InSituX-RayComputedTomography(CT)Investigationon ...downloads.hindawi.com/journals/ace/2020/8851817.pdf · for loose and dense sand, using direct shear test, triaxial compression

Research ArticleIn Situ X-Ray Computed Tomography (CT) Investigation onLocalized Deformation and Crack Damage Evolution in aBimrock by Tracking Rock Blocks

H J Meng1 Y Wang 2 and J Y Ren2

1Key Laboratory of Neotectonic Movement and Geohazard Institute of Geomechanics Chinese Academy of Geological SciencesBeijing 100081 China2Beijing Key Laboratory of Urban Underground Space Engineering Department of Civil EngineeringSchool of Civil amp Resource Engineering University of Science amp Technology Beijing Beijing 100083 China

Correspondence should be addressed to Y Wang good541571889126com

Received 9 September 2020 Accepted 5 October 2020 Published 20 October 2020

Academic Editor Qian Yin

Copyright copy 2020 H J Meng et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Instability of rock mass with block-in-matrix-rocks (bimrocks) often poses a threat to the geological and ecological environment thusinvestigation of the localized deformation and crack damage evolution is critical to predict the bimrock hazards In this work triaxialcompression testing on block-in-matrix-soils (bimsoils) with a rock block percentage of 40 (mass ratio) was performed undertomographic monitoring using an original experimental setup specially designed to match the 450 kV industrial x-ray ComputerizedTomography (CT) apparatus A series of 2DCTimages were obtained by carrying out CTscanning at key points throughout the test andfrom different positions in the sample e physical strain localization phenomenon was well investigated using the proposed BlockTracking Movement (BTM) method to track the trajectory of rock blocks during deformation e distribution and morphology ofcracks are strongly influenced by the interactions between the rock block and the soil matrix including the repeating contact andseparation between them that finally results in themacroscopic pattern of crackinge displacement vector analysis revealed the spatialkinematics of rock blocks during sample deformation and the associated localized band evolution which was consistent with themacroscopic crack pattern observatione cracks corresponding to the low-density regions in the bimrock sample further indicate theinhomogeneous pattern of localized deformation e meso-structural changes and strain localization of the bimrock under triaxialdeformation are discussed first by analyzing the rock block movement using x-ray CT data

1 Introduction

e phenomenon of strain localization is widely known bymany scholars and it is generally associated with plasticdeformation and fracturing in a solid material especially inthe geomaterials such as the soil and rock material Duringthe damage and fracture process of the geomaterials thestrain localization phenomenon viewed as the onset offailure is one of the most important issues in the field ofgeomechanics e formation of landslides unstable damsembankments foundations and debris flows can be con-sidered to be the macroscopic failure events resulting fromthe propagation of localized bands Strain localization is thephenomenon involving multiscales and it can be observed

on the kilometer scale (faults) in nature down to the meterscale (eg outcrops and cliffs) and in the laboratory fromthe millimeter down to the micrometer scale (laboratorysample) (Lenoir et al 2007) So as to improve the ability tounderstand and model the strain localization the initiationand propagation of this phenomenon and the associatedcrack damage evolution must be experimentallyinvestigated

In the past plenty of researches have been devoted to thestrain localization in geomaterials e discussions about thestrain localization phenomenon of the geomaterial are in-vestigated for soil (eg sand clay etc) at the earliest [1ndash3]Bishop and Henkel [4] focused on the relationship betweenthe strain softening behaviors and localized bands

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8851817 14 pageshttpsdoiorg10115520208851817

Afterwards many scholars conducted many studies on theformation of strain localization and localized band inclinationfor loose and dense sand using direct shear test triaxialcompression test tensile test and true triaxial test [2] Manyeffects have been done on the deformation characteristics inthe localized bands by systematic observation analysis Ex-perimental investigations have revealed that the mechanismof the strain localization through the use of laser techniques[5] image analysis techniques [6 7] x-ray radiography[8ndash13] and x-ray computed tomography [14ndash19] explainedthe strain localization theoretically as a bifurcation fromhomogeneous deformation From the macroscopic stress-strain experiments the whole evolution process of the lo-calized band cannot be captured with the naked eye and themorphology of the localized band can only be observed afterthe failure of the sample However by using some advancedmethods (eg in situ 3D x-ray diffraction in situ x-ray micro-tomography grain ID-tracking 3D-volumetric digital imageanalysis and spatially resolved neutron diffraction) the strainlocalization phenomenon can be successfully investigated inreal-time during deformation

After the literature review almost all the studies aboutstrain localization are focused on soil and rock materialreports on the strain localization for block-in-matrix-rocks(bimrocks) are rarely published Bimrocks are chaotic unitsmainly consisting of mixtures of stronger rock blocks withvarious sizes and weak matrix When subjected to the in-ternal and external loadings those individual componentsalways have different mechanical responses us differentmechanical behaviors exist between the bimrock and otherhomogeneous soil and rock materials Compared to thegeneral rock and soil material owing to the complicatedinterior structure and their components the physical andmechanical properties of bimrock are much more complex[10ndash22] Although many significant experiments proved theexistence of localized bands by in situ shear testing [23 24]in situ large scale horizontal push-shear testing [25] labo-ratory shear testing [26] laboratory uniaxial testing duringstatic loading [27] laboratory uniaxial test during quasi-dynamic loading [28] laboratory triaxial testing [29]mesomechanical laboratory testing [30] mesomechanicalnumerical testing [31] and numerical methods [32] almostall those laboratory experiments are based on the analysis ofthe macroscopic stress and strain at the scale of the wholesample whereas mapping of the strain localization is typ-ically only observed after the failure Fortunately thanks tothe development of the x-ray CT technique we can observethe evolution process of strain localization in the laboratory

Application of x-ray CT in bimrock is not among themost common experiments In our recent experiments onbimrock CTscanning was used for bimrock with rock blockpercentage of 40 under uniaxial compression stress paththe experimental results demonstrated that crack initiatedfrom the rock-soil interface and propagated into soil matrixand CT value in ROI (region of interest) decreased with theincrease of axial deformation [33] In this work we continueto study the strain localization behaviors through laboratoryexperimentation some of the experimental data are usedfrom the published research however a new method was

proposed to characterize the damage evolution of bimrockUnlike in our previous work recent bimrock experimentwas carried out under triaxial compressive stress path Anovel experiment using a self-specially designed loadingdevice in combination with high-energy x-ray CT scanningtechnique was designed A simple confining pressure systemwith independent control of isotropic and deviation com-ponents of the applied stress and transparent to x-ray wasdesigned Rather than focusing on the macroscopic stress-strain characteristics this paper explores the onset andpropagation of strain localization by tracking the spatialkinematics of rock blocks in bimrock using an imageanalysis technique on the CT images obtained from triaxialdeformation e method proposed for tracking the rockblocks was applied to the results of triaxial compression testand the displacement fields of bimrock are discussed ismethod is a new and effective approach for the investigationof strain localization in bimrock

