GrainSizeEffectontheMechanicalBehaviorofCohesionless...
7
Research Article Grain Size Effect on the Mechanical Behavior of Cohesionless Coarse-Grained Soils with the Discrete Element Method Renjie Wen , 1 Cai Tan, 2 Yong Wu, 3 and Chen Wang 1 1 StateKeyLaboratoryofHydraulicsandMountainRiverEngineering,CollegeofWaterResourceandHydropowerEngineering, Sichuan University, Chengdu 610065, China 2 Guangdong Research Institute of Water Resources and Hydropower, Guangzhou 510610, China 3 e Upper Reaches of the Huadian Jinsha River Hydropower Development Co., Ltd., Chengdu 610041, China Correspondence should be addressed to Chen Wang; [email protected] Received 23 November 2017; Accepted 5 June 2018; Published 26 June 2018 Academic Editor: Cumaraswamy Vipulanandan Copyright©2018RenjieWenetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Biaxialcompressiontestswiththesamespecimensizeanddifferentmaximumgrainsizesweresimulatedforcoarse-grainedsoils usingthediscreteelementmethodtostudytheinfluenceofgrainsizeonthemechanicalpropertiesandforcechain.emaximum grainsizeswere40,20,10,and5mm,respectively.egradingwithself-similarfractalstructureinmassisdesignedtoensurethe same pore structure for soils. e shear strength increased with the increase in maximum grain size. Evident increase in shear strength and significant size effect were observed when the ratio of the specimen diameter to maximum grain size was less than five. e shear dilation of coarse-grained soils increases with the increase in maximum grain size. e contact force distribution was uniform when maximum grain size was small but tends to be uneven with the increase in maximum grain size, thereby causing the increase in shear strength by stable strong force chains. is finding demonstrates size effect on the mechanical properties and force chain of cohesionless coarse-grained soils under the biaxial compression condition. 1. Introduction e size effect on cohesionless coarse-grained soils is an important topic in geotechnical engineering. Size effect, including sample and particle size effect, can be studied throughtestsandnumericalsimulations.Alargenumberof test results for coarse-grained soils have been obtained. Whenthemaximumgrainsizeislargeorthespecimensize is small, the shear strength is high [1–7]. However, a few factors in laboratory tests, such as particle shape, gradation, uniformity, and particle breakage of soil, affect the test re- sults [8–12]. e grading with the self-similar fractal structure in mass was used in triaxial compression tests to ensure the same pore characteristics for specimens with different maximum grain sizes and avoid the influence of grading [7]. However, the laboratory tests can only obtain afewmacroscopicbehaviors.Withtheincreaseinnumerical simulation methods, the size effect of coarse-grained soils was simulated based on numerical tests, thereby controlling the error from the test material. Furthermore, the load transfer and fabric change in the deformation and failure process can be obtained, and the mechanism of size effect can be analyzed. erefore, analyzing the size effect on coarse-grained soils using numerical tests is significant. e discrete element method (DEM), which is an im- portantmethodinnumericalsimulation,hasbeenwidelyused to investigate coarse-grained soils since it was proposed by CundallandStrack[13].esizeeffectofcoarse-grainedsoilis oneofthemaincontentsofDEM.PotyondyandCundall[14] studied the influence of the ratio of specimen size to particle size on the elastic modulus and internal friction angle of thesampleusingparticleflowcode(PFC).eresultsshowed that the mechanical parameters are later the same in the two-dimensional tests, whereas the parameters in the three- dimensional tests are related to the size. Matthew and Katalin [15]usedtheDEMtocarryoutthebiaxialsimulationtestsfor four cohesionless particle materials with different specimen sizes. eir results showed that sample shear strength reduces Hindawi Advances in Civil Engineering Volume 2018, Article ID 4608930, 6 pages https://doi.org/10.1155/2018/4608930
Transcript of GrainSizeEffectontheMechanicalBehaviorofCohesionless...
Research ArticleGrain Size Effect on the Mechanical Behavior of CohesionlessCoarse-Grained Soils with the Discrete Element Method
Renjie Wen 1 Cai Tan2 Yong Wu3 and Chen Wang 1
1State Key Laboratory of Hydraulics and Mountain River Engineering College of Water Resource and Hydropower EngineeringSichuan University Chengdu 610065 China2Guangdong Research Institute of Water Resources and Hydropower Guangzhou 510610 China3e Upper Reaches of the Huadian Jinsha River Hydropower Development Co Ltd Chengdu 610041 China
Correspondence should be addressed to Chen Wang cwangscueducn
Received 23 November 2017 Accepted 5 June 2018 Published 26 June 2018
Academic Editor Cumaraswamy Vipulanandan
Copyright copy 2018 Renjie Wen et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Biaxial compression tests with the same specimen size and different maximum grain sizes were simulated for coarse-grained soilsusing the discrete elementmethod to study the influence of grain size on the mechanical properties and force chainemaximumgrain sizes were 40 20 10 and 5mm respectively e grading with self-similar fractal structure in mass is designed to ensure thesame pore structure for soils e shear strength increased with the increase in maximum grain size Evident increase in shearstrength and significant size effect were observed when the ratio of the specimen diameter to maximum grain size was less thanfive e shear dilation of coarse-grained soils increases with the increase in maximum grain size e contact force distributionwas uniform when maximum grain size was small but tends to be uneven with the increase in maximum grain size therebycausing the increase in shear strength by stable strong force chains is finding demonstrates size effect on the mechanicalproperties and force chain of cohesionless coarse-grained soils under the biaxial compression condition
1 Introduction
e size effect on cohesionless coarse-grained soils is animportant topic in geotechnical engineering Size effectincluding sample and particle size effect can be studiedthrough tests and numerical simulations A large number oftest results for coarse-grained soils have been obtainedWhen the maximum grain size is large or the specimen sizeis small the shear strength is high [1ndash7] However a fewfactors in laboratory tests such as particle shape gradationuniformity and particle breakage of soil affect the test re-sults [8ndash12] e grading with the self-similar fractalstructure in mass was used in triaxial compression tests toensure the same pore characteristics for specimens withdifferent maximum grain sizes and avoid the influence ofgrading [7] However the laboratory tests can only obtaina fewmacroscopic behaviors With the increase in numericalsimulation methods the size effect of coarse-grained soilswas simulated based on numerical tests thereby controlling
the error from the test material Furthermore the loadtransfer and fabric change in the deformation and failureprocess can be obtained and the mechanism of size effectcan be analyzed erefore analyzing the size effect oncoarse-grained soils using numerical tests is significant
e discrete element method (DEM) which is an im-portant method in numerical simulation has been widely usedto investigate coarse-grained soils since it was proposed byCundall and Strack [13]e size effect of coarse-grained soil isone of the main contents of DEM Potyondy and Cundall [14]studied the influence of the ratio of specimen size to particlesize on the elastic modulus and internal friction angle ofthe sample using particle flow code (PFC) e results showedthat the mechanical parameters are later the same in thetwo-dimensional tests whereas the parameters in the three-dimensional tests are related to the size Matthew and Katalin[15] used the DEM to carry out the biaxial simulation tests forfour cohesionless particle materials with different specimensizes eir results showed that sample shear strength reduces
HindawiAdvances in Civil EngineeringVolume 2018 Article ID 4608930 6 pageshttpsdoiorg10115520184608930
with the increase in specimen size A series of triaxial com-pression tests were carried out on coarse-grained soil throughPFC e results demonstrated that the change in the ratio ofspecimen size to particle size has no evident influence on theshear strength of coarse-grained soils when the ratio is greaterthan 40 [16] Rao andChang [17] studied the influence of grainsize on stress-strain-strength behaviors by using PFC2D forsoils with the maximum grain sizes of 60 80 and 120mm andthe same ratios of specimen size to maximum particle size
Scholars have attempted to explain the phenomenon of sizeeffect in terms of its formation mechanism due to the com-plexity and uncertainty of the size effect of coarse-grained soilsZhu et al [12] believed that boundary constraints of thespecimen can be attributed to the size effect However thespecific action of the constraint on the formation of the sizeeffect is not explained Zhang and Hou [18] explained the sizeeffect of granularmaterials due to the boundary constraint basedon force chain theorye contact force between the particles isevidently affected by the boundary when the specimen size issmaller than the characteristic length of the force chain
e biaxial compression tests for cohesionless granularsoils with different maximum grain sizes and self-similarfractal structures were performed based on the DEM toanalyze the effect of maximum grain size on the mechanicalproperties and force chain of coarse-grained soils with thesame specimen size e mechanism of size effect of co-hesionless coarse-grained soils was preliminarily discussedby the concept of the force chain
2 Numerical Modeling of BiaxialCompression Tests
