Research ArticleCompositional Effects and Mechanical ParametricAnalysis of Outwash Deposits Based on the RandomisedGeneration of Stone Blocks

Chong Shi12 and Jinzhou Bai12

1Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering Hohai University Nanjing 210098 China2Institute of Geotechnical Engineering Hohai University Nanjing 210098 China

Correspondence should be addressed to Chong Shi shichong81126com

Received 17 September 2014 Accepted 25 November 2014

Academic Editor Zhaohui Li

Copyright copy 2015 C Shi and J Bai This 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

Based on the distribution of the stone blocks in outwash deposits the paper present a modeling method for the random structureof outwash deposits in which the long axis of the stone blocks is supposed obeying a lognormal distribution Then numericalexperiments of biaxial compression using the granular discrete element method are used in the macro- and micro parametricanalysis The influences of strength of the cementation the sizes of stone blocks and the content of stone blocks on the peakcompressive and shear strength are discussed The micromechanical parameters of the outwash deposits are also analyzed Theproposed method offers a supplement to the mechanical characterization of outwash deposits and accounts for the limitation thatindoor experiments cannot consider large stone blocks

1 Introduction

Outwash deposits are a particular type of geological mediumand are formed by glacial movement The media are com-posed primarily of irregular stone blocks with high strengthand weak fine-grained debris as shown in Figure 1 They arewidely distributed in southwestern China where the waterresources are rich and the geological conditions are suitablefor the construction of hydropower plants According tothe program ldquoaccelerating the development of hydropowerproject in Chinardquo outwash deposits should be an importantand difficult issue and will receive more attention from thedepartments of geological engineering geotechnical engi-neering and hydropower engineering However due to thecomposition of outwash deposits the mechanical parametersof outwash deposits are difficult to be determined by currentanalysis methods as well as reinforcement measures

Outwash deposits are different from common homoge-neous materials because of the presence of stone blocks andthe cementation of fine-grained debris For any structuralcharacteristics and material composition the mechanicalproperties and the water-physical properties of them are

uniqueAt presentmost studies consider the outwash depositas a homogeneous medium The analytical approaches relymainly on indoor experiments and numerical simulationsHowever because large stone blocks cannot be used inthe indoor experiments the mechanical characterizationof outwash deposits has some limitations Some scholars[1 2] found that the existence of boulders increased thestrength and density of outwash deposits which also leadsto deviations in their mechanical properties Others studiedthe relationships among the cementation of fine-graineddebris dry density water content block shapes block dis-tribution and the shear strength of the stone and debrismixture by experimental tests such as the large triaxial shearexperiment the medium-sized triaxial shear experimentand the large horizontal push shear experiment [3ndash7] Theresults demonstrate that the stress-strain of this medium isapproximately taken on nonlinear hardening characteristicswhich agrees well with the hyperbola assumption of Duncan-Chang model and the shear strength of the stone anddebris mixture is related closely to the concentration anddistribution of the stone blocks However it is difficult togain a thorough understanding of outwash deposits without

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2015 Article ID 863915 13 pageshttpdxdoiorg1011552015863915

2 Advances in Materials Science and Engineering

Outwash deposit

Gully

(c)

(b)(a)

Grade i

Grade i + 1

3220m2910m

2790m

2200m

2650m

2560m

2180m

Figure 1 A typical outwash deposit formed by glacial movement

considering the effects of heterogeneity and randomness onthe distribution and concentration of stone blocks in theconventional geotechnical experimentsThe limited field testsare discrete and not representative Therefore it is necessaryto consider the composition of the outwash deposit in theexperiments and numerical calculations when studying themechanical characteristics Digital image processing is aconvenient toolThe sizes and shapes of the debris in outwashdeposits were studied by Lebourg et al [8] The real internalstructure of geological materials was also detected by suchtechnology [9ndash12] So it can provide an effective approach forresearch into the composition of outwash deposits [13 14]Because the structure composition of outwash deposits ismainly determined by stone blocks a model considering thedistribution and randomness of stone blocks is meaningful

According to the field statistics the geometric shapes ofthe stone blocks are assumed to be approximately elliptic-polygon and obey a normal distribution in this work Then ageomechanical model for biaxial compression is establishedusing the particle flow code The effects of the stone blocksand fine-grained debris on the mechanical properties ofoutwash deposit are studiedThe changes in the macroscopiccompressive strength and shear strength of the medium arealso discussed

2 Structural Characteristics ofOutwash Deposits

21 The Structural Composition of Outwash Deposits Out-wash deposits are a type of binarymixturemedium consistingof fine-grained debris and stone blocks where both the debrisand stone blocks are made of the same material and aredistinguished by the grain size but not by the compositionHowever not all sizes of stone blocks have a positive influenceon the strength of the medium There is a threshold thatdistinguishes debris from stone blocks The threshold size ofstone blocks can be determined only in certain geologicalconditions and scales which shows that the large grainsplay a greater role in the macroscopic mechanical properties

during the smaller scale studies When the scale of researchis increased the former large grains will lose their dominanteffect to mechanical property and can be regarded as debrisThe following criterion to distinguish stones from debris isproposed [15]

119891 = 119877 119889 ge 119889thr119878 119889 lt 119889thr

(1)

where119889thr is the threshold of stone and debris (119889thr = 005119871119888)119871119888is the characteristic engineering size 119877 denotes the stone

and 119878 denotes the debrisIn addition the indoor geotechnical test on similar

media the direct shear test and triaxial compression test canonly consider grains below 2 cm due to the limitations of theinstruments Therefore 119889thr is set to be 2 cm in this workwhich means that if the grain size is less than 2 cm the grainwill be defined as debris Conversely if the grain size is greaterthan 2 cm the grain will be considered as a stone block

By above measure grains of debris and stone blocks willbe endowed attributes separately to reflect the change rule ofmedium composition and mechanical property

22 The Aggregate Gradation of Outwash Deposits The sizesand shapes of stone blocks differ greatly at different part asshown in Figure 1(c)Themicrostructure of outwash depositswhich can be explained as grain contact and interaction isjust related to content size and roughness of stone blocks Inorder to construct a stochasticmodel of outwash deposits thegrains regarded as stone can be divided into several gradationaccording to the grain size Then according to the resultsof the grain size analysis and field statistics the proportionquality volume and area of the stone blocks in the researchregion can be obtained easily The grains smaller than thethreshold will be considered as debris and can be describedusing the conventional geotechnical experiments Numericalsimulation method will be used to reflect its influence onmechanical property of outwash deposit in which the stoneblocks are supposed to be unbroken

Advances in Materials Science and Engineering 3

O

N polygon

Random polygon

Ni

120579

Figure 2 An arbitrarily shaped stone block depicted by a particlescluster

If the density of the stone blocks is 120588119877 the debris density

is 120588119878 Therefore the 2D area of the stone blocks in grade 119894 can

be written as follows

119860119894=

41199032119866119894120588119877

1198660120588119878+ sum119899

119896=1119866119894120588119877

(2)

where 119860119894is the 2D area percentage of stone blocks in grade

119894 1198660is the weight of the medium with grain sizes below the

threshold and sum119899119896=1

119866119896120588119877is the total weight of stone blocks

23 The Randomised Generation of Aggregates Each stoneblock can be regarded as an arbitrary polygon in the planeso a number of polygons are generated randomly in thedesignated region to simulate blocks During the generationprocess every polygon should be judged to avoid overlappingwith others Then the area in the polygons is regarded asstone blocks of different grades When the polygon is convexit has difficulty in considering the interaction force dueto mosaic effect of rough block surface which will leadto deviations in the mechanical parameter research so thepolygon generation should consider convexity and concavityat the same time

To generate the arbitrary shapes of the stone blocks thestone blocks are assumed to be initially elliptical then theoutline is divided as polygon and the vertices of polygon arerandom as shown in Figure 2The ellipses can be determinedusing three parameters the length of long axis 119886 length of theshort axis 119887 (or the axis ratio defined as ratio of the short axislength to the long axis) and the azimuth of the long axis 120579Field investigation shows that the angle of long axis azimuth isin poor statistical correlation so it can be regarded as obeyinguniform distribution over 0sim360∘

As shown in Figure 3(a) the lengths of the long axis andthe axis ratio are approximately obeying normal distributionwith variance as shown in Figures 3(c) and 3(d) So the length

of the long axis the axial ratio and the azimuth angle of longaxis whose definition is shown in Figure 3(b) are given asshown in the following formula

119886 = 1198860+ 2120590119886(rand (1) minus 1)

119903 = 1199030+ 2120590119903(rand (1) minus 1)

120579 = 360 sdot rand (1)

(3)

where 119886 120590119886 119903 120590119903are the mean of the long axis the variance

of the long axis the mean of the axial ratio and the varianceof axial ratio respectively 120579 is the azimuth of long axisrand(1) returns a random number between 0 and 1 119886 120590

119886

119903 120590119903should be obtained using the statistics according to the

stone blocks in outwash deposit medium Here 05 times thecorresponding mean value is used as an empirical parameterfor variance if there is no statistical information

Then every stone block is hypothesised to be a polygoncomposed of119873 sides as shown in Figure 2The elliptical arc isaccordingly divided into119873 arcs Each point of the arc can bemoved towards the centre of the ellipse The correspondingcoordinate of each point can be defined as follows

119909119894= 1199090+ 119886 sdot cos (120579 + 119873Δ120593)

119910119894= 1199100+ 119886 sdot 119903 sdot sin (120579 + 119873Δ120593)

(4)

where 119909119894and 119910

119894are the coordinates of the 119894th node in a

polygon 1199090and 119910

0are the coordinates of the centre of the

ellipse 1205930is the azimuth of ellipse and Δ120593 is the angle

between two vertexes of the polygon where Δ120593 = 360119873The steps of the random structure generation are shown

in Figure 4The generated polygons can be convex or concaveThe polygons are divided into 119899 triangles using the centreand vertexes of the polygon Therefore once the centre of anelement is determined to be within one triangle the elementcan be set as a stone block and numbered

To ensure that the stone blocks do not overlap theelements are set as debris by default Once one of the elementsin the current trial has been defined as a stone block thecurrent step will end and a new position will be tried as thecentre of the generated polygon until all of the elements inthe generated polygon are no longer debris When all of thegenerated polygons are finished in this way the numericalmodel is complete

To avoid setting adjacent polygons as the same stoneblock each stone block should be numbered a uniquenumber The particle contact parameters within one stoneblock are endowed the parameters of the stone blocks andthe contact parameter between two stone blocks is taken asthat of debris Therefore the contact characteristics betweenstone blocks can be approximately simulated

The content rate of stone block of grade 119894 in a two-dimension model can be defined as the ratio of the stoneblock area within grade 119894 to the total area of the model It canbe expressed as follows

119899119894=sum119860119895

119860 (5)

4 Advances in Materials Science and Engineering

000005010015020025030035

040 050 060 070 080 090

Size statics of rock blocks

(a)

(d)(b)

000

010

020

030

040

050

002 004 056 007 009 011

(c)

Length of long axis (m)

Freq

uenc

yFr

eque

ncy

Ratio of the long axis length to the short axis

2a

2b

Figure 3 The statistical results of the size and the lengths of the long axis of stone blocks (a) the in situ outwash deposits (b) definition ofthe long axis and short axis for stone blocks the long axis is the largest distance between vertices along the stone outline while the short axisis the maximum segment length normal to the long axis direction (c) the statistical results of the size of stone blocks (d) the statistical resultsof the lengths of the long axis of stone blocks

where 119860 is the total area of the model 119860119895is the area of the

119895th stone block and grade 119894 and 119899119894is the content rate of stone

blocks of grade 119894The area of the total stone blocks is counted until the

grade requirement is metThe structure of the outwash deposit model is generated

randomly according to the method of multigradations Theinfluences of the azimuth concavity and convexity of thestone blocks on the outwash deposit are also taken intoconsideration The generation of stone blocks occurs fromthe largest to the smallest size according to the grain sizeaccumulation curve

3 Analysis Based on Micromechanical Model

31 The Principle of the Granular Discrete Element MethodThe granular discrete element method is adopted to simulatethe micromechanical properties of the granular materials inthe form of discs or spherical particles using the explicitdifference algorithm [16] Newtonrsquos Second Law is used inorder to determine the particle movement that is caused bycontact or the force of a body while the force-displacementlaw is used to calculate the contact force that is changingrelative to movement The two laws are then used alternatelyuntil the total system reaches equilibrium as shown inFigure 5(a) The particles can be combined into any shape orcombination to simulate the stone or debris mass structures

As shown in Figure 5(b) when there is no bondingbetween particles the mechanical behaviour of the particles

in contact is determined by their own normal stiffness (119896119899)

tangential stiffness (119896119904) and friction coefficient (120583) When

two particles are in contact the contact and tangentialstiffness can be calculated as follows

119896119899=

119896(119860)119899119896(119861)119899

119896(119860)119899

+ 119896(119861)119899

119896119904=

119896(119860)119904119896(119861)119904

119896(119860)119904

+ 119896(119861)119904

(6)

The normal force of contact particles is depicted as

119865119899= 119870119899119880119899 (7)

where 119880119899is the normal contact depth

In the calculation process the tangential force is zeroinitially so the incremental form of the equation is used asfollows

Δ119865119904= minus119896119904Δ119880119904 (8)

If 119880119899le 0 a gap exists between the particles the normal

and shear force are both zero and the slipping force betweenthe particles should be calculated with the friction coefficientThis coefficient is calculated as 120583 = min(120583(119860) 120583(119861)) where120583(119860) and 120583(119861) are the particle friction coefficients of 119860 and 119861respectively and 119865

119904= 120583119865119899is used when 119865

119904ge 120583119865119899

The stiffness contact model is adopted for the outwashdeposit in this work because the point contact and the

Advances in Materials Science and Engineering 5

Select model scope (width and height)

Assign particle radius generate particles and set default flag 0 as soil

Number i level

Specify the aggregate gradation of outwash deposits in N designlevels (limit of size mean-variance)

Find out particles within the special polygon

If the flag of particle within the polygon is 0 or not

Yes

Statistic area of particles within the polygons add it to the total area of this level and give a new number of stone block

Judge whether the total area of current level meets the requirements

of the design level or not

No

Exit the current design levels

YesNo

Output the random model and distribute the particle properties

The flag of 0 is soilThe flag of 1 is rock

Generate polygons randomly controlled by block size (from 3 cm to20 cm) length of long axis axial ratio and the azimuth of long axis

Figure 4 The flowchart for the randomised generation of stone blocks

Update contact force between particles and position of wall and build up new contact

Newtonrsquos laws of motion applied to calculate resultant

force and resultant moment of each particle

Law of force-displacementapplied to illustrate relative movement and constitutive

relation of each contact

Contact force

(a) Calculation principle in PFC2D

N-normal directionT-tangential directiondirection

N

T

i

j

z

y

x

(b) Two contacting particles

Figure 5 Contact force between particles and calculation principle

linear contact in the debris-debris debris-stone and stone-stone are the main kind of contact types the point contactsare especially dominant Five microparameters need to becalibrated the normal stiffness the stiffness ratio of tangentstiffness and normal stiffness the friction coefficient the

normal bonding strength and the tangent bonding strengthaccording to PFC2D manual [17]

32TheConversion from the GeologicalModel to aMechanicalModel According to the theory of granular discrete element

6 Advances in Materials Science and Engineering

0 1 0 1

1 0 0 1

1 1 1 0

0 0 1 1

Wall load plate

Wall load plate x

y

Outwash deposit Particle modelConversion relationship

ro

Servo mechanism

radic3r 2r

j998400

i998400

Figure 6 Construction of a debris-stone micromodel using a spot matrix and PFC2D

method 2D disk particles are used to transform the geolog-ical model to a mechanical model If the particle is too largein the model the shape of stone block and microstructurecharacteristic will be distorted However the larger numberof particles in amodel will lead to very slow calculation speedA significant amount of timewill be sacrificed whichmay notbe tolerable So a proper particle size should be determinedempirically

The width and the height of the model in this work aretaken to 050 times 050m the constant radius of particles is25mm and the arrangement of the particles is shown inFigure 6 The distance between the centres of two adjacentparticles in the vertical direction is radic3119903 (r is the radiusof particle) The distance between the centres of adjacentparticles in the horizontal direction is 2119903 Therefore thecoordinates of the particle centre (119909

11989410158401198951015840 11991011989410158401198951015840) in the 1198941015840 line and

1198951015840 column can be expressed as follows

11990911989410158401198951015840 =

(21198951015840 minus 1) 119903 (1198941015840 = 2119896 + 1)

21198951015840119903 (1198941015840 = 2119896) (119896 isin 119873)

11991011989410158401198951015840 = 119903 + radic3119903 (119894 minus 1)

(9)

According to the modelling steps the particles arearranged initially as shown in Figure 6 The even rows aredislocated to ensure that the particles are tangential withadjacent rowsWhen a particlemodel filling the research zoneis generated every particle within the model will be judgedto determine whether its centre is located in some randompolygon If it is in a polygon the particle belongs to a stoneblockwith a certain flag If it is not in any polygon the particleis regarded as debrisThe initial structural information can beobtained from site research or by random generation

Several particleswith the samepolygonflag are assembledtogether by the high bonding force to simulate the character-istics of the stone blocks The structural effect of the outwashdeposit is thus simulated The separation of the debris fromthe stone is also convenient for the determination of themechanical parameters

33 The Relationship between the Macro- and Microme-chanical Parameters Youngrsquos modulus and Poissonrsquos ratio

000

005

010

015

020

025

030

035

00 02 04 06 08 10 12

Poiss

on ra

tio

kskn

kn = 500MPan bond = 1000Ns bond = 1000N

Figure 7 The relationship between Poissonrsquos ratio and the stiffnessratio

determined in the indoor geotechnical tests are used todescribe the macrodeformation properties of the materialsMany studies have shown that Youngrsquos modulus is related tothe microparameter 119896

119899and the stiffness ratio 119896

119904119896119899 while

Poissonrsquos ratio is mainly related to the stiffness ratio [1819] However these changes are all affected by the particlecompositions such as the mean radius and the ratio of themaximum radius to the minimum radius Since a constantradius is used in this work the problem can be neglected

To reflect the relation between Poissonrsquos ratio and thestiffness ratio 119896

119904119896119899 the normal stiffness is initially fixed at

a constant 50MPa The relationship between Poissonrsquos ratioand the stiffness ratio is shown in Figure 7 It can be foundthat Poissonrsquos ratio in the debris shows a nonlinear inverserelationshipwith the stiffness ratio of debris when the particleradius is unchanged

It can also be concluded in Figure 7 that the tangentstiffness is usually less than the normal stiffness Once thetangent stiffness is equal to or greater than the normalstiffness Poissonrsquos ratio will reach zero This situation onlyexists in very loose cellular structures However for outwashdeposits it is obviously unreasonable when the medium isin a compacted state Poissonrsquos ratio declines as the stiffnessratio increases When the tangent stiffness is equal to the

Advances in Materials Science and Engineering 7

08

07

06

05

04

03

Ek

n

kn (GPa)

015

25

35

45

0908

0706

0504

0302

010

k skn

Figure 8The changes in Youngrsquos modulus with the microdeforma-tion parameters

Poiss

onrsquos

ratio

030

025

020

015

010

005

kn (GPa)

015

25

35

4509

0807

0605

0403

0201

0

k sk n

Figure 9The changes in Poissonrsquos ratio with the microdeformationparameters

normal stiffness Poissonrsquos ratio is close to zero When thestiffness ratio decreases the lateral deformation increasesWhen the tangent stiffness is zero Poissonrsquos ratio reaches itsmaximumvalueThe relationship between Poissonrsquos ratio andthe stiffness ratio based on a series of numerical tests can beexpressed using the following equation

1205830= 012781205782 minus 04061120578 + 03177 (10)

where 120583 is Poissonrsquos ratio and 120578 = 119896119904119896119899is the ratio of

the tangent stiffness to the normal stiffness which lies inthe range 0sim05 Once 120578 is greater than 10 Poissonrsquos ratiomay be greater than 10 or negative which disagrees with theproperties of common solid media

It should be noted that (10) does not consider the influ-ence of the stiffness If the stiffness is taken into considerationYoungrsquos modulus and Poissonrsquos ratio can be estimated withdifferent normal stiffness as follows

119864 = (02259120578 minus 00058119896119899minus 00042120578119896

119899+ 05346) 119896

119899

120583 = minus02760120578 minus 00029119896119899+ 00031120578119896

119899+ 03200

(11)

Friction coefficient

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Inte

rnal

fric

tion

angl

e (∘

)

4200

4000

3800

3600

3400

3200

300000 05 10 15 20 25

Figure 10 The changes in the internal friction angle at differentcoefficients of friction

The changes in Youngrsquos modulus and Poissonrsquos ratio withthe changes in the microparameters are shown in Figures8 and 9 The figures illustrate that the relationship betweenYoungrsquos modulus of an outwash deposit and the correspond-ing Poissonrsquos ratio is not a simple linear relation but adouble linear correlation in the calculation of the granulardiscrete element method When the microparameters needto be determined Youngrsquos modulus and Poissonrsquos ratio caninitially be assumed Then more reasonable values can bedetermined using (11) The steps should be repeated manytimes until Youngrsquosmodulus andPoissonrsquos ratio agreewith theresults of the macroscopic tests In addition the debris andstone blocks should be calibrated separately to obtain propermicroparameters

34TheMicromechanical Parameters of theOutwashDepositsThe normal contact force (119899 bond) tangent contact force(119904 bond) and the coefficient of friction 120583 are the mainmicroparameters related to macrostrength in a granularmodel based on PFC2D These parameters correspond tothe macrocohesion and the internal friction in the Mohr-Coulomb criterion The coefficient of friction is the purefrictional force when the outwash deposit is completelydestroyed It determines the residual strength of the mediumand can be approximately equal to the pure friction coefficienttan120593 of the stone and debris mass

As shown in Figure 10 when the coefficient of friction islow the deformation of the stone and debris mass shows alinear variation By contrast when the friction coefficient ishigh the deformation of the stone and debris mass showsa nonlinear variation The internal friction angle of themedium first increases and then remains unchanged as thecoefficient of friction increases The cohesion shows similarbehaviour but it remains constant if the coefficient of frictionis lowThe cohesion will increase as the coefficient of frictionincreases as shown in Figure 11

It is not difficult to find that the microcoefficient offriction is sensitive to the macro-internal-friction angleWhen the microparameters need to be determined thebonding forces should initially be set to zero then the friction

8 Advances in Materials Science and Engineering

000

020

040

060

080

100

120

00 05 10 15 20 25Friction coefficient

Coh

esio

n (M

Pa)

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Figure 11 The cohesion remains constant if the coefficient of friction is low

180

160

140

120

100

080

060

040

020

000000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 10

(a)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 35

200

180

160

140

120

100

080

060

040

020

000

(b)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

Stone rate = 45200

150

100

050

000

(c)

1205901minus1205903

(MPa

)

000 001 002 003 004

1205761

Stone rate = 60

1200

1000

800

600

400

200

000

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

(d)

Figure 12 The biaxial compression curve at different confining pressures and stone block content (a) Stone block content is 10 (b) stoneblock content is 35 (c) stone block content is 45 and (d) stone block content is 60

Advances in Materials Science and Engineering 9

Table 1 The micromechanical parameters of outwash deposits

Material Density (kgm3) Bonding force (N) Stiffness ratio Normal stiffness (Nm) Friction coefficientNormal Tangential

Debris 2200 11198903 11198903 00 11198908 025Stone 2700 21198906 21198906 02 951198909 120

Table 2 The macromechanical parameters of outwash deposits

Material Youngrsquos modules (MPa) Poissonrsquos ratio Internal friction angel (∘) Cohesion (MPa)Debris 559 032 2794 007Stone 4950 020 56 120

coefficient can be determined using trial calculations until themacromechanical properties are in linewith the experimentalresults Finally the bonding forces are adjusted so thatthe parameters are consistent with the macromechanicalproperties of the outwash deposit

When the bonding force is zero the internal friction anglewill reach its minimum value Therefore the determinationof the internal friction angle should take the effect of thestiffness ratio into consideration If the internal friction angleis unchanged when the coefficient of friction increases thebonding force can be adjusted to be in agreement with thepeak strength of the stress In this work the microparametersare shown in Table 1 and the corresponding macroparame-ters are shown in Table 2

4 The Analysis of the Mechanical Behaviour ofthe Outwash Deposits

As a case study shown in Figure 1 the stone rate of outwashbased on the statistical results is about 30 to 40 themean length of long axis is about 413 cm with a variance015 and the mean axis ratio is 064 with a variance 017Then the random structure models of outwash depositsare generated according to the above information Finallynumerical simulation and comparison are executed in orderto analyse the effect of comprehensive mechanical behaviour

41 The Stress-Strain Curve Based on the Biaxial CompressionTest The stress-strain curves from the numerical simulationtests of an outwash deposit under biaxial compression con-ditions can be divided into three stages the elastic stagethe hardening stage and the residual strength stage (shownin Figure 12) In the elastic stage the deformation modulusis determined by the undamaged debris particles and stoneblock assemblies As the deformation increases fractureswill first appear in the debris because of its low modulusand strength When the outwash deposit enters into thehardening stage the debris particle bonding forces will failgradually and the deformation modulus will decrease slowlyHowever the strength will increase continually due to theinteraction force caused by mosaic effect between the debrisparticles and the stone blocks When the stress reaches itspeak strength the outwash deposit will enter into the residualstrength stage The cementation ability between the debris

particles is almost completely lost The compressive-bearingcapability of the sample cannot continue to increase Thecompressive-bearing capability is controlled mainly by theinterparticle friction When the strain continues to increasethe stone blocks may rotate and tumble which leads tothe complete destruction of the structure of the outwashdeposit However there is still some compression-bearingcapability which causes the residual strength of the outwashdeposit The residual strength shows fluctuations because ofthe contact action between the debris and the stone blocks

As shown in Figure 13 the damage of a model withcontent ratio of stone block 40 length of long axis about2 to 6 cm and the axial ratio 05 to 08 is compared in theloading process It shows that cracks occur firstly betweensome blocks and then develop among the boundary of stoneblocks and fill with the debris particles The crack numberwill increase shapely with the strain increase until all bondcontacts between debris particles are destroyed

The curves for different debris bonding forces in Figure 14show that the cementation strength of the debris particlesdecides the strength of outwash deposit and has a dominantrole in the mechanical properties when the other condi-tions are fixed With a stronger cementation force of debrisparticles there is a smaller increase in the internal frictionangle and a bigger increase for the cohesion The mechanicalproperties of an outwash deposit with high cementationstrength aremore similar to the properties of the stone blocksConversely if the cementation strength of the debris particlesis weak there is a bigger increase in the internal frictionangle and a smaller increase in the cohesionThe mechanicalproperties of the outwash deposit are much closer to theelastic-plastic debris

42 The Influence of the Aggregate Size As shown in Fig-ure 15 the larger the size of stone blocks is the smaller thepeak strength is This situation can be interpreted by theperimeter ratio which is defined as the ratio of all boundariesrsquoperimeters of stone blocks and themodel areaThe perimeterratio under the same stone ratio varies greatly The smalleraggregate size has more stone blocks so the perimeter ratiowill reach a high level and form larger contact areas Thecompressive strength also increases When the number ofstone blocks increases the contact area of the debris and stoneblocks and the interaction force between the debris and the

10 Advances in Materials Science and Engineering

(a) Crk num = 0 (b) Crk num = 39

(c) Crk num = 189 (d) Crk num = 563

Figure 13 The damage of outwash deposits with different stone block content (a) shows a model with the initial content rate of stone block40 (b) shows the cracks which first appear between some blocks (c) shows fracture development among the boundary of stone blocks and(d) shows the damaged outwash deposits

stone blocks will increase which just explains the reason whythe macromechanical properties of the outwash deposit areimproved with the number of stone blocks

43 The Influence of the Stone Block Content As shown inFigure 16 when there are few stone blocks in the outwashdeposit the debris-debris contact between particles willbe the main contact type The existence of stone blocksleads to the concentration of stress along their boundarieswhich can aggravate the debris contacts to damage the peakcompressive strength keeps close to the pure debriswith slightfluctuation Meanwhile due to the stress concentration theoutwash deposits become more brittle The shear strength isdecreased Many experiments show that when the contentof stone blocks is less than 25 the characteristic is moreclose to pure debris By contrast when the content of stoneblocks is greater than 25 there is not only debris-stonecontact in the outwash deposits but also stone-stone contact

The compressive and shear strengths are improved Whenthe content of stone blocks is more than 50 the maincontact type in the outwash deposits is stone-stone Themechanical properties are better in stone-filledmaterialsThecompressive and shear strengths are significantly improved inthe stone-filled materials

However when the stress-strain curves enter the residualstrength stage there is an obvious fluctuation after the peakof the curve the amplitude of which is related to the size andcontent ratio of stone blocks so in order to study the macro-shear strength the peak value of stress-strain curves is usedto calculate shear property

44 The Macroparameter Analysis of the Outwash DepositsIn terms of the stress-strain curves for any content rateof stone block cementation strength and block size themajor factor that influences the mechanical properties of the

Advances in Materials Science and Engineering 11

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

n bond = s bond = 0Nn bond = s bond = 1000N

n bond = s bond = 2000Nn bond = s bond = 3000N

Figure 14 The biaxial compression curves with different debris bonding force

Stone average size = 1 cmStone average size = 3 cm

Stone average size = 5 cmStone average size = 7 cm

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

Figure 15 The biaxial compression curves with different averagesizes of stone blocks

Stone content = 10

Stone content = 20Stone content = 30

Stone content = 40

Stone content = 50

Stone content = 60Stone content = 70

1400

1200

1000

800

600

400

200

0000 002 004 006 008 01 012

(1205901minus1205903) (

MPa

)

1205761

Figure 16The biaxial compression curve with different stone blockcontents

The content of stone blocks ()

The p

eak

com

pres

sive s

treng

th (M

Pa) 1600

1400

1200

1000

800

600

400

200

0000 10 20 30 40 50 60 70 80

Figure 17The peak compressive strength with different stone blockcontents

outwash deposits can be attributed to the dominant contacttype which is defined as the ratio of some particle contactnumber and total contact number in numerical models Theparticle contact can be divided into three kinds respectivelythe debris-debris debris-stone or stone-stone contact

If ratio of stone block is high enough to make stone-stonecontact becoming dominant contact type the characteristicof outwash deposit is close to rockfill For the naturemediumseveral kinds of contacts exist at that time which will affectthe comprehensive mechanical property greatly Althoughthe different geometries and distributions also affect themechanical properties the content of stone blocks is thedecisive factor For the different stone block contents thepeak strength under the confining pressure of 15MPa canbe calculated approximately using formula (12) as a cubicparabola curve (shown in Figure 17)

119875119896= 141841205723 minus 90441205722 + 1600120572 + 02894 (12)

where 120572 is the content ratio of stone blocks and 119875119896is the peak

strengthIt should be noted that the compressive strength of the

outwash deposit increases slowly when content ratio of stone

12 Advances in Materials Science and Engineering

Stone block ()

Inte

rnal

fric

tion

angl

e (∘

)40

36

32

28

24

200 10 20 30 40 50 60 70 80

(a)

20

40

60

80

100

120

140

160

180

0 20 40 60 80Stone block ()

Incr

emen

tal c

ohes

ion

(MPa

)

(b)

Figure 18 Changes of shear strength of outwash deposits with different contents and distributions of stone blocks (a) shows changes of theinternal friction of outwash deposit (b) shows changes of the cohesion of outwash deposit

blocks lies between 25 and 50 Once the content of stoneblocks is greater than 50 the stone-stone contact becomesthe dominant factor which causes the compressive strengthto increase sharply The internal friction angle versus thestone block content can be described using three stages asshown below

120593 =

18093931205722 minus 495165120572 + 265026 120572 lt 25194271120572 + 221719 25 lt 120572 lt 50234286120572 + 191429 120572 gt 50

(13)

where 120593 is the internal friction angle of the outwash depositand 120572 is the stone block content

Furthermore it can be observed from Figure 18(a) thatthe fluctuation of the internal friction angle is approximately0sim8∘ for the same stone blocks content which agrees withthe fluctuations in the stress-strain curves By contrast thecohesion of outwash deposit increases clearly with the stoneblock content due to the interaction force between stoneblocks as shown in Figure 18(b) The amplitude of variationwill increase significantly with the content of stone blocksHowever it is usually difficult to quantify the amplitude dueto roughness size characteristic of stone block and so on

Therefore for outwash deposits with extremely unevenshapes and distributions of stones the compressive strengthand shear strength are primarily controlled by the stone blockcontent The randomness of the stone block distributionscauses large deviations in the mechanical parameters Forexample the internal friction angle may have a large fluctua-tion at the same stone block content This feature is the causeof the poor results of the geotechnical experiments

5 Discussions

Outwash deposits are a type of debris-stone mixture Themechanical properties of these deposits are affected by thecomposition of the debris and stone blocks As the debriscementation increases the compressive strength increasesHowever the internal friction angle has a negative correlation

with the cementation force The stone block content is thedecisive factor for the mechanical properties of outwashdepositsThe randomness of the structural composition leadsto significant fluctuations in the properties which also createslarge discrepancies in the mechanical parameters

The major influences of the particle sizes geometricdistribution and stone block content are to determine thecontact type in the outwash deposits When the debris-debris contact is the dominant contact type there is littleinfluence from the stone blocks on the mechanical propertiesof the outwash depositsWhen the debris-stone contact is thedominant contact type the stone block content has a positiveinfluence on the compressive and shear strengths When thestone-stone contact is the dominant contact type the roles ofthe debris and stone blocks are reversed and the properties ofthe outwash deposits aremuch closer to a rock-filledmaterial

Although it is difficult to determine the mechanicalparameters of an outwash deposit using indoor experimentsthe properties of the medium can still be researched usingindirect approachesThemechanical parameters of the debrisand stone blocks can be determined from the indoor experi-ments Then the biaxial compression numerical experimentusing the granular discrete element method can be carriedout to analyse the influence of the stone blocks on theproperties of outwash deposits which makes up for thelimitation that the indoor experiments cannot consider thelarge stone blocks and offers a beneficial supplement to aid inthe geological parameter determination

