岩体广义多层结构模型研究
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摘要
岩石是由多种矿物晶粒、孔隙和胶结物组成的混杂体。经过亿万年的地质演变和多期复杂的构造运动,使岩石含有不同阶次随机分布的微孔隙与裂纹。在宏观尺度上天然岩体又为多种地质构造面(节理、断层和弱面)所切割。这些重要特点表征岩石是一种很复杂很特殊的材料,它不是离散介质,也不是连续介质,而是属于连续与离散(或局部离散)的耦合介质。岩石破坏过程也可看成是其内部结构面形成、重构的过程,在这个过程中,微裂纹萌生、宏观裂纹形成、结构面贯通及沿接触面滑移等现象交织在一起。由于破坏过程的跨学科性、多层次性和状态方程不清,岩石破坏问题一直是研究的热点与难点。本文将岩石结构面空间分布的结构性、尺度的结构性与分形特征的结构性称为广义多层结构,分别研究了脆性岩石、岩石节理及非贯通节理岩体的多层结构模型,模型的数值计算通过ABAQUS平台内嵌子程序UMAT与UEL实现。具体内容有:
(1)介绍了用户材料子程序(UMAT)与用户单元子程序(UEL)实现方法。包括:弹塑性比例因子计算、变子增量步的修正Euler显式应力积分方法、应力修正方法、刚度矩阵AMATRX与残余荷载矩阵RHS计算方法及计算流程等。为验证UMAT的有效性,将Drucke-Prager模型写入UMAT并与ABAQUS材料库Drucke-Prager模型进行对比,采用UEL将Cosserate介质弹塑性模型嵌入ABAQUS并进行性状分析。
(2)介绍了基于渐近展开法的双尺度边值方程、切线模量计算方法及计算步骤,给出了有限元列式及计算流程。将细观统计模型与渐近展开法相结合,提出了脆性岩石双尺度计算模型。模型在细观尺度采用基于Rankine准则的弹脆性本构关系,并考虑材料的统计性,采用切线模量为零作为材料软化判据,软化后采用考虑复合模式的钝断裂带裂纹模型。采用双尺度计算方法不仅能得到非均质材料的有效性能,更重要的是不必引入虚拟的损伤参数,使材料宏观力学性状与材料真实物理进程相对应。
(3)基于节理分形特征,将节理面分解为不同层次结构面,结合Plesha节理本构提出岩石节理多层结构模型。采用单层结构时,该模型退化为Plesha节理模型。模型将接触面的损伤与破坏拟为不同层次结构面渐次破坏的过程,能考虑界面滑移、剪损、压碎、分离等作用机理。通过将界面粗糙度定义为等效起伏角,模型能模拟节理循环剪切性状。模型适用于中低压力下岩体节理、也可用于分析结构物与围岩相互作用性状等。
(4)基于共线非贯通节理岩体破坏机理,提出非贯通节理岩体多层结构模型。节理贯通时,该模型退化为Zienkiewicz节理材料模型。节理岩体多层结构模型包括节理滑移与节理扩展模型。节理滑移模型考虑节理细观形态;在节理扩展模型中,结构面剪切强度由节理剪切强度与岩桥强度共同组成,节理剪切强度体现为界面基本摩擦角与粗糙角,岩桥强度体现为等效粘聚力,等效粘聚力不断弱化的过程就是结构面由非贯通向贯通转化的过程。非贯通节理岩体多层结构模型假定岩桥为共面剪切破坏,模型适用于岩体节理共面并且岩桥长度远小于节理长度的情形。
Rock is a combination of mineral grains, porosity and composition of cement mixed body. After millions of years of geological evolution and a complex multi-stage tectonic movements, the rock contains a random distribution at different levels of sub-micro-pores and cracks. At the macro-scale natural rock is cut by a variety of geological structures (joints, faults and weak-side).The rock is a very complex and very special material, it is not a discrete medium, nor is it a continuous medium, but under the continuous and discrete (or local discrete) coupling medium. Rock failure can also be seen as a process of their internal structure surface formation and reconstruction, the micro-crack initiate, macro-crack formate, structure surface slide along the contact surface in this process. As the failure process involing in cross-disciplinary, multi-level nature and the equation of state is unclear, the study of rock destruction issue has been hot and difficult. This paper define the spatial distribution of structure of rock, scale structure and fractal as the generalized hierarchical, put forward the hierarchical models of brittle rock, rock joints and non-persistent jointed rock mass respectively. The numerical model are implemented by ABAQUS subroutine UMAT and UEL. Details including:
(1) Describes the user material subroutine (UMAT) and the user element subroutine (UEL). Including: elastic-plastic scale factor calculation, changing the amendment to sub-incremental-step explicit Euler stress integration method, the stress correction method, stiffness matrix AMATRX and residual load matrix RHS calculation method. In order to verify the validity of UMAT, comparing the results calculated by Drucke-Prager model embedded into the UMAT and the results calculated by the ABAQUS library Drcuke-Prager model. The elastic-plastic constitutive of Cosserate media is embedded into UEL and the behaviors of the Cosserate media is analyzed.
(2) Describes the asymptotic expansion method, tangent modulus calculation method and calculation procedures. The two-scale computational model of brittle rock is proposed based on the combination of the micro-statistical model and the asymptotic expansion. Rankine-based criteria for brittle elastic constitutive is adopted in micro-scale , taking into account the statistical nature of materials, using the zero-value of material tangent modulus as the softening criterion, the blunt crack model is used in the softening process. Using two-scale method the effective properties of non-homogeneous material can be gotten easily, more importantly, there is no need to introduce virtual damage parameters, and the macroscopic mechanical behavior of material corresponds to the real physical processes.
(3) Based on the fractal characteristics, the joint roughness is decomposed into different levels of structural surface, hierarchical model of rock joints is proposed combined with Plesha joints model. Using single-layer structure, the hierarchical model degenerates to Plesha joints model. the failure of joint is conceived as process of damage and destruction for the different levels of surfacess gradually, this model consider the mechanisms of interfacial slipping, shearing, crushing and separating. After the joint roughness is defined as the equivalent inclination angle, the model can simulate the behaviors of joints under cyclic loading. The model is applicable to analyze the interaction between structures and rock under low pressure.
(4) Based on failure mechanism of coplanar non-persistent jointed rock mass, the hierarchical model of non-persistent jointed rock mass is proposed. the model degenerates to Zienkiewicz jointed material model when the joints become persistent. This model includie joints slip model and joints crack model. Joints slip model considers the joint micro-configuration. In the joint crack model, the shear strength constitute the shear strength of joints and rock bridges strength, joint shear strength reflected in the basic friction angle and rough angle, rock bridge stregth reflected in the equivalent cohesion, the continuous weakening process of the equivalent cohesion is the process of the transformation from discontinuous to continuous of joint. This model assumes the coplanar shear failure mechanism of the rock bridge, so it can be used under the circumstance that the length of rock bridges is far less than of the length of the joint.
(1)介绍了用户材料子程序(UMAT)与用户单元子程序(UEL)实现方法。包括:弹塑性比例因子计算、变子增量步的修正Euler显式应力积分方法、应力修正方法、刚度矩阵AMATRX与残余荷载矩阵RHS计算方法及计算流程等。为验证UMAT的有效性,将Drucke-Prager模型写入UMAT并与ABAQUS材料库Drucke-Prager模型进行对比,采用UEL将Cosserate介质弹塑性模型嵌入ABAQUS并进行性状分析。
(2)介绍了基于渐近展开法的双尺度边值方程、切线模量计算方法及计算步骤,给出了有限元列式及计算流程。将细观统计模型与渐近展开法相结合,提出了脆性岩石双尺度计算模型。模型在细观尺度采用基于Rankine准则的弹脆性本构关系,并考虑材料的统计性,采用切线模量为零作为材料软化判据,软化后采用考虑复合模式的钝断裂带裂纹模型。采用双尺度计算方法不仅能得到非均质材料的有效性能,更重要的是不必引入虚拟的损伤参数,使材料宏观力学性状与材料真实物理进程相对应。
(3)基于节理分形特征,将节理面分解为不同层次结构面,结合Plesha节理本构提出岩石节理多层结构模型。采用单层结构时,该模型退化为Plesha节理模型。模型将接触面的损伤与破坏拟为不同层次结构面渐次破坏的过程,能考虑界面滑移、剪损、压碎、分离等作用机理。通过将界面粗糙度定义为等效起伏角,模型能模拟节理循环剪切性状。模型适用于中低压力下岩体节理、也可用于分析结构物与围岩相互作用性状等。
(4)基于共线非贯通节理岩体破坏机理,提出非贯通节理岩体多层结构模型。节理贯通时,该模型退化为Zienkiewicz节理材料模型。节理岩体多层结构模型包括节理滑移与节理扩展模型。节理滑移模型考虑节理细观形态;在节理扩展模型中,结构面剪切强度由节理剪切强度与岩桥强度共同组成,节理剪切强度体现为界面基本摩擦角与粗糙角,岩桥强度体现为等效粘聚力,等效粘聚力不断弱化的过程就是结构面由非贯通向贯通转化的过程。非贯通节理岩体多层结构模型假定岩桥为共面剪切破坏,模型适用于岩体节理共面并且岩桥长度远小于节理长度的情形。
Rock is a combination of mineral grains, porosity and composition of cement mixed body. After millions of years of geological evolution and a complex multi-stage tectonic movements, the rock contains a random distribution at different levels of sub-micro-pores and cracks. At the macro-scale natural rock is cut by a variety of geological structures (joints, faults and weak-side).The rock is a very complex and very special material, it is not a discrete medium, nor is it a continuous medium, but under the continuous and discrete (or local discrete) coupling medium. Rock failure can also be seen as a process of their internal structure surface formation and reconstruction, the micro-crack initiate, macro-crack formate, structure surface slide along the contact surface in this process. As the failure process involing in cross-disciplinary, multi-level nature and the equation of state is unclear, the study of rock destruction issue has been hot and difficult. This paper define the spatial distribution of structure of rock, scale structure and fractal as the generalized hierarchical, put forward the hierarchical models of brittle rock, rock joints and non-persistent jointed rock mass respectively. The numerical model are implemented by ABAQUS subroutine UMAT and UEL. Details including:
(1) Describes the user material subroutine (UMAT) and the user element subroutine (UEL). Including: elastic-plastic scale factor calculation, changing the amendment to sub-incremental-step explicit Euler stress integration method, the stress correction method, stiffness matrix AMATRX and residual load matrix RHS calculation method. In order to verify the validity of UMAT, comparing the results calculated by Drucke-Prager model embedded into the UMAT and the results calculated by the ABAQUS library Drcuke-Prager model. The elastic-plastic constitutive of Cosserate media is embedded into UEL and the behaviors of the Cosserate media is analyzed.
(2) Describes the asymptotic expansion method, tangent modulus calculation method and calculation procedures. The two-scale computational model of brittle rock is proposed based on the combination of the micro-statistical model and the asymptotic expansion. Rankine-based criteria for brittle elastic constitutive is adopted in micro-scale , taking into account the statistical nature of materials, using the zero-value of material tangent modulus as the softening criterion, the blunt crack model is used in the softening process. Using two-scale method the effective properties of non-homogeneous material can be gotten easily, more importantly, there is no need to introduce virtual damage parameters, and the macroscopic mechanical behavior of material corresponds to the real physical processes.
(3) Based on the fractal characteristics, the joint roughness is decomposed into different levels of structural surface, hierarchical model of rock joints is proposed combined with Plesha joints model. Using single-layer structure, the hierarchical model degenerates to Plesha joints model. the failure of joint is conceived as process of damage and destruction for the different levels of surfacess gradually, this model consider the mechanisms of interfacial slipping, shearing, crushing and separating. After the joint roughness is defined as the equivalent inclination angle, the model can simulate the behaviors of joints under cyclic loading. The model is applicable to analyze the interaction between structures and rock under low pressure.
(4) Based on failure mechanism of coplanar non-persistent jointed rock mass, the hierarchical model of non-persistent jointed rock mass is proposed. the model degenerates to Zienkiewicz jointed material model when the joints become persistent. This model includie joints slip model and joints crack model. Joints slip model considers the joint micro-configuration. In the joint crack model, the shear strength constitute the shear strength of joints and rock bridges strength, joint shear strength reflected in the basic friction angle and rough angle, rock bridge stregth reflected in the equivalent cohesion, the continuous weakening process of the equivalent cohesion is the process of the transformation from discontinuous to continuous of joint. This model assumes the coplanar shear failure mechanism of the rock bridge, so it can be used under the circumstance that the length of rock bridges is far less than of the length of the joint.
引文
Aliakbar Golshani, Yoshiaki Okui, Masanobu Oda, Takato Takemura. A micromechanical model for brittle failure of rock and its relation to crack growth observed in triaxial compression tests of granite[J].Mechanics of Materials,2006, 38: 287-303
Allaire G. Mathematical approaches and methods, in: U. Hornung (Ed.), Homogenization and Porous Media[M], Springer, New York, 1996, pp. 225-250.
Alsaleh M I. Numerical modeling of strain localization in granular Materials using cosserat theory enhanced with Microfabric properties[D]. 2007,Louisiana State University, doctor thesis Amadei B, Saeb S. Constitutive models of rock joints [C]. Proc. Int. Con. Rock. Joints, Leon,Norway, 581 -594,1990
Amadei B, Wibowo J, Sture S, Price R H. Applicability of existing models to predict the behavior of replicas of natural fractures of welded tuff under different boundary conditions[J]. Geotechnical and Geological Engineering, 1998, 16, 79-128
Amaziane B, Pankratov L, Piatnitski A. Homogenization of a single phase flow through a porous medium in a thin layer[J]. Mathematical Models and Methods in Applied Sciences, 2007,17( 9):1317-1349
Andrade P S, Saraiva A A. Estimating the joint roughness coefficient of discontinuities found in metamorphic rocks[J]. Bulletin Of Engineering Geology And The Environment, 2008, 67(3): 425-434
Aydan O, Shimizu Y, Kawamoto T. The Anisotropy of Surface Morphology Characteristics of Rock Discontinuities[J]. Rock Mechanics and. Rock Engineering, 1996, 29 (1):47-59
Asada T, Ohno N. Fully implicit formulation of elastoplastic homogenization problem for two-scale analysis[J]. International Journal of Solids and Structures,2007, 44: 7261-7275
Asada T, Tanaka Y, Ohno N. Two-scale and full-scale analyses of elastoplastic honeycomb blocks subjected to flat-punch indentation[J]. International Journal of Solids and Structures, 2009, 46(7-8):1755-1763
Bandis S C, Lumden A C, Barton N R. Fundamentals of rock joint deformation[J]. International Journal of Rock Mechanical and Mining Sciences & Geomechanical Abstracts. 1983,22:121
Bao G, Hutchinson J W, Mcmeeking R M. Particle reinforcement of ductile matrices against plastic flow and creep[J]. Acta metallurgica et materialia, 1991,39(8): 1871 -1882
Barbero M, Barla G, Zaninetti A. Dynamic Shear Strength of Rock Joints Subjected to Impulse Loading[J]. International Journal of Rock Mechanical and Mining Science & Geomechanical Abstracts,1996,33(2): 141-151
Barton N R. Estimation of in situ shear strength from back analysis of failed rock slopes[C]. In:Proceedings of international symposium on rock mechanics, Nancy, france, 1971(1):2-27
Barton N, Bandis S. Effects of block size on the shear behavior of jointed rock[C]. 23~(rd) U. S symp. on rock mechanics, Berkley,CA, 739-760,1982
Barton N, Bandis S, Bakhtar K. Strength deformation and conductivity coupling of rock joints[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstract, 1985,22(3):121-140
Barton N. Review of a new shear strength criterion for rock joints[J]. Engineering Geology, 1973; 7:287-332.