21 Introduction of Contact Stiffness Model e linearcontact stiffness model of PFC2D was adopted in this paper[19] In the contact plane the contact force vector betweentwo contact entities can be decomposed into normal andtangential components e normal contact force compo-nent is the normal contact stiffness product and the overlapof particles and the normal unit vector of the contact surfacewhich can be written as follows [19]
Fni k
nU
nni (1)
where Fni is the normal contact force component kn is the
contact normal secant stiffness Un is the relative contactdisplacement in the normal direction and ni is the normalvector unit that defines the contact plane
e shear force is computed in an incremental fashionWhen the contact is formed total shear force is initialized tozero Each subsequent relative shear displacement incrementleads to an increment of elastic shear force that is added tothe current value which can be written as follows [19]
ΔFsi minusksΔUs
i (2)
where ΔFsi is the shear contact force component ks is the
shear stiffness and ΔUsi is the relative contact displacement
in the shear directionBased on the assumption that the stiffness of the two
contacting entities acts in succession the contact stiffness for
the linear contact model is computed e contact normalsecant stiffness is given by the following equation
kn
k[A]n k[B]
n
k[A]n + k[B]
n (3)
e contact shear tangent stiffness is calculated asfollows
ks
k[A]s k[B]
s
k[A]s + k[B]
s (4)
where superscripts [A] and [B] denote the two particles incontact
22 Specimen Figure 1 shows the specimen of cohesionlesscoarse-grained soils with a diameter of 101mm and a heightof 200mm Among which 1 and 3 walls were the lowerand upper loading plates respectively and 2 and 4 wereflexible boundaries which can simulate the rubber mem-brane in triaxial tests
e test soils with self-similar fractal structure in mass asused in the biaxial compression test were utilized to ensure thesame pore characteristics for specimens with different max-imum grain sizes e grading was achieved as follows [20]
M dltdi( 1113857
Mt
di
dmax1113888 1113889
3minusD
(5)
whereM(dlt di) is themass of grains with the grain size d lessthan a certain grain size diMt is the grossmass of grains dmaxis the maximum grain size and D is the fractal dimension
Four different scaling methods were adopted to scaledrockfill materials e results showed that the range of the
Flexible boundaries
Loading plates
3
2
1
4
10120
0
Figure 1 Biaxial compression test sample
2 Advances in Civil Engineering
fractal dimension value is between 1463 and 1783 [21]erefore D was set to 15 in the numerical tests A total offour specimens with the similar grading were used in thenumerical tests e maximum grain size dmax was 5 10 20and 40mm and the minimum grain size dmin was 025 051 and 2mm respectively e particles of size less than dminwere dealt with the equivalent replacement method eaverage grain size d50 was 31 63 126 and 252mm re-spectively e coefficient of uniformity Cu and the co-efficient of curvature of the specimens are 33 and 130respectively e graining curves are shown in Figure 2
e confining pressures (σ3) were 100 200 300 and400 kPa After consolidation the confining pressure wasmaintained constant and then vertical pressure was applied
23 Parameters us far the parameters used in DEMsimulation cannot be directly obtained by laboratory testsbecause no definite relation exists between the mesostructure
0
20
40
60
80
100
01110100Grain size d (mm)
Perc
enta
ge p
assin
g (
)
Maximum grain size dmax5 mm10 mm
20 mm40 mm
Figure 2 Distribution curves of grain sizes
0
300
600
900
1200
0 4 8 12 16Axial strain εa (mm)
Dev
iato
r stre
ss q
()
Maximum grain size dmax5 mm10 mm
20 mm40 mm
Figure 3 Behaviors of qminus εa (confining pressure of 300 kPa)
q f (kPa
)
300
600
900
1200
1500
0 5 10 15 20 25Ddmax
Confining pressure100 kPa200 kPa
300 kPa400 kPa
Figure 4 Behaviors of qf minusDdmax
Volu
met
ric st
rain
εv (
)
ndash4
ndash3
ndash2
ndash1
0
1
2
3
0 4 8 12 16Axial strain εa (mm)
Maximum grain size dmax 5 mm10 mm
20 mm40 mm
Figure 5 Behaviors of εa minus εv (confining pressure of 300 kPa)
ε v (
)
ndash5
ndash4
ndash3
ndash2
ndash1
00 5 10 15 20 25
Ddmax
Confining pressure100 kPa200 kPa
300 kPa400 kPa
Figure 6 Behaviors of εv minusDdmax
Advances in Civil Engineering 3
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(a)
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(b)
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(c)
Figure 7 Continued
4 Advances in Civil Engineering
and macroparameters e trial and error method is used toensure that the numerical test results are in agreement with thelaboratory test results After repeated trial and error themesostructure parameters of biaxial numerical tests were ob-tained e normal and tangential contact stiffness of theparticles was 4times107Nm the normal and tangential contactstiffness of the wall was 2times108 and 0Nm respectively thefriction coefficient between particles was 24 the particledensity was 2600kgm3 the porosity of specimens was 015and the loading rate was 03ms
3 Results and Analyses
31 Size Effects on Strength e deviator stress q-axial strain εacurves with different maximum grain sizes under the confiningpressure of 300kPa are shown in Figure 3 e curves underother confining pressures possess similar behaviors e speci-men was found to exhibit a strain softening behavior e peakdeviator stress is considered to be the failure deviator stress qf e qf minusDdmax curves are shown inFigure 4edeviator stressqf increases with the decrease in Ddmax and the increasingtendencies of qf are evident when Ddmax le 5 is result isconsistent with the laboratory test under the same conditions [7]
32 SizeEffects onDeformation evolumetric strain εv-axialstrain εa curves with different maximum grain sizes undera confining pressure of 300 kPa are shown in Figure 5 ecurves under other confining pressures have similar behaviorse volume of the specimen contracts initially and then dilatesand eventually reaches a steady state when the axial strain is upto 15 e behaviors between the volumetric strain corre-sponding to the axial strain of 15 and Ddmax are shown inFigure 6 e shear dilatancy of cohesionless coarse-grainedsoils is evident with the decrease in Ddmax
33 Size Effects onForceChain emechanical properties ofgranular materials are determined by the force chain
network formed by the mutual contact of particles [22ndash24]e size effect mechanism of coarse-grained soils can beexplained by the distribution and transfer law of contactforce Figure 7 is the force chain distribution of coarse-grained soils with different maximum particle sizes underthe peak stress As shown in Figure 7 ldquoblackrdquo is denoted asthe contact force which is larger than the average value andits width is proportional to the contact force
Figure 7 shows that the contact force is transferredmainly through the strong force chain e strong forcechain is mainly distributed along the direction of the majorprincipal stress and the weak force chain is distributedaround the strong chain and acts as support Both chainsform a force chain network structure With the increase inconfining pressure the lateral strong force chains graduallydevelop to support the axial strong force chains and bothchains form a stable force chain network e macroscopicbehavior indicates that when the confining pressure is highthe shear strength is also high thus indirectly proving therationality of the numerical simulation
e breakage of the contact points causes the entire forcechain to disintegrate and recombine Maintaining stability isdifficult whenmore particles exist on the force chain In generalmaintaining the stability of the force chain is difficult when itsparticle number exceeds five [25 26] When the maximumparticle size is small more particles exist in the sample and thecontact force is uniformly distributed thus forming the strongforce chain is difficult erefore the sliding and dislocationbetween particles easily occur and the macroscopic behavior ofparticles shows that the soils have low shear strength e in-crease in the maximum particle size results in evident sampleboundary restrainte contact force becomes uniform and thestable strong chain becomes long due to the decrease in theparticle number Extending the strong force chains fromone sideof the sample to the other is easy thereby forming a stablestructure that is failure resistant Macroscopically the sampleshows high shear strength and evident size effect
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(d)
Figure 7 Force chain distribution of four different maximum particle sizes and four confining pressure conditions under peak stress state(a) 100 kPa (b) 200 kPa (c) 300 kPa (d) 400 kPa
Advances in Civil Engineering 5
4 Conclusion
eDEM simulation of biaxial compression tests for coarse-grained soils with different maximum grain sizes and self-similar fractal structures in mass was carried out e effectof grain size on the mechanical properties and force chain ofcoarse-grained soils was also discussed e main conclu-sions are as follows
(1) e shear strength of coarse-grained soils increaseswith the increase in the maximum particle size eshear strength of soils evidently increases when theratio of the sample diameter to the maximum par-ticle size is less than five
(2) When the maximum particle size increases the sheardilatancy of cohesionless coarse-grained soil alsoincreases
(3) When the maximum particle size is small manyparticles exist in the sample and the contact forcedistribution is uniform thus forming a strong forcechain is difficult When the maximum particle sizeincreases the particle number decreases the contactforce distribution of particles tends to be uneven andthe stable strong force chain increases the shearstrength thereby resulting in size effect
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] C Li C He C Wang and H Zhao ldquoStudy of scale effect oflarge-scale triaxial test of coarse-grained materialsrdquo Rock andSoil Mechanics vol 29 no s1 pp 563ndash566 2008