6 Conclusions

According to the grain size and shape statistics from fieldstatistics the numerical granular discrete elementmodel withrandomised generation of stone blocks can be used withhypothesis that the length of the long axis and the axial ratioall follow normal distributions and the azimuth of the longaxis follows uniformdistribution in 0sim360∘The relationshipsbetween the macro- and micromechanical parameters arediscussed and the mechanical behaviour of the outwash

Advances in Materials Science and Engineering 13

deposit is affected by the cementation strength the size ofstone blocks the stone block content and the distribution ofthe stone blocks These properties are analysed so that theycan be better understood by the geologists working on thedemocratisation of the Engineering Project

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (no 51309089 and no 51379065)the National Key Technology RampD Program (no2013BAB06B00) the National Basic Research Programof China (973 Program) (no 2015CB057903) the NaturalScience Foundation of Jiangsu Province (no BK20130846)and the Fundamental Research Funds for the CentralUniversities (no 2014B04914)

References

[1] W G Holtz and H J Gibbs ldquoTriaxial shear tests on perviousgravelly soilsrdquo Journal of the Soil Mechanics and FoundationsDivision vol 82 no 1 pp 1ndash22 1956

[2] R J Chandler ldquoThe inclination of Talus Arctic Talus Terracesand other slopes composed of granular materialsrdquo The Journalof Geology vol 81 no 1 pp 1ndash14 1973

[3] X H You Stochastic structural model of the earth-rock aggregateand its application [PhD thesis] Beijing Jiaotong UniversityBeijing China 2001

[4] X H You and J S Tang ldquoResearch on horizontal push-shearin-situ test of debris and rock-mixturerdquo Chinese Journal of RockMechanics and Engineering vol 21 no 10 pp 1537ndash1540 2002

[5] X H You G He and X Li ldquoMicro-handling technologyof earth-rock aggregate sloperdquo Hydrogeology and EngineeringGeology vol 30 no 1 pp 18ndash21 2003

[6] J M He Study of deformation and failure mechanisms of rock-debris aggregate in three gorges reservoir area [PhD thesis]China University of Mining and Technology Beijing China2004

[7] X Li Q L Liao J M He and J Chen ldquoStudy on in-situ testsof mechanical characteristics on soil-rock aggregaterdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 12 pp2377ndash2384 2007

[8] T Lebourg J Riss and E Pirard ldquoInfluence of morphologicalcharacteristics of heterogeneous moraine formations on theirmechanical behaviour using image and statistical analysisrdquoEngineering Geology vol 73 no 1-2 pp 37ndash50 2004

[9] T R Reid and J P Harrison ldquoA semi-automated methodologyfor discontinuity trace detection in digital images of rock massexposuresrdquo International Journal of Rock Mechanics andMiningSciences vol 37 no 7 pp 1073ndash1089 2000

[10] Z Q Yue S Chen and L G Tham ldquoFinite element modelingof geomaterials using digital image processingrdquo Computers andGeotechnics vol 30 no 5 pp 375ndash397 2003

[11] Z Q Yue S Chen H Zheng and G H Tang ldquoDigital imageproceeding based on finite element method for geomaterialsrdquo

Chinese Journal of Rock Mechanics and Engineering vol 23 no6 pp 889ndash897 2004

[12] Q L Liao X Li W C Zhu and J S Liu ldquoStructure modelconstruction of rock and soil aggregate based on digital imagetechnology and its numerical simulation on mechanical struc-ture effectsrdquoChinese Journal of RockMechanics and Engineeringvol 29 no 1 pp 155ndash162 2010

[13] W J Xu R L Hu Z Q Yue and R J Tan ldquoMesostructuralcharacter and numerical simulation of mechanical propertiesof soil-rock mixturesrdquo Chinese Journal of Rock Mechanics andEngineering vol 26 no 2 pp 300ndash311 2007

[14] W J Xu Z Q Yue and R L Hu ldquoA current status of digitalimage based quantitative analysis of internal structures ofdebris rock and concretes and associated numerical simula-tionrdquo Journal of Engineering Geology vol 15 no 3 pp 289ndash3132007

[15] W J Xu R L Hu Z Q Yue R Zhang and G L WangldquoResearch on relationship between rock block proportion andshear strength of soil-rock mixtures based on digital imageanalysis and large direct shear testrdquo Chinese Journal of RockMechanics and Engineering vol 27 no 5 pp 996ndash1007 2008

[16] P A Cundall and O D L Strack ldquoA discrete numerical modelfor granular assembliesrdquo Geotechnique vol 29 no 1 pp 47ndash651979

[17] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) (Version 31) Itasca Consulting Group Minneapo-lis Minn USA 2004

[18] J Yoon ldquoApplication of experimental design and optimizationto PFC model calibration in uniaxial compression simulationrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 6 pp 871ndash889 2007

[19] Y C Wang and P Mora ldquoMacroscopic elastic properties ofregular latticesrdquo Journal of the Mechanics and Physics of Solidsvol 56 no 12 pp 3459ndash3474 2008

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

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NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

2 Advances in Materials Science and Engineering

Outwash deposit

Gully

(c)

(b)(a)

Grade i

Grade i + 1

3220m2910m

2790m

2200m

2650m

2560m

2180m

Figure 1 A typical outwash deposit formed by glacial movement

considering the effects of heterogeneity and randomness onthe distribution and concentration of stone blocks in theconventional geotechnical experimentsThe limited field testsare discrete and not representative Therefore it is necessaryto consider the composition of the outwash deposit in theexperiments and numerical calculations when studying themechanical characteristics Digital image processing is aconvenient toolThe sizes and shapes of the debris in outwashdeposits were studied by Lebourg et al [8] The real internalstructure of geological materials was also detected by suchtechnology [9ndash12] So it can provide an effective approach forresearch into the composition of outwash deposits [13 14]Because the structure composition of outwash deposits ismainly determined by stone blocks a model considering thedistribution and randomness of stone blocks is meaningful

According to the field statistics the geometric shapes ofthe stone blocks are assumed to be approximately elliptic-polygon and obey a normal distribution in this work Then ageomechanical model for biaxial compression is establishedusing the particle flow code The effects of the stone blocksand fine-grained debris on the mechanical properties ofoutwash deposit are studiedThe changes in the macroscopiccompressive strength and shear strength of the medium arealso discussed

2 Structural Characteristics ofOutwash Deposits

21 The Structural Composition of Outwash Deposits Out-wash deposits are a type of binarymixturemedium consistingof fine-grained debris and stone blocks where both the debrisand stone blocks are made of the same material and aredistinguished by the grain size but not by the compositionHowever not all sizes of stone blocks have a positive influenceon the strength of the medium There is a threshold thatdistinguishes debris from stone blocks The threshold size ofstone blocks can be determined only in certain geologicalconditions and scales which shows that the large grainsplay a greater role in the macroscopic mechanical properties

during the smaller scale studies When the scale of researchis increased the former large grains will lose their dominanteffect to mechanical property and can be regarded as debrisThe following criterion to distinguish stones from debris isproposed [15]

119891 = 119877 119889 ge 119889thr119878 119889 lt 119889thr

(1)

where119889thr is the threshold of stone and debris (119889thr = 005119871119888)119871119888is the characteristic engineering size 119877 denotes the stone

and 119878 denotes the debrisIn addition the indoor geotechnical test on similar

media the direct shear test and triaxial compression test canonly consider grains below 2 cm due to the limitations of theinstruments Therefore 119889thr is set to be 2 cm in this workwhich means that if the grain size is less than 2 cm the grainwill be defined as debris Conversely if the grain size is greaterthan 2 cm the grain will be considered as a stone block

By above measure grains of debris and stone blocks willbe endowed attributes separately to reflect the change rule ofmedium composition and mechanical property

22 The Aggregate Gradation of Outwash Deposits The sizesand shapes of stone blocks differ greatly at different part asshown in Figure 1(c)Themicrostructure of outwash depositswhich can be explained as grain contact and interaction isjust related to content size and roughness of stone blocks Inorder to construct a stochasticmodel of outwash deposits thegrains regarded as stone can be divided into several gradationaccording to the grain size Then according to the resultsof the grain size analysis and field statistics the proportionquality volume and area of the stone blocks in the researchregion can be obtained easily The grains smaller than thethreshold will be considered as debris and can be describedusing the conventional geotechnical experiments Numericalsimulation method will be used to reflect its influence onmechanical property of outwash deposit in which the stoneblocks are supposed to be unbroken

Advances in Materials Science and Engineering 3

O

N polygon

Random polygon

Ni

120579

Figure 2 An arbitrarily shaped stone block depicted by a particlescluster

If the density of the stone blocks is 120588119877 the debris density

is 120588119878 Therefore the 2D area of the stone blocks in grade 119894 can

be written as follows

119860119894=

41199032119866119894120588119877

1198660120588119878+ sum119899

119896=1119866119894120588119877

(2)

where 119860119894is the 2D area percentage of stone blocks in grade

119894 1198660is the weight of the medium with grain sizes below the

threshold and sum119899119896=1

119866119896120588119877is the total weight of stone blocks

23 The Randomised Generation of Aggregates Each stoneblock can be regarded as an arbitrary polygon in the planeso a number of polygons are generated randomly in thedesignated region to simulate blocks During the generationprocess every polygon should be judged to avoid overlappingwith others Then the area in the polygons is regarded asstone blocks of different grades When the polygon is convexit has difficulty in considering the interaction force dueto mosaic effect of rough block surface which will leadto deviations in the mechanical parameter research so thepolygon generation should consider convexity and concavityat the same time

To generate the arbitrary shapes of the stone blocks thestone blocks are assumed to be initially elliptical then theoutline is divided as polygon and the vertices of polygon arerandom as shown in Figure 2The ellipses can be determinedusing three parameters the length of long axis 119886 length of theshort axis 119887 (or the axis ratio defined as ratio of the short axislength to the long axis) and the azimuth of the long axis 120579Field investigation shows that the angle of long axis azimuth isin poor statistical correlation so it can be regarded as obeyinguniform distribution over 0sim360∘

As shown in Figure 3(a) the lengths of the long axis andthe axis ratio are approximately obeying normal distributionwith variance as shown in Figures 3(c) and 3(d) So the length

of the long axis the axial ratio and the azimuth angle of longaxis whose definition is shown in Figure 3(b) are given asshown in the following formula

119886 = 1198860+ 2120590119886(rand (1) minus 1)

119903 = 1199030+ 2120590119903(rand (1) minus 1)

120579 = 360 sdot rand (1)

(3)

where 119886 120590119886 119903 120590119903are the mean of the long axis the variance

of the long axis the mean of the axial ratio and the varianceof axial ratio respectively 120579 is the azimuth of long axisrand(1) returns a random number between 0 and 1 119886 120590

119886

119903 120590119903should be obtained using the statistics according to the

stone blocks in outwash deposit medium Here 05 times thecorresponding mean value is used as an empirical parameterfor variance if there is no statistical information

Then every stone block is hypothesised to be a polygoncomposed of119873 sides as shown in Figure 2The elliptical arc isaccordingly divided into119873 arcs Each point of the arc can bemoved towards the centre of the ellipse The correspondingcoordinate of each point can be defined as follows

119909119894= 1199090+ 119886 sdot cos (120579 + 119873Δ120593)

119910119894= 1199100+ 119886 sdot 119903 sdot sin (120579 + 119873Δ120593)

(4)

where 119909119894and 119910

119894are the coordinates of the 119894th node in a

polygon 1199090and 119910

0are the coordinates of the centre of the

ellipse 1205930is the azimuth of ellipse and Δ120593 is the angle

between two vertexes of the polygon where Δ120593 = 360119873The steps of the random structure generation are shown

in Figure 4The generated polygons can be convex or concaveThe polygons are divided into 119899 triangles using the centreand vertexes of the polygon Therefore once the centre of anelement is determined to be within one triangle the elementcan be set as a stone block and numbered

To ensure that the stone blocks do not overlap theelements are set as debris by default Once one of the elementsin the current trial has been defined as a stone block thecurrent step will end and a new position will be tried as thecentre of the generated polygon until all of the elements inthe generated polygon are no longer debris When all of thegenerated polygons are finished in this way the numericalmodel is complete

To avoid setting adjacent polygons as the same stoneblock each stone block should be numbered a uniquenumber The particle contact parameters within one stoneblock are endowed the parameters of the stone blocks andthe contact parameter between two stone blocks is taken asthat of debris Therefore the contact characteristics betweenstone blocks can be approximately simulated

The content rate of stone block of grade 119894 in a two-dimension model can be defined as the ratio of the stoneblock area within grade 119894 to the total area of the model It canbe expressed as follows

119899119894=sum119860119895

119860 (5)

4 Advances in Materials Science and Engineering

000005010015020025030035

040 050 060 070 080 090

Size statics of rock blocks

(a)

(d)(b)

000

010

020

030

040

050

002 004 056 007 009 011

(c)

Length of long axis (m)

Freq

uenc

yFr

eque

ncy

Ratio of the long axis length to the short axis

2a

2b

Figure 3 The statistical results of the size and the lengths of the long axis of stone blocks (a) the in situ outwash deposits (b) definition ofthe long axis and short axis for stone blocks the long axis is the largest distance between vertices along the stone outline while the short axisis the maximum segment length normal to the long axis direction (c) the statistical results of the size of stone blocks (d) the statistical resultsof the lengths of the long axis of stone blocks

where 119860 is the total area of the model 119860119895is the area of the

119895th stone block and grade 119894 and 119899119894is the content rate of stone

blocks of grade 119894The area of the total stone blocks is counted until the

grade requirement is metThe structure of the outwash deposit model is generated

randomly according to the method of multigradations Theinfluences of the azimuth concavity and convexity of thestone blocks on the outwash deposit are also taken intoconsideration The generation of stone blocks occurs fromthe largest to the smallest size according to the grain sizeaccumulation curve

3 Analysis Based on Micromechanical Model

31 The Principle of the Granular Discrete Element MethodThe granular discrete element method is adopted to simulatethe micromechanical properties of the granular materials inthe form of discs or spherical particles using the explicitdifference algorithm [16] Newtonrsquos Second Law is used inorder to determine the particle movement that is caused bycontact or the force of a body while the force-displacementlaw is used to calculate the contact force that is changingrelative to movement The two laws are then used alternatelyuntil the total system reaches equilibrium as shown inFigure 5(a) The particles can be combined into any shape orcombination to simulate the stone or debris mass structures

As shown in Figure 5(b) when there is no bondingbetween particles the mechanical behaviour of the particles

in contact is determined by their own normal stiffness (119896119899)

tangential stiffness (119896119904) and friction coefficient (120583) When

two particles are in contact the contact and tangentialstiffness can be calculated as follows

119896119899=

119896(119860)119899119896(119861)119899

119896(119860)119899

+ 119896(119861)119899

119896119904=

119896(119860)119904119896(119861)119904

119896(119860)119904

+ 119896(119861)119904

(6)

The normal force of contact particles is depicted as

119865119899= 119870119899119880119899 (7)

where 119880119899is the normal contact depth

In the calculation process the tangential force is zeroinitially so the incremental form of the equation is used asfollows

Δ119865119904= minus119896119904Δ119880119904 (8)

If 119880119899le 0 a gap exists between the particles the normal

and shear force are both zero and the slipping force betweenthe particles should be calculated with the friction coefficientThis coefficient is calculated as 120583 = min(120583(119860) 120583(119861)) where120583(119860) and 120583(119861) are the particle friction coefficients of 119860 and 119861respectively and 119865

119904= 120583119865119899is used when 119865

119904ge 120583119865119899

The stiffness contact model is adopted for the outwashdeposit in this work because the point contact and the

Advances in Materials Science and Engineering 5

Select model scope (width and height)

Assign particle radius generate particles and set default flag 0 as soil

Number i level

Specify the aggregate gradation of outwash deposits in N designlevels (limit of size mean-variance)

Find out particles within the special polygon

If the flag of particle within the polygon is 0 or not

Yes

Statistic area of particles within the polygons add it to the total area of this level and give a new number of stone block

Judge whether the total area of current level meets the requirements

of the design level or not

No

Exit the current design levels

YesNo

Output the random model and distribute the particle properties

The flag of 0 is soilThe flag of 1 is rock

Generate polygons randomly controlled by block size (from 3 cm to20 cm) length of long axis axial ratio and the azimuth of long axis

Figure 4 The flowchart for the randomised generation of stone blocks

Update contact force between particles and position of wall and build up new contact

Newtonrsquos laws of motion applied to calculate resultant

force and resultant moment of each particle

Law of force-displacementapplied to illustrate relative movement and constitutive

relation of each contact

Contact force

(a) Calculation principle in PFC2D

N-normal directionT-tangential directiondirection

N

T

i

j

z

y

x

(b) Two contacting particles

Figure 5 Contact force between particles and calculation principle

linear contact in the debris-debris debris-stone and stone-stone are the main kind of contact types the point contactsare especially dominant Five microparameters need to becalibrated the normal stiffness the stiffness ratio of tangentstiffness and normal stiffness the friction coefficient the

normal bonding strength and the tangent bonding strengthaccording to PFC2D manual [17]

32TheConversion from the GeologicalModel to aMechanicalModel According to the theory of granular discrete element

6 Advances in Materials Science and Engineering

0 1 0 1

1 0 0 1

1 1 1 0

0 0 1 1

Wall load plate

Wall load plate x

y

Outwash deposit Particle modelConversion relationship

ro

Servo mechanism

radic3r 2r

j998400

i998400

Figure 6 Construction of a debris-stone micromodel using a spot matrix and PFC2D

method 2D disk particles are used to transform the geolog-ical model to a mechanical model If the particle is too largein the model the shape of stone block and microstructurecharacteristic will be distorted However the larger numberof particles in amodel will lead to very slow calculation speedA significant amount of timewill be sacrificed whichmay notbe tolerable So a proper particle size should be determinedempirically

The width and the height of the model in this work aretaken to 050 times 050m the constant radius of particles is25mm and the arrangement of the particles is shown inFigure 6 The distance between the centres of two adjacentparticles in the vertical direction is radic3119903 (r is the radiusof particle) The distance between the centres of adjacentparticles in the horizontal direction is 2119903 Therefore thecoordinates of the particle centre (119909

11989410158401198951015840 11991011989410158401198951015840) in the 1198941015840 line and

1198951015840 column can be expressed as follows

11990911989410158401198951015840 =

(21198951015840 minus 1) 119903 (1198941015840 = 2119896 + 1)

21198951015840119903 (1198941015840 = 2119896) (119896 isin 119873)

11991011989410158401198951015840 = 119903 + radic3119903 (119894 minus 1)

(9)

According to the modelling steps the particles arearranged initially as shown in Figure 6 The even rows aredislocated to ensure that the particles are tangential withadjacent rowsWhen a particlemodel filling the research zoneis generated every particle within the model will be judgedto determine whether its centre is located in some randompolygon If it is in a polygon the particle belongs to a stoneblockwith a certain flag If it is not in any polygon the particleis regarded as debrisThe initial structural information can beobtained from site research or by random generation

Several particleswith the samepolygonflag are assembledtogether by the high bonding force to simulate the character-istics of the stone blocks The structural effect of the outwashdeposit is thus simulated The separation of the debris fromthe stone is also convenient for the determination of themechanical parameters

33 The Relationship between the Macro- and Microme-chanical Parameters Youngrsquos modulus and Poissonrsquos ratio

000

005

010

015

020

025

030

035

00 02 04 06 08 10 12

Poiss

on ra

tio

kskn

kn = 500MPan bond = 1000Ns bond = 1000N

Figure 7 The relationship between Poissonrsquos ratio and the stiffnessratio

determined in the indoor geotechnical tests are used todescribe the macrodeformation properties of the materialsMany studies have shown that Youngrsquos modulus is related tothe microparameter 119896

119899and the stiffness ratio 119896

119904119896119899 while

Poissonrsquos ratio is mainly related to the stiffness ratio [1819] However these changes are all affected by the particlecompositions such as the mean radius and the ratio of themaximum radius to the minimum radius Since a constantradius is used in this work the problem can be neglected

To reflect the relation between Poissonrsquos ratio and thestiffness ratio 119896

119904119896119899 the normal stiffness is initially fixed at

a constant 50MPa The relationship between Poissonrsquos ratioand the stiffness ratio is shown in Figure 7 It can be foundthat Poissonrsquos ratio in the debris shows a nonlinear inverserelationshipwith the stiffness ratio of debris when the particleradius is unchanged

It can also be concluded in Figure 7 that the tangentstiffness is usually less than the normal stiffness Once thetangent stiffness is equal to or greater than the normalstiffness Poissonrsquos ratio will reach zero This situation onlyexists in very loose cellular structures However for outwashdeposits it is obviously unreasonable when the medium isin a compacted state Poissonrsquos ratio declines as the stiffnessratio increases When the tangent stiffness is equal to the

Advances in Materials Science and Engineering 7

08

07

06

05

04

03

Ek

n

kn (GPa)

015

25

35

45

0908

0706

0504

0302

010

k skn

Figure 8The changes in Youngrsquos modulus with the microdeforma-tion parameters

Poiss

onrsquos

ratio

030

025

020

015

010

005

kn (GPa)

015

25

35

4509

0807

0605

0403

0201

0

k sk n

Figure 9The changes in Poissonrsquos ratio with the microdeformationparameters

normal stiffness Poissonrsquos ratio is close to zero When thestiffness ratio decreases the lateral deformation increasesWhen the tangent stiffness is zero Poissonrsquos ratio reaches itsmaximumvalueThe relationship between Poissonrsquos ratio andthe stiffness ratio based on a series of numerical tests can beexpressed using the following equation

1205830= 012781205782 minus 04061120578 + 03177 (10)

where 120583 is Poissonrsquos ratio and 120578 = 119896119904119896119899is the ratio of

the tangent stiffness to the normal stiffness which lies inthe range 0sim05 Once 120578 is greater than 10 Poissonrsquos ratiomay be greater than 10 or negative which disagrees with theproperties of common solid media

It should be noted that (10) does not consider the influ-ence of the stiffness If the stiffness is taken into considerationYoungrsquos modulus and Poissonrsquos ratio can be estimated withdifferent normal stiffness as follows

119864 = (02259120578 minus 00058119896119899minus 00042120578119896

119899+ 05346) 119896

119899

120583 = minus02760120578 minus 00029119896119899+ 00031120578119896

119899+ 03200

(11)

Friction coefficient

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Inte

rnal

fric

tion

angl

e (∘

)

4200

4000

3800

3600

3400

3200

300000 05 10 15 20 25

Figure 10 The changes in the internal friction angle at differentcoefficients of friction

The changes in Youngrsquos modulus and Poissonrsquos ratio withthe changes in the microparameters are shown in Figures8 and 9 The figures illustrate that the relationship betweenYoungrsquos modulus of an outwash deposit and the correspond-ing Poissonrsquos ratio is not a simple linear relation but adouble linear correlation in the calculation of the granulardiscrete element method When the microparameters needto be determined Youngrsquos modulus and Poissonrsquos ratio caninitially be assumed Then more reasonable values can bedetermined using (11) The steps should be repeated manytimes until Youngrsquosmodulus andPoissonrsquos ratio agreewith theresults of the macroscopic tests In addition the debris andstone blocks should be calibrated separately to obtain propermicroparameters

34TheMicromechanical Parameters of theOutwashDepositsThe normal contact force (119899 bond) tangent contact force(119904 bond) and the coefficient of friction 120583 are the mainmicroparameters related to macrostrength in a granularmodel based on PFC2D These parameters correspond tothe macrocohesion and the internal friction in the Mohr-Coulomb criterion The coefficient of friction is the purefrictional force when the outwash deposit is completelydestroyed It determines the residual strength of the mediumand can be approximately equal to the pure friction coefficienttan120593 of the stone and debris mass

As shown in Figure 10 when the coefficient of friction islow the deformation of the stone and debris mass shows alinear variation By contrast when the friction coefficient ishigh the deformation of the stone and debris mass showsa nonlinear variation The internal friction angle of themedium first increases and then remains unchanged as thecoefficient of friction increases The cohesion shows similarbehaviour but it remains constant if the coefficient of frictionis lowThe cohesion will increase as the coefficient of frictionincreases as shown in Figure 11

It is not difficult to find that the microcoefficient offriction is sensitive to the macro-internal-friction angleWhen the microparameters need to be determined thebonding forces should initially be set to zero then the friction

8 Advances in Materials Science and Engineering

000

020

040

060

080

100

120

00 05 10 15 20 25Friction coefficient

Coh

esio

n (M

Pa)

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Figure 11 The cohesion remains constant if the coefficient of friction is low

180

160

140

120

100

080

060

040

020

000000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 10

(a)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 35

200

180

160

140

120

100

080

060

040

020

000

(b)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

Stone rate = 45200

150

100

050

000

(c)

1205901minus1205903

(MPa

)

000 001 002 003 004

1205761

Stone rate = 60

1200

1000

800

600

400

200

000

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

(d)

Figure 12 The biaxial compression curve at different confining pressures and stone block content (a) Stone block content is 10 (b) stoneblock content is 35 (c) stone block content is 45 and (d) stone block content is 60

Advances in Materials Science and Engineering 9

Table 1 The micromechanical parameters of outwash deposits

Material Density (kgm3) Bonding force (N) Stiffness ratio Normal stiffness (Nm) Friction coefficientNormal Tangential

Debris 2200 11198903 11198903 00 11198908 025Stone 2700 21198906 21198906 02 951198909 120

Table 2 The macromechanical parameters of outwash deposits

Material Youngrsquos modules (MPa) Poissonrsquos ratio Internal friction angel (∘) Cohesion (MPa)Debris 559 032 2794 007Stone 4950 020 56 120

coefficient can be determined using trial calculations until themacromechanical properties are in linewith the experimentalresults Finally the bonding forces are adjusted so thatthe parameters are consistent with the macromechanicalproperties of the outwash deposit

When the bonding force is zero the internal friction anglewill reach its minimum value Therefore the determinationof the internal friction angle should take the effect of thestiffness ratio into consideration If the internal friction angleis unchanged when the coefficient of friction increases thebonding force can be adjusted to be in agreement with thepeak strength of the stress In this work the microparametersare shown in Table 1 and the corresponding macroparame-ters are shown in Table 2

4 The Analysis of the Mechanical Behaviour ofthe Outwash Deposits

As a case study shown in Figure 1 the stone rate of outwashbased on the statistical results is about 30 to 40 themean length of long axis is about 413 cm with a variance015 and the mean axis ratio is 064 with a variance 017Then the random structure models of outwash depositsare generated according to the above information Finallynumerical simulation and comparison are executed in orderto analyse the effect of comprehensive mechanical behaviour

41 The Stress-Strain Curve Based on the Biaxial CompressionTest The stress-strain curves from the numerical simulationtests of an outwash deposit under biaxial compression con-ditions can be divided into three stages the elastic stagethe hardening stage and the residual strength stage (shownin Figure 12) In the elastic stage the deformation modulusis determined by the undamaged debris particles and stoneblock assemblies As the deformation increases fractureswill first appear in the debris because of its low modulusand strength When the outwash deposit enters into thehardening stage the debris particle bonding forces will failgradually and the deformation modulus will decrease slowlyHowever the strength will increase continually due to theinteraction force caused by mosaic effect between the debrisparticles and the stone blocks When the stress reaches itspeak strength the outwash deposit will enter into the residualstrength stage The cementation ability between the debris

particles is almost completely lost The compressive-bearingcapability of the sample cannot continue to increase Thecompressive-bearing capability is controlled mainly by theinterparticle friction When the strain continues to increasethe stone blocks may rotate and tumble which leads tothe complete destruction of the structure of the outwashdeposit However there is still some compression-bearingcapability which causes the residual strength of the outwashdeposit The residual strength shows fluctuations because ofthe contact action between the debris and the stone blocks

As shown in Figure 13 the damage of a model withcontent ratio of stone block 40 length of long axis about2 to 6 cm and the axial ratio 05 to 08 is compared in theloading process It shows that cracks occur firstly betweensome blocks and then develop among the boundary of stoneblocks and fill with the debris particles The crack numberwill increase shapely with the strain increase until all bondcontacts between debris particles are destroyed

The curves for different debris bonding forces in Figure 14show that the cementation strength of the debris particlesdecides the strength of outwash deposit and has a dominantrole in the mechanical properties when the other condi-tions are fixed With a stronger cementation force of debrisparticles there is a smaller increase in the internal frictionangle and a bigger increase for the cohesion The mechanicalproperties of an outwash deposit with high cementationstrength aremore similar to the properties of the stone blocksConversely if the cementation strength of the debris particlesis weak there is a bigger increase in the internal frictionangle and a smaller increase in the cohesionThe mechanicalproperties of the outwash deposit are much closer to theelastic-plastic debris

42 The Influence of the Aggregate Size As shown in Fig-ure 15 the larger the size of stone blocks is the smaller thepeak strength is This situation can be interpreted by theperimeter ratio which is defined as the ratio of all boundariesrsquoperimeters of stone blocks and themodel areaThe perimeterratio under the same stone ratio varies greatly The smalleraggregate size has more stone blocks so the perimeter ratiowill reach a high level and form larger contact areas Thecompressive strength also increases When the number ofstone blocks increases the contact area of the debris and stoneblocks and the interaction force between the debris and the

10 Advances in Materials Science and Engineering

(a) Crk num = 0 (b) Crk num = 39

(c) Crk num = 189 (d) Crk num = 563

Figure 13 The damage of outwash deposits with different stone block content (a) shows a model with the initial content rate of stone block40 (b) shows the cracks which first appear between some blocks (c) shows fracture development among the boundary of stone blocks and(d) shows the damaged outwash deposits

stone blocks will increase which just explains the reason whythe macromechanical properties of the outwash deposit areimproved with the number of stone blocks

43 The Influence of the Stone Block Content As shown inFigure 16 when there are few stone blocks in the outwashdeposit the debris-debris contact between particles willbe the main contact type The existence of stone blocksleads to the concentration of stress along their boundarieswhich can aggravate the debris contacts to damage the peakcompressive strength keeps close to the pure debriswith slightfluctuation Meanwhile due to the stress concentration theoutwash deposits become more brittle The shear strength isdecreased Many experiments show that when the contentof stone blocks is less than 25 the characteristic is moreclose to pure debris By contrast when the content of stoneblocks is greater than 25 there is not only debris-stonecontact in the outwash deposits but also stone-stone contact

The compressive and shear strengths are improved Whenthe content of stone blocks is more than 50 the maincontact type in the outwash deposits is stone-stone Themechanical properties are better in stone-filledmaterialsThecompressive and shear strengths are significantly improved inthe stone-filled materials

However when the stress-strain curves enter the residualstrength stage there is an obvious fluctuation after the peakof the curve the amplitude of which is related to the size andcontent ratio of stone blocks so in order to study the macro-shear strength the peak value of stress-strain curves is usedto calculate shear property

44 The Macroparameter Analysis of the Outwash DepositsIn terms of the stress-strain curves for any content rateof stone block cementation strength and block size themajor factor that influences the mechanical properties of the

Advances in Materials Science and Engineering 11

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

n bond = s bond = 0Nn bond = s bond = 1000N

n bond = s bond = 2000Nn bond = s bond = 3000N

Figure 14 The biaxial compression curves with different debris bonding force

Stone average size = 1 cmStone average size = 3 cm

Stone average size = 5 cmStone average size = 7 cm

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

Figure 15 The biaxial compression curves with different averagesizes of stone blocks

Stone content = 10

Stone content = 20Stone content = 30

Stone content = 40

Stone content = 50

Stone content = 60Stone content = 70

1400

1200

1000

800

600

400

200

0000 002 004 006 008 01 012

(1205901minus1205903) (

MPa

)

1205761

Figure 16The biaxial compression curve with different stone blockcontents

The content of stone blocks ()

The p

eak

com

pres

sive s

treng

th (M

Pa) 1600

1400

1200

1000

800

600

400

200

0000 10 20 30 40 50 60 70 80

Figure 17The peak compressive strength with different stone blockcontents

outwash deposits can be attributed to the dominant contacttype which is defined as the ratio of some particle contactnumber and total contact number in numerical models Theparticle contact can be divided into three kinds respectivelythe debris-debris debris-stone or stone-stone contact

If ratio of stone block is high enough to make stone-stonecontact becoming dominant contact type the characteristicof outwash deposit is close to rockfill For the naturemediumseveral kinds of contacts exist at that time which will affectthe comprehensive mechanical property greatly Althoughthe different geometries and distributions also affect themechanical properties the content of stone blocks is thedecisive factor For the different stone block contents thepeak strength under the confining pressure of 15MPa canbe calculated approximately using formula (12) as a cubicparabola curve (shown in Figure 17)

119875119896= 141841205723 minus 90441205722 + 1600120572 + 02894 (12)

where 120572 is the content ratio of stone blocks and 119875119896is the peak

strengthIt should be noted that the compressive strength of the

outwash deposit increases slowly when content ratio of stone

12 Advances in Materials Science and Engineering

Stone block ()

Inte

rnal

fric

tion

angl

e (∘

)40

36

32

28

24

200 10 20 30 40 50 60 70 80

(a)

20

40

60

80

100

120

140

160

180

0 20 40 60 80Stone block ()

Incr

emen

tal c

ohes

ion

(MPa

)

(b)

Figure 18 Changes of shear strength of outwash deposits with different contents and distributions of stone blocks (a) shows changes of theinternal friction of outwash deposit (b) shows changes of the cohesion of outwash deposit

blocks lies between 25 and 50 Once the content of stoneblocks is greater than 50 the stone-stone contact becomesthe dominant factor which causes the compressive strengthto increase sharply The internal friction angle versus thestone block content can be described using three stages asshown below

120593 =

18093931205722 minus 495165120572 + 265026 120572 lt 25194271120572 + 221719 25 lt 120572 lt 50234286120572 + 191429 120572 gt 50

(13)

where 120593 is the internal friction angle of the outwash depositand 120572 is the stone block content