2 Methods

21 Tested Material and Sample Preparation e testedsample used in the experiment is a mixture of soil matrixwith water content of 10 and rock blocks randomlydistributed in the soil matrix Dynamic compact test wasused to prepare the bimrock samples with cylindrical shape(50mm diametertimes 100mm height) According to the soilsample preparation standard of GBT 50123-1999 for thesample diameter studied here diameter of rock block shouldbe less than 10mm the rock blocksoil matrix thresholdvalue is determined as 2mm e soil matrix belongs to akind of high-plasticity clay with its natural density166 gcm3 dry density 150 gcm3 and specific density (Gs)about 272 A lot of clay minerals with strong hydrophilicexisted in soil matrix the plastic limit and liquid limit of thesoil matrix were about 2632 and 6354 respectively ecorresponding liquidity index and plasticity index were about005ndash0127 and 2722 respectively From the water-physicalproperties analysis the soil matrix was a kind of typical highand hard plastic clay material In addition XRD and SEMexperiments were used to determine the mineral content andtype in the soil matrix From the SEM tests rod-like andirregular quartz grains with grain size about 001sim003mmsurrounded by clay minerals can be seen e XRD testsrevealed that the soil matrix has a high percentage of claymineral and three kinds of typical clay minerals were foundsuch as kaolinite montmorillonite and illite e content ofthem was 2673 6152 and 625 respectively Rockblocks used in the study are marble stone with sizes 2sim4mmand 6sim8mm with the mass ratio of 1 1 mixed Naturaldensity of rock blocks is 267 gcm3 and the compressivestrength is about 945MPa by unconfined compression test

During the preparation of bimrock samples rock blockpercentage was designed as 40 A certain content of waterwas added in the mixtures e optimal water ratio wasdesigned as 10 according to the relationship between thehammer counts and soil density rough the compactiontest the optimal hammer count was determined as 18 timesfor bimrock sample preparation First the needs of soil

2 Advances in Civil Engineering

matrix and rock blocks for each sample were homogenizedand mixed in a mixer en the soil-rock mixtures wereplaced into a cast iron module with its volume of 50mm(diameter)times 100mm (height) e sample was compactedwith three layers after the compaction of each layer the topsurface of the layer was disturbed in order to make theconnectivity between the layers homogeneous e sampleswere then sealed with plastic film to prevent waterevaporation

22 X-Ray Tomography X-ray CT as a kind of excellentnondestructive imaging technique can detect the internalcharacteristics of an object in 2D or 3D quantificationallyAccording to differences in the atomic composition anddensity this method reveals the microscopic structure of thetested material X-ray CT is first designed for medical im-aging now it has been widely used in the field of materialfield Recently more and more valuable studies have beenpublished using CT method on geosciences (Otani andObara 2004 Viggiani et al 2004) By recording x-ray ra-diographic images of an object at several different angularpositions this technique achieves the imaging process Basedon either the algebraic algorithms or back projectionprinciple virtual slices can be reconstructed from thesedifferent projections We can further reconstruct a 3D imageof an object by stacking several sequential slices Adoptingthe famous Lamber-beerrsquos law we can obtain the rela-tionship between the intensity of incident radiation andintensity of transmitted radiation as follows

I I0 exp(minusux) (1)

where I and I0 are the x-ray intensity after and before passingthe object of the x-rays respectively u is the linear atten-uation coefficient and x is the passing path of the x-raysthrough the tested object e images can be reconstructedfrom the signals in each point and we call the signal as theCT value A term of ldquoCT valuerdquo is expressed in Hounsfieldunits and can be defined as follows

CT value 1000 u minus uw( 1113857

uw

(2)

where uw is the attenuation coefficient of pure water ecalibration usually gives CT minus1000 for air and CT 0 forwater A high CTvalue usually corresponds to a high densitymaterial Actually the linear attenuation coefficient ismainly influenced by both the effective atomic number Zand the electron bulk density ρ (Van 2003 Van et al 2000Akin and Kovscek 2003) it can be expressed as follows

u ρa + bZ

38

E321113888 1113889 (3)

where a is the KleinndashNishina coefficient b is a constant andE is the energy of x-rays

23Experimental Setup In this work a specifically built loaddevice that could be transparent to the x-ray beam is used

e total system allows conducting the experiments underfully in situ condition As far as we know in situ x-ray CT isused here for the first time for the bimrock under triaxialcompression e present work uses a high-energy x-ray CTfacility Here a high-energy x-ray CT facility was used toperform the CT scanning test the machine is located at theInstitute of High Energy Physics (China) e workingprinciple of the high-energy x-ray computed tomography isthe same as the medical computed tomography For itssimplest working principle from all orientations in a planean x-ray fan beam or cone beam is casted at an object and a16-bit linear array of detectors is used to measure the in-tensity attenuation when the x-ray goes through the objectas also seen in Figure 1(a) By rotating the object on acomputer-controlled turntable the x-ray attenuation rec-ords are performed equally spaced for 360deg to differentangles A cross-sectional image of the tested object along theplane was then created from the resulting data Each CTimage is called a ldquoslicerdquo it seems that the object was openedup along a plane which can be clearly seen By collecting astack of contiguous slices we can build a complete 3D datamodel It is polychromatic for the x-ray source the sourcegenerates x-rays over a continuum of energies from about 30up to 420 kV which is up to the operating voltage In thepresent work due to the relatively large sample(φ50mmtimesH100mm) the sample was conducted via CTscanning at an operating voltage of 400 kV and an electriccurrent of 20mA conditions e detailed specifications ofthe used CT machine are listed in Table 1

In order to follow in real-time deformation of a samplesubmitted to classical triaxial test conditions a test devicewas designed that was consistent with the requirement of theCT apparatus e loading device is composed of the re-action frame displacement measuring system and loadmeasurement system e reaction frame of the testingdevice has to be transparent to x-rays and is therefore madewith low attenuation material a glass fiber reinforced withnylon resin (PA66+GF30) with a density of about 138 gcm3

is used for the reaction column Glass fiber with a mass ratioof 30 is added to the nylon resin and this material exhibitsgood performance of heat resistance strength and stiffnessWhen it is subjected to tension stress the deformation isrelatively small e tensile strength of PA66 +GF30 is about7546sim833MPa the yield strength is about 5488MPa thecompressive strength is about 10388MPa and the elasticitymodulus is 330MPa e force measurement system isbattery-driven avoiding wire wrapping during rotation ofthe rotation device Figure 1(b) gives the loading device usedin the experiment

e confining pressure is imposed by a speciallydesigned gasbag Hoek cell the material of the cell is the sameas the reaction column which is transparent to x-rays econfining pressure can be read from the gas-pressure meterand the measuring range is 600 kPa with a precision of05 kPa For bimrock as it is a kind of extreme heteroge-neous geological materials this material contains plenty ofrandom rock-soil interfaces and the elasticity contrast existsbetween the soil matrix and rock blocks During sampledeformation the stress distribution in bimrock is extremely

Advances in Civil Engineering 3

uneven the real stress state is that stress acting on everypoint of the sample surface is equal erefore the gasbagconfining pressure subsystem which can provide flexibleboundary condition is used to impose the confining pressurein order to realize the equivalent stress boundary for bim-rock samples

24 Testing Programme During the test first the loadingdevice was placed on the rotation table of the 450 kV x-rayCT machine en the bimrock sample was placed in theHoek cell which is almost completely transparent to x-rayse confining pressure was applied by the air pump Itshould be noted that no drained water was measured duringthe triaxial tests e axial stress was applied through a loadsystem with a constant rate of 01 kNstep (ie every 01 kNwe recorded the axial deformation) and complete infor-mation regarding the axial stress and axial displacementcould be recorded X-ray CT data were obtained along thethree central cross sections of the sample the initial position

was 35mm 50mm and 65mm respectively from top of thesample as shown in Figure 2 For each CT slice a completescan was obtained by recording 3600 measurements projectsat different angles equally 360deg this took about 1min AfterCT scanning 2min was used to conduct real-time recon-struction for the original CT data erefore a section wasrecorded in approximately 3min After completing CTscanning the linear array detector went down 15mm andstarting on the next CT scanning there were 3600 projectsagain A total of three CT sections were obtained for eachloading stage In our research six loading stages wereperformed for the bimrock sample with a RBP of 40 thuswe obtained 648000 projects and this took about 90min forthe experiment e data consist of radiological densities foreach voxel of this cross section that can be visualized as grayscale image on a grid where each pixel is indexed to theHounsfield value e gray scale has a dynamic which isfitted to the range of crack variations inside the sample evariation of crack inside the sample is computed from thevariation of radiological densityWhen damage occurs in thebimrock sample the color is black at the position of cracksas shown in Figure 3

