Experimental investigation of creep behavior of clastic rock in Xiangjiaba Hydropower Project

Yu Zhang*，Wei-ya Xu，Jian-fu Shao，Hai-in Zhao，WeiWangaCollege of Pipeline and Civil Engineering，China University of Petroleum，Qingdao 266555，PRChinaGeotehnial Researh Institute，HohaiUniversity，Nanjing 210098，PRChinaHunan Provinial Key Laoratory of Key Tehnology on Hydropower Development，Changsha 410014，PRChina Reeived 10 April 2014；aepted 2 Deemer 2014Availale online 21 January 2015

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Experimental investigation of creep behavior of clastic rock in Xiangjiaba Hydropower Project

Yu Zhanga，b，*，Wei-ya Xub，Jian-fu Shaob，Hai-bin Zhaoc，WeiWangbaCollege of Pipeline and Civil Engineering，China University of Petroleum，Qingdao 266555，PRChinabGeotechnical Research Institute，HohaiUniversity，Nanjing 210098，PRChinacHunan Provincial Key Laboratory of Key Technology on Hydropower Development，Changsha 410014，PRChina Received 10 April 2014；accepted 2 December 2014
Available online 21 January 2015

Abstract

There aremany fracture zones crossing the dam foundation of the X iangjiaba Hydropow er Project in southw estern China.Clastic rock is the main media of the fracture zone and has poor physical and mechanical properties.In order to investigate the creep behavior of clastic rock，triaxial creep testsw ere conducted using a rock servo-controlling rheological testingmachine.The results show that the creep behavior of clastic rock issignificantatahigh levelof deviatoric stress，and less time-dependentdeformation occursathigh confining pressure.Based on the creep test results，the relationship between axialstrain and timeunder differentconfining pressureswas investigated，and the relationship between axial strain rate and deviatoric stresswas also discussed.The strain rate increases rapidly，and the rock sample failseventually underhigh deviatoric stress.Moreover，the creep failuremechanism under different confining pressureswas analyzed.Themain failuremechanism of clastic rock is p lastic shear，accompanied by a significant com pression and ductile dilatancy.On the other hand，w ith the determ ined parameters，the Burgers creepmodelw asused to fit the creep curves.The results indicate that the Burgersmodel can exactly describe the creep behavior of clastic rock in the Xiangjiaba Hydropower Project. ?2015 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license（http:// creativecommons.org/licenses/by-nc-nd/4.0/）.

Rock mechanics；Clastic rock；Creep behavior；Triaxial creep test；Burgers creep model；Xiangjiaba Hydropower Project

1.Introduction

The time-dependent（creep）behavior of rock refers to the continued deformation under the effects of constant stress，including deformations，slips，and failures（Sun，2007；M a，2004；Brantut et al.，2013）.It is one of the most important m echanical properties of rockmaterial，and can be considered an importantbasis forexplaining and analyzing thephenomena of geological tectonic movement，as well as predicting longterm stability for rock engineering（Tsaietal.，2008；Yang and Jiang，2010；Zhang etal.，2013）.Therefore，the time effectof geotechnical engineering stability is increasingly considered. Taking into accountdelayed deformations，it isconsidered that failure can take p lace over a large span of tim e in many geotechnical projects（Bayraktar et al.，2009；Yin et al.，2013；Yang et al.，2014）.A lot of deformation failures and losses of stability in geotechnical projectsare not instancesof transient destruction，but develop over time（Dusseault and Fordham，1993；Boukharov etal.，1995；Dam janac and Fairhurst，2010）. Deformation of thedam foundationsand abutmentscan last for severaldecades，and creep failureof rock tunnelscanoccurafter construction for several decades（Fan，1993；Gudmundsson etal.，2010；Zhang etal.，2012，2014b）.Therefore，itisessential to study the creep propertiesof rocks.