Furthermore it can be observed from Figure 18(a) thatthe fluctuation of the internal friction angle is approximately0sim8∘ for the same stone blocks content which agrees withthe fluctuations in the stress-strain curves By contrast thecohesion of outwash deposit increases clearly with the stoneblock content due to the interaction force between stoneblocks as shown in Figure 18(b) The amplitude of variationwill increase significantly with the content of stone blocksHowever it is usually difficult to quantify the amplitude dueto roughness size characteristic of stone block and so on

Therefore for outwash deposits with extremely unevenshapes and distributions of stones the compressive strengthand shear strength are primarily controlled by the stone blockcontent The randomness of the stone block distributionscauses large deviations in the mechanical parameters Forexample the internal friction angle may have a large fluctua-tion at the same stone block content This feature is the causeof the poor results of the geotechnical experiments

5 Discussions

Outwash deposits are a type of debris-stone mixture Themechanical properties of these deposits are affected by thecomposition of the debris and stone blocks As the debriscementation increases the compressive strength increasesHowever the internal friction angle has a negative correlation

with the cementation force The stone block content is thedecisive factor for the mechanical properties of outwashdepositsThe randomness of the structural composition leadsto significant fluctuations in the properties which also createslarge discrepancies in the mechanical parameters

The major influences of the particle sizes geometricdistribution and stone block content are to determine thecontact type in the outwash deposits When the debris-debris contact is the dominant contact type there is littleinfluence from the stone blocks on the mechanical propertiesof the outwash depositsWhen the debris-stone contact is thedominant contact type the stone block content has a positiveinfluence on the compressive and shear strengths When thestone-stone contact is the dominant contact type the roles ofthe debris and stone blocks are reversed and the properties ofthe outwash deposits aremuch closer to a rock-filledmaterial

Although it is difficult to determine the mechanicalparameters of an outwash deposit using indoor experimentsthe properties of the medium can still be researched usingindirect approachesThemechanical parameters of the debrisand stone blocks can be determined from the indoor experi-ments Then the biaxial compression numerical experimentusing the granular discrete element method can be carriedout to analyse the influence of the stone blocks on theproperties of outwash deposits which makes up for thelimitation that the indoor experiments cannot consider thelarge stone blocks and offers a beneficial supplement to aid inthe geological parameter determination

6 Conclusions

According to the grain size and shape statistics from fieldstatistics the numerical granular discrete elementmodel withrandomised generation of stone blocks can be used withhypothesis that the length of the long axis and the axial ratioall follow normal distributions and the azimuth of the longaxis follows uniformdistribution in 0sim360∘The relationshipsbetween the macro- and micromechanical parameters arediscussed and the mechanical behaviour of the outwash

Advances in Materials Science and Engineering 13

deposit is affected by the cementation strength the size ofstone blocks the stone block content and the distribution ofthe stone blocks These properties are analysed so that theycan be better understood by the geologists working on thedemocratisation of the Engineering Project

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (no 51309089 and no 51379065)the National Key Technology RampD Program (no2013BAB06B00) the National Basic Research Programof China (973 Program) (no 2015CB057903) the NaturalScience Foundation of Jiangsu Province (no BK20130846)and the Fundamental Research Funds for the CentralUniversities (no 2014B04914)

References

[1] W G Holtz and H J Gibbs ldquoTriaxial shear tests on perviousgravelly soilsrdquo Journal of the Soil Mechanics and FoundationsDivision vol 82 no 1 pp 1ndash22 1956

[2] R J Chandler ldquoThe inclination of Talus Arctic Talus Terracesand other slopes composed of granular materialsrdquo The Journalof Geology vol 81 no 1 pp 1ndash14 1973

[3] X H You Stochastic structural model of the earth-rock aggregateand its application [PhD thesis] Beijing Jiaotong UniversityBeijing China 2001

[4] X H You and J S Tang ldquoResearch on horizontal push-shearin-situ test of debris and rock-mixturerdquo Chinese Journal of RockMechanics and Engineering vol 21 no 10 pp 1537ndash1540 2002

[5] X H You G He and X Li ldquoMicro-handling technologyof earth-rock aggregate sloperdquo Hydrogeology and EngineeringGeology vol 30 no 1 pp 18ndash21 2003

[6] J M He Study of deformation and failure mechanisms of rock-debris aggregate in three gorges reservoir area [PhD thesis]China University of Mining and Technology Beijing China2004

[7] X Li Q L Liao J M He and J Chen ldquoStudy on in-situ testsof mechanical characteristics on soil-rock aggregaterdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 12 pp2377ndash2384 2007

[8] T Lebourg J Riss and E Pirard ldquoInfluence of morphologicalcharacteristics of heterogeneous moraine formations on theirmechanical behaviour using image and statistical analysisrdquoEngineering Geology vol 73 no 1-2 pp 37ndash50 2004

[9] T R Reid and J P Harrison ldquoA semi-automated methodologyfor discontinuity trace detection in digital images of rock massexposuresrdquo International Journal of Rock Mechanics andMiningSciences vol 37 no 7 pp 1073ndash1089 2000

[10] Z Q Yue S Chen and L G Tham ldquoFinite element modelingof geomaterials using digital image processingrdquo Computers andGeotechnics vol 30 no 5 pp 375ndash397 2003

[11] Z Q Yue S Chen H Zheng and G H Tang ldquoDigital imageproceeding based on finite element method for geomaterialsrdquo

Chinese Journal of Rock Mechanics and Engineering vol 23 no6 pp 889ndash897 2004

[12] Q L Liao X Li W C Zhu and J S Liu ldquoStructure modelconstruction of rock and soil aggregate based on digital imagetechnology and its numerical simulation on mechanical struc-ture effectsrdquoChinese Journal of RockMechanics and Engineeringvol 29 no 1 pp 155ndash162 2010

[13] W J Xu R L Hu Z Q Yue and R J Tan ldquoMesostructuralcharacter and numerical simulation of mechanical propertiesof soil-rock mixturesrdquo Chinese Journal of Rock Mechanics andEngineering vol 26 no 2 pp 300ndash311 2007

[14] W J Xu Z Q Yue and R L Hu ldquoA current status of digitalimage based quantitative analysis of internal structures ofdebris rock and concretes and associated numerical simula-tionrdquo Journal of Engineering Geology vol 15 no 3 pp 289ndash3132007

[15] W J Xu R L Hu Z Q Yue R Zhang and G L WangldquoResearch on relationship between rock block proportion andshear strength of soil-rock mixtures based on digital imageanalysis and large direct shear testrdquo Chinese Journal of RockMechanics and Engineering vol 27 no 5 pp 996ndash1007 2008

[16] P A Cundall and O D L Strack ldquoA discrete numerical modelfor granular assembliesrdquo Geotechnique vol 29 no 1 pp 47ndash651979

[17] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) (Version 31) Itasca Consulting Group Minneapo-lis Minn USA 2004

[18] J Yoon ldquoApplication of experimental design and optimizationto PFC model calibration in uniaxial compression simulationrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 6 pp 871ndash889 2007

[19] Y C Wang and P Mora ldquoMacroscopic elastic properties ofregular latticesrdquo Journal of the Mechanics and Physics of Solidsvol 56 no 12 pp 3459ndash3474 2008

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Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 3

O

N polygon

Random polygon

Ni

120579

Figure 2 An arbitrarily shaped stone block depicted by a particlescluster

If the density of the stone blocks is 120588119877 the debris density

is 120588119878 Therefore the 2D area of the stone blocks in grade 119894 can

be written as follows

119860119894=

41199032119866119894120588119877

1198660120588119878+ sum119899

119896=1119866119894120588119877

(2)

where 119860119894is the 2D area percentage of stone blocks in grade

119894 1198660is the weight of the medium with grain sizes below the

threshold and sum119899119896=1

119866119896120588119877is the total weight of stone blocks

23 The Randomised Generation of Aggregates Each stoneblock can be regarded as an arbitrary polygon in the planeso a number of polygons are generated randomly in thedesignated region to simulate blocks During the generationprocess every polygon should be judged to avoid overlappingwith others Then the area in the polygons is regarded asstone blocks of different grades When the polygon is convexit has difficulty in considering the interaction force dueto mosaic effect of rough block surface which will leadto deviations in the mechanical parameter research so thepolygon generation should consider convexity and concavityat the same time

To generate the arbitrary shapes of the stone blocks thestone blocks are assumed to be initially elliptical then theoutline is divided as polygon and the vertices of polygon arerandom as shown in Figure 2The ellipses can be determinedusing three parameters the length of long axis 119886 length of theshort axis 119887 (or the axis ratio defined as ratio of the short axislength to the long axis) and the azimuth of the long axis 120579Field investigation shows that the angle of long axis azimuth isin poor statistical correlation so it can be regarded as obeyinguniform distribution over 0sim360∘

As shown in Figure 3(a) the lengths of the long axis andthe axis ratio are approximately obeying normal distributionwith variance as shown in Figures 3(c) and 3(d) So the length

of the long axis the axial ratio and the azimuth angle of longaxis whose definition is shown in Figure 3(b) are given asshown in the following formula

119886 = 1198860+ 2120590119886(rand (1) minus 1)

119903 = 1199030+ 2120590119903(rand (1) minus 1)

120579 = 360 sdot rand (1)

(3)

where 119886 120590119886 119903 120590119903are the mean of the long axis the variance

of the long axis the mean of the axial ratio and the varianceof axial ratio respectively 120579 is the azimuth of long axisrand(1) returns a random number between 0 and 1 119886 120590

119886

119903 120590119903should be obtained using the statistics according to the

stone blocks in outwash deposit medium Here 05 times thecorresponding mean value is used as an empirical parameterfor variance if there is no statistical information

Then every stone block is hypothesised to be a polygoncomposed of119873 sides as shown in Figure 2The elliptical arc isaccordingly divided into119873 arcs Each point of the arc can bemoved towards the centre of the ellipse The correspondingcoordinate of each point can be defined as follows

119909119894= 1199090+ 119886 sdot cos (120579 + 119873Δ120593)

119910119894= 1199100+ 119886 sdot 119903 sdot sin (120579 + 119873Δ120593)

(4)

where 119909119894and 119910

119894are the coordinates of the 119894th node in a

polygon 1199090and 119910

0are the coordinates of the centre of the

ellipse 1205930is the azimuth of ellipse and Δ120593 is the angle

between two vertexes of the polygon where Δ120593 = 360119873The steps of the random structure generation are shown

in Figure 4The generated polygons can be convex or concaveThe polygons are divided into 119899 triangles using the centreand vertexes of the polygon Therefore once the centre of anelement is determined to be within one triangle the elementcan be set as a stone block and numbered

To ensure that the stone blocks do not overlap theelements are set as debris by default Once one of the elementsin the current trial has been defined as a stone block thecurrent step will end and a new position will be tried as thecentre of the generated polygon until all of the elements inthe generated polygon are no longer debris When all of thegenerated polygons are finished in this way the numericalmodel is complete

To avoid setting adjacent polygons as the same stoneblock each stone block should be numbered a uniquenumber The particle contact parameters within one stoneblock are endowed the parameters of the stone blocks andthe contact parameter between two stone blocks is taken asthat of debris Therefore the contact characteristics betweenstone blocks can be approximately simulated

The content rate of stone block of grade 119894 in a two-dimension model can be defined as the ratio of the stoneblock area within grade 119894 to the total area of the model It canbe expressed as follows

119899119894=sum119860119895

119860 (5)

4 Advances in Materials Science and Engineering

000005010015020025030035

040 050 060 070 080 090

Size statics of rock blocks

(a)

(d)(b)

000

010

020

030

040

050

002 004 056 007 009 011

(c)

Length of long axis (m)

Freq

uenc

yFr

eque

ncy

Ratio of the long axis length to the short axis

2a

2b

Figure 3 The statistical results of the size and the lengths of the long axis of stone blocks (a) the in situ outwash deposits (b) definition ofthe long axis and short axis for stone blocks the long axis is the largest distance between vertices along the stone outline while the short axisis the maximum segment length normal to the long axis direction (c) the statistical results of the size of stone blocks (d) the statistical resultsof the lengths of the long axis of stone blocks

where 119860 is the total area of the model 119860119895is the area of the

119895th stone block and grade 119894 and 119899119894is the content rate of stone

blocks of grade 119894The area of the total stone blocks is counted until the

grade requirement is metThe structure of the outwash deposit model is generated

randomly according to the method of multigradations Theinfluences of the azimuth concavity and convexity of thestone blocks on the outwash deposit are also taken intoconsideration The generation of stone blocks occurs fromthe largest to the smallest size according to the grain sizeaccumulation curve

3 Analysis Based on Micromechanical Model

31 The Principle of the Granular Discrete Element MethodThe granular discrete element method is adopted to simulatethe micromechanical properties of the granular materials inthe form of discs or spherical particles using the explicitdifference algorithm [16] Newtonrsquos Second Law is used inorder to determine the particle movement that is caused bycontact or the force of a body while the force-displacementlaw is used to calculate the contact force that is changingrelative to movement The two laws are then used alternatelyuntil the total system reaches equilibrium as shown inFigure 5(a) The particles can be combined into any shape orcombination to simulate the stone or debris mass structures

As shown in Figure 5(b) when there is no bondingbetween particles the mechanical behaviour of the particles

in contact is determined by their own normal stiffness (119896119899)

tangential stiffness (119896119904) and friction coefficient (120583) When

two particles are in contact the contact and tangentialstiffness can be calculated as follows

119896119899=

119896(119860)119899119896(119861)119899

119896(119860)119899

+ 119896(119861)119899

119896119904=

119896(119860)119904119896(119861)119904

119896(119860)119904

+ 119896(119861)119904

(6)

The normal force of contact particles is depicted as

119865119899= 119870119899119880119899 (7)

where 119880119899is the normal contact depth

In the calculation process the tangential force is zeroinitially so the incremental form of the equation is used asfollows

Δ119865119904= minus119896119904Δ119880119904 (8)

If 119880119899le 0 a gap exists between the particles the normal

and shear force are both zero and the slipping force betweenthe particles should be calculated with the friction coefficientThis coefficient is calculated as 120583 = min(120583(119860) 120583(119861)) where120583(119860) and 120583(119861) are the particle friction coefficients of 119860 and 119861respectively and 119865

119904= 120583119865119899is used when 119865

119904ge 120583119865119899

The stiffness contact model is adopted for the outwashdeposit in this work because the point contact and the

Advances in Materials Science and Engineering 5

Select model scope (width and height)

Assign particle radius generate particles and set default flag 0 as soil

Number i level

Specify the aggregate gradation of outwash deposits in N designlevels (limit of size mean-variance)

Find out particles within the special polygon

If the flag of particle within the polygon is 0 or not

Yes

Statistic area of particles within the polygons add it to the total area of this level and give a new number of stone block

Judge whether the total area of current level meets the requirements

of the design level or not

No

Exit the current design levels

YesNo

Output the random model and distribute the particle properties

The flag of 0 is soilThe flag of 1 is rock

Generate polygons randomly controlled by block size (from 3 cm to20 cm) length of long axis axial ratio and the azimuth of long axis

Figure 4 The flowchart for the randomised generation of stone blocks

Update contact force between particles and position of wall and build up new contact

Newtonrsquos laws of motion applied to calculate resultant

force and resultant moment of each particle

Law of force-displacementapplied to illustrate relative movement and constitutive

relation of each contact

Contact force

(a) Calculation principle in PFC2D

N-normal directionT-tangential directiondirection

N

T

i

j

z

y

x

(b) Two contacting particles

Figure 5 Contact force between particles and calculation principle

linear contact in the debris-debris debris-stone and stone-stone are the main kind of contact types the point contactsare especially dominant Five microparameters need to becalibrated the normal stiffness the stiffness ratio of tangentstiffness and normal stiffness the friction coefficient the

normal bonding strength and the tangent bonding strengthaccording to PFC2D manual [17]

32TheConversion from the GeologicalModel to aMechanicalModel According to the theory of granular discrete element

6 Advances in Materials Science and Engineering

0 1 0 1

1 0 0 1

1 1 1 0

0 0 1 1

Wall load plate

Wall load plate x

y

Outwash deposit Particle modelConversion relationship

ro

Servo mechanism

radic3r 2r

j998400

i998400

Figure 6 Construction of a debris-stone micromodel using a spot matrix and PFC2D

method 2D disk particles are used to transform the geolog-ical model to a mechanical model If the particle is too largein the model the shape of stone block and microstructurecharacteristic will be distorted However the larger numberof particles in amodel will lead to very slow calculation speedA significant amount of timewill be sacrificed whichmay notbe tolerable So a proper particle size should be determinedempirically

The width and the height of the model in this work aretaken to 050 times 050m the constant radius of particles is25mm and the arrangement of the particles is shown inFigure 6 The distance between the centres of two adjacentparticles in the vertical direction is radic3119903 (r is the radiusof particle) The distance between the centres of adjacentparticles in the horizontal direction is 2119903 Therefore thecoordinates of the particle centre (119909

11989410158401198951015840 11991011989410158401198951015840) in the 1198941015840 line and

1198951015840 column can be expressed as follows

11990911989410158401198951015840 =

(21198951015840 minus 1) 119903 (1198941015840 = 2119896 + 1)

21198951015840119903 (1198941015840 = 2119896) (119896 isin 119873)

11991011989410158401198951015840 = 119903 + radic3119903 (119894 minus 1)

(9)

According to the modelling steps the particles arearranged initially as shown in Figure 6 The even rows aredislocated to ensure that the particles are tangential withadjacent rowsWhen a particlemodel filling the research zoneis generated every particle within the model will be judgedto determine whether its centre is located in some randompolygon If it is in a polygon the particle belongs to a stoneblockwith a certain flag If it is not in any polygon the particleis regarded as debrisThe initial structural information can beobtained from site research or by random generation

Several particleswith the samepolygonflag are assembledtogether by the high bonding force to simulate the character-istics of the stone blocks The structural effect of the outwashdeposit is thus simulated The separation of the debris fromthe stone is also convenient for the determination of themechanical parameters

33 The Relationship between the Macro- and Microme-chanical Parameters Youngrsquos modulus and Poissonrsquos ratio

000

005

010

015

020

025

030

035

00 02 04 06 08 10 12

Poiss

on ra

tio

kskn

kn = 500MPan bond = 1000Ns bond = 1000N

Figure 7 The relationship between Poissonrsquos ratio and the stiffnessratio

determined in the indoor geotechnical tests are used todescribe the macrodeformation properties of the materialsMany studies have shown that Youngrsquos modulus is related tothe microparameter 119896

119899and the stiffness ratio 119896

119904119896119899 while

Poissonrsquos ratio is mainly related to the stiffness ratio [1819] However these changes are all affected by the particlecompositions such as the mean radius and the ratio of themaximum radius to the minimum radius Since a constantradius is used in this work the problem can be neglected

To reflect the relation between Poissonrsquos ratio and thestiffness ratio 119896

119904119896119899 the normal stiffness is initially fixed at

a constant 50MPa The relationship between Poissonrsquos ratioand the stiffness ratio is shown in Figure 7 It can be foundthat Poissonrsquos ratio in the debris shows a nonlinear inverserelationshipwith the stiffness ratio of debris when the particleradius is unchanged

It can also be concluded in Figure 7 that the tangentstiffness is usually less than the normal stiffness Once thetangent stiffness is equal to or greater than the normalstiffness Poissonrsquos ratio will reach zero This situation onlyexists in very loose cellular structures However for outwashdeposits it is obviously unreasonable when the medium isin a compacted state Poissonrsquos ratio declines as the stiffnessratio increases When the tangent stiffness is equal to the

Advances in Materials Science and Engineering 7

08

07

06

05

04

03

Ek

n

kn (GPa)

015

25

35

45

0908

0706

0504

0302

010

k skn

Figure 8The changes in Youngrsquos modulus with the microdeforma-tion parameters

Poiss

onrsquos

ratio

030

025

020

015

010

005

kn (GPa)

015

25

35

4509

0807

0605

0403

0201

0

k sk n

Figure 9The changes in Poissonrsquos ratio with the microdeformationparameters

normal stiffness Poissonrsquos ratio is close to zero When thestiffness ratio decreases the lateral deformation increasesWhen the tangent stiffness is zero Poissonrsquos ratio reaches itsmaximumvalueThe relationship between Poissonrsquos ratio andthe stiffness ratio based on a series of numerical tests can beexpressed using the following equation

1205830= 012781205782 minus 04061120578 + 03177 (10)

where 120583 is Poissonrsquos ratio and 120578 = 119896119904119896119899is the ratio of

the tangent stiffness to the normal stiffness which lies inthe range 0sim05 Once 120578 is greater than 10 Poissonrsquos ratiomay be greater than 10 or negative which disagrees with theproperties of common solid media

It should be noted that (10) does not consider the influ-ence of the stiffness If the stiffness is taken into considerationYoungrsquos modulus and Poissonrsquos ratio can be estimated withdifferent normal stiffness as follows

119864 = (02259120578 minus 00058119896119899minus 00042120578119896

119899+ 05346) 119896

119899

120583 = minus02760120578 minus 00029119896119899+ 00031120578119896

119899+ 03200

(11)

Friction coefficient

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Inte

rnal

fric

tion

angl

e (∘

)

4200

4000

3800

3600

3400

3200

300000 05 10 15 20 25

Figure 10 The changes in the internal friction angle at differentcoefficients of friction

The changes in Youngrsquos modulus and Poissonrsquos ratio withthe changes in the microparameters are shown in Figures8 and 9 The figures illustrate that the relationship betweenYoungrsquos modulus of an outwash deposit and the correspond-ing Poissonrsquos ratio is not a simple linear relation but adouble linear correlation in the calculation of the granulardiscrete element method When the microparameters needto be determined Youngrsquos modulus and Poissonrsquos ratio caninitially be assumed Then more reasonable values can bedetermined using (11) The steps should be repeated manytimes until Youngrsquosmodulus andPoissonrsquos ratio agreewith theresults of the macroscopic tests In addition the debris andstone blocks should be calibrated separately to obtain propermicroparameters

34TheMicromechanical Parameters of theOutwashDepositsThe normal contact force (119899 bond) tangent contact force(119904 bond) and the coefficient of friction 120583 are the mainmicroparameters related to macrostrength in a granularmodel based on PFC2D These parameters correspond tothe macrocohesion and the internal friction in the Mohr-Coulomb criterion The coefficient of friction is the purefrictional force when the outwash deposit is completelydestroyed It determines the residual strength of the mediumand can be approximately equal to the pure friction coefficienttan120593 of the stone and debris mass

As shown in Figure 10 when the coefficient of friction islow the deformation of the stone and debris mass shows alinear variation By contrast when the friction coefficient ishigh the deformation of the stone and debris mass showsa nonlinear variation The internal friction angle of themedium first increases and then remains unchanged as thecoefficient of friction increases The cohesion shows similarbehaviour but it remains constant if the coefficient of frictionis lowThe cohesion will increase as the coefficient of frictionincreases as shown in Figure 11

It is not difficult to find that the microcoefficient offriction is sensitive to the macro-internal-friction angleWhen the microparameters need to be determined thebonding forces should initially be set to zero then the friction

8 Advances in Materials Science and Engineering

000

020

040

060

080

100

120

00 05 10 15 20 25Friction coefficient

Coh

esio

n (M

Pa)

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Figure 11 The cohesion remains constant if the coefficient of friction is low

180

160

140

120

100

080

060

040

020

000000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 10

(a)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 35

200

180

160

140

120

100

080

060

040

020

000

(b)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

Stone rate = 45200

150

100

050

000

(c)

1205901minus1205903

(MPa

)

000 001 002 003 004

1205761

Stone rate = 60

1200

1000

800

600

400

200

000

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

(d)

Figure 12 The biaxial compression curve at different confining pressures and stone block content (a) Stone block content is 10 (b) stoneblock content is 35 (c) stone block content is 45 and (d) stone block content is 60

Advances in Materials Science and Engineering 9

Table 1 The micromechanical parameters of outwash deposits

Material Density (kgm3) Bonding force (N) Stiffness ratio Normal stiffness (Nm) Friction coefficientNormal Tangential

Debris 2200 11198903 11198903 00 11198908 025Stone 2700 21198906 21198906 02 951198909 120

Table 2 The macromechanical parameters of outwash deposits

Material Youngrsquos modules (MPa) Poissonrsquos ratio Internal friction angel (∘) Cohesion (MPa)Debris 559 032 2794 007Stone 4950 020 56 120

coefficient can be determined using trial calculations until themacromechanical properties are in linewith the experimentalresults Finally the bonding forces are adjusted so thatthe parameters are consistent with the macromechanicalproperties of the outwash deposit

When the bonding force is zero the internal friction anglewill reach its minimum value Therefore the determinationof the internal friction angle should take the effect of thestiffness ratio into consideration If the internal friction angleis unchanged when the coefficient of friction increases thebonding force can be adjusted to be in agreement with thepeak strength of the stress In this work the microparametersare shown in Table 1 and the corresponding macroparame-ters are shown in Table 2

4 The Analysis of the Mechanical Behaviour ofthe Outwash Deposits

As a case study shown in Figure 1 the stone rate of outwashbased on the statistical results is about 30 to 40 themean length of long axis is about 413 cm with a variance015 and the mean axis ratio is 064 with a variance 017Then the random structure models of outwash depositsare generated according to the above information Finallynumerical simulation and comparison are executed in orderto analyse the effect of comprehensive mechanical behaviour

41 The Stress-Strain Curve Based on the Biaxial CompressionTest The stress-strain curves from the numerical simulationtests of an outwash deposit under biaxial compression con-ditions can be divided into three stages the elastic stagethe hardening stage and the residual strength stage (shownin Figure 12) In the elastic stage the deformation modulusis determined by the undamaged debris particles and stoneblock assemblies As the deformation increases fractureswill first appear in the debris because of its low modulusand strength When the outwash deposit enters into thehardening stage the debris particle bonding forces will failgradually and the deformation modulus will decrease slowlyHowever the strength will increase continually due to theinteraction force caused by mosaic effect between the debrisparticles and the stone blocks When the stress reaches itspeak strength the outwash deposit will enter into the residualstrength stage The cementation ability between the debris

particles is almost completely lost The compressive-bearingcapability of the sample cannot continue to increase Thecompressive-bearing capability is controlled mainly by theinterparticle friction When the strain continues to increasethe stone blocks may rotate and tumble which leads tothe complete destruction of the structure of the outwashdeposit However there is still some compression-bearingcapability which causes the residual strength of the outwashdeposit The residual strength shows fluctuations because ofthe contact action between the debris and the stone blocks

As shown in Figure 13 the damage of a model withcontent ratio of stone block 40 length of long axis about2 to 6 cm and the axial ratio 05 to 08 is compared in theloading process It shows that cracks occur firstly betweensome blocks and then develop among the boundary of stoneblocks and fill with the debris particles The crack numberwill increase shapely with the strain increase until all bondcontacts between debris particles are destroyed

The curves for different debris bonding forces in Figure 14show that the cementation strength of the debris particlesdecides the strength of outwash deposit and has a dominantrole in the mechanical properties when the other condi-tions are fixed With a stronger cementation force of debrisparticles there is a smaller increase in the internal frictionangle and a bigger increase for the cohesion The mechanicalproperties of an outwash deposit with high cementationstrength aremore similar to the properties of the stone blocksConversely if the cementation strength of the debris particlesis weak there is a bigger increase in the internal frictionangle and a smaller increase in the cohesionThe mechanicalproperties of the outwash deposit are much closer to theelastic-plastic debris

42 The Influence of the Aggregate Size As shown in Fig-ure 15 the larger the size of stone blocks is the smaller thepeak strength is This situation can be interpreted by theperimeter ratio which is defined as the ratio of all boundariesrsquoperimeters of stone blocks and themodel areaThe perimeterratio under the same stone ratio varies greatly The smalleraggregate size has more stone blocks so the perimeter ratiowill reach a high level and form larger contact areas Thecompressive strength also increases When the number ofstone blocks increases the contact area of the debris and stoneblocks and the interaction force between the debris and the

10 Advances in Materials Science and Engineering

(a) Crk num = 0 (b) Crk num = 39

(c) Crk num = 189 (d) Crk num = 563

Figure 13 The damage of outwash deposits with different stone block content (a) shows a model with the initial content rate of stone block40 (b) shows the cracks which first appear between some blocks (c) shows fracture development among the boundary of stone blocks and(d) shows the damaged outwash deposits

stone blocks will increase which just explains the reason whythe macromechanical properties of the outwash deposit areimproved with the number of stone blocks

43 The Influence of the Stone Block Content As shown inFigure 16 when there are few stone blocks in the outwashdeposit the debris-debris contact between particles willbe the main contact type The existence of stone blocksleads to the concentration of stress along their boundarieswhich can aggravate the debris contacts to damage the peakcompressive strength keeps close to the pure debriswith slightfluctuation Meanwhile due to the stress concentration theoutwash deposits become more brittle The shear strength isdecreased Many experiments show that when the contentof stone blocks is less than 25 the characteristic is moreclose to pure debris By contrast when the content of stoneblocks is greater than 25 there is not only debris-stonecontact in the outwash deposits but also stone-stone contact

The compressive and shear strengths are improved Whenthe content of stone blocks is more than 50 the maincontact type in the outwash deposits is stone-stone Themechanical properties are better in stone-filledmaterialsThecompressive and shear strengths are significantly improved inthe stone-filled materials

However when the stress-strain curves enter the residualstrength stage there is an obvious fluctuation after the peakof the curve the amplitude of which is related to the size andcontent ratio of stone blocks so in order to study the macro-shear strength the peak value of stress-strain curves is usedto calculate shear property

44 The Macroparameter Analysis of the Outwash DepositsIn terms of the stress-strain curves for any content rateof stone block cementation strength and block size themajor factor that influences the mechanical properties of the

Advances in Materials Science and Engineering 11

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

n bond = s bond = 0Nn bond = s bond = 1000N

n bond = s bond = 2000Nn bond = s bond = 3000N

Figure 14 The biaxial compression curves with different debris bonding force

Stone average size = 1 cmStone average size = 3 cm

Stone average size = 5 cmStone average size = 7 cm

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

Figure 15 The biaxial compression curves with different averagesizes of stone blocks

Stone content = 10

Stone content = 20Stone content = 30

Stone content = 40

Stone content = 50

Stone content = 60Stone content = 70

1400

1200

1000

800

600

400

200

0000 002 004 006 008 01 012

(1205901minus1205903) (

MPa

)

1205761

Figure 16The biaxial compression curve with different stone blockcontents

The content of stone blocks ()

The p

eak

com

pres

sive s

treng

th (M

Pa) 1600

1400

1200

1000

800

600

400

200

0000 10 20 30 40 50 60 70 80

Figure 17The peak compressive strength with different stone blockcontents

outwash deposits can be attributed to the dominant contacttype which is defined as the ratio of some particle contactnumber and total contact number in numerical models Theparticle contact can be divided into three kinds respectivelythe debris-debris debris-stone or stone-stone contact

If ratio of stone block is high enough to make stone-stonecontact becoming dominant contact type the characteristicof outwash deposit is close to rockfill For the naturemediumseveral kinds of contacts exist at that time which will affectthe comprehensive mechanical property greatly Althoughthe different geometries and distributions also affect themechanical properties the content of stone blocks is thedecisive factor For the different stone block contents thepeak strength under the confining pressure of 15MPa canbe calculated approximately using formula (12) as a cubicparabola curve (shown in Figure 17)

119875119896= 141841205723 minus 90441205722 + 1600120572 + 02894 (12)

where 120572 is the content ratio of stone blocks and 119875119896is the peak

strengthIt should be noted that the compressive strength of the

outwash deposit increases slowly when content ratio of stone

12 Advances in Materials Science and Engineering

Stone block ()

Inte

rnal

fric

tion

angl

e (∘

)40

36

32

28

24

200 10 20 30 40 50 60 70 80

(a)

20

40

60

80

100

120

140

160

180

0 20 40 60 80Stone block ()

Incr

emen

tal c

ohes

ion

(MPa

)

(b)

Figure 18 Changes of shear strength of outwash deposits with different contents and distributions of stone blocks (a) shows changes of theinternal friction of outwash deposit (b) shows changes of the cohesion of outwash deposit

blocks lies between 25 and 50 Once the content of stoneblocks is greater than 50 the stone-stone contact becomesthe dominant factor which causes the compressive strengthto increase sharply The internal friction angle versus thestone block content can be described using three stages asshown below

120593 =

18093931205722 minus 495165120572 + 265026 120572 lt 25194271120572 + 221719 25 lt 120572 lt 50234286120572 + 191429 120572 gt 50

(13)

where 120593 is the internal friction angle of the outwash depositand 120572 is the stone block content

Furthermore it can be observed from Figure 18(a) thatthe fluctuation of the internal friction angle is approximately0sim8∘ for the same stone blocks content which agrees withthe fluctuations in the stress-strain curves By contrast thecohesion of outwash deposit increases clearly with the stoneblock content due to the interaction force between stoneblocks as shown in Figure 18(b) The amplitude of variationwill increase significantly with the content of stone blocksHowever it is usually difficult to quantify the amplitude dueto roughness size characteristic of stone block and so on

Therefore for outwash deposits with extremely unevenshapes and distributions of stones the compressive strengthand shear strength are primarily controlled by the stone blockcontent The randomness of the stone block distributionscauses large deviations in the mechanical parameters Forexample the internal friction angle may have a large fluctua-tion at the same stone block content This feature is the causeof the poor results of the geotechnical experiments

5 Discussions

Outwash deposits are a type of debris-stone mixture Themechanical properties of these deposits are affected by thecomposition of the debris and stone blocks As the debriscementation increases the compressive strength increasesHowever the internal friction angle has a negative correlation

with the cementation force The stone block content is thedecisive factor for the mechanical properties of outwashdepositsThe randomness of the structural composition leadsto significant fluctuations in the properties which also createslarge discrepancies in the mechanical parameters

The major influences of the particle sizes geometricdistribution and stone block content are to determine thecontact type in the outwash deposits When the debris-debris contact is the dominant contact type there is littleinfluence from the stone blocks on the mechanical propertiesof the outwash depositsWhen the debris-stone contact is thedominant contact type the stone block content has a positiveinfluence on the compressive and shear strengths When thestone-stone contact is the dominant contact type the roles ofthe debris and stone blocks are reversed and the properties ofthe outwash deposits aremuch closer to a rock-filledmaterial