Figure 3 plots the typical stress-strain curve and thedesigned scanning points in the experiment We tested thesample until a maximum axial strain of 8 Six loadingstages were performed with x-ray CT scanning and thecorresponding strain was designed as 0 15 3 4 6and 8 respectively In the practical operation the axialstrain was 0 1756 3106 4424 6649 and 8042respectively When conducting CT scanning the axialloading was stopped to avoid the movement of the sampledue to the loading After the CT scanning the axial loadingstarted again with the same loading rate It should be notedthat stress relaxation phenomenon occurs at each step of thescanning process because the axial displacement is fixedduring CT scanning As the stress drop owing to stressrelaxation is relatively small this part was not drawn in thestress-strain curve

X-ray source(450kV)

Linear array detector

Loading device

Rotation table

(a)

Micrometergauge (254mm)

Hydraulic jack

Hoek cell system

Nylon resinreaction column

Force sensorController

(b)

Figure 1 e testing devices for bimrock sample (cited fromWang et al [28]) (a) Industrial CTmachine with its voltage of 450 kV (b) theloading device to match the CT device

Table 1e detailed performance index of the 450 kV industrial x-ray CT system

Performance parameter of the CTdevice Index UnitEffective scanning diameter Φ800 mmEffective scanning height Φ1000 mmMaximum scanned weight 200 kgPenetration thickness for Fe 50 mmSpatial resolution 007times 007times 007 mm3

Perspective of relative sensitivity 1 Density resolution 01 Minimum scanning thickness 003 mmFastest scanning time 1 minImage reconstruction time 30 sResolution capacity for crack 005times15 mm2

Stomata resolution Φ03 mmResolution for inclusion 01 mmLocalization accuracy of the workbench plusmn002 mmAccuracy of the turntable plusmn5deg s


25 Image Analysis To extract the rock block crack andrealize the rock block ID tracking for the CT images atdifferent loading stages a method called Block TrackingDisplacement (BTD) was proposed e basic purpose ofthis method is to track the rock block in bimrock sample andanalyze the displacement vector during triaxial deformatione CT images are 16-bit digital images composed of the so-called ldquoCTvaluerdquo which is the preliminary output presentedin monotonic dark shades for low CT values and lightshades for high CT values with 256 possible variations Inour x-ray CT apparatus the CT image is constructed by1024times1024 pixels the thickness of x-ray attenuation evoxel is 007mmtimes 007mmtimes 03mm for images with a50mm diameter sample cross section A typical histogram isshown in Figure 4(b) with a peak and a trough on the curveone representing the rock blocks and the other representingthe cracks In addition the steady portion on the curverepresents the soil matrix

As shown in Figure 4(b) it plots the changes of gray value(or Hounsfield value) along the profile line (Figure 4(a))From the variation of H value the H value can be divided intothree intervals for rock blocks soil matrix and crack re-spectivelye rock block and crack can be extracted from theoriginal CT images based on the difference of CT value Amethod called a region growing method has been attemptedto identify the rock blocks soil matrix and crack individuallyby a trinarization technique From the trinarized images areasof the rock blocks the soil matrix and the crack in the localtwo-dimensional scanning domain have been quantified bycounting the number of voxels which occupies each materialmultiplied by the area of the unit voxel [34ndash37] e methodcan be summarized as follows

(1) In the region growing method one voxel repre-senting one material is firstly chosen We sample thegray values for rock block crack and soil matrix asmuch as possible and calculate the average anddispersion for the rock block microblock and σblock soilmatrix microsoil and σsoil and crack microcrack and σcrack

(2) We determine the tolerance of the rock block phaseand crack phase Tr and Tc respectively e grayvalues of each phase are assumed to comply withnormally distribution determine the domain of eachphase between the two values xi plusmn 2σi (i r s c)

(3) e adjacent voxels with similar gray values to theoriginal voxel are assimilated into the same mediumSubsequently the same procedure is done for thenewly assimilated voxels ie the adjacent voxels ofthe newly assimilated voxels are assimilated into thesame phase if the gray values are similar to theoriginal one Repeating this procedure eventuallyleads to the formation of one cluster composed ofvoxels with similar gray values [38 39] Starting fromthe voxels with the average gray value of each phaseassimilate the adjacent voxels with gray valuesgreater than tolerances value into the each mediumRepeat this procedure for the newly assimilatedvoxels until no voxels are assimilated e rockblocks and cracks by the region growing method areshown in Figures 5 and 6 respectively

(4) After segmenting the rock blocks from the soil matrixedge detection algorithms were used to determine theboundary of rock blocks then the spatial position ofeach rock block was determined according to thecentroid coordinates e displacement vector of rockblocks at different deformation can be calculatedFigure 7 shows the edge detection result of rockblocks In order to better interpret the strain locali-zation phenomena the detection results were over-lapped on the original data

3 Experimental Results

31 Rock Block ID Tracking Due to the differential defor-mation that occurs at rock-soil interfaces a series of non-linear behaviors of rock block rotation movement and

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zprime

2030 3040 40

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(c)

(a)

(b)

Figure 2 e sample grayscale image data is a bimrock sample (a)BMP image stack (b) extraction of the 28th layer of CT (c) ex-traction of CT slice cracks

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00

Axi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10 11Axial strain ()

SRM sampleWC = 10RBP = 40σ3 = 120 kPa

Six CT scanning stages

1

(2)

(1)

(3) (4) (5) (6)

2

3 4 5

6

Figure 3 Drawing the axial stress-strain curve of the studiedbimrock specimen and selecting 6 key points for CT scanning


Soil matrix

Soil matrix

Rock block

Rock block

CrackCrack

Crack

Crack

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52mm

ndash829ndash834ndash839ndash844ndash849ndash854ndash859ndash864ndash869ndash874ndash879ndash884ndash889ndash894ndash899

ndash909ndash904

ndash914ndash919ndash924ndash929ndash934ndash939ndash944ndash949

Relat

ive h

ouns

field

uni

ts

Hcrack

Hsoil

Hblock

Rock block

Hoek cell

Crack

ROI of SRM

(μcrack plusmn σcrack)

(μsoil plusmn σsoil)

(μblock plusmn σblock)

(b)(a)

Figure 4 Illustration of the method to extract the cracks and rock blocks in CT image (a) Cross-sectional slice (16-bit) and (b) gray levelhistogram

(a)

(b)

(c)

(d)

Figure 5 Continued


(e)

(f )

Figure 5 Rock block extraction from the CTimages at different deformation stages (a) ε 0 (b) ε 1756 (c) ε 3106 (d) ε 4427(e) ε 6649 (f ) ε 8059

70

65

60

5550454035302520

z (m

m)

x (mm)

010

2030

4050

y (mm)

010

2030

4050

H = 65mm

H = 50mm

H = 35mm

(a)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)

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z (m

m)

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(b)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

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z (m

m)

54

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(c)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

30

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z (m

m)

70

65

60

55

(d)

Figure 6 Spatial positions of rock blocks during deformation for the three x-ray CT scanned sections


(a)

(b)

(c)

(d)

(e)

(f )