[2] G Ma W Zhou X Chang and C Zhou ldquoMesoscopicmechanism study of scale effects of rockfillrdquo Chinese Journalof Rock Mechanics and Engineering vol 31 no 12 pp 2473ndash2482 2012
[3] A Varadarajan K G Sharma K Venkatachalam andA K Gupta ldquoTesting and modeling two rockfill materialsrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 129 no 3 pp 206ndash218 2003
[4] N Li T Zhu and Z Mi ldquoStrength and deformation prop-erties of transition zone material of Xiaolangdi dam and scaleeffectrdquo Water Resources and Power vol 19 no 2 pp 40ndash432001
[5] R Dadkhah M Ghafoori R Ajalloeian and G R Lashkaripourldquoe effect of scale direct shear test on the strength parameters ofclayey sand in Isfahan city Iranrdquo Journal of Applied Sciencevol 10 no 18 pp 2027ndash2033 2010
[6] C Tan CWang YWu andW Li ldquoSize effects on strength ofcohesionless coarse-grained soil under direct shear condi-tionrdquo Journal of Sichuan University Natural Science Editionvol 48 no s1 pp 94ndash99 2016
[7] C Tan Y Wu L Wan C Wang and W Li ldquoSize effects onthe shear strength of the cohesionless coarse-grained soilsunder the triaxial compression conditionrdquo Journal of Jian-gnan University Natural Science Edition vol 14 no 6pp 810ndash813 2015
[8] A K Gupta ldquoEffect of particle size and confining pressure onbreakage and strength parameters of rockfill materialsrdquoElectronic Journal of Geotechnical Engineering vol 14 pp 1ndash12 2009
[9] R J Marsal ldquoLarge scale testing of rockfill materialsrdquo Journalof Soil Mechanics and Foundation Division vol 93 no 2pp 27ndash43 1967
[10] J A Charles and K S Watts ldquoe influence of confiningpressure on the shear strength of compacted rockfillrdquo Geo-technique vol 30 no 4 pp 353ndash367 1980
[11] H Ling Z Yin J Zhu and Z Cai ldquoExperimental study of scaleeffect on strength of rockfill materialsrdquo Journal of Hehai Uni-versity Natural Sciences Edition vol 39 no 5 pp 540ndash544 2011
[12] J Zhu Z Liu H Weng Z Wu and H fu ldquoStudy on effect ofspecimen size upon strength and deformation behavior ofcoarse-grained soil in triaxial testrdquo Journal of Sichuan UniversityEngineering Science Edition vol 44 no 6 pp 92ndash96 2012
[13] P A Cundall and O D L Strack ldquoA discrete numericalmodel for granular assembliesrdquo Geotechnique vol 29 no 1pp 47ndash65 1979
[14] D O Potyondy and P A Cundall ldquoA bonded -particle modelfor rockrdquo International Journal of RockMechanics andMiningSciences vol 41 no 8 pp 1329ndash1364 2004
[15] R K Matthew and B Katalin ldquoSpecimen size effect in discreteelement simulations of granular assembliesrdquo Journal of En-gineering Mechanics vol 135 no 6 pp 485ndash492 2009
[16] H Liu and X Cheng ldquoDiscrete element analysis for size effectsof coarse-grained soilsrdquo Rock and Soil Mechanics vol 30no s1 pp 287ndash292 2009
[17] G Rao and X Chang ldquoA study of scale effect of rockfill basedon PFC2Drdquo China Rural Water and Hydropower no 11pp 88ndash90 2011
[18] Q Zhang and M Hou ldquoResearch on size effect of direct sheartestrdquo Acta Physica Sinica vol 61 no 24 pp 2445041ndash2445046 2012
[19] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) Itasca Consulting Group Minneapolis MNUSA 2008
[20] S W Tyler and S W Wheatcraft ldquoFractal scaling of soilparticle-size distributions analysis and limitationsrdquo Soil ScienceSociety of America Journal vol 56 no 2 pp 362ndash369 1992
[21] T Zhao W Zhou X Chang G Ma and X Ma ldquoFractalcharacteristics and scaling effect of the scaling method forrockfill materialsrdquo Rock and Soil Mechanics vol 36 no 4pp 1093ndash1101 2015
[22] H Tian Y Jiao H Wang and J Ma ldquoResearch on biaxial testof mechanical characteristics on soil-rock aggregate(SRA)based on particle flow code simulationrdquo Chinese Journal ofRock Mechanics and Engineering vol 34 no s1 pp 3564ndash3573 2015
[23] T S Majmudar and R P Behringer ldquoContact force mea-surements and stress-induced anisotropy in granular mate-rialsrdquo Nature vol 435 no 7045 pp 1079ndash1082 2005
[24] R R Hartley and R P Behringer ldquoLogarithmic rate de-pendence of force networks in sheared granular materialsrdquoNature vol 421 no 6926 pp 928ndash931 2003
[25] A Tordesillas A Hunt and J Shi ldquoA characteristic lengthscale in confined elastic buckling of a force chainrdquo GranularMatter vol 13 no 3 pp 215ndash218 2011
[26] A Tordesillas Q Lin J Zhang R P Behringer and J ShildquoStructural stability and jamming of self-organized cluster con-formations in dense granular materialsrdquo Journal of theMechanicsand Physics of Solids vol 59 no 2 pp 265ndash296 2011
6 Advances in Civil Engineering
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with the increase in specimen size A series of triaxial com-pression tests were carried out on coarse-grained soil throughPFC e results demonstrated that the change in the ratio ofspecimen size to particle size has no evident influence on theshear strength of coarse-grained soils when the ratio is greaterthan 40 [16] Rao andChang [17] studied the influence of grainsize on stress-strain-strength behaviors by using PFC2D forsoils with the maximum grain sizes of 60 80 and 120mm andthe same ratios of specimen size to maximum particle size
Scholars have attempted to explain the phenomenon of sizeeffect in terms of its formation mechanism due to the com-plexity and uncertainty of the size effect of coarse-grained soilsZhu et al [12] believed that boundary constraints of thespecimen can be attributed to the size effect However thespecific action of the constraint on the formation of the sizeeffect is not explained Zhang and Hou [18] explained the sizeeffect of granularmaterials due to the boundary constraint basedon force chain theorye contact force between the particles isevidently affected by the boundary when the specimen size issmaller than the characteristic length of the force chain
e biaxial compression tests for cohesionless granularsoils with different maximum grain sizes and self-similarfractal structures were performed based on the DEM toanalyze the effect of maximum grain size on the mechanicalproperties and force chain of coarse-grained soils with thesame specimen size e mechanism of size effect of co-hesionless coarse-grained soils was preliminarily discussedby the concept of the force chain
2 Numerical Modeling of BiaxialCompression Tests
21 Introduction of Contact Stiffness Model e linearcontact stiffness model of PFC2D was adopted in this paper[19] In the contact plane the contact force vector betweentwo contact entities can be decomposed into normal andtangential components e normal contact force compo-nent is the normal contact stiffness product and the overlapof particles and the normal unit vector of the contact surfacewhich can be written as follows [19]
Fni k
nU
nni (1)
where Fni is the normal contact force component kn is the
contact normal secant stiffness Un is the relative contactdisplacement in the normal direction and ni is the normalvector unit that defines the contact plane
e shear force is computed in an incremental fashionWhen the contact is formed total shear force is initialized tozero Each subsequent relative shear displacement incrementleads to an increment of elastic shear force that is added tothe current value which can be written as follows [19]
ΔFsi minusksΔUs
i (2)
where ΔFsi is the shear contact force component ks is the
shear stiffness and ΔUsi is the relative contact displacement
in the shear directionBased on the assumption that the stiffness of the two
contacting entities acts in succession the contact stiffness for
the linear contact model is computed e contact normalsecant stiffness is given by the following equation
kn
k[A]n k[B]
n
k[A]n + k[B]
n (3)
e contact shear tangent stiffness is calculated asfollows
ks
k[A]s k[B]
s
k[A]s + k[B]
s (4)
where superscripts [A] and [B] denote the two particles incontact
22 Specimen Figure 1 shows the specimen of cohesionlesscoarse-grained soils with a diameter of 101mm and a heightof 200mm Among which 1 and 3 walls were the lowerand upper loading plates respectively and 2 and 4 wereflexible boundaries which can simulate the rubber mem-brane in triaxial tests
e test soils with self-similar fractal structure in mass asused in the biaxial compression test were utilized to ensure thesame pore characteristics for specimens with different max-imum grain sizes e grading was achieved as follows [20]
M dltdi( 1113857
Mt
di
dmax1113888 1113889
3minusD
(5)
whereM(dlt di) is themass of grains with the grain size d lessthan a certain grain size diMt is the grossmass of grains dmaxis the maximum grain size and D is the fractal dimension
Four different scaling methods were adopted to scaledrockfill materials e results showed that the range of the
Flexible boundaries
Loading plates
3
2
1
4
10120
0
Figure 1 Biaxial compression test sample
2 Advances in Civil Engineering
fractal dimension value is between 1463 and 1783 [21]erefore D was set to 15 in the numerical tests A total offour specimens with the similar grading were used in thenumerical tests e maximum grain size dmax was 5 10 20and 40mm and the minimum grain size dmin was 025 051 and 2mm respectively e particles of size less than dminwere dealt with the equivalent replacement method eaverage grain size d50 was 31 63 126 and 252mm re-spectively e coefficient of uniformity Cu and the co-efficient of curvature of the specimens are 33 and 130respectively e graining curves are shown in Figure 2
e confining pressures (σ3) were 100 200 300 and400 kPa After consolidation the confining pressure wasmaintained constant and then vertical pressure was applied
23 Parameters us far the parameters used in DEMsimulation cannot be directly obtained by laboratory testsbecause no definite relation exists between the mesostructure
0
20
40
60
80
100
01110100Grain size d (mm)
Perc
enta
ge p
assin
g (
)
Maximum grain size dmax5 mm10 mm
20 mm40 mm
Figure 2 Distribution curves of grain sizes
0
300
600
900
1200
0 4 8 12 16Axial strain εa (mm)
Dev