Although it is difficult to determine the mechanicalparameters of an outwash deposit using indoor experimentsthe properties of the medium can still be researched usingindirect approachesThemechanical parameters of the debrisand stone blocks can be determined from the indoor experi-ments Then the biaxial compression numerical experimentusing the granular discrete element method can be carriedout to analyse the influence of the stone blocks on theproperties of outwash deposits which makes up for thelimitation that the indoor experiments cannot consider thelarge stone blocks and offers a beneficial supplement to aid inthe geological parameter determination

6 Conclusions

According to the grain size and shape statistics from fieldstatistics the numerical granular discrete elementmodel withrandomised generation of stone blocks can be used withhypothesis that the length of the long axis and the axial ratioall follow normal distributions and the azimuth of the longaxis follows uniformdistribution in 0sim360∘The relationshipsbetween the macro- and micromechanical parameters arediscussed and the mechanical behaviour of the outwash

Advances in Materials Science and Engineering 13

deposit is affected by the cementation strength the size ofstone blocks the stone block content and the distribution ofthe stone blocks These properties are analysed so that theycan be better understood by the geologists working on thedemocratisation of the Engineering Project

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (no 51309089 and no 51379065)the National Key Technology RampD Program (no2013BAB06B00) the National Basic Research Programof China (973 Program) (no 2015CB057903) the NaturalScience Foundation of Jiangsu Province (no BK20130846)and the Fundamental Research Funds for the CentralUniversities (no 2014B04914)

References

[1] W G Holtz and H J Gibbs ldquoTriaxial shear tests on perviousgravelly soilsrdquo Journal of the Soil Mechanics and FoundationsDivision vol 82 no 1 pp 1ndash22 1956

[2] R J Chandler ldquoThe inclination of Talus Arctic Talus Terracesand other slopes composed of granular materialsrdquo The Journalof Geology vol 81 no 1 pp 1ndash14 1973

[3] X H You Stochastic structural model of the earth-rock aggregateand its application [PhD thesis] Beijing Jiaotong UniversityBeijing China 2001

[4] X H You and J S Tang ldquoResearch on horizontal push-shearin-situ test of debris and rock-mixturerdquo Chinese Journal of RockMechanics and Engineering vol 21 no 10 pp 1537ndash1540 2002

[5] X H You G He and X Li ldquoMicro-handling technologyof earth-rock aggregate sloperdquo Hydrogeology and EngineeringGeology vol 30 no 1 pp 18ndash21 2003

[6] J M He Study of deformation and failure mechanisms of rock-debris aggregate in three gorges reservoir area [PhD thesis]China University of Mining and Technology Beijing China2004

[7] X Li Q L Liao J M He and J Chen ldquoStudy on in-situ testsof mechanical characteristics on soil-rock aggregaterdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 12 pp2377ndash2384 2007

[8] T Lebourg J Riss and E Pirard ldquoInfluence of morphologicalcharacteristics of heterogeneous moraine formations on theirmechanical behaviour using image and statistical analysisrdquoEngineering Geology vol 73 no 1-2 pp 37ndash50 2004

[9] T R Reid and J P Harrison ldquoA semi-automated methodologyfor discontinuity trace detection in digital images of rock massexposuresrdquo International Journal of Rock Mechanics andMiningSciences vol 37 no 7 pp 1073ndash1089 2000

[10] Z Q Yue S Chen and L G Tham ldquoFinite element modelingof geomaterials using digital image processingrdquo Computers andGeotechnics vol 30 no 5 pp 375ndash397 2003

[11] Z Q Yue S Chen H Zheng and G H Tang ldquoDigital imageproceeding based on finite element method for geomaterialsrdquo

Chinese Journal of Rock Mechanics and Engineering vol 23 no6 pp 889ndash897 2004

[12] Q L Liao X Li W C Zhu and J S Liu ldquoStructure modelconstruction of rock and soil aggregate based on digital imagetechnology and its numerical simulation on mechanical struc-ture effectsrdquoChinese Journal of RockMechanics and Engineeringvol 29 no 1 pp 155ndash162 2010

[13] W J Xu R L Hu Z Q Yue and R J Tan ldquoMesostructuralcharacter and numerical simulation of mechanical propertiesof soil-rock mixturesrdquo Chinese Journal of Rock Mechanics andEngineering vol 26 no 2 pp 300ndash311 2007

[14] W J Xu Z Q Yue and R L Hu ldquoA current status of digitalimage based quantitative analysis of internal structures ofdebris rock and concretes and associated numerical simula-tionrdquo Journal of Engineering Geology vol 15 no 3 pp 289ndash3132007

[15] W J Xu R L Hu Z Q Yue R Zhang and G L WangldquoResearch on relationship between rock block proportion andshear strength of soil-rock mixtures based on digital imageanalysis and large direct shear testrdquo Chinese Journal of RockMechanics and Engineering vol 27 no 5 pp 996ndash1007 2008

[16] P A Cundall and O D L Strack ldquoA discrete numerical modelfor granular assembliesrdquo Geotechnique vol 29 no 1 pp 47ndash651979

[17] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) (Version 31) Itasca Consulting Group Minneapo-lis Minn USA 2004

[18] J Yoon ldquoApplication of experimental design and optimizationto PFC model calibration in uniaxial compression simulationrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 6 pp 871ndash889 2007

[19] Y C Wang and P Mora ldquoMacroscopic elastic properties ofregular latticesrdquo Journal of the Mechanics and Physics of Solidsvol 56 no 12 pp 3459ndash3474 2008

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Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

4 Advances in Materials Science and Engineering

000005010015020025030035

040 050 060 070 080 090

Size statics of rock blocks

(a)

(d)(b)

000

010

020

030

040

050

002 004 056 007 009 011

(c)

Length of long axis (m)

Freq

uenc

yFr

eque

ncy

Ratio of the long axis length to the short axis

2a

2b

Figure 3 The statistical results of the size and the lengths of the long axis of stone blocks (a) the in situ outwash deposits (b) definition ofthe long axis and short axis for stone blocks the long axis is the largest distance between vertices along the stone outline while the short axisis the maximum segment length normal to the long axis direction (c) the statistical results of the size of stone blocks (d) the statistical resultsof the lengths of the long axis of stone blocks

where 119860 is the total area of the model 119860119895is the area of the

119895th stone block and grade 119894 and 119899119894is the content rate of stone

blocks of grade 119894The area of the total stone blocks is counted until the

grade requirement is metThe structure of the outwash deposit model is generated

randomly according to the method of multigradations Theinfluences of the azimuth concavity and convexity of thestone blocks on the outwash deposit are also taken intoconsideration The generation of stone blocks occurs fromthe largest to the smallest size according to the grain sizeaccumulation curve

3 Analysis Based on Micromechanical Model

31 The Principle of the Granular Discrete Element MethodThe granular discrete element method is adopted to simulatethe micromechanical properties of the granular materials inthe form of discs or spherical particles using the explicitdifference algorithm [16] Newtonrsquos Second Law is used inorder to determine the particle movement that is caused bycontact or the force of a body while the force-displacementlaw is used to calculate the contact force that is changingrelative to movement The two laws are then used alternatelyuntil the total system reaches equilibrium as shown inFigure 5(a) The particles can be combined into any shape orcombination to simulate the stone or debris mass structures

As shown in Figure 5(b) when there is no bondingbetween particles the mechanical behaviour of the particles

in contact is determined by their own normal stiffness (119896119899)

tangential stiffness (119896119904) and friction coefficient (120583) When

two particles are in contact the contact and tangentialstiffness can be calculated as follows

119896119899=

119896(119860)119899119896(119861)119899

119896(119860)119899

+ 119896(119861)119899

119896119904=

119896(119860)119904119896(119861)119904

119896(119860)119904

+ 119896(119861)119904

(6)

The normal force of contact particles is depicted as

119865119899= 119870119899119880119899 (7)

where 119880119899is the normal contact depth

In the calculation process the tangential force is zeroinitially so the incremental form of the equation is used asfollows

Δ119865119904= minus119896119904Δ119880119904 (8)

If 119880119899le 0 a gap exists between the particles the normal

and shear force are both zero and the slipping force betweenthe particles should be calculated with the friction coefficientThis coefficient is calculated as 120583 = min(120583(119860) 120583(119861)) where120583(119860) and 120583(119861) are the particle friction coefficients of 119860 and 119861respectively and 119865

119904= 120583119865119899is used when 119865

119904ge 120583119865119899

The stiffness contact model is adopted for the outwashdeposit in this work because the point contact and the

Advances in Materials Science and Engineering 5

Select model scope (width and height)

Assign particle radius generate particles and set default flag 0 as soil

Number i level

Specify the aggregate gradation of outwash deposits in N designlevels (limit of size mean-variance)

Find out particles within the special polygon

If the flag of particle within the polygon is 0 or not

Yes

Statistic area of particles within the polygons add it to the total area of this level and give a new number of stone block

Judge whether the total area of current level meets the requirements

of the design level or not

No

Exit the current design levels

YesNo

Output the random model and distribute the particle properties

The flag of 0 is soilThe flag of 1 is rock

Generate polygons randomly controlled by block size (from 3 cm to20 cm) length of long axis axial ratio and the azimuth of long axis

Figure 4 The flowchart for the randomised generation of stone blocks

Update contact force between particles and position of wall and build up new contact

Newtonrsquos laws of motion applied to calculate resultant

force and resultant moment of each particle

Law of force-displacementapplied to illustrate relative movement and constitutive

relation of each contact

Contact force

(a) Calculation principle in PFC2D

N-normal directionT-tangential directiondirection

N

T

i

j

z

y

x

(b) Two contacting particles

Figure 5 Contact force between particles and calculation principle

linear contact in the debris-debris debris-stone and stone-stone are the main kind of contact types the point contactsare especially dominant Five microparameters need to becalibrated the normal stiffness the stiffness ratio of tangentstiffness and normal stiffness the friction coefficient the

normal bonding strength and the tangent bonding strengthaccording to PFC2D manual [17]

32TheConversion from the GeologicalModel to aMechanicalModel According to the theory of granular discrete element

6 Advances in Materials Science and Engineering

0 1 0 1

1 0 0 1

1 1 1 0

0 0 1 1

Wall load plate

Wall load plate x

y

Outwash deposit Particle modelConversion relationship

ro

Servo mechanism

radic3r 2r

j998400

i998400

Figure 6 Construction of a debris-stone micromodel using a spot matrix and PFC2D

method 2D disk particles are used to transform the geolog-ical model to a mechanical model If the particle is too largein the model the shape of stone block and microstructurecharacteristic will be distorted However the larger numberof particles in amodel will lead to very slow calculation speedA significant amount of timewill be sacrificed whichmay notbe tolerable So a proper particle size should be determinedempirically

The width and the height of the model in this work aretaken to 050 times 050m the constant radius of particles is25mm and the arrangement of the particles is shown inFigure 6 The distance between the centres of two adjacentparticles in the vertical direction is radic3119903 (r is the radiusof particle) The distance between the centres of adjacentparticles in the horizontal direction is 2119903 Therefore thecoordinates of the particle centre (119909

11989410158401198951015840 11991011989410158401198951015840) in the 1198941015840 line and

1198951015840 column can be expressed as follows

11990911989410158401198951015840 =

(21198951015840 minus 1) 119903 (1198941015840 = 2119896 + 1)

21198951015840119903 (1198941015840 = 2119896) (119896 isin 119873)

11991011989410158401198951015840 = 119903 + radic3119903 (119894 minus 1)

(9)

According to the modelling steps the particles arearranged initially as shown in Figure 6 The even rows aredislocated to ensure that the particles are tangential withadjacent rowsWhen a particlemodel filling the research zoneis generated every particle within the model will be judgedto determine whether its centre is located in some randompolygon If it is in a polygon the particle belongs to a stoneblockwith a certain flag If it is not in any polygon the particleis regarded as debrisThe initial structural information can beobtained from site research or by random generation

Several particleswith the samepolygonflag are assembledtogether by the high bonding force to simulate the character-istics of the stone blocks The structural effect of the outwashdeposit is thus simulated The separation of the debris fromthe stone is also convenient for the determination of themechanical parameters

33 The Relationship between the Macro- and Microme-chanical Parameters Youngrsquos modulus and Poissonrsquos ratio

000

005

010

015

020

025

030

035

00 02 04 06 08 10 12

Poiss

on ra

tio

kskn

kn = 500MPan bond = 1000Ns bond = 1000N

Figure 7 The relationship between Poissonrsquos ratio and the stiffnessratio

determined in the indoor geotechnical tests are used todescribe the macrodeformation properties of the materialsMany studies have shown that Youngrsquos modulus is related tothe microparameter 119896

119899and the stiffness ratio 119896

119904119896119899 while

Poissonrsquos ratio is mainly related to the stiffness ratio [1819] However these changes are all affected by the particlecompositions such as the mean radius and the ratio of themaximum radius to the minimum radius Since a constantradius is used in this work the problem can be neglected

To reflect the relation between Poissonrsquos ratio and thestiffness ratio 119896

119904119896119899 the normal stiffness is initially fixed at

a constant 50MPa The relationship between Poissonrsquos ratioand the stiffness ratio is shown in Figure 7 It can be foundthat Poissonrsquos ratio in the debris shows a nonlinear inverserelationshipwith the stiffness ratio of debris when the particleradius is unchanged

It can also be concluded in Figure 7 that the tangentstiffness is usually less than the normal stiffness Once thetangent stiffness is equal to or greater than the normalstiffness Poissonrsquos ratio will reach zero This situation onlyexists in very loose cellular structures However for outwashdeposits it is obviously unreasonable when the medium isin a compacted state Poissonrsquos ratio declines as the stiffnessratio increases When the tangent stiffness is equal to the

Advances in Materials Science and Engineering 7

08

07

06

05

04

03

Ek

n

kn (GPa)

015

25

35

45

0908

0706

0504

0302

010

k skn

Figure 8The changes in Youngrsquos modulus with the microdeforma-tion parameters

Poiss

onrsquos

ratio

030

025

020

015

010

005

kn (GPa)

015

25

35

4509

0807

0605

0403

0201

0

k sk n

Figure 9The changes in Poissonrsquos ratio with the microdeformationparameters

normal stiffness Poissonrsquos ratio is close to zero When thestiffness ratio decreases the lateral deformation increasesWhen the tangent stiffness is zero Poissonrsquos ratio reaches itsmaximumvalueThe relationship between Poissonrsquos ratio andthe stiffness ratio based on a series of numerical tests can beexpressed using the following equation

1205830= 012781205782 minus 04061120578 + 03177 (10)

where 120583 is Poissonrsquos ratio and 120578 = 119896119904119896119899is the ratio of

the tangent stiffness to the normal stiffness which lies inthe range 0sim05 Once 120578 is greater than 10 Poissonrsquos ratiomay be greater than 10 or negative which disagrees with theproperties of common solid media

It should be noted that (10) does not consider the influ-ence of the stiffness If the stiffness is taken into considerationYoungrsquos modulus and Poissonrsquos ratio can be estimated withdifferent normal stiffness as follows

119864 = (02259120578 minus 00058119896119899minus 00042120578119896

119899+ 05346) 119896

119899

120583 = minus02760120578 minus 00029119896119899+ 00031120578119896

119899+ 03200

(11)

Friction coefficient

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Inte

rnal

fric

tion

angl

e (∘

)

4200

4000

3800

3600

3400

3200

300000 05 10 15 20 25

Figure 10 The changes in the internal friction angle at differentcoefficients of friction

The changes in Youngrsquos modulus and Poissonrsquos ratio withthe changes in the microparameters are shown in Figures8 and 9 The figures illustrate that the relationship betweenYoungrsquos modulus of an outwash deposit and the correspond-ing Poissonrsquos ratio is not a simple linear relation but adouble linear correlation in the calculation of the granulardiscrete element method When the microparameters needto be determined Youngrsquos modulus and Poissonrsquos ratio caninitially be assumed Then more reasonable values can bedetermined using (11) The steps should be repeated manytimes until Youngrsquosmodulus andPoissonrsquos ratio agreewith theresults of the macroscopic tests In addition the debris andstone blocks should be calibrated separately to obtain propermicroparameters

34TheMicromechanical Parameters of theOutwashDepositsThe normal contact force (119899 bond) tangent contact force(119904 bond) and the coefficient of friction 120583 are the mainmicroparameters related to macrostrength in a granularmodel based on PFC2D These parameters correspond tothe macrocohesion and the internal friction in the Mohr-Coulomb criterion The coefficient of friction is the purefrictional force when the outwash deposit is completelydestroyed It determines the residual strength of the mediumand can be approximately equal to the pure friction coefficienttan120593 of the stone and debris mass

As shown in Figure 10 when the coefficient of friction islow the deformation of the stone and debris mass shows alinear variation By contrast when the friction coefficient ishigh the deformation of the stone and debris mass showsa nonlinear variation The internal friction angle of themedium first increases and then remains unchanged as thecoefficient of friction increases The cohesion shows similarbehaviour but it remains constant if the coefficient of frictionis lowThe cohesion will increase as the coefficient of frictionincreases as shown in Figure 11

It is not difficult to find that the microcoefficient offriction is sensitive to the macro-internal-friction angleWhen the microparameters need to be determined thebonding forces should initially be set to zero then the friction

8 Advances in Materials Science and Engineering

000

020

040

060

080

100

120

00 05 10 15 20 25Friction coefficient

Coh

esio

n (M

Pa)

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Figure 11 The cohesion remains constant if the coefficient of friction is low

180

160

140

120

100

080

060

040

020

000000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 10

(a)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 35

200

180

160

140

120

100

080

060

040

020

000

(b)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

Stone rate = 45200

150

100

050

000

(c)

1205901minus1205903

(MPa

)

000 001 002 003 004

1205761

Stone rate = 60

1200

1000

800

600

400

200

000

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

(d)

Figure 12 The biaxial compression curve at different confining pressures and stone block content (a) Stone block content is 10 (b) stoneblock content is 35 (c) stone block content is 45 and (d) stone block content is 60

Advances in Materials Science and Engineering 9

Table 1 The micromechanical parameters of outwash deposits

Material Density (kgm3) Bonding force (N) Stiffness ratio Normal stiffness (Nm) Friction coefficientNormal Tangential

Debris 2200 11198903 11198903 00 11198908 025Stone 2700 21198906 21198906 02 951198909 120

Table 2 The macromechanical parameters of outwash deposits

Material Youngrsquos modules (MPa) Poissonrsquos ratio Internal friction angel (∘) Cohesion (MPa)Debris 559 032 2794 007Stone 4950 020 56 120

coefficient can be determined using trial calculations until themacromechanical properties are in linewith the experimentalresults Finally the bonding forces are adjusted so thatthe parameters are consistent with the macromechanicalproperties of the outwash deposit

When the bonding force is zero the internal friction anglewill reach its minimum value Therefore the determinationof the internal friction angle should take the effect of thestiffness ratio into consideration If the internal friction angleis unchanged when the coefficient of friction increases thebonding force can be adjusted to be in agreement with thepeak strength of the stress In this work the microparametersare shown in Table 1 and the corresponding macroparame-ters are shown in Table 2

4 The Analysis of the Mechanical Behaviour ofthe Outwash Deposits

As a case study shown in Figure 1 the stone rate of outwashbased on the statistical results is about 30 to 40 themean length of long axis is about 413 cm with a variance015 and the mean axis ratio is 064 with a variance 017Then the random structure models of outwash depositsare generated according to the above information Finallynumerical simulation and comparison are executed in orderto analyse the effect of comprehensive mechanical behaviour

41 The Stress-Strain Curve Based on the Biaxial CompressionTest The stress-strain curves from the numerical simulationtests of an outwash deposit under biaxial compression con-ditions can be divided into three stages the elastic stagethe hardening stage and the residual strength stage (shownin Figure 12) In the elastic stage the deformation modulusis determined by the undamaged debris particles and stoneblock assemblies As the deformation increases fractureswill first appear in the debris because of its low modulusand strength When the outwash deposit enters into thehardening stage the debris particle bonding forces will failgradually and the deformation modulus will decrease slowlyHowever the strength will increase continually due to theinteraction force caused by mosaic effect between the debrisparticles and the stone blocks When the stress reaches itspeak strength the outwash deposit will enter into the residualstrength stage The cementation ability between the debris

particles is almost completely lost The compressive-bearingcapability of the sample cannot continue to increase Thecompressive-bearing capability is controlled mainly by theinterparticle friction When the strain continues to increasethe stone blocks may rotate and tumble which leads tothe complete destruction of the structure of the outwashdeposit However there is still some compression-bearingcapability which causes the residual strength of the outwashdeposit The residual strength shows fluctuations because ofthe contact action between the debris and the stone blocks

As shown in Figure 13 the damage of a model withcontent ratio of stone block 40 length of long axis about2 to 6 cm and the axial ratio 05 to 08 is compared in theloading process It shows that cracks occur firstly betweensome blocks and then develop among the boundary of stoneblocks and fill with the debris particles The crack numberwill increase shapely with the strain increase until all bondcontacts between debris particles are destroyed

The curves for different debris bonding forces in Figure 14show that the cementation strength of the debris particlesdecides the strength of outwash deposit and has a dominantrole in the mechanical properties when the other condi-tions are fixed With a stronger cementation force of debrisparticles there is a smaller increase in the internal frictionangle and a bigger increase for the cohesion The mechanicalproperties of an outwash deposit with high cementationstrength aremore similar to the properties of the stone blocksConversely if the cementation strength of the debris particlesis weak there is a bigger increase in the internal frictionangle and a smaller increase in the cohesionThe mechanicalproperties of the outwash deposit are much closer to theelastic-plastic debris

42 The Influence of the Aggregate Size As shown in Fig-ure 15 the larger the size of stone blocks is the smaller thepeak strength is This situation can be interpreted by theperimeter ratio which is defined as the ratio of all boundariesrsquoperimeters of stone blocks and themodel areaThe perimeterratio under the same stone ratio varies greatly The smalleraggregate size has more stone blocks so the perimeter ratiowill reach a high level and form larger contact areas Thecompressive strength also increases When the number ofstone blocks increases the contact area of the debris and stoneblocks and the interaction force between the debris and the

10 Advances in Materials Science and Engineering

(a) Crk num = 0 (b) Crk num = 39

(c) Crk num = 189 (d) Crk num = 563

Figure 13 The damage of outwash deposits with different stone block content (a) shows a model with the initial content rate of stone block40 (b) shows the cracks which first appear between some blocks (c) shows fracture development among the boundary of stone blocks and(d) shows the damaged outwash deposits

stone blocks will increase which just explains the reason whythe macromechanical properties of the outwash deposit areimproved with the number of stone blocks

43 The Influence of the Stone Block Content As shown inFigure 16 when there are few stone blocks in the outwashdeposit the debris-debris contact between particles willbe the main contact type The existence of stone blocksleads to the concentration of stress along their boundarieswhich can aggravate the debris contacts to damage the peakcompressive strength keeps close to the pure debriswith slightfluctuation Meanwhile due to the stress concentration theoutwash deposits become more brittle The shear strength isdecreased Many experiments show that when the contentof stone blocks is less than 25 the characteristic is moreclose to pure debris By contrast when the content of stoneblocks is greater than 25 there is not only debris-stonecontact in the outwash deposits but also stone-stone contact

The compressive and shear strengths are improved Whenthe content of stone blocks is more than 50 the maincontact type in the outwash deposits is stone-stone Themechanical properties are better in stone-filledmaterialsThecompressive and shear strengths are significantly improved inthe stone-filled materials

However when the stress-strain curves enter the residualstrength stage there is an obvious fluctuation after the peakof the curve the amplitude of which is related to the size andcontent ratio of stone blocks so in order to study the macro-shear strength the peak value of stress-strain curves is usedto calculate shear property

44 The Macroparameter Analysis of the Outwash DepositsIn terms of the stress-strain curves for any content rateof stone block cementation strength and block size themajor factor that influences the mechanical properties of the

Advances in Materials Science and Engineering 11

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

n bond = s bond = 0Nn bond = s bond = 1000N

n bond = s bond = 2000Nn bond = s bond = 3000N

Figure 14 The biaxial compression curves with different debris bonding force

Stone average size = 1 cmStone average size = 3 cm

Stone average size = 5 cmStone average size = 7 cm

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

Figure 15 The biaxial compression curves with different averagesizes of stone blocks

Stone content = 10

Stone content = 20Stone content = 30

Stone content = 40

Stone content = 50

Stone content = 60Stone content = 70

1400

1200

1000

800

600

400

200

0000 002 004 006 008 01 012

(1205901minus1205903) (

MPa

)

1205761

Figure 16The biaxial compression curve with different stone blockcontents

The content of stone blocks ()

The p

eak

com

pres

sive s

treng

th (M

Pa) 1600

1400

1200

1000

800

600

400

200

0000 10 20 30 40 50 60 70 80

Figure 17The peak compressive strength with different stone blockcontents

outwash deposits can be attributed to the dominant contacttype which is defined as the ratio of some particle contactnumber and total contact number in numerical models Theparticle contact can be divided into three kinds respectivelythe debris-debris debris-stone or stone-stone contact

If ratio of stone block is high enough to make stone-stonecontact becoming dominant contact type the characteristicof outwash deposit is close to rockfill For the naturemediumseveral kinds of contacts exist at that time which will affectthe comprehensive mechanical property greatly Althoughthe different geometries and distributions also affect themechanical properties the content of stone blocks is thedecisive factor For the different stone block contents thepeak strength under the confining pressure of 15MPa canbe calculated approximately using formula (12) as a cubicparabola curve (shown in Figure 17)

119875119896= 141841205723 minus 90441205722 + 1600120572 + 02894 (12)

where 120572 is the content ratio of stone blocks and 119875119896is the peak

strengthIt should be noted that the compressive strength of the

outwash deposit increases slowly when content ratio of stone

12 Advances in Materials Science and Engineering

Stone block ()

Inte

rnal

fric

tion

angl

e (∘

)40

36

32

28

24

200 10 20 30 40 50 60 70 80

(a)

20

40

60

80

100

120

140

160

180

0 20 40 60 80Stone block ()

Incr

emen

tal c

ohes

ion

(MPa

)

(b)

Figure 18 Changes of shear strength of outwash deposits with different contents and distributions of stone blocks (a) shows changes of theinternal friction of outwash deposit (b) shows changes of the cohesion of outwash deposit

blocks lies between 25 and 50 Once the content of stoneblocks is greater than 50 the stone-stone contact becomesthe dominant factor which causes the compressive strengthto increase sharply The internal friction angle versus thestone block content can be described using three stages asshown below

120593 =

18093931205722 minus 495165120572 + 265026 120572 lt 25194271120572 + 221719 25 lt 120572 lt 50234286120572 + 191429 120572 gt 50

(13)

where 120593 is the internal friction angle of the outwash depositand 120572 is the stone block content

Furthermore it can be observed from Figure 18(a) thatthe fluctuation of the internal friction angle is approximately0sim8∘ for the same stone blocks content which agrees withthe fluctuations in the stress-strain curves By contrast thecohesion of outwash deposit increases clearly with the stoneblock content due to the interaction force between stoneblocks as shown in Figure 18(b) The amplitude of variationwill increase significantly with the content of stone blocksHowever it is usually difficult to quantify the amplitude dueto roughness size characteristic of stone block and so on

Therefore for outwash deposits with extremely unevenshapes and distributions of stones the compressive strengthand shear strength are primarily controlled by the stone blockcontent The randomness of the stone block distributionscauses large deviations in the mechanical parameters Forexample the internal friction angle may have a large fluctua-tion at the same stone block content This feature is the causeof the poor results of the geotechnical experiments

5 Discussions

Outwash deposits are a type of debris-stone mixture Themechanical properties of these deposits are affected by thecomposition of the debris and stone blocks As the debriscementation increases the compressive strength increasesHowever the internal friction angle has a negative correlation

with the cementation force The stone block content is thedecisive factor for the mechanical properties of outwashdepositsThe randomness of the structural composition leadsto significant fluctuations in the properties which also createslarge discrepancies in the mechanical parameters

The major influences of the particle sizes geometricdistribution and stone block content are to determine thecontact type in the outwash deposits When the debris-debris contact is the dominant contact type there is littleinfluence from the stone blocks on the mechanical propertiesof the outwash depositsWhen the debris-stone contact is thedominant contact type the stone block content has a positiveinfluence on the compressive and shear strengths When thestone-stone contact is the dominant contact type the roles ofthe debris and stone blocks are reversed and the properties ofthe outwash deposits aremuch closer to a rock-filledmaterial

Although it is difficult to determine the mechanicalparameters of an outwash deposit using indoor experimentsthe properties of the medium can still be researched usingindirect approachesThemechanical parameters of the debrisand stone blocks can be determined from the indoor experi-ments Then the biaxial compression numerical experimentusing the granular discrete element method can be carriedout to analyse the influence of the stone blocks on theproperties of outwash deposits which makes up for thelimitation that the indoor experiments cannot consider thelarge stone blocks and offers a beneficial supplement to aid inthe geological parameter determination

6 Conclusions

According to the grain size and shape statistics from fieldstatistics the numerical granular discrete elementmodel withrandomised generation of stone blocks can be used withhypothesis that the length of the long axis and the axial ratioall follow normal distributions and the azimuth of the longaxis follows uniformdistribution in 0sim360∘The relationshipsbetween the macro- and micromechanical parameters arediscussed and the mechanical behaviour of the outwash

Advances in Materials Science and Engineering 13

deposit is affected by the cementation strength the size ofstone blocks the stone block content and the distribution ofthe stone blocks These properties are analysed so that theycan be better understood by the geologists working on thedemocratisation of the Engineering Project

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (no 51309089 and no 51379065)the National Key Technology RampD Program (no2013BAB06B00) the National Basic Research Programof China (973 Program) (no 2015CB057903) the NaturalScience Foundation of Jiangsu Province (no BK20130846)and the Fundamental Research Funds for the CentralUniversities (no 2014B04914)

References

[1] W G Holtz and H J Gibbs ldquoTriaxial shear tests on perviousgravelly soilsrdquo Journal of the Soil Mechanics and FoundationsDivision vol 82 no 1 pp 1ndash22 1956

[2] R J Chandler ldquoThe inclination of Talus Arctic Talus Terracesand other slopes composed of granular materialsrdquo The Journalof Geology vol 81 no 1 pp 1ndash14 1973

[3] X H You Stochastic structural model of the earth-rock aggregateand its application [PhD thesis] Beijing Jiaotong UniversityBeijing China 2001

[4] X H You and J S Tang ldquoResearch on horizontal push-shearin-situ test of debris and rock-mixturerdquo Chinese Journal of RockMechanics and Engineering vol 21 no 10 pp 1537ndash1540 2002

[5] X H You G He and X Li ldquoMicro-handling technologyof earth-rock aggregate sloperdquo Hydrogeology and EngineeringGeology vol 30 no 1 pp 18ndash21 2003

[6] J M He Study of deformation and failure mechanisms of rock-debris aggregate in three gorges reservoir area [PhD thesis]China University of Mining and Technology Beijing China2004

[7] X Li Q L Liao J M He and J Chen ldquoStudy on in-situ testsof mechanical characteristics on soil-rock aggregaterdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 12 pp2377ndash2384 2007

[8] T Lebourg J Riss and E Pirard ldquoInfluence of morphologicalcharacteristics of heterogeneous moraine formations on theirmechanical behaviour using image and statistical analysisrdquoEngineering Geology vol 73 no 1-2 pp 37ndash50 2004

[9] T R Reid and J P Harrison ldquoA semi-automated methodologyfor discontinuity trace detection in digital images of rock massexposuresrdquo International Journal of Rock Mechanics andMiningSciences vol 37 no 7 pp 1073ndash1089 2000

[10] Z Q Yue S Chen and L G Tham ldquoFinite element modelingof geomaterials using digital image processingrdquo Computers andGeotechnics vol 30 no 5 pp 375ndash397 2003

[11] Z Q Yue S Chen H Zheng and G H Tang ldquoDigital imageproceeding based on finite element method for geomaterialsrdquo

Chinese Journal of Rock Mechanics and Engineering vol 23 no6 pp 889ndash897 2004

[12] Q L Liao X Li W C Zhu and J S Liu ldquoStructure modelconstruction of rock and soil aggregate based on digital imagetechnology and its numerical simulation on mechanical struc-ture effectsrdquoChinese Journal of RockMechanics and Engineeringvol 29 no 1 pp 155ndash162 2010

[13] W J Xu R L Hu Z Q Yue and R J Tan ldquoMesostructuralcharacter and numerical simulation of mechanical propertiesof soil-rock mixturesrdquo Chinese Journal of Rock Mechanics andEngineering vol 26 no 2 pp 300ndash311 2007

[14] W J Xu Z Q Yue and R L Hu ldquoA current status of digitalimage based quantitative analysis of internal structures ofdebris rock and concretes and associated numerical simula-tionrdquo Journal of Engineering Geology vol 15 no 3 pp 289ndash3132007

[15] W J Xu R L Hu Z Q Yue R Zhang and G L WangldquoResearch on relationship between rock block proportion andshear strength of soil-rock mixtures based on digital imageanalysis and large direct shear testrdquo Chinese Journal of RockMechanics and Engineering vol 27 no 5 pp 996ndash1007 2008

[16] P A Cundall and O D L Strack ldquoA discrete numerical modelfor granular assembliesrdquo Geotechnique vol 29 no 1 pp 47ndash651979

[17] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) (Version 31) Itasca Consulting Group Minneapo-lis Minn USA 2004

[18] J Yoon ldquoApplication of experimental design and optimizationto PFC model calibration in uniaxial compression simulationrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 6 pp 871ndash889 2007

[19] Y C Wang and P Mora ldquoMacroscopic elastic properties ofregular latticesrdquo Journal of the Mechanics and Physics of Solidsvol 56 no 12 pp 3459ndash3474 2008

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

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NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

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MetallurgyJournal of

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BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 5

Select model scope (width and height)

Assign particle radius generate particles and set default flag 0 as soil

Number i level

Specify the aggregate gradation of outwash deposits in N designlevels (limit of size mean-variance)

Find out particles within the special polygon

If the flag of particle within the polygon is 0 or not

Yes

Statistic area of particles within the polygons add it to the total area of this level and give a new number of stone block