Figure 7 Edge detection of rock blocks in CT images (the edge detection result was plotted on the original CT images) (a) ε 0 (b)ε 1756 (c) ε 3106 (d) ε 4427 (e) ε 6649 (f ) ε 8059


translation can lead to the development of localized bandsIn this section the changes of the spatial positions of rockblocks in bimrock are discussed using the proposed methodof Block Tracking Movement (BTM) e initial positions ofall the blocks transmitted by x-rays are plotted in Figure 6(a)e number of rock blocks in the three sections is 42 37 and36 respectively e initial positions are 35mm 50mm and65mm respectively Because under compression the heightof the sample changes therefore the scanning position andinterval are variable and not constant at each CT scanningstage With the decrease of sample height the scanninginterval change is smaller and this can be determined fromthe total variation of the sample height To do so it canensure the same position of every CT scanning at a differentloading stage as much as possible Figures 6(b)sim6(d) plot thespatial position of rock blocks at axial strains of 0 14803083 4012 6012 and 8032 respectively from thethree positions It can be seen that the movement of rockblocks becomes severe with the increase of axial deforma-tion Especially at the bottom of the sample movement ofrock blocks is much more serious than at other parts of thesample ese results indicate that localized bands graduallyform with increasing deformation Due to the formation oflocalized bands the volume of the sample becomes largeraccordingly Due to the existence of rock blocks in bimrocknon-linear movement such as rotation or translation ag-gravates the strain localization phenomenon rough thestatistical analysis of the number of rock blocks at differentaxial strains we can also find that the number of rock blocksis not the same even though scanned at the same positionDuring deformation interactions between the rock blockand soil matrix lead to the disappearance of the rock blocksand the appearance of new rock blocks in the specified CTscanning sectionse number of rock blocks in the bimrocksample under deformation is shown in Figure 8

32 Displacement Vector Analysis e positions of the rockblocks can be tracked from the initial point to their positionafter vertical loading and then the displacement vectorsbased on the movement of rock blocks are computedFigure 9 plots the displacement vector of the rock blockduring triaxial deformation and from the distribution of thedisplacement vector the progressive localized deformationcan be clearly seen In Figure 9(a) when the axial strain isfrom 0 to 1480 movement of rock blocks takes thepriority of vertical movement and is parallel to the axialdirection In Figure 9(b) when the axial strain is from1480 to 3083 the stress-strain curve records thecompaction stage to the strain hardening onset movementof the rock block begins in the lateral direction and thelateral expansion begins at this stage In Figures 9(c)sim9(e)when the axial strain is from 1480 to 8032 the strainlocalization phenomenon becomes obvious with increasingdeformation Expansion of the sample is the most distinctwhen the axial strain reaches 8032 Figure 9(f ) shows thestrain localization of the sample from the state of unloadingto failure Compared with its initial state the rock blocksmove in two lateral directions when the axial deformation

reaches the maximum and the apparent localized bands canbe seen in Figure 9(f) From the evolution of localized bandsin the bimrock sample the inhomogeneous localized regionspropagate with the increase of sample deformation In ad-dition the localized bands are located at the rock blockcentralized zones and the distribution of the rock blockstrongly influences the distribution and morphology oflocalized bands

Because the rock-soil interfaces are the weakest part inbimrock the evolution of localized bands is often accom-panied by the occurrence of cracks in the low-density regionCracks in the bimrock sample are the reflection of stressdistribution heterogeneity and the associated strain locali-zation Figure 10 plots the crack morphology in the bimrocksample We can see that the number of cracks increases withincreasing deformation this result is consistent with theevolution of localized bands When the axial strain equals1480 a small number of cracks can be observed in CTimages marked with lower density region Two kinds ofcracks coexist in the bimrock sample one kind is the maincrack which propagates into the soil matrix the other kindis called a secondary crack which develops around rockblocks e morphology of the crack is close to the distri-bution and shape of rock blocks In addition interlockingphenomenon occurs around rock blocks the alreadyexisting cracks close due to the movement of rock blockeresult implies that the rock block is the main factor con-trolling the crack geometry distribution and the associateddeformation of the bimrock When the strain exceeds1480 a few cracks initiate from the rock-soil interface withlow-density region when the stress exceeds 3106 thenumber of cracks increases sharply and the main crackpropagates into the soil matrix bypassing rock blocks estrain localization becomes obvious at the strain hardeningstage and a large scaled shearing band forms It can beinferred that the shearing band is discontinuous and by-passes rock blocks from the crack distribution According tothe crack distribution in Figure 10 cracking in the bimrockis attributed to the interface cracking mechanism stressconcentration and the deformation incompatibility leads tothe cracking We can see that cracking first occurs at blocktips the adjacent block makes the soil body around themrotate in the opposite direction and the rotation torqueresults in the cracking of the soil In addition the separationphenomena of the soil and the rock block can be clearlyobserved During triaxial deformation rotation torqueforms at rock block tips and the rock-soil interface owing tothe incompatible deformation between the rock block andsoil matrix and large porosity forms

33 Macroscopic Failure Morphology Analysis Failuremorphology of bimrock is strongly controlled by the rockblock content e macroscopic failure pattern of rock is theexternal reflection of its internal damage evolution [40 41]Wang et al [22] pointed out that the failure process ofbimrock is the rearrangement of soil and rock block par-ticles During the process the rock blocks and soil matrixbear axial loading in their unique ways Rock block


1 2 3 4 5 6 7 8 90Axial strain ()

Upper sectionMiddle sectionLower section

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52Bl

ock

coun

ts

(a)

0

5

10

15

20

Bloc

k co

unts

Upper section disappearanceMiddle section disappearanceLower section disappearance

Upper section appearanceMiddle section appearanceLower section appearance

2 3 85 6 7 91 4Axial strain ()

(b)

Figure 8 Statistical number of rock blocks in bimrock under deformation for the three scanned sections (a) Total number of rock blocks atdifferent axial strains (b) number change of rock block at different axial strains

x (mm) y (mm)

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Figure 9 Continued


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50

5060

60

(e)

70

65

60

55

50

45

40

35302520

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(f )

Figure 9 3D displacement vectors of rock blocks during compression (a) Axial strain 0 to 1480 (b) Axial strain 1480 to 3083 (c)Axial strain 3083 to 4012 (d) Axial strain 4012 to 6012 (e) Axial strain 6012 to 8032 (f ) Axial strain 0 to 8032

(a)

(b)

(c)

Figure 10 Continued


(d)

(e)

Figure 10 e cracks segmentation from the original CT slices at the five loading levels (a) ε 1756 (b) ε 3106 (c) ε 4427 (d)ε 6649 (e) ε 8059

(a) (b) (c) (d)

(e) (f ) (g) (h)

Figure 11e failure morphology of the tested bimrock sample (a)sim(d) Failure morphology corresponding to the anterior left posteriorand right side of the sample (e)sim(f ) Crack sketch maps of the four sides


percentage is the most important factor resulting in thefailure mechanism of bimrock With increasing rock blockpercentage in bimrock the failure pattern is from shearfailure to bulging failure For the bimrock sample with RBPof 40 the strain localization analysis in the above sectionindicates that the shear failure is not obvious for this samplein other words it is influenced by the distribution of lo-calized bands and the bulging deformation plays a domi-nant role After the experiment the sample was removed andwe observed the macroscopic failure morphology by nakedeyes the sample was observed in four directions as shown inFigure 11 From these results it was determined that thelocalized bands propagated and coalesced in the soil matrixand then the main failure plane formed Shearing slidingoccurs along the rock-soil interfaces and makes the for-mation of localized bands ose bands are distributedrelatively homogeneously inside the sample which implies abulging deformation pattern for this sample e resultfurther proves the reasonability of the displacement vectorresult e accuracy of the rock block ID-tracking methodcan be acceptable since the obtained displacement is almostthe same as the macroscopic failure morphology