Laboratory testing is the most importantmethod of studying rock mechanical properties（Maranini and Brignoli，1999；Li and Xia，2000）.It is also used to analyze rock creep constitutive relations and parameters meant to evaluate the long-term stability of rock engineering（Dahou et al.，1995；Pietruszczak et al.，2002；Barla et al.，2012）.Many achievements in the experimental study of creep behavior of different types of rocks have been made in China and other countries. Based on a number of uniaxial and triaxial creep test results，the effects of confining pressure and axial pressure on the creep stress-strain behavior of salt rock were analyzed by Yang etal.（1999），and an exponential function was suggested tomodel the creep strain from transient to steady states.Carter etal.（1993）investigated the influence of temperature on creep behavior and found that the time-dependent properties of salt rock were strongly dependent on temperature.Chan et al.（1997）reported a large number of uniaxial and triaxial test resultsand analyzed the confining pressureeffectson the creep strain.Li et al.（2008）studied the relation of complete creep processesand triaxial stress-strain curves of rocks.Fabre and Pellet（2006）demonstrated the creep behavior of three kinds of rocks characterized by a high proportion of clay particles，and theviscosity of thesesedimentary rockswasstudied under different loading conditions.However，concerning thestudy of creepmechanical properties of rocks in some specific projects such as hydropower projects，little experimental data have been reported.

There aremany existing large-scale hydropower projects in southwestern China，which create severe challenges for experiments and the theoretical and numerical research on the creep behavior of rocks and long-term stability of rock engineering.This study focused on the creep behavior of the clastic rock core from the Limeiwan fracture zone in the dam foundation of the Xiangjiaba Hydropower Project，which is located on the lower pool of the Jinsha River，at the border of Sichuan and Yunnan provinces.The dam is a concrete gravity dam w ith amaximum height of 161m and a length of 909m. The fracture zone crosses the dam foundation，and the area and thicknessof the fracture zone are relatively large（Fig.1）. Clastic rock is themainmedia of the fracture zone and ithas poor physical and mechanical properties.The creep mechanical behavior of such rock has an important impact on the long-term stability of engineering structures and should be investigated carefully.This paper presents the results of triaxial creep tests on this clastic rock.Based on creep experim ents under different confining pressures，the creep constitutive relation and param eters have been determ ined.

Fig.1.Xiangjiaba Hydropower Project and fracture zone in dam foundation.

Fig.2.Geological distribution of clastic rock in Xiangjiaba Hydropower Project.

2.Lithologic characteristics and experim ental p rogram

2.1.Lithologic characteristics of rock samples

The clastic rock materials were obtained from the T32-6sub-petrofabric in the fracture zone in cataclastic and clastic shapes（Fig.2）.They were soft rocks w ith poor integrity，which were highly weathered and had the characteristics of low specific gravity，medium porosity，loose organizational structure，and high moisture content.The results of basic physical property tests showed that the averages of natural density and dry density were 2.375 g/cm3and 2.225 g/cm3，respectively.The averages of moisture content and porosity were 6.59%and 18.23%，respectively.Furthermore，the flow behavior showed that the permeability coefficient varied from 0.14×10-5to 16.3×10-5cm/s in the natural state，and its values were alm ost the sam e in the directions parallel and perpendicular to the bedding plane.In view of this，it can be concluded that at the sample scale，the rock wasmid-permeablew ith isotropic permeability（Zhang etal.，2014a）.

Opticalmicroscopic tests were performed to analyze the m icrostructure and mineral composition of the clastic rock（Fig.3）.The results indicated that the clastic rock retained fine-grained texture w ith an extremely complex microstructure.Also，themainmineral composition consisted of quartz，chalcedony，feldspar（K-feldspar and plagioclase），sericite，chlorite，a small amount of iron com pounds，and tracem inerals.The trace minerals mainly included tourmaline，zircon，phosphorites，zoisite，and glauconite.The main chemical constituent was SiO2（accounting for 80.75%-83.52%），followed by Al2O3，and asmallamountofmixtureof Fe2O3，CaO，and MgO.

2.2.Test equipment and procedure

The experiments were performed w ith the rock servocontrolling rheological testingmachine（Zhang etal.，2014b）. This equipment can be used to carry out conventional compression testsand rheological tests such asuniaxial creep tests and triaxial creep tests.The confining pressure ranged from 0 to 60 MPa，and themaximum deviatoric stress could reach 500MPa.Themulti-step loadingmethod wasadopted in axial loading，with steps ranged from 4 to 6.The temperature and hum idity were kept constant during all tests.The sam ples were standard cylindrical，50 mm in diameter and 100 mm in height.Due to the poor quality of some rock samples，extreme care was necessary in handling of the samples，and some special preparationswere required.For instance，the samples were stored with a sealing technique.Thesame testprocedures were described in Zhang et al.（2013）.