Judge whether the total area of current level meets the requirements

of the design level or not

No

Exit the current design levels

YesNo

Output the random model and distribute the particle properties

The flag of 0 is soilThe flag of 1 is rock

Generate polygons randomly controlled by block size (from 3 cm to20 cm) length of long axis axial ratio and the azimuth of long axis

Figure 4 The flowchart for the randomised generation of stone blocks

Update contact force between particles and position of wall and build up new contact

Newtonrsquos laws of motion applied to calculate resultant

force and resultant moment of each particle

Law of force-displacementapplied to illustrate relative movement and constitutive

relation of each contact

Contact force

(a) Calculation principle in PFC2D

N-normal directionT-tangential directiondirection

N

T

i

j

z

y

x

(b) Two contacting particles

Figure 5 Contact force between particles and calculation principle

linear contact in the debris-debris debris-stone and stone-stone are the main kind of contact types the point contactsare especially dominant Five microparameters need to becalibrated the normal stiffness the stiffness ratio of tangentstiffness and normal stiffness the friction coefficient the

normal bonding strength and the tangent bonding strengthaccording to PFC2D manual [17]

32TheConversion from the GeologicalModel to aMechanicalModel According to the theory of granular discrete element

6 Advances in Materials Science and Engineering

0 1 0 1

1 0 0 1

1 1 1 0

0 0 1 1

Wall load plate

Wall load plate x

y

Outwash deposit Particle modelConversion relationship

ro

Servo mechanism

radic3r 2r

j998400

i998400

Figure 6 Construction of a debris-stone micromodel using a spot matrix and PFC2D

method 2D disk particles are used to transform the geolog-ical model to a mechanical model If the particle is too largein the model the shape of stone block and microstructurecharacteristic will be distorted However the larger numberof particles in amodel will lead to very slow calculation speedA significant amount of timewill be sacrificed whichmay notbe tolerable So a proper particle size should be determinedempirically

The width and the height of the model in this work aretaken to 050 times 050m the constant radius of particles is25mm and the arrangement of the particles is shown inFigure 6 The distance between the centres of two adjacentparticles in the vertical direction is radic3119903 (r is the radiusof particle) The distance between the centres of adjacentparticles in the horizontal direction is 2119903 Therefore thecoordinates of the particle centre (119909

11989410158401198951015840 11991011989410158401198951015840) in the 1198941015840 line and

1198951015840 column can be expressed as follows

11990911989410158401198951015840 =

(21198951015840 minus 1) 119903 (1198941015840 = 2119896 + 1)

21198951015840119903 (1198941015840 = 2119896) (119896 isin 119873)

11991011989410158401198951015840 = 119903 + radic3119903 (119894 minus 1)

(9)

According to the modelling steps the particles arearranged initially as shown in Figure 6 The even rows aredislocated to ensure that the particles are tangential withadjacent rowsWhen a particlemodel filling the research zoneis generated every particle within the model will be judgedto determine whether its centre is located in some randompolygon If it is in a polygon the particle belongs to a stoneblockwith a certain flag If it is not in any polygon the particleis regarded as debrisThe initial structural information can beobtained from site research or by random generation

Several particleswith the samepolygonflag are assembledtogether by the high bonding force to simulate the character-istics of the stone blocks The structural effect of the outwashdeposit is thus simulated The separation of the debris fromthe stone is also convenient for the determination of themechanical parameters

33 The Relationship between the Macro- and Microme-chanical Parameters Youngrsquos modulus and Poissonrsquos ratio

000

005

010

015

020

025

030

035

00 02 04 06 08 10 12

Poiss

on ra

tio

kskn

kn = 500MPan bond = 1000Ns bond = 1000N

Figure 7 The relationship between Poissonrsquos ratio and the stiffnessratio

determined in the indoor geotechnical tests are used todescribe the macrodeformation properties of the materialsMany studies have shown that Youngrsquos modulus is related tothe microparameter 119896

119899and the stiffness ratio 119896

119904119896119899 while

Poissonrsquos ratio is mainly related to the stiffness ratio [1819] However these changes are all affected by the particlecompositions such as the mean radius and the ratio of themaximum radius to the minimum radius Since a constantradius is used in this work the problem can be neglected

To reflect the relation between Poissonrsquos ratio and thestiffness ratio 119896

119904119896119899 the normal stiffness is initially fixed at

a constant 50MPa The relationship between Poissonrsquos ratioand the stiffness ratio is shown in Figure 7 It can be foundthat Poissonrsquos ratio in the debris shows a nonlinear inverserelationshipwith the stiffness ratio of debris when the particleradius is unchanged

It can also be concluded in Figure 7 that the tangentstiffness is usually less than the normal stiffness Once thetangent stiffness is equal to or greater than the normalstiffness Poissonrsquos ratio will reach zero This situation onlyexists in very loose cellular structures However for outwashdeposits it is obviously unreasonable when the medium isin a compacted state Poissonrsquos ratio declines as the stiffnessratio increases When the tangent stiffness is equal to the

Advances in Materials Science and Engineering 7

08

07

06

05

04

03

Ek

n

kn (GPa)

015

25

35

45

0908

0706

0504

0302

010

k skn

Figure 8The changes in Youngrsquos modulus with the microdeforma-tion parameters

Poiss

onrsquos

ratio

030

025

020

015

010

005

kn (GPa)

015

25

35

4509

0807

0605

0403

0201

0

k sk n

Figure 9The changes in Poissonrsquos ratio with the microdeformationparameters

normal stiffness Poissonrsquos ratio is close to zero When thestiffness ratio decreases the lateral deformation increasesWhen the tangent stiffness is zero Poissonrsquos ratio reaches itsmaximumvalueThe relationship between Poissonrsquos ratio andthe stiffness ratio based on a series of numerical tests can beexpressed using the following equation

1205830= 012781205782 minus 04061120578 + 03177 (10)

where 120583 is Poissonrsquos ratio and 120578 = 119896119904119896119899is the ratio of

the tangent stiffness to the normal stiffness which lies inthe range 0sim05 Once 120578 is greater than 10 Poissonrsquos ratiomay be greater than 10 or negative which disagrees with theproperties of common solid media

It should be noted that (10) does not consider the influ-ence of the stiffness If the stiffness is taken into considerationYoungrsquos modulus and Poissonrsquos ratio can be estimated withdifferent normal stiffness as follows

119864 = (02259120578 minus 00058119896119899minus 00042120578119896

119899+ 05346) 119896

119899

120583 = minus02760120578 minus 00029119896119899+ 00031120578119896

119899+ 03200

(11)

Friction coefficient

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Inte

rnal

fric

tion

angl

e (∘

)

4200

4000

3800

3600

3400

3200

300000 05 10 15 20 25

Figure 10 The changes in the internal friction angle at differentcoefficients of friction

The changes in Youngrsquos modulus and Poissonrsquos ratio withthe changes in the microparameters are shown in Figures8 and 9 The figures illustrate that the relationship betweenYoungrsquos modulus of an outwash deposit and the correspond-ing Poissonrsquos ratio is not a simple linear relation but adouble linear correlation in the calculation of the granulardiscrete element method When the microparameters needto be determined Youngrsquos modulus and Poissonrsquos ratio caninitially be assumed Then more reasonable values can bedetermined using (11) The steps should be repeated manytimes until Youngrsquosmodulus andPoissonrsquos ratio agreewith theresults of the macroscopic tests In addition the debris andstone blocks should be calibrated separately to obtain propermicroparameters

34TheMicromechanical Parameters of theOutwashDepositsThe normal contact force (119899 bond) tangent contact force(119904 bond) and the coefficient of friction 120583 are the mainmicroparameters related to macrostrength in a granularmodel based on PFC2D These parameters correspond tothe macrocohesion and the internal friction in the Mohr-Coulomb criterion The coefficient of friction is the purefrictional force when the outwash deposit is completelydestroyed It determines the residual strength of the mediumand can be approximately equal to the pure friction coefficienttan120593 of the stone and debris mass

As shown in Figure 10 when the coefficient of friction islow the deformation of the stone and debris mass shows alinear variation By contrast when the friction coefficient ishigh the deformation of the stone and debris mass showsa nonlinear variation The internal friction angle of themedium first increases and then remains unchanged as thecoefficient of friction increases The cohesion shows similarbehaviour but it remains constant if the coefficient of frictionis lowThe cohesion will increase as the coefficient of frictionincreases as shown in Figure 11

It is not difficult to find that the microcoefficient offriction is sensitive to the macro-internal-friction angleWhen the microparameters need to be determined thebonding forces should initially be set to zero then the friction

8 Advances in Materials Science and Engineering

000

020

040

060

080

100

120

00 05 10 15 20 25Friction coefficient

Coh

esio

n (M

Pa)

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Figure 11 The cohesion remains constant if the coefficient of friction is low

180

160

140

120

100

080

060

040

020

000000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 10

(a)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 35

200

180

160

140

120

100

080

060

040

020

000

(b)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

Stone rate = 45200

150

100

050

000

(c)

1205901minus1205903

(MPa

)

000 001 002 003 004

1205761

Stone rate = 60

1200

1000

800

600

400

200

000

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

(d)

Figure 12 The biaxial compression curve at different confining pressures and stone block content (a) Stone block content is 10 (b) stoneblock content is 35 (c) stone block content is 45 and (d) stone block content is 60

Advances in Materials Science and Engineering 9

Table 1 The micromechanical parameters of outwash deposits

Material Density (kgm3) Bonding force (N) Stiffness ratio Normal stiffness (Nm) Friction coefficientNormal Tangential

Debris 2200 11198903 11198903 00 11198908 025Stone 2700 21198906 21198906 02 951198909 120

Table 2 The macromechanical parameters of outwash deposits

Material Youngrsquos modules (MPa) Poissonrsquos ratio Internal friction angel (∘) Cohesion (MPa)Debris 559 032 2794 007Stone 4950 020 56 120

coefficient can be determined using trial calculations until themacromechanical properties are in linewith the experimentalresults Finally the bonding forces are adjusted so thatthe parameters are consistent with the macromechanicalproperties of the outwash deposit

When the bonding force is zero the internal friction anglewill reach its minimum value Therefore the determinationof the internal friction angle should take the effect of thestiffness ratio into consideration If the internal friction angleis unchanged when the coefficient of friction increases thebonding force can be adjusted to be in agreement with thepeak strength of the stress In this work the microparametersare shown in Table 1 and the corresponding macroparame-ters are shown in Table 2

4 The Analysis of the Mechanical Behaviour ofthe Outwash Deposits

As a case study shown in Figure 1 the stone rate of outwashbased on the statistical results is about 30 to 40 themean length of long axis is about 413 cm with a variance015 and the mean axis ratio is 064 with a variance 017Then the random structure models of outwash depositsare generated according to the above information Finallynumerical simulation and comparison are executed in orderto analyse the effect of comprehensive mechanical behaviour

41 The Stress-Strain Curve Based on the Biaxial CompressionTest The stress-strain curves from the numerical simulationtests of an outwash deposit under biaxial compression con-ditions can be divided into three stages the elastic stagethe hardening stage and the residual strength stage (shownin Figure 12) In the elastic stage the deformation modulusis determined by the undamaged debris particles and stoneblock assemblies As the deformation increases fractureswill first appear in the debris because of its low modulusand strength When the outwash deposit enters into thehardening stage the debris particle bonding forces will failgradually and the deformation modulus will decrease slowlyHowever the strength will increase continually due to theinteraction force caused by mosaic effect between the debrisparticles and the stone blocks When the stress reaches itspeak strength the outwash deposit will enter into the residualstrength stage The cementation ability between the debris

particles is almost completely lost The compressive-bearingcapability of the sample cannot continue to increase Thecompressive-bearing capability is controlled mainly by theinterparticle friction When the strain continues to increasethe stone blocks may rotate and tumble which leads tothe complete destruction of the structure of the outwashdeposit However there is still some compression-bearingcapability which causes the residual strength of the outwashdeposit The residual strength shows fluctuations because ofthe contact action between the debris and the stone blocks

As shown in Figure 13 the damage of a model withcontent ratio of stone block 40 length of long axis about2 to 6 cm and the axial ratio 05 to 08 is compared in theloading process It shows that cracks occur firstly betweensome blocks and then develop among the boundary of stoneblocks and fill with the debris particles The crack numberwill increase shapely with the strain increase until all bondcontacts between debris particles are destroyed

The curves for different debris bonding forces in Figure 14show that the cementation strength of the debris particlesdecides the strength of outwash deposit and has a dominantrole in the mechanical properties when the other condi-tions are fixed With a stronger cementation force of debrisparticles there is a smaller increase in the internal frictionangle and a bigger increase for the cohesion The mechanicalproperties of an outwash deposit with high cementationstrength aremore similar to the properties of the stone blocksConversely if the cementation strength of the debris particlesis weak there is a bigger increase in the internal frictionangle and a smaller increase in the cohesionThe mechanicalproperties of the outwash deposit are much closer to theelastic-plastic debris

42 The Influence of the Aggregate Size As shown in Fig-ure 15 the larger the size of stone blocks is the smaller thepeak strength is This situation can be interpreted by theperimeter ratio which is defined as the ratio of all boundariesrsquoperimeters of stone blocks and themodel areaThe perimeterratio under the same stone ratio varies greatly The smalleraggregate size has more stone blocks so the perimeter ratiowill reach a high level and form larger contact areas Thecompressive strength also increases When the number ofstone blocks increases the contact area of the debris and stoneblocks and the interaction force between the debris and the

10 Advances in Materials Science and Engineering

(a) Crk num = 0 (b) Crk num = 39

(c) Crk num = 189 (d) Crk num = 563

Figure 13 The damage of outwash deposits with different stone block content (a) shows a model with the initial content rate of stone block40 (b) shows the cracks which first appear between some blocks (c) shows fracture development among the boundary of stone blocks and(d) shows the damaged outwash deposits

stone blocks will increase which just explains the reason whythe macromechanical properties of the outwash deposit areimproved with the number of stone blocks

43 The Influence of the Stone Block Content As shown inFigure 16 when there are few stone blocks in the outwashdeposit the debris-debris contact between particles willbe the main contact type The existence of stone blocksleads to the concentration of stress along their boundarieswhich can aggravate the debris contacts to damage the peakcompressive strength keeps close to the pure debriswith slightfluctuation Meanwhile due to the stress concentration theoutwash deposits become more brittle The shear strength isdecreased Many experiments show that when the contentof stone blocks is less than 25 the characteristic is moreclose to pure debris By contrast when the content of stoneblocks is greater than 25 there is not only debris-stonecontact in the outwash deposits but also stone-stone contact

The compressive and shear strengths are improved Whenthe content of stone blocks is more than 50 the maincontact type in the outwash deposits is stone-stone Themechanical properties are better in stone-filledmaterialsThecompressive and shear strengths are significantly improved inthe stone-filled materials

However when the stress-strain curves enter the residualstrength stage there is an obvious fluctuation after the peakof the curve the amplitude of which is related to the size andcontent ratio of stone blocks so in order to study the macro-shear strength the peak value of stress-strain curves is usedto calculate shear property

44 The Macroparameter Analysis of the Outwash DepositsIn terms of the stress-strain curves for any content rateof stone block cementation strength and block size themajor factor that influences the mechanical properties of the

Advances in Materials Science and Engineering 11

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

n bond = s bond = 0Nn bond = s bond = 1000N

n bond = s bond = 2000Nn bond = s bond = 3000N

Figure 14 The biaxial compression curves with different debris bonding force

Stone average size = 1 cmStone average size = 3 cm

Stone average size = 5 cmStone average size = 7 cm

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

Figure 15 The biaxial compression curves with different averagesizes of stone blocks

Stone content = 10

Stone content = 20Stone content = 30

Stone content = 40

Stone content = 50

Stone content = 60Stone content = 70

1400

1200

1000

800

600

400

200

0000 002 004 006 008 01 012

(1205901minus1205903) (

MPa

)

1205761

Figure 16The biaxial compression curve with different stone blockcontents

The content of stone blocks ()

The p

eak

com

pres

sive s

treng

th (M

Pa) 1600

1400

1200

1000

800

600

400

200

0000 10 20 30 40 50 60 70 80

Figure 17The peak compressive strength with different stone blockcontents

outwash deposits can be attributed to the dominant contacttype which is defined as the ratio of some particle contactnumber and total contact number in numerical models Theparticle contact can be divided into three kinds respectivelythe debris-debris debris-stone or stone-stone contact

If ratio of stone block is high enough to make stone-stonecontact becoming dominant contact type the characteristicof outwash deposit is close to rockfill For the naturemediumseveral kinds of contacts exist at that time which will affectthe comprehensive mechanical property greatly Althoughthe different geometries and distributions also affect themechanical properties the content of stone blocks is thedecisive factor For the different stone block contents thepeak strength under the confining pressure of 15MPa canbe calculated approximately using formula (12) as a cubicparabola curve (shown in Figure 17)

119875119896= 141841205723 minus 90441205722 + 1600120572 + 02894 (12)

where 120572 is the content ratio of stone blocks and 119875119896is the peak

strengthIt should be noted that the compressive strength of the

outwash deposit increases slowly when content ratio of stone

12 Advances in Materials Science and Engineering

Stone block ()

Inte

rnal

fric

tion

angl

e (∘

)40

36

32

28

24

200 10 20 30 40 50 60 70 80

(a)

20

40

60

80

100

120

140

160

180

0 20 40 60 80Stone block ()

Incr

emen

tal c

ohes

ion

(MPa

)

(b)

Figure 18 Changes of shear strength of outwash deposits with different contents and distributions of stone blocks (a) shows changes of theinternal friction of outwash deposit (b) shows changes of the cohesion of outwash deposit

blocks lies between 25 and 50 Once the content of stoneblocks is greater than 50 the stone-stone contact becomesthe dominant factor which causes the compressive strengthto increase sharply The internal friction angle versus thestone block content can be described using three stages asshown below

120593 =

18093931205722 minus 495165120572 + 265026 120572 lt 25194271120572 + 221719 25 lt 120572 lt 50234286120572 + 191429 120572 gt 50

(13)

where 120593 is the internal friction angle of the outwash depositand 120572 is the stone block content

Furthermore it can be observed from Figure 18(a) thatthe fluctuation of the internal friction angle is approximately0sim8∘ for the same stone blocks content which agrees withthe fluctuations in the stress-strain curves By contrast thecohesion of outwash deposit increases clearly with the stoneblock content due to the interaction force between stoneblocks as shown in Figure 18(b) The amplitude of variationwill increase significantly with the content of stone blocksHowever it is usually difficult to quantify the amplitude dueto roughness size characteristic of stone block and so on

Therefore for outwash deposits with extremely unevenshapes and distributions of stones the compressive strengthand shear strength are primarily controlled by the stone blockcontent The randomness of the stone block distributionscauses large deviations in the mechanical parameters Forexample the internal friction angle may have a large fluctua-tion at the same stone block content This feature is the causeof the poor results of the geotechnical experiments

5 Discussions

Outwash deposits are a type of debris-stone mixture Themechanical properties of these deposits are affected by thecomposition of the debris and stone blocks As the debriscementation increases the compressive strength increasesHowever the internal friction angle has a negative correlation

with the cementation force The stone block content is thedecisive factor for the mechanical properties of outwashdepositsThe randomness of the structural composition leadsto significant fluctuations in the properties which also createslarge discrepancies in the mechanical parameters

The major influences of the particle sizes geometricdistribution and stone block content are to determine thecontact type in the outwash deposits When the debris-debris contact is the dominant contact type there is littleinfluence from the stone blocks on the mechanical propertiesof the outwash depositsWhen the debris-stone contact is thedominant contact type the stone block content has a positiveinfluence on the compressive and shear strengths When thestone-stone contact is the dominant contact type the roles ofthe debris and stone blocks are reversed and the properties ofthe outwash deposits aremuch closer to a rock-filledmaterial

Although it is difficult to determine the mechanicalparameters of an outwash deposit using indoor experimentsthe properties of the medium can still be researched usingindirect approachesThemechanical parameters of the debrisand stone blocks can be determined from the indoor experi-ments Then the biaxial compression numerical experimentusing the granular discrete element method can be carriedout to analyse the influence of the stone blocks on theproperties of outwash deposits which makes up for thelimitation that the indoor experiments cannot consider thelarge stone blocks and offers a beneficial supplement to aid inthe geological parameter determination

6 Conclusions

According to the grain size and shape statistics from fieldstatistics the numerical granular discrete elementmodel withrandomised generation of stone blocks can be used withhypothesis that the length of the long axis and the axial ratioall follow normal distributions and the azimuth of the longaxis follows uniformdistribution in 0sim360∘The relationshipsbetween the macro- and micromechanical parameters arediscussed and the mechanical behaviour of the outwash

Advances in Materials Science and Engineering 13

deposit is affected by the cementation strength the size ofstone blocks the stone block content and the distribution ofthe stone blocks These properties are analysed so that theycan be better understood by the geologists working on thedemocratisation of the Engineering Project

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (no 51309089 and no 51379065)the National Key Technology RampD Program (no2013BAB06B00) the National Basic Research Programof China (973 Program) (no 2015CB057903) the NaturalScience Foundation of Jiangsu Province (no BK20130846)and the Fundamental Research Funds for the CentralUniversities (no 2014B04914)

References

[1] W G Holtz and H J Gibbs ldquoTriaxial shear tests on perviousgravelly soilsrdquo Journal of the Soil Mechanics and FoundationsDivision vol 82 no 1 pp 1ndash22 1956

[2] R J Chandler ldquoThe inclination of Talus Arctic Talus Terracesand other slopes composed of granular materialsrdquo The Journalof Geology vol 81 no 1 pp 1ndash14 1973

[3] X H You Stochastic structural model of the earth-rock aggregateand its application [PhD thesis] Beijing Jiaotong UniversityBeijing China 2001

[4] X H You and J S Tang ldquoResearch on horizontal push-shearin-situ test of debris and rock-mixturerdquo Chinese Journal of RockMechanics and Engineering vol 21 no 10 pp 1537ndash1540 2002

[5] X H You G He and X Li ldquoMicro-handling technologyof earth-rock aggregate sloperdquo Hydrogeology and EngineeringGeology vol 30 no 1 pp 18ndash21 2003

[6] J M He Study of deformation and failure mechanisms of rock-debris aggregate in three gorges reservoir area [PhD thesis]China University of Mining and Technology Beijing China2004

[7] X Li Q L Liao J M He and J Chen ldquoStudy on in-situ testsof mechanical characteristics on soil-rock aggregaterdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 12 pp2377ndash2384 2007

[8] T Lebourg J Riss and E Pirard ldquoInfluence of morphologicalcharacteristics of heterogeneous moraine formations on theirmechanical behaviour using image and statistical analysisrdquoEngineering Geology vol 73 no 1-2 pp 37ndash50 2004

[9] T R Reid and J P Harrison ldquoA semi-automated methodologyfor discontinuity trace detection in digital images of rock massexposuresrdquo International Journal of Rock Mechanics andMiningSciences vol 37 no 7 pp 1073ndash1089 2000

[10] Z Q Yue S Chen and L G Tham ldquoFinite element modelingof geomaterials using digital image processingrdquo Computers andGeotechnics vol 30 no 5 pp 375ndash397 2003

[11] Z Q Yue S Chen H Zheng and G H Tang ldquoDigital imageproceeding based on finite element method for geomaterialsrdquo

Chinese Journal of Rock Mechanics and Engineering vol 23 no6 pp 889ndash897 2004

[12] Q L Liao X Li W C Zhu and J S Liu ldquoStructure modelconstruction of rock and soil aggregate based on digital imagetechnology and its numerical simulation on mechanical struc-ture effectsrdquoChinese Journal of RockMechanics and Engineeringvol 29 no 1 pp 155ndash162 2010

[13] W J Xu R L Hu Z Q Yue and R J Tan ldquoMesostructuralcharacter and numerical simulation of mechanical propertiesof soil-rock mixturesrdquo Chinese Journal of Rock Mechanics andEngineering vol 26 no 2 pp 300ndash311 2007

[14] W J Xu Z Q Yue and R L Hu ldquoA current status of digitalimage based quantitative analysis of internal structures ofdebris rock and concretes and associated numerical simula-tionrdquo Journal of Engineering Geology vol 15 no 3 pp 289ndash3132007

[15] W J Xu R L Hu Z Q Yue R Zhang and G L WangldquoResearch on relationship between rock block proportion andshear strength of soil-rock mixtures based on digital imageanalysis and large direct shear testrdquo Chinese Journal of RockMechanics and Engineering vol 27 no 5 pp 996ndash1007 2008

[16] P A Cundall and O D L Strack ldquoA discrete numerical modelfor granular assembliesrdquo Geotechnique vol 29 no 1 pp 47ndash651979

[17] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) (Version 31) Itasca Consulting Group Minneapo-lis Minn USA 2004

[18] J Yoon ldquoApplication of experimental design and optimizationto PFC model calibration in uniaxial compression simulationrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 6 pp 871ndash889 2007

[19] Y C Wang and P Mora ldquoMacroscopic elastic properties ofregular latticesrdquo Journal of the Mechanics and Physics of Solidsvol 56 no 12 pp 3459ndash3474 2008

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

6 Advances in Materials Science and Engineering

0 1 0 1

1 0 0 1

1 1 1 0

0 0 1 1

Wall load plate

Wall load plate x

y

Outwash deposit Particle modelConversion relationship

ro

Servo mechanism

radic3r 2r

j998400

i998400

Figure 6 Construction of a debris-stone micromodel using a spot matrix and PFC2D

method 2D disk particles are used to transform the geolog-ical model to a mechanical model If the particle is too largein the model the shape of stone block and microstructurecharacteristic will be distorted However the larger numberof particles in amodel will lead to very slow calculation speedA significant amount of timewill be sacrificed whichmay notbe tolerable So a proper particle size should be determinedempirically

The width and the height of the model in this work aretaken to 050 times 050m the constant radius of particles is25mm and the arrangement of the particles is shown inFigure 6 The distance between the centres of two adjacentparticles in the vertical direction is radic3119903 (r is the radiusof particle) The distance between the centres of adjacentparticles in the horizontal direction is 2119903 Therefore thecoordinates of the particle centre (119909

11989410158401198951015840 11991011989410158401198951015840) in the 1198941015840 line and

1198951015840 column can be expressed as follows

11990911989410158401198951015840 =

(21198951015840 minus 1) 119903 (1198941015840 = 2119896 + 1)

21198951015840119903 (1198941015840 = 2119896) (119896 isin 119873)

11991011989410158401198951015840 = 119903 + radic3119903 (119894 minus 1)

(9)

According to the modelling steps the particles arearranged initially as shown in Figure 6 The even rows aredislocated to ensure that the particles are tangential withadjacent rowsWhen a particlemodel filling the research zoneis generated every particle within the model will be judgedto determine whether its centre is located in some randompolygon If it is in a polygon the particle belongs to a stoneblockwith a certain flag If it is not in any polygon the particleis regarded as debrisThe initial structural information can beobtained from site research or by random generation

Several particleswith the samepolygonflag are assembledtogether by the high bonding force to simulate the character-istics of the stone blocks The structural effect of the outwashdeposit is thus simulated The separation of the debris fromthe stone is also convenient for the determination of themechanical parameters

33 The Relationship between the Macro- and Microme-chanical Parameters Youngrsquos modulus and Poissonrsquos ratio

000

005

010

015

020

025

030

035

00 02 04 06 08 10 12

Poiss

on ra

tio

kskn

kn = 500MPan bond = 1000Ns bond = 1000N

Figure 7 The relationship between Poissonrsquos ratio and the stiffnessratio

determined in the indoor geotechnical tests are used todescribe the macrodeformation properties of the materialsMany studies have shown that Youngrsquos modulus is related tothe microparameter 119896

119899and the stiffness ratio 119896

119904119896119899 while

Poissonrsquos ratio is mainly related to the stiffness ratio [1819] However these changes are all affected by the particlecompositions such as the mean radius and the ratio of themaximum radius to the minimum radius Since a constantradius is used in this work the problem can be neglected

To reflect the relation between Poissonrsquos ratio and thestiffness ratio 119896

119904119896119899 the normal stiffness is initially fixed at

a constant 50MPa The relationship between Poissonrsquos ratioand the stiffness ratio is shown in Figure 7 It can be foundthat Poissonrsquos ratio in the debris shows a nonlinear inverserelationshipwith the stiffness ratio of debris when the particleradius is unchanged

It can also be concluded in Figure 7 that the tangentstiffness is usually less than the normal stiffness Once thetangent stiffness is equal to or greater than the normalstiffness Poissonrsquos ratio will reach zero This situation onlyexists in very loose cellular structures However for outwashdeposits it is obviously unreasonable when the medium isin a compacted state Poissonrsquos ratio declines as the stiffnessratio increases When the tangent stiffness is equal to the

Advances in Materials Science and Engineering 7

08

07

06

05

04

03

Ek

n

kn (GPa)

015

25

35

45

0908

0706

0504

0302

010

k skn

Figure 8The changes in Youngrsquos modulus with the microdeforma-tion parameters

Poiss

onrsquos

ratio

030

025

020

015

010

005

kn (GPa)

015

25

35

4509

0807

0605

0403

0201

0

k sk n

Figure 9The changes in Poissonrsquos ratio with the microdeformationparameters

normal stiffness Poissonrsquos ratio is close to zero When thestiffness ratio decreases the lateral deformation increasesWhen the tangent stiffness is zero Poissonrsquos ratio reaches itsmaximumvalueThe relationship between Poissonrsquos ratio andthe stiffness ratio based on a series of numerical tests can beexpressed using the following equation

1205830= 012781205782 minus 04061120578 + 03177 (10)

where 120583 is Poissonrsquos ratio and 120578 = 119896119904119896119899is the ratio of

the tangent stiffness to the normal stiffness which lies inthe range 0sim05 Once 120578 is greater than 10 Poissonrsquos ratiomay be greater than 10 or negative which disagrees with theproperties of common solid media

It should be noted that (10) does not consider the influ-ence of the stiffness If the stiffness is taken into considerationYoungrsquos modulus and Poissonrsquos ratio can be estimated withdifferent normal stiffness as follows

119864 = (02259120578 minus 00058119896119899minus 00042120578119896

119899+ 05346) 119896

119899

120583 = minus02760120578 minus 00029119896119899+ 00031120578119896

119899+ 03200

(11)

Friction coefficient

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Inte

rnal

fric

tion

angl

e (∘

)

4200

4000

3800

3600

3400

3200

300000 05 10 15 20 25

Figure 10 The changes in the internal friction angle at differentcoefficients of friction

The changes in Youngrsquos modulus and Poissonrsquos ratio withthe changes in the microparameters are shown in Figures8 and 9 The figures illustrate that the relationship betweenYoungrsquos modulus of an outwash deposit and the correspond-ing Poissonrsquos ratio is not a simple linear relation but adouble linear correlation in the calculation of the granulardiscrete element method When the microparameters needto be determined Youngrsquos modulus and Poissonrsquos ratio caninitially be assumed Then more reasonable values can bedetermined using (11) The steps should be repeated manytimes until Youngrsquosmodulus andPoissonrsquos ratio agreewith theresults of the macroscopic tests In addition the debris andstone blocks should be calibrated separately to obtain propermicroparameters

34TheMicromechanical Parameters of theOutwashDepositsThe normal contact force (119899 bond) tangent contact force(119904 bond) and the coefficient of friction 120583 are the mainmicroparameters related to macrostrength in a granularmodel based on PFC2D These parameters correspond tothe macrocohesion and the internal friction in the Mohr-Coulomb criterion The coefficient of friction is the purefrictional force when the outwash deposit is completelydestroyed It determines the residual strength of the mediumand can be approximately equal to the pure friction coefficienttan120593 of the stone and debris mass

As shown in Figure 10 when the coefficient of friction islow the deformation of the stone and debris mass shows alinear variation By contrast when the friction coefficient ishigh the deformation of the stone and debris mass showsa nonlinear variation The internal friction angle of themedium first increases and then remains unchanged as thecoefficient of friction increases The cohesion shows similarbehaviour but it remains constant if the coefficient of frictionis lowThe cohesion will increase as the coefficient of frictionincreases as shown in Figure 11

It is not difficult to find that the microcoefficient offriction is sensitive to the macro-internal-friction angleWhen the microparameters need to be determined thebonding forces should initially be set to zero then the friction

8 Advances in Materials Science and Engineering

000

020

040

060

080

100

120

00 05 10 15 20 25Friction coefficient

Coh

esio

n (M

Pa)

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Figure 11 The cohesion remains constant if the coefficient of friction is low

180

160

140

120

100

080

060

040

020

000000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 10

(a)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 35

200

180

160

140

120

100

080

060

040

020

000

(b)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

Stone rate = 45200

150

100

050

000

(c)

1205901minus1205903

(MPa

)

000 001 002 003 004

1205761

Stone rate = 60

1200

1000

800

600

400

200

000

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

(d)

Figure 12 The biaxial compression curve at different confining pressures and stone block content (a) Stone block content is 10 (b) stoneblock content is 35 (c) stone block content is 45 and (d) stone block content is 60

Advances in Materials Science and Engineering 9

Table 1 The micromechanical parameters of outwash deposits

Material Density (kgm3) Bonding force (N) Stiffness ratio Normal stiffness (Nm) Friction coefficientNormal Tangential

Debris 2200 11198903 11198903 00 11198908 025Stone 2700 21198906 21198906 02 951198909 120

Table 2 The macromechanical parameters of outwash deposits

Material Youngrsquos modules (MPa) Poissonrsquos ratio Internal friction angel (∘) Cohesion (MPa)Debris 559 032 2794 007Stone 4950 020 56 120

coefficient can be determined using trial calculations until themacromechanical properties are in linewith the experimentalresults Finally the bonding forces are adjusted so thatthe parameters are consistent with the macromechanicalproperties of the outwash deposit

When the bonding force is zero the internal friction anglewill reach its minimum value Therefore the determinationof the internal friction angle should take the effect of thestiffness ratio into consideration If the internal friction angleis unchanged when the coefficient of friction increases thebonding force can be adjusted to be in agreement with thepeak strength of the stress In this work the microparametersare shown in Table 1 and the corresponding macroparame-ters are shown in Table 2