iato
r stre
ss q
()
Maximum grain size dmax5 mm10 mm
20 mm40 mm
Figure 3 Behaviors of qminus εa (confining pressure of 300 kPa)
q f (kPa
)
300
600
900
1200
1500
0 5 10 15 20 25Ddmax
Confining pressure100 kPa200 kPa
300 kPa400 kPa
Figure 4 Behaviors of qf minusDdmax
Volu
met
ric st
rain
εv (
)
ndash4
ndash3
ndash2
ndash1
0
1
2
3
0 4 8 12 16Axial strain εa (mm)
Maximum grain size dmax 5 mm10 mm
20 mm40 mm
Figure 5 Behaviors of εa minus εv (confining pressure of 300 kPa)
ε v (
)
ndash5
ndash4
ndash3
ndash2
ndash1
00 5 10 15 20 25
Ddmax
Confining pressure100 kPa200 kPa
300 kPa400 kPa
Figure 6 Behaviors of εv minusDdmax
Advances in Civil Engineering 3
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(a)
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(b)
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(c)
Figure 7 Continued
4 Advances in Civil Engineering
and macroparameters e trial and error method is used toensure that the numerical test results are in agreement with thelaboratory test results After repeated trial and error themesostructure parameters of biaxial numerical tests were ob-tained e normal and tangential contact stiffness of theparticles was 4times107Nm the normal and tangential contactstiffness of the wall was 2times108 and 0Nm respectively thefriction coefficient between particles was 24 the particledensity was 2600kgm3 the porosity of specimens was 015and the loading rate was 03ms
3 Results and Analyses
31 Size Effects on Strength e deviator stress q-axial strain εacurves with different maximum grain sizes under the confiningpressure of 300kPa are shown in Figure 3 e curves underother confining pressures possess similar behaviors e speci-men was found to exhibit a strain softening behavior e peakdeviator stress is considered to be the failure deviator stress qf e qf minusDdmax curves are shown inFigure 4edeviator stressqf increases with the decrease in Ddmax and the increasingtendencies of qf are evident when Ddmax le 5 is result isconsistent with the laboratory test under the same conditions [7]
32 SizeEffects onDeformation evolumetric strain εv-axialstrain εa curves with different maximum grain sizes undera confining pressure of 300 kPa are shown in Figure 5 ecurves under other confining pressures have similar behaviorse volume of the specimen contracts initially and then dilatesand eventually reaches a steady state when the axial strain is upto 15 e behaviors between the volumetric strain corre-sponding to the axial strain of 15 and Ddmax are shown inFigure 6 e shear dilatancy of cohesionless coarse-grainedsoils is evident with the decrease in Ddmax
33 Size Effects onForceChain emechanical properties ofgranular materials are determined by the force chain
network formed by the mutual contact of particles [22ndash24]e size effect mechanism of coarse-grained soils can beexplained by the distribution and transfer law of contactforce Figure 7 is the force chain distribution of coarse-grained soils with different maximum particle sizes underthe peak stress As shown in Figure 7 ldquoblackrdquo is denoted asthe contact force which is larger than the average value andits width is proportional to the contact force
Figure 7 shows that the contact force is transferredmainly through the strong force chain e strong forcechain is mainly distributed along the direction of the majorprincipal stress and the weak force chain is distributedaround the strong chain and acts as support Both chainsform a force chain network structure With the increase inconfining pressure the lateral strong force chains graduallydevelop to support the axial strong force chains and bothchains form a stable force chain network e macroscopicbehavior indicates that when the confining pressure is highthe shear strength is also high thus indirectly proving therationality of the numerical simulation
e breakage of the contact points causes the entire forcechain to disintegrate and recombine Maintaining stability isdifficult whenmore particles exist on the force chain In generalmaintaining the stability of the force chain is difficult when itsparticle number exceeds five [25 26] When the maximumparticle size is small more particles exist in the sample and thecontact force is uniformly distributed thus forming the strongforce chain is difficult erefore the sliding and dislocationbetween particles easily occur and the macroscopic behavior ofparticles shows that the soils have low shear strength e in-crease in the maximum particle size results in evident sampleboundary restrainte contact force becomes uniform and thestable strong chain becomes long due to the decrease in theparticle number Extending the strong force chains fromone sideof the sample to the other is easy thereby forming a stablestructure that is failure resistant Macroscopically the sampleshows high shear strength and evident size effect
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(d)
Figure 7 Force chain distribution of four different maximum particle sizes and four confining pressure conditions under peak stress state(a) 100 kPa (b) 200 kPa (c) 300 kPa (d) 400 kPa
Advances in Civil Engineering 5
4 Conclusion
eDEM simulation of biaxial compression tests for coarse-grained soils with different maximum grain sizes and self-similar fractal structures in mass was carried out e effectof grain size on the mechanical properties and force chain ofcoarse-grained soils was also discussed e main conclu-sions are as follows
(1) e shear strength of coarse-grained soils increaseswith the increase in the maximum particle size eshear strength of soils evidently increases when theratio of the sample diameter to the maximum par-ticle size is less than five
(2) When the maximum particle size increases the sheardilatancy of cohesionless coarse-grained soil alsoincreases
(3) When the maximum particle size is small manyparticles exist in the sample and the contact forcedistribution is uniform thus forming a strong forcechain is difficult When the maximum particle sizeincreases the particle number decreases the contactforce distribution of particles tends to be uneven andthe stable strong force chain increases the shearstrength thereby resulting in size effect
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] C Li C He C Wang and H Zhao ldquoStudy of scale effect oflarge-scale triaxial test of coarse-grained materialsrdquo Rock andSoil Mechanics vol 29 no s1 pp 563ndash566 2008
[2] G Ma W Zhou X Chang and C Zhou ldquoMesoscopicmechanism study of scale effects of rockfillrdquo Chinese Journalof Rock Mechanics and Engineering vol 31 no 12 pp 2473ndash2482 2012
[3] A Varadarajan K G Sharma K Venkatachalam andA K Gupta ldquoTesting and modeling two rockfill materialsrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 129 no 3 pp 206ndash218 2003
[4] N Li T Zhu and Z Mi ldquoStrength and deformation prop-erties of transition zone material of Xiaolangdi dam and scaleeffectrdquo Water Resources and Power vol 19 no 2 pp 40ndash432001
[5] R Dadkhah M Ghafoori R Ajalloeian and G R Lashkaripourldquoe effect of scale direct shear test on the strength parameters ofclayey sand in Isfahan city Iranrdquo Journal of Applied Sciencevol 10 no 18 pp 2027ndash2033 2010
[6] C Tan CWang YWu andW Li ldquoSize effects on strength ofcohesionless coarse-grained soil under direct shear condi-tionrdquo Journal of Sichuan University Natural Science Editionvol 48 no s1 pp 94ndash99 2016
[7] C Tan Y Wu L Wan C Wang and W Li ldquoSize effects onthe shear strength of the cohesionless coarse-grained soilsunder the triaxial compression conditionrdquo Journal of Jian-gnan University Natural Science Edition vol 14 no 6pp 810ndash813 2015
[8] A K Gupta ldquoEffect of particle size and confining pressure onbreakage and strength parameters of rockfill materialsrdquoElectronic Journal of Geotechnical Engineering vol 14 pp 1ndash12 2009
[9] R J Marsal ldquoLarge scale testing of rockfill materialsrdquo Journalof Soil Mechanics and Foundation Division vol 93 no 2pp 27ndash43 1967
[10] J A Charles and K S Watts ldquoe influence of confiningpressure on the shear strength of compacted rockfillrdquo Geo-technique vol 30 no 4 pp 353ndash367 1980
[11] H Ling Z Yin J Zhu and Z Cai ldquoExperimental study of scaleeffect on strength of rockfill materialsrdquo Journal of Hehai Uni-versity Natural Sciences Edition vol 39 no 5 pp 540ndash544 2011
[12] J Zhu Z Liu H Weng Z Wu and H fu ldquoStudy on effect ofspecimen size upon strength and deformation behavior ofcoarse-grained soil in triaxial testrdquo Journal of Sichuan UniversityEngineering Science Edition vol 44 no 6 pp 92ndash96 2012
[13] P A Cundall and O D L Strack ldquoA discrete numericalmodel for granular assembliesrdquo Geotechnique vol 29 no 1pp 47ndash65 1979
[14] D O Potyondy and P A Cundall ldquoA bonded -particle modelfor rockrdquo International Journal of RockMechanics andMiningSciences vol 41 no 8 pp 1329ndash1364 2004
[15] R K Matthew and B Katalin ldquoSpecimen size effect in discreteelement simulations of granular assembliesrdquo Journal of En-gineering Mechanics vol 135 no 6 pp 485ndash492 2009
[16] H Liu and X Cheng ldquoDiscrete element analysis for size effectsof coarse-grained soilsrdquo Rock and Soil Mechanics vol 30no s1 pp 287ndash292 2009
[17] G Rao and X Chang ldquoA study of scale effect of rockfill basedon PFC2Drdquo China Rural Water and Hydropower no 11pp 88ndash90 2011
[18] Q Zhang and M Hou ldquoResearch on size effect of direct sheartestrdquo Acta Physica Sinica vol 61 no 24 pp 2445041ndash2445046 2012
[19] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) Itasca Consulting Group Minneapolis MNUSA 2008
[20] S W Tyler and S W Wheatcraft ldquoFractal scaling of soilparticle-size distributions analysis and limitationsrdquo Soil ScienceSociety of America Journal vol 56 no 2 pp 362ndash369 1992
[21] T Zhao W Zhou X Chang G Ma and X Ma ldquoFractalcharacteristics and scaling effect of the scaling method forrockfill materialsrdquo Rock and Soil Mechanics vol 36 no 4pp 1093ndash1101 2015
