not visible. Greater volumet-ric contraction, if compared with the response of unce-mented sand, can be measured.

    The underlying mechanisms of strength enhancement andvolumetric dilation observed in the Portland cement sand arerevealed by the aid of DEM simulations. In the simulations,the arrangement of the smaller cementing particles aroundthe contacts between sand grains indicates the real featuresof cementation, and the use of flexible membrane bounda-

    ries improves the simulation of the deformation characteris-tics. The simulation results demonstrate that all of the

    Fig. 23. Records of force-chain distributions around the region of shear band II.

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    particles in the bonding network jointly share the load and

    many micro force-chains associated with cementation aregenerated. Compared with uncemented sand, a more stableand stronger force-chain network subjected to smaller forceor stress concentrations is formed in cemented sand. Therisk of force-chain buckling is therefore minimized andhigher strength is measured. The simulation also revealsthat intensive bond breakage, concentrated relative particlemovement, column-like force chains (instead of a webbedpattern) with force concentrations, great particle rotation,and high local porosity can be found at similar locations inthe sample, especially inside the shear band. The bondedcluster is essential to help stabilize the particle arch andmaintain large voids for the volumetric dilation.

    Acknowledgments

    This research was supported by the Hong Kong ResearchGrants Council (HKUST6034/02E) and the Hong Kong Uni-versity of Science and Technology (HIA04/05.EG02). Theauthors are grateful to the reviewers for their valuable com-ments.

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