Fig.3.Opticalm icroscopic test results of clastic rock sample.

Fig.4.Typical com pression stress-strain curves under different confining pressures.

3.Behavior of conventional triaxial com pression tests

In order to confirm multi-step stress levels of triaxial creep tests，conventional triaxial compression tests on clastic rock samples under the confining pressures of 1.0 MPa，1.5 MPa，and 2.0 MPa were carried out first.Typical conventional compression stress-strain curvesof the clastic rock are shown in Fig.4，whereσandεare the deviatoric stress and strain of rock，respectively，and mechanical parameters are listed in Table 1.The stress-strain curves show approximate plastic platforms when the strain exceeds a limit value.It is also worthwhile to point out that the samp le fails when the axial strain exceeds 5.0%，which ismuch larger than that for hard rock.We can conclude that the peak strength increases gradually with the confining pressure.It can be seen that the sample is not at an obvious stage of crack closure.

In general，the response can be decomposed into four phases for all tests.During the initial loading，a quasi-linear and reversible stress-strain relation is obtained，indicating the elastic compressibility of the rock skeleton，and the elastic modulus can be determined from the slope of the stress-strain curve in this phase.W hen the stress reaches a certain value，called the yield stress，a nonlinear p lastic phase is observed，w ith significant increase of strain，and the slope of the curve decreases.Under different confining pressures，nonlinear behavior begins at axial strains of about 1.0%.With the incremental stress，a general strain-hardening phase is produced w ith the increase of the contact surface among grains.Followed by a large axial strain，the phase of plastic failure occurs，in which cracks coalesce.These phases are similar to plastic consolidation in soilmechanics.Due to the hardening behavior of stress-strain curves of the clastic rock，the deformationmodulus is slightly lower than the elasticmodulus.The deformation modulus of the rock sample has a close relation w ith the nonlinear deformation under prim ary loading.

Table 1 Conventionalmechanical parameters of compression tests of clastic rock（MPa）.

4.Results of triaxial creep tests

4.1.Analysis of creep strain

Triaxial creep tests were performed at ambient temperatures of（20.0±1.5）°C.The confining pressures in the creep tests were the same as those in the conventional triaxial compression tests.Under the confining pressure of 1.0 MPa，the deviatoric stresses of 1.00，1.50，2.50，and 3.00 MPawereselected，while under the confining pressures of 1.5 and 2.0 MPa，the deviatoric stress was increased by 0.75 MPa per step from 1.00 to 4.75MPa until failure of laboratory samp les occurred.Ateach loading step，the deviatoric stresswas kept constant for a time interval ofmore than 48 h w ith the axial strain continuously recorded.

The axial strain-time curves under different confining pressures are presented in Fig.5.Creep curves are smooth w ithout fluctuation，indicating that the creep strain has continuity over time.The resultsshow thatata low deviatoric stress level，the axial creep strain is unnoticeable，while the creep phenomenon of the clastic rock becom es significantw ith the increase of the deviatoric stress.The main feature associated w ith the failure is the high axial plastic strain as well as the high strain ratedue to long-term accumulation of creep effects. Therefore，no brittle damage is observed in the rock samples.

As shown in Fig.5（a），under the confining pressure of 1.0 MPa，when the deviatoric stress is less than 2.5MPa，the creep strain is unnoticeable.When the deviatoric stress increases to 2.5 MPa，the increment of axial creep strain is 0.71%.W hen the deviatoric stress reaches 3.00MPa，the creep strain isgreater than at previous stress levels.After five hours of constant loading，the creep strain increases by 0.83%，and，eventually，the rock sample fails via the large creep strain.

As shown in Fig.5（b），under the confining pressure of 2.0MPa，when the deviatoric stress is less than 3.25MPa，the creep strain is unnoticeable.When the deviatoric stress reaches 4.75 MPa，the creep strain increasesmore quickly than before.After three hours of constant loading，the creep strain increases by 0.82%，and the rock samp le fails eventually.In general，the confining pressure has a significant influence on the creep strain of rock samples.Under the same condition，the greater the confining pressure is，the lesser the corresponding creep strain w ill be.