[22] H Tian Y Jiao H Wang and J Ma ldquoResearch on biaxial testof mechanical characteristics on soil-rock aggregate(SRA)based on particle flow code simulationrdquo Chinese Journal ofRock Mechanics and Engineering vol 34 no s1 pp 3564ndash3573 2015
[23] T S Majmudar and R P Behringer ldquoContact force mea-surements and stress-induced anisotropy in granular mate-rialsrdquo Nature vol 435 no 7045 pp 1079ndash1082 2005
[24] R R Hartley and R P Behringer ldquoLogarithmic rate de-pendence of force networks in sheared granular materialsrdquoNature vol 421 no 6926 pp 928ndash931 2003
[25] A Tordesillas A Hunt and J Shi ldquoA characteristic lengthscale in confined elastic buckling of a force chainrdquo GranularMatter vol 13 no 3 pp 215ndash218 2011
[26] A Tordesillas Q Lin J Zhang R P Behringer and J ShildquoStructural stability and jamming of self-organized cluster con-formations in dense granular materialsrdquo Journal of theMechanicsand Physics of Solids vol 59 no 2 pp 265ndash296 2011
6 Advances in Civil Engineering
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
fractal dimension value is between 1463 and 1783 [21]erefore D was set to 15 in the numerical tests A total offour specimens with the similar grading were used in thenumerical tests e maximum grain size dmax was 5 10 20and 40mm and the minimum grain size dmin was 025 051 and 2mm respectively e particles of size less than dminwere dealt with the equivalent replacement method eaverage grain size d50 was 31 63 126 and 252mm re-spectively e coefficient of uniformity Cu and the co-efficient of curvature of the specimens are 33 and 130respectively e graining curves are shown in Figure 2
e confining pressures (σ3) were 100 200 300 and400 kPa After consolidation the confining pressure wasmaintained constant and then vertical pressure was applied
23 Parameters us far the parameters used in DEMsimulation cannot be directly obtained by laboratory testsbecause no definite relation exists between the mesostructure
0
20
40
60
80
100
01110100Grain size d (mm)
Perc
enta
ge p
assin
g (
)
Maximum grain size dmax5 mm10 mm
20 mm40 mm
Figure 2 Distribution curves of grain sizes
0
300
600
900
1200
0 4 8 12 16Axial strain εa (mm)
Dev
iato
r stre
ss q
()
Maximum grain size dmax5 mm10 mm
20 mm40 mm
Figure 3 Behaviors of qminus εa (confining pressure of 300 kPa)
q f (kPa
)
300
600
900
1200
1500
0 5 10 15 20 25Ddmax
Confining pressure100 kPa200 kPa
300 kPa400 kPa
Figure 4 Behaviors of qf minusDdmax
Volu
met
ric st
rain
εv (
)
ndash4
ndash3
ndash2
ndash1
0
1
2
3
0 4 8 12 16Axial strain εa (mm)
Maximum grain size dmax 5 mm10 mm
20 mm40 mm
Figure 5 Behaviors of εa minus εv (confining pressure of 300 kPa)
ε v (
)
ndash5
ndash4
ndash3
ndash2
ndash1
00 5 10 15 20 25
Ddmax
Confining pressure100 kPa200 kPa
300 kPa400 kPa
Figure 6 Behaviors of εv minusDdmax
Advances in Civil Engineering 3
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(a)
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(b)
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(c)
Figure 7 Continued
4 Advances in Civil Engineering
and macroparameters e trial and error method is used toensure that the numerical test results are in agreement with thelaboratory test results After repeated trial and error themesostructure parameters of biaxial numerical tests were ob-tained e normal and tangential contact stiffness of theparticles was 4times107Nm the normal and tangential contactstiffness of the wall was 2times108 and 0Nm respectively thefriction coefficient between particles was 24 the particledensity was 2600kgm3 the porosity of specimens was 015and the loading rate was 03ms
3 Results and Analyses
31 Size Effects on Strength e deviator stress q-axial strain εacurves with different maximum grain sizes under the confiningpressure of 300kPa are shown in Figure 3 e curves underother confining pressures possess similar behaviors e speci-men was found to exhibit a strain softening behavior e peakdeviator stress is considered to be the failure deviator stress qf e qf minusDdmax curves are shown inFigure 4edeviator stressqf increases with the decrease in Ddmax and the increasingtendencies of qf are evident when Ddmax le 5 is result isconsistent with the laboratory test under the same conditions [7]
32 SizeEffects onDeformation evolumetric strain εv-axialstrain εa curves with different maximum grain sizes undera confining pressure of 300 kPa are shown in Figure 5 ecurves under other confining pressures have similar behaviorse volume of the specimen contracts initially and then dilatesand eventually reaches a steady state when the axial strain is upto 15 e behaviors between the volumetric strain corre-sponding to the axial strain of 15 and Ddmax are shown inFigure 6 e shear dilatancy of cohesionless coarse-grainedsoils is evident with the decrease in Ddmax
33 Size Effects onForceChain emechanical properties ofgranular materials are determined by the force chain
network formed by the mutual contact of particles [22ndash24]e size effect mechanism of coarse-grained soils can beexplained by the distribution and transfer law of contactforce Figure 7 is the force chain distribution of coarse-grained soils with different maximum particle sizes underthe peak stress As shown in Figure 7 ldquoblackrdquo is denoted asthe contact force which is larger than the average value andits width is proportional to the contact force
Figure 7 shows that the contact force is transferredmainly through the strong force chain e strong forcechain is mainly distributed along the direction of the majorprincipal stress and the weak force chain is distributedaround the strong chain and acts as support Both chainsform a force chain network structure With the increase inconfining pressure the lateral strong force chains graduallydevelop to support the axial strong force chains and bothchains form a stable force chain network e macroscopicbehavior indicates that when the confining pressure is highthe shear strength is also high thus indirectly proving therationality of the numerical simulation
e breakage of the contact points causes the entire forcechain to disintegrate and recombine Maintaining stability isdifficult whenmore particles exist on the force chain In generalmaintaining the stability of the force chain is difficult when itsparticle number exceeds five [25 26] When the maximumparticle size is small more particles exist in the sample and thecontact force is uniformly distributed thus forming the strongforce chain is difficult erefore the sliding and dislocationbetween particles easily occur and the macroscopic behavior ofparticles shows that the soils have low shear strength e in-crease in the maximum particle size results in evident sampleboundary restrainte contact force becomes uniform and thestable strong chain becomes long due to the decrease in theparticle number Extending the strong force chains fromone sideof the sample to the other is easy thereby forming a stablestructure that is failure resistant Macroscopically the sampleshows high shear strength and evident size effect
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(d)
Figure 7 Force chain distribution of four different maximum particle sizes and four confining pressure conditions under peak stress state(a) 100 kPa (b) 200 kPa (c) 300 kPa (d) 400 kPa
Advances in Civil Engineering 5
4 Conclusion
eDEM simulation of biaxial compression tests for coarse-grained soils with different maximum grain sizes and self-similar fractal structures in mass was carried out e effectof grain size on the mechanical properties and force chain ofcoarse-grained soils was also discussed e main conclu-sions are as follows
(1) e shear strength of coarse-grained soils increaseswith the increase in the maximum particle size eshear strength of soils evidently increases when theratio of the sample diameter to the maximum par-ticle size is less than five
(2) When the maximum particle size increases the sheardilatancy of cohesionless coarse-grained soil alsoincreases
(3) When the maximum particle size is small manyparticles exist in the sample and the contact forcedistribution is uniform thus forming a strong forcechain is difficult When the maximum particle sizeincreases the particle number decreases the contactforce distribution of particles tends to be uneven andthe stable strong force chain increases the shearstrength thereby resulting in size effect
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] C Li C He C Wang and H Zhao ldquoStudy of scale effect oflarge-scale triaxial test of coarse-grained materialsrdquo Rock andSoil Mechanics vol 29 no s1 pp 563ndash566 2008
[2] G Ma W Zhou X Chang and C Zhou ldquoMesoscopicmechanism study of scale effects of rockfillrdquo Chinese Journalof Rock Mechanics and Engineering vol 31 no 12 pp 2473ndash2482 2012
[3] A Varadarajan K G Sharma K Venkatachalam andA K Gupta ldquoTesting and modeling two rockfill materialsrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 129 no 3 pp 206ndash218 2003
[4] N Li T Zhu and Z Mi ldquoStrength and deformation prop-erties of transition zone material of Xiaolangdi dam and scaleeffectrdquo Water Resources and Power vol 19 no 2 pp 40ndash432001
[5] R Dadkhah M Ghafoori R Ajalloeian and G R Lashkaripourldquoe effect of scale direct shear test on the strength parameters ofclayey sand in Isfahan city Iranrdquo Journal of Applied Sciencevol 10 no 18 pp 2027ndash2033 2010
[6] C Tan CWang YWu andW Li ldquoSize effects on strength ofcohesionless coarse-grained soil under direct shear condi-tionrdquo Journal of Sichuan University Natural Science Editionvol 48 no s1 pp 94ndash99 2016
[7] C Tan Y Wu L Wan C Wang and W Li ldquoSize effects onthe shear strength of the cohesionless coarse-grained soilsunder the triaxial compression conditionrdquo Journal of Jian-gnan University Natural Science Edition vol 14 no 6pp 810ndash813 2015