4 The Analysis of the Mechanical Behaviour ofthe Outwash Deposits

As a case study shown in Figure 1 the stone rate of outwashbased on the statistical results is about 30 to 40 themean length of long axis is about 413 cm with a variance015 and the mean axis ratio is 064 with a variance 017Then the random structure models of outwash depositsare generated according to the above information Finallynumerical simulation and comparison are executed in orderto analyse the effect of comprehensive mechanical behaviour

41 The Stress-Strain Curve Based on the Biaxial CompressionTest The stress-strain curves from the numerical simulationtests of an outwash deposit under biaxial compression con-ditions can be divided into three stages the elastic stagethe hardening stage and the residual strength stage (shownin Figure 12) In the elastic stage the deformation modulusis determined by the undamaged debris particles and stoneblock assemblies As the deformation increases fractureswill first appear in the debris because of its low modulusand strength When the outwash deposit enters into thehardening stage the debris particle bonding forces will failgradually and the deformation modulus will decrease slowlyHowever the strength will increase continually due to theinteraction force caused by mosaic effect between the debrisparticles and the stone blocks When the stress reaches itspeak strength the outwash deposit will enter into the residualstrength stage The cementation ability between the debris

particles is almost completely lost The compressive-bearingcapability of the sample cannot continue to increase Thecompressive-bearing capability is controlled mainly by theinterparticle friction When the strain continues to increasethe stone blocks may rotate and tumble which leads tothe complete destruction of the structure of the outwashdeposit However there is still some compression-bearingcapability which causes the residual strength of the outwashdeposit The residual strength shows fluctuations because ofthe contact action between the debris and the stone blocks

As shown in Figure 13 the damage of a model withcontent ratio of stone block 40 length of long axis about2 to 6 cm and the axial ratio 05 to 08 is compared in theloading process It shows that cracks occur firstly betweensome blocks and then develop among the boundary of stoneblocks and fill with the debris particles The crack numberwill increase shapely with the strain increase until all bondcontacts between debris particles are destroyed

The curves for different debris bonding forces in Figure 14show that the cementation strength of the debris particlesdecides the strength of outwash deposit and has a dominantrole in the mechanical properties when the other condi-tions are fixed With a stronger cementation force of debrisparticles there is a smaller increase in the internal frictionangle and a bigger increase for the cohesion The mechanicalproperties of an outwash deposit with high cementationstrength aremore similar to the properties of the stone blocksConversely if the cementation strength of the debris particlesis weak there is a bigger increase in the internal frictionangle and a smaller increase in the cohesionThe mechanicalproperties of the outwash deposit are much closer to theelastic-plastic debris

42 The Influence of the Aggregate Size As shown in Fig-ure 15 the larger the size of stone blocks is the smaller thepeak strength is This situation can be interpreted by theperimeter ratio which is defined as the ratio of all boundariesrsquoperimeters of stone blocks and themodel areaThe perimeterratio under the same stone ratio varies greatly The smalleraggregate size has more stone blocks so the perimeter ratiowill reach a high level and form larger contact areas Thecompressive strength also increases When the number ofstone blocks increases the contact area of the debris and stoneblocks and the interaction force between the debris and the

10 Advances in Materials Science and Engineering

(a) Crk num = 0 (b) Crk num = 39

(c) Crk num = 189 (d) Crk num = 563

Figure 13 The damage of outwash deposits with different stone block content (a) shows a model with the initial content rate of stone block40 (b) shows the cracks which first appear between some blocks (c) shows fracture development among the boundary of stone blocks and(d) shows the damaged outwash deposits

stone blocks will increase which just explains the reason whythe macromechanical properties of the outwash deposit areimproved with the number of stone blocks

43 The Influence of the Stone Block Content As shown inFigure 16 when there are few stone blocks in the outwashdeposit the debris-debris contact between particles willbe the main contact type The existence of stone blocksleads to the concentration of stress along their boundarieswhich can aggravate the debris contacts to damage the peakcompressive strength keeps close to the pure debriswith slightfluctuation Meanwhile due to the stress concentration theoutwash deposits become more brittle The shear strength isdecreased Many experiments show that when the contentof stone blocks is less than 25 the characteristic is moreclose to pure debris By contrast when the content of stoneblocks is greater than 25 there is not only debris-stonecontact in the outwash deposits but also stone-stone contact

The compressive and shear strengths are improved Whenthe content of stone blocks is more than 50 the maincontact type in the outwash deposits is stone-stone Themechanical properties are better in stone-filledmaterialsThecompressive and shear strengths are significantly improved inthe stone-filled materials

However when the stress-strain curves enter the residualstrength stage there is an obvious fluctuation after the peakof the curve the amplitude of which is related to the size andcontent ratio of stone blocks so in order to study the macro-shear strength the peak value of stress-strain curves is usedto calculate shear property

44 The Macroparameter Analysis of the Outwash DepositsIn terms of the stress-strain curves for any content rateof stone block cementation strength and block size themajor factor that influences the mechanical properties of the

Advances in Materials Science and Engineering 11

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

n bond = s bond = 0Nn bond = s bond = 1000N

n bond = s bond = 2000Nn bond = s bond = 3000N

Figure 14 The biaxial compression curves with different debris bonding force

Stone average size = 1 cmStone average size = 3 cm

Stone average size = 5 cmStone average size = 7 cm

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

Figure 15 The biaxial compression curves with different averagesizes of stone blocks

Stone content = 10

Stone content = 20Stone content = 30

Stone content = 40

Stone content = 50

Stone content = 60Stone content = 70

1400

1200

1000

800

600

400

200

0000 002 004 006 008 01 012

(1205901minus1205903) (

MPa

)

1205761

Figure 16The biaxial compression curve with different stone blockcontents

The content of stone blocks ()

The p

eak

com

pres

sive s

treng

th (M

Pa) 1600

1400

1200

1000

800

600

400

200

0000 10 20 30 40 50 60 70 80

Figure 17The peak compressive strength with different stone blockcontents

outwash deposits can be attributed to the dominant contacttype which is defined as the ratio of some particle contactnumber and total contact number in numerical models Theparticle contact can be divided into three kinds respectivelythe debris-debris debris-stone or stone-stone contact

If ratio of stone block is high enough to make stone-stonecontact becoming dominant contact type the characteristicof outwash deposit is close to rockfill For the naturemediumseveral kinds of contacts exist at that time which will affectthe comprehensive mechanical property greatly Althoughthe different geometries and distributions also affect themechanical properties the content of stone blocks is thedecisive factor For the different stone block contents thepeak strength under the confining pressure of 15MPa canbe calculated approximately using formula (12) as a cubicparabola curve (shown in Figure 17)

119875119896= 141841205723 minus 90441205722 + 1600120572 + 02894 (12)

where 120572 is the content ratio of stone blocks and 119875119896is the peak

strengthIt should be noted that the compressive strength of the

outwash deposit increases slowly when content ratio of stone

12 Advances in Materials Science and Engineering

Stone block ()

Inte

rnal

fric

tion

angl

e (∘

)40

36

32

28

24

200 10 20 30 40 50 60 70 80

(a)

20

40

60

80

100

120

140

160

180

0 20 40 60 80Stone block ()

Incr

emen

tal c

ohes

ion

(MPa

)

(b)

Figure 18 Changes of shear strength of outwash deposits with different contents and distributions of stone blocks (a) shows changes of theinternal friction of outwash deposit (b) shows changes of the cohesion of outwash deposit

blocks lies between 25 and 50 Once the content of stoneblocks is greater than 50 the stone-stone contact becomesthe dominant factor which causes the compressive strengthto increase sharply The internal friction angle versus thestone block content can be described using three stages asshown below

120593 =

18093931205722 minus 495165120572 + 265026 120572 lt 25194271120572 + 221719 25 lt 120572 lt 50234286120572 + 191429 120572 gt 50

(13)

where 120593 is the internal friction angle of the outwash depositand 120572 is the stone block content

Furthermore it can be observed from Figure 18(a) thatthe fluctuation of the internal friction angle is approximately0sim8∘ for the same stone blocks content which agrees withthe fluctuations in the stress-strain curves By contrast thecohesion of outwash deposit increases clearly with the stoneblock content due to the interaction force between stoneblocks as shown in Figure 18(b) The amplitude of variationwill increase significantly with the content of stone blocksHowever it is usually difficult to quantify the amplitude dueto roughness size characteristic of stone block and so on

Therefore for outwash deposits with extremely unevenshapes and distributions of stones the compressive strengthand shear strength are primarily controlled by the stone blockcontent The randomness of the stone block distributionscauses large deviations in the mechanical parameters Forexample the internal friction angle may have a large fluctua-tion at the same stone block content This feature is the causeof the poor results of the geotechnical experiments

5 Discussions

Outwash deposits are a type of debris-stone mixture Themechanical properties of these deposits are affected by thecomposition of the debris and stone blocks As the debriscementation increases the compressive strength increasesHowever the internal friction angle has a negative correlation

with the cementation force The stone block content is thedecisive factor for the mechanical properties of outwashdepositsThe randomness of the structural composition leadsto significant fluctuations in the properties which also createslarge discrepancies in the mechanical parameters

The major influences of the particle sizes geometricdistribution and stone block content are to determine thecontact type in the outwash deposits When the debris-debris contact is the dominant contact type there is littleinfluence from the stone blocks on the mechanical propertiesof the outwash depositsWhen the debris-stone contact is thedominant contact type the stone block content has a positiveinfluence on the compressive and shear strengths When thestone-stone contact is the dominant contact type the roles ofthe debris and stone blocks are reversed and the properties ofthe outwash deposits aremuch closer to a rock-filledmaterial

Although it is difficult to determine the mechanicalparameters of an outwash deposit using indoor experimentsthe properties of the medium can still be researched usingindirect approachesThemechanical parameters of the debrisand stone blocks can be determined from the indoor experi-ments Then the biaxial compression numerical experimentusing the granular discrete element method can be carriedout to analyse the influence of the stone blocks on theproperties of outwash deposits which makes up for thelimitation that the indoor experiments cannot consider thelarge stone blocks and offers a beneficial supplement to aid inthe geological parameter determination

6 Conclusions

According to the grain size and shape statistics from fieldstatistics the numerical granular discrete elementmodel withrandomised generation of stone blocks can be used withhypothesis that the length of the long axis and the axial ratioall follow normal distributions and the azimuth of the longaxis follows uniformdistribution in 0sim360∘The relationshipsbetween the macro- and micromechanical parameters arediscussed and the mechanical behaviour of the outwash

Advances in Materials Science and Engineering 13

deposit is affected by the cementation strength the size ofstone blocks the stone block content and the distribution ofthe stone blocks These properties are analysed so that theycan be better understood by the geologists working on thedemocratisation of the Engineering Project

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (no 51309089 and no 51379065)the National Key Technology RampD Program (no2013BAB06B00) the National Basic Research Programof China (973 Program) (no 2015CB057903) the NaturalScience Foundation of Jiangsu Province (no BK20130846)and the Fundamental Research Funds for the CentralUniversities (no 2014B04914)

References

[1] W G Holtz and H J Gibbs ldquoTriaxial shear tests on perviousgravelly soilsrdquo Journal of the Soil Mechanics and FoundationsDivision vol 82 no 1 pp 1ndash22 1956

[2] R J Chandler ldquoThe inclination of Talus Arctic Talus Terracesand other slopes composed of granular materialsrdquo The Journalof Geology vol 81 no 1 pp 1ndash14 1973

[3] X H You Stochastic structural model of the earth-rock aggregateand its application [PhD thesis] Beijing Jiaotong UniversityBeijing China 2001

[4] X H You and J S Tang ldquoResearch on horizontal push-shearin-situ test of debris and rock-mixturerdquo Chinese Journal of RockMechanics and Engineering vol 21 no 10 pp 1537ndash1540 2002

[5] X H You G He and X Li ldquoMicro-handling technologyof earth-rock aggregate sloperdquo Hydrogeology and EngineeringGeology vol 30 no 1 pp 18ndash21 2003

[6] J M He Study of deformation and failure mechanisms of rock-debris aggregate in three gorges reservoir area [PhD thesis]China University of Mining and Technology Beijing China2004

[7] X Li Q L Liao J M He and J Chen ldquoStudy on in-situ testsof mechanical characteristics on soil-rock aggregaterdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 12 pp2377ndash2384 2007

[8] T Lebourg J Riss and E Pirard ldquoInfluence of morphologicalcharacteristics of heterogeneous moraine formations on theirmechanical behaviour using image and statistical analysisrdquoEngineering Geology vol 73 no 1-2 pp 37ndash50 2004

[9] T R Reid and J P Harrison ldquoA semi-automated methodologyfor discontinuity trace detection in digital images of rock massexposuresrdquo International Journal of Rock Mechanics andMiningSciences vol 37 no 7 pp 1073ndash1089 2000

[10] Z Q Yue S Chen and L G Tham ldquoFinite element modelingof geomaterials using digital image processingrdquo Computers andGeotechnics vol 30 no 5 pp 375ndash397 2003

[11] Z Q Yue S Chen H Zheng and G H Tang ldquoDigital imageproceeding based on finite element method for geomaterialsrdquo

Chinese Journal of Rock Mechanics and Engineering vol 23 no6 pp 889ndash897 2004

[12] Q L Liao X Li W C Zhu and J S Liu ldquoStructure modelconstruction of rock and soil aggregate based on digital imagetechnology and its numerical simulation on mechanical struc-ture effectsrdquoChinese Journal of RockMechanics and Engineeringvol 29 no 1 pp 155ndash162 2010

[13] W J Xu R L Hu Z Q Yue and R J Tan ldquoMesostructuralcharacter and numerical simulation of mechanical propertiesof soil-rock mixturesrdquo Chinese Journal of Rock Mechanics andEngineering vol 26 no 2 pp 300ndash311 2007

[14] W J Xu Z Q Yue and R L Hu ldquoA current status of digitalimage based quantitative analysis of internal structures ofdebris rock and concretes and associated numerical simula-tionrdquo Journal of Engineering Geology vol 15 no 3 pp 289ndash3132007

[15] W J Xu R L Hu Z Q Yue R Zhang and G L WangldquoResearch on relationship between rock block proportion andshear strength of soil-rock mixtures based on digital imageanalysis and large direct shear testrdquo Chinese Journal of RockMechanics and Engineering vol 27 no 5 pp 996ndash1007 2008

[16] P A Cundall and O D L Strack ldquoA discrete numerical modelfor granular assembliesrdquo Geotechnique vol 29 no 1 pp 47ndash651979

[17] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) (Version 31) Itasca Consulting Group Minneapo-lis Minn USA 2004

[18] J Yoon ldquoApplication of experimental design and optimizationto PFC model calibration in uniaxial compression simulationrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 6 pp 871ndash889 2007

[19] Y C Wang and P Mora ldquoMacroscopic elastic properties ofregular latticesrdquo Journal of the Mechanics and Physics of Solidsvol 56 no 12 pp 3459ndash3474 2008

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 7

08

07

06

05

04

03

Ek

n

kn (GPa)

015

25

35

45

0908

0706

0504

0302

010

k skn

Figure 8The changes in Youngrsquos modulus with the microdeforma-tion parameters

Poiss

onrsquos

ratio

030

025

020

015

010

005

kn (GPa)

015

25

35

4509

0807

0605

0403

0201

0

k sk n

Figure 9The changes in Poissonrsquos ratio with the microdeformationparameters

normal stiffness Poissonrsquos ratio is close to zero When thestiffness ratio decreases the lateral deformation increasesWhen the tangent stiffness is zero Poissonrsquos ratio reaches itsmaximumvalueThe relationship between Poissonrsquos ratio andthe stiffness ratio based on a series of numerical tests can beexpressed using the following equation

1205830= 012781205782 minus 04061120578 + 03177 (10)

where 120583 is Poissonrsquos ratio and 120578 = 119896119904119896119899is the ratio of

the tangent stiffness to the normal stiffness which lies inthe range 0sim05 Once 120578 is greater than 10 Poissonrsquos ratiomay be greater than 10 or negative which disagrees with theproperties of common solid media

It should be noted that (10) does not consider the influ-ence of the stiffness If the stiffness is taken into considerationYoungrsquos modulus and Poissonrsquos ratio can be estimated withdifferent normal stiffness as follows

119864 = (02259120578 minus 00058119896119899minus 00042120578119896

119899+ 05346) 119896

119899

120583 = minus02760120578 minus 00029119896119899+ 00031120578119896

119899+ 03200

(11)

Friction coefficient

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Inte

rnal

fric

tion

angl

e (∘

)

4200

4000

3800

3600

3400

3200

300000 05 10 15 20 25

Figure 10 The changes in the internal friction angle at differentcoefficients of friction

The changes in Youngrsquos modulus and Poissonrsquos ratio withthe changes in the microparameters are shown in Figures8 and 9 The figures illustrate that the relationship betweenYoungrsquos modulus of an outwash deposit and the correspond-ing Poissonrsquos ratio is not a simple linear relation but adouble linear correlation in the calculation of the granulardiscrete element method When the microparameters needto be determined Youngrsquos modulus and Poissonrsquos ratio caninitially be assumed Then more reasonable values can bedetermined using (11) The steps should be repeated manytimes until Youngrsquosmodulus andPoissonrsquos ratio agreewith theresults of the macroscopic tests In addition the debris andstone blocks should be calibrated separately to obtain propermicroparameters

34TheMicromechanical Parameters of theOutwashDepositsThe normal contact force (119899 bond) tangent contact force(119904 bond) and the coefficient of friction 120583 are the mainmicroparameters related to macrostrength in a granularmodel based on PFC2D These parameters correspond tothe macrocohesion and the internal friction in the Mohr-Coulomb criterion The coefficient of friction is the purefrictional force when the outwash deposit is completelydestroyed It determines the residual strength of the mediumand can be approximately equal to the pure friction coefficienttan120593 of the stone and debris mass

As shown in Figure 10 when the coefficient of friction islow the deformation of the stone and debris mass shows alinear variation By contrast when the friction coefficient ishigh the deformation of the stone and debris mass showsa nonlinear variation The internal friction angle of themedium first increases and then remains unchanged as thecoefficient of friction increases The cohesion shows similarbehaviour but it remains constant if the coefficient of frictionis lowThe cohesion will increase as the coefficient of frictionincreases as shown in Figure 11

It is not difficult to find that the microcoefficient offriction is sensitive to the macro-internal-friction angleWhen the microparameters need to be determined thebonding forces should initially be set to zero then the friction

8 Advances in Materials Science and Engineering

000

020

040

060

080

100

120

00 05 10 15 20 25Friction coefficient

Coh

esio

n (M

Pa)

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Figure 11 The cohesion remains constant if the coefficient of friction is low

180

160

140

120

100

080

060

040

020

000000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 10

(a)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 35

200

180

160

140

120

100

080

060

040

020

000

(b)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

Stone rate = 45200

150

100

050

000

(c)

1205901minus1205903

(MPa

)

000 001 002 003 004

1205761

Stone rate = 60

1200

1000

800

600

400

200

000

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

(d)

Figure 12 The biaxial compression curve at different confining pressures and stone block content (a) Stone block content is 10 (b) stoneblock content is 35 (c) stone block content is 45 and (d) stone block content is 60

Advances in Materials Science and Engineering 9

Table 1 The micromechanical parameters of outwash deposits

Material Density (kgm3) Bonding force (N) Stiffness ratio Normal stiffness (Nm) Friction coefficientNormal Tangential

Debris 2200 11198903 11198903 00 11198908 025Stone 2700 21198906 21198906 02 951198909 120

Table 2 The macromechanical parameters of outwash deposits

Material Youngrsquos modules (MPa) Poissonrsquos ratio Internal friction angel (∘) Cohesion (MPa)Debris 559 032 2794 007Stone 4950 020 56 120

coefficient can be determined using trial calculations until themacromechanical properties are in linewith the experimentalresults Finally the bonding forces are adjusted so thatthe parameters are consistent with the macromechanicalproperties of the outwash deposit

When the bonding force is zero the internal friction anglewill reach its minimum value Therefore the determinationof the internal friction angle should take the effect of thestiffness ratio into consideration If the internal friction angleis unchanged when the coefficient of friction increases thebonding force can be adjusted to be in agreement with thepeak strength of the stress In this work the microparametersare shown in Table 1 and the corresponding macroparame-ters are shown in Table 2

4 The Analysis of the Mechanical Behaviour ofthe Outwash Deposits

As a case study shown in Figure 1 the stone rate of outwashbased on the statistical results is about 30 to 40 themean length of long axis is about 413 cm with a variance015 and the mean axis ratio is 064 with a variance 017Then the random structure models of outwash depositsare generated according to the above information Finallynumerical simulation and comparison are executed in orderto analyse the effect of comprehensive mechanical behaviour

41 The Stress-Strain Curve Based on the Biaxial CompressionTest The stress-strain curves from the numerical simulationtests of an outwash deposit under biaxial compression con-ditions can be divided into three stages the elastic stagethe hardening stage and the residual strength stage (shownin Figure 12) In the elastic stage the deformation modulusis determined by the undamaged debris particles and stoneblock assemblies As the deformation increases fractureswill first appear in the debris because of its low modulusand strength When the outwash deposit enters into thehardening stage the debris particle bonding forces will failgradually and the deformation modulus will decrease slowlyHowever the strength will increase continually due to theinteraction force caused by mosaic effect between the debrisparticles and the stone blocks When the stress reaches itspeak strength the outwash deposit will enter into the residualstrength stage The cementation ability between the debris

particles is almost completely lost The compressive-bearingcapability of the sample cannot continue to increase Thecompressive-bearing capability is controlled mainly by theinterparticle friction When the strain continues to increasethe stone blocks may rotate and tumble which leads tothe complete destruction of the structure of the outwashdeposit However there is still some compression-bearingcapability which causes the residual strength of the outwashdeposit The residual strength shows fluctuations because ofthe contact action between the debris and the stone blocks

As shown in Figure 13 the damage of a model withcontent ratio of stone block 40 length of long axis about2 to 6 cm and the axial ratio 05 to 08 is compared in theloading process It shows that cracks occur firstly betweensome blocks and then develop among the boundary of stoneblocks and fill with the debris particles The crack numberwill increase shapely with the strain increase until all bondcontacts between debris particles are destroyed

The curves for different debris bonding forces in Figure 14show that the cementation strength of the debris particlesdecides the strength of outwash deposit and has a dominantrole in the mechanical properties when the other condi-tions are fixed With a stronger cementation force of debrisparticles there is a smaller increase in the internal frictionangle and a bigger increase for the cohesion The mechanicalproperties of an outwash deposit with high cementationstrength aremore similar to the properties of the stone blocksConversely if the cementation strength of the debris particlesis weak there is a bigger increase in the internal frictionangle and a smaller increase in the cohesionThe mechanicalproperties of the outwash deposit are much closer to theelastic-plastic debris

42 The Influence of the Aggregate Size As shown in Fig-ure 15 the larger the size of stone blocks is the smaller thepeak strength is This situation can be interpreted by theperimeter ratio which is defined as the ratio of all boundariesrsquoperimeters of stone blocks and themodel areaThe perimeterratio under the same stone ratio varies greatly The smalleraggregate size has more stone blocks so the perimeter ratiowill reach a high level and form larger contact areas Thecompressive strength also increases When the number ofstone blocks increases the contact area of the debris and stoneblocks and the interaction force between the debris and the

10 Advances in Materials Science and Engineering

(a) Crk num = 0 (b) Crk num = 39

(c) Crk num = 189 (d) Crk num = 563

Figure 13 The damage of outwash deposits with different stone block content (a) shows a model with the initial content rate of stone block40 (b) shows the cracks which first appear between some blocks (c) shows fracture development among the boundary of stone blocks and(d) shows the damaged outwash deposits

stone blocks will increase which just explains the reason whythe macromechanical properties of the outwash deposit areimproved with the number of stone blocks

43 The Influence of the Stone Block Content As shown inFigure 16 when there are few stone blocks in the outwashdeposit the debris-debris contact between particles willbe the main contact type The existence of stone blocksleads to the concentration of stress along their boundarieswhich can aggravate the debris contacts to damage the peakcompressive strength keeps close to the pure debriswith slightfluctuation Meanwhile due to the stress concentration theoutwash deposits become more brittle The shear strength isdecreased Many experiments show that when the contentof stone blocks is less than 25 the characteristic is moreclose to pure debris By contrast when the content of stoneblocks is greater than 25 there is not only debris-stonecontact in the outwash deposits but also stone-stone contact

The compressive and shear strengths are improved Whenthe content of stone blocks is more than 50 the maincontact type in the outwash deposits is stone-stone Themechanical properties are better in stone-filledmaterialsThecompressive and shear strengths are significantly improved inthe stone-filled materials

However when the stress-strain curves enter the residualstrength stage there is an obvious fluctuation after the peakof the curve the amplitude of which is related to the size andcontent ratio of stone blocks so in order to study the macro-shear strength the peak value of stress-strain curves is usedto calculate shear property

44 The Macroparameter Analysis of the Outwash DepositsIn terms of the stress-strain curves for any content rateof stone block cementation strength and block size themajor factor that influences the mechanical properties of the

Advances in Materials Science and Engineering 11

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

n bond = s bond = 0Nn bond = s bond = 1000N

n bond = s bond = 2000Nn bond = s bond = 3000N

Figure 14 The biaxial compression curves with different debris bonding force

Stone average size = 1 cmStone average size = 3 cm

Stone average size = 5 cmStone average size = 7 cm

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

Figure 15 The biaxial compression curves with different averagesizes of stone blocks

Stone content = 10

Stone content = 20Stone content = 30

Stone content = 40

Stone content = 50

Stone content = 60Stone content = 70

1400

1200

1000

800

600

400

200

0000 002 004 006 008 01 012

(1205901minus1205903) (

MPa

)

1205761

Figure 16The biaxial compression curve with different stone blockcontents

The content of stone blocks ()

The p

eak

com

pres

sive s

treng

th (M

Pa) 1600

1400

1200

1000

800

600

400

200

0000 10 20 30 40 50 60 70 80

Figure 17The peak compressive strength with different stone blockcontents

outwash deposits can be attributed to the dominant contacttype which is defined as the ratio of some particle contactnumber and total contact number in numerical models Theparticle contact can be divided into three kinds respectivelythe debris-debris debris-stone or stone-stone contact

If ratio of stone block is high enough to make stone-stonecontact becoming dominant contact type the characteristicof outwash deposit is close to rockfill For the naturemediumseveral kinds of contacts exist at that time which will affectthe comprehensive mechanical property greatly Althoughthe different geometries and distributions also affect themechanical properties the content of stone blocks is thedecisive factor For the different stone block contents thepeak strength under the confining pressure of 15MPa canbe calculated approximately using formula (12) as a cubicparabola curve (shown in Figure 17)

119875119896= 141841205723 minus 90441205722 + 1600120572 + 02894 (12)

where 120572 is the content ratio of stone blocks and 119875119896is the peak

strengthIt should be noted that the compressive strength of the

outwash deposit increases slowly when content ratio of stone

12 Advances in Materials Science and Engineering

Stone block ()

Inte

rnal

fric

tion

angl

e (∘

)40

36

32

28

24

200 10 20 30 40 50 60 70 80

(a)

20

40

60

80

100

120

140

160

180

0 20 40 60 80Stone block ()

Incr

emen

tal c

ohes

ion

(MPa

)

(b)

Figure 18 Changes of shear strength of outwash deposits with different contents and distributions of stone blocks (a) shows changes of theinternal friction of outwash deposit (b) shows changes of the cohesion of outwash deposit

blocks lies between 25 and 50 Once the content of stoneblocks is greater than 50 the stone-stone contact becomesthe dominant factor which causes the compressive strengthto increase sharply The internal friction angle versus thestone block content can be described using three stages asshown below

120593 =

18093931205722 minus 495165120572 + 265026 120572 lt 25194271120572 + 221719 25 lt 120572 lt 50234286120572 + 191429 120572 gt 50

(13)

where 120593 is the internal friction angle of the outwash depositand 120572 is the stone block content

Furthermore it can be observed from Figure 18(a) thatthe fluctuation of the internal friction angle is approximately0sim8∘ for the same stone blocks content which agrees withthe fluctuations in the stress-strain curves By contrast thecohesion of outwash deposit increases clearly with the stoneblock content due to the interaction force between stoneblocks as shown in Figure 18(b) The amplitude of variationwill increase significantly with the content of stone blocksHowever it is usually difficult to quantify the amplitude dueto roughness size characteristic of stone block and so on

Therefore for outwash deposits with extremely unevenshapes and distributions of stones the compressive strengthand shear strength are primarily controlled by the stone blockcontent The randomness of the stone block distributionscauses large deviations in the mechanical parameters Forexample the internal friction angle may have a large fluctua-tion at the same stone block content This feature is the causeof the poor results of the geotechnical experiments

5 Discussions

Outwash deposits are a type of debris-stone mixture Themechanical properties of these deposits are affected by thecomposition of the debris and stone blocks As the debriscementation increases the compressive strength increasesHowever the internal friction angle has a negative correlation

with the cementation force The stone block content is thedecisive factor for the mechanical properties of outwashdepositsThe randomness of the structural composition leadsto significant fluctuations in the properties which also createslarge discrepancies in the mechanical parameters

The major influences of the particle sizes geometricdistribution and stone block content are to determine thecontact type in the outwash deposits When the debris-debris contact is the dominant contact type there is littleinfluence from the stone blocks on the mechanical propertiesof the outwash depositsWhen the debris-stone contact is thedominant contact type the stone block content has a positiveinfluence on the compressive and shear strengths When thestone-stone contact is the dominant contact type the roles ofthe debris and stone blocks are reversed and the properties ofthe outwash deposits aremuch closer to a rock-filledmaterial

Although it is difficult to determine the mechanicalparameters of an outwash deposit using indoor experimentsthe properties of the medium can still be researched usingindirect approachesThemechanical parameters of the debrisand stone blocks can be determined from the indoor experi-ments Then the biaxial compression numerical experimentusing the granular discrete element method can be carriedout to analyse the influence of the stone blocks on theproperties of outwash deposits which makes up for thelimitation that the indoor experiments cannot consider thelarge stone blocks and offers a beneficial supplement to aid inthe geological parameter determination

6 Conclusions

According to the grain size and shape statistics from fieldstatistics the numerical granular discrete elementmodel withrandomised generation of stone blocks can be used withhypothesis that the length of the long axis and the axial ratioall follow normal distributions and the azimuth of the longaxis follows uniformdistribution in 0sim360∘The relationshipsbetween the macro- and micromechanical parameters arediscussed and the mechanical behaviour of the outwash

Advances in Materials Science and Engineering 13

deposit is affected by the cementation strength the size ofstone blocks the stone block content and the distribution ofthe stone blocks These properties are analysed so that theycan be better understood by the geologists working on thedemocratisation of the Engineering Project

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (no 51309089 and no 51379065)the National Key Technology RampD Program (no2013BAB06B00) the National Basic Research Programof China (973 Program) (no 2015CB057903) the NaturalScience Foundation of Jiangsu Province (no BK20130846)and the Fundamental Research Funds for the CentralUniversities (no 2014B04914)

References

[1] W G Holtz and H J Gibbs ldquoTriaxial shear tests on perviousgravelly soilsrdquo Journal of the Soil Mechanics and FoundationsDivision vol 82 no 1 pp 1ndash22 1956

[2] R J Chandler ldquoThe inclination of Talus Arctic Talus Terracesand other slopes composed of granular materialsrdquo The Journalof Geology vol 81 no 1 pp 1ndash14 1973

[3] X H You Stochastic structural model of the earth-rock aggregateand its application [PhD thesis] Beijing Jiaotong UniversityBeijing China 2001

[4] X H You and J S Tang ldquoResearch on horizontal push-shearin-situ test of debris and rock-mixturerdquo Chinese Journal of RockMechanics and Engineering vol 21 no 10 pp 1537ndash1540 2002

[5] X H You G He and X Li ldquoMicro-handling technologyof earth-rock aggregate sloperdquo Hydrogeology and EngineeringGeology vol 30 no 1 pp 18ndash21 2003

[6] J M He Study of deformation and failure mechanisms of rock-debris aggregate in three gorges reservoir area [PhD thesis]China University of Mining and Technology Beijing China2004

[7] X Li Q L Liao J M He and J Chen ldquoStudy on in-situ testsof mechanical characteristics on soil-rock aggregaterdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 12 pp2377ndash2384 2007

[8] T Lebourg J Riss and E Pirard ldquoInfluence of morphologicalcharacteristics of heterogeneous moraine formations on theirmechanical behaviour using image and statistical analysisrdquoEngineering Geology vol 73 no 1-2 pp 37ndash50 2004

[9] T R Reid and J P Harrison ldquoA semi-automated methodologyfor discontinuity trace detection in digital images of rock massexposuresrdquo International Journal of Rock Mechanics andMiningSciences vol 37 no 7 pp 1073ndash1089 2000

[10] Z Q Yue S Chen and L G Tham ldquoFinite element modelingof geomaterials using digital image processingrdquo Computers andGeotechnics vol 30 no 5 pp 375ndash397 2003

[11] Z Q Yue S Chen H Zheng and G H Tang ldquoDigital imageproceeding based on finite element method for geomaterialsrdquo

Chinese Journal of Rock Mechanics and Engineering vol 23 no6 pp 889ndash897 2004

[12] Q L Liao X Li W C Zhu and J S Liu ldquoStructure modelconstruction of rock and soil aggregate based on digital imagetechnology and its numerical simulation on mechanical struc-ture effectsrdquoChinese Journal of RockMechanics and Engineeringvol 29 no 1 pp 155ndash162 2010

[13] W J Xu R L Hu Z Q Yue and R J Tan ldquoMesostructuralcharacter and numerical simulation of mechanical propertiesof soil-rock mixturesrdquo Chinese Journal of Rock Mechanics andEngineering vol 26 no 2 pp 300ndash311 2007

[14] W J Xu Z Q Yue and R L Hu ldquoA current status of digitalimage based quantitative analysis of internal structures ofdebris rock and concretes and associated numerical simula-tionrdquo Journal of Engineering Geology vol 15 no 3 pp 289ndash3132007