4 Conclusions

In order to investigate the geomechanical properties ofbimrock such as deformation and failure more quantitativeinformation about the strain field is required In this work anoriginal experimental device has been designed for testing abimrock sample at relatively low ambient pressures (120 kPa)which allows for tomography imaging of the sample underdeviatoric loading A method called Block Tracking Move-ment has been proposed to monitor the displacement of rockbocks in the sample Using this method the 3D displacementvectors have been calculated and the strain localizationevolution during deformation has been discussed e mainconclusions can be drawn as follows

(1) A proper method of image processing analysis calledBTM method that can well track the non-linearmovement of rock blocks and reflect the structuralchanges of localized bands is developed Duringsample deformation deformation evolution in-volving localization changes in bulk density can beindirectly probed by rock block movement fromthose CT images

(2) Interactions among the soil and block componentsare the main reason resulting in the strain locali-zation in bimrock e morphology and distributionof the localized bands are influenced by the rockblock in bimrock Existence of rock blocks and theirrelative positions significantly alter the stress dis-tribution in bimrock e spatial kinematics of rockblocks promotes the strain localization and theforming of shear bands Movement and rotation ofthe rock block also lead to the closure of existingcracks and the formation of new cracks

(3) Cracks in the low-density region have been wellextracted by using the trinarized images e

volumetric expansion behaviors of bimrock resultingfrom the appearance of cracks are investigated etrajectory of localized bands is strongly related to thecrack propagation path

Data Availability

e experimental data used to support the findings of thisstudy are included within the article

Conflicts of Interest

e authors declare no conflicts of interest

Acknowledgments

is study was supported by the China Geological SurveyProject (No DD20190318) Beijing Science and TechnologyProject (Z191100001419015) the Beijing Natural ScienceFoundation (82020033) and the Fundamental ResearchFunds for the Central Universities (FRF-TP-20-004A2)

References

[1] I Vardoulakis ldquoBifurcation analysis of the triaxial test on sandsamplesrdquo Acta Mechanica vol 32 no 1ndash3 pp 35ndash54 1979

[2] I Vardoulakis M Goldscheider and G Gudehus ldquoForma-tion of shear bands in sand bodies as a bifurcation problemrdquoInternational Journal for Numerical and Analytical Methods inGeomechanics vol 2 no 2 pp 99ndash128 1978

[3] H E Read and G A Hegemier ldquoStrain softening of rock soiland concrete-a review articlerdquo Mechanics of Materials vol 3no 4 pp 271ndash294 1984

[4] A W Bishop and D J Henkel ldquoe Measurement of SoilProperties in the Triaxial testrdquo Coefficient of Internal FrictionCornell University Ithaca NY USA 1962

[5] F Tatsuoka M S A Siddiquee and C Park ldquoModelingstress-strain relations of sandrdquo Soils and Foundations vol 33no 2 pp 60ndash81 1993

[6] T Kodaka Y Higo and T Takyu ldquoDeformation and failurecharacteristics of rectangular clay specimens under three-dimensional conditionrdquo in Proceedings of the Internationalconference on Soil Mechanics and Geotechnical Engineeringvol 1 pp 167ndash170 Aa balkema Publishers Tokyo JapanAugust 2001

[7] R L Michalowski and L Shi ldquoDeformation patterns ofreinforced foundation sand at failurerdquo Journal of Geotechnicaland Geoenvironmental Engineering vol 129 no 5 pp 439ndash449 2003

[8] M Mokni and J Desrues ldquoStrain localization measurementsin undrained plane-strain biaxial tests on Hostun RF sandrdquoMechanics of Cohesive-Frictional Materials vol 4 no 4pp 419ndash441 1999

[9] K H Roscoe ldquoe influence of strains in soil mechanicsrdquoGeotechnique vol 20 no 2 pp 129ndash170 1970

[10] J Desrues and G Viggiani ldquoStrain localization in sand anoverview of the experimental results obtained in Grenobleusing stereophotogrammetryrdquo International Journal for Nu-merical and Analytical Methods in Geomechanics vol 28no 4 pp 279ndash321 2004

[11] D Liu Z Gu R Liang et al ldquoImpacts of pore-throat systemon fractal characterization of tight sandstonesrdquo Geofluidsvol 2020 no 9 Article ID 4941501 17 pages 2020


[12] X Wang C Liu S Chen L Chen K Li and N Liu ldquoImpactof coal sectorrsquos de-capacity policy on coal pricerdquo AppliedEnergy vol 265 p 114802 2020

[13] J Wang Y Zhang Z Qin S Song and P Lin ldquoAnalysismethod of water inrush for tunnels with damaged water-resisting rock mass based on finite element method-smoothparticle hydrodynamics couplingrdquo Computers and Geo-technics vol 126 p 103725 2020

[14] J Otani T Mukunoki and Y Obara ldquoCharacterization offailure in sand under triaxial compression using an industrialX-ray CT scannerrdquo International Journal of Physical Model-ling in Geotechnics vol 2 no 1 pp 15ndash22 2002

[15] Y Wang W K Feng and C H Li ldquoOn anisotropic fractureand energy evolution of marble subjected to triaxial fatiguecyclic-confining pressure unloading conditionsrdquo Interna-tional Journal of Fatigue vol 134 p 105524 2020

[16] Y Wang S Gao D Liu and C Li ldquoAnisotropic fatiguebehaviour of interbeded marble subjected to uniaxial cycliccompressive loadsrdquo Fatigue amp Fracture of Engineering Ma-terials amp Structures vol 43 no 6 pp 1170ndash1183 2020

[17] Y Wang W K Feng H J Wang C H Li and Z Q HouldquoRock bridge fracturing characteristics in granite induced byfreeze-thaw and uniaxial deformation revealed by AE mon-itoring and post-test CT scanningrdquo Cold Regions Science andTechnology vol 177 2020

[18] K A Alshibli S Sture N C Costes et al ldquoAssessment oflocalized deformations in sand using X-ray computed to-mographyrdquo Geotechnical Testing Journal vol 23 no 3pp 274ndash299 2000

[19] Y Wang S H Gao C H Li and J Q Han ldquoEnergy dis-sipation and damage evolution for dynamic fracture of marblesubjected to freeze-thaw and multiple level compressive fa-tigue loadingrdquo International Journal of Fatigue vol 142 2021

[20] E Medley and E S Lindquist ldquoe engineering significanceof the scale-independence of some Franciscan Melanges inCalifornia USArdquo in Proceedings Of De 35th US Rock Me-chanics Symposium vol 1 pp 907ndash914 Balkema RotterdamNetherlands January 1995

[21] N Coli P Berry and D Boldini ldquoIn situ non-conventionalshear tests for the mechanical characterisation of a bimrockrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 48 no 1 pp 95ndash102 2011

[22] Y Wang C H Li and Y Z Hu ldquo3D image visualization ofmeso-structural changes in a bimsoil under uniaxial com-pression using X-ray computed tomography (CT)rdquo Engi-neering Geology vol 248 pp 61ndash69 2019

[23] E S Lindquist De Strength and Deformation Properties ofMelange University of California Berkeley CA USA 1995

[24] Y Wang J M Que C Wang and C H Li ldquoree-dimensional observations of meso-structural changes inbimsoil using X-ray computed tomography (CT) under tri-axial compressionrdquo Construction and Building Materialsvol 190 pp 773ndash786 2018

[25] H-Y Zhang W-J Xu and Y-Z Yu ldquoTriaxial tests of soil-rock mixtures with different rock block distributionsrdquo Soilsand Foundations vol 56 no 1 pp 44ndash56 2016

[26] W J Xu Q Xu and R L Hu ldquoStudy on the shear strength ofsoilndashrock mixture by large scale direct shear testrdquo Interna-tional Journal of Rock Mechanics and Mining Sciences vol 45pp 1235ndash1247 2011