[8] A K Gupta ldquoEffect of particle size and confining pressure onbreakage and strength parameters of rockfill materialsrdquoElectronic Journal of Geotechnical Engineering vol 14 pp 1ndash12 2009
[9] R J Marsal ldquoLarge scale testing of rockfill materialsrdquo Journalof Soil Mechanics and Foundation Division vol 93 no 2pp 27ndash43 1967
[10] J A Charles and K S Watts ldquoe influence of confiningpressure on the shear strength of compacted rockfillrdquo Geo-technique vol 30 no 4 pp 353ndash367 1980
[11] H Ling Z Yin J Zhu and Z Cai ldquoExperimental study of scaleeffect on strength of rockfill materialsrdquo Journal of Hehai Uni-versity Natural Sciences Edition vol 39 no 5 pp 540ndash544 2011
[12] J Zhu Z Liu H Weng Z Wu and H fu ldquoStudy on effect ofspecimen size upon strength and deformation behavior ofcoarse-grained soil in triaxial testrdquo Journal of Sichuan UniversityEngineering Science Edition vol 44 no 6 pp 92ndash96 2012
[13] P A Cundall and O D L Strack ldquoA discrete numericalmodel for granular assembliesrdquo Geotechnique vol 29 no 1pp 47ndash65 1979
[14] D O Potyondy and P A Cundall ldquoA bonded -particle modelfor rockrdquo International Journal of RockMechanics andMiningSciences vol 41 no 8 pp 1329ndash1364 2004
[15] R K Matthew and B Katalin ldquoSpecimen size effect in discreteelement simulations of granular assembliesrdquo Journal of En-gineering Mechanics vol 135 no 6 pp 485ndash492 2009
[16] H Liu and X Cheng ldquoDiscrete element analysis for size effectsof coarse-grained soilsrdquo Rock and Soil Mechanics vol 30no s1 pp 287ndash292 2009
[17] G Rao and X Chang ldquoA study of scale effect of rockfill basedon PFC2Drdquo China Rural Water and Hydropower no 11pp 88ndash90 2011
[18] Q Zhang and M Hou ldquoResearch on size effect of direct sheartestrdquo Acta Physica Sinica vol 61 no 24 pp 2445041ndash2445046 2012
[19] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) Itasca Consulting Group Minneapolis MNUSA 2008
[20] S W Tyler and S W Wheatcraft ldquoFractal scaling of soilparticle-size distributions analysis and limitationsrdquo Soil ScienceSociety of America Journal vol 56 no 2 pp 362ndash369 1992
[21] T Zhao W Zhou X Chang G Ma and X Ma ldquoFractalcharacteristics and scaling effect of the scaling method forrockfill materialsrdquo Rock and Soil Mechanics vol 36 no 4pp 1093ndash1101 2015
[22] H Tian Y Jiao H Wang and J Ma ldquoResearch on biaxial testof mechanical characteristics on soil-rock aggregate(SRA)based on particle flow code simulationrdquo Chinese Journal ofRock Mechanics and Engineering vol 34 no s1 pp 3564ndash3573 2015
[23] T S Majmudar and R P Behringer ldquoContact force mea-surements and stress-induced anisotropy in granular mate-rialsrdquo Nature vol 435 no 7045 pp 1079ndash1082 2005
[24] R R Hartley and R P Behringer ldquoLogarithmic rate de-pendence of force networks in sheared granular materialsrdquoNature vol 421 no 6926 pp 928ndash931 2003
[25] A Tordesillas A Hunt and J Shi ldquoA characteristic lengthscale in confined elastic buckling of a force chainrdquo GranularMatter vol 13 no 3 pp 215ndash218 2011
[26] A Tordesillas Q Lin J Zhang R P Behringer and J ShildquoStructural stability and jamming of self-organized cluster con-formations in dense granular materialsrdquo Journal of theMechanicsand Physics of Solids vol 59 no 2 pp 265ndash296 2011
6 Advances in Civil Engineering
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(a)
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(b)
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(c)
Figure 7 Continued
4 Advances in Civil Engineering
and macroparameters e trial and error method is used toensure that the numerical test results are in agreement with thelaboratory test results After repeated trial and error themesostructure parameters of biaxial numerical tests were ob-tained e normal and tangential contact stiffness of theparticles was 4times107Nm the normal and tangential contactstiffness of the wall was 2times108 and 0Nm respectively thefriction coefficient between particles was 24 the particledensity was 2600kgm3 the porosity of specimens was 015and the loading rate was 03ms
3 Results and Analyses
31 Size Effects on Strength e deviator stress q-axial strain εacurves with different maximum grain sizes under the confiningpressure of 300kPa are shown in Figure 3 e curves underother confining pressures possess similar behaviors e speci-men was found to exhibit a strain softening behavior e peakdeviator stress is considered to be the failure deviator stress qf e qf minusDdmax curves are shown inFigure 4edeviator stressqf increases with the decrease in Ddmax and the increasingtendencies of qf are evident when Ddmax le 5 is result isconsistent with the laboratory test under the same conditions [7]
32 SizeEffects onDeformation evolumetric strain εv-axialstrain εa curves with different maximum grain sizes undera confining pressure of 300 kPa are shown in Figure 5 ecurves under other confining pressures have similar behaviorse volume of the specimen contracts initially and then dilatesand eventually reaches a steady state when the axial strain is upto 15 e behaviors between the volumetric strain corre-sponding to the axial strain of 15 and Ddmax are shown inFigure 6 e shear dilatancy of cohesionless coarse-grainedsoils is evident with the decrease in Ddmax
33 Size Effects onForceChain emechanical properties ofgranular materials are determined by the force chain
network formed by the mutual contact of particles [22ndash24]e size effect mechanism of coarse-grained soils can beexplained by the distribution and transfer law of contactforce Figure 7 is the force chain distribution of coarse-grained soils with different maximum particle sizes underthe peak stress As shown in Figure 7 ldquoblackrdquo is denoted asthe contact force which is larger than the average value andits width is proportional to the contact force
Figure 7 shows that the contact force is transferredmainly through the strong force chain e strong forcechain is mainly distributed along the direction of the majorprincipal stress and the weak force chain is distributedaround the strong chain and acts as support Both chainsform a force chain network structure With the increase inconfining pressure the lateral strong force chains graduallydevelop to support the axial strong force chains and bothchains form a stable force chain network e macroscopicbehavior indicates that when the confining pressure is highthe shear strength is also high thus indirectly proving therationality of the numerical simulation
e breakage of the contact points causes the entire forcechain to disintegrate and recombine Maintaining stability isdifficult whenmore particles exist on the force chain In generalmaintaining the stability of the force chain is difficult when itsparticle number exceeds five [25 26] When the maximumparticle size is small more particles exist in the sample and thecontact force is uniformly distributed thus forming the strongforce chain is difficult erefore the sliding and dislocationbetween particles easily occur and the macroscopic behavior ofparticles shows that the soils have low shear strength e in-crease in the maximum particle size results in evident sampleboundary restrainte contact force becomes uniform and thestable strong chain becomes long due to the decrease in theparticle number Extending the strong force chains fromone sideof the sample to the other is easy thereby forming a stablestructure that is failure resistant Macroscopically the sampleshows high shear strength and evident size effect
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(d)
Figure 7 Force chain distribution of four different maximum particle sizes and four confining pressure conditions under peak stress state(a) 100 kPa (b) 200 kPa (c) 300 kPa (d) 400 kPa
Advances in Civil Engineering 5
4 Conclusion
eDEM simulation of biaxial compression tests for coarse-grained soils with different maximum grain sizes and self-similar fractal structures in mass was carried out e effectof grain size on the mechanical properties and force chain ofcoarse-grained soils was also discussed e main conclu-sions are as follows
(1) e shear strength of coarse-grained soils increaseswith the increase in the maximum particle size eshear strength of soils evidently increases when theratio of the sample diameter to the maximum par-ticle size is less than five
(2) When the maximum particle size increases the sheardilatancy of cohesionless coarse-grained soil alsoincreases
(3) When the maximum particle size is small manyparticles exist in the sample and the contact forcedistribution is uniform thus forming a strong forcechain is difficult When the maximum particle sizeincreases the particle number decreases the contactforce distribution of particles tends to be uneven andthe stable strong force chain increases the shearstrength thereby resulting in size effect
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] C Li C He C Wang and H Zhao ldquoStudy of scale effect oflarge-scale triaxial test of coarse-grained materialsrdquo Rock andSoil Mechanics vol 29 no s1 pp 563ndash566 2008
[2] G Ma W Zhou X Chang and C Zhou ldquoMesoscopicmechanism study of scale effects of rockfillrdquo Chinese Journalof Rock Mechanics and Engineering vol 31 no 12 pp 2473ndash2482 2012
[3] A Varadarajan K G Sharma K Venkatachalam andA K Gupta ldquoTesting and modeling two rockfill materialsrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 129 no 3 pp 206ndash218 2003
[4] N Li T Zhu and Z Mi ldquoStrength and deformation prop-erties of transition zone material of Xiaolangdi dam and scaleeffectrdquo Water Resources and Power vol 19 no 2 pp 40ndash432001
[5] R Dadkhah M Ghafoori R Ajalloeian and G R Lashkaripourldquoe effect of scale direct shear test on the strength parameters ofclayey sand in Isfahan city Iranrdquo Journal of Applied Sciencevol 10 no 18 pp 2027ndash2033 2010
[6] C Tan CWang YWu andW Li ldquoSize effects on strength ofcohesionless coarse-grained soil under direct shear condi-tionrdquo Journal of Sichuan University Natural Science Editionvol 48 no s1 pp 94ndash99 2016