Fig.5.Relation between creep strain and time under different confining pressures.

4.2.Analysis of creep strain rate

It can be deduced from Fig.（5）that for a certain value of the deviatoric stress，the strain rate increases first and then gradually decreases to a constant value after a period of time. According to the evolution of the creep strain rate，the creep curve can be divided into transient and steady stages.The creep strain rate tends to be a value close to zero at low deviatoric stress.Athigh deviatoric stress，the evolution of the creep strain rate is similar to itsperformance at low deviatoric stress，but thevalue isgreater.Under the confining pressure of 2.00MPa，the creep strain rate tends to be a constant value of 0.8×10-3h-1ata deviatoric stressof 1.0MPa，and thevalue increases to 5.53×10-3h-1atadeviatoric stressof 4.00MPa. After the stressof 4.75MPa isapplied at the last loading step，the strain rate significantly increases until the rock sam ple fails，and the process lasts about three hours.Therefore，the strain rate increases w ith the deviatoric stress.

4.3.Creep failuremode and mechanism

The creep failure patterns under different confining pressuresare shown in Fig.6.Themain failuremechanism of the rock sample is plastic shear accompanied by a significant compression and ductile dilatancy.Sample failure is classically produced by the pore compression and crack coalescence.It can be said that the essential failure is the result of synthetic effects of the material defects，heterogeneity，and long-term accum ulation of m icrocrack dam age.Under time and loading effects，micromovement is caused by the crystal displacement and m ineral cleavage.Thus，the rock deformation includes the diffusion of lattice dislocations，crack expansion，and compatible deformation among grains.The rock has different scales of initialmicrodefects，such as fissures，joints，dislocations，etc.，which determine the macroscopic behavior of the rock.It is very easy form icrodefects to develop and dislocate between grains and cleavages under constant loading.Then，ductile deform ation accom panied by m oderate dilation or even com paction results in a number of smallmacrocracks on the sample surface.

Fig.6.Typical creep failure patterns of clastic rock.

Based on the m icroscale and m esoscale analyses，this section discusses the shapes of internal m icrodefects after creep failure.The sampleswere selected along the surface of the fracture zone in this study.From the scanning electron m icroscope（SEM）observations（Fig.7），itcan be seen that the m icroscopic failure patterns are slightly different under various confining pressures.There aremore grow ing cracks，and the fracture surface is coarsew ith lessmicro grainsunder low confining pressures.With the increase of the confining pressure，the porosity decreasesw ithmoremicro grainson the fracture surface.During the testing process，m icrofissure damage inside the rock sample continuously accumulates，and then，the cracks，originating from the defectsof initial internal voids，extend and interpenetrate，and eventually lead to the failure.

Fig.7.SEM observations of rock samples after creep failure at magnification of 1000.

5.Creep m odel and param eter identification

The creep curves in Fig.5 show that the clastic rock sample experiences a transient creep stage and a steady creep stage under each step of loading，and the creep strain rate first increasesand then decreases toward a constantvalue.According to the creep behaviorshown by these curves，the Burgerscreep model，which can be regarded as the combination of the Maxwell m odel and Kelvin model，was chosen to describe those results（Fig.8）.

Fig.8.Illustration of Burgers creep model.

The constitutive equation of the Burgers creepmodel isas follows:

whereσM，εM，and˙εMare thedeviatoricstress，strain，and strain rate of the Maxwell body，respectively；σK，εK，and˙εKare the deviatoric stress，strain，and strain rate of the Kelvin body，respectively；EMandηMare the elastic modulus and viscosity coefficientof the Maxwellbody；and EKandηKare the elastic modulusand viscosity coefficientof the Kelvin body.

Using the Laplace transform to solve Eq.（1），the corresponding creep constitutive equation can be expressed:

The datameasured undermulti-step loading in the testwere processed using Boltzmann superposition（Zhang，2012）.In order to determ ine creep m echanical parameters at different deviatoric stresses，an iteration procedure was used based on the Quasi-New ton searchmethod.The relevant parametersof the Burgerscreepmodelwere identified from data processing，as shown in Table 2，and the fitted curves could be obtained w ith the required precision.Through analysis of the obtained creep mechanical parameters（Table 2），it can be determ ined that the Burgersmodel parameters vary w ith the deviatoric stress and the time-dependent deformation of the clastic rock increases w ith the long-term constant deviatoric stress.