[27] L E Vallejo and R Mawby ldquoPorosity influence on the shearstrength of granular material-clay mixturesrdquo EngineeringGeology vol 58 no 2 pp 125ndash136 2000

[28] Y Wang C H Li and Y Z Hu ldquoUse of X-ray computedtomography to investigate the effect of rock blocks on meso-structural changes in soil-rock mixture under triaxial de-formationrdquo Construction and Building Materials vol 164pp 386ndash399 2018

[29] Y Wang X Li B Zheng B Zhang J M He and S D LildquoMacro-meso failure mechanism of soil-rock mixture atmedium strain ratesrdquo Geotechnique Letters vol 6 no 1pp 28ndash33 2016

[30] S M Springman C Jommi and P Teysseire ldquoInstabilities onmoraine slopes induced by loss of suction a case historyrdquoGeotechnique vol 53 no 1 pp 3ndash10 2003

[31] Y Wang and X Li ldquoResearch on damage cracking for rockand soil aggregate using calculation meso-mechanicsrdquo Chi-nese Journal of Rock Mechanics and Engineering vol 33 no 2pp 4020ndash4031 2014

[32] W-J Xu S Wang H-Y Zhang and Z-L Zhang ldquoDiscreteelement modelling of a soil-rock mixture used in an em-bankment damrdquo International Journal of Rock Mechanics andMining Sciences vol 86 pp 141ndash156 2016

[33] Y Wang X Li and Y-F Wu ldquoDamage evolution analysis ofSRM under compression using X-ray tomography and nu-merical simulationrdquo European Journal of Environmental andCivil Engineering vol 19 no 4 pp 400ndash417 2015

[34] Y Wang C-H Li J-Q Han J and H-J Wang ldquoMechanicalbehaviours of granite containing two flaws under uniaxialincreasing amplitude fatigue loading conditions an insightinto fracture evolution analysesrdquo Fatigue amp Fracture of En-gineering Materials amp Structures vol 43 pp 1ndash16 2020

[35] Y Wang D Q Liu J-Q Han C H Li and H Liu ldquoEffect offatigue loading-confining stress unloading rate on marblemechanical behaviors an insight into fracture evolutionanalysesrdquo Journal of Rock Mechanics and Geotechnical En-gineering vol 34 2020

[36] B Chen S-C Zhang Y-Y Li Z K Li and H J ZhouldquoPhysical simulation study of crack propagation and insta-bility information discrimination of rock-like materials withfaultsrdquo Arabian Journal of Geosciences vol 18 no 13pp 1ndash13 2020

[37] C Zhu Z G Tao S Yang and S Zhao ldquoV shaped gullymethod for controlling rockfall of high-steep slope in ChinardquoBulletin of Engineering Geology and the Environment vol 78no 4 pp 2731ndash2747 2019

[38] Y Higo F Oka T Sato Y Matsushima and S KimotoldquoInvestigation of localized deformation in partially saturatedsand under triaxial compression using microfocus X-ray CTwith digital image correlationrdquo Soils and Foundations vol 53no 2 pp 181ndash198 2013

[39] J-T Chen J-H Zhao S C Zhang Y Zhang F Yang andM Li ldquoAn experimental and analytical research on theevolution of mining cracks in deep floor rock massrdquo Pure andApplied Geophysics vol 15 2020

[40] G Viggiani N Lenoir and P Besuelle ldquoX-ray micro-tomography for studying localized deformation in fine-grained geomaterials under triaxial compressionrdquo ComptesRendus Mecanique vol 332 no 10 pp 819ndash826 2014

[41] S Akin and A R Kovscek ldquoComputed tomography in pe-troleum engineering researchrdquo Geological Society LondonSpecial Publications vol 215 no 1 pp 23ndash38 2003


Afterwards many scholars conducted many studies on theformation of strain localization and localized band inclinationfor loose and dense sand using direct shear test triaxialcompression test tensile test and true triaxial test [2] Manyeffects have been done on the deformation characteristics inthe localized bands by systematic observation analysis Ex-perimental investigations have revealed that the mechanismof the strain localization through the use of laser techniques[5] image analysis techniques [6 7] x-ray radiography[8ndash13] and x-ray computed tomography [14ndash19] explainedthe strain localization theoretically as a bifurcation fromhomogeneous deformation From the macroscopic stress-strain experiments the whole evolution process of the lo-calized band cannot be captured with the naked eye and themorphology of the localized band can only be observed afterthe failure of the sample However by using some advancedmethods (eg in situ 3D x-ray diffraction in situ x-ray micro-tomography grain ID-tracking 3D-volumetric digital imageanalysis and spatially resolved neutron diffraction) the strainlocalization phenomenon can be successfully investigated inreal-time during deformation

After the literature review almost all the studies aboutstrain localization are focused on soil and rock materialreports on the strain localization for block-in-matrix-rocks(bimrocks) are rarely published Bimrocks are chaotic unitsmainly consisting of mixtures of stronger rock blocks withvarious sizes and weak matrix When subjected to the in-ternal and external loadings those individual componentsalways have different mechanical responses us differentmechanical behaviors exist between the bimrock and otherhomogeneous soil and rock materials Compared to thegeneral rock and soil material owing to the complicatedinterior structure and their components the physical andmechanical properties of bimrock are much more complex[10ndash22] Although many significant experiments proved theexistence of localized bands by in situ shear testing [23 24]in situ large scale horizontal push-shear testing [25] labo-ratory shear testing [26] laboratory uniaxial testing duringstatic loading [27] laboratory uniaxial test during quasi-dynamic loading [28] laboratory triaxial testing [29]mesomechanical laboratory testing [30] mesomechanicalnumerical testing [31] and numerical methods [32] almostall those laboratory experiments are based on the analysis ofthe macroscopic stress and strain at the scale of the wholesample whereas mapping of the strain localization is typ-ically only observed after the failure Fortunately thanks tothe development of the x-ray CT technique we can observethe evolution process of strain localization in the laboratory

Application of x-ray CT in bimrock is not among themost common experiments In our recent experiments onbimrock CTscanning was used for bimrock with rock blockpercentage of 40 under uniaxial compression stress paththe experimental results demonstrated that crack initiatedfrom the rock-soil interface and propagated into soil matrixand CT value in ROI (region of interest) decreased with theincrease of axial deformation [33] In this work we continueto study the strain localization behaviors through laboratoryexperimentation some of the experimental data are usedfrom the published research however a new method was

proposed to characterize the damage evolution of bimrockUnlike in our previous work recent bimrock experimentwas carried out under triaxial compressive stress path Anovel experiment using a self-specially designed loadingdevice in combination with high-energy x-ray CT scanningtechnique was designed A simple confining pressure systemwith independent control of isotropic and deviation com-ponents of the applied stress and transparent to x-ray wasdesigned Rather than focusing on the macroscopic stress-strain characteristics this paper explores the onset andpropagation of strain localization by tracking the spatialkinematics of rock blocks in bimrock using an imageanalysis technique on the CT images obtained from triaxialdeformation e method proposed for tracking the rockblocks was applied to the results of triaxial compression testand the displacement fields of bimrock are discussed ismethod is a new and effective approach for the investigationof strain localization in bimrock