[15] W J Xu R L Hu Z Q Yue R Zhang and G L WangldquoResearch on relationship between rock block proportion andshear strength of soil-rock mixtures based on digital imageanalysis and large direct shear testrdquo Chinese Journal of RockMechanics and Engineering vol 27 no 5 pp 996ndash1007 2008

[16] P A Cundall and O D L Strack ldquoA discrete numerical modelfor granular assembliesrdquo Geotechnique vol 29 no 1 pp 47ndash651979

[17] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) (Version 31) Itasca Consulting Group Minneapo-lis Minn USA 2004

[18] J Yoon ldquoApplication of experimental design and optimizationto PFC model calibration in uniaxial compression simulationrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 6 pp 871ndash889 2007

[19] Y C Wang and P Mora ldquoMacroscopic elastic properties ofregular latticesrdquo Journal of the Mechanics and Physics of Solidsvol 56 no 12 pp 3459ndash3474 2008

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MaterialsJournal of

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Nano

materials

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Journal ofNanomaterials

8 Advances in Materials Science and Engineering

000

020

040

060

080

100

120

00 05 10 15 20 25Friction coefficient

Coh

esio

n (M

Pa)

kskn = 13kn = 50MPan bond = 1000Ns bond = 1000N

Figure 11 The cohesion remains constant if the coefficient of friction is low

180

160

140

120

100

080

060

040

020

000000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 10

(a)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Stone rate = 35

200

180

160

140

120

100

080

060

040

020

000

(b)

000 001 002 003 004

1205761

1205901minus1205903

(MPa

)

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

Stone rate = 45200

150

100

050

000

(c)

1205901minus1205903

(MPa

)

000 001 002 003 004

1205761

Stone rate = 60

1200

1000

800

600

400

200

000

Confining pressure = 01MPaConfining pressure = 03MPaConfining pressure = 05MPa

(d)

Figure 12 The biaxial compression curve at different confining pressures and stone block content (a) Stone block content is 10 (b) stoneblock content is 35 (c) stone block content is 45 and (d) stone block content is 60

Advances in Materials Science and Engineering 9

Table 1 The micromechanical parameters of outwash deposits

Material Density (kgm3) Bonding force (N) Stiffness ratio Normal stiffness (Nm) Friction coefficientNormal Tangential

Debris 2200 11198903 11198903 00 11198908 025Stone 2700 21198906 21198906 02 951198909 120

Table 2 The macromechanical parameters of outwash deposits

Material Youngrsquos modules (MPa) Poissonrsquos ratio Internal friction angel (∘) Cohesion (MPa)Debris 559 032 2794 007Stone 4950 020 56 120

coefficient can be determined using trial calculations until themacromechanical properties are in linewith the experimentalresults Finally the bonding forces are adjusted so thatthe parameters are consistent with the macromechanicalproperties of the outwash deposit

When the bonding force is zero the internal friction anglewill reach its minimum value Therefore the determinationof the internal friction angle should take the effect of thestiffness ratio into consideration If the internal friction angleis unchanged when the coefficient of friction increases thebonding force can be adjusted to be in agreement with thepeak strength of the stress In this work the microparametersare shown in Table 1 and the corresponding macroparame-ters are shown in Table 2

4 The Analysis of the Mechanical Behaviour ofthe Outwash Deposits

As a case study shown in Figure 1 the stone rate of outwashbased on the statistical results is about 30 to 40 themean length of long axis is about 413 cm with a variance015 and the mean axis ratio is 064 with a variance 017Then the random structure models of outwash depositsare generated according to the above information Finallynumerical simulation and comparison are executed in orderto analyse the effect of comprehensive mechanical behaviour

41 The Stress-Strain Curve Based on the Biaxial CompressionTest The stress-strain curves from the numerical simulationtests of an outwash deposit under biaxial compression con-ditions can be divided into three stages the elastic stagethe hardening stage and the residual strength stage (shownin Figure 12) In the elastic stage the deformation modulusis determined by the undamaged debris particles and stoneblock assemblies As the deformation increases fractureswill first appear in the debris because of its low modulusand strength When the outwash deposit enters into thehardening stage the debris particle bonding forces will failgradually and the deformation modulus will decrease slowlyHowever the strength will increase continually due to theinteraction force caused by mosaic effect between the debrisparticles and the stone blocks When the stress reaches itspeak strength the outwash deposit will enter into the residualstrength stage The cementation ability between the debris

particles is almost completely lost The compressive-bearingcapability of the sample cannot continue to increase Thecompressive-bearing capability is controlled mainly by theinterparticle friction When the strain continues to increasethe stone blocks may rotate and tumble which leads tothe complete destruction of the structure of the outwashdeposit However there is still some compression-bearingcapability which causes the residual strength of the outwashdeposit The residual strength shows fluctuations because ofthe contact action between the debris and the stone blocks

As shown in Figure 13 the damage of a model withcontent ratio of stone block 40 length of long axis about2 to 6 cm and the axial ratio 05 to 08 is compared in theloading process It shows that cracks occur firstly betweensome blocks and then develop among the boundary of stoneblocks and fill with the debris particles The crack numberwill increase shapely with the strain increase until all bondcontacts between debris particles are destroyed

The curves for different debris bonding forces in Figure 14show that the cementation strength of the debris particlesdecides the strength of outwash deposit and has a dominantrole in the mechanical properties when the other condi-tions are fixed With a stronger cementation force of debrisparticles there is a smaller increase in the internal frictionangle and a bigger increase for the cohesion The mechanicalproperties of an outwash deposit with high cementationstrength aremore similar to the properties of the stone blocksConversely if the cementation strength of the debris particlesis weak there is a bigger increase in the internal frictionangle and a smaller increase in the cohesionThe mechanicalproperties of the outwash deposit are much closer to theelastic-plastic debris

42 The Influence of the Aggregate Size As shown in Fig-ure 15 the larger the size of stone blocks is the smaller thepeak strength is This situation can be interpreted by theperimeter ratio which is defined as the ratio of all boundariesrsquoperimeters of stone blocks and themodel areaThe perimeterratio under the same stone ratio varies greatly The smalleraggregate size has more stone blocks so the perimeter ratiowill reach a high level and form larger contact areas Thecompressive strength also increases When the number ofstone blocks increases the contact area of the debris and stoneblocks and the interaction force between the debris and the

10 Advances in Materials Science and Engineering

(a) Crk num = 0 (b) Crk num = 39

(c) Crk num = 189 (d) Crk num = 563

Figure 13 The damage of outwash deposits with different stone block content (a) shows a model with the initial content rate of stone block40 (b) shows the cracks which first appear between some blocks (c) shows fracture development among the boundary of stone blocks and(d) shows the damaged outwash deposits

stone blocks will increase which just explains the reason whythe macromechanical properties of the outwash deposit areimproved with the number of stone blocks

43 The Influence of the Stone Block Content As shown inFigure 16 when there are few stone blocks in the outwashdeposit the debris-debris contact between particles willbe the main contact type The existence of stone blocksleads to the concentration of stress along their boundarieswhich can aggravate the debris contacts to damage the peakcompressive strength keeps close to the pure debriswith slightfluctuation Meanwhile due to the stress concentration theoutwash deposits become more brittle The shear strength isdecreased Many experiments show that when the contentof stone blocks is less than 25 the characteristic is moreclose to pure debris By contrast when the content of stoneblocks is greater than 25 there is not only debris-stonecontact in the outwash deposits but also stone-stone contact

The compressive and shear strengths are improved Whenthe content of stone blocks is more than 50 the maincontact type in the outwash deposits is stone-stone Themechanical properties are better in stone-filledmaterialsThecompressive and shear strengths are significantly improved inthe stone-filled materials

However when the stress-strain curves enter the residualstrength stage there is an obvious fluctuation after the peakof the curve the amplitude of which is related to the size andcontent ratio of stone blocks so in order to study the macro-shear strength the peak value of stress-strain curves is usedto calculate shear property

44 The Macroparameter Analysis of the Outwash DepositsIn terms of the stress-strain curves for any content rateof stone block cementation strength and block size themajor factor that influences the mechanical properties of the

Advances in Materials Science and Engineering 11

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

n bond = s bond = 0Nn bond = s bond = 1000N

n bond = s bond = 2000Nn bond = s bond = 3000N

Figure 14 The biaxial compression curves with different debris bonding force

Stone average size = 1 cmStone average size = 3 cm

Stone average size = 5 cmStone average size = 7 cm

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

Figure 15 The biaxial compression curves with different averagesizes of stone blocks

Stone content = 10

Stone content = 20Stone content = 30

Stone content = 40

Stone content = 50

Stone content = 60Stone content = 70

1400

1200

1000

800

600

400

200

0000 002 004 006 008 01 012

(1205901minus1205903) (

MPa

)

1205761

Figure 16The biaxial compression curve with different stone blockcontents

The content of stone blocks ()

The p

eak

com

pres

sive s

treng

th (M

Pa) 1600

1400

1200

1000

800

600

400

200

0000 10 20 30 40 50 60 70 80

Figure 17The peak compressive strength with different stone blockcontents

outwash deposits can be attributed to the dominant contacttype which is defined as the ratio of some particle contactnumber and total contact number in numerical models Theparticle contact can be divided into three kinds respectivelythe debris-debris debris-stone or stone-stone contact

If ratio of stone block is high enough to make stone-stonecontact becoming dominant contact type the characteristicof outwash deposit is close to rockfill For the naturemediumseveral kinds of contacts exist at that time which will affectthe comprehensive mechanical property greatly Althoughthe different geometries and distributions also affect themechanical properties the content of stone blocks is thedecisive factor For the different stone block contents thepeak strength under the confining pressure of 15MPa canbe calculated approximately using formula (12) as a cubicparabola curve (shown in Figure 17)

119875119896= 141841205723 minus 90441205722 + 1600120572 + 02894 (12)

where 120572 is the content ratio of stone blocks and 119875119896is the peak

strengthIt should be noted that the compressive strength of the

outwash deposit increases slowly when content ratio of stone

12 Advances in Materials Science and Engineering

Stone block ()

Inte

rnal

fric

tion

angl

e (∘

)40

36

32

28

24

200 10 20 30 40 50 60 70 80

(a)

20

40

60

80

100

120

140

160

180

0 20 40 60 80Stone block ()

Incr

emen

tal c

ohes

ion

(MPa

)

(b)

Figure 18 Changes of shear strength of outwash deposits with different contents and distributions of stone blocks (a) shows changes of theinternal friction of outwash deposit (b) shows changes of the cohesion of outwash deposit

blocks lies between 25 and 50 Once the content of stoneblocks is greater than 50 the stone-stone contact becomesthe dominant factor which causes the compressive strengthto increase sharply The internal friction angle versus thestone block content can be described using three stages asshown below

120593 =

18093931205722 minus 495165120572 + 265026 120572 lt 25194271120572 + 221719 25 lt 120572 lt 50234286120572 + 191429 120572 gt 50

(13)

where 120593 is the internal friction angle of the outwash depositand 120572 is the stone block content

Furthermore it can be observed from Figure 18(a) thatthe fluctuation of the internal friction angle is approximately0sim8∘ for the same stone blocks content which agrees withthe fluctuations in the stress-strain curves By contrast thecohesion of outwash deposit increases clearly with the stoneblock content due to the interaction force between stoneblocks as shown in Figure 18(b) The amplitude of variationwill increase significantly with the content of stone blocksHowever it is usually difficult to quantify the amplitude dueto roughness size characteristic of stone block and so on

Therefore for outwash deposits with extremely unevenshapes and distributions of stones the compressive strengthand shear strength are primarily controlled by the stone blockcontent The randomness of the stone block distributionscauses large deviations in the mechanical parameters Forexample the internal friction angle may have a large fluctua-tion at the same stone block content This feature is the causeof the poor results of the geotechnical experiments

5 Discussions

Outwash deposits are a type of debris-stone mixture Themechanical properties of these deposits are affected by thecomposition of the debris and stone blocks As the debriscementation increases the compressive strength increasesHowever the internal friction angle has a negative correlation

with the cementation force The stone block content is thedecisive factor for the mechanical properties of outwashdepositsThe randomness of the structural composition leadsto significant fluctuations in the properties which also createslarge discrepancies in the mechanical parameters

The major influences of the particle sizes geometricdistribution and stone block content are to determine thecontact type in the outwash deposits When the debris-debris contact is the dominant contact type there is littleinfluence from the stone blocks on the mechanical propertiesof the outwash depositsWhen the debris-stone contact is thedominant contact type the stone block content has a positiveinfluence on the compressive and shear strengths When thestone-stone contact is the dominant contact type the roles ofthe debris and stone blocks are reversed and the properties ofthe outwash deposits aremuch closer to a rock-filledmaterial

Although it is difficult to determine the mechanicalparameters of an outwash deposit using indoor experimentsthe properties of the medium can still be researched usingindirect approachesThemechanical parameters of the debrisand stone blocks can be determined from the indoor experi-ments Then the biaxial compression numerical experimentusing the granular discrete element method can be carriedout to analyse the influence of the stone blocks on theproperties of outwash deposits which makes up for thelimitation that the indoor experiments cannot consider thelarge stone blocks and offers a beneficial supplement to aid inthe geological parameter determination

6 Conclusions

According to the grain size and shape statistics from fieldstatistics the numerical granular discrete elementmodel withrandomised generation of stone blocks can be used withhypothesis that the length of the long axis and the axial ratioall follow normal distributions and the azimuth of the longaxis follows uniformdistribution in 0sim360∘The relationshipsbetween the macro- and micromechanical parameters arediscussed and the mechanical behaviour of the outwash

Advances in Materials Science and Engineering 13

deposit is affected by the cementation strength the size ofstone blocks the stone block content and the distribution ofthe stone blocks These properties are analysed so that theycan be better understood by the geologists working on thedemocratisation of the Engineering Project

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (no 51309089 and no 51379065)the National Key Technology RampD Program (no2013BAB06B00) the National Basic Research Programof China (973 Program) (no 2015CB057903) the NaturalScience Foundation of Jiangsu Province (no BK20130846)and the Fundamental Research Funds for the CentralUniversities (no 2014B04914)

References

[1] W G Holtz and H J Gibbs ldquoTriaxial shear tests on perviousgravelly soilsrdquo Journal of the Soil Mechanics and FoundationsDivision vol 82 no 1 pp 1ndash22 1956

[2] R J Chandler ldquoThe inclination of Talus Arctic Talus Terracesand other slopes composed of granular materialsrdquo The Journalof Geology vol 81 no 1 pp 1ndash14 1973

[3] X H You Stochastic structural model of the earth-rock aggregateand its application [PhD thesis] Beijing Jiaotong UniversityBeijing China 2001

[4] X H You and J S Tang ldquoResearch on horizontal push-shearin-situ test of debris and rock-mixturerdquo Chinese Journal of RockMechanics and Engineering vol 21 no 10 pp 1537ndash1540 2002

[5] X H You G He and X Li ldquoMicro-handling technologyof earth-rock aggregate sloperdquo Hydrogeology and EngineeringGeology vol 30 no 1 pp 18ndash21 2003

[6] J M He Study of deformation and failure mechanisms of rock-debris aggregate in three gorges reservoir area [PhD thesis]China University of Mining and Technology Beijing China2004

[7] X Li Q L Liao J M He and J Chen ldquoStudy on in-situ testsof mechanical characteristics on soil-rock aggregaterdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 12 pp2377ndash2384 2007

[8] T Lebourg J Riss and E Pirard ldquoInfluence of morphologicalcharacteristics of heterogeneous moraine formations on theirmechanical behaviour using image and statistical analysisrdquoEngineering Geology vol 73 no 1-2 pp 37ndash50 2004

[9] T R Reid and J P Harrison ldquoA semi-automated methodologyfor discontinuity trace detection in digital images of rock massexposuresrdquo International Journal of Rock Mechanics andMiningSciences vol 37 no 7 pp 1073ndash1089 2000

[10] Z Q Yue S Chen and L G Tham ldquoFinite element modelingof geomaterials using digital image processingrdquo Computers andGeotechnics vol 30 no 5 pp 375ndash397 2003

[11] Z Q Yue S Chen H Zheng and G H Tang ldquoDigital imageproceeding based on finite element method for geomaterialsrdquo

Chinese Journal of Rock Mechanics and Engineering vol 23 no6 pp 889ndash897 2004

[12] Q L Liao X Li W C Zhu and J S Liu ldquoStructure modelconstruction of rock and soil aggregate based on digital imagetechnology and its numerical simulation on mechanical struc-ture effectsrdquoChinese Journal of RockMechanics and Engineeringvol 29 no 1 pp 155ndash162 2010

[13] W J Xu R L Hu Z Q Yue and R J Tan ldquoMesostructuralcharacter and numerical simulation of mechanical propertiesof soil-rock mixturesrdquo Chinese Journal of Rock Mechanics andEngineering vol 26 no 2 pp 300ndash311 2007

[14] W J Xu Z Q Yue and R L Hu ldquoA current status of digitalimage based quantitative analysis of internal structures ofdebris rock and concretes and associated numerical simula-tionrdquo Journal of Engineering Geology vol 15 no 3 pp 289ndash3132007

[15] W J Xu R L Hu Z Q Yue R Zhang and G L WangldquoResearch on relationship between rock block proportion andshear strength of soil-rock mixtures based on digital imageanalysis and large direct shear testrdquo Chinese Journal of RockMechanics and Engineering vol 27 no 5 pp 996ndash1007 2008

[16] P A Cundall and O D L Strack ldquoA discrete numerical modelfor granular assembliesrdquo Geotechnique vol 29 no 1 pp 47ndash651979

[17] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) (Version 31) Itasca Consulting Group Minneapo-lis Minn USA 2004

[18] J Yoon ldquoApplication of experimental design and optimizationto PFC model calibration in uniaxial compression simulationrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 6 pp 871ndash889 2007

[19] Y C Wang and P Mora ldquoMacroscopic elastic properties ofregular latticesrdquo Journal of the Mechanics and Physics of Solidsvol 56 no 12 pp 3459ndash3474 2008

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 9

Table 1 The micromechanical parameters of outwash deposits

Material Density (kgm3) Bonding force (N) Stiffness ratio Normal stiffness (Nm) Friction coefficientNormal Tangential

Debris 2200 11198903 11198903 00 11198908 025Stone 2700 21198906 21198906 02 951198909 120

Table 2 The macromechanical parameters of outwash deposits

Material Youngrsquos modules (MPa) Poissonrsquos ratio Internal friction angel (∘) Cohesion (MPa)Debris 559 032 2794 007Stone 4950 020 56 120

coefficient can be determined using trial calculations until themacromechanical properties are in linewith the experimentalresults Finally the bonding forces are adjusted so thatthe parameters are consistent with the macromechanicalproperties of the outwash deposit

When the bonding force is zero the internal friction anglewill reach its minimum value Therefore the determinationof the internal friction angle should take the effect of thestiffness ratio into consideration If the internal friction angleis unchanged when the coefficient of friction increases thebonding force can be adjusted to be in agreement with thepeak strength of the stress In this work the microparametersare shown in Table 1 and the corresponding macroparame-ters are shown in Table 2

4 The Analysis of the Mechanical Behaviour ofthe Outwash Deposits

As a case study shown in Figure 1 the stone rate of outwashbased on the statistical results is about 30 to 40 themean length of long axis is about 413 cm with a variance015 and the mean axis ratio is 064 with a variance 017Then the random structure models of outwash depositsare generated according to the above information Finallynumerical simulation and comparison are executed in orderto analyse the effect of comprehensive mechanical behaviour

41 The Stress-Strain Curve Based on the Biaxial CompressionTest The stress-strain curves from the numerical simulationtests of an outwash deposit under biaxial compression con-ditions can be divided into three stages the elastic stagethe hardening stage and the residual strength stage (shownin Figure 12) In the elastic stage the deformation modulusis determined by the undamaged debris particles and stoneblock assemblies As the deformation increases fractureswill first appear in the debris because of its low modulusand strength When the outwash deposit enters into thehardening stage the debris particle bonding forces will failgradually and the deformation modulus will decrease slowlyHowever the strength will increase continually due to theinteraction force caused by mosaic effect between the debrisparticles and the stone blocks When the stress reaches itspeak strength the outwash deposit will enter into the residualstrength stage The cementation ability between the debris

particles is almost completely lost The compressive-bearingcapability of the sample cannot continue to increase Thecompressive-bearing capability is controlled mainly by theinterparticle friction When the strain continues to increasethe stone blocks may rotate and tumble which leads tothe complete destruction of the structure of the outwashdeposit However there is still some compression-bearingcapability which causes the residual strength of the outwashdeposit The residual strength shows fluctuations because ofthe contact action between the debris and the stone blocks

As shown in Figure 13 the damage of a model withcontent ratio of stone block 40 length of long axis about2 to 6 cm and the axial ratio 05 to 08 is compared in theloading process It shows that cracks occur firstly betweensome blocks and then develop among the boundary of stoneblocks and fill with the debris particles The crack numberwill increase shapely with the strain increase until all bondcontacts between debris particles are destroyed

The curves for different debris bonding forces in Figure 14show that the cementation strength of the debris particlesdecides the strength of outwash deposit and has a dominantrole in the mechanical properties when the other condi-tions are fixed With a stronger cementation force of debrisparticles there is a smaller increase in the internal frictionangle and a bigger increase for the cohesion The mechanicalproperties of an outwash deposit with high cementationstrength aremore similar to the properties of the stone blocksConversely if the cementation strength of the debris particlesis weak there is a bigger increase in the internal frictionangle and a smaller increase in the cohesionThe mechanicalproperties of the outwash deposit are much closer to theelastic-plastic debris

42 The Influence of the Aggregate Size As shown in Fig-ure 15 the larger the size of stone blocks is the smaller thepeak strength is This situation can be interpreted by theperimeter ratio which is defined as the ratio of all boundariesrsquoperimeters of stone blocks and themodel areaThe perimeterratio under the same stone ratio varies greatly The smalleraggregate size has more stone blocks so the perimeter ratiowill reach a high level and form larger contact areas Thecompressive strength also increases When the number ofstone blocks increases the contact area of the debris and stoneblocks and the interaction force between the debris and the

10 Advances in Materials Science and Engineering

(a) Crk num = 0 (b) Crk num = 39

(c) Crk num = 189 (d) Crk num = 563

Figure 13 The damage of outwash deposits with different stone block content (a) shows a model with the initial content rate of stone block40 (b) shows the cracks which first appear between some blocks (c) shows fracture development among the boundary of stone blocks and(d) shows the damaged outwash deposits

stone blocks will increase which just explains the reason whythe macromechanical properties of the outwash deposit areimproved with the number of stone blocks

43 The Influence of the Stone Block Content As shown inFigure 16 when there are few stone blocks in the outwashdeposit the debris-debris contact between particles willbe the main contact type The existence of stone blocksleads to the concentration of stress along their boundarieswhich can aggravate the debris contacts to damage the peakcompressive strength keeps close to the pure debriswith slightfluctuation Meanwhile due to the stress concentration theoutwash deposits become more brittle The shear strength isdecreased Many experiments show that when the contentof stone blocks is less than 25 the characteristic is moreclose to pure debris By contrast when the content of stoneblocks is greater than 25 there is not only debris-stonecontact in the outwash deposits but also stone-stone contact

The compressive and shear strengths are improved Whenthe content of stone blocks is more than 50 the maincontact type in the outwash deposits is stone-stone Themechanical properties are better in stone-filledmaterialsThecompressive and shear strengths are significantly improved inthe stone-filled materials

However when the stress-strain curves enter the residualstrength stage there is an obvious fluctuation after the peakof the curve the amplitude of which is related to the size andcontent ratio of stone blocks so in order to study the macro-shear strength the peak value of stress-strain curves is usedto calculate shear property

44 The Macroparameter Analysis of the Outwash DepositsIn terms of the stress-strain curves for any content rateof stone block cementation strength and block size themajor factor that influences the mechanical properties of the

Advances in Materials Science and Engineering 11

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

n bond = s bond = 0Nn bond = s bond = 1000N

n bond = s bond = 2000Nn bond = s bond = 3000N

Figure 14 The biaxial compression curves with different debris bonding force

Stone average size = 1 cmStone average size = 3 cm

Stone average size = 5 cmStone average size = 7 cm

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

Figure 15 The biaxial compression curves with different averagesizes of stone blocks

Stone content = 10

Stone content = 20Stone content = 30

Stone content = 40

Stone content = 50

Stone content = 60Stone content = 70

1400

1200

1000

800

600

400

200

0000 002 004 006 008 01 012

(1205901minus1205903) (

MPa

)

1205761

Figure 16The biaxial compression curve with different stone blockcontents

The content of stone blocks ()

The p

eak

com

pres

sive s

treng

th (M

Pa) 1600

1400

1200

1000

800

600

400

200

0000 10 20 30 40 50 60 70 80

Figure 17The peak compressive strength with different stone blockcontents

outwash deposits can be attributed to the dominant contacttype which is defined as the ratio of some particle contactnumber and total contact number in numerical models Theparticle contact can be divided into three kinds respectivelythe debris-debris debris-stone or stone-stone contact

If ratio of stone block is high enough to make stone-stonecontact becoming dominant contact type the characteristicof outwash deposit is close to rockfill For the naturemediumseveral kinds of contacts exist at that time which will affectthe comprehensive mechanical property greatly Althoughthe different geometries and distributions also affect themechanical properties the content of stone blocks is thedecisive factor For the different stone block contents thepeak strength under the confining pressure of 15MPa canbe calculated approximately using formula (12) as a cubicparabola curve (shown in Figure 17)

119875119896= 141841205723 minus 90441205722 + 1600120572 + 02894 (12)

where 120572 is the content ratio of stone blocks and 119875119896is the peak

strengthIt should be noted that the compressive strength of the

outwash deposit increases slowly when content ratio of stone

12 Advances in Materials Science and Engineering

Stone block ()

Inte

rnal

fric

tion

angl

e (∘

)40

36

32

28

24

200 10 20 30 40 50 60 70 80

(a)

20

40

60

80

100

120

140

160

180

0 20 40 60 80Stone block ()

Incr

emen

tal c

ohes

ion

(MPa

)

(b)

Figure 18 Changes of shear strength of outwash deposits with different contents and distributions of stone blocks (a) shows changes of theinternal friction of outwash deposit (b) shows changes of the cohesion of outwash deposit

blocks lies between 25 and 50 Once the content of stoneblocks is greater than 50 the stone-stone contact becomesthe dominant factor which causes the compressive strengthto increase sharply The internal friction angle versus thestone block content can be described using three stages asshown below

120593 =

18093931205722 minus 495165120572 + 265026 120572 lt 25194271120572 + 221719 25 lt 120572 lt 50234286120572 + 191429 120572 gt 50

(13)

where 120593 is the internal friction angle of the outwash depositand 120572 is the stone block content

Furthermore it can be observed from Figure 18(a) thatthe fluctuation of the internal friction angle is approximately0sim8∘ for the same stone blocks content which agrees withthe fluctuations in the stress-strain curves By contrast thecohesion of outwash deposit increases clearly with the stoneblock content due to the interaction force between stoneblocks as shown in Figure 18(b) The amplitude of variationwill increase significantly with the content of stone blocksHowever it is usually difficult to quantify the amplitude dueto roughness size characteristic of stone block and so on

Therefore for outwash deposits with extremely unevenshapes and distributions of stones the compressive strengthand shear strength are primarily controlled by the stone blockcontent The randomness of the stone block distributionscauses large deviations in the mechanical parameters Forexample the internal friction angle may have a large fluctua-tion at the same stone block content This feature is the causeof the poor results of the geotechnical experiments

5 Discussions

Outwash deposits are a type of debris-stone mixture Themechanical properties of these deposits are affected by thecomposition of the debris and stone blocks As the debriscementation increases the compressive strength increasesHowever the internal friction angle has a negative correlation

with the cementation force The stone block content is thedecisive factor for the mechanical properties of outwashdepositsThe randomness of the structural composition leadsto significant fluctuations in the properties which also createslarge discrepancies in the mechanical parameters

The major influences of the particle sizes geometricdistribution and stone block content are to determine thecontact type in the outwash deposits When the debris-debris contact is the dominant contact type there is littleinfluence from the stone blocks on the mechanical propertiesof the outwash depositsWhen the debris-stone contact is thedominant contact type the stone block content has a positiveinfluence on the compressive and shear strengths When thestone-stone contact is the dominant contact type the roles ofthe debris and stone blocks are reversed and the properties ofthe outwash deposits aremuch closer to a rock-filledmaterial

Although it is difficult to determine the mechanicalparameters of an outwash deposit using indoor experimentsthe properties of the medium can still be researched usingindirect approachesThemechanical parameters of the debrisand stone blocks can be determined from the indoor experi-ments Then the biaxial compression numerical experimentusing the granular discrete element method can be carriedout to analyse the influence of the stone blocks on theproperties of outwash deposits which makes up for thelimitation that the indoor experiments cannot consider thelarge stone blocks and offers a beneficial supplement to aid inthe geological parameter determination

6 Conclusions

According to the grain size and shape statistics from fieldstatistics the numerical granular discrete elementmodel withrandomised generation of stone blocks can be used withhypothesis that the length of the long axis and the axial ratioall follow normal distributions and the azimuth of the longaxis follows uniformdistribution in 0sim360∘The relationshipsbetween the macro- and micromechanical parameters arediscussed and the mechanical behaviour of the outwash

Advances in Materials Science and Engineering 13

deposit is affected by the cementation strength the size ofstone blocks the stone block content and the distribution ofthe stone blocks These properties are analysed so that theycan be better understood by the geologists working on thedemocratisation of the Engineering Project

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (no 51309089 and no 51379065)the National Key Technology RampD Program (no2013BAB06B00) the National Basic Research Programof China (973 Program) (no 2015CB057903) the NaturalScience Foundation of Jiangsu Province (no BK20130846)and the Fundamental Research Funds for the CentralUniversities (no 2014B04914)

References

[1] W G Holtz and H J Gibbs ldquoTriaxial shear tests on perviousgravelly soilsrdquo Journal of the Soil Mechanics and FoundationsDivision vol 82 no 1 pp 1ndash22 1956

[2] R J Chandler ldquoThe inclination of Talus Arctic Talus Terracesand other slopes composed of granular materialsrdquo The Journalof Geology vol 81 no 1 pp 1ndash14 1973

[3] X H You Stochastic structural model of the earth-rock aggregateand its application [PhD thesis] Beijing Jiaotong UniversityBeijing China 2001

[4] X H You and J S Tang ldquoResearch on horizontal push-shearin-situ test of debris and rock-mixturerdquo Chinese Journal of RockMechanics and Engineering vol 21 no 10 pp 1537ndash1540 2002

[5] X H You G He and X Li ldquoMicro-handling technologyof earth-rock aggregate sloperdquo Hydrogeology and EngineeringGeology vol 30 no 1 pp 18ndash21 2003

[6] J M He Study of deformation and failure mechanisms of rock-debris aggregate in three gorges reservoir area [PhD thesis]China University of Mining and Technology Beijing China2004

[7] X Li Q L Liao J M He and J Chen ldquoStudy on in-situ testsof mechanical characteristics on soil-rock aggregaterdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 12 pp2377ndash2384 2007

[8] T Lebourg J Riss and E Pirard ldquoInfluence of morphologicalcharacteristics of heterogeneous moraine formations on theirmechanical behaviour using image and statistical analysisrdquoEngineering Geology vol 73 no 1-2 pp 37ndash50 2004

[9] T R Reid and J P Harrison ldquoA semi-automated methodologyfor discontinuity trace detection in digital images of rock massexposuresrdquo International Journal of Rock Mechanics andMiningSciences vol 37 no 7 pp 1073ndash1089 2000

[10] Z Q Yue S Chen and L G Tham ldquoFinite element modelingof geomaterials using digital image processingrdquo Computers andGeotechnics vol 30 no 5 pp 375ndash397 2003

[11] Z Q Yue S Chen H Zheng and G H Tang ldquoDigital imageproceeding based on finite element method for geomaterialsrdquo

Chinese Journal of Rock Mechanics and Engineering vol 23 no6 pp 889ndash897 2004

[12] Q L Liao X Li W C Zhu and J S Liu ldquoStructure modelconstruction of rock and soil aggregate based on digital imagetechnology and its numerical simulation on mechanical struc-ture effectsrdquoChinese Journal of RockMechanics and Engineeringvol 29 no 1 pp 155ndash162 2010

[13] W J Xu R L Hu Z Q Yue and R J Tan ldquoMesostructuralcharacter and numerical simulation of mechanical propertiesof soil-rock mixturesrdquo Chinese Journal of Rock Mechanics andEngineering vol 26 no 2 pp 300ndash311 2007

[14] W J Xu Z Q Yue and R L Hu ldquoA current status of digitalimage based quantitative analysis of internal structures ofdebris rock and concretes and associated numerical simula-tionrdquo Journal of Engineering Geology vol 15 no 3 pp 289ndash3132007

[15] W J Xu R L Hu Z Q Yue R Zhang and G L WangldquoResearch on relationship between rock block proportion andshear strength of soil-rock mixtures based on digital imageanalysis and large direct shear testrdquo Chinese Journal of RockMechanics and Engineering vol 27 no 5 pp 996ndash1007 2008

[16] P A Cundall and O D L Strack ldquoA discrete numerical modelfor granular assembliesrdquo Geotechnique vol 29 no 1 pp 47ndash651979

[17] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) (Version 31) Itasca Consulting Group Minneapo-lis Minn USA 2004

[18] J Yoon ldquoApplication of experimental design and optimizationto PFC model calibration in uniaxial compression simulationrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 6 pp 871ndash889 2007

[19] Y C Wang and P Mora ldquoMacroscopic elastic properties ofregular latticesrdquo Journal of the Mechanics and Physics of Solidsvol 56 no 12 pp 3459ndash3474 2008

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

10 Advances in Materials Science and Engineering

(a) Crk num = 0 (b) Crk num = 39

(c) Crk num = 189 (d) Crk num = 563

Figure 13 The damage of outwash deposits with different stone block content (a) shows a model with the initial content rate of stone block40 (b) shows the cracks which first appear between some blocks (c) shows fracture development among the boundary of stone blocks and(d) shows the damaged outwash deposits

stone blocks will increase which just explains the reason whythe macromechanical properties of the outwash deposit areimproved with the number of stone blocks