Table 2 Creep parameters of clastic rock under different confining pressures.

As shown in Table 2，under the confining pressures of 1.5 MPa and 2.0MPa，the elastic modulus EMis high at the first deviatoric stress.Then，EMgradually decreases w ith the increase of the deviatoric stress.The rock is linear elastic in this stage.W hen the deviatoric stress increases to a certain value，the rock sample enters the plastic phase and，at this stage，eventually fails.During this stage，EMshows a further decrease.Therefore，by analyzing the evolutions of EM，we observe that the degradation of the elastic modulus is decelerated w ith the increase of the deviatoric stress，and the value of EMvaries by a power function w ith the deviatoric stress during creep tests（Fig.9（a））.Because of the high heterogeneity of the rock sample，the evolution of the elasticmodulus is insignificant under the confining pressure of 1.0MPa.

The viscosity coefficientηMcan reflect the variation of the strain rate of steady creep.Generally，the strain rateof thisstage isquasi-independentof the loading history and dependsonly on the currentstressstate（Yang etal.，1999）.Asshown in Table2，ηMdemonstratesan overall increasing trendw ith thedeviatoric stress，indicating thatthestrain rateofsteady creep continues to increase until the deviatoric stress reaches itsmaximum.The relationships betweenηMand deviatoric stress can also be expressed by a power function（Fig.9（b））.EK/ηKreflects the duration from the transient creep to steady creep.It takes the rock more time to reach a steady statewhen EK/ηKis lower. Results show that relationship between EK/ηKand deviatoric stress can be expressed by an exponential function（Fig.9（c））.

The comparison between the Burgersmodel's predictionsof creep curvesand tested creep resultsunder different confining pressures is shown in Fig.10.The Burgersmodel can describe well the time-dependentbehaviorof the clastic rock aswell as transient and steady creeps.

Fig.9.Relations between Burgersmodel parameters and deviatoric stress.

6.Conclusions

（1）The creep behavior of clastic rock is not significant at low deviatoric stress.However，at high deviatoric stress，the creep behavior is very significant，and the time-dependent deformation is large.Two creep phases，the transient and steady stages，appear to a significant degree when the deviatoric stress ishigh.The time-dependent deformation decreases w ith the increase of the confining pressure，indicating that less creep of the rock samp lemay occur athigh confining pressure.

（2）The creep strain rate of the rock sam ple varies w ith the deviatoric stress.The strain rate tends to be a value close to zero over timeat low deviatoric stress.However，the strain rate increasesw ith the deviatoric stress.When the deviatoric stress is increased to a certain value，the strain rate increases rapidly，and the rock sample fails eventually.

（3）Themain failure mechanism of clastic rock is plastic shear，accompanied by a significant compression and ductile dilatancy.The failure may be due to the occurrence，development，and coalescence of m icrocracks under long-term constant stresses.As shown by SEM experiments，creepstrains and microscopic failure patterns are different under different confining pressures.The reason is that the microfissure damages inside the rock sample continuously accumulate in the process of creep testing.

（4）Based on the tested results，the creep parametersof the Burgers creep model are determ ined through curve fitting of measured data.The results demonstrate a high precision of the Burgers creep model in prediction of the creep curve as compared w ith the measured curve.Thus，the model can describe the overall time-dependentbehaviorof clastic rock.It can provide a basis for creep numerical simulation，which is vital for predicting the long-term stability of the Xiangjiaba Hydropower Project.

Fig.10.Comparison between Burgers model's prediction of creep curves and tested results.

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This work was supported by the National Natural Science Foundation of China（Grants No.51409261 and 11172090），the Natural Science Foundation of Shandong Province（Grants No.ZR2014EEQ014），and the Applied Basic Research Programs of Qingdao City（Grant No.14-2-4-67-jch）.

*Corresponding author.

E-mail address:zhangyuhohai@gmail.com（Yu Zhang）.

Peer review under responsibility of HohaiUniversity.

http://dx.doi.org/10.1016/j.w se.2015.01.005

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