2 Methods

21 Tested Material and Sample Preparation e testedsample used in the experiment is a mixture of soil matrixwith water content of 10 and rock blocks randomlydistributed in the soil matrix Dynamic compact test wasused to prepare the bimrock samples with cylindrical shape(50mm diametertimes 100mm height) According to the soilsample preparation standard of GBT 50123-1999 for thesample diameter studied here diameter of rock block shouldbe less than 10mm the rock blocksoil matrix thresholdvalue is determined as 2mm e soil matrix belongs to akind of high-plasticity clay with its natural density166 gcm3 dry density 150 gcm3 and specific density (Gs)about 272 A lot of clay minerals with strong hydrophilicexisted in soil matrix the plastic limit and liquid limit of thesoil matrix were about 2632 and 6354 respectively ecorresponding liquidity index and plasticity index were about005ndash0127 and 2722 respectively From the water-physicalproperties analysis the soil matrix was a kind of typical highand hard plastic clay material In addition XRD and SEMexperiments were used to determine the mineral content andtype in the soil matrix From the SEM tests rod-like andirregular quartz grains with grain size about 001sim003mmsurrounded by clay minerals can be seen e XRD testsrevealed that the soil matrix has a high percentage of claymineral and three kinds of typical clay minerals were foundsuch as kaolinite montmorillonite and illite e content ofthem was 2673 6152 and 625 respectively Rockblocks used in the study are marble stone with sizes 2sim4mmand 6sim8mm with the mass ratio of 1 1 mixed Naturaldensity of rock blocks is 267 gcm3 and the compressivestrength is about 945MPa by unconfined compression test

During the preparation of bimrock samples rock blockpercentage was designed as 40 A certain content of waterwas added in the mixtures e optimal water ratio wasdesigned as 10 according to the relationship between thehammer counts and soil density rough the compactiontest the optimal hammer count was determined as 18 timesfor bimrock sample preparation First the needs of soil







uw

(2)


u ρa + bZ

38

E321113888 1113889 (3)












X-ray source(450kV)


Loading device

Rotation table

(a)


Hydraulic jack

Hoek cell system



(b)















100

90

80

70

60

50

40

30

20

10

0

z (m

m)

x (mm) y (mm)

0

0

10

10

20

0yprime

xprime

zprime

2030 3040 40

5050

60

60

(c)

(a)

(b)


20

18

16

14

12

10

08

06

04

02

00

Axi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10 11Axial strain ()



1

(2)

(1)

(3) (4) (5) (6)

2

3 4 5

6



Soil matrix

Soil matrix

Rock block

Rock block

CrackCrack

Crack

Crack

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52mm


ndash909ndash904


Relat

ive h

ouns

field

uni

ts

Hcrack

Hsoil

Hblock

Rock block

Hoek cell

Crack

ROI of SRM




(b)(a)


(a)

(b)

(c)

(d)

Figure 5 Continued


(e)

(f )


70

65

60

5550454035302520

z (m

m)

x (mm)

010

2030

4050

y (mm)

010

2030

4050

H = 65mm

H = 50mm

H = 35mm

(a)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)

0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

38

36

34

32

30

28

26

24

(b)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

54

52

50

48

46

44

42

40

38

(c)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

70

65

60

55

(d)



(a)

(b)

(c)

(d)

(e)

(f )









1 2 3 4 5 6 7 8 90Axial strain ()


34

36

38

40

42

44

46

48

50

52Bl

ock

coun

ts

(a)

0

5

10

15

20

Bloc

k co

unts



2 3 85 6 7 91 4Axial strain ()

(b)


x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

25

z (m

m)

(a)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(b)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(c)

70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

1020 2030

30

40

40

50

50

60

(d)

Figure 9 Continued


70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(e)

70

65

60

55

50

45

40

35302520

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(f )


(a)

(b)

(c)

Figure 10 Continued


(d)

(e)


(a) (b) (c) (d)

(e) (f ) (g) (h)




4 Conclusions






Data Availability




Acknowledgments


References

















































uw

(2)


u ρa + bZ

38

E321113888 1113889 (3)












X-ray source(450kV)


Loading device

Rotation table

(a)


Hydraulic jack

Hoek cell system



(b)















100

90

80

70

60

50

40

30

20

10

0

z (m

m)

x (mm) y (mm)

0

0

10

10

20

0yprime

xprime

zprime

2030 3040 40

5050

60

60

(c)

(a)

(b)


20

18

16

14

12

10

08

06

04

02

00

Axi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10 11Axial strain ()



1

(2)

(1)

(3) (4) (5) (6)

2

3 4 5

6



Soil matrix

Soil matrix

Rock block

Rock block

CrackCrack

Crack

Crack

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52mm


ndash909ndash904


Relat

ive h

ouns

field

uni

ts

Hcrack

Hsoil

Hblock

Rock block

Hoek cell

Crack

ROI of SRM




(b)(a)


(a)

(b)

(c)

(d)

Figure 5 Continued


(e)

(f )


70

65

60

5550454035302520

z (m

m)

x (mm)

010

2030

4050

y (mm)

010

2030

4050

H = 65mm

H = 50mm

H = 35mm

(a)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)

0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

38

36

34

32

30

28

26

24

(b)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

54

52

50

48

46

44

42

40

38

(c)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

70

65

60

55

(d)



(a)

(b)

(c)

(d)

(e)

(f )









1 2 3 4 5 6 7 8 90Axial strain ()


34

36

38

40

42

44

46

48

50

52Bl

ock

coun

ts

(a)

0

5

10

15

20

Bloc

k co

unts



2 3 85 6 7 91 4Axial strain ()

(b)


x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

25

z (m

m)

(a)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(b)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(c)

70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

1020 2030

30

40

40

50

50

60

(d)

Figure 9 Continued


70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(e)

70

65

60

55

50

45

40

35302520

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(f )


(a)

(b)

(c)

Figure 10 Continued


(d)

(e)


(a) (b) (c) (d)

(e) (f ) (g) (h)




4 Conclusions






Data Availability




Acknowledgments


References
















































X-ray source(450kV)


Loading device

Rotation table

(a)


Hydraulic jack

Hoek cell system



(b)















100

90

80

70

60

50

40

30

20

10

0

z (m

m)

x (mm) y (mm)

0

0

10

10

20

0yprime

xprime

zprime

2030 3040 40

5050

60

60

(c)

(a)

(b)


20

18

16

14

12

10

08

06

04

02

00

Axi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10 11Axial strain ()



1

(2)

(1)

(3) (4) (5) (6)

2

3 4 5

6



Soil matrix

Soil matrix

Rock block

Rock block

CrackCrack

Crack

Crack

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52mm


ndash909ndash904


Relat

ive h

ouns

field

uni

ts

Hcrack

Hsoil

Hblock

Rock block

Hoek cell

Crack

ROI of SRM




(b)(a)


(a)

(b)

(c)

(d)

Figure 5 Continued


(e)

(f )


70

65

60

5550454035302520

z (m

m)

x (mm)

010

2030

4050

y (mm)

010

2030

4050

H = 65mm

H = 50mm

H = 35mm

(a)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)

0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

38

36

34

32

30

28

26

24

(b)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

54

52

50

48

46

44

42

40

38

(c)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

70

65

60

55

(d)



(a)

(b)

(c)

(d)

(e)

(f )









1 2 3 4 5 6 7 8 90Axial strain ()


34

36

38

40

42

44

46

48

50

52Bl

ock

coun

ts

(a)

0

5

10

15

20

Bloc

k co

unts



2 3 85 6 7 91 4Axial strain ()

(b)


x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

25

z (m

m)

(a)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(b)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(c)

70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

1020 2030

30

40

40

50

50

60

(d)

Figure 9 Continued


70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(e)

70

65

60

55

50

45

40

35302520

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(f )


(a)

(b)

(c)

Figure 10 Continued


(d)

(e)


(a) (b) (c) (d)

(e) (f ) (g) (h)




4 Conclusions






Data Availability




Acknowledgments


References




















































100

90

80

70

60

50

40

30

20

10

0

z (m

m)

x (mm) y (mm)