[7] C Tan Y Wu L Wan C Wang and W Li ldquoSize effects onthe shear strength of the cohesionless coarse-grained soilsunder the triaxial compression conditionrdquo Journal of Jian-gnan University Natural Science Edition vol 14 no 6pp 810ndash813 2015
[8] A K Gupta ldquoEffect of particle size and confining pressure onbreakage and strength parameters of rockfill materialsrdquoElectronic Journal of Geotechnical Engineering vol 14 pp 1ndash12 2009
[9] R J Marsal ldquoLarge scale testing of rockfill materialsrdquo Journalof Soil Mechanics and Foundation Division vol 93 no 2pp 27ndash43 1967
[10] J A Charles and K S Watts ldquoe influence of confiningpressure on the shear strength of compacted rockfillrdquo Geo-technique vol 30 no 4 pp 353ndash367 1980
[11] H Ling Z Yin J Zhu and Z Cai ldquoExperimental study of scaleeffect on strength of rockfill materialsrdquo Journal of Hehai Uni-versity Natural Sciences Edition vol 39 no 5 pp 540ndash544 2011
[12] J Zhu Z Liu H Weng Z Wu and H fu ldquoStudy on effect ofspecimen size upon strength and deformation behavior ofcoarse-grained soil in triaxial testrdquo Journal of Sichuan UniversityEngineering Science Edition vol 44 no 6 pp 92ndash96 2012
[13] P A Cundall and O D L Strack ldquoA discrete numericalmodel for granular assembliesrdquo Geotechnique vol 29 no 1pp 47ndash65 1979
[14] D O Potyondy and P A Cundall ldquoA bonded -particle modelfor rockrdquo International Journal of RockMechanics andMiningSciences vol 41 no 8 pp 1329ndash1364 2004
[15] R K Matthew and B Katalin ldquoSpecimen size effect in discreteelement simulations of granular assembliesrdquo Journal of En-gineering Mechanics vol 135 no 6 pp 485ndash492 2009
[16] H Liu and X Cheng ldquoDiscrete element analysis for size effectsof coarse-grained soilsrdquo Rock and Soil Mechanics vol 30no s1 pp 287ndash292 2009
[17] G Rao and X Chang ldquoA study of scale effect of rockfill basedon PFC2Drdquo China Rural Water and Hydropower no 11pp 88ndash90 2011
[18] Q Zhang and M Hou ldquoResearch on size effect of direct sheartestrdquo Acta Physica Sinica vol 61 no 24 pp 2445041ndash2445046 2012
[19] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) Itasca Consulting Group Minneapolis MNUSA 2008
[20] S W Tyler and S W Wheatcraft ldquoFractal scaling of soilparticle-size distributions analysis and limitationsrdquo Soil ScienceSociety of America Journal vol 56 no 2 pp 362ndash369 1992
[21] T Zhao W Zhou X Chang G Ma and X Ma ldquoFractalcharacteristics and scaling effect of the scaling method forrockfill materialsrdquo Rock and Soil Mechanics vol 36 no 4pp 1093ndash1101 2015
[22] H Tian Y Jiao H Wang and J Ma ldquoResearch on biaxial testof mechanical characteristics on soil-rock aggregate(SRA)based on particle flow code simulationrdquo Chinese Journal ofRock Mechanics and Engineering vol 34 no s1 pp 3564ndash3573 2015
[23] T S Majmudar and R P Behringer ldquoContact force mea-surements and stress-induced anisotropy in granular mate-rialsrdquo Nature vol 435 no 7045 pp 1079ndash1082 2005
[24] R R Hartley and R P Behringer ldquoLogarithmic rate de-pendence of force networks in sheared granular materialsrdquoNature vol 421 no 6926 pp 928ndash931 2003
[25] A Tordesillas A Hunt and J Shi ldquoA characteristic lengthscale in confined elastic buckling of a force chainrdquo GranularMatter vol 13 no 3 pp 215ndash218 2011
[26] A Tordesillas Q Lin J Zhang R P Behringer and J ShildquoStructural stability and jamming of self-organized cluster con-formations in dense granular materialsrdquo Journal of theMechanicsand Physics of Solids vol 59 no 2 pp 265ndash296 2011
6 Advances in Civil Engineering
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
and macroparameters e trial and error method is used toensure that the numerical test results are in agreement with thelaboratory test results After repeated trial and error themesostructure parameters of biaxial numerical tests were ob-tained e normal and tangential contact stiffness of theparticles was 4times107Nm the normal and tangential contactstiffness of the wall was 2times108 and 0Nm respectively thefriction coefficient between particles was 24 the particledensity was 2600kgm3 the porosity of specimens was 015and the loading rate was 03ms
3 Results and Analyses
31 Size Effects on Strength e deviator stress q-axial strain εacurves with different maximum grain sizes under the confiningpressure of 300kPa are shown in Figure 3 e curves underother confining pressures possess similar behaviors e speci-men was found to exhibit a strain softening behavior e peakdeviator stress is considered to be the failure deviator stress qf e qf minusDdmax curves are shown inFigure 4edeviator stressqf increases with the decrease in Ddmax and the increasingtendencies of qf are evident when Ddmax le 5 is result isconsistent with the laboratory test under the same conditions [7]
32 SizeEffects onDeformation evolumetric strain εv-axialstrain εa curves with different maximum grain sizes undera confining pressure of 300 kPa are shown in Figure 5 ecurves under other confining pressures have similar behaviorse volume of the specimen contracts initially and then dilatesand eventually reaches a steady state when the axial strain is upto 15 e behaviors between the volumetric strain corre-sponding to the axial strain of 15 and Ddmax are shown inFigure 6 e shear dilatancy of cohesionless coarse-grainedsoils is evident with the decrease in Ddmax
33 Size Effects onForceChain emechanical properties ofgranular materials are determined by the force chain
network formed by the mutual contact of particles [22ndash24]e size effect mechanism of coarse-grained soils can beexplained by the distribution and transfer law of contactforce Figure 7 is the force chain distribution of coarse-grained soils with different maximum particle sizes underthe peak stress As shown in Figure 7 ldquoblackrdquo is denoted asthe contact force which is larger than the average value andits width is proportional to the contact force
Figure 7 shows that the contact force is transferredmainly through the strong force chain e strong forcechain is mainly distributed along the direction of the majorprincipal stress and the weak force chain is distributedaround the strong chain and acts as support Both chainsform a force chain network structure With the increase inconfining pressure the lateral strong force chains graduallydevelop to support the axial strong force chains and bothchains form a stable force chain network e macroscopicbehavior indicates that when the confining pressure is highthe shear strength is also high thus indirectly proving therationality of the numerical simulation
e breakage of the contact points causes the entire forcechain to disintegrate and recombine Maintaining stability isdifficult whenmore particles exist on the force chain In generalmaintaining the stability of the force chain is difficult when itsparticle number exceeds five [25 26] When the maximumparticle size is small more particles exist in the sample and thecontact force is uniformly distributed thus forming the strongforce chain is difficult erefore the sliding and dislocationbetween particles easily occur and the macroscopic behavior ofparticles shows that the soils have low shear strength e in-crease in the maximum particle size results in evident sampleboundary restrainte contact force becomes uniform and thestable strong chain becomes long due to the decrease in theparticle number Extending the strong force chains fromone sideof the sample to the other is easy thereby forming a stablestructure that is failure resistant Macroscopically the sampleshows high shear strength and evident size effect
dmax = 40 mm dmax = 20 mm dmax = 10 mm dmax = 5 mm
(d)
Figure 7 Force chain distribution of four different maximum particle sizes and four confining pressure conditions under peak stress state(a) 100 kPa (b) 200 kPa (c) 300 kPa (d) 400 kPa
Advances in Civil Engineering 5
4 Conclusion
eDEM simulation of biaxial compression tests for coarse-grained soils with different maximum grain sizes and self-similar fractal structures in mass was carried out e effectof grain size on the mechanical properties and force chain ofcoarse-grained soils was also discussed e main conclu-sions are as follows
(1) e shear strength of coarse-grained soils increaseswith the increase in the maximum particle size eshear strength of soils evidently increases when theratio of the sample diameter to the maximum par-ticle size is less than five
(2) When the maximum particle size increases the sheardilatancy of cohesionless coarse-grained soil alsoincreases
(3) When the maximum particle size is small manyparticles exist in the sample and the contact forcedistribution is uniform thus forming a strong forcechain is difficult When the maximum particle sizeincreases the particle number decreases the contactforce distribution of particles tends to be uneven andthe stable strong force chain increases the shearstrength thereby resulting in size effect
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] C Li C He C Wang and H Zhao ldquoStudy of scale effect oflarge-scale triaxial test of coarse-grained materialsrdquo Rock andSoil Mechanics vol 29 no s1 pp 563ndash566 2008
[2] G Ma W Zhou X Chang and C Zhou ldquoMesoscopicmechanism study of scale effects of rockfillrdquo Chinese Journalof Rock Mechanics and Engineering vol 31 no 12 pp 2473ndash2482 2012
[3] A Varadarajan K G Sharma K Venkatachalam andA K Gupta ldquoTesting and modeling two rockfill materialsrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 129 no 3 pp 206ndash218 2003
[4] N Li T Zhu and Z Mi ldquoStrength and deformation prop-erties of transition zone material of Xiaolangdi dam and scaleeffectrdquo Water Resources and Power vol 19 no 2 pp 40ndash432001
