IP-CH006

Keynote lectures

Harmonising Rock Engineering and the Environment–Qian&Zhou(eds)

?2012Taylor&Francis Group,London,ISBN978-0-415-80444-8

New rock mechanics developments in China

Xia-Ting Feng

State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,

Chinese Academy of Sciences,Wuhan,China

ABSTRACT:This paper reviews new rock mechanics developments in China in the last ten years.A series of devices for laboratory tests,in situ tests and monitoring have been developed.Also,strength criteria based on energy and for hard rocks, progressive and anisotropic damage models,coupled THM models,new creep models,the vector sum method,reinforcement theory,and a multi-scale and non-linear thermodynamic theory were established.There have been major developments in studying zonal disintegration,rock dynamics,fractals in rock mechanics,rock fracturing process simulation methods,and intelligent rock mechanics methodology.The3-D limit equilibrium methods,strength reduction method,FEM,BEM,NMM, Meshless method,and DDA were updated.There have been considerable efforts on mechanism understanding through lab and real time field monitoring,prediction and the mitigation of rockbursts.The need for rock engineering projects has largely promoted the development of rock mechanics;and rock mechanics has provided a practical tool to support complicated rock engineering problems.Further development of rock mechanics in China is anticipated and more applications of rock mechanics to rock engineering are expected.

Subject:Modelling and numerical methods

Keywords:Lab tests,field measurements,back analysis,neural network,numerical modelling,dynamics

1INTRODUCTION

Rock Mechanics is a discipline having strong practical appli-cations.The construction of large-scale rock engineering projects in China,including high/steep slopes,large cavern groups,mining stopes,tunnels,oil wells,and foundations, has promoted the development of rock mechanics in China. Oil and gas underground storage,nuclear waste disposal, CO2sequestration,and geothermal development have pro-moted the development of couplingTHMC processes in rocks. Sun&Wang(2000)have summarised the development and the state-of-the-art of rock mechanics in China before2000. The‘century achievement’in rock mechanics in China has been summarised in the book published by Hohai University Press(Wang,2004).

In memory of Tan Tjong Kie,who initiated the Interna-tional Society for Rock Mechanics(ISRM)China National Group in1979,was the first President of the Chinese Soci-ety for Rock Mechanics and Engineering(CSRME)and was the ISRM Vice-President for Asia during1983–1987,the Tan Tjong Kie Lecture series was initiated in2008.Three lectures have been given by:

?Sun Jun(2007),ISRM Vice-President at Large1995–1999 and President of CSRME1994–1998;

?Wang Sijing(2009),President of CSRME1999–2003;and ?Qian Qihu(2009),ISRM Vice-President at Large2003–2007and President of CSRME2003–present.

The4th Tan Tjong Kie Lecture will be given by Ge Xiuren this year on the measurement of in situ stress and its estima-tion.Following the development of Chinese Journals,such as the Chinese Journal of Rock Mechanics,the Chinese Jour-nal of Underground Space and Engineering,Rock and Soil Mechanics,a new English language journal,the Journal of Rock Mechanics and Geotechnical Engineering,was launched in2009.

This paper just provides a brief review of the new devel-opments in rock mechanics in China over the latest ten years and covers lab and field tests,mechanical models and crite-ria,analysis methods for rock samples,slopes,tunnels,and cavern groups,rock dynamics and zonal disintegration of a deep rock mass,and applications of rock mechanics to rock engineering.In the years ahead,further development of rock mechanics in China is anticipated and more applications of rock mechanics in rock engineering are expected.

2LABORATOR Y&FIELD TESTING TECHNIQUES 2.1Laboratory testing techniques

In order to enhance understanding of the rock fracturing process under complicated environmental conditions,test-ing systems were developed using a medical or industrial CT scanner with a loading system and a microscope with CCD cameras.Ge(2004)developed firstly a CT real-time testing technique for triaxial testing and study of the meso-damage evolution law.Through CT scanning,clear CT images can be obtained which include the micro-hole(microcrack) compressed?the microcrack growth?the microcrack bifurcation?the microcrack development?crack frac-ture?rock sample destroyed?unloading.This technique was further developed by Xie Heping’s group using an indus-trial CT scanner.Chen Houqun led a group in developing a portable real-time dynamic loading apparatus with the sup-port of the medical CT(Tian et al.,2010).The apparatus is available for performing tests such as dynamic tension,com-pression test with impact,triangular and sine wave with the greatest load output being100kN,and frequency of5Hz. Under dynamic loading,the whole process of crack propaga-tion and coalescence,CT images are obtained.It is laying the foundation for dynamic CT testing of brittle materials.

A loading and microscopic observation apparatus for the meso-mechanical experiments on rock was developed by Ge et al.(2000).The testing devices were further developed to investigate the coupling process of chemical flow/permeability–stress by using a microscope,two CCD cameras,and a servo-control system(Feng&Ding,2007). The following testing systems have also been developed or updated for different purposes.

?Remote sensing techniques have been used to test the frac-turing process of rock samples,and‘remote sensing rock mechanics’was developed(Wu et al.,2004).With the techniques,precursors for rock fracturing and failure were found(Wu et al.,2006a,b).

?A testing machine for coupled seepage and triaxial stress measurements in rocks(Liu,2007).

?The RMT testing machine developed by Ge has become one of the main rock mechanics testing systems in institutes and universities in https://www.360docs.net/doc/e94188069.html,ing this machine,a series of fatigue,uniaxial/triaxial compressive and shearing tests have been conducted(Ge,2008).

?A testing device for rock subjected to coupled static and dynamic loads(Li et al.,2008).

?A20MN servo-controlled rock triaxial testing system with high temperature/pressure(Zhao et al.,2008).

?A Storage-variable transient pulse testing device(Li et al., 2008).

?A testing apparatus for simultaneously measuring adsorp-tion,deformation and permeability of coal(Fang et al., 2009).

?A coupled shear-seepage test system for rock joints(Xia et al.,2008).

?A rockburst simulation experimental system for loading in three directions independently and suddenly unloading on one side of the sample.A rockburst criterion was established (He et al.,2010).

2.2Field test and monitoring technique

In situ testing techniques have been significantly developed in China.Ge proposed a new method for stress measurement,i.e., the Borehole Wall Stress Relief Method,BWSRM.This has been successfully used,in particular in the deep tunnels of the Jinping hydropower station having an overburden of2430m.

A full temperature compensation technique was invented to eliminate measuring errors caused by temperature changes in overcoring stress measurement devices which use strain gauges as the sensing elements.An interpretation method for rock stress was developed using the measurement strain caused by stress relief considering the practical behaviour of a rock mass,such as non-linearity,anisotropy,discontinuity and non-homogeneity(Cai et al.,2009).These techniques make the measuring reliability and accuracy of stress relief by overcoring technique much better.New hydraulic fracturing equipment with high pressure capacity was developed which surmounted the shortcoming of the traditional hydraulic frac-turing technique which cannot be used at high depth if there is insufficient hydraulic pressure capacity.With the newly devel-oped equipment,stress measurement with hydraulic fracturing technique has been successfully completed at up to2800m depth(Cai et al.,2004).

A new remote real-time monitoring warning system for landslide disaster(SPRM)has been established based on the mechanical principle of interaction between the land-slide body,landslide bed and a constant-resistance large deformation cable(He et al.,2010).It has been installed in10 areas,and158monitoring points,in fields such as slopes at open-pits,mountains,gas pipelines and active faults.

3MECHANICAL MODELS AND FAILURE CRITERIA Much effort has been put into developing strength criteria for rock and rock masses,as follows.

?A Unified Strength criterion for rock material(Yu et al., 2002).

?A criterion for strength and structural failure of rocks based on energy dissipation and energy release principles(Xie et al.,2009).

?A triple shear energy yield criterion(Gao et al.,2007).?A strain criterion for ductile shear failure based on the maximum principal shear strain(Gao et al.,2007).

?A new three shear strength criterion for hard rock(Chen& Feng,2007).

?An anisotropic strength criterion for jointed rock masses (Chen et al.,2008).

?A generalized polyaxial strain energy(GPSE)strength criterion(Huang et al.,2008).

?A true-triaxial strength criterion for rock(Y ou,2009).?Mechanical characteristics of the exponential strength cri-terion under conventional triaxial stresses(Y ou,2010a,b). Some typical mechanical models for intact rock and rock masses have been developed.Examples are given below.?Analysis of the strain softening size effect for rock speci-mens based on shear strain gradient plasticity theory(Pan et al.,2002),

?A localised progressive damage model for fractured rock-like materials(Zhang et al.,2006),

?A coupled model for anisotropic damage and permeability variation(Zhou et al.,2007),

?A new Cosserat-like constitutive model for bedded salt rocks(Li et al.,2009),and

?A new model to describe the unloading behaviour of rock (Li et al.,2010).

4ANAL YSIS METHODS AND THEORIES

4.1Methods for slope stability analysis

Ge(2008)developed a vector sum method for slope stability analysis,believing that associated with a given failure surface there exists a direction,referred to as the critical slip direction s,the factor of safety F can be calculated

as

Here,S denotes the failure surface;τis the resultant shear stress vector acting on dS and[τ]is the vector of shear stress strength in the same direction asτ.

The following methods have also been developed for analysis of slope stability.

?A3-D slope stability analysis method using the upper bound theorem(Chen et al.,2001a and b).

?A generalised solution for tetrahedral rock wedge stability analysis(Chen,2004).

?The rigorous and quasi-rigorous limit equilibrium solutions to3-D slope stability,which satisfy six or five equilibrium conditions respectively,are derived(Zhu&Qian,2007).?The finite element strength reduction method has been developed—such as,the definition and computation method for double safety factor(double reduction factor), the structure instability and failure criteria in computation, and the numerical methods based on strength reduction for 3-D slope analysis(Zheng,2007).

?A3-D rigorous method that reduces the3-D analysis of slope stability to an algebraic eigenvalue problem and thus overcomes numerical problems inherent in the existing3-D methods(Zheng,2009).

?A Cauchy problem for3-D critical slip surfaces based on the stress field in slopes at the limit equilibrium state(Zheng et al.2011).Once the Cauchy problem is solved,the3-D critical slip surface of the slope can be determined without specifying the shape and the location.

?The meshless method and shortest path algorithm for rock slope stability analysis(Zhuang et al.,2008).

?Four criteria for stability analysis and assessment of high rock slopes(Li&Qian,2010).

4.2Study of fractals in rock mechanics

The geometry and configuration of the discontinuous geo-metry and irregular sub-structures,such as joints,pores and faults,of rock masses are investigated and characterised by means of3D laser scanning,the CT imaging process,statis-tics and fractal theories.The morphology and the distribution laws of joints and pores are extracted and analysed(Zhou et al., 2003,2004;Ju et al.,2007,2008).The novel3-D reconstruc-tion approaches are developed based on the investigation,plus fractals and statistical algorithms,to reconstruct those sub-structures that govern the apparent physical responses of rocks (Xie et al.,2001;Zhou et al.,2003;Ju et al.,2007,2008).The mechanical performance of rock masses subjected to static and impact loads,as well as the influences of sub-structures on the properties,are discussed based on reconstructed model simu-lations and experimental investigations(Xie et al.,2008;Zhou et al.,2003;Ju et al.,2007,2008,2009,2010).The intrinsic micro-or meso-scale processes that damage and invalidate the bearing capability of rocks are established(Xie et al.,2000, 2008;Ju et al.,2007,2008,2009,2010).This study opens a new window for understanding and quantifying the effects of complex sub-structures on rock performance.

Theoretical and experimental studies indicate that energy plays a key role in causing rock deformation and failure.The relations among energy dissipation,energy release,strength and catastrophic breakdown of rock systems during defor-mation are discussed.It is shown that the energy dissipated induces damage and irreversible deformations and leads to reduction in rock strength.The releasable strain energy results in catastrophic failure of the entire rock system.The criteria for strength reduction and catastrophic breakdown of rocks have been established on the basis of the energy principles. The experiments on marbles and layered limestones subjected to uniaxial and biaxial loads illustrate that the proposed energy criteria are in good agreement with the experimental results (Xie et al.,2009;Ju et al.,2007,2010).

The physical properties of rocks under high tempera-ture circumstances is one of the primary concerns in deep mine excavation.A series of laboratory tests on inves-tigating the mechanisms at the meso-scale level and for thermal-mechanical coupling effects of sandstones show that, with the temperature increase,thermal cracking exhibits a fractal property.A segmented strength model for sand-stone considering the coupled thermal-mechanical process is established(Zuo et al.,2010).

4.3Study on rock reinforcement and thermodynamic theory Y ang et al.(2007)proposed a reinforcement theory that the reinforcement force required by a geotechnical structure is just the residual unbalanced force obtained through elasto-plastic FEM analysis.A principle of minimum plastic complemen-tary energy is established,which requires that a structure always trends to the state of minimum reinforcement force and maximum self-bearing force for given loads.Because every load state characterised by an overloading factor K cor-responds to a minimum plastic complementary energy E min, the K? E min curve can be used to evaluate the global sta-bility of an arch dam.The theory has been widely used in the reinforcement design of the highest arch dams and rock slopes in China,e.g.Xiaowan arch dam(292m high),Jinping I arch dam(305m high)and Xiluodu arch dam(278m high),and was adopted in the latest version of the“Handbook of Arch Dam Design”released by the Chinese Hydroelectrical Authority. The multi-scale and non-linear thermodynamic theory of solids by J.R.Rice,has been substantially developed by Y ang et al.(2005).The evolution laws of second-order fabric tensors were derived within the extended normality structure.Based on Eshelby’s equivalent inclusion method,the solution of a3-D penny-shaped inhomogeneity surrounded by an unbounded isotropic matrix in a uniform stress field was developed as a much more versatile defect model.This model has been used for tunnels and dams,back analysis(Xiang et al.,Computers& Structures,80,1429–1440,2002),and dynamic damage (Zhang et al.,Int.J.Eng.Sci.,41,917–929,2003).By extend-ing the strain gradient theory and introducing an intrinsic material length scale into the constitutive law,the damage model is extended to model damage localisation analysis and applied to arch dam analysis by Zhou et al.(2002).

4.4Study of intelligent rock mechanics methodology

The intelligent rock mechanics methodology has been fur-ther developed.The fracturing and rockburst processes in the surrounding rock in deep TBM and D&B tunnels having an overburden of1900–2500m was understood through a series of in situ monitorings of deformation,wave velocity,crack-ing seen by digital borehole camera,acoustic emission,and micro-seismicity conducted at the Jinping hydropower sta-tion(Li et al.,2010;Chen et al.,2011).New indices,such as R VI,failure approach index(FAI)and local energy release rate(LERR),were proposed for prediction of rockbursts and rock failure in the Jinping headrace tunnels.

A hybrid evolutionary algorithm has been established to recognise the structure of non-linear mechanical models and parameters(Feng et al.,2006).An intelligent back analy-sis method was proposed to recognise mechanical rock mass parameters from the monitored displacement and excavation damaged zone(EDZ).

An elasto-plastic cellular automaton,EPCA2D and EPCA3D, utilising deformation and strength parameters evolving with damage,a failure approach index,FAI,and the local energy release rate,LERR,have been developed for numerical anal-ysis of the rock fracturing process and has been used for the simulation of the coupled THM process in the EDZ,the

thermal effect on a rock shaft at the Swedish?sp?Hard Rock Laboratory in the DECOV ALEX International Co-operative Project(Pan et al.,2009).

An intelligent rock design methodology has been developed and applied to stability analysis and design optimisation of the excavation and support systems for underground powerhouses at Jinping II,Laxiwa and Shuibuya power stations,the slopes at Longtan and Nuozhadu hydro-power stations,and the head-race tunnels at the Jinping II power station(Feng&Hudson, 2011).The results were adopted for the design of the projects and validated in practice.

4.5Numerical analysis methods

A rock failure process analysis code,RFP A2D and RFPA3D has been further developed by Tang’s group(Tang&Hudson, 2010).The codes have been used to simulate rock failure in uniaxial/indirect tension,uniaxial/triaxial compression,and failure induced by thermal stress,cutting,time dependency, dynamic loading,and longwall coal mining,plus around tun-nels in jointed rock,gas outbursts in coal mines,and the coalescence of fractures.

A coupled THM model for analysis of multiphase flow, thermal transport and stress/deformation in fractured porous media was developed and validated by the CEA Mock-up test and the FEBEX in situ experiment(Chen et al.,2009). Stress/strain-dependent hydraulic conductivity tensor models were proposed to describe the effects of post-peak mechan-ical behaviour,e.g.shear dilatancy and strain softening of fractures,on the macroscopic permeability of fractured rocks (Zhou et al.,2008).A parabolic variational inequality method of Signorini’s condition,combined with the sub-structure technique,was proposed to solve non-steady seepage flow problems with complex drainage systems(Chen et al.,2010). The FEM,DEM,DDA and numerical manifold methods have been developed further,as listed below.

?Viscous boundary of DDA for modelling stress wave propagation in jointed rock(Jiao,et al.,2007),

?A general composite element concept for a fully-grouted rock bolted element model in FEM analysis(Chen et al., 2003),

?A3-D boundary element method,dual boundary control technique of material parameter identification,and the infinite element for‘infinite problems’in geomechanics (Liu et al.,2008),

?Determining relative movements on boundaries,analysing fluid–structure interaction and simulating the static and dynamic responses of discontinuous rock tunnel excava-tion based on discontinuous boundary element,DDA and deformation block distinct element method(Zhang et al., 2001;Jin et al.,2001),

?Viscoelastic BEM,natural element method coupling with FEM for stability analysis of the surrounding rocks of rock-bolted and shotcreted tunnels(Xu,2008;Pang,2004),?A meshless method to analyse the joint rock structures (Zhang et al.,2001;Cai&Zhu,2003),?Combined MLS with hybrid displacement variational principle,the hybrid boundary node method and dual reciprocity hybrid boundary node method to the analysis of geomechanics problems(Zhang et al.,2002;Miao et al., 2008),

?Element-Free Galerkin method for joint rock and slope excavation simulation(Zhang&Lu,2000;Zhang&Peng, 2000;Pang et al.,2000;Lu et al.,2008),?The boundary meshfree method based on the modified MLS and boundary integral equation to analyse a beam on a non-linear foundation(Li et al.,2008),

?The distinct/discrete element method to analyse a jointed rock mass,slope stability and influence of the structural surface in geotechnical blasting engineering(Zhou et al., 2006,Han et al.,2010),

?Numerical manifold method and DDA to improve the quality of the stiffness matrix(Jiang et al.,2002;Peng& Ge,2004;Lin et al.,2006),simplify the integration scheme (Lin,2005),and obtain high order manifold element (Zhang&Peng,2000),

?The augmented Lagrange multiplier method to reduce the sensitivity of the spring stiffness parameters(Cai et al., 2004),

?The complementary discontinuous deformation method to avoid the introduction of the virtual spring and the‘open-close’iteration process(Zheng&Jiang,2009),?Numerical estimation of the REV and permeability ten-sor for fractured rock masses by the composite element method(Chen et al.,2008),and

?Parallel FEM based on Jacobi condition and domain decom-position(Zhang et al.,2004).

There are developments in methods for stability analysis of underground engineering projects,for example as below.?The safety factor analysis method for stability estimation of tunnels(Zheng et al.,2010).

?Monitoring,mechanism understanding and prediction of rockburst and mining seismicity(Cai et al.2005;Tang et al., 2010;Wu et al.,2010).

?Analysis of rock structure stability in coal mines(Pan&Li, 2005).

?An automatic analysis platform for tunnels based on expert experiences,numerical test results,and the neural network method(Li et al.,2006).

?A study on sidewall displacement prediction and stability evaluations for large underground power station caverns (Zhu et al.,2010;Sun&Li,2010).

?Study on mechanical behaviors of mining rock mass and its related engineering technological innovation progress (Miao,2010).

?Deformation and failure mechanism analysis for the under-ground powerhouse of Jinping I hydropower project using artificial intelligent back analysis method,extended finite element method,and unloading method(Li et al.,2010; Zhou&Qian,2011;Huang et al.,2011).

?Elasto-plastic analysis and analytical stress solutions for a circular tunnel(Lu et al.,2010;Lu et al.,2011).

There have also been considerable efforts in rock mechan-ics studies for environmental and energy issues in China,as indicated below.

?The geological survey study via deep boreholes and rock mechanics tests and THMC coupling behaviour for the simulation of granite for the Baishan site,a potential nuclear waste disposal site(Wang,2010).

?The related rock mechanics studies for CO2underground storage to investigate the interaction mechanism of CO2 and coal,sandstone,etc.

?The behaviour of layered rock salt caverns within or without gas or oil storage,which are used as a guide for the design of understand oil/gas storage caverns.

5ROCK DYNAMICS

The formation mechanism of the structural hierarchy of frac-turing in a rock mass was discovered.Based on the relations between the deformation and fracture temporal scales and the structural size scales of a rock mass at different structural levels,the principle of equal density of work,the principle of equal energy flow and the principle of equal power of the fracture of rock mass are derived.These principles can serve as a tool for the study of the deformation and fracture of a rock mass at different structural levels(Qian,2009).

The physical mechanism of strength–strain rate sensitiv-ity in different strain rate regions and the transition between them was discovered.A unified model of the co-existence and competition between the thermo-activational mecha-nism and phonon viscosity mechanism is proposed,the relation between dynamic strength,strain rate,plastic defor-mation and stress state is determined,and the structural aspects of the mechanism o deformation and fracture are clarified.

According to the measured wave forms in a comminuted region under penetration and explosion in geomaterials and concrete,by using‘short wave’and‘weak wave’theories,it is clarified that the internal friction stress state change deter-mines the deformation properties,and the generalised model with internal friction and compression is proposed.

The resistance acting upon targets is obtained,the dis-tribution of pressure from the elasto-plastic state to the hydrodynamic state is obtained.Based on the criterion for propagation of a crack,the similarity laws for penetration and perforation are obtained(Qian,2009).

Based on analysis of the measured dynamic constitutive curves,and combining a statistical damage model and a vis-coelastic model,a time-dependent damage model of rock under dynamic loading is established(Shan et al.,2003). Analytical simulation of the dynamic compressive strength of a granite using the sliding crack model was also developed (Li et al.,2001).Bifurcation of a collinear crack system under dynamic compression was also studied(Zhou et al.,2010). 6RHEOLOGICAL ROCK MECHANICS

The study on rheological rock mechanics has achieved great development since it was initiated by Tan Tjong Kie.Due to the needs of many rock engineering projects,various lab-oratory and in situ rheological tests were conducted,e.g., creep and relaxation tests under uniaxial compression,split tension,shear,tension-shear,triaxial compression of grading loading–unloading,and three point bending,etc.It is inter-esting to investigate the rheological behaviour of hard and soft rocks such as marble,sandstone,granite,basalt,tripoli (siliceous material),tuff,coal,salt rock,shale,mudstone, green schist,diabase,gypsum breccias,rigid joints,and soft rock strata.Based on these experiments and theoretical analy-ses,the rheological models and their parameters are identified which enables interpretation of the tests results,via non-linear rheological behaviour,rheological damage and the fracture mechanism of specific rocks(Sun,2007).Some typical results are listed as follows.

?A formula developed by introducing the principle of dam-age mechanics to calculate the rheological cracking of jointed rocks is derived under the action of both compres-sion and shear(Xiao et al.,

2000).Figure1.An experiment result of circular failure of a rock sample (He et al.,2008).

?The rheological rock characteristics at high temperature (Liu&Chen,2003;Deng&Wang,2004;Xi et al.,2008) and under water conditions.

?A unified rheological model theory which could describe the most complicated rheological characteristics based on conventional component models(Sun,2007;Xia et al., 2008).

?A new seven-component non-linear visco-elasto-plastic rheological model of rock by connecting the non-linear viscoplastic body(NVPB)model and five-component visco-elastic model in series(Xu et al.,2006).?Intelligent method for rheological model coupling recogni-tion and their parameters(Chen et al.,2006).

?A robust statistical estimation theory for parameter iden-tification by using a double quadratic iteratively weighted least squares algorithm(Han&Wang,2008).

?The effect of water content on shear creep behaviour of a weak structural plane of sandstone(Li et al.,2008),?Unified approach for modelling elastic–plastic and visco-plastic behaviour plus induced damage over a long time scale in quasi-brittle rocks(Zhou et al.,2008).

?The long-term strength of rocks for evaluating long-term stability in rock engineering(Cui&Fu,2006;Li et al., 2010;Wang et al.,2010;Li et al.,2010).

7ZONAL DISINTEGRATION OF DEEP ROCK MASS

The temporal process of zonal disintegration is studied by physical experimentation(Fig.1,He et al.,2008),field test-ing,and on the basis of irreversible thermal dynamics,and the theory of continuous phase transitions and elasticity–plasticity theories.The spatial and temporal evolution equations of zonal disintegration are derived and the analytical solution is obtained(Qi et al.,2009).

The unified description of the temporal evolution of zonal disintegration in different surrounding rock masses is inves-tigated using the theory of continuous phase transitions.This points out that the evolution equation of order parameter K=r/d(the ratio of the mean length,r,of cracks to the mean distance,d,between cracks may describe the zonal

disintegration phenomenon,deformation wave and‘drastic’fracture

phenomenon.

Based on the laws of the spatial and temporal evolution of zonal disintegration,some supporting methods are sug-gested for the strengthening of the tunnels in the case of the occurrence of such zonal disintegration.

The theory of continuous phase transition is employed to study the incremental strain sign change effect,and the gov-erning equation and its solution are derived.The numerical results obtained demonstrate that this approach provides an adequate description of the sign-change effect for strain incre-ments in rock samples under compression(Wang et al.,2010). 8CONCLUSIONS AND DISCUSSION

There have been significant developments in rock mechanics studies in China over the last ten years due to needs of large rock engineering projects and through the support of adequate funding.Several points relating to these developments can be mentioned as follows.

1)Investigation and the mechanistic understanding of the

fracturing process of rocks and rock masses have been enhanced through the development of new lab testing systems,field monitoring and observations by different methods of the excavation process,plus numerical simu-lation techniques.The CT microscope,nuclear magnetic resonance,digital borehole,and remote sensing tech-niques,etc.,play important roles in developing new test-ing systems.The post-peak and unloading behaviour in rock failure and the unloading effect of excavation have been emphasised.The monitored displacement,micro-seismicity,cracking,wave velocity etc.have been studied to obtain comprehensive information reflecting the behaviour of a rock mass under complicated conditions.

2)There has been much effort in investigating the effect of the

environment,such as high stress,temperature,permeabil-ity,chemical erosion and their coupling processes,on the fracturing behaviour of rocks by developing new testing systems,new models and codes.

3)Analysis methods which consider inhomogeneous,non-

linear,discontinuous,and anisotropic behaviour of rocks and rock masses have been developed further.

4)Greater application of rock mechanics models,theories and

methods in rock engineering are emphasised.

5)More powerful methods,such as fully-coupled models,

internet-based methods,methods based memory,inte-grated methods and virtual rock mechanics laboratories can be developed for new applications.

6)It is a good idea to establish deep underground rock

mechanical laboratories—which can be used for in situ tests for studying the fracturing process in the surround-ing rocks as induced by excavation,plus time dependency, and control through reinforcement,and for nuclear waste disposal and other projects. ACKNOWLEDGEMENTS

The Chinese Society for Rock Mechanics and Engineering gave me the opportunity to write this paper.Professors Qian Qihu,Wang Sijing,Ge Xiurun,and Zheng Yinren provided helpful advice.Professors Cai Meifeng,He Manchao,Wang Mingyang,Y ang Qiang,Xu Dongjun,Li Haibo,Li Xiaochun, Zheng Hong,JuY ang,Huang Lixing,Zhou Hui,Pan Pengzhi, Y an Fei,Qi Chenzhi,Dr.Zhao Ying,Dr.Liuyaqun,Dr.Jing Feng,Dr.Xia Qiang,and Mr.Zhu Y ong supplied infor-mation and references.Professor John A.Hudson offered some suggestions and polished the English text.The work received financial support from the China National Basic Research Program under Grant no.2010CB7320006.They are all acknowledged.

REFERENCES

Cai,M.F.2004.Techniques for in-situ stress measurement at great depth.Journal of University of Science and Technology Beijing 11(6):486–488.

Cai,M.F.Ji,H.G.&Wang,J.A.2005.Study of the time-space-strength relation for mining seismicity at Laohutai coal mine and its prediction.International Journal of Rock Mechanics and Mining Sciences42(1):145–151.

Cai,M.F.Peng,H.Ma,X.Jiang,J.2009.Evolution of the in situ rock stain observed at Shandan monitoring station during the M8.0 earthquake in Wenchuan,China.International Journal of Rock Mechanics and Mining Sciences46(5):952–955.

Cai,Y.C.&Zhu,H.H.2003.Meshless method for numerical cal-culation of geotechnical engineering and its auto-arrangement of discrete nodes.Rock and Soil Mechanics24(1):21–24.

Chen, B.R.Feng,X.T.Zeng,X.H.Xiao,Y.X.Zhang,Z.T.

Ming,H.J.&Feng,G.L.2011.Real-time microseismic moni-toring and its characteristic analysis during TBM tunneling in deep-buried tunnel.Chinese Journal of Rock Mechanics and Engineering30(2):275–283.

Chen,J.T.&Feng,X.T.2007.Study on constitutive model for hard rock under high geostresses.Rock and Soil Mechanics28(11): 2271–2278.

Chen,S.H.Feng,X.M.&Isam,S.2008.Numerical estimation of REV and permeability tensor for fractured rock masses by com-posite element method.International Journal for Numerical and Analytical Methods in Geomechanics32:1459–77.

Chen,S.H.Qiang,S.&Chen,S.F.2003.Study on the three-dimensional composite element model of bolted rock masses.

Chinese Journal of Rock and Engineering22(1):1–8.

Chen W.S.Zheng,H.Cheng,Y.M.Ge X.R.2004.Detection of3D rock block contacts by penetration edges.Chinese Journal of Rock Mechanics and Engineering,23(4):565–571.

Chen,X.Y ang,Q.Qiu,K.B.&Feng,J.L.2008.An anisotropic strength criterion for jointed rock masses and its application in wellbore stability analyses.International Journal for Numerical and Analytical Methods in Geomechanics32:607–31.

Chen,Y.F.Zhou,C.B.&Jing,L.R.2009.Modeling coupled THM processes of geological porous media with multiphase flow:the-ory and validation against laboratory and field scale experiments.

Computers and Geotechnics36(8):1308–1329.

Chen,Y.F.Zhou,C.B.&Jing,L.R.2010.Numerical modeling of coupled thermo-mechanical response of a rock pillar.Journal of Rock Mechanics and Geotechnical Engineering2(3):262–273. Chen,Z.2004.A generalized solution for tetrahedral rock wedge stability analysis.International Journal of Rock Mechanics and Mining Sciences41(4):613–628.

Chen,Z.Wang,X.Haberfield,C.Yin,J.&Wang,Y.2001a.A three-dimensional slope stability analysis method using the upper bound theorem:Part I:theory and methods.International Journal of Rock Mechanics and Mining Sciences38(3):369–378.

Chen,Z.Wang,J.Wang,Y.Yin,J.&Haberfield,C.2001b.A three-dimensional slope stability analysis method using the upper bound theorem Part II:numerical approaches,applications and extensions.International Journal of Rock Mechanics and Mining Sciences38(3):379–397.

Cui,X.H.&Fu,Z.L.2006.Experimental study on rheology prop-erties and long-term strength of rocks.Chinese Journal of Rock Mechanics and Engineering25(5):1021–1024.

Fang,Z.M.,Li,X.C.&Bai,B.2009.Study of method for simulta-neously measuring adsorption deformation permeability of coal. Chinese Journal of Rock Mechanics and Engineering28(9): 1828–1833.

Feng,X.T.,Chen,B.R.,Y ang,C.X.,Zhou,H.&Ding,X.L.2006. Identification of visco-elastic models for rocks using genetic pro-gramming coupled with the modified particle swarm optimization algorithm.International Journal of Rock Mechanics and Mining Sciences.43(5):789–801

Feng,X.T.&Ding,W.X.2007.Experimental study of limestone micro-fracturing under a coupled stress,fluid flow and changing chemical environment.International Journal of Rock Mechanics and Mining Sciences44(3):437–448.

Feng,X.T.&Hudson,J.A.2011.Rock engineering design.Taylor& Francis,London.

Gao,H.Zheng,Y.R.&Feng,X.T.2007a.Study on energy yield criterion of geomaterials.Chinese Journal of Rock Mechanics and Engineering26(12):2437–2443.

Gao,H.Zheng,Y.R.&Feng,X.T.2007b.Deduction of failure criterion for geomaterials based on maximum principal shear strain.Chinese Journal of Rock Mechanics and Engineering26(3): 518–524.

Ge,X.R.,Li,T.J.,Zhang,M.Y.,Liu,J.G.2000.Loading apparatus for the meso mechanical experiment rock.Rock and Soil Mechanics, 21(3):289–293.

Ge,X.R.,Ren,J.X.,Pu,Y.B.,Ma,W.&Sun H.2004.Macro-meso testing of rock and soil damage mechanics.Beijing:Science Press. Ge,X.R.2008.Deformation control law of rock fatigue failure,real-time X-ray CT scan of geotechnical testing,and new method of stability analysis of slopes and dam foundations.Chinese Journal of Geotechnical Engineering30(1):1–20.

Han,Y.C.Liu X.Y.&Li S.H.2010.Discrete element model-ing of brittle failure process of rock materials.Mechanics in Engineering.32(3):50–56.

He,Y.N.Jiang,B.S.Han,L.J.Shao,P.Zhang,H.Q.2008.Study of Intermit tent Zonal Fr acturing of Surrounding Rock in Deep Roadways.Journal of China University of Mining&Technology 37(3):300–304.

He,M.C.Miao,J.L.&Feng,J.L.2010.Rock burst process of lime-stone and its acoustic emission characteristics under true-triaxial unloading conditions International Journal of Rock Mechanics and Mining Sciences47(2):286–298.

He,M.C.Wang,Y.&Tao,Z.G.2010.A new early-warning prediction system for monitoring shear force of fault plane in an active fault. Journal of Rock Mechanics and Geotechnical Engineering2(3): 223–231.

Huang S.L.Feng,X.T.&Zhang,C.Q.2008.A new generalized polyaxial strain energy strength criterion of brittle rock and polyaxial test validation.Chinese Journal of Rock Mechanics and Engineering27(1):124–134.

Huang R.Q.Huang,D.Duan,S.H.&Wu,Q.2011.Geomechan-ics mechanism and characteristics of surrounding rock mass deformation failure in construction phase for underground powerhouse of Jinping I hydropower station.Chinese Journal of Rock Mechanics and Engineering,30(1):223–235

Jiang,Q.H.Y oung,M.R.&Feng,D.X.2002.Three-dimension dis-continuous deformation analysis for forward modeling.Chinese Journal of Rock Mechanics and Engineering21(12):1765–1769. Jiao,Y.Y.Zhang,X.L.Zhao,J.&Liu,Q.S.2007.Viscous boundary of DDA for modeling stress wave propagation in jointed rock. International Journal of Rock Mechanics and Mining Sciences 44(7):1070–1076.

Jin,F.,Jia,W.W.&Wang,G.L.2001.Coupling model of distinct element-boundary element.Journal of Hydraulic Engineering1: 23–27.

Ju,Y.Sudak,L.&Xie,H.2007.Study on stress wave propagation in fractured rocks with fractal joint surfaces.International Journal of Solids and Structures44:4256–4271Li,H.B.Zhao,J.Li,T.J.&Yuan,J.X.2001.Analytical simulation of the dynamic compressive strength of a granite using the sliding crack model.International Journal for Numerical and Analytical Methods in Geomechanics25:853–69.

Li,J.L.Wang,L.H.Wang,X.X.Wang,R.H.Cheng,Z.&Dang,L. 2010.Research on unloading nonlinear mechanical character-istics of jointed rock masses.Journal of Rock Mechanics and Geotechnical Engineering2(4):357–364.

Li,L.Q.Xu,W.Y.Wang,W.Guo,Y.Q.&Zhao,H.B.2010.Estimation of long-term strength for Xiangjiaba sandstone based on creep tests.Engineering Mechanics27(11):127–136.

Li,N.Luo,J.Z.Chang,B.&Zhang,Z.Q.2006.New method for design and analysis of underground caverns.Chinese Journal of Rock Mechanics and Engineering25(10):2155–2159.

Li,N.&Qian,Q.H.2010.Four criteria of stability analysis and assessment of high rock slope.Chinese Journal of Rock Mechan-ics and Engineering29(9):1754–1759.

Li,P.Liu,J.Zhu J.B.&He,H.J.2008.Research on effects of water content on shear creep behavior of weak structural plane of sandstone.Rock and Soil Mechanics29(7):1865–1871.

Li,S.C.Li,S.C.Sui,B.&Zhu,W.S.2008.The meshless method for analyzing seepage of rockmass.Rock and Soil Mechanics29(1): 256–260.

Li,S.J.Feng,X.T.Zhang,C.S.Li,Z.H.Zhou,H.Hou,J.& Chu,W.J.2010.Testing on formation and evolution of TBM excavation damaged zone in deep-buried tunnel based on digital panoramic borehole camera technique.Chinese Journal of Rock Mechanics and Engineering29(6):1106–1112.

Li,X.Zhou,Z.Lok,T.Hong,L.&Yin,T.2008.Innovative testing technique of rock subjected to coupled static and dynamic loads. International Journal of Rock Mechanics and Mining Sciences 45(5):739–748.

Li,X.C.Wang,Y.Wei,N.2008.Research on measuring method of permeability by using storage-variable transient pulse method.Chinese Journal of Rock Mechanics and Engineering 27(12):2482–2487.

Li,Y.P.Y ang,C.H.Daemen,JJK.Yin,X.Y.&Chen,F.2009.

A new Cosserat-like constitutive model for bedded salt rocks. International Journal for Numerical and Analytical Methods in Geomechanics33:1691–720.

Li,Z.K.Zhou,Z.Xu,Q.J.Liao,C.G.Yin,H.L.,Zhang,Z.Z.Cheng, L.J.Liu,Z.G.&Guo,K.2010.Implementation and development of AI back analysis for the underground powerhouse of Jinping-1 hydropower project.Journal of Hydroelectric Engineering.29(3): 177–183.

Liu,C.L.Zhang,L.Z.Zhao,Q.Q.&Zheng,Y.Z.2008.Devel-opment of three-dimensional boundary element numerical sys-tem FSM.DDM with rock hole and anchor bolt line elements. Chinese Journal of Rock Mechanics and Engineering27(12): 2528–2534.

Liu,G.T.Y e,Y.X.&Xu,Z.H.2007.Development of testing machine for coupled seepage and triaxial stress measurements in rocks. Journal of Tsinghua University(Science and Technology)47(3): 323–326.

Lin,S.Z.2005.Recursive formula for simplex integration.Journal of Yangtze River Scientific Research Institute22(3):32–34. Lin,S.Z.Qi,Y.F.&Su,H.D.2006.Improved local cover func-tion of numerical manifold method and its application.Journal of Yangtze River Scientific Research Institute23(6):55–58.

Liu,J.&Li,Z.K.2004.Choice of some control constants in DDA method.Journal of Chengdu University of Technology(Science& Technology Edition)31(5):522–526.

Liu,Q.S.&Chen,G.2003.Further verification of time—temperature equivalence for granite.Chinese Journal of Rock Mechanics and Engineering22(10):1601–1606.

Lu,A.Xu,G.Sun,F.&Sun,W.2010.Elasto-plastic analysis of a circular tunnel including the effect of the axial in situ stress. International Journal of Rock Mechanics and Mining Sciences 47(1):50–59.

Lu,A.Zhang,L.&Zhang,N.2011.Analytic stress solutions for a circular pressure tunnel at pressure and great depth including

support delay.International Journal of Rock Mechanics and Mining Sciences48(3):514–519.

Lu,B.Ding,X.L.&Wu,A.Q.2008.Modeling of rock discontinuity with meshless method.Chinese Journal of Rock Mechanics and Engineering27(10):2108–2117.

Miao X.X.2010.Review of research on mechanical behaviors of min-ing rock mass and its related engineering technological innovation progress.Chinese Journal of Rock Mechanics and Engineering, 29(10):1988–1998.

Miao,Y.Y an,F.Wang,Y.H.&Wan,Y.D.2008.Dual reciprocity hybrid boundary node method in geotechnical engineering.Rock and Soil Mechanics29(7):1872–1876.

Pan,P.Z.Feng,X.T.Huang,X.H.Cui,Q.&Zhou,H.2009.Coupled THM processes in EDZ of crystalline rocks using an elasto-plastic cellular automaton.Environmental Geology57(6):1299–1311. Pan,Y.&Li,Z.2005.Analysis of rock structure stability in coal mines.International Journal for Numerical and Analytical Methods in Geomechanics29(10):1045–1063.

Pan,Y.Wang,X.&Li,Z.2002.Analysis of the strain softening size effect for rock specimens based on shear strain gradient plastic-ity theory.International Journal of Rock Mechanics and Mining Sciences39(6):801–805.

Pang,Z.H.Ge,X.R.&Wang,S.L.2000.Simulation discontinu-ity with element free Galerkin method.Journal of Engineering Geology8(3):364–368.

Peng,Z.Q.&Ge,X.R.2004.Suggestion to choice of physical cover functions in numerical manifold method.Rock and Soil Mechanics 25(4):624–627.

Qi,C.Z.,Qian,Q.H.&Wang M.Y.2009.Constitutive relations of porous elasto-plastic media.Journal of Mining Science45(4): 339–346.

Qian,Q.H.2009.Some advances in rock blasting dynamics.Chinese Journal of Rock Mechanics and Engineering28(10):1945–1968. Qian,Q.H.Qi,C.Z.&Wang,M.Y.2009.Dynamic strength of rocks and physical nature of rock strength.Journal of Rock Mechanics and Geotechnical Engineering2(1):1–10.

Qian,Q.H.&Zhou,X.P.2011.Non-Euclidean continuum model of the zonal disintegration of surrounding rocks around a deep cir-cular tunnel in a non-hydrostatic pressure state.Journal of Mining Science47(1):42–52

Shan,R.L.Xue,Y.S&Zhang,Q.2003.Time dependent damage model of rock under dynamic loading.Chinese Journal of Rock Mechanics and Engineering22(11):1771–1776.

Sun,A.H.&Li,S.C.2010.A study on sidewall displacement predic-tion and stability evaluations for large underground power station caverns.International Journal of Rock Mechanics and Mining Sciences47(7):1055–1062.

Sun,J.2007.Rock rheological mechanics and its advance in engi-neering applications.Chinese Journal of Rock Mechanics and Engineering26(6):1081–1106.

Sun,J.&Wang,S.J.2000.Rock mechanics and rock engineering in China:developments and current state-of-the-art.Interna-tional Journal of Rock Mechanics and Mining Sciences37(3): 447–465.

Tang C.A.&Hudson,J.A.2010.Rock Failure Mechanisms–Explained and Illustrated.Taylor&Francis,London,322p. Tang,C.A.Wang,J.M.&Zhang,J.J.2010.Preliminary engineer-ing application of microseismic monitoring technique to rockburst prediction in tunneling of Jinping II project.Journal of Rock Mechanics and Geotechnical Engineering2(3):193–208. Tian,W.Dang,F.N.Ding,W.H.Liang,X.Y.&Chen,H.Q.2010. Development of a dynamic loading apparatus for CT exper-iment and its application,Rock and Soil Mechanics31(1): 309–313.

Wang,J.2010.High-level radioactive waste disposal in China:update 2010.Journal of Rock Mechanics and Geotechnical Engineering 2(1):1–11.

Wang,L.G.Li,L.Liu,X.&Wang,J.G.2010.Life expectation of an rock engineered slope based on the long-term stability.Chinese Journal of Geological Hazard and Control21(3):97–100.Wang,M.Y.Qi,C.Z.&Qian Q.H.2010.Modeling of the incremental strain sign-change effect in rocks under compression.Journal of Mining Science46(4):359–366.

Wang,S.J.Editor.2004.Century achievements in Chinese Rock mechanics and Rock Engineering.Nanjing:Hohai University Press.

Wang,S.J.2009.Geological nature of rock and its deduction for rock mechanics.Chinese Journal of Rock Mechanics and Engineering 28(3):433–450.

Wu,F.Q.Wu,J.&Qi S.W.2010.Theoretical analysis on mechanism of rock burst of brittle rock mass.Journal of Engineering Geology 18(5):589–595.

Wu,L.X.Liu,S.J.Wu,Y.H.&Wang,J.Z.2004.From qualitative to quantitative information:the development of remote sensing rock mechanics(RSRM).International Journal of Rock Mechanics and Mining Sciences41(3):415–416.

Wu,L.X.Liu,S.J.Wu,Y.H.&Wang,J.Z.2006a.Precursors for rock fracturing and failure–Part I:IRR image abnormalities.Interna-tional Journal of Rock Mechanics and Mining Sciences43(3): 473–482.

Wu,L.X.Liu,S.J.Wu,Y.H.&Wang,J.Z.2006b.Precursors for rock fracturing and failure–Part II:IRR T-Curve abnormalities.

International Journal of Rock Mechanics and Mining Sciences 43(3):483–493.

Xi,B.P.Zhao,Y.S.Wan,Z.J.Dong,F.K.Feng,Z.J.&Zhang, N.2008.Rheological experimental investigation on surround-ing rock mass of granite under high temperature and hydrostatic stress.Chinese Journal of Rock Mechanics and Engineering27(8): 1659–1666.

Xia,C.C.Wang,W.&Wang,X.R.2008.Development of coupling shear-seepage test system for rock joints.Chinese Journal of Rock Mechanics and Engineering27(6):1285–1291.

Xia,C.C.Wang,X.D.Xu,C.B.&Zhang,C.S.2008.Method to iden-tify rheological models by unified rheological model theory and case study.Chinese Journal of Rock Mechanics and Engineering 27(8):1594–1600.

Xiao,H.T.Zhou,W.Y.&Y ang,R.Q.2000.A new model of rheolog-ical damage for slope stability analysis.China Civil Engineering Journal33(6):94–98.

Xie,H.&Gao,F.2000.The mechanics of cracks and a statistical strength theory for rocks.International Journal of Rock Mechanics and Mining Sciences37:477–488

Xie,H.Li,L.Y.Peng,R.D.&Ju,Y.2009.Energy analysis and criteria for structural failure of rocks.J Rock Mechanics and Geotechnical Engineering1(1):11–20

Xie,H.Sun,H.Ju,Y.&Feng,Z.G.2001.Study on generation of rock fracture surfaces by using fractal interpolation.Int J Solids &Structures38:5765–5787

Xie,H.&Zhou,H.W.2008.Application of fractal theory to top coal caving.Chaos,Solitons and Fractals36:797–807

Xu,W.Y.Y ang,S.Q.&Chu,W.J.2006.Nonlinear viscoelasto-plastic rheological model(hohai model)of rock and its engineering application.Chinese Journal of Rock Mechanics and Engineering 25(3):433–447.

Xu,Z.H.Liu,G.T.Y e,Y.X.&Hu,Y.2006.Research on Effect of Temperature on Permeability of Soft Rock.Journal of ChinaThree Gorges University(Natural Sciences)28(4):301–311.

Y ang,Q.Chen,Y.R.&Liu,Y.R.2007.On monolithic stability and reinforcement analysis of high arch dams.Science in China Series E50:90–97.

Y ang,Q.Tham,L.G.&Swoboda,G.2005.Normality structures with homogeneous kinetic rate laws.ASME Journal of Applied Mechanics72:322–329.

Y ou,M.Q.2009.True-triaxial strength criteria for rock.Interna-tional Journal of Rock Mechanics and Mining Sciences46(1): 115–127.

Y ou,M.Q.2010a.Mechanical characteristics of the exponential strength criterion under conventional triaxial stresses.Interna-tional Journal of Rock Mechanics and Mining Sciences47(2): 195–204.

Y ou,M.Q.2010b.Three independent parameters to describe con-ventional triaxial compressive strength of intact rocks.Journal of Rock Mechanics and Geotechnical Engineering2(4):350–356. Yu,M.Zan,Y.Zhao,J.&Y oshimine,M.2002.A Unified Strength cri-terion for rock material.International Journal of Rock Mechanics and Mining Sciences39(8):975–989.

Zhang,G.X.&Peng,J.2000.Second-order manifold method in structure failure analysis.Acta Mechanica Sinica34(2):261–269 Zhang,J.M.Y ao,Z.H.&Li,H.2002.A Hybrid boundary node method.International Journal for Numerical Methods in Engi-neering53:751–63.

Zhang,P.Li,N.&He,R.L.2006.Research on localized progressive damage model for fractured rocklike materials.Chinese Journal of Rock Mechanics and Engineering25(10):2043–2050. Zhang X.&Lu,M.W.2000.A2-D meshless model for joint rock structures.International Journal for Numerical method in Engineering47(10):1649–1661.

Zhang,X.Lu,X.H.&Song,K.Z.2001.Least-squares collocation meshless method.International Journal for Numerical Method in Engineering51:1089–1100.

Zhang,X.Song,K.Z.&Lu,M.W.2000.Meshless methods based on collocation with radial basis https://www.360docs.net/doc/e94188069.html,putational Mechanics 26(4):333–343.

Zhang,X.S.Y e,T.Q.&Ge,S.L.2001.Several problems associ-ated with discontinuous boundary elements.Chinese Journal of Computational Mechanics18(3):331–334.

Zhang,Y.L.Feng,X.T.&Ru,https://www.360docs.net/doc/e94188069.html,rge-scale high perfor-mance parallel finite element system based on domain decom-position method in geomechanics.Chinese Journal of Rock and Engineering23(21):3636–3641.

Zhao,Y.S.Wan,Z.J.Zhang,Y.Qu,F.Xie,G.Y.Wei,X.J.&Ma,W.

2008.Research and development of20MN servo-controlled rock triaxial testing system with high temperature and high pressure.

Chinese Journal of Rock Mechanics and Engineering27(1):1–8. Zheng,H.2009.Eigenvalue Problem from the Stability Analy-sis of Slopes.Journal of Geotechnical and Geoenvironmental Engineering,ASCE135(5):647–656.

Zheng,H.&Jiang,https://www.360docs.net/doc/e94188069.html,plementary theory based on discon-tinuous deformation analysis.Science in China E Series39(10): 1702–1708.

Zheng,H.Sun,G.H.&Li,C.G.2011.Cauchy problem of three-dimensional critical slip surfaces of slopes.International Journal for Numerical&Analytical Methods in Geomechanics35(4): 519–527.

Zheng,Y.R.2007.Discussion on yield and failure of geomateri-als and stability analysis methods of slope/landslide—communion and discussion summary of special topic forum on geologic dis-asters in the three gorges project region.Chinese Journal of Rock Mechanics and Engineering.26(4):649–661.

Zheng,Y.R.Xu,H.Wang C.&Xiao Q.2010.Failure mecha-nism of tunnel and dividing line standard between shallow and deep bury.Journal of Zhejiang University(Engineering Science), 44(10):1851–1856.Zhou,C.B.Sharma,R.S.Chen,Y.F.&Rong,G.2008.Flow-Stress Coupled Permeability Tensor for Fractured Rock Masses.Int J for Numerical and Analytical Methods in Geomechanics32(11): 1289–1309.

Zhou, C.B.Sharma,R.S.Chen,Y.F.&Rong,G.2010.A New Parabolic Variational Inequality Formulation of Signorini’s Condition for Non-steady Seepage Problems with Complex Seep-age Control Systems.International Journal for Numerical and Analytical Methods in Geomechanics DOI:10.1002/nag.944. Zhou,H.Jia,Y.Shao,&J.F.2008.A unified elastic-plastic and viscoplastic damage model for quasi-brittle rocks.International Journal of Rock Mechanics&Mining Sciences45:1237–1251. Zhou,H.W.&Xie,H.2003.Direct estimation of the fractal dimen-sions of a fracture surface of rock.Surface Review and Letters 10(5):751–762

Zhou,H.W.&Xie,H.2004.Anisotropic characterization of rock fracture surfaces subjected to profile analysis.Physics Letters A 325(5–6):355–362

Zhou,J.J.Zhou,H.&Shao,J.F.2007.Coupled micromechanical model for anisotropic damage and permeability variation in brittle rocks.Chinese Journal of Rock Mechanics and Engineering26(2): 368–373.

Zhou,T.Zhang,J.S.&Chen,X.B.2006.T wo dimensional elasto-plastic distinct element analysis of rock slope in navigation route of longtan hydropower station.Journal of Railway Science and Engineering3(4):63–67.

Zhou,X.P.Xie,W.T.&Qian,Q.H.2010.Bifurcation of collinear crack system under dynamic compression.Theoretical andApplied Fracture Mechanics54:166–171.

Zhou,X.P.&Qian,Q.H.2011.Deformation and failure Mechanism of surrounding rock mass around underground caverns in Jinping I hydropower station.Proceeding of the12th ISRM International Congress on Rock Mechanics,Taylor&Francis,London. Zhou,W.Y.Zhao,J.D.Liu,Y.G.&Y ang,Q.2002.Simulation of local-ization failure with strain-gradient-enhanced damage mechanics. International Journal for Numerical and Analytical Methods in Geomechanics26:793–813.

Zhu,D.Y.&Qian,Q.H.2007.Rigorous and quasi-rigorous limit equilibrium solutions of3d slope stability and application to engi-neering.Chinese Journal of Rock Mechanics and Engineering 26(8):1513–1528.

Zhu,W.S.Li,X.J.Zhang,Q.B.Zheng,W.H.Xin,X.L.Sun,A.H.& Li,S.C.2010.A study on sidewall displacement prediction and stability evaluations for large underground power station caverns. International Journal of Rock Mechanics and Mining Sciences 47(7):1055–1062.

Zhuang,X.Y.Cai,Y.C.Zhu,H.H.&Zhou,D.H.2008.Rock slope stability analysis based on meshless method and shortest path algorithm.Chinese Quarterly of Mechanics29(4):538–543. Zuo,J.P.Xie,H.Zhou,H.W.&Peng,S.P.2010.SEM in-situ investigation on thermal cracking behavior of Pingdingshan sand-stone at elevated temperatures.Geophysical Journal International 181(2):593–603.