0

0

10

10

20

0yprime

xprime

zprime

2030 3040 40

5050

60

60

(c)

(a)

(b)


20

18

16

14

12

10

08

06

04

02

00

Axi

al st

ress

(MPa

)

0 1 2 3 4 5 6 7 8 9 10 11Axial strain ()



1

(2)

(1)

(3) (4) (5) (6)

2

3 4 5

6



Soil matrix

Soil matrix

Rock block

Rock block

CrackCrack

Crack

Crack

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52mm


ndash909ndash904


Relat

ive h

ouns

field

uni

ts

Hcrack

Hsoil

Hblock

Rock block

Hoek cell

Crack

ROI of SRM




(b)(a)


(a)

(b)

(c)

(d)

Figure 5 Continued


(e)

(f )


70

65

60

5550454035302520

z (m

m)

x (mm)

010

2030

4050

y (mm)

010

2030

4050

H = 65mm

H = 50mm

H = 35mm

(a)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)

0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

38

36

34

32

30

28

26

24

(b)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

54

52

50

48

46

44

42

40

38

(c)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

70

65

60

55

(d)



(a)

(b)

(c)

(d)

(e)

(f )









1 2 3 4 5 6 7 8 90Axial strain ()


34

36

38

40

42

44

46

48

50

52Bl

ock

coun

ts

(a)

0

5

10

15

20

Bloc

k co

unts



2 3 85 6 7 91 4Axial strain ()

(b)


x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

25

z (m

m)

(a)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(b)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(c)

70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

1020 2030

30

40

40

50

50

60

(d)

Figure 9 Continued


70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(e)

70

65

60

55

50

45

40

35302520

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(f )


(a)

(b)

(c)

Figure 10 Continued


(d)

(e)


(a) (b) (c) (d)

(e) (f ) (g) (h)




4 Conclusions






Data Availability




Acknowledgments


References












































Soil matrix

Soil matrix

Rock block

Rock block

CrackCrack

Crack

Crack

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52mm


ndash909ndash904


Relat

ive h

ouns

field

uni

ts

Hcrack

Hsoil

Hblock

Rock block

Hoek cell

Crack

ROI of SRM




(b)(a)


(a)

(b)

(c)

(d)

Figure 5 Continued


(e)

(f )


70

65

60

5550454035302520

z (m

m)

x (mm)

010

2030

4050

y (mm)

010

2030

4050

H = 65mm

H = 50mm

H = 35mm

(a)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)

0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

38

36

34

32

30

28

26

24

(b)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

54

52

50

48

46

44

42

40

38

(c)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

70

65

60

55

(d)



(a)

(b)

(c)

(d)

(e)

(f )









1 2 3 4 5 6 7 8 90Axial strain ()


34

36

38

40

42

44

46

48

50

52Bl

ock

coun

ts

(a)

0

5

10

15

20

Bloc

k co

unts



2 3 85 6 7 91 4Axial strain ()

(b)


x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

25

z (m

m)

(a)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(b)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(c)

70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

1020 2030

30

40

40

50

50

60

(d)

Figure 9 Continued


70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(e)

70

65

60

55

50

45

40

35302520

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(f )


(a)

(b)

(c)

Figure 10 Continued


(d)

(e)


(a) (b) (c) (d)

(e) (f ) (g) (h)




4 Conclusions






Data Availability




Acknowledgments


References












































(e)

(f )


70

65

60

5550454035302520

z (m

m)

x (mm)

010

2030

4050

y (mm)

010

2030

4050

H = 65mm

H = 50mm

H = 35mm

(a)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)

0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

38

36

34

32

30

28

26

24

(b)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

54

52

50

48

46

44

42

40

38

(c)

ε = 0ε = 1480ε = 3083ε = 4012ε = 6012ε = 8032

x (mm)y (m

m)0

0

10

1020 2030

30

40

40

50

50

60

60

z (m

m)

70

65

60

55

(d)



(a)

(b)

(c)

(d)

(e)

(f )









1 2 3 4 5 6 7 8 90Axial strain ()


34

36

38

40

42

44

46

48

50

52Bl

ock

coun

ts

(a)

0

5

10

15

20

Bloc

k co

unts



2 3 85 6 7 91 4Axial strain ()

(b)


x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

25

z (m

m)

(a)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(b)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(c)

70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

1020 2030

30

40

40

50

50

60

(d)

Figure 9 Continued


70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(e)

70

65

60

55

50

45

40

35302520

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(f )


(a)

(b)

(c)

Figure 10 Continued


(d)

(e)


(a) (b) (c) (d)

(e) (f ) (g) (h)




4 Conclusions






Data Availability




Acknowledgments


References












































(a)

(b)

(c)

(d)

(e)

(f )









1 2 3 4 5 6 7 8 90Axial strain ()


34

36

38

40

42

44

46

48

50

52Bl

ock

coun

ts

(a)

0

5

10

15

20

Bloc

k co

unts



2 3 85 6 7 91 4Axial strain ()

(b)


x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

25

z (m

m)

(a)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(b)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(c)

70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

1020 2030

30

40

40

50

50

60

(d)

Figure 9 Continued


70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(e)

70

65

60

55

50

45

40

35302520

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(f )


(a)

(b)

(c)

Figure 10 Continued


(d)

(e)


(a) (b) (c) (d)

(e) (f ) (g) (h)




4 Conclusions






Data Availability




Acknowledgments


References


















































1 2 3 4 5 6 7 8 90Axial strain ()


34

36

38

40

42

44

46

48

50

52Bl

ock

coun

ts

(a)

0

5

10

15

20

Bloc

k co

unts



2 3 85 6 7 91 4Axial strain ()

(b)


x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

25

z (m

m)

(a)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(b)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(c)

70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

1020 2030

30

40

40

50

50

60

(d)

Figure 9 Continued


70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(e)

70

65

60

55

50

45

40

35302520

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(f )


(a)

(b)

(c)

Figure 10 Continued


(d)

(e)


(a) (b) (c) (d)

(e) (f ) (g) (h)




4 Conclusions






Data Availability




Acknowledgments


References












































1 2 3 4 5 6 7 8 90Axial strain ()


34

36

38

40

42

44

46

48

50

52Bl

ock

coun

ts

(a)

0

5

10

15

20

Bloc

k co

unts



2 3 85 6 7 91 4Axial strain ()

(b)


x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

25

z (m

m)

(a)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(b)

x (mm) y (mm)

0

0

10

1020 20

30

30

40

40

50

50

70

65

60

55

50

45

40

35

30

z (m

m)

(c)

70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

1020 2030

30

40

40

50

50

60

(d)

Figure 9 Continued


70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(e)

70

65

60

55

50

45

40

35302520

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(f )


(a)

(b)

(c)

Figure 10 Continued


(d)

(e)


(a) (b) (c) (d)

(e) (f ) (g) (h)




4 Conclusions






Data Availability




Acknowledgments


References












































70

65

60

55

50

45

40

35

30

25

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(e)

70

65

60

55

50

45

40

35302520

z (m

m)

x (mm) y (mm)

0

0

10

10

20 203030

40

40

50

5060

60

(f )


(a)

(b)

(c)

Figure 10 Continued


(d)

(e)


(a) (b) (c) (d)

(e) (f ) (g) (h)




4 Conclusions






Data Availability




Acknowledgments


References












































(d)

(e)


(a) (b) (c) (d)

(e) (f ) (g) (h)




4 Conclusions






Data Availability




Acknowledgments


References













































4 Conclusions






Data Availability




Acknowledgments


References











































































Documents

InSituX-RayComputedTomography(CT)Investigationon ...downloads.hindawi.com/journals/ace/2020/8851817.pdf · for loose and dense sand, using direct shear test, triaxial compression