[5] R Dadkhah M Ghafoori R Ajalloeian and G R Lashkaripourldquoe effect of scale direct shear test on the strength parameters ofclayey sand in Isfahan city Iranrdquo Journal of Applied Sciencevol 10 no 18 pp 2027ndash2033 2010
[6] C Tan CWang YWu andW Li ldquoSize effects on strength ofcohesionless coarse-grained soil under direct shear condi-tionrdquo Journal of Sichuan University Natural Science Editionvol 48 no s1 pp 94ndash99 2016
[7] C Tan Y Wu L Wan C Wang and W Li ldquoSize effects onthe shear strength of the cohesionless coarse-grained soilsunder the triaxial compression conditionrdquo Journal of Jian-gnan University Natural Science Edition vol 14 no 6pp 810ndash813 2015
[8] A K Gupta ldquoEffect of particle size and confining pressure onbreakage and strength parameters of rockfill materialsrdquoElectronic Journal of Geotechnical Engineering vol 14 pp 1ndash12 2009
[9] R J Marsal ldquoLarge scale testing of rockfill materialsrdquo Journalof Soil Mechanics and Foundation Division vol 93 no 2pp 27ndash43 1967
[10] J A Charles and K S Watts ldquoe influence of confiningpressure on the shear strength of compacted rockfillrdquo Geo-technique vol 30 no 4 pp 353ndash367 1980
[11] H Ling Z Yin J Zhu and Z Cai ldquoExperimental study of scaleeffect on strength of rockfill materialsrdquo Journal of Hehai Uni-versity Natural Sciences Edition vol 39 no 5 pp 540ndash544 2011
[12] J Zhu Z Liu H Weng Z Wu and H fu ldquoStudy on effect ofspecimen size upon strength and deformation behavior ofcoarse-grained soil in triaxial testrdquo Journal of Sichuan UniversityEngineering Science Edition vol 44 no 6 pp 92ndash96 2012
[13] P A Cundall and O D L Strack ldquoA discrete numericalmodel for granular assembliesrdquo Geotechnique vol 29 no 1pp 47ndash65 1979
[14] D O Potyondy and P A Cundall ldquoA bonded -particle modelfor rockrdquo International Journal of RockMechanics andMiningSciences vol 41 no 8 pp 1329ndash1364 2004
[15] R K Matthew and B Katalin ldquoSpecimen size effect in discreteelement simulations of granular assembliesrdquo Journal of En-gineering Mechanics vol 135 no 6 pp 485ndash492 2009
[16] H Liu and X Cheng ldquoDiscrete element analysis for size effectsof coarse-grained soilsrdquo Rock and Soil Mechanics vol 30no s1 pp 287ndash292 2009
[17] G Rao and X Chang ldquoA study of scale effect of rockfill basedon PFC2Drdquo China Rural Water and Hydropower no 11pp 88ndash90 2011
[18] Q Zhang and M Hou ldquoResearch on size effect of direct sheartestrdquo Acta Physica Sinica vol 61 no 24 pp 2445041ndash2445046 2012
[19] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) Itasca Consulting Group Minneapolis MNUSA 2008
[20] S W Tyler and S W Wheatcraft ldquoFractal scaling of soilparticle-size distributions analysis and limitationsrdquo Soil ScienceSociety of America Journal vol 56 no 2 pp 362ndash369 1992
[21] T Zhao W Zhou X Chang G Ma and X Ma ldquoFractalcharacteristics and scaling effect of the scaling method forrockfill materialsrdquo Rock and Soil Mechanics vol 36 no 4pp 1093ndash1101 2015
[22] H Tian Y Jiao H Wang and J Ma ldquoResearch on biaxial testof mechanical characteristics on soil-rock aggregate(SRA)based on particle flow code simulationrdquo Chinese Journal ofRock Mechanics and Engineering vol 34 no s1 pp 3564ndash3573 2015
[23] T S Majmudar and R P Behringer ldquoContact force mea-surements and stress-induced anisotropy in granular mate-rialsrdquo Nature vol 435 no 7045 pp 1079ndash1082 2005
[24] R R Hartley and R P Behringer ldquoLogarithmic rate de-pendence of force networks in sheared granular materialsrdquoNature vol 421 no 6926 pp 928ndash931 2003
[25] A Tordesillas A Hunt and J Shi ldquoA characteristic lengthscale in confined elastic buckling of a force chainrdquo GranularMatter vol 13 no 3 pp 215ndash218 2011
[26] A Tordesillas Q Lin J Zhang R P Behringer and J ShildquoStructural stability and jamming of self-organized cluster con-formations in dense granular materialsrdquo Journal of theMechanicsand Physics of Solids vol 59 no 2 pp 265ndash296 2011
6 Advances in Civil Engineering
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
4 Conclusion
eDEM simulation of biaxial compression tests for coarse-grained soils with different maximum grain sizes and self-similar fractal structures in mass was carried out e effectof grain size on the mechanical properties and force chain ofcoarse-grained soils was also discussed e main conclu-sions are as follows
(1) e shear strength of coarse-grained soils increaseswith the increase in the maximum particle size eshear strength of soils evidently increases when theratio of the sample diameter to the maximum par-ticle size is less than five
(2) When the maximum particle size increases the sheardilatancy of cohesionless coarse-grained soil alsoincreases
(3) When the maximum particle size is small manyparticles exist in the sample and the contact forcedistribution is uniform thus forming a strong forcechain is difficult When the maximum particle sizeincreases the particle number decreases the contactforce distribution of particles tends to be uneven andthe stable strong force chain increases the shearstrength thereby resulting in size effect
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] C Li C He C Wang and H Zhao ldquoStudy of scale effect oflarge-scale triaxial test of coarse-grained materialsrdquo Rock andSoil Mechanics vol 29 no s1 pp 563ndash566 2008
[2] G Ma W Zhou X Chang and C Zhou ldquoMesoscopicmechanism study of scale effects of rockfillrdquo Chinese Journalof Rock Mechanics and Engineering vol 31 no 12 pp 2473ndash2482 2012
[3] A Varadarajan K G Sharma K Venkatachalam andA K Gupta ldquoTesting and modeling two rockfill materialsrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 129 no 3 pp 206ndash218 2003
[4] N Li T Zhu and Z Mi ldquoStrength and deformation prop-erties of transition zone material of Xiaolangdi dam and scaleeffectrdquo Water Resources and Power vol 19 no 2 pp 40ndash432001
[5] R Dadkhah M Ghafoori R Ajalloeian and G R Lashkaripourldquoe effect of scale direct shear test on the strength parameters ofclayey sand in Isfahan city Iranrdquo Journal of Applied Sciencevol 10 no 18 pp 2027ndash2033 2010
[6] C Tan CWang YWu andW Li ldquoSize effects on strength ofcohesionless coarse-grained soil under direct shear condi-tionrdquo Journal of Sichuan University Natural Science Editionvol 48 no s1 pp 94ndash99 2016
[7] C Tan Y Wu L Wan C Wang and W Li ldquoSize effects onthe shear strength of the cohesionless coarse-grained soilsunder the triaxial compression conditionrdquo Journal of Jian-gnan University Natural Science Edition vol 14 no 6pp 810ndash813 2015
[8] A K Gupta ldquoEffect of particle size and confining pressure onbreakage and strength parameters of rockfill materialsrdquoElectronic Journal of Geotechnical Engineering vol 14 pp 1ndash12 2009
[9] R J Marsal ldquoLarge scale testing of rockfill materialsrdquo Journalof Soil Mechanics and Foundation Division vol 93 no 2pp 27ndash43 1967
[10] J A Charles and K S Watts ldquoe influence of confiningpressure on the shear strength of compacted rockfillrdquo Geo-technique vol 30 no 4 pp 353ndash367 1980
[11] H Ling Z Yin J Zhu and Z Cai ldquoExperimental study of scaleeffect on strength of rockfill materialsrdquo Journal of Hehai Uni-versity Natural Sciences Edition vol 39 no 5 pp 540ndash544 2011
[12] J Zhu Z Liu H Weng Z Wu and H fu ldquoStudy on effect ofspecimen size upon strength and deformation behavior ofcoarse-grained soil in triaxial testrdquo Journal of Sichuan UniversityEngineering Science Edition vol 44 no 6 pp 92ndash96 2012
[13] P A Cundall and O D L Strack ldquoA discrete numericalmodel for granular assembliesrdquo Geotechnique vol 29 no 1pp 47ndash65 1979
[14] D O Potyondy and P A Cundall ldquoA bonded -particle modelfor rockrdquo International Journal of RockMechanics andMiningSciences vol 41 no 8 pp 1329ndash1364 2004
[15] R K Matthew and B Katalin ldquoSpecimen size effect in discreteelement simulations of granular assembliesrdquo Journal of En-gineering Mechanics vol 135 no 6 pp 485ndash492 2009
[16] H Liu and X Cheng ldquoDiscrete element analysis for size effectsof coarse-grained soilsrdquo Rock and Soil Mechanics vol 30no s1 pp 287ndash292 2009
[17] G Rao and X Chang ldquoA study of scale effect of rockfill basedon PFC2Drdquo China Rural Water and Hydropower no 11pp 88ndash90 2011
[18] Q Zhang and M Hou ldquoResearch on size effect of direct sheartestrdquo Acta Physica Sinica vol 61 no 24 pp 2445041ndash2445046 2012
[19] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) Itasca Consulting Group Minneapolis MNUSA 2008
[20] S W Tyler and S W Wheatcraft ldquoFractal scaling of soilparticle-size distributions analysis and limitationsrdquo Soil ScienceSociety of America Journal vol 56 no 2 pp 362ndash369 1992
[21] T Zhao W Zhou X Chang G Ma and X Ma ldquoFractalcharacteristics and scaling effect of the scaling method forrockfill materialsrdquo Rock and Soil Mechanics vol 36 no 4pp 1093ndash1101 2015
[22] H Tian Y Jiao H Wang and J Ma ldquoResearch on biaxial testof mechanical characteristics on soil-rock aggregate(SRA)based on particle flow code simulationrdquo Chinese Journal ofRock Mechanics and Engineering vol 34 no s1 pp 3564ndash3573 2015
[23] T S Majmudar and R P Behringer ldquoContact force mea-surements and stress-induced anisotropy in granular mate-rialsrdquo Nature vol 435 no 7045 pp 1079ndash1082 2005
[24] R R Hartley and R P Behringer ldquoLogarithmic rate de-pendence of force networks in sheared granular materialsrdquoNature vol 421 no 6926 pp 928ndash931 2003
[25] A Tordesillas A Hunt and J Shi ldquoA characteristic lengthscale in confined elastic buckling of a force chainrdquo GranularMatter vol 13 no 3 pp 215ndash218 2011
[26] A Tordesillas Q Lin J Zhang R P Behringer and J ShildquoStructural stability and jamming of self-organized cluster con-formations in dense granular materialsrdquo Journal of theMechanicsand Physics of Solids vol 59 no 2 pp 265ndash296 2011
6 Advances in Civil Engineering
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