Barton N, choubey V. The shear strength of rock joints in theory and practice[J]. Rock Mechanics and Rock Engineering, 1977,10:1 -54
Ba(?)ant Z P. Size effect[J]. Inernational Journal of Solids and Structures, 2000,37:69-80
Ba(?)ant Z P, Pijaudier-Cabot G. Measurement of characteristic length of nonlocal continuum. Journal of Engineering Mechanics, 1989,115(4):755-767
Bazant Z P Cedolin L. Finite element modeling of crack band propagation[J] .Journal of structural engineering, ASCE, 1983a,109(1):6-2
Bazant Z P Oh B H. Crack band theory for fracture of concrete[J].Material and structures, 1983b,16(93):155-177
Belem T, Homand E F,souley M. Fractal analysis of shear joint roughness[J]. International Journal of Rock Mechanics and Mining sciences, 1997, 34(3-4) ,paper No,130
Benssousan A, Lions J L, Papanicoulau G. Asymptotic analysis for periodic structure [M].North Holland,Amsterdam, 1978
Bendsor M P, Kikuchi N. Generating optimal topologies in structural design using a homogeniza-tion method[J]. Computer Methods in Applied Mechanics and Engineering, 1988, (71): 197—224.
Benhamida A, Djeran-Maigre I, Dumontet H, et al. Clay compaction modelling by homogenization theory[J]. International Journal Of Rock Mechanics And Mining Sciences, 2005, 42 (7-8) :996-1005
Bro A. Failure of stepped joints: an analysis and comparison with a measured failure geometry[J].International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1992,29(2): 179-186.
Brown S R, Scholz C H. Closure of random elastic surface in contact[J]. Journal of geophysics research,1985,90:5531-5545
Brown S R, Scholz C H. Closure of rock joints. Journal of geophysics research[J], 1986, 91,4939-Myers N O. Characterization of surface roughness[J]. Wear, 1962, 5: 182-189
Budiansky B, O Connel R J. Elastic moduli of cracked solid. International journal of solids and structures[J], 1976,12(2):81-97.
Budiansky B. On the elastic moduli of heterogeneous materials[J]. Journal of Mechanics and Physics of Solids, 1965, 13(4):223-227
Cai M, Horn H. A constitutive model and FEM analysis of jointed masses[J]. International Journal of Rock and Mining Sciences & Geomechanical Abstracts,1993,30(4):351-359
Caballero A, Willam K J,Carol I. consistent tangent formulation for 3D interface modeling of cracking fracture in quasi-brittle materials. Computer Methods in Applied Mechanics and Engineering, 2008,197:2804-2822
Chang C S, Chang Y, Kabir G. Micromechanics modeling for stress strain behavior of granular soils. Part l:theory[J]. Journal of Geotechnical Engineering, 1992b, 118(12):1959-1974
Chang C S, Kabir M, Chang Y. Micromechanics modeling for the stress-strain behavior of granular soil-II: Evaluation[J]. Journal of Geotechnical Engineering, 1992a, 118(12):1975-1994
Christensen R M, Lo K H. Solution for effective shear properties in three phase sphere and cylinder[J] models. Journal of the Mechanics and Physics Of Solids, 1979,27(4):315-330
Coelho P G, Fernandes P R, Guedes J M, Rodrigues H C. A hierarchical model for concurrent material and topology optimisation of three-dimensional structures[J], Struct Multidisc Optim,2008,35:107-115
Cording E, Jamil M. Slide geometries on rock slopes and walls[C]. In: Fourth South American congress on rock mechanics, Santiago, vol 3,1997. p. 199-221.
Davison, L. and Stevens, A. L. Thermomechanical constitution of spalling elastic bodies[J]. Journal of Applied Physics, 1993, 44, 667-674.
Desai C S, Zaman M M, Lightner J G,et al. Thin-layer element for interface and joints[J]. International Journal of Numerical Methods in Geomechanics, 1984,8:19-43
Dragon, A, Mroz, Z., A continuum model for plastic-brittle behavior of rock and concrete[J].International Journal of Engineering Science, 1979, 17, 121-137.
Drugan W J, Willis J R. A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites[J]. Journal of the Mechanics and Physics of Solids,1996,44(4):497-524
Dong J J, Pan Y W. A hierarchical model of rough rock joints based on micromechanics[J].International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1996,33(2): 111-123.
Douglous K J. The shear strength of rock masses[D]. Ph.D.thesis .the university of new wouth wales,sydeny,Australia.2002
Ehlen J. Fractal analysis of joint patterns in granite[J]. International Journal of Rock Mechanics and Mining Sciences, 2000, 37: 909-922
Fang Z, Harrison JP. Development of a local degradation approach to the modeling of brittle fracture in heterogeneous rocks[J]. International Journal of Rock Mechanics and Mining Sciences,2002,39:443-457
Fanella D, krajcinovic D. A micromechanical damage model for concrete in compressive[J].Engineering Fracture Mechanics,1988,29(1):49-66
Fardin N, Stephansson O, Jing L. The scale dependence of rock joint surface roughness[J]. International Journal of Rock Mechanics & Mining Sciences, 2001, 38: 659-669
Fardin N, Feng O, Stephansson O. Application of a new in situ 3D laser scanner to study the scale effect on the rock joint surface roughness[J]. International Journal of Rock Mechanics & Mining Sciences,2004,41:329-335
Forest S, Pradel F, Sab K . Asymptotic analysis of heterogeneous Cosserat media[J]. International Journal of Solids and Structures,2001,38 (26-27) :4585-4608
Fish J, Shek K, Pandheeradi M, Shephard M S. Computational plasticity for composite structures based on mathematical homogenization: Theory and practice[J]. Computer Methods in Applied Mechanics and Engineering,1997,148:53-73
Fish J, Shek K. Finite deformation plasticity for composite structures.'Computational models and adaptive strategies[J]. Computer Methods in Applied Mechanics and Engineering, 1999B, 172:145-174
Fish J, Yu Q, Shek K. Computational damage mechanics for composite materials based on mathematical homogenization[J]. International Journal for Numerical Methods in Engineering, 1999A,45:1657-1679
Fish J, Yu Q. Multiscale damage modeling for composite materials: theory and computational framework. International Journal for Numerical Methods in Engineering 2001; 52(1—2): 161—192.
Fish J, Fan R. Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading. International journal for numerical methods in engineering 2008,76:1044-1064
Fox D J, Kana D D, Hsiung S M. Influence of interface roughness on dynamic shear behavior in joint rock[J]. International Journal of Rock Mechanics and Mining Sciences, 1998,35(7):923-940
Gehle C, Kutter H K. Breakage and shear behavior of intermittent rock joints[J]. International Journal of Rock Mechanics & Mining Sciences,2003, 40: 687-700
Gentier S, Riss J, Archambault G, Flamand R, Hopkins D. Influence of fracture geometry on shear behavior[J]. International Journal of Rock Mechanics and Mining Sciences,2000, 37:161-174
Gerrard C. Shear failure of rock joints: appropriate constraints for empirical relations[J]. International Journal of Rock Mechanical and Mining Science & Geomechanical Abstracts, 1986;23:421-429.
Ghaboussi J, Wilson E L, Isenberg J. Finite element for rock joints and interfaces[J]ASCE journal of the soil mechanics and foundations division, 99(1973):833-848
Ghoniem N M, Busso E P, Kioussis N, Huang H C. Multiscale modeling of nanomechanics and micromechanics: an overview[J]. Philosophical Magazine, 2003,83(31-34) :3475-3528
Ghosh S, Lee K, Moorthy S. Multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method[J]. International Journal of Solids and Structures, 1995, 32(1):27-62
Ghosh S, Li M S, Moorthy S, Lee K. Microstructural characterization, meso-scale modeling and multiple-scale analysis of discretely reinforced materials[J]. Materials Science and Engineering, 1998,A249: 62-70
Ghosh S, Bai J, Raghavan P. Concurrent multi-level model for damage evolution in micro structurally debonding composites[J], Mechanics of Materials, 2007, 39: 241-266
Ghosh A, Hsiung S M, Chowdhury A H. Seismic response of rock joints and jointed mass. 1995,NUREG/CR-6388, 2-35
Giraud A, Huynh Q V, Hoxha D, Kondo D. Effective poroelastic properties of transversely isotropic rock-like composites with arbitrarily oriented ellipsoidal inclusions[J]. Mechanics of Materials, 2007,39:1006-1024
Gitman I.M, Askes H, Sluys L.J. Coupled-volume multi-scale modeling of quasi-brittle material[J]. European Journal of Mechanics A/Solids,2008, 27: 302-327
Goodman R E, Taylor R L, Brekke T L. A model for the mechanics of jointed rock[J]. ASCE Journal of Soil Mechanics and Foundations division, 1968, 94; 637-659.
Goodman R E. Methods of geological engineering in discontinuous rocks. San Francisco: west publishing company, 1976
Grasselli G, Wirth J, Egger P. Quantitative three-dimensional description of a rough surface and parameter evolution with shearing[J]. International Journal of Rock Mechanics and Mining Sciences,2002,39 (6) : 789-800
Grasselli G, Egger P. Constitutive law for the shear strength of rock joints based on three-dimensional surface parameters[J]. International Journal of Rock Mechanics & Mining Sciences,2003,40: 25-40
Grasselli G. Shear strength of rock joints based on quantified surface description[J]. Rock mechanics and rock engineering, 2006,39(4): 295-314
Graham S, Yang N. Representative volumes of materials based on microstructural Statistics[J]. Scripta Materialia, 2003, 48:269-274
Greenwood J A, Williamson J B P. Contact of nominally flat surface[C]. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1966,295(1442):300-319
Greenwood J A, Tripp J H. The contact of two nominally flat rough surfaces[C]. Proc. Inst. mech.eng.1971,185:625-633
Guedes JM, Kikuchi N. Preprocessing and post-processing for materials based on the homogenization method with adaptive finite element methods[J]. Computer Methods in Applied Mechanics and Engineering, 1990, 83:143-198
Halm, D, Dragon, A. A model of anisotropic damage by mecrocrack growth; unilateral effect[J].International journal of Damage Mechanics, 1996, 5,384-402.
Harberfield C M, seidel J P. Some advances in the modeling of soft joints in direct shear[J].Geotechnical and Geological Engineering, 1999, 17:177-195
Herrmann L R. Finite element analysis of contact problems[J]. Journal of Engineering Mechanics (ASCE), 1978, 104:1043-1059.
Hills R. A self-consistent mechanics of composite materials[J]. Journal of Mechanics and Physics of Solids, 1965,13(4):213-222
Hills R. Elastic properties of reinforced solids: some theoretical principles[J]. Journal of Mechanics And Physics of Solids, 1963, 11,357-372
Hillerborg, A.,M.Modeer, P.E. Petersson. Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements, Cement and Concrete Research, 1976, (6):773-782
Homand F, Belem T, Souley M. Friction and degradation of rock joint surfaces under shear loads[J].International Journal for Numerical and Analytical Methods in Geomechanic,2001,25:973-999.
Hopkins D L. The implications of joint deformation in analyzing the properties and behavior of International Journal of Rock Mechanics and Mining Sciences,2000, 37:175-202
Horii H, Nemat-Nasser S. Overall moduli of solids with microcracks: load-induced anisotropy[J].Journal of Mechanics and Physics of Solids, 1983,31(2):155-171
Huang, S. L., Oelfke, S. M., Speck, R. C. Applicability of fractal characterization and modeling to rock joint profiles[J]. Internationa] Journal of Rock Mechanical and Mining Science & Geomechanical Abstracts, 1992, 29(2):89-98.
Huang T H, Chang C S, Yang Z Y. Elastic moduli for fracture rock mass[J]. Rock Mechanical and Rock Engineering, 1995,28(3): 135-144
Huang T H, Chang C S,Cchao C Y. Experimental and mathematical modeling for fracture of rock joint with regular asperity[J]. Engineering Fracture Mechanics, 2002, 69: 1977-1996
Huang T H, Chang C S, Yang Z Y. Elastic Moduli for Fractured Rock Mass[J]. Rock Mechanics and .Rock Engineering, 1995, 28 (3): 135-144
Huang x, Haimson B C, Plesha M E, Qiu X.. An investigation of the mechanics of rock joints part 1:laboratory investigation[J]. International Journal of Rock Mechanical and Mining Science &Geomechanical Abstracts,1993,30(3):257-269
Huston R W, Dowding C H. Joint asperity degradation during cyclic shear[J]. International Journal of Rock Mechanical and Mining Science & Geomechanical Abstracts, 1990,27(2): 109-119
Ichikawa Y, Kawamura K, Uesugi K, Seo Yong-seok, Fujii N. Micro and macrobehavior of granite rock:observation and viscoelastic homogenization analysis[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 191:47-72
Indraratna B, haque A, Aziz N. Laboratory modeling of shear behavior of soft joints under constant normal stiffness conditions[J]. Geotechnical and Geological Engineering, 1998, 16:17-44
Jaeger J C. Friction of rocks and stability of rock slopes[J]. Geotechnique, 1971,21(2): 97-134
Jafari M K, hosseini K A, Pellet F, et al. Evaluation of shear strength of rock joints subjected to cyclic loading[J]. Soil Dynamics and Earthquake Engineering,2003,23:619-630
Jafari M K, Pellet F, Boulon M, Hosseini K A. .Experimental Study of Mechanical Behaviour of Rock Joints Under Cyclic Loading[J]. Rock Mechanics and Rock Engineering,2004,37 (1):3—23
Jager J. A new principle in contact mechanics[J]. Journal of Tribology,1998, 120:677-684
Jakobsen K. P, Lade P. V. Implementation algorithm for a single hardening constitutive model for frictional materials[J]. International Journal For Numerical And Analytical Methods In Geomechanics,2002,26 (26) :661-681
Jennings JE. A mathematical theory for the calculation of the stability of open cast mines[C]. In:Proceedings of the symposium on theoretical background to the planning of open pit mines.Johannesburg, 1970, p. 87-102.
Jiang Y J, Li B, Tanabashi Y. Estimating the relation between surface roughness and mechanical properties of rock joints[J]. International Journal of Rock Mechanics & Mining Sciences, 2006, 43:837-846
Jing L, Nordlund E, Stephansson O. An experimental study on the anisotropy and stress dependency of the strength and deformability of rock joints[J]. International Journal of Rock Mechanics and
Mining Sciences& Geomechanics Abstracts, 1992,29:535-542
Jing L, stephansson O, nordlund E. Study of rocks under cyclic loading conditions[J]. Rock Mechanics and Rock Engineering, 1993, 26(3): 215-232
Ju, J. W. On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects[J]. International Journal of Solids and Structure, 1989, 25,803-833
Kachanov M L. A micromechanical model of rock inelasticity part 1:frictional sliding on microcracks[J].Mechanics of materials, 1982,1 (1): 19-27
Kachanov M L.A micromechanical model of rock inelasticity part 2:propagation of microcracks[J].Mechanics of materials, 1982,1 (1 ):29-41
Kana D D, Fox D J, Hsiung S M. Interlock /friction model for dynamic shear response in natural jointed rock[J]. International Journal of Rock Mechanics and Mining Sciences, 1996,33(4): 371-386
Kaneko K, Terada K, Kyoya T, Kishino Y. Global-local analysis of granular media in quasi-static equilibrium[J]. International Journal of Solids and Structures, 2003, 40: 4043-4069
Kawamoto, T., Ichikawa, Y. and Kyoya, T. Deformation and fracturing behavior of discontinuous rock mass and damage mechanics theory[J]. International Journal for Numerical and Analytical Methods in.Geomechanics, 1988, 12:1-30.
Kanit T, Forest S, Galliet I, Mounoury V, Jeulin D. Determination of the size of the representative volume element for random composites: statistical and numerical approach[J]. International Journal of Solids and Structures,2003,40:3647-3679
Kemeny J. the time-dependent reduction of sliding cohesion due to rock bridges along discontinuities: a fracture mechanics approach[J]. Rock mechanics and rock engineering, 2003,36(1):27-38
Klein E, Reuschle T. A pore crack model for the mechanical behavior of porous granular Rocks in the brittle deformation regime[J]. International Journal of Rock Mechanics & Mining Sciences ,2004, 41:975-986
Kouznetsova V G. Computational homogenization for the multi-scale analysis of multi-phase materials[D]. PhD thesis, Technical University Eindhoven, 2002.
Kulatilake P H S W, Shou g, Huang T H. Spectral based peak shear strength criterion for rock joints[J].Journal of geotechnical engineering, 1995, 121(11): 789-796
Kulatilake P H S W,Balasingam P,Park J, Morgan R. Natural rock joint rough quantification through fractal techniques[J]. Geotechnical and Geological Engineering, 2006, 24: 1181-1202
Kusumi H, Teraoka K, Nishida K. Study on new formulation of shear strength for irregular rock joints[J]. International Journal of Rock Mechanics & Mining Sciences, 1997, 34(3-4)
Kuhl E,Ramn E, Willam K. Failure analysis of elasto-plastic material models on different levels of observation[J]. international journal of solids and structures, 2000,37:7259-7280
Kyoya T, terada K, kawamoto T. Multi-scale limit load analysis for Discontinuous rock mass based on the Homogenization method[J].International journal for Numerical and Analytical Methods in Geomechanics, 1999, 23: 995-1019
Ladanyi B, Archambault G. Simulation of shear behavior of a jointed rock mass[C]. Proc.11th Symp. Rock. Mech, AIME, New York, 105-125,1970
Lajai E Z.Shear strength of weakness planes in rock[J]. International Journal of Rock Mechanics and Mining Sciences, 1969,6(7):499—515
Lacy T E, McDowell D L, Talreja R. Gradient concept for evolution of Damage[J]. Mechanics of Materials, 1999, 31:831-860
Lee J S, G. N. Pande G N. A new joint element for the analysis of media having discrete discontinuities [J]. Mechanics of Cohesive-Frictional Materials, 1999,4:487-504
Lee, Y. H., Cart, J. R., Barr, D. J., Haas, C. J. The fractal dimension as a measure of the roughness of rock discontinuity profiles[J]. International Journal of Rock Mechanical and Mining Science &Geomechanical Abstracts, 1990, 27 (6):453 464.
Lee X, Ju J W. Micromechanical damage models for brittle solids 2:compressive loadings[J]. Journal of Engineering Mechanics, 1991,117(7): 1515-1536
Lee K, Ghosh S. Small deformation multi-scale analysis of heterogeneous materials with the Voronoi cell finite element model and homogenization theory[J]. Computational Materials Science, 1996, 7:131-146
Lee K, Ghosh S. A microstructure based numerical method for constitutive modeling of composite and porous materials[J]. Materials Science and Engineering, 1999, A272:120-133
Lee H S, Park Y J, Choc T F, You K H. Influence of asperity degradation on the mechanical behavior of rough rock joints under cyclic shear loading[J]. International Journal of Rock Mechanics & Mining Sciences, 2001,38:967-980
Lee S D, Moon H K. HM modeling of tunnel excavation in fractured rock masses by a 3D discete fracture network approach[C]. International Journal of rock mechanics and mining sciences, 2001. 41,sinorock 2004 symposium
Lee S D, Lee C I, Park Y. Characterization of joint profiles and their roughness parameters[J].Internationa] Journal of Rock Mechanics and Mining Sciences, 1997, 34(3-4), paper No, 174
Lei X Y, Swoboda G, Zenz G. Application of contact friction interface element to tunnel excavation in faulted rock[J]. Computers and Geotechnics, 1995,17:349-370.
Lemaitre J. A course on damage mechanics[M]. 2nd ed. Berlin: Springer; 1992.
Lemaitre J. Continuum Damage Mechanics Theory and Applications[M]. Springer,Wien-New York,1987.
Lewandowska J, Laurent J P. Humidity Transfer in Unsaturated Heterogeneous Porous Media by Homogenization[J].Physics and Chemistry of The Earth Part A,2000,25, No. 2, pp. 175-181
Lewandowska J, Szymkiewicz A, Kazimierz Burzynski, Michel Vauclin. Modeling of unsaturated water flow in double-porosity soils by the homogenization approach[J]. Advances in Water Resources,2004, 27: 283-296
Li Aiqin, Li Renge, Fish J. Generalized Mathematical Homogenization: From theory to practice[J].Computer Methods in Applied Mechanics and Engineering, 2008,197: 3225-3248
Lopez P, Riss J, Archambault G. An experimental method to link morphological properties of rock fracture surfaces to their mechanical properties[J]. International Journal of Rock Mechanics & Mining Sciences, 2003, 40: 947-954
Lubarda V A, Krajcinovic D. Some fundamental issues in rate theory of damage-elastoplasticity[J].International Journal of Plasticity, 1995,11(7):763-797
Maksimovic M. The Shear Strength Components of a Rough Rock Joint[J]. International Journal of Rock Mechanical and Mining Science & Geomechanical Abstracts, 1996, 33(8): 769-783
Malama B,Kulatilake P H S W. Models for normal fracture deformation under compressive loading[J].International Journal of Rock Mechanics and Mining Sciences,2003,40(6):893-901.
Marmier R, Jeannin I, Barthe' le' my J F. Homogenized constitutive laws for rocks with elastoplastic fractures[J]. International Journal for Numerical and Analytical Methods in Geomechanics 2007;31:1217-1237
Mandelbrot B. B. Self-affine fractals and fractal dimensions[J]. Physica Scripta, 1985, 32:257-260.
Markovic, D, Ibrahimbegovic, A. On micro-macro interface conditions for micro scale based FEM for inelastic behavior of heterogeneous materials[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193:5503-5523.
Massart, T.J. Multi-scale modeling of damage in masonry structures[D]. PhD thesis, Technical University Eindhoven. 2003,Available from http://www.mate.tue.nl
Matsuki K, Wang E Q, Sakaguchi K, Okumura K. Time-dependent closure of a fracture with rough surfaces under constant normal stress[J]. International Journal of Rock Mechanics & Mining Sciences,2001,38:607-619
Matsui K, Terada K, Yuge K. Two-scale finite element analysis of heterogeneous solids with periodic microstructures[J]. Computers and Structures, 2004, 82:593-606
Mindlin RD. Compliance of elastic bodies in contact[J]. Journal of Applied Physics, 1949, 16:259-268
Mindlin RD and Deresiewicz H (1953) ASME J. Appl. Mech., 20:327-344
Misra A. Mechanistic model for contact between rough surfaces[J]. Journal of Engineering Mechanics,1997,123(5):475-484
Misra A. Effect of asperity damage on shear behavior of single fracture[J]. Engineering Fracture Mechanics, 2002,69:1997-2014
Mroz Z. An interface model for analysis of deformation behavior of discontinuities[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1996, 20:1-33
Moorthy S, Ghosh S. A Voronoi cell finite element model for particle plastic composite materials cracking in elastic-plastic composite materials[J]. Computer Methods in Applied Mechanics and ngineering, 1998,151:377-400
Moorthy S ,Ghosh S. Adaptivity and convergence in the Voronoi cell finite element model for analyzing heterogeneous materials[J]. Computer Methods in Applied Mechanics and Engineering,2000,185:37-74
Mori T, Tanaka K. Average stress in matrix and average energy of materials with misfitting inclusions[J]. Acta Metallurgica et Materialia, 1973,21: 571-574
Mughieda O, abdel kareem alzo'ubi. Fracture mechanisms of offset rock joints-A laboratory investigation[J]. Geotechnical and Geological engineering, 2004, 22: 545-562
Mughieda O, Maher T. Omar. Stress Analysis for Rock Mass Failure with Offset Joints[J]. Geotechnical and Geological Engineering, 2008, 26:543-552
Murakami S, Kamika K. constitutive and damage evolution equations of elastic brittle materials based on irreversible thermodynamics[J]. International Journal of Mechanics Sciences, 1997,39:473-486
Murakami, S. Ohno, N. A continuum theory of creep and creep damage[C].Proceedings of 3rd IUTAM Symp. on Creep in Structures, ed. A. R. S. Ponter and D. R. Hayhust. Springer±Verlag, Berlin, 1980,422-443.
Murad M A, Moyne C. A three-scale computational model of reactive pollutant transport in smectitic clays[J]. Communications in Numerical Methods in Engineering, 2006, 22:875-891
Nemat-Nasser S, Obata M. A microcrack model of dilatancy in brittle materials[J]. Journal of Applied Mechanics,1986,55:24-35
Nemat-Nasser S, Yu N, Hori M. Solids with periodically distributed cracks[J]. International journal of solids and structures, 2009, 30(15):2071-2095
Ng K. L. A, Small J. C. Behavior of Joints and Interfaces Subjected to Water Pressure[J]. Computers and Geotechnics, 1997,20(1): 71-93
Odling N E. natural fracture profiles fractal dimension and joint roughness coefficients[J]. Rock Mechanics and Rock Engineering, 1994, 27(3): 135-153
O van der Sluis, Vosbeek P H J, Schreurs P J G, Meijer H E. Homogenization of heterogeneous polymers[J]. International Journal of Solids and Structures 1999,36:3193-3214
Oskay C, Fish J. Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials[J]. Computer Methods in Applied Mechanics and Engineering,2007, 196:1216-1243
Pande GN, Sharma KG. On joint /interface elements and associated problems of numerical ill-conditioning[J]. International Journal for Numerical and Analytical for Geomechanics, 1979,2:293-300
Park C H, Bobet A. Crack coalescence in specimens with open and closed flaws: A comparison[J].International Journal of Rock Mechanics & Mining Sciences2009, 46: 819-829
Patton F D. Multiple model of shear failure inrock[C]. Proceedings of the First Congress of ISRM,Lisbon, 509-513,1966
Pensee V, Kondo D, Dormieux L. Micromechanical Analysis of Anisotropic Damage in Brittle Materials[J]. Journal of Engineering Mechanics, 2002,128(8): 889-897
Pereira J P, de fireitas M H. Mechanism of shear failure in artificial fractures of sandstoneand their implication for models of hydromechanical coupling[J]. Rock Mechanical and Rock Engineering,1993,26(3): 195-214
Plesha M E, Ballarini R, Parulekar A. Constitutive model and finite element procedure for dilatant contact problems[J].Journal of Engineering Mechanics, 1989,115(12): 2649- 2668
Plesha M E. Constitutive models for rock discontinuities with dilatancy and surface degradation[J]. International Journal of Numerical and Analytical Methods in Geomechanics, 1987,11:345-362
Plesha M E, Haimson B C. An advanced model for rock joint behavior: analytical, experimental and implementational consideration[C].proc 29~(th) u s. symp on key question in rock mechanics,pp119-126,1988
Prudencio M, Van Sint Jan M. Strength and failure modes of rock mass models with non-persistent joints[J]. International Journal of Rock Mechanics & Mining Sciences, 2007, 44 :890-902
Puntel E, Bolzon G, Saouma V E. Fracture Mechanics Based Model for Joints under Cyclic Loading[J]. Journal of Engineering Mechanics, 2006,132(11): 1151-1159
Pyrak-Nolte L J, Morris J P. Single fracture under normal stress: the relation between fracture specific stiffness and fluid flow[J]. International journal of rock mechanics and mining sciences, 2000,37:245-262
Qiu X J, Plesha M E, Huang X, Haimson B C. An investigation of the mechanics of rock joints. Part II. Analytical investigation[J]. International Journal of Rock Mechanical and Mining Sciences &Geomechanics Abstracts, 1993, 30:271-287
Raghavan P, Ghosh S. Concurrent multiscale analysis of elastic composites by a multilevel computational model[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193 (6-8 ):497-538
Ren Z Y, Zheng Q S. A quantitative study of minimum size of representativevolume elements of cubic polycrystals_numerical experiments[J]. International Journal of Physics of Solids, 2002,50:881-893
Ren Z Y, Zheng Q S. Effects of grain sizes, shapes, and distribution on minimum sizes of representative volume elements of cubic polycrystals[J]. Mechanicsof Materials, 2004,36:1217-1229
Riss J, Gentier S, Archambault C, Flamand R. Sheared rock joints dependence of damage Zones on morphological anisotropy[J]. International Journal of Rock Mechanics & Mining Sciences, 1997,34( 3-4)
Robina, Wong H C, Chau K T. Crack Coalescence in a Rock-like Material Containing Two Cracks[J].International Journal of Rock Mechanics and Mining Sciences, 1998, 35(2): 147-164
Roosta R M,Sadaghiani A H,Pak A, Saleh Y. Rock joint modeling using a visco-plastic multilaminate model at constant normal load condition[J]. Geotechnical and geological engineering, 2006, 24:1449-1468
Rooke,D, Cartwright D. Compendium of stress intensity factors. H M S O, London,330PP,1976
Sab K. On the homogenization and simulation of random materials[J]. European Journal of Mechanics-A/Solids II 5,585-607
Saeb S, Amadei B. Modeling rock joints under shear and normal loading[J]. International Journal of Rock Mechanical and Mining Science & Geomechanica! Abstracts, 1992,29(3):267-278
Sagong M, Bobet A. Coalescence of multiple flaws in a rock-model material in uniaxial compression[J].International Journal of Rock Mechanics & Mining Sciences,2002,39: 229-241
Saikia 1, Terada K, Ikeda K, Hori M. Appropriate number of unit cells in a representative volume element for micro-structural bifurcation encountered in a multi-scale modeling[J]. Computer Methods in Applied Mechanics and Engineering, 2002, 191:2561-2585
Sakaguchi K, Tomono J, Okumura K, Ogawa Y, Matsuki K. Asperity Height and Aperture of an Artificial Tensile Fracture of Metric Size[J]. Rock Mechanics and Rock Engineering, 2008, 41 (2):325-341
Salari M R, Saeb S, Willam K J, Patchet S J, Carrasco R C.A coupled elastoplastic damage model for geomaterials[J]. Computer Methods in Applied Mechanics and Engineering,2004,193:2625-2643
Sanchez-Paiencia E. Non-homogeneous media and vibration theory[M]. Lecture notes in physics, 127,Springer-Verlag,Berlin, 1980
Seidel J P, Haberfield C M. A theoretical model for rock joints subjected to constant normal stiffness direct shear[J]. International Journal of Rock Mechanics and Mining Sciences, 2002, 39:539-553
Seidel J P, Haberfield C M. Toward an understand of joint roughness[J]. Rock Mechanics and Rock Engineering, 1995, 28(2): 69-92
Selvadurai A.P.S, Yu Q. Mechanics of a discontinuity in a geomaterial, Computers and Geotechnics,2005,32:92-106
Sevostianov I, Kachanov M. Contact of rough surfaces: A simple model for elasticity conductivity and cross-property connections[J]. Journal of the Mechanics and Physics of Solids,2008, 56: 1380-1400
Shah K R, wong T F. Fracture at contact surfaces subjected to normal and tangential loads[J].International Journal of Rock Mechanics and Mining Sciences, 1997, 34(5):727-739
Shan Z, Gokhale A M. Representative volume element for non-uniform microstructure[J].Computational Materials Science,2002,24:361-379
Souley M, Homand F, Amadei B. An extension to the saeb and amadei constitutive model for rock joints to include cyclic loading paths[J]. International Journal of Rock Mechanical and Mining Science& Geomechanical Astracts, 1995,32(2):101-109
Son B K, Lee Y K, Lee C I. Elasto-plastic simulation of a direct shear test on rough rock joints[J].International Journal of Rock Mechanics & Mining Sciences,2004,41(3),Paper 2A 07
Suquet P M. Element of homogenization theory for inelastic solid mechanics. In:Sanchez-Palencia E,Zaoui A(Eds). Homogenization technique for composite media[M]. Springer-Verlag, Berlin, Heidelberg,New York,pp,194-275
Sumarac D, Krajcinovic D. A self-consistent model for microcrack-weakened solids[J]. Mechanics of materials, 1987,6,39-52
Swan G. Determination of stiffness and other joint properties from roughness measurements[J]. Rockmechanics and rock engineering, 1983,16:19-38
Swan G, Zongqi S. Prediction of shear behavior of joints using profiles[J]. Rock Mechanics and Rock Engineering, 1985, 18: 183-212
Swoboda G, Shen X P, Rosas L. Damage Model for Jointed Rock Mass and Its Application to TunneIing[J]. Computers and Geotechnics, 1998,22(3/4): 183-203
Terada K, Miura T, Kikuchi N. Digital image-based modeling applied to the homogenization analysis of composite materials[J].Computational Mechanics, 1997,20: 331-346
Terada K,Ito T, Kikuchi N. characterization of the mechanical behavior of solid-fluid mixture by the homogenization method[J]. Computer Methods In Applied Mechanics And Engineering, 1998, 153(3-4) :223-257
Terada K, Hori M, Kyoya T, Kikuchi N. Simulation of the multi-scale convergence in computational homogenization approaches[J]. International Journal of Solids and Structures, 2000, 37: 2285-2311
Terada K, Kikuchi N. A class of general algorithms for multi-scale analysis of heterogeneous medis[J].Computer Methods in Applied Mechanics and Engineering, 2001,190:5427-5464
Terada K, Kyoya T, Kazama M, Lee K, Oyang L Z. Image-based modeling and analysis of microstructures for two-scale problems in geomechanics[J]. International journal for Numerical and Analytical Methods in Geomechanics, 2002; 26:273-297
Terada K, Saiki I, Matsui K, Yamakawa Y. Two-scale kinematics and linearization for simultaneous two-scale analysis of periodic heterogeneous solids at finite strain[J]. Computer Methods in Applied Mechanics and Engineering,2003,192:3531-3563
Van vliet M R A. Size effect in tensile fracture of concrete and rock[D]. PhD thesis,Delft University of Technology, 2000.
Villard P. Modeling of Interface Problems by the Finite Element Method with Considerable Displacements[J]. Computers and Geotechnics, 1996,1991 ):2345
Walsh, J.B, Grosenbaugh, M.A. A new model for analyzing the effect of fractures on compressibility[J].Journal of Geophysics Research, 1979,84: 3532-3536.
Wang J G, Ichikawa Y, Leung C F. A constitutive model for rock interfaces and joints[J].International Journal of Rock Mechanics & Mining Sciences, 2003, 40: 41-53
Watanabe I, Terada K, Akiyama M. Two-scale analysis for deformation-induced anisotropy of polycrystalline metals[J].Computational Materials Science,2005, 32:240-250
Watanabe I, Terada K, Eduardo Alberto de Souza Neto, Djordje Peric. Characterization of macroscopic tensile strength of polycrystalline metals with two-scale finite element analysis[J]. Journal of the Mechanics and Physics of Solids,2008,56 : 1105-1125
Willam K J, Iordache M M. On the lack of symmetry in materials[C]. trends in computational structural mechanics, Wall W A, Bletzinger K U and Schweizerhof K(Eds.). CIMNE, Barcelona, Spain,2001,1-10
Xie H P, Wang J A, KwasAniewski M A. Multifractal characterization of rock fracture surfaces[J].International Journal of Rock Mechanics and Mining Sciences, 1999, 36:19-27
Yamada, K, Takeda, N, Kagami, J, Naoi, T. Mechanisms of elastic contact and friction between rough surfaces[J]. Wear, 1978b, 48: 15-34.
Yang Z Y, Chiang D Y. An experimental study on the progressive shear behavior of rock joints with tooth-shaped asperities[J]. Internationa] Journal of Rock Mechanics & Mining Sciences,2000, 37:1247-1259
Yang Z Y, Di C C, Yen K C. The effect of asperity order on the roughness of rock joints[J].International Journal of Rock Mechanics & Mining Sciences,2001,38:745-752
Yang Z Y,Lo S C.An Index for Describing the Anisotropy of Joint Surfaces[J].International Journal of Rock Mechanics & Mining Sciences,1997,34(6):1031-1044
Yoshioka,N.The role of plastic deformation in normal loading and unloading cycles[J].Journal of Geophysics Research,1994,99:15561-15568.
Yoshida H,Horii H.Micromechanics-based continuum model for a jointed,rock mass and excavation analyses of a large-scale cavern[J].International Journal of Rock Mechanics & Mining Sciences,2004,41:119-145
Yong Ming Tien,Ming Chuan Kuo.A failure criterion for transversely isotropic rocks[J].International Journal of Rock Mechanics & Mining Sciences,2001,38:399-412
Yu Xianbin,vayssade b.joint profiles and their roughness parameters[J].International Journal of Rock Mechanical and Mining Science & Geomechanical Abstracts,1991,28(4):333-336
Yu Qing,Fish J.Multiscale asymptotic homogenization for multiphysics problems with multiple spatial and temporal scales:a coupled thermo-viscoelastic example problem[J].International Journal of Solids and Structures,2002,39:6429-6452
Yuan S C,Harrison J P.Development of a hydro-mechanical local degradation approach and its application to modeling fluid flow during progressive fracturing of heterogeneous rocks[J].International Journal of Rock Mechanics and Mining Sciences,2005,42:961-984
Zangerl C,Evans K F,Eberhardt E,Loew S.Normal stiffness of fractures in granitic rock:A compilation of laboratory and in-situ experiments[J].International Journal of Rock Mechanics &Mining Sciences,2008,45:1500-1507
Zheng Yuan,Fish J.Toward Realization Of Computational Homogenization In Practice[J].International Journal For Numerical Methods In Engineering,2008;73:361-380
Zhu Qizhi,Kondo D,Shao J F,Pensee V.Micromechanical modelling of anisotropic damage in brittle rocks and application[J].International Journal of Rock Mechanics & Mining Sciences,2008,45:467-477
Zhao J.Joint surface matching and shear strength part B:JRC-JMC shear strength criterion[J]International Journal of Rock Mechanics and Mining Sciences,1997,34(2):179-185
Zienkiewicz O C,Best B,Dullage C et al.Analysis of nonlinear problems in rock mechanics with particular reference to jointed rock systems[C].In:proc 2~(nd) confofthe society of rock mechanics,Belgrade,1970,8-14
Zienkiewicz,O.C.,G.N.Pande,Time Dependent Multilaminate Model of Rocks--A Numerical Study of Deformation and Failure of Rock Masses," International Journal for Numerical and Analytical Methods in Geomechanics,1977,1:219-247
Zubelewice A,O' connor K,Dowing C H,Belytschko T,Plesha M E.A constitutive model for cyclic behavior of dlatant rock joints[C].Proc.2~(nd).conf.constitutive laws for engng materials,1987,1137-1144
保长汉.节理岩体的随面本构关系[J].工程力学(增刊),1996:274-278
白世伟,任伟中,丰定祥等.平面应力条件下闭合断续节理岩体破坏机理及强度特性[J].岩石力学 与工程学报,1999,18(6):635-640
陈乃明.岩体节理形貌的分形维数与摩擦角的关系研究.岩土力学[J],1996,17(3):54-58
陈蕴生,李宁,李爱国等.非贯通节理介质细观损伤演化的CT分析[J].岩石力学与工程学报,2000.19(6):702-706
曹文贵,速宝玉.模拟夹层的大变形有限元等厚度节理单元模型[J].河海大学学报,2000,28(3):26-29
曹文贵,李翔,刘峰等.裂隙化岩体应变软化损伤本构模型探讨[J].岩石力学与工程学报,2007,26(12):2488-2494
曹玉新,许兰民,沈宇鹏.土工格栅在青藏铁路多年冻土区的应用[J].北京交通大学学报,2008,32(1):16-19
曹礼群,罗剑兰.多孔复合介质周期结构热传导和质扩散问题的多尺度数值方法[J].工程热物理学报,2000,21(5):610-614
曹礼群.材料物性的多尺度关联与数值模拟[J].世界科技研究与发展,2002,24(6):23-29
陈卫忠,李术才,朱维申.考虑裂隙闭合和摩擦效应的节理岩体能量损伤理论与应用.岩石力学与工程学报,2000,19(2):131-135
崔俊芝,曹礼群.基于双尺度渐近分析的有限元算法[J].计算数学,1998,20(1):89-102
崔俊芝,曹礼群.具有小周期孔洞弹性结构的双尺度渐近分析[J],系统科学与数学,1999,19(4):490-495
岑威钧,朱岳明.基于ABAQUS的土石料本构模型二次开发及其应用[J].水利水电科技进展,2005,25(6):78-81
陈祖煜、汪小刚、杨健等。岩质边坡稳定分析。北京:中国水利水电出版社,2005
戴永浩,陈卫忠,伍国军等.非饱和岩体弹塑性损伤模型研究与应用[J].岩石力学与工程学报,2008,27(4):728-735
杜守继.朱建栋,职洪涛.岩石节理经历不同变形的剪切试验研究[J].岩石力学与工程学报,2006,25(1):56-60
方理刚.岩石节理弹塑性本构关系[J].岩土工程学报,1996,18(3):91-95
方岱宁,周储伟.有限元计算细观力学对复合材料力学行为的数值分析[J].力学进展,1998,(28):173-188.
冯淼林,吴长春.基于三维均匀化方法的复合材料本构数值模拟.中国科学技术大学学报,2000,30(6):693-699
傅冰骏。岩石力学研究的现状和未来。岩石力学研究的现状和未来--傅冰骏教授在全国岩土与工程学术大会报告,2003
付凯敏,黄晓明.基于ABAQUS的修正Burgers蠕变模型二次开发[J].公路工程,2008,33(3):132-137
付丽,杜星文.基于非局部理论的一维损伤模型的有限元算法[J].航空学报,2009,30(5):879-885
范景伟,何江达.含定向闭合断续节理岩体的强度特性[J].岩石力学与工程学报,1992,11(2):190-199
冯永平,崔俊芝,邓明香.周期孔洞区域中热力耦合问题的双尺度有限元计算[J].物理学报,2009,58:S327-S337
范庆来,栾茂田,杨庆.修正剑桥模型的隐式积分算法在ABAQUS中的数值实施[J].岩土力学,2008,29(1):269-273
郭少华,孙宗颀,谢晓晴.压缩条件下岩石断裂模式与断裂判据的研究[J].岩土工程学报,2002,24(3):304-308
冀宾,陈万吉,赵杰.岩土软化行为的网格依赖性问题研究[J].工程力学,2008,25(8):36-41
冀宾,陈万吉,赵杰.基于偶应力理论剪切带问题的弹塑性有限元分析[J].力学学报,2009,41(2):1992-199
李浩,陶振宇.非贯通节理岩体的有效场和损伤本构关系[J].武汉水利电力大学学报,2000,33(3):5-8
李银平,王元汉,肖四喜.岩石类材料压剪裂纹的相互作用分析[J].岩石力学与工程学报,2003,22(4):552-555
李银平,王元汉,陈龙珠等.含预制裂纹大理岩的压剪试验分析[J].岩土工程学报,2004,26(1):120-124
李建林,哈秋林.节理岩体拉剪断裂与强度研究[J].岩石力学与工程学报,1998,17(3):259-266
李建林,孙志宏.节理岩体压剪断裂及其强度研究[J].岩石力学与工程学报,2000,19(4):444-448
李树荣,高峰,廖孟柯等.岩石粗糙节理剪切强度的分形分析[J].煤炭科学技术,2006,34(11):64-66
李同录,罗世毅,何剑等.节理岩体力学参数的选取与应用[J].岩石力学与工程学报,2004,23(13):2182-2186
李海波,刘博,冯海鹏等.模拟岩石节理试样剪切变形特征和破坏机制研究[J].岩土力学,2008,29(7):1741-1746
凌道盛,徐兴.非线性有限元及程序.浙江:浙江大学出版社,2004
林鹏,黄凯珠,王仁坤,周维垣.不同角度单裂纹缺陷试样的裂纹扩展与破坏行为[J].岩石力学与工程学报,2005,2(增2):5652-5657
梁作元,朱维申.压剪应力作用下含共面闭合节理岩石材料的切破坏准则探讨[A].见:朱维申编.中国青年学者岩土工程力学及其应用讨论会议论文集[C].北京:科学出版社。
刘远明,夏才初.非贯通节理岩体直剪贯通模型和强度研究[J].岩土工程学报,2006,28(10)
刘东燕,朱可善.含断续节理岩体强度的各向异性研究[J].岩石力学与工程学,1998,17(4):366-371
刘晓丽,梁冰,薛强.多孔介质渗透率的分形描述[J].水科学进展,2003,14(6):769-773
刘飞禹,蔡袁强,徐长节等.交通荷载作用下软基加筋道路变形机制研究[J].岩土力学,2009,30(1):129-134
刘泉声,胡云华,刘滨.基于试验的花岗岩渐进破坏本构模型研究[J].岩土力学,2009,30(2):289-296
刘军.岩体在冲击载荷作用下的各向异性损伤模型及其应用[J].岩石力学与工程学报,2004,23(4):635-640
刘萌成,黄晓明,林云龙.交通荷载作用下近桥台处差异沉降与路面结构开裂研究[J].岩土力学,2006,27(12):2203-2212
刘元高,周维垣,赵吉东,等.裂隙岩体损伤局部化破坏分岔模型及其应用.力学学报,2003,35(4):411-418
连尉平,崔俊芝.三维编织复合材料模量的双尺度有限元计算[J].计算力学学报,2005,22(3):268-273
连志龙,张劲,吴恒安等.水力压裂扩展的流固耦合数值模拟研究[J].岩土力学,2008,29(11):3021-3026
梁正召,唐春安,张永彬,等.准脆性材料的物理力学参数随机概率模型及破坏力学行为特征.岩石力学与工程学报,2008,27(4):718-727
马志涛,谭云亮.岩石破坏演化细观非均质物理元胞自动机模拟研究.岩石力学与工程学报,2005,24(15):2704-2708
牛斌,杨海天.基于均匀化方法的斜交节理岩体复合本构关系研究[J].岩土工程学报,2007,29(5):773-778
潘燕环、秘醒、薛松涛。复合材料中的渐近均匀化方法。上海力学,1997,18(4):290-297
秦娟,耿克勤.节理岩体的代表单元集合体模型及弹性参数预测[J].水利学报,2001,9:45-50
乔春生,张清.岩石节理非线性变形分析[J].北方交通大学学报,22(1),1-6,1998
任伟中,王庚荪,白世伟,等.共面闭合断续节理岩体的直剪强度研究[J].岩石力学与工程学报,2003,22(10):1667-1672
任强,徐卫亚.基于均匀化方法的节理岩体等效弹性性能预测[J].工程力学,2008,25(4):75-79,92
芮勇勤,唐春安.岩石剪切破坏过程的RFPA2D数值模拟.岩石力学与工程学报,2002,21(3):364-368
宋岩新,杨庆,唐小微等.ABAQUS后处理二次开发在海底管线稳定性分析中的应用[J].中国海洋平台2008,23(4):18-22
孙宗颀.不连续面应力应变性质研究[J].岩石力学与工程学报,1978,6(4):287-300
孙吉主,高晖.ABAQUS在软基固结过程分析中的应用[J].岩土力学,2007,28(增):919-922
孙毅,戴龙侠,范春竹等.淋溪河水电站地下厂房开挖过程中材料敏感性的非线性有限元分析[J].岩土力学,2008,29(增):149-154
孙德安,甄文战,黄文雄.三维弹塑性模型在路堤软基固结分析中应用[J].岩土力学,2009,30(3):66-674
孙卫军,周维垣.裂隙岩体弹塑性一损伤本构模型[J].岩石力学与工程学报,1990,9(2):108-119
沈婷,丰定祥,任伟中,白世伟.由结构面和岩桥组成的剪切面强度特性研究[J].岩土力学,1999,20(1):33-38
唐春安,朱万成.混凝土损伤与断裂--数值试验.科学出版社,北京,2003
王建华,范巍,王卫东等.空间m法在深基坑支护结构分析中的应用[J].岩土工程学报,2006,28(增):1332-1335
王镜波,崔俊芝,聂玉峰.单向纤维增强复合材料的双尺度分析模型及其力学参数计算.数值计算与计算机应用[J],2009,30(1):30-40
吴世平,唐绍锋,梁军,杜善义.周期性复合材料热力耦合性能的多尺度方法[J].哈尔滨工业大学学报,2006,38(12):2049-2053
王安明,杨春和,陈剑文等.层状盐岩体非线性蠕变本构模型[J].岩石力学与工程学报,2009,28(增1):2708-2714
王栋、年廷凯、陈煜淼。边坡稳定有限元分析中的三个问题[J].岩土力学,2007,28(11):2309-2318
王士民,朱合华,冯夏庭,等.细观非均匀性对脆性岩石材料宏观破坏形式的影响.岩土力学,2006,27(2):224-227
徐涛,唐春安,张哲,等.单轴压缩条件下脆性岩石变形破坏的理论,试验与数值模拟.东北大学学报(自然科学版),2003,24(1):87-90
徐晗,朱以文,蔡元奇等.降雨入渗条件下非饱和土边坡稳定分析[J].岩土力学,2005,26(12):1957-1962
徐卫亚,张贵科.节理岩体正交各向异性等效强度参数研究[J].岩土工程学报,2007,29(6):806-810
徐光黎,潘别桐,晏同珍.节理岩体变形模量估算新方法[J].地球科学-中国地质大学学报,1991,16(5):573-580
谢卫红,钟卫平,卢爱红,等.岩石分形节理的强度和变形特性研究[J].西安科技学院学报,2004,24(1):31-33
谢和平,Pariseau W G.岩石节理粗糙系数(JRC)的分形估计[J].中国科学(B辑),1994,24(5):524-530
谢和平,陈忠辉。岩石力学。科学出版社,2004,北京
夏才初,孙宗颀.工程岩体节理力学[M].上海:同济大学出版社,2002
夏才初,孙宗顽,潘长良.节理接触机理与闭合性质研究[J].同济大学学报,1995,23(2):147-152
夏才初,孙宗顽,潘长良.表面形貌含波纹度的节理的闭合模型[J].工程地质学报,1994,2(2):38-47
肖涛,左正兴.虚拟裂纹闭合法在结构断裂分析中的应用[J].计算力学学报,2008,25(增):16-19
许宏发,金丰年.岩体节理剪切变形的幂函数模型[J].岩石力学与工程学报,2000,19(3):314-317
杨圣奇,苏承东,徐卫亚.大理岩常规三轴压缩下强度和变形特性的试验研究.岩土力学,2005,26(3):475-478
杨天鸿,唐春安,梁正召,等.脆性岩石破裂过程损伤与渗流耦合数值模型研究.力学学报,2003,35(5):533-541
杨庆,李强,赵维等.翼型裂纹扩展特性的试验和数值分析[J].水利学报,2009,40(8):934-940
杨强,陈新,周维垣.基于二阶损伤张量的节理岩体各向异性屈服准则[J].岩石力学与工程学报,2005,24(8):1275-1282
殷有泉.考虑损伤的节理本构模型[J].工程地质学报,1994,2(4):1-6
袁凡凡,詹云刚,栾茂田.弹塑性无厚度接触面单元的本构积分算法及验证[J].岩土力学,2008,29(3):734-740
叶志才,徐磊,王超.基于ABAQUS的三维锚杆单元开发[J].三峡大学学报(自然科学版),2008,30(5):29-32
俞缙,赵晓豹,赵维炳,等.改进的岩石节理弹性非线性法向变形本构模型研究[J].岩土工程学报,2008,30(9):1316-1321
张强勇,向文,朱维申.节理岩体能量损伤本构模型与工程应用[J].工程地质学报,1999,7(4):310-314
张盛,张洪武,毕金英等.多维非经典热传导问题的时间-空间多尺度高阶均匀化分析[J].复合材料学报,2009,26(1):123-133
张均锋,祁涛,李正国.岩石材料的三维各向异性损伤破坏模型与数值模拟[J].岩土力学,2006,27(增):27-30
张平,李宁,贺若兰.含裂隙类岩石材料的局部化渐进破损模型研究[J].岩石力学与工程学报,2006,25(10):2043-2050
张欣,丁秀丽,李术才.ABAQUS有限元分析软件中Duncan-Chang模型的二次开发[J].长江科学院院报,2005,22(4):45-51
周太全,华渊,吕宝华.金华山软岩铁路隧道施工过程围岩屈服接近度分析[J].工程地质学报,2008,16(4):0546-550
周建军,周辉,邵建富.脆性岩石各向异性损伤和渗流耦合细观模型[J].岩石力学与工程学报,2007,26(2):368-373
周建民,许宏发,杨红禹.岩体节理法向变形的数学模型分析[J].岩石力学与工程学报,2000,19(增),853-855
周维垣,杨延毅.节理岩体的损伤断裂模型及验证.岩石力学与工程学报,1991,10(1):43-54
赵德安.节理型岩体损伤弹性的损伤力学算法[J].兰州铁道学院(自然科学版),2001,20(3):1-3
赵坚.岩石节理剪切强度的JRC-JMC新模型[J].岩石力学与工程学报,1998,17(4):349-357
朱维申,陈卫忠,申晋.雁形裂纹扩展的模型试验及断裂力学机制研究[J].固体力学学报,1998,19(4):355-360
朱以文,徐晗,蔡元奇等.边坡稳定的剪切带计算[J].计算力学学报,2007,24(4):441-446
朱万成,唐春安,杨天鸿,等.岩石破裂过程分析(RFPA)系统的细观单元本构关系及验证.岩石力学与工程学报,2003,22(1):24-29
詹云刚,袁凡凡,栾茂田.纯摩擦型岩土介质本构积分算法及其在ABAQUS中开发应用[J].岩土力学,2007,28(12):2619-2628
Allaire G. Mathematical approaches and methods, in: U. Hornung (Ed.), Homogenization and Porous Media[M], Springer, New York, 1996, pp. 225-250.
Alsaleh M I. Numerical modeling of strain localization in granular Materials using cosserat theory enhanced with Microfabric properties[D]. 2007,Louisiana State University, doctor thesis Amadei B, Saeb S. Constitutive models of rock joints [C]. Proc. Int. Con. Rock. Joints, Leon,Norway, 581 -594,1990
Amadei B, Wibowo J, Sture S, Price R H. Applicability of existing models to predict the behavior of replicas of natural fractures of welded tuff under different boundary conditions[J]. Geotechnical and Geological Engineering, 1998, 16, 79-128
Amaziane B, Pankratov L, Piatnitski A. Homogenization of a single phase flow through a porous medium in a thin layer[J]. Mathematical Models and Methods in Applied Sciences, 2007,17( 9):1317-1349
Andrade P S, Saraiva A A. Estimating the joint roughness coefficient of discontinuities found in metamorphic rocks[J]. Bulletin Of Engineering Geology And The Environment, 2008, 67(3): 425-434
Aydan O, Shimizu Y, Kawamoto T. The Anisotropy of Surface Morphology Characteristics of Rock Discontinuities[J]. Rock Mechanics and. Rock Engineering, 1996, 29 (1):47-59
Asada T, Ohno N. Fully implicit formulation of elastoplastic homogenization problem for two-scale analysis[J]. International Journal of Solids and Structures,2007, 44: 7261-7275
Asada T, Tanaka Y, Ohno N. Two-scale and full-scale analyses of elastoplastic honeycomb blocks subjected to flat-punch indentation[J]. International Journal of Solids and Structures, 2009, 46(7-8):1755-1763
Bandis S C, Lumden A C, Barton N R. Fundamentals of rock joint deformation[J]. International Journal of Rock Mechanical and Mining Sciences & Geomechanical Abstracts. 1983,22:121
Bao G, Hutchinson J W, Mcmeeking R M. Particle reinforcement of ductile matrices against plastic flow and creep[J]. Acta metallurgica et materialia, 1991,39(8): 1871 -1882
Barbero M, Barla G, Zaninetti A. Dynamic Shear Strength of Rock Joints Subjected to Impulse Loading[J]. International Journal of Rock Mechanical and Mining Science & Geomechanical Abstracts,1996,33(2): 141-151
Barton N R. Estimation of in situ shear strength from back analysis of failed rock slopes[C]. In:Proceedings of international symposium on rock mechanics, Nancy, france, 1971(1):2-27
Barton N, Bandis S. Effects of block size on the shear behavior of jointed rock[C]. 23~(rd) U. S symp. on rock mechanics, Berkley,CA, 739-760,1982
Barton N, Bandis S, Bakhtar K. Strength deformation and conductivity coupling of rock joints[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstract, 1985,22(3):121-140
Barton N. Review of a new shear strength criterion for rock joints[J]. Engineering Geology, 1973; 7:287-332.
Barton N, choubey V. The shear strength of rock joints in theory and practice[J]. Rock Mechanics and Rock Engineering, 1977,10:1 -54
Ba(?)ant Z P. Size effect[J]. Inernational Journal of Solids and Structures, 2000,37:69-80
Ba(?)ant Z P, Pijaudier-Cabot G. Measurement of characteristic length of nonlocal continuum. Journal of Engineering Mechanics, 1989,115(4):755-767
Bazant Z P Cedolin L. Finite element modeling of crack band propagation[J] .Journal of structural engineering, ASCE, 1983a,109(1):6-2
Bazant Z P Oh B H. Crack band theory for fracture of concrete[J].Material and structures, 1983b,16(93):155-177
Belem T, Homand E F,souley M. Fractal analysis of shear joint roughness[J]. International Journal of Rock Mechanics and Mining sciences, 1997, 34(3-4) ,paper No,130
Benssousan A, Lions J L, Papanicoulau G. Asymptotic analysis for periodic structure [M].North Holland,Amsterdam, 1978
Bendsor M P, Kikuchi N. Generating optimal topologies in structural design using a homogeniza-tion method[J]. Computer Methods in Applied Mechanics and Engineering, 1988, (71): 197—224.
Benhamida A, Djeran-Maigre I, Dumontet H, et al. Clay compaction modelling by homogenization theory[J]. International Journal Of Rock Mechanics And Mining Sciences, 2005, 42 (7-8) :996-1005
Bro A. Failure of stepped joints: an analysis and comparison with a measured failure geometry[J].International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1992,29(2): 179-186.
Brown S R, Scholz C H. Closure of random elastic surface in contact[J]. Journal of geophysics research,1985,90:5531-5545
Brown S R, Scholz C H. Closure of rock joints. Journal of geophysics research[J], 1986, 91,4939-Myers N O. Characterization of surface roughness[J]. Wear, 1962, 5: 182-189
Budiansky B, O Connel R J. Elastic moduli of cracked solid. International journal of solids and structures[J], 1976,12(2):81-97.
Budiansky B. On the elastic moduli of heterogeneous materials[J]. Journal of Mechanics and Physics of Solids, 1965, 13(4):223-227
Cai M, Horn H. A constitutive model and FEM analysis of jointed masses[J]. International Journal of Rock and Mining Sciences & Geomechanical Abstracts,1993,30(4):351-359
Caballero A, Willam K J,Carol I. consistent tangent formulation for 3D interface modeling of cracking fracture in quasi-brittle materials. Computer Methods in Applied Mechanics and Engineering, 2008,197:2804-2822
Chang C S, Chang Y, Kabir G. Micromechanics modeling for stress strain behavior of granular soils. Part l:theory[J]. Journal of Geotechnical Engineering, 1992b, 118(12):1959-1974
Chang C S, Kabir M, Chang Y. Micromechanics modeling for the stress-strain behavior of granular soil-II: Evaluation[J]. Journal of Geotechnical Engineering, 1992a, 118(12):1975-1994
Christensen R M, Lo K H. Solution for effective shear properties in three phase sphere and cylinder[J] models. Journal of the Mechanics and Physics Of Solids, 1979,27(4):315-330
Coelho P G, Fernandes P R, Guedes J M, Rodrigues H C. A hierarchical model for concurrent material and topology optimisation of three-dimensional structures[J], Struct Multidisc Optim,2008,35:107-115
Cording E, Jamil M. Slide geometries on rock slopes and walls[C]. In: Fourth South American congress on rock mechanics, Santiago, vol 3,1997. p. 199-221.
Davison, L. and Stevens, A. L. Thermomechanical constitution of spalling elastic bodies[J]. Journal of Applied Physics, 1993, 44, 667-674.
Desai C S, Zaman M M, Lightner J G,et al. Thin-layer element for interface and joints[J]. International Journal of Numerical Methods in Geomechanics, 1984,8:19-43
Dragon, A, Mroz, Z., A continuum model for plastic-brittle behavior of rock and concrete[J].International Journal of Engineering Science, 1979, 17, 121-137.
Drugan W J, Willis J R. A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites[J]. Journal of the Mechanics and Physics of Solids,1996,44(4):497-524
Dong J J, Pan Y W. A hierarchical model of rough rock joints based on micromechanics[J].International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1996,33(2): 111-123.
Douglous K J. The shear strength of rock masses[D]. Ph.D.thesis .the university of new wouth wales,sydeny,Australia.2002
Ehlen J. Fractal analysis of joint patterns in granite[J]. International Journal of Rock Mechanics and Mining Sciences, 2000, 37: 909-922
Fang Z, Harrison JP. Development of a local degradation approach to the modeling of brittle fracture in heterogeneous rocks[J]. International Journal of Rock Mechanics and Mining Sciences,2002,39:443-457
Fanella D, krajcinovic D. A micromechanical damage model for concrete in compressive[J].Engineering Fracture Mechanics,1988,29(1):49-66
Fardin N, Stephansson O, Jing L. The scale dependence of rock joint surface roughness[J]. International Journal of Rock Mechanics & Mining Sciences, 2001, 38: 659-669
Fardin N, Feng O, Stephansson O. Application of a new in situ 3D laser scanner to study the scale effect on the rock joint surface roughness[J]. International Journal of Rock Mechanics & Mining Sciences,2004,41:329-335
Forest S, Pradel F, Sab K . Asymptotic analysis of heterogeneous Cosserat media[J]. International Journal of Solids and Structures,2001,38 (26-27) :4585-4608
Fish J, Shek K, Pandheeradi M, Shephard M S. Computational plasticity for composite structures based on mathematical homogenization: Theory and practice[J]. Computer Methods in Applied Mechanics and Engineering,1997,148:53-73
Fish J, Shek K. Finite deformation plasticity for composite structures.'Computational models and adaptive strategies[J]. Computer Methods in Applied Mechanics and Engineering, 1999B, 172:145-174
Fish J, Yu Q, Shek K. Computational damage mechanics for composite materials based on mathematical homogenization[J]. International Journal for Numerical Methods in Engineering, 1999A,45:1657-1679
Fish J, Yu Q. Multiscale damage modeling for composite materials: theory and computational framework. International Journal for Numerical Methods in Engineering 2001; 52(1—2): 161—192.
Fish J, Fan R. Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading. International journal for numerical methods in engineering 2008,76:1044-1064
Fox D J, Kana D D, Hsiung S M. Influence of interface roughness on dynamic shear behavior in joint rock[J]. International Journal of Rock Mechanics and Mining Sciences, 1998,35(7):923-940
Gehle C, Kutter H K. Breakage and shear behavior of intermittent rock joints[J]. International Journal of Rock Mechanics & Mining Sciences,2003, 40: 687-700
Gentier S, Riss J, Archambault G, Flamand R, Hopkins D. Influence of fracture geometry on shear behavior[J]. International Journal of Rock Mechanics and Mining Sciences,2000, 37:161-174
Gerrard C. Shear failure of rock joints: appropriate constraints for empirical relations[J]. International Journal of Rock Mechanical and Mining Science & Geomechanical Abstracts, 1986;23:421-429.
Ghaboussi J, Wilson E L, Isenberg J. Finite element for rock joints and interfaces[J]ASCE journal of the soil mechanics and foundations division, 99(1973):833-848
Ghoniem N M, Busso E P, Kioussis N, Huang H C. Multiscale modeling of nanomechanics and micromechanics: an overview[J]. Philosophical Magazine, 2003,83(31-34) :3475-3528
Ghosh S, Lee K, Moorthy S. Multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method[J]. International Journal of Solids and Structures, 1995, 32(1):27-62
Ghosh S, Li M S, Moorthy S, Lee K. Microstructural characterization, meso-scale modeling and multiple-scale analysis of discretely reinforced materials[J]. Materials Science and Engineering, 1998,A249: 62-70
Ghosh S, Bai J, Raghavan P. Concurrent multi-level model for damage evolution in micro structurally debonding composites[J], Mechanics of Materials, 2007, 39: 241-266
Ghosh A, Hsiung S M, Chowdhury A H. Seismic response of rock joints and jointed mass. 1995,NUREG/CR-6388, 2-35
Giraud A, Huynh Q V, Hoxha D, Kondo D. Effective poroelastic properties of transversely isotropic rock-like composites with arbitrarily oriented ellipsoidal inclusions[J]. Mechanics of Materials, 2007,39:1006-1024
Gitman I.M, Askes H, Sluys L.J. Coupled-volume multi-scale modeling of quasi-brittle material[J]. European Journal of Mechanics A/Solids,2008, 27: 302-327
Goodman R E, Taylor R L, Brekke T L. A model for the mechanics of jointed rock[J]. ASCE Journal of Soil Mechanics and Foundations division, 1968, 94; 637-659.
Goodman R E. Methods of geological engineering in discontinuous rocks. San Francisco: west publishing company, 1976
Grasselli G, Wirth J, Egger P. Quantitative three-dimensional description of a rough surface and parameter evolution with shearing[J]. International Journal of Rock Mechanics and Mining Sciences,2002,39 (6) : 789-800
Grasselli G, Egger P. Constitutive law for the shear strength of rock joints based on three-dimensional surface parameters[J]. International Journal of Rock Mechanics & Mining Sciences,2003,40: 25-40
Grasselli G. Shear strength of rock joints based on quantified surface description[J]. Rock mechanics and rock engineering, 2006,39(4): 295-314
Graham S, Yang N. Representative volumes of materials based on microstructural Statistics[J]. Scripta Materialia, 2003, 48:269-274
Greenwood J A, Williamson J B P. Contact of nominally flat surface[C]. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1966,295(1442):300-319
Greenwood J A, Tripp J H. The contact of two nominally flat rough surfaces[C]. Proc. Inst. mech.eng.1971,185:625-633
Guedes JM, Kikuchi N. Preprocessing and post-processing for materials based on the homogenization method with adaptive finite element methods[J]. Computer Methods in Applied Mechanics and Engineering, 1990, 83:143-198
Halm, D, Dragon, A. A model of anisotropic damage by mecrocrack growth; unilateral effect[J].International journal of Damage Mechanics, 1996, 5,384-402.
Harberfield C M, seidel J P. Some advances in the modeling of soft joints in direct shear[J].Geotechnical and Geological Engineering, 1999, 17:177-195
Herrmann L R. Finite element analysis of contact problems[J]. Journal of Engineering Mechanics (ASCE), 1978, 104:1043-1059.
Hills R. A self-consistent mechanics of composite materials[J]. Journal of Mechanics and Physics of Solids, 1965,13(4):213-222
Hills R. Elastic properties of reinforced solids: some theoretical principles[J]. Journal of Mechanics And Physics of Solids, 1963, 11,357-372
Hillerborg, A.,M.Modeer, P.E. Petersson. Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements, Cement and Concrete Research, 1976, (6):773-782
Homand F, Belem T, Souley M. Friction and degradation of rock joint surfaces under shear loads[J].International Journal for Numerical and Analytical Methods in Geomechanic,2001,25:973-999.
Hopkins D L. The implications of joint deformation in analyzing the properties and behavior of International Journal of Rock Mechanics and Mining Sciences,2000, 37:175-202
Horii H, Nemat-Nasser S. Overall moduli of solids with microcracks: load-induced anisotropy[J].Journal of Mechanics and Physics of Solids, 1983,31(2):155-171
Huang, S. L., Oelfke, S. M., Speck, R. C. Applicability of fractal characterization and modeling to rock joint profiles[J]. Internationa] Journal of Rock Mechanical and Mining Science & Geomechanical Abstracts, 1992, 29(2):89-98.
Huang T H, Chang C S, Yang Z Y. Elastic moduli for fracture rock mass[J]. Rock Mechanical and Rock Engineering, 1995,28(3): 135-144
Huang T H, Chang C S,Cchao C Y. Experimental and mathematical modeling for fracture of rock joint with regular asperity[J]. Engineering Fracture Mechanics, 2002, 69: 1977-1996
Huang T H, Chang C S, Yang Z Y. Elastic Moduli for Fractured Rock Mass[J]. Rock Mechanics and .Rock Engineering, 1995, 28 (3): 135-144
Huang x, Haimson B C, Plesha M E, Qiu X.. An investigation of the mechanics of rock joints part 1:laboratory investigation[J]. International Journal of Rock Mechanical and Mining Science &Geomechanical Abstracts,1993,30(3):257-269
Huston R W, Dowding C H. Joint asperity degradation during cyclic shear[J]. International Journal of Rock Mechanical and Mining Science & Geomechanical Abstracts, 1990,27(2): 109-119
Ichikawa Y, Kawamura K, Uesugi K, Seo Yong-seok, Fujii N. Micro and macrobehavior of granite rock:observation and viscoelastic homogenization analysis[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 191:47-72
Indraratna B, haque A, Aziz N. Laboratory modeling of shear behavior of soft joints under constant normal stiffness conditions[J]. Geotechnical and Geological Engineering, 1998, 16:17-44
Jaeger J C. Friction of rocks and stability of rock slopes[J]. Geotechnique, 1971,21(2): 97-134
Jafari M K, hosseini K A, Pellet F, et al. Evaluation of shear strength of rock joints subjected to cyclic loading[J]. Soil Dynamics and Earthquake Engineering,2003,23:619-630
Jafari M K, Pellet F, Boulon M, Hosseini K A. .Experimental Study of Mechanical Behaviour of Rock Joints Under Cyclic Loading[J]. Rock Mechanics and Rock Engineering,2004,37 (1):3—23
Jager J. A new principle in contact mechanics[J]. Journal of Tribology,1998, 120:677-684
Jakobsen K. P, Lade P. V. Implementation algorithm for a single hardening constitutive model for frictional materials[J]. International Journal For Numerical And Analytical Methods In Geomechanics,2002,26 (26) :661-681
Jennings JE. A mathematical theory for the calculation of the stability of open cast mines[C]. In:Proceedings of the symposium on theoretical background to the planning of open pit mines.Johannesburg, 1970, p. 87-102.
Jiang Y J, Li B, Tanabashi Y. Estimating the relation between surface roughness and mechanical properties of rock joints[J]. International Journal of Rock Mechanics & Mining Sciences, 2006, 43:837-846
Jing L, Nordlund E, Stephansson O. An experimental study on the anisotropy and stress dependency of the strength and deformability of rock joints[J]. International Journal of Rock Mechanics and
Mining Sciences& Geomechanics Abstracts, 1992,29:535-542
Jing L, stephansson O, nordlund E. Study of rocks under cyclic loading conditions[J]. Rock Mechanics and Rock Engineering, 1993, 26(3): 215-232
Ju, J. W. On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects[J]. International Journal of Solids and Structure, 1989, 25,803-833
Kachanov M L. A micromechanical model of rock inelasticity part 1:frictional sliding on microcracks[J].Mechanics of materials, 1982,1 (1): 19-27
Kachanov M L.A micromechanical model of rock inelasticity part 2:propagation of microcracks[J].Mechanics of materials, 1982,1 (1 ):29-41
Kana D D, Fox D J, Hsiung S M. Interlock /friction model for dynamic shear response in natural jointed rock[J]. International Journal of Rock Mechanics and Mining Sciences, 1996,33(4): 371-386
Kaneko K, Terada K, Kyoya T, Kishino Y. Global-local analysis of granular media in quasi-static equilibrium[J]. International Journal of Solids and Structures, 2003, 40: 4043-4069
Kawamoto, T., Ichikawa, Y. and Kyoya, T. Deformation and fracturing behavior of discontinuous rock mass and damage mechanics theory[J]. International Journal for Numerical and Analytical Methods in.Geomechanics, 1988, 12:1-30.
Kanit T, Forest S, Galliet I, Mounoury V, Jeulin D. Determination of the size of the representative volume element for random composites: statistical and numerical approach[J]. International Journal of Solids and Structures,2003,40:3647-3679
Kemeny J. the time-dependent reduction of sliding cohesion due to rock bridges along discontinuities: a fracture mechanics approach[J]. Rock mechanics and rock engineering, 2003,36(1):27-38
Klein E, Reuschle T. A pore crack model for the mechanical behavior of porous granular Rocks in the brittle deformation regime[J]. International Journal of Rock Mechanics & Mining Sciences ,2004, 41:975-986
Kouznetsova V G. Computational homogenization for the multi-scale analysis of multi-phase materials[D]. PhD thesis, Technical University Eindhoven, 2002.
Kulatilake P H S W, Shou g, Huang T H. Spectral based peak shear strength criterion for rock joints[J].Journal of geotechnical engineering, 1995, 121(11): 789-796
Kulatilake P H S W,Balasingam P,Park J, Morgan R. Natural rock joint rough quantification through fractal techniques[J]. Geotechnical and Geological Engineering, 2006, 24: 1181-1202
Kusumi H, Teraoka K, Nishida K. Study on new formulation of shear strength for irregular rock joints[J]. International Journal of Rock Mechanics & Mining Sciences, 1997, 34(3-4)
Kuhl E,Ramn E, Willam K. Failure analysis of elasto-plastic material models on different levels of observation[J]. international journal of solids and structures, 2000,37:7259-7280
Kyoya T, terada K, kawamoto T. Multi-scale limit load analysis for Discontinuous rock mass based on the Homogenization method[J].International journal for Numerical and Analytical Methods in Geomechanics, 1999, 23: 995-1019
Ladanyi B, Archambault G. Simulation of shear behavior of a jointed rock mass[C]. Proc.11th Symp. Rock. Mech, AIME, New York, 105-125,1970
Lajai E Z.Shear strength of weakness planes in rock[J]. International Journal of Rock Mechanics and Mining Sciences, 1969,6(7):499—515
Lacy T E, McDowell D L, Talreja R. Gradient concept for evolution of Damage[J]. Mechanics of Materials, 1999, 31:831-860
Lee J S, G. N. Pande G N. A new joint element for the analysis of media having discrete discontinuities [J]. Mechanics of Cohesive-Frictional Materials, 1999,4:487-504
Lee, Y. H., Cart, J. R., Barr, D. J., Haas, C. J. The fractal dimension as a measure of the roughness of rock discontinuity profiles[J]. International Journal of Rock Mechanical and Mining Science &Geomechanical Abstracts, 1990, 27 (6):453 464.
Lee X, Ju J W. Micromechanical damage models for brittle solids 2:compressive loadings[J]. Journal of Engineering Mechanics, 1991,117(7): 1515-1536
Lee K, Ghosh S. Small deformation multi-scale analysis of heterogeneous materials with the Voronoi cell finite element model and homogenization theory[J]. Computational Materials Science, 1996, 7:131-146
Lee K, Ghosh S. A microstructure based numerical method for constitutive modeling of composite and porous materials[J]. Materials Science and Engineering, 1999, A272:120-133
Lee H S, Park Y J, Choc T F, You K H. Influence of asperity degradation on the mechanical behavior of rough rock joints under cyclic shear loading[J]. International Journal of Rock Mechanics & Mining Sciences, 2001,38:967-980
Lee S D, Moon H K. HM modeling of tunnel excavation in fractured rock masses by a 3D discete fracture network approach[C]. International Journal of rock mechanics and mining sciences, 2001. 41,sinorock 2004 symposium
Lee S D, Lee C I, Park Y. Characterization of joint profiles and their roughness parameters[J].Internationa] Journal of Rock Mechanics and Mining Sciences, 1997, 34(3-4), paper No, 174
Lei X Y, Swoboda G, Zenz G. Application of contact friction interface element to tunnel excavation in faulted rock[J]. Computers and Geotechnics, 1995,17:349-370.
Lemaitre J. A course on damage mechanics[M]. 2nd ed. Berlin: Springer; 1992.
Lemaitre J. Continuum Damage Mechanics Theory and Applications[M]. Springer,Wien-New York,1987.
Lewandowska J, Laurent J P. Humidity Transfer in Unsaturated Heterogeneous Porous Media by Homogenization[J].Physics and Chemistry of The Earth Part A,2000,25, No. 2, pp. 175-181
Lewandowska J, Szymkiewicz A, Kazimierz Burzynski, Michel Vauclin. Modeling of unsaturated water flow in double-porosity soils by the homogenization approach[J]. Advances in Water Resources,2004, 27: 283-296
Li Aiqin, Li Renge, Fish J. Generalized Mathematical Homogenization: From theory to practice[J].Computer Methods in Applied Mechanics and Engineering, 2008,197: 3225-3248
Lopez P, Riss J, Archambault G. An experimental method to link morphological properties of rock fracture surfaces to their mechanical properties[J]. International Journal of Rock Mechanics & Mining Sciences, 2003, 40: 947-954
Lubarda V A, Krajcinovic D. Some fundamental issues in rate theory of damage-elastoplasticity[J].International Journal of Plasticity, 1995,11(7):763-797
Maksimovic M. The Shear Strength Components of a Rough Rock Joint[J]. International Journal of Rock Mechanical and Mining Science & Geomechanical Abstracts, 1996, 33(8): 769-783
Malama B,Kulatilake P H S W. Models for normal fracture deformation under compressive loading[J].International Journal of Rock Mechanics and Mining Sciences,2003,40(6):893-901.
Marmier R, Jeannin I, Barthe' le' my J F. Homogenized constitutive laws for rocks with elastoplastic fractures[J]. International Journal for Numerical and Analytical Methods in Geomechanics 2007;31:1217-1237
Mandelbrot B. B. Self-affine fractals and fractal dimensions[J]. Physica Scripta, 1985, 32:257-260.
Markovic, D, Ibrahimbegovic, A. On micro-macro interface conditions for micro scale based FEM for inelastic behavior of heterogeneous materials[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193:5503-5523.
Massart, T.J. Multi-scale modeling of damage in masonry structures[D]. PhD thesis, Technical University Eindhoven. 2003,Available from http://www.mate.tue.nl
Matsuki K, Wang E Q, Sakaguchi K, Okumura K. Time-dependent closure of a fracture with rough surfaces under constant normal stress[J]. International Journal of Rock Mechanics & Mining Sciences,2001,38:607-619
Matsui K, Terada K, Yuge K. Two-scale finite element analysis of heterogeneous solids with periodic microstructures[J]. Computers and Structures, 2004, 82:593-606
Mindlin RD. Compliance of elastic bodies in contact[J]. Journal of Applied Physics, 1949, 16:259-268
Mindlin RD and Deresiewicz H (1953) ASME J. Appl. Mech., 20:327-344
Misra A. Mechanistic model for contact between rough surfaces[J]. Journal of Engineering Mechanics,1997,123(5):475-484
Misra A. Effect of asperity damage on shear behavior of single fracture[J]. Engineering Fracture Mechanics, 2002,69:1997-2014
Mroz Z. An interface model for analysis of deformation behavior of discontinuities[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1996, 20:1-33
Moorthy S, Ghosh S. A Voronoi cell finite element model for particle plastic composite materials cracking in elastic-plastic composite materials[J]. Computer Methods in Applied Mechanics and ngineering, 1998,151:377-400
Moorthy S ,Ghosh S. Adaptivity and convergence in the Voronoi cell finite element model for analyzing heterogeneous materials[J]. Computer Methods in Applied Mechanics and Engineering,2000,185:37-74
Mori T, Tanaka K. Average stress in matrix and average energy of materials with misfitting inclusions[J]. Acta Metallurgica et Materialia, 1973,21: 571-574
Mughieda O, abdel kareem alzo'ubi. Fracture mechanisms of offset rock joints-A laboratory investigation[J]. Geotechnical and Geological engineering, 2004, 22: 545-562
Mughieda O, Maher T. Omar. Stress Analysis for Rock Mass Failure with Offset Joints[J]. Geotechnical and Geological Engineering, 2008, 26:543-552
Murakami S, Kamika K. constitutive and damage evolution equations of elastic brittle materials based on irreversible thermodynamics[J]. International Journal of Mechanics Sciences, 1997,39:473-486
Murakami, S. Ohno, N. A continuum theory of creep and creep damage[C].Proceedings of 3rd IUTAM Symp. on Creep in Structures, ed. A. R. S. Ponter and D. R. Hayhust. Springer±Verlag, Berlin, 1980,422-443.
Murad M A, Moyne C. A three-scale computational model of reactive pollutant transport in smectitic clays[J]. Communications in Numerical Methods in Engineering, 2006, 22:875-891
Nemat-Nasser S, Obata M. A microcrack model of dilatancy in brittle materials[J]. Journal of Applied Mechanics,1986,55:24-35
Nemat-Nasser S, Yu N, Hori M. Solids with periodically distributed cracks[J]. International journal of solids and structures, 2009, 30(15):2071-2095
Ng K. L. A, Small J. C. Behavior of Joints and Interfaces Subjected to Water Pressure[J]. Computers and Geotechnics, 1997,20(1): 71-93
Odling N E. natural fracture profiles fractal dimension and joint roughness coefficients[J]. Rock Mechanics and Rock Engineering, 1994, 27(3): 135-153
O van der Sluis, Vosbeek P H J, Schreurs P J G, Meijer H E. Homogenization of heterogeneous polymers[J]. International Journal of Solids and Structures 1999,36:3193-3214
Oskay C, Fish J. Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials[J]. Computer Methods in Applied Mechanics and Engineering,2007, 196:1216-1243
Pande GN, Sharma KG. On joint /interface elements and associated problems of numerical ill-conditioning[J]. International Journal for Numerical and Analytical for Geomechanics, 1979,2:293-300
Park C H, Bobet A. Crack coalescence in specimens with open and closed flaws: A comparison[J].International Journal of Rock Mechanics & Mining Sciences2009, 46: 819-829
Patton F D. Multiple model of shear failure inrock[C]. Proceedings of the First Congress of ISRM,Lisbon, 509-513,1966
Pensee V, Kondo D, Dormieux L. Micromechanical Analysis of Anisotropic Damage in Brittle Materials[J]. Journal of Engineering Mechanics, 2002,128(8): 889-897
Pereira J P, de fireitas M H. Mechanism of shear failure in artificial fractures of sandstoneand their implication for models of hydromechanical coupling[J]. Rock Mechanical and Rock Engineering,1993,26(3): 195-214
Plesha M E, Ballarini R, Parulekar A. Constitutive model and finite element procedure for dilatant contact problems[J].Journal of Engineering Mechanics, 1989,115(12): 2649- 2668
Plesha M E. Constitutive models for rock discontinuities with dilatancy and surface degradation[J]. International Journal of Numerical and Analytical Methods in Geomechanics, 1987,11:345-362
Plesha M E, Haimson B C. An advanced model for rock joint behavior: analytical, experimental and implementational consideration[C].proc 29~(th) u s. symp on key question in rock mechanics,pp119-126,1988
Prudencio M, Van Sint Jan M. Strength and failure modes of rock mass models with non-persistent joints[J]. International Journal of Rock Mechanics & Mining Sciences, 2007, 44 :890-902
Puntel E, Bolzon G, Saouma V E. Fracture Mechanics Based Model for Joints under Cyclic Loading[J]. Journal of Engineering Mechanics, 2006,132(11): 1151-1159
Pyrak-Nolte L J, Morris J P. Single fracture under normal stress: the relation between fracture specific stiffness and fluid flow[J]. International journal of rock mechanics and mining sciences, 2000,37:245-262
Qiu X J, Plesha M E, Huang X, Haimson B C. An investigation of the mechanics of rock joints. Part II. Analytical investigation[J]. International Journal of Rock Mechanical and Mining Sciences &Geomechanics Abstracts, 1993, 30:271-287
Raghavan P, Ghosh S. Concurrent multiscale analysis of elastic composites by a multilevel computational model[J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193 (6-8 ):497-538
Ren Z Y, Zheng Q S. A quantitative study of minimum size of representativevolume elements of cubic polycrystals_numerical experiments[J]. International Journal of Physics of Solids, 2002,50:881-893
Ren Z Y, Zheng Q S. Effects of grain sizes, shapes, and distribution on minimum sizes of representative volume elements of cubic polycrystals[J]. Mechanicsof Materials, 2004,36:1217-1229
Riss J, Gentier S, Archambault C, Flamand R. Sheared rock joints dependence of damage Zones on morphological anisotropy[J]. International Journal of Rock Mechanics & Mining Sciences, 1997,34( 3-4)
Robina, Wong H C, Chau K T. Crack Coalescence in a Rock-like Material Containing Two Cracks[J].International Journal of Rock Mechanics and Mining Sciences, 1998, 35(2): 147-164
Roosta R M,Sadaghiani A H,Pak A, Saleh Y. Rock joint modeling using a visco-plastic multilaminate model at constant normal load condition[J]. Geotechnical and geological engineering, 2006, 24:1449-1468
Rooke,D, Cartwright D. Compendium of stress intensity factors. H M S O, London,330PP,1976
Sab K. On the homogenization and simulation of random materials[J]. European Journal of Mechanics-A/Solids II 5,585-607
Saeb S, Amadei B. Modeling rock joints under shear and normal loading[J]. International Journal of Rock Mechanical and Mining Science & Geomechanica! Abstracts, 1992,29(3):267-278
Sagong M, Bobet A. Coalescence of multiple flaws in a rock-model material in uniaxial compression[J].International Journal of Rock Mechanics & Mining Sciences,2002,39: 229-241
Saikia 1, Terada K, Ikeda K, Hori M. Appropriate number of unit cells in a representative volume element for micro-structural bifurcation encountered in a multi-scale modeling[J]. Computer Methods in Applied Mechanics and Engineering, 2002, 191:2561-2585
Sakaguchi K, Tomono J, Okumura K, Ogawa Y, Matsuki K. Asperity Height and Aperture of an Artificial Tensile Fracture of Metric Size[J]. Rock Mechanics and Rock Engineering, 2008, 41 (2):325-341
Salari M R, Saeb S, Willam K J, Patchet S J, Carrasco R C.A coupled elastoplastic damage model for geomaterials[J]. Computer Methods in Applied Mechanics and Engineering,2004,193:2625-2643
Sanchez-Paiencia E. Non-homogeneous media and vibration theory[M]. Lecture notes in physics, 127,Springer-Verlag,Berlin, 1980
Seidel J P, Haberfield C M. A theoretical model for rock joints subjected to constant normal stiffness direct shear[J]. International Journal of Rock Mechanics and Mining Sciences, 2002, 39:539-553
Seidel J P, Haberfield C M. Toward an understand of joint roughness[J]. Rock Mechanics and Rock Engineering, 1995, 28(2): 69-92
Selvadurai A.P.S, Yu Q. Mechanics of a discontinuity in a geomaterial, Computers and Geotechnics,2005,32:92-106
Sevostianov I, Kachanov M. Contact of rough surfaces: A simple model for elasticity conductivity and cross-property connections[J]. Journal of the Mechanics and Physics of Solids,2008, 56: 1380-1400
Shah K R, wong T F. Fracture at contact surfaces subjected to normal and tangential loads[J].International Journal of Rock Mechanics and Mining Sciences, 1997, 34(5):727-739
Shan Z, Gokhale A M. Representative volume element for non-uniform microstructure[J].Computational Materials Science,2002,24:361-379
Souley M, Homand F, Amadei B. An extension to the saeb and amadei constitutive model for rock joints to include cyclic loading paths[J]. International Journal of Rock Mechanical and Mining Science& Geomechanical Astracts, 1995,32(2):101-109
Son B K, Lee Y K, Lee C I. Elasto-plastic simulation of a direct shear test on rough rock joints[J].International Journal of Rock Mechanics & Mining Sciences,2004,41(3),Paper 2A 07
Suquet P M. Element of homogenization theory for inelastic solid mechanics. In:Sanchez-Palencia E,Zaoui A(Eds). Homogenization technique for composite media[M]. Springer-Verlag, Berlin, Heidelberg,New York,pp,194-275
Sumarac D, Krajcinovic D. A self-consistent model for microcrack-weakened solids[J]. Mechanics of materials, 1987,6,39-52
Swan G. Determination of stiffness and other joint properties from roughness measurements[J]. Rockmechanics and rock engineering, 1983,16:19-38
Swan G, Zongqi S. Prediction of shear behavior of joints using profiles[J]. Rock Mechanics and Rock Engineering, 1985, 18: 183-212
Swoboda G, Shen X P, Rosas L. Damage Model for Jointed Rock Mass and Its Application to TunneIing[J]. Computers and Geotechnics, 1998,22(3/4): 183-203
Terada K, Miura T, Kikuchi N. Digital image-based modeling applied to the homogenization analysis of composite materials[J].Computational Mechanics, 1997,20: 331-346
Terada K,Ito T, Kikuchi N. characterization of the mechanical behavior of solid-fluid mixture by the homogenization method[J]. Computer Methods In Applied Mechanics And Engineering, 1998, 153(3-4) :223-257
Terada K, Hori M, Kyoya T, Kikuchi N. Simulation of the multi-scale convergence in computational homogenization approaches[J]. International Journal of Solids and Structures, 2000, 37: 2285-2311
Terada K, Kikuchi N. A class of general algorithms for multi-scale analysis of heterogeneous medis[J].Computer Methods in Applied Mechanics and Engineering, 2001,190:5427-5464
Terada K, Kyoya T, Kazama M, Lee K, Oyang L Z. Image-based modeling and analysis of microstructures for two-scale problems in geomechanics[J]. International journal for Numerical and Analytical Methods in Geomechanics, 2002; 26:273-297
Terada K, Saiki I, Matsui K, Yamakawa Y. Two-scale kinematics and linearization for simultaneous two-scale analysis of periodic heterogeneous solids at finite strain[J]. Computer Methods in Applied Mechanics and Engineering,2003,192:3531-3563
Van vliet M R A. Size effect in tensile fracture of concrete and rock[D]. PhD thesis,Delft University of Technology, 2000.
Villard P. Modeling of Interface Problems by the Finite Element Method with Considerable Displacements[J]. Computers and Geotechnics, 1996,1991 ):2345
Walsh, J.B, Grosenbaugh, M.A. A new model for analyzing the effect of fractures on compressibility[J].Journal of Geophysics Research, 1979,84: 3532-3536.
Wang J G, Ichikawa Y, Leung C F. A constitutive model for rock interfaces and joints[J].International Journal of Rock Mechanics & Mining Sciences, 2003, 40: 41-53
Watanabe I, Terada K, Akiyama M. Two-scale analysis for deformation-induced anisotropy of polycrystalline metals[J].Computational Materials Science,2005, 32:240-250
Watanabe I, Terada K, Eduardo Alberto de Souza Neto, Djordje Peric. Characterization of macroscopic tensile strength of polycrystalline metals with two-scale finite element analysis[J]. Journal of the Mechanics and Physics of Solids,2008,56 : 1105-1125
Willam K J, Iordache M M. On the lack of symmetry in materials[C]. trends in computational structural mechanics, Wall W A, Bletzinger K U and Schweizerhof K(Eds.). CIMNE, Barcelona, Spain,2001,1-10
Xie H P, Wang J A, KwasAniewski M A. Multifractal characterization of rock fracture surfaces[J].International Journal of Rock Mechanics and Mining Sciences, 1999, 36:19-27
Yamada, K, Takeda, N, Kagami, J, Naoi, T. Mechanisms of elastic contact and friction between rough surfaces[J]. Wear, 1978b, 48: 15-34.
Yang Z Y, Chiang D Y. An experimental study on the progressive shear behavior of rock joints with tooth-shaped asperities[J]. Internationa] Journal of Rock Mechanics & Mining Sciences,2000, 37:1247-1259
Yang Z Y, Di C C, Yen K C. The effect of asperity order on the roughness of rock joints[J].International Journal of Rock Mechanics & Mining Sciences,2001,38:745-752
Yang Z Y,Lo S C.An Index for Describing the Anisotropy of Joint Surfaces[J].International Journal of Rock Mechanics & Mining Sciences,1997,34(6):1031-1044
Yoshioka,N.The role of plastic deformation in normal loading and unloading cycles[J].Journal of Geophysics Research,1994,99:15561-15568.
Yoshida H,Horii H.Micromechanics-based continuum model for a jointed,rock mass and excavation analyses of a large-scale cavern[J].International Journal of Rock Mechanics & Mining Sciences,2004,41:119-145
Yong Ming Tien,Ming Chuan Kuo.A failure criterion for transversely isotropic rocks[J].International Journal of Rock Mechanics & Mining Sciences,2001,38:399-412
Yu Xianbin,vayssade b.joint profiles and their roughness parameters[J].International Journal of Rock Mechanical and Mining Science & Geomechanical Abstracts,1991,28(4):333-336
Yu Qing,Fish J.Multiscale asymptotic homogenization for multiphysics problems with multiple spatial and temporal scales:a coupled thermo-viscoelastic example problem[J].International Journal of Solids and Structures,2002,39:6429-6452
Yuan S C,Harrison J P.Development of a hydro-mechanical local degradation approach and its application to modeling fluid flow during progressive fracturing of heterogeneous rocks[J].International Journal of Rock Mechanics and Mining Sciences,2005,42:961-984
Zangerl C,Evans K F,Eberhardt E,Loew S.Normal stiffness of fractures in granitic rock:A compilation of laboratory and in-situ experiments[J].International Journal of Rock Mechanics &Mining Sciences,2008,45:1500-1507
Zheng Yuan,Fish J.Toward Realization Of Computational Homogenization In Practice[J].International Journal For Numerical Methods In Engineering,2008;73:361-380
Zhu Qizhi,Kondo D,Shao J F,Pensee V.Micromechanical modelling of anisotropic damage in brittle rocks and application[J].International Journal of Rock Mechanics & Mining Sciences,2008,45:467-477
Zhao J.Joint surface matching and shear strength part B:JRC-JMC shear strength criterion[J]International Journal of Rock Mechanics and Mining Sciences,1997,34(2):179-185
Zienkiewicz O C,Best B,Dullage C et al.Analysis of nonlinear problems in rock mechanics with particular reference to jointed rock systems[C].In:proc 2~(nd) confofthe society of rock mechanics,Belgrade,1970,8-14
Zienkiewicz,O.C.,G.N.Pande,Time Dependent Multilaminate Model of Rocks--A Numerical Study of Deformation and Failure of Rock Masses," International Journal for Numerical and Analytical Methods in Geomechanics,1977,1:219-247
Zubelewice A,O' connor K,Dowing C H,Belytschko T,Plesha M E.A constitutive model for cyclic behavior of dlatant rock joints[C].Proc.2~(nd).conf.constitutive laws for engng materials,1987,1137-1144
保长汉.节理岩体的随面本构关系[J].工程力学(增刊),1996:274-278
白世伟,任伟中,丰定祥等.平面应力条件下闭合断续节理岩体破坏机理及强度特性[J].岩石力学 与工程学报,1999,18(6):635-640
陈乃明.岩体节理形貌的分形维数与摩擦角的关系研究.岩土力学[J],1996,17(3):54-58
陈蕴生,李宁,李爱国等.非贯通节理介质细观损伤演化的CT分析[J].岩石力学与工程学报,2000.19(6):702-706
曹文贵,速宝玉.模拟夹层的大变形有限元等厚度节理单元模型[J].河海大学学报,2000,28(3):26-29
曹文贵,李翔,刘峰等.裂隙化岩体应变软化损伤本构模型探讨[J].岩石力学与工程学报,2007,26(12):2488-2494
曹玉新,许兰民,沈宇鹏.土工格栅在青藏铁路多年冻土区的应用[J].北京交通大学学报,2008,32(1):16-19
曹礼群,罗剑兰.多孔复合介质周期结构热传导和质扩散问题的多尺度数值方法[J].工程热物理学报,2000,21(5):610-614
曹礼群.材料物性的多尺度关联与数值模拟[J].世界科技研究与发展,2002,24(6):23-29
陈卫忠,李术才,朱维申.考虑裂隙闭合和摩擦效应的节理岩体能量损伤理论与应用.岩石力学与工程学报,2000,19(2):131-135
崔俊芝,曹礼群.基于双尺度渐近分析的有限元算法[J].计算数学,1998,20(1):89-102
崔俊芝,曹礼群.具有小周期孔洞弹性结构的双尺度渐近分析[J],系统科学与数学,1999,19(4):490-495
岑威钧,朱岳明.基于ABAQUS的土石料本构模型二次开发及其应用[J].水利水电科技进展,2005,25(6):78-81
陈祖煜、汪小刚、杨健等。岩质边坡稳定分析。北京:中国水利水电出版社,2005
戴永浩,陈卫忠,伍国军等.非饱和岩体弹塑性损伤模型研究与应用[J].岩石力学与工程学报,2008,27(4):728-735
杜守继.朱建栋,职洪涛.岩石节理经历不同变形的剪切试验研究[J].岩石力学与工程学报,2006,25(1):56-60
方理刚.岩石节理弹塑性本构关系[J].岩土工程学报,1996,18(3):91-95
方岱宁,周储伟.有限元计算细观力学对复合材料力学行为的数值分析[J].力学进展,1998,(28):173-188.
冯淼林,吴长春.基于三维均匀化方法的复合材料本构数值模拟.中国科学技术大学学报,2000,30(6):693-699
傅冰骏。岩石力学研究的现状和未来。岩石力学研究的现状和未来--傅冰骏教授在全国岩土与工程学术大会报告,2003
付凯敏,黄晓明.基于ABAQUS的修正Burgers蠕变模型二次开发[J].公路工程,2008,33(3):132-137
付丽,杜星文.基于非局部理论的一维损伤模型的有限元算法[J].航空学报,2009,30(5):879-885
范景伟,何江达.含定向闭合断续节理岩体的强度特性[J].岩石力学与工程学报,1992,11(2):190-199
冯永平,崔俊芝,邓明香.周期孔洞区域中热力耦合问题的双尺度有限元计算[J].物理学报,2009,58:S327-S337
范庆来,栾茂田,杨庆.修正剑桥模型的隐式积分算法在ABAQUS中的数值实施[J].岩土力学,2008,29(1):269-273
郭少华,孙宗颀,谢晓晴.压缩条件下岩石断裂模式与断裂判据的研究[J].岩土工程学报,2002,24(3):304-308
冀宾,陈万吉,赵杰.岩土软化行为的网格依赖性问题研究[J].工程力学,2008,25(8):36-41
冀宾,陈万吉,赵杰.基于偶应力理论剪切带问题的弹塑性有限元分析[J].力学学报,2009,41(2):1992-199
李浩,陶振宇.非贯通节理岩体的有效场和损伤本构关系[J].武汉水利电力大学学报,2000,33(3):5-8
李银平,王元汉,肖四喜.岩石类材料压剪裂纹的相互作用分析[J].岩石力学与工程学报,2003,22(4):552-555
李银平,王元汉,陈龙珠等.含预制裂纹大理岩的压剪试验分析[J].岩土工程学报,2004,26(1):120-124
李建林,哈秋林.节理岩体拉剪断裂与强度研究[J].岩石力学与工程学报,1998,17(3):259-266
李建林,孙志宏.节理岩体压剪断裂及其强度研究[J].岩石力学与工程学报,2000,19(4):444-448
李树荣,高峰,廖孟柯等.岩石粗糙节理剪切强度的分形分析[J].煤炭科学技术,2006,34(11):64-66
李同录,罗世毅,何剑等.节理岩体力学参数的选取与应用[J].岩石力学与工程学报,2004,23(13):2182-2186
李海波,刘博,冯海鹏等.模拟岩石节理试样剪切变形特征和破坏机制研究[J].岩土力学,2008,29(7):1741-1746
凌道盛,徐兴.非线性有限元及程序.浙江:浙江大学出版社,2004
林鹏,黄凯珠,王仁坤,周维垣.不同角度单裂纹缺陷试样的裂纹扩展与破坏行为[J].岩石力学与工程学报,2005,2(增2):5652-5657
梁作元,朱维申.压剪应力作用下含共面闭合节理岩石材料的切破坏准则探讨[A].见:朱维申编.中国青年学者岩土工程力学及其应用讨论会议论文集[C].北京:科学出版社。
刘远明,夏才初.非贯通节理岩体直剪贯通模型和强度研究[J].岩土工程学报,2006,28(10)
刘东燕,朱可善.含断续节理岩体强度的各向异性研究[J].岩石力学与工程学,1998,17(4):366-371
刘晓丽,梁冰,薛强.多孔介质渗透率的分形描述[J].水科学进展,2003,14(6):769-773
刘飞禹,蔡袁强,徐长节等.交通荷载作用下软基加筋道路变形机制研究[J].岩土力学,2009,30(1):129-134
刘泉声,胡云华,刘滨.基于试验的花岗岩渐进破坏本构模型研究[J].岩土力学,2009,30(2):289-296
刘军.岩体在冲击载荷作用下的各向异性损伤模型及其应用[J].岩石力学与工程学报,2004,23(4):635-640
刘萌成,黄晓明,林云龙.交通荷载作用下近桥台处差异沉降与路面结构开裂研究[J].岩土力学,2006,27(12):2203-2212
刘元高,周维垣,赵吉东,等.裂隙岩体损伤局部化破坏分岔模型及其应用.力学学报,2003,35(4):411-418
连尉平,崔俊芝.三维编织复合材料模量的双尺度有限元计算[J].计算力学学报,2005,22(3):268-273
连志龙,张劲,吴恒安等.水力压裂扩展的流固耦合数值模拟研究[J].岩土力学,2008,29(11):3021-3026
梁正召,唐春安,张永彬,等.准脆性材料的物理力学参数随机概率模型及破坏力学行为特征.岩石力学与工程学报,2008,27(4):718-727
马志涛,谭云亮.岩石破坏演化细观非均质物理元胞自动机模拟研究.岩石力学与工程学报,2005,24(15):2704-2708
牛斌,杨海天.基于均匀化方法的斜交节理岩体复合本构关系研究[J].岩土工程学报,2007,29(5):773-778
潘燕环、秘醒、薛松涛。复合材料中的渐近均匀化方法。上海力学,1997,18(4):290-297
秦娟,耿克勤.节理岩体的代表单元集合体模型及弹性参数预测[J].水利学报,2001,9:45-50
乔春生,张清.岩石节理非线性变形分析[J].北方交通大学学报,22(1),1-6,1998
任伟中,王庚荪,白世伟,等.共面闭合断续节理岩体的直剪强度研究[J].岩石力学与工程学报,2003,22(10):1667-1672
任强,徐卫亚.基于均匀化方法的节理岩体等效弹性性能预测[J].工程力学,2008,25(4):75-79,92
芮勇勤,唐春安.岩石剪切破坏过程的RFPA2D数值模拟.岩石力学与工程学报,2002,21(3):364-368
宋岩新,杨庆,唐小微等.ABAQUS后处理二次开发在海底管线稳定性分析中的应用[J].中国海洋平台2008,23(4):18-22
孙宗颀.不连续面应力应变性质研究[J].岩石力学与工程学报,1978,6(4):287-300
孙吉主,高晖.ABAQUS在软基固结过程分析中的应用[J].岩土力学,2007,28(增):919-922
孙毅,戴龙侠,范春竹等.淋溪河水电站地下厂房开挖过程中材料敏感性的非线性有限元分析[J].岩土力学,2008,29(增):149-154
孙德安,甄文战,黄文雄.三维弹塑性模型在路堤软基固结分析中应用[J].岩土力学,2009,30(3):66-674
孙卫军,周维垣.裂隙岩体弹塑性一损伤本构模型[J].岩石力学与工程学报,1990,9(2):108-119
沈婷,丰定祥,任伟中,白世伟.由结构面和岩桥组成的剪切面强度特性研究[J].岩土力学,1999,20(1):33-38
唐春安,朱万成.混凝土损伤与断裂--数值试验.科学出版社,北京,2003
王建华,范巍,王卫东等.空间m法在深基坑支护结构分析中的应用[J].岩土工程学报,2006,28(增):1332-1335
王镜波,崔俊芝,聂玉峰.单向纤维增强复合材料的双尺度分析模型及其力学参数计算.数值计算与计算机应用[J],2009,30(1):30-40
吴世平,唐绍锋,梁军,杜善义.周期性复合材料热力耦合性能的多尺度方法[J].哈尔滨工业大学学报,2006,38(12):2049-2053
王安明,杨春和,陈剑文等.层状盐岩体非线性蠕变本构模型[J].岩石力学与工程学报,2009,28(增1):2708-2714
王栋、年廷凯、陈煜淼。边坡稳定有限元分析中的三个问题[J].岩土力学,2007,28(11):2309-2318
王士民,朱合华,冯夏庭,等.细观非均匀性对脆性岩石材料宏观破坏形式的影响.岩土力学,2006,27(2):224-227
徐涛,唐春安,张哲,等.单轴压缩条件下脆性岩石变形破坏的理论,试验与数值模拟.东北大学学报(自然科学版),2003,24(1):87-90
徐晗,朱以文,蔡元奇等.降雨入渗条件下非饱和土边坡稳定分析[J].岩土力学,2005,26(12):1957-1962
徐卫亚,张贵科.节理岩体正交各向异性等效强度参数研究[J].岩土工程学报,2007,29(6):806-810
徐光黎,潘别桐,晏同珍.节理岩体变形模量估算新方法[J].地球科学-中国地质大学学报,1991,16(5):573-580
谢卫红,钟卫平,卢爱红,等.岩石分形节理的强度和变形特性研究[J].西安科技学院学报,2004,24(1):31-33
谢和平,Pariseau W G.岩石节理粗糙系数(JRC)的分形估计[J].中国科学(B辑),1994,24(5):524-530
谢和平,陈忠辉。岩石力学。科学出版社,2004,北京
夏才初,孙宗颀.工程岩体节理力学[M].上海:同济大学出版社,2002
夏才初,孙宗顽,潘长良.节理接触机理与闭合性质研究[J].同济大学学报,1995,23(2):147-152
夏才初,孙宗顽,潘长良.表面形貌含波纹度的节理的闭合模型[J].工程地质学报,1994,2(2):38-47
肖涛,左正兴.虚拟裂纹闭合法在结构断裂分析中的应用[J].计算力学学报,2008,25(增):16-19
许宏发,金丰年.岩体节理剪切变形的幂函数模型[J].岩石力学与工程学报,2000,19(3):314-317
杨圣奇,苏承东,徐卫亚.大理岩常规三轴压缩下强度和变形特性的试验研究.岩土力学,2005,26(3):475-478
杨天鸿,唐春安,梁正召,等.脆性岩石破裂过程损伤与渗流耦合数值模型研究.力学学报,2003,35(5):533-541
杨庆,李强,赵维等.翼型裂纹扩展特性的试验和数值分析[J].水利学报,2009,40(8):934-940
杨强,陈新,周维垣.基于二阶损伤张量的节理岩体各向异性屈服准则[J].岩石力学与工程学报,2005,24(8):1275-1282
殷有泉.考虑损伤的节理本构模型[J].工程地质学报,1994,2(4):1-6
袁凡凡,詹云刚,栾茂田.弹塑性无厚度接触面单元的本构积分算法及验证[J].岩土力学,2008,29(3):734-740
叶志才,徐磊,王超.基于ABAQUS的三维锚杆单元开发[J].三峡大学学报(自然科学版),2008,30(5):29-32
俞缙,赵晓豹,赵维炳,等.改进的岩石节理弹性非线性法向变形本构模型研究[J].岩土工程学报,2008,30(9):1316-1321
张强勇,向文,朱维申.节理岩体能量损伤本构模型与工程应用[J].工程地质学报,1999,7(4):310-314
张盛,张洪武,毕金英等.多维非经典热传导问题的时间-空间多尺度高阶均匀化分析[J].复合材料学报,2009,26(1):123-133
张均锋,祁涛,李正国.岩石材料的三维各向异性损伤破坏模型与数值模拟[J].岩土力学,2006,27(增):27-30
张平,李宁,贺若兰.含裂隙类岩石材料的局部化渐进破损模型研究[J].岩石力学与工程学报,2006,25(10):2043-2050
张欣,丁秀丽,李术才.ABAQUS有限元分析软件中Duncan-Chang模型的二次开发[J].长江科学院院报,2005,22(4):45-51
周太全,华渊,吕宝华.金华山软岩铁路隧道施工过程围岩屈服接近度分析[J].工程地质学报,2008,16(4):0546-550
周建军,周辉,邵建富.脆性岩石各向异性损伤和渗流耦合细观模型[J].岩石力学与工程学报,2007,26(2):368-373
周建民,许宏发,杨红禹.岩体节理法向变形的数学模型分析[J].岩石力学与工程学报,2000,19(增),853-855
周维垣,杨延毅.节理岩体的损伤断裂模型及验证.岩石力学与工程学报,1991,10(1):43-54
赵德安.节理型岩体损伤弹性的损伤力学算法[J].兰州铁道学院(自然科学版),2001,20(3):1-3
赵坚.岩石节理剪切强度的JRC-JMC新模型[J].岩石力学与工程学报,1998,17(4):349-357
朱维申,陈卫忠,申晋.雁形裂纹扩展的模型试验及断裂力学机制研究[J].固体力学学报,1998,19(4):355-360
朱以文,徐晗,蔡元奇等.边坡稳定的剪切带计算[J].计算力学学报,2007,24(4):441-446
朱万成,唐春安,杨天鸿,等.岩石破裂过程分析(RFPA)系统的细观单元本构关系及验证.岩石力学与工程学报,2003,22(1):24-29
詹云刚,袁凡凡,栾茂田.纯摩擦型岩土介质本构积分算法及其在ABAQUS中开发应用[J].岩土力学,2007,28(12):2619-2628
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