43 The Influence of the Stone Block Content As shown inFigure 16 when there are few stone blocks in the outwashdeposit the debris-debris contact between particles willbe the main contact type The existence of stone blocksleads to the concentration of stress along their boundarieswhich can aggravate the debris contacts to damage the peakcompressive strength keeps close to the pure debriswith slightfluctuation Meanwhile due to the stress concentration theoutwash deposits become more brittle The shear strength isdecreased Many experiments show that when the contentof stone blocks is less than 25 the characteristic is moreclose to pure debris By contrast when the content of stoneblocks is greater than 25 there is not only debris-stonecontact in the outwash deposits but also stone-stone contact

The compressive and shear strengths are improved Whenthe content of stone blocks is more than 50 the maincontact type in the outwash deposits is stone-stone Themechanical properties are better in stone-filledmaterialsThecompressive and shear strengths are significantly improved inthe stone-filled materials

However when the stress-strain curves enter the residualstrength stage there is an obvious fluctuation after the peakof the curve the amplitude of which is related to the size andcontent ratio of stone blocks so in order to study the macro-shear strength the peak value of stress-strain curves is usedto calculate shear property

44 The Macroparameter Analysis of the Outwash DepositsIn terms of the stress-strain curves for any content rateof stone block cementation strength and block size themajor factor that influences the mechanical properties of the

Advances in Materials Science and Engineering 11

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

n bond = s bond = 0Nn bond = s bond = 1000N

n bond = s bond = 2000Nn bond = s bond = 3000N

Figure 14 The biaxial compression curves with different debris bonding force

Stone average size = 1 cmStone average size = 3 cm

Stone average size = 5 cmStone average size = 7 cm

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

Figure 15 The biaxial compression curves with different averagesizes of stone blocks

Stone content = 10

Stone content = 20Stone content = 30

Stone content = 40

Stone content = 50

Stone content = 60Stone content = 70

1400

1200

1000

800

600

400

200

0000 002 004 006 008 01 012

(1205901minus1205903) (

MPa

)

1205761

Figure 16The biaxial compression curve with different stone blockcontents

The content of stone blocks ()

The p

eak

com

pres

sive s

treng

th (M

Pa) 1600

1400

1200

1000

800

600

400

200

0000 10 20 30 40 50 60 70 80

Figure 17The peak compressive strength with different stone blockcontents

outwash deposits can be attributed to the dominant contacttype which is defined as the ratio of some particle contactnumber and total contact number in numerical models Theparticle contact can be divided into three kinds respectivelythe debris-debris debris-stone or stone-stone contact

If ratio of stone block is high enough to make stone-stonecontact becoming dominant contact type the characteristicof outwash deposit is close to rockfill For the naturemediumseveral kinds of contacts exist at that time which will affectthe comprehensive mechanical property greatly Althoughthe different geometries and distributions also affect themechanical properties the content of stone blocks is thedecisive factor For the different stone block contents thepeak strength under the confining pressure of 15MPa canbe calculated approximately using formula (12) as a cubicparabola curve (shown in Figure 17)

119875119896= 141841205723 minus 90441205722 + 1600120572 + 02894 (12)

where 120572 is the content ratio of stone blocks and 119875119896is the peak

strengthIt should be noted that the compressive strength of the

outwash deposit increases slowly when content ratio of stone

12 Advances in Materials Science and Engineering

Stone block ()

Inte

rnal

fric

tion

angl

e (∘

)40

36

32

28

24

200 10 20 30 40 50 60 70 80

(a)

20

40

60

80

100

120

140

160

180

0 20 40 60 80Stone block ()

Incr

emen

tal c

ohes

ion

(MPa

)

(b)

Figure 18 Changes of shear strength of outwash deposits with different contents and distributions of stone blocks (a) shows changes of theinternal friction of outwash deposit (b) shows changes of the cohesion of outwash deposit

blocks lies between 25 and 50 Once the content of stoneblocks is greater than 50 the stone-stone contact becomesthe dominant factor which causes the compressive strengthto increase sharply The internal friction angle versus thestone block content can be described using three stages asshown below

120593 =

18093931205722 minus 495165120572 + 265026 120572 lt 25194271120572 + 221719 25 lt 120572 lt 50234286120572 + 191429 120572 gt 50

(13)

where 120593 is the internal friction angle of the outwash depositand 120572 is the stone block content

Furthermore it can be observed from Figure 18(a) thatthe fluctuation of the internal friction angle is approximately0sim8∘ for the same stone blocks content which agrees withthe fluctuations in the stress-strain curves By contrast thecohesion of outwash deposit increases clearly with the stoneblock content due to the interaction force between stoneblocks as shown in Figure 18(b) The amplitude of variationwill increase significantly with the content of stone blocksHowever it is usually difficult to quantify the amplitude dueto roughness size characteristic of stone block and so on

Therefore for outwash deposits with extremely unevenshapes and distributions of stones the compressive strengthand shear strength are primarily controlled by the stone blockcontent The randomness of the stone block distributionscauses large deviations in the mechanical parameters Forexample the internal friction angle may have a large fluctua-tion at the same stone block content This feature is the causeof the poor results of the geotechnical experiments

5 Discussions

Outwash deposits are a type of debris-stone mixture Themechanical properties of these deposits are affected by thecomposition of the debris and stone blocks As the debriscementation increases the compressive strength increasesHowever the internal friction angle has a negative correlation

with the cementation force The stone block content is thedecisive factor for the mechanical properties of outwashdepositsThe randomness of the structural composition leadsto significant fluctuations in the properties which also createslarge discrepancies in the mechanical parameters

The major influences of the particle sizes geometricdistribution and stone block content are to determine thecontact type in the outwash deposits When the debris-debris contact is the dominant contact type there is littleinfluence from the stone blocks on the mechanical propertiesof the outwash depositsWhen the debris-stone contact is thedominant contact type the stone block content has a positiveinfluence on the compressive and shear strengths When thestone-stone contact is the dominant contact type the roles ofthe debris and stone blocks are reversed and the properties ofthe outwash deposits aremuch closer to a rock-filledmaterial

Although it is difficult to determine the mechanicalparameters of an outwash deposit using indoor experimentsthe properties of the medium can still be researched usingindirect approachesThemechanical parameters of the debrisand stone blocks can be determined from the indoor experi-ments Then the biaxial compression numerical experimentusing the granular discrete element method can be carriedout to analyse the influence of the stone blocks on theproperties of outwash deposits which makes up for thelimitation that the indoor experiments cannot consider thelarge stone blocks and offers a beneficial supplement to aid inthe geological parameter determination

6 Conclusions

According to the grain size and shape statistics from fieldstatistics the numerical granular discrete elementmodel withrandomised generation of stone blocks can be used withhypothesis that the length of the long axis and the axial ratioall follow normal distributions and the azimuth of the longaxis follows uniformdistribution in 0sim360∘The relationshipsbetween the macro- and micromechanical parameters arediscussed and the mechanical behaviour of the outwash

Advances in Materials Science and Engineering 13

deposit is affected by the cementation strength the size ofstone blocks the stone block content and the distribution ofthe stone blocks These properties are analysed so that theycan be better understood by the geologists working on thedemocratisation of the Engineering Project

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (no 51309089 and no 51379065)the National Key Technology RampD Program (no2013BAB06B00) the National Basic Research Programof China (973 Program) (no 2015CB057903) the NaturalScience Foundation of Jiangsu Province (no BK20130846)and the Fundamental Research Funds for the CentralUniversities (no 2014B04914)

References

[1] W G Holtz and H J Gibbs ldquoTriaxial shear tests on perviousgravelly soilsrdquo Journal of the Soil Mechanics and FoundationsDivision vol 82 no 1 pp 1ndash22 1956

[2] R J Chandler ldquoThe inclination of Talus Arctic Talus Terracesand other slopes composed of granular materialsrdquo The Journalof Geology vol 81 no 1 pp 1ndash14 1973

[3] X H You Stochastic structural model of the earth-rock aggregateand its application [PhD thesis] Beijing Jiaotong UniversityBeijing China 2001

[4] X H You and J S Tang ldquoResearch on horizontal push-shearin-situ test of debris and rock-mixturerdquo Chinese Journal of RockMechanics and Engineering vol 21 no 10 pp 1537ndash1540 2002

[5] X H You G He and X Li ldquoMicro-handling technologyof earth-rock aggregate sloperdquo Hydrogeology and EngineeringGeology vol 30 no 1 pp 18ndash21 2003

[6] J M He Study of deformation and failure mechanisms of rock-debris aggregate in three gorges reservoir area [PhD thesis]China University of Mining and Technology Beijing China2004

[7] X Li Q L Liao J M He and J Chen ldquoStudy on in-situ testsof mechanical characteristics on soil-rock aggregaterdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 12 pp2377ndash2384 2007

[8] T Lebourg J Riss and E Pirard ldquoInfluence of morphologicalcharacteristics of heterogeneous moraine formations on theirmechanical behaviour using image and statistical analysisrdquoEngineering Geology vol 73 no 1-2 pp 37ndash50 2004

[9] T R Reid and J P Harrison ldquoA semi-automated methodologyfor discontinuity trace detection in digital images of rock massexposuresrdquo International Journal of Rock Mechanics andMiningSciences vol 37 no 7 pp 1073ndash1089 2000

[10] Z Q Yue S Chen and L G Tham ldquoFinite element modelingof geomaterials using digital image processingrdquo Computers andGeotechnics vol 30 no 5 pp 375ndash397 2003

[11] Z Q Yue S Chen H Zheng and G H Tang ldquoDigital imageproceeding based on finite element method for geomaterialsrdquo

Chinese Journal of Rock Mechanics and Engineering vol 23 no6 pp 889ndash897 2004

[12] Q L Liao X Li W C Zhu and J S Liu ldquoStructure modelconstruction of rock and soil aggregate based on digital imagetechnology and its numerical simulation on mechanical struc-ture effectsrdquoChinese Journal of RockMechanics and Engineeringvol 29 no 1 pp 155ndash162 2010

[13] W J Xu R L Hu Z Q Yue and R J Tan ldquoMesostructuralcharacter and numerical simulation of mechanical propertiesof soil-rock mixturesrdquo Chinese Journal of Rock Mechanics andEngineering vol 26 no 2 pp 300ndash311 2007

[14] W J Xu Z Q Yue and R L Hu ldquoA current status of digitalimage based quantitative analysis of internal structures ofdebris rock and concretes and associated numerical simula-tionrdquo Journal of Engineering Geology vol 15 no 3 pp 289ndash3132007

[15] W J Xu R L Hu Z Q Yue R Zhang and G L WangldquoResearch on relationship between rock block proportion andshear strength of soil-rock mixtures based on digital imageanalysis and large direct shear testrdquo Chinese Journal of RockMechanics and Engineering vol 27 no 5 pp 996ndash1007 2008

[16] P A Cundall and O D L Strack ldquoA discrete numerical modelfor granular assembliesrdquo Geotechnique vol 29 no 1 pp 47ndash651979

[17] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) (Version 31) Itasca Consulting Group Minneapo-lis Minn USA 2004

[18] J Yoon ldquoApplication of experimental design and optimizationto PFC model calibration in uniaxial compression simulationrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 6 pp 871ndash889 2007

[19] Y C Wang and P Mora ldquoMacroscopic elastic properties ofregular latticesrdquo Journal of the Mechanics and Physics of Solidsvol 56 no 12 pp 3459ndash3474 2008

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 11

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

n bond = s bond = 0Nn bond = s bond = 1000N

n bond = s bond = 2000Nn bond = s bond = 3000N

Figure 14 The biaxial compression curves with different debris bonding force

Stone average size = 1 cmStone average size = 3 cm

Stone average size = 5 cmStone average size = 7 cm

(1205901minus1205903) (

MPa

)

180

160

140

120

100

080

060

040

020

0000 001 002 003 004 005 006

1205761

Figure 15 The biaxial compression curves with different averagesizes of stone blocks

Stone content = 10

Stone content = 20Stone content = 30

Stone content = 40

Stone content = 50

Stone content = 60Stone content = 70

1400

1200

1000

800

600

400

200

0000 002 004 006 008 01 012

(1205901minus1205903) (

MPa

)

1205761

Figure 16The biaxial compression curve with different stone blockcontents

The content of stone blocks ()

The p

eak

com

pres

sive s

treng

th (M

Pa) 1600

1400

1200

1000

800

600

400

200

0000 10 20 30 40 50 60 70 80

Figure 17The peak compressive strength with different stone blockcontents

outwash deposits can be attributed to the dominant contacttype which is defined as the ratio of some particle contactnumber and total contact number in numerical models Theparticle contact can be divided into three kinds respectivelythe debris-debris debris-stone or stone-stone contact

If ratio of stone block is high enough to make stone-stonecontact becoming dominant contact type the characteristicof outwash deposit is close to rockfill For the naturemediumseveral kinds of contacts exist at that time which will affectthe comprehensive mechanical property greatly Althoughthe different geometries and distributions also affect themechanical properties the content of stone blocks is thedecisive factor For the different stone block contents thepeak strength under the confining pressure of 15MPa canbe calculated approximately using formula (12) as a cubicparabola curve (shown in Figure 17)

119875119896= 141841205723 minus 90441205722 + 1600120572 + 02894 (12)

where 120572 is the content ratio of stone blocks and 119875119896is the peak

strengthIt should be noted that the compressive strength of the

outwash deposit increases slowly when content ratio of stone

12 Advances in Materials Science and Engineering

Stone block ()

Inte

rnal

fric

tion

angl

e (∘

)40

36

32

28

24

200 10 20 30 40 50 60 70 80

(a)

20

40

60

80

100

120

140

160

180

0 20 40 60 80Stone block ()

Incr

emen

tal c

ohes

ion

(MPa

)

(b)

Figure 18 Changes of shear strength of outwash deposits with different contents and distributions of stone blocks (a) shows changes of theinternal friction of outwash deposit (b) shows changes of the cohesion of outwash deposit

blocks lies between 25 and 50 Once the content of stoneblocks is greater than 50 the stone-stone contact becomesthe dominant factor which causes the compressive strengthto increase sharply The internal friction angle versus thestone block content can be described using three stages asshown below

120593 =

18093931205722 minus 495165120572 + 265026 120572 lt 25194271120572 + 221719 25 lt 120572 lt 50234286120572 + 191429 120572 gt 50

(13)

where 120593 is the internal friction angle of the outwash depositand 120572 is the stone block content

Furthermore it can be observed from Figure 18(a) thatthe fluctuation of the internal friction angle is approximately0sim8∘ for the same stone blocks content which agrees withthe fluctuations in the stress-strain curves By contrast thecohesion of outwash deposit increases clearly with the stoneblock content due to the interaction force between stoneblocks as shown in Figure 18(b) The amplitude of variationwill increase significantly with the content of stone blocksHowever it is usually difficult to quantify the amplitude dueto roughness size characteristic of stone block and so on

Therefore for outwash deposits with extremely unevenshapes and distributions of stones the compressive strengthand shear strength are primarily controlled by the stone blockcontent The randomness of the stone block distributionscauses large deviations in the mechanical parameters Forexample the internal friction angle may have a large fluctua-tion at the same stone block content This feature is the causeof the poor results of the geotechnical experiments

5 Discussions

Outwash deposits are a type of debris-stone mixture Themechanical properties of these deposits are affected by thecomposition of the debris and stone blocks As the debriscementation increases the compressive strength increasesHowever the internal friction angle has a negative correlation

with the cementation force The stone block content is thedecisive factor for the mechanical properties of outwashdepositsThe randomness of the structural composition leadsto significant fluctuations in the properties which also createslarge discrepancies in the mechanical parameters

The major influences of the particle sizes geometricdistribution and stone block content are to determine thecontact type in the outwash deposits When the debris-debris contact is the dominant contact type there is littleinfluence from the stone blocks on the mechanical propertiesof the outwash depositsWhen the debris-stone contact is thedominant contact type the stone block content has a positiveinfluence on the compressive and shear strengths When thestone-stone contact is the dominant contact type the roles ofthe debris and stone blocks are reversed and the properties ofthe outwash deposits aremuch closer to a rock-filledmaterial

Although it is difficult to determine the mechanicalparameters of an outwash deposit using indoor experimentsthe properties of the medium can still be researched usingindirect approachesThemechanical parameters of the debrisand stone blocks can be determined from the indoor experi-ments Then the biaxial compression numerical experimentusing the granular discrete element method can be carriedout to analyse the influence of the stone blocks on theproperties of outwash deposits which makes up for thelimitation that the indoor experiments cannot consider thelarge stone blocks and offers a beneficial supplement to aid inthe geological parameter determination

6 Conclusions

According to the grain size and shape statistics from fieldstatistics the numerical granular discrete elementmodel withrandomised generation of stone blocks can be used withhypothesis that the length of the long axis and the axial ratioall follow normal distributions and the azimuth of the longaxis follows uniformdistribution in 0sim360∘The relationshipsbetween the macro- and micromechanical parameters arediscussed and the mechanical behaviour of the outwash

Advances in Materials Science and Engineering 13

deposit is affected by the cementation strength the size ofstone blocks the stone block content and the distribution ofthe stone blocks These properties are analysed so that theycan be better understood by the geologists working on thedemocratisation of the Engineering Project

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (no 51309089 and no 51379065)the National Key Technology RampD Program (no2013BAB06B00) the National Basic Research Programof China (973 Program) (no 2015CB057903) the NaturalScience Foundation of Jiangsu Province (no BK20130846)and the Fundamental Research Funds for the CentralUniversities (no 2014B04914)

References

[1] W G Holtz and H J Gibbs ldquoTriaxial shear tests on perviousgravelly soilsrdquo Journal of the Soil Mechanics and FoundationsDivision vol 82 no 1 pp 1ndash22 1956

[2] R J Chandler ldquoThe inclination of Talus Arctic Talus Terracesand other slopes composed of granular materialsrdquo The Journalof Geology vol 81 no 1 pp 1ndash14 1973

[3] X H You Stochastic structural model of the earth-rock aggregateand its application [PhD thesis] Beijing Jiaotong UniversityBeijing China 2001

[4] X H You and J S Tang ldquoResearch on horizontal push-shearin-situ test of debris and rock-mixturerdquo Chinese Journal of RockMechanics and Engineering vol 21 no 10 pp 1537ndash1540 2002

[5] X H You G He and X Li ldquoMicro-handling technologyof earth-rock aggregate sloperdquo Hydrogeology and EngineeringGeology vol 30 no 1 pp 18ndash21 2003

[6] J M He Study of deformation and failure mechanisms of rock-debris aggregate in three gorges reservoir area [PhD thesis]China University of Mining and Technology Beijing China2004

[7] X Li Q L Liao J M He and J Chen ldquoStudy on in-situ testsof mechanical characteristics on soil-rock aggregaterdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 12 pp2377ndash2384 2007

[8] T Lebourg J Riss and E Pirard ldquoInfluence of morphologicalcharacteristics of heterogeneous moraine formations on theirmechanical behaviour using image and statistical analysisrdquoEngineering Geology vol 73 no 1-2 pp 37ndash50 2004

[9] T R Reid and J P Harrison ldquoA semi-automated methodologyfor discontinuity trace detection in digital images of rock massexposuresrdquo International Journal of Rock Mechanics andMiningSciences vol 37 no 7 pp 1073ndash1089 2000

[10] Z Q Yue S Chen and L G Tham ldquoFinite element modelingof geomaterials using digital image processingrdquo Computers andGeotechnics vol 30 no 5 pp 375ndash397 2003

[11] Z Q Yue S Chen H Zheng and G H Tang ldquoDigital imageproceeding based on finite element method for geomaterialsrdquo

Chinese Journal of Rock Mechanics and Engineering vol 23 no6 pp 889ndash897 2004

[12] Q L Liao X Li W C Zhu and J S Liu ldquoStructure modelconstruction of rock and soil aggregate based on digital imagetechnology and its numerical simulation on mechanical struc-ture effectsrdquoChinese Journal of RockMechanics and Engineeringvol 29 no 1 pp 155ndash162 2010

[13] W J Xu R L Hu Z Q Yue and R J Tan ldquoMesostructuralcharacter and numerical simulation of mechanical propertiesof soil-rock mixturesrdquo Chinese Journal of Rock Mechanics andEngineering vol 26 no 2 pp 300ndash311 2007

[14] W J Xu Z Q Yue and R L Hu ldquoA current status of digitalimage based quantitative analysis of internal structures ofdebris rock and concretes and associated numerical simula-tionrdquo Journal of Engineering Geology vol 15 no 3 pp 289ndash3132007

[15] W J Xu R L Hu Z Q Yue R Zhang and G L WangldquoResearch on relationship between rock block proportion andshear strength of soil-rock mixtures based on digital imageanalysis and large direct shear testrdquo Chinese Journal of RockMechanics and Engineering vol 27 no 5 pp 996ndash1007 2008

[16] P A Cundall and O D L Strack ldquoA discrete numerical modelfor granular assembliesrdquo Geotechnique vol 29 no 1 pp 47ndash651979

[17] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) (Version 31) Itasca Consulting Group Minneapo-lis Minn USA 2004

[18] J Yoon ldquoApplication of experimental design and optimizationto PFC model calibration in uniaxial compression simulationrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 6 pp 871ndash889 2007

[19] Y C Wang and P Mora ldquoMacroscopic elastic properties ofregular latticesrdquo Journal of the Mechanics and Physics of Solidsvol 56 no 12 pp 3459ndash3474 2008

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

12 Advances in Materials Science and Engineering

Stone block ()

Inte

rnal

fric

tion

angl

e (∘

)40

36

32

28

24

200 10 20 30 40 50 60 70 80

(a)

20

40

60

80

100

120

140

160

180

0 20 40 60 80Stone block ()

Incr

emen

tal c

ohes

ion

(MPa

)

(b)

Figure 18 Changes of shear strength of outwash deposits with different contents and distributions of stone blocks (a) shows changes of theinternal friction of outwash deposit (b) shows changes of the cohesion of outwash deposit

blocks lies between 25 and 50 Once the content of stoneblocks is greater than 50 the stone-stone contact becomesthe dominant factor which causes the compressive strengthto increase sharply The internal friction angle versus thestone block content can be described using three stages asshown below

120593 =

18093931205722 minus 495165120572 + 265026 120572 lt 25194271120572 + 221719 25 lt 120572 lt 50234286120572 + 191429 120572 gt 50

(13)

where 120593 is the internal friction angle of the outwash depositand 120572 is the stone block content

Furthermore it can be observed from Figure 18(a) thatthe fluctuation of the internal friction angle is approximately0sim8∘ for the same stone blocks content which agrees withthe fluctuations in the stress-strain curves By contrast thecohesion of outwash deposit increases clearly with the stoneblock content due to the interaction force between stoneblocks as shown in Figure 18(b) The amplitude of variationwill increase significantly with the content of stone blocksHowever it is usually difficult to quantify the amplitude dueto roughness size characteristic of stone block and so on

Therefore for outwash deposits with extremely unevenshapes and distributions of stones the compressive strengthand shear strength are primarily controlled by the stone blockcontent The randomness of the stone block distributionscauses large deviations in the mechanical parameters Forexample the internal friction angle may have a large fluctua-tion at the same stone block content This feature is the causeof the poor results of the geotechnical experiments

5 Discussions

Outwash deposits are a type of debris-stone mixture Themechanical properties of these deposits are affected by thecomposition of the debris and stone blocks As the debriscementation increases the compressive strength increasesHowever the internal friction angle has a negative correlation

with the cementation force The stone block content is thedecisive factor for the mechanical properties of outwashdepositsThe randomness of the structural composition leadsto significant fluctuations in the properties which also createslarge discrepancies in the mechanical parameters

The major influences of the particle sizes geometricdistribution and stone block content are to determine thecontact type in the outwash deposits When the debris-debris contact is the dominant contact type there is littleinfluence from the stone blocks on the mechanical propertiesof the outwash depositsWhen the debris-stone contact is thedominant contact type the stone block content has a positiveinfluence on the compressive and shear strengths When thestone-stone contact is the dominant contact type the roles ofthe debris and stone blocks are reversed and the properties ofthe outwash deposits aremuch closer to a rock-filledmaterial

Although it is difficult to determine the mechanicalparameters of an outwash deposit using indoor experimentsthe properties of the medium can still be researched usingindirect approachesThemechanical parameters of the debrisand stone blocks can be determined from the indoor experi-ments Then the biaxial compression numerical experimentusing the granular discrete element method can be carriedout to analyse the influence of the stone blocks on theproperties of outwash deposits which makes up for thelimitation that the indoor experiments cannot consider thelarge stone blocks and offers a beneficial supplement to aid inthe geological parameter determination

6 Conclusions

According to the grain size and shape statistics from fieldstatistics the numerical granular discrete elementmodel withrandomised generation of stone blocks can be used withhypothesis that the length of the long axis and the axial ratioall follow normal distributions and the azimuth of the longaxis follows uniformdistribution in 0sim360∘The relationshipsbetween the macro- and micromechanical parameters arediscussed and the mechanical behaviour of the outwash

Advances in Materials Science and Engineering 13

deposit is affected by the cementation strength the size ofstone blocks the stone block content and the distribution ofthe stone blocks These properties are analysed so that theycan be better understood by the geologists working on thedemocratisation of the Engineering Project

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (no 51309089 and no 51379065)the National Key Technology RampD Program (no2013BAB06B00) the National Basic Research Programof China (973 Program) (no 2015CB057903) the NaturalScience Foundation of Jiangsu Province (no BK20130846)and the Fundamental Research Funds for the CentralUniversities (no 2014B04914)

References

[1] W G Holtz and H J Gibbs ldquoTriaxial shear tests on perviousgravelly soilsrdquo Journal of the Soil Mechanics and FoundationsDivision vol 82 no 1 pp 1ndash22 1956

[2] R J Chandler ldquoThe inclination of Talus Arctic Talus Terracesand other slopes composed of granular materialsrdquo The Journalof Geology vol 81 no 1 pp 1ndash14 1973

[3] X H You Stochastic structural model of the earth-rock aggregateand its application [PhD thesis] Beijing Jiaotong UniversityBeijing China 2001

[4] X H You and J S Tang ldquoResearch on horizontal push-shearin-situ test of debris and rock-mixturerdquo Chinese Journal of RockMechanics and Engineering vol 21 no 10 pp 1537ndash1540 2002

[5] X H You G He and X Li ldquoMicro-handling technologyof earth-rock aggregate sloperdquo Hydrogeology and EngineeringGeology vol 30 no 1 pp 18ndash21 2003

[6] J M He Study of deformation and failure mechanisms of rock-debris aggregate in three gorges reservoir area [PhD thesis]China University of Mining and Technology Beijing China2004

[7] X Li Q L Liao J M He and J Chen ldquoStudy on in-situ testsof mechanical characteristics on soil-rock aggregaterdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 12 pp2377ndash2384 2007

[8] T Lebourg J Riss and E Pirard ldquoInfluence of morphologicalcharacteristics of heterogeneous moraine formations on theirmechanical behaviour using image and statistical analysisrdquoEngineering Geology vol 73 no 1-2 pp 37ndash50 2004

[9] T R Reid and J P Harrison ldquoA semi-automated methodologyfor discontinuity trace detection in digital images of rock massexposuresrdquo International Journal of Rock Mechanics andMiningSciences vol 37 no 7 pp 1073ndash1089 2000

[10] Z Q Yue S Chen and L G Tham ldquoFinite element modelingof geomaterials using digital image processingrdquo Computers andGeotechnics vol 30 no 5 pp 375ndash397 2003

[11] Z Q Yue S Chen H Zheng and G H Tang ldquoDigital imageproceeding based on finite element method for geomaterialsrdquo

Chinese Journal of Rock Mechanics and Engineering vol 23 no6 pp 889ndash897 2004

[12] Q L Liao X Li W C Zhu and J S Liu ldquoStructure modelconstruction of rock and soil aggregate based on digital imagetechnology and its numerical simulation on mechanical struc-ture effectsrdquoChinese Journal of RockMechanics and Engineeringvol 29 no 1 pp 155ndash162 2010

[13] W J Xu R L Hu Z Q Yue and R J Tan ldquoMesostructuralcharacter and numerical simulation of mechanical propertiesof soil-rock mixturesrdquo Chinese Journal of Rock Mechanics andEngineering vol 26 no 2 pp 300ndash311 2007

[14] W J Xu Z Q Yue and R L Hu ldquoA current status of digitalimage based quantitative analysis of internal structures ofdebris rock and concretes and associated numerical simula-tionrdquo Journal of Engineering Geology vol 15 no 3 pp 289ndash3132007

[15] W J Xu R L Hu Z Q Yue R Zhang and G L WangldquoResearch on relationship between rock block proportion andshear strength of soil-rock mixtures based on digital imageanalysis and large direct shear testrdquo Chinese Journal of RockMechanics and Engineering vol 27 no 5 pp 996ndash1007 2008

[16] P A Cundall and O D L Strack ldquoA discrete numerical modelfor granular assembliesrdquo Geotechnique vol 29 no 1 pp 47ndash651979

[17] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) (Version 31) Itasca Consulting Group Minneapo-lis Minn USA 2004

[18] J Yoon ldquoApplication of experimental design and optimizationto PFC model calibration in uniaxial compression simulationrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 6 pp 871ndash889 2007

[19] Y C Wang and P Mora ldquoMacroscopic elastic properties ofregular latticesrdquo Journal of the Mechanics and Physics of Solidsvol 56 no 12 pp 3459ndash3474 2008

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 13

deposit is affected by the cementation strength the size ofstone blocks the stone block content and the distribution ofthe stone blocks These properties are analysed so that theycan be better understood by the geologists working on thedemocratisation of the Engineering Project

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (no 51309089 and no 51379065)the National Key Technology RampD Program (no2013BAB06B00) the National Basic Research Programof China (973 Program) (no 2015CB057903) the NaturalScience Foundation of Jiangsu Province (no BK20130846)and the Fundamental Research Funds for the CentralUniversities (no 2014B04914)

References

[1] W G Holtz and H J Gibbs ldquoTriaxial shear tests on perviousgravelly soilsrdquo Journal of the Soil Mechanics and FoundationsDivision vol 82 no 1 pp 1ndash22 1956

[2] R J Chandler ldquoThe inclination of Talus Arctic Talus Terracesand other slopes composed of granular materialsrdquo The Journalof Geology vol 81 no 1 pp 1ndash14 1973

[3] X H You Stochastic structural model of the earth-rock aggregateand its application [PhD thesis] Beijing Jiaotong UniversityBeijing China 2001

[4] X H You and J S Tang ldquoResearch on horizontal push-shearin-situ test of debris and rock-mixturerdquo Chinese Journal of RockMechanics and Engineering vol 21 no 10 pp 1537ndash1540 2002

[5] X H You G He and X Li ldquoMicro-handling technologyof earth-rock aggregate sloperdquo Hydrogeology and EngineeringGeology vol 30 no 1 pp 18ndash21 2003

[6] J M He Study of deformation and failure mechanisms of rock-debris aggregate in three gorges reservoir area [PhD thesis]China University of Mining and Technology Beijing China2004

[7] X Li Q L Liao J M He and J Chen ldquoStudy on in-situ testsof mechanical characteristics on soil-rock aggregaterdquo ChineseJournal of Rock Mechanics and Engineering vol 26 no 12 pp2377ndash2384 2007

[8] T Lebourg J Riss and E Pirard ldquoInfluence of morphologicalcharacteristics of heterogeneous moraine formations on theirmechanical behaviour using image and statistical analysisrdquoEngineering Geology vol 73 no 1-2 pp 37ndash50 2004

[9] T R Reid and J P Harrison ldquoA semi-automated methodologyfor discontinuity trace detection in digital images of rock massexposuresrdquo International Journal of Rock Mechanics andMiningSciences vol 37 no 7 pp 1073ndash1089 2000

[10] Z Q Yue S Chen and L G Tham ldquoFinite element modelingof geomaterials using digital image processingrdquo Computers andGeotechnics vol 30 no 5 pp 375ndash397 2003

[11] Z Q Yue S Chen H Zheng and G H Tang ldquoDigital imageproceeding based on finite element method for geomaterialsrdquo

Chinese Journal of Rock Mechanics and Engineering vol 23 no6 pp 889ndash897 2004

[12] Q L Liao X Li W C Zhu and J S Liu ldquoStructure modelconstruction of rock and soil aggregate based on digital imagetechnology and its numerical simulation on mechanical struc-ture effectsrdquoChinese Journal of RockMechanics and Engineeringvol 29 no 1 pp 155ndash162 2010

[13] W J Xu R L Hu Z Q Yue and R J Tan ldquoMesostructuralcharacter and numerical simulation of mechanical propertiesof soil-rock mixturesrdquo Chinese Journal of Rock Mechanics andEngineering vol 26 no 2 pp 300ndash311 2007

[14] W J Xu Z Q Yue and R L Hu ldquoA current status of digitalimage based quantitative analysis of internal structures ofdebris rock and concretes and associated numerical simula-tionrdquo Journal of Engineering Geology vol 15 no 3 pp 289ndash3132007

[15] W J Xu R L Hu Z Q Yue R Zhang and G L WangldquoResearch on relationship between rock block proportion andshear strength of soil-rock mixtures based on digital imageanalysis and large direct shear testrdquo Chinese Journal of RockMechanics and Engineering vol 27 no 5 pp 996ndash1007 2008

[16] P A Cundall and O D L Strack ldquoA discrete numerical modelfor granular assembliesrdquo Geotechnique vol 29 no 1 pp 47ndash651979

[17] Itasca Consulting Group PFC2D (Particle Flow Code in 2Dimensions) (Version 31) Itasca Consulting Group Minneapo-lis Minn USA 2004

[18] J Yoon ldquoApplication of experimental design and optimizationto PFC model calibration in uniaxial compression simulationrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 44 no 6 pp 871ndash889 2007

[19] Y C Wang and P Mora ldquoMacroscopic elastic properties ofregular latticesrdquo Journal of the Mechanics and Physics of Solidsvol 56 no 12 pp 3459ndash3474 2008

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials