泥质板岩横观各向同性弹塑性耦合变形与强度准则的试验研究
|
摘要
岩石在微观、细观和宏观尺度上都表现出各向异性。微观层次上,晶体形成矿物集合体的排列方式会引起岩石细观矿物集合体的各向异性。在细观层次上,岩石组分和矿物集合体的结合方式将对岩石宏观力学各向异性产生极大的影响。
为此,本文针对含有明显层理状结构的泥质板岩,开展了微观矿物成分、细观岩石结构和宏观力学性质的试验研究。
(1)在微观尺度上,借助XRD试验,分析出泥质板岩含有石英、高岭石、白云母和斜绿泥石等矿物成分,并指出这些矿物的晶体以一定方式排列时将对细观矿物集合体的各向异性产生影响。
(2)在细观尺度上,通过扫描电镜试验,获得了泥质板岩细观结构的显微照片。分析发现,泥质板岩的结构以变晶结构为主,包含了由石英晶体形成的颗粒状矿物集合体和由高岭石、白云母和斜绿泥石形成的片状矿物集合体,但以片状集合体为主。这些矿物集合体在重力作用下以水平方向为优势方向排列,从而决定了泥质板岩具有横观各向同性的力学性质。
(3)在宏观尺度上,通过泥质板岩不同倾角岩样的单轴压缩和三轴循环加卸载试验,研究了泥质板岩的变形性质和强度行为。发现泥质板岩的变形存在明显的弹塑性耦合现象。不同加载角度下的视弹性模量随塑性应变的增大而呈指数规律衰减。采用数据拟合的方法获得了视弹性模量与塑性应变间的经验函数关系。通过对循环加卸载应力应变曲线的分析,将塑性应变、弹性应变和弹塑性耦合应变从总应变中分离出来。加载初期,泥质板岩以塑性变形为主,随着加载和总应变的增大,塑性应变在总应变中所占的比重逐渐降低,而弹性应变和弹塑性耦合应变的比重却在增大。泥质板岩的抗压强度与围压和加载方向有关。强度的各向异性受围压影响显著,随着围压的增大,强度各向异性降低。提出泥质板岩的粘聚力与摩擦系数随角度变化的经验Mohr-Coulomb强度准则。通过数据拟合,得到了准则中相关参数的值,并在σ1、β和σ3组成的三维空间中绘制了这个准则的强度面。
Anisotropy of rocks can occur at the micro, meso and macro scales in all. The crystals of minerals have some degree effects on the anisotropy of rocks. The effects mainly depend on the arrangement of mineral aggregates which were formed by the collection of the mineral crystals. At the mesoscopic level, the combining form of components and mineral aggregates of rocks have great effects on the anisotropy of rock mechanics behavior
Analysis of mineral micro-components and meso structure, experiments of macroscopic mechanical properties of argillite with a clear stratification structure were launched in this paper.
(1) At the micro scale, the components of argillite:quartz, kaolinite, muscovite and clinochlore were analyzed by XRD. Arrangements of the crystals of these minerals have effects on the anisotropy of mineral aggregates was pointed out.
(2) At the mesoscopic scale, by scanning electron microscopy experiment, the micrographs of microscopic structure of the argillite were photographed. Analysis showed that the main type of structure in argillite was crystalloblastic texture, which contains granular mineral aggregates made of quartz crystal, and schistose mineral aggregates made of the crystals of kaolinite, muscovite and clinochlore. But the main component was schistose mineral aggregates. Under gravity, these mineral aggregates arranged to the dominant horizontal direction, and this kind of arrangement determined the argillite with transversely isotropic mechanical properties.
(3) At the macro scale, experiments of uniaxial compression and triaxial cyclic loading tests of argillite rock samples with different angles were launched. Studied the deformation and strength properties of argillite, and found the obvious existence of elastoplastic coupling deformation. Under different loading angles, the apparent elastic moduli decayed exponentially with the increase of plastic strain. Obtained the relation of experience function between apparent elastic moduli and plastic strain by fitting method. Through the analysis of cyclic loading and unloading stress-strain curve, plastic strain, elastic strain and elastoplastic coupling strain were separated from the total strain. At the beginning of loading, the main deformation was plastic. With the increasing of load and total strain, the proportion of plastic strain in total strain gradually decreased, while the proportions of elastic strain and elastoplastic coupling strain increased. The compressive strength of argillite varied with the difference of confining pressures and loading directions. Strength anisotropy of argillite significantly affected by the confining pressures, and with the gradual increasing of confining pressures, the degree of strength anisotropy reduced. Proposed anisotropic empirical Mohr-Coulomb strength criterion with cohesion and the friction coefficient changing with loading directions. Through the data fitting method, obtained the values of relevant parameters, and graphed the strength surface of this criterion in three-dimensional space composed ofσ1,βandσ3.
为此,本文针对含有明显层理状结构的泥质板岩,开展了微观矿物成分、细观岩石结构和宏观力学性质的试验研究。
(1)在微观尺度上,借助XRD试验,分析出泥质板岩含有石英、高岭石、白云母和斜绿泥石等矿物成分,并指出这些矿物的晶体以一定方式排列时将对细观矿物集合体的各向异性产生影响。
(2)在细观尺度上,通过扫描电镜试验,获得了泥质板岩细观结构的显微照片。分析发现,泥质板岩的结构以变晶结构为主,包含了由石英晶体形成的颗粒状矿物集合体和由高岭石、白云母和斜绿泥石形成的片状矿物集合体,但以片状集合体为主。这些矿物集合体在重力作用下以水平方向为优势方向排列,从而决定了泥质板岩具有横观各向同性的力学性质。
(3)在宏观尺度上,通过泥质板岩不同倾角岩样的单轴压缩和三轴循环加卸载试验,研究了泥质板岩的变形性质和强度行为。发现泥质板岩的变形存在明显的弹塑性耦合现象。不同加载角度下的视弹性模量随塑性应变的增大而呈指数规律衰减。采用数据拟合的方法获得了视弹性模量与塑性应变间的经验函数关系。通过对循环加卸载应力应变曲线的分析,将塑性应变、弹性应变和弹塑性耦合应变从总应变中分离出来。加载初期,泥质板岩以塑性变形为主,随着加载和总应变的增大,塑性应变在总应变中所占的比重逐渐降低,而弹性应变和弹塑性耦合应变的比重却在增大。泥质板岩的抗压强度与围压和加载方向有关。强度的各向异性受围压影响显著,随着围压的增大,强度各向异性降低。提出泥质板岩的粘聚力与摩擦系数随角度变化的经验Mohr-Coulomb强度准则。通过数据拟合,得到了准则中相关参数的值,并在σ1、β和σ3组成的三维空间中绘制了这个准则的强度面。
Anisotropy of rocks can occur at the micro, meso and macro scales in all. The crystals of minerals have some degree effects on the anisotropy of rocks. The effects mainly depend on the arrangement of mineral aggregates which were formed by the collection of the mineral crystals. At the mesoscopic level, the combining form of components and mineral aggregates of rocks have great effects on the anisotropy of rock mechanics behavior
Analysis of mineral micro-components and meso structure, experiments of macroscopic mechanical properties of argillite with a clear stratification structure were launched in this paper.
(1) At the micro scale, the components of argillite:quartz, kaolinite, muscovite and clinochlore were analyzed by XRD. Arrangements of the crystals of these minerals have effects on the anisotropy of mineral aggregates was pointed out.
(2) At the mesoscopic scale, by scanning electron microscopy experiment, the micrographs of microscopic structure of the argillite were photographed. Analysis showed that the main type of structure in argillite was crystalloblastic texture, which contains granular mineral aggregates made of quartz crystal, and schistose mineral aggregates made of the crystals of kaolinite, muscovite and clinochlore. But the main component was schistose mineral aggregates. Under gravity, these mineral aggregates arranged to the dominant horizontal direction, and this kind of arrangement determined the argillite with transversely isotropic mechanical properties.
(3) At the macro scale, experiments of uniaxial compression and triaxial cyclic loading tests of argillite rock samples with different angles were launched. Studied the deformation and strength properties of argillite, and found the obvious existence of elastoplastic coupling deformation. Under different loading angles, the apparent elastic moduli decayed exponentially with the increase of plastic strain. Obtained the relation of experience function between apparent elastic moduli and plastic strain by fitting method. Through the analysis of cyclic loading and unloading stress-strain curve, plastic strain, elastic strain and elastoplastic coupling strain were separated from the total strain. At the beginning of loading, the main deformation was plastic. With the increasing of load and total strain, the proportion of plastic strain in total strain gradually decreased, while the proportions of elastic strain and elastoplastic coupling strain increased. The compressive strength of argillite varied with the difference of confining pressures and loading directions. Strength anisotropy of argillite significantly affected by the confining pressures, and with the gradual increasing of confining pressures, the degree of strength anisotropy reduced. Proposed anisotropic empirical Mohr-Coulomb strength criterion with cohesion and the friction coefficient changing with loading directions. Through the data fitting method, obtained the values of relevant parameters, and graphed the strength surface of this criterion in three-dimensional space composed ofσ1,βandσ3.
引文
[1]陈祖煜,汪小刚等.岩质边坡稳定分析-原理·方法·程序[M].北京：中国水利水电出版社,2005,1～8.
[2]王崇军.浅变质岩风化层边坡稳定性研究：[硕士学位论文].武汉：武汉理工大学,2008.1～4.
[3]张学民.岩石材料各向异性特征及其对隧道围岩稳定性影响研究[D].长沙：中南大学,2007,1～35.
[4]鲜学福,谭学术.层状岩体破坏机理[M].重庆：重庆大学出版社,1989.8-15.
[5]Dieter G E. Mechanical Metallurgy. McGraw-Hill,1987, NewYork.751～752.
[6]Hobbs B E, Means W D,Williams P F. An Outline of Structural Geology.1976, Wiley, New York,571～572.
[7]方理刚.节理化岩体的弹性变形性状及在湘西金矿的初步应用.长沙：长沙矿冶研究院,1987,16～44.
[8]马光,方理刚.湘西金矿炼厂保安矿柱开采的岩石力学研究.矿冶工程,1991,11(4)：1～5.
[9]朱明新,王河锦.长沙—澧陵—浏阳一带冷家溪群及板溪群的甚低级变质作用.岩石学报,2001,17(2)：291～300.
[10]宋忠宝,陈向阳,任有祥,等.东昆仑德尔尼铜矿“碳质(砂)板岩”的岩类学、岩石化学及其地质意义.西北地质,2008,41(4)：77～81.
[11]肖渊甫,郑荣才,邓江红.岩石学简明教程.北京：地质出版社,2009,244～250.
[12]Aufmuth R E, Aleszka J C. A scanning electron microscope investigation of statically stressed foundation materials. Bull. Assoc. Eng. Geol.,1976,13:137～149.
[13]Myer L R et al. Extensile Crack in Porous Rock under Differential Compressive Stress. Appl Mech Rev,1992,45(8):263～280.
[14]余煜.材料结构分析基础[M].北京：科学出版社,2000,284～290.
[15]朱珍德,张勇,徐卫亚,等.高围压高水压条件下大理岩断微观机理分析与试验研究.岩石力学与工程学报,2005,24(1)：44～51.
[16]朱珍德,渠文平,蒋志坚.岩石细观结构量化试验研究.岩石力学与工程学报,2007,26(7)：1313～1324.
[17]Louis L, David D, Metz V et al. Microstructural control on the anisotropy of elastic and transport properties in undeformed sandstones. Int. J. Rock Mech.& Min. Sci.,2005,42:911～923.
[18]Lempriere B M. Poisson's ratios in orthotropic materials. J. Am. Inst. Aeronaut. Astronaul,1968,6:2222～2227.
[19]Exadaktylos G E. On the constraints and relations of elastic constants of transversely isotropic geomaterials. Int. J. Rock Mech.& Min. Sci.,2001,38: 941～956.
[20]Amadei B. Importance of Anisotropy When Estimating and Measuring In Situ Stresses in Rock[J]. Int. J. Rock Mech. Min. Sci.& Geomech.1996,33(3):293～325.
[21]Nasseri M H B, Rao K S, Ramamurthy T. Anisotropic strength and deformational behavior of Himalayan schists. Int. J. Rock Mech.& Min. Sci.,2003,40:3～23.
[22]Hakala M, Kuula H, Hudson J A. Estimating the transversely isotropic elastic intact rock properties for in situ stress measurement data reduction:A case study of the Olkiluoto mica gneiss, Finland. Int. J. Rock Mech.& Min. Sci.,2007,44:14～46.
[23]Gonzaga G G, Leite M H, Corthesy R. Determination of anisotropic deformability parameters from a single standard rock specimen. Int. J. Rock Mech.& Min. Sci.,2008,45:1420～1438.
[24]Liao J J, Hu T B, Chang C W. Determination of Dynamic Elastic Constants of Transversely Isotropic Rocks Using a Single Cylindrical. Int J Rock Mech Min Sci, 1997,34(7):1045～1054.
[25]Mah M K, Schmitt D R. Determination of the complete elastic stiffnesses from ultrasonic phase velocity measurements. Journal of Geophysical Research.2003, 108(B1):ECV 6-1～6-11.
[26]Insun Song, Mancheol Suh, et al. Determination of the elastic modulus set of foliated rocks from ultrasonic velocity measurements. Engineering Geology,2004,72: 293～308.
[27]Amadei B, Rogers J D, Goodman R E. Elastic constants and tensile strength of the anisotropic rocks. Proc.5th ISRM Congr., Melbourne,1983,189～196.
[28]Chen C S, Pan E, Amadei B. Determination deformability and tensile strength of anisotropic rock of using Brazilian tests. Int. J. Rock Mech.& Min. Sci.,1998,35(1): 43～61.
[29]Claesson J, Bohloli B. Brazilian test:stress field and tensile strength of anisotropic rocks using an analytical solution. Int. J. Rock Mech.& Min. Sci.,2002, 39:991～1004.
[30]Talesnick M L, Ringel M. Completing the hollow cylinder methodology for testing of transversely isotropic rocks:torsion testing. Int. J. Rock Mech.& Min. Sci., 1999,36:627～639.
[31]Anna Laura L. S. Nunes. A new method for determination of transverse isotropic orientation and the associated elastic parameters for intact rock. Int. J. Rock Mech.& Min. Sci.,2002,39:257～273.
[32]Liao J J, Yang M T, Hsieh H Y. Direct tensile behavior of a transversely isotropic rock. Int. J. Rock Mech.& Min. Sci.,1997,34(5):837～849.
[33]Dafalias Y. F. Il'iushins postulate and resulting thermodynamic condition on elasto-plastic coupling [J]. Int. J. Solids Structures.1997,13:239～251.
[34]方理刚.岩石节理弹塑性本构关系[J].岩土工程学报,1996,18(3)：95～99.
[35]Niandou H, Shao J F, Henry J P, Fourmaintraux D. Laboratory investigation of the mechanical behaviour of Tournemire shale. Int. J. Rock Mech.& Min. Sci.,1997, 34(1):3～16.
[36]Duveau D, Shao J F, Henry J P. Assessment of some failure criteria for strongly anisotropic geomaterials. Mech. Cohes.-Frict. Mater.,1998,3:1～26.
[37]Hill R. The Mathematical Theory of Plasticity. Oxford University Press, Oxford, 1950.
[38]Pariseau W G. Plasticity theory for anisotropic rocks and soils. Proc.10th Symp. on Rock Mech.,1972,1:267.
[39]Cazacu O, Cristescu N D. A paraboloid failure surface for transversely isotropic materials. Mechanics of Materials,1999,31:381～393.
[40]Jaeger J C. Frietion of roeks and stability of roek slope. Geotechnique,1971, 21(2):97.
[41]McLamore R, Gray K E. The mechanical behavior of anisotropic sedimentary roeks. Trans. Am. Soe. Mech. Eng. Series B.1967,89:62～76.
[42]Ramamurthy T, Rao G V, Singh J. A strength criterion for anisotropic rocks. Proceedings of the Fifth Australia-Newzeland Conference on Geomechanics, Sydney, 1988,1:253～257.
[43]Jager J C. Shear failure of anisotropic roeks. Geol. Mang.1960,97:65～72.
[44]Duveau G, Shao J F. A Modified Single Plane of Weakness Theory for the Failure of Highly Stratified Rocks. Int. J. Rock Mech.& Min. Sci.,1998,35(6):807～813.
[45]Hoek E, Brown E T. Empirical strength criterion for rockmasses. J. of the Geotech. Eng. Div., A. S. C. E.,1980,106:1013.
[46]Hoek E. Strength of jointed rockmasses. Geotechnique,1983,33(3):187.
[47]Yong Ming Tien, Ming Chuan Kuo. A failure criterion for transversely isotropic rocks. Int. J. Rock Mech.& Min. Sci.,2001,38:399～412.
[48]郑颖人,沈珠江,龚晓南.岩土塑性力学原理[M].北京：中国建筑工业出版社,2002,1～11.
[49]谢守益,徐卫亚,邵建富.多孔岩石塑性压缩本构模型研究.岩石力学与工程学报,2005,24(17)：3154～3158.
[50]褚卫江.低孔隙度岩石细观本构模型及损伤—渗流祸合研究[D].南京：河海大学,2007,5～7.
[51]袁聚云,赵锡宏,董建国.上海粘性土各向异性弹塑性模型的研究.同济大学学报,1999.27(4)：402～406.
[52]Pietruszczak S, Krucinski S. Description of anisotropic response of clays using a tensorial measure of structural disorder. J. Mech. Mater., Abstr,1989,8:237～249.
[53]Pietruszczak S, Krucinski S. Considerations on soil response to the rotation of principal stress directions. Comput. Geotech., Abstr,1989,8:89～110.
[54]Pietruszczak S. On inelastic behaviour of anisotropic frictional materials. Mech. Cohes.-Frict. Mater.,1999,4:281～293.
[55]Pietruszczaka S, Mrozb Z. Formulation of anisotropic failure criteria incorporating a microstructure tensor. Computers and Geotechnics,2000,26: 105～112.
[56]Pietruszczak S, Mroz Z. On failure criteria for anisotropic cohesive-frictional materials. Int. J. Numer. Anal. Meth. Geomech.,2001,25:509～524.
[57]Pietruszczak S, Lydzba D, Shao J F. Modelling of inherent anisotropy in sedimentary rocks. International Journal of Solids and Structures,2002,39:637～648.
[58]Poul V. Lade. Modeling failure in cross-anisotropic frictional materials. International Journal of Solids and Structures,2007,44:5146～5162.
[59]中华人民共和国水利部.水利水电工程岩石试验规程(SL264-2001).北京：中国水利水电出版社,2001.55～60.
[60]中华人民共和国国家标准编写组.工程岩体试验方法标准(GB／T50266-99).北京：中国计划出版社,1999.17～21.
[2]王崇军.浅变质岩风化层边坡稳定性研究：[硕士学位论文].武汉：武汉理工大学,2008.1～4.
[3]张学民.岩石材料各向异性特征及其对隧道围岩稳定性影响研究[D].长沙：中南大学,2007,1～35.
[4]鲜学福,谭学术.层状岩体破坏机理[M].重庆：重庆大学出版社,1989.8-15.
[5]Dieter G E. Mechanical Metallurgy. McGraw-Hill,1987, NewYork.751～752.
[6]Hobbs B E, Means W D,Williams P F. An Outline of Structural Geology.1976, Wiley, New York,571～572.
[7]方理刚.节理化岩体的弹性变形性状及在湘西金矿的初步应用.长沙：长沙矿冶研究院,1987,16～44.
[8]马光,方理刚.湘西金矿炼厂保安矿柱开采的岩石力学研究.矿冶工程,1991,11(4)：1～5.
[9]朱明新,王河锦.长沙—澧陵—浏阳一带冷家溪群及板溪群的甚低级变质作用.岩石学报,2001,17(2)：291～300.
[10]宋忠宝,陈向阳,任有祥,等.东昆仑德尔尼铜矿“碳质(砂)板岩”的岩类学、岩石化学及其地质意义.西北地质,2008,41(4)：77～81.
[11]肖渊甫,郑荣才,邓江红.岩石学简明教程.北京：地质出版社,2009,244～250.
[12]Aufmuth R E, Aleszka J C. A scanning electron microscope investigation of statically stressed foundation materials. Bull. Assoc. Eng. Geol.,1976,13:137～149.
[13]Myer L R et al. Extensile Crack in Porous Rock under Differential Compressive Stress. Appl Mech Rev,1992,45(8):263～280.
[14]余煜.材料结构分析基础[M].北京：科学出版社,2000,284～290.
[15]朱珍德,张勇,徐卫亚,等.高围压高水压条件下大理岩断微观机理分析与试验研究.岩石力学与工程学报,2005,24(1)：44～51.
[16]朱珍德,渠文平,蒋志坚.岩石细观结构量化试验研究.岩石力学与工程学报,2007,26(7)：1313～1324.
[17]Louis L, David D, Metz V et al. Microstructural control on the anisotropy of elastic and transport properties in undeformed sandstones. Int. J. Rock Mech.& Min. Sci.,2005,42:911～923.
[18]Lempriere B M. Poisson's ratios in orthotropic materials. J. Am. Inst. Aeronaut. Astronaul,1968,6:2222～2227.
[19]Exadaktylos G E. On the constraints and relations of elastic constants of transversely isotropic geomaterials. Int. J. Rock Mech.& Min. Sci.,2001,38: 941～956.
[20]Amadei B. Importance of Anisotropy When Estimating and Measuring In Situ Stresses in Rock[J]. Int. J. Rock Mech. Min. Sci.& Geomech.1996,33(3):293～325.
[21]Nasseri M H B, Rao K S, Ramamurthy T. Anisotropic strength and deformational behavior of Himalayan schists. Int. J. Rock Mech.& Min. Sci.,2003,40:3～23.
[22]Hakala M, Kuula H, Hudson J A. Estimating the transversely isotropic elastic intact rock properties for in situ stress measurement data reduction:A case study of the Olkiluoto mica gneiss, Finland. Int. J. Rock Mech.& Min. Sci.,2007,44:14～46.
[23]Gonzaga G G, Leite M H, Corthesy R. Determination of anisotropic deformability parameters from a single standard rock specimen. Int. J. Rock Mech.& Min. Sci.,2008,45:1420～1438.
[24]Liao J J, Hu T B, Chang C W. Determination of Dynamic Elastic Constants of Transversely Isotropic Rocks Using a Single Cylindrical. Int J Rock Mech Min Sci, 1997,34(7):1045～1054.
[25]Mah M K, Schmitt D R. Determination of the complete elastic stiffnesses from ultrasonic phase velocity measurements. Journal of Geophysical Research.2003, 108(B1):ECV 6-1～6-11.
[26]Insun Song, Mancheol Suh, et al. Determination of the elastic modulus set of foliated rocks from ultrasonic velocity measurements. Engineering Geology,2004,72: 293～308.
[27]Amadei B, Rogers J D, Goodman R E. Elastic constants and tensile strength of the anisotropic rocks. Proc.5th ISRM Congr., Melbourne,1983,189～196.
[28]Chen C S, Pan E, Amadei B. Determination deformability and tensile strength of anisotropic rock of using Brazilian tests. Int. J. Rock Mech.& Min. Sci.,1998,35(1): 43～61.
[29]Claesson J, Bohloli B. Brazilian test:stress field and tensile strength of anisotropic rocks using an analytical solution. Int. J. Rock Mech.& Min. Sci.,2002, 39:991～1004.
[30]Talesnick M L, Ringel M. Completing the hollow cylinder methodology for testing of transversely isotropic rocks:torsion testing. Int. J. Rock Mech.& Min. Sci., 1999,36:627～639.
[31]Anna Laura L. S. Nunes. A new method for determination of transverse isotropic orientation and the associated elastic parameters for intact rock. Int. J. Rock Mech.& Min. Sci.,2002,39:257～273.
[32]Liao J J, Yang M T, Hsieh H Y. Direct tensile behavior of a transversely isotropic rock. Int. J. Rock Mech.& Min. Sci.,1997,34(5):837～849.
[33]Dafalias Y. F. Il'iushins postulate and resulting thermodynamic condition on elasto-plastic coupling [J]. Int. J. Solids Structures.1997,13:239～251.
[34]方理刚.岩石节理弹塑性本构关系[J].岩土工程学报,1996,18(3)：95～99.
[35]Niandou H, Shao J F, Henry J P, Fourmaintraux D. Laboratory investigation of the mechanical behaviour of Tournemire shale. Int. J. Rock Mech.& Min. Sci.,1997, 34(1):3～16.
[36]Duveau D, Shao J F, Henry J P. Assessment of some failure criteria for strongly anisotropic geomaterials. Mech. Cohes.-Frict. Mater.,1998,3:1～26.
[37]Hill R. The Mathematical Theory of Plasticity. Oxford University Press, Oxford, 1950.
[38]Pariseau W G. Plasticity theory for anisotropic rocks and soils. Proc.10th Symp. on Rock Mech.,1972,1:267.
[39]Cazacu O, Cristescu N D. A paraboloid failure surface for transversely isotropic materials. Mechanics of Materials,1999,31:381～393.
[40]Jaeger J C. Frietion of roeks and stability of roek slope. Geotechnique,1971, 21(2):97.
[41]McLamore R, Gray K E. The mechanical behavior of anisotropic sedimentary roeks. Trans. Am. Soe. Mech. Eng. Series B.1967,89:62～76.
[42]Ramamurthy T, Rao G V, Singh J. A strength criterion for anisotropic rocks. Proceedings of the Fifth Australia-Newzeland Conference on Geomechanics, Sydney, 1988,1:253～257.
[43]Jager J C. Shear failure of anisotropic roeks. Geol. Mang.1960,97:65～72.
[44]Duveau G, Shao J F. A Modified Single Plane of Weakness Theory for the Failure of Highly Stratified Rocks. Int. J. Rock Mech.& Min. Sci.,1998,35(6):807～813.
[45]Hoek E, Brown E T. Empirical strength criterion for rockmasses. J. of the Geotech. Eng. Div., A. S. C. E.,1980,106:1013.
[46]Hoek E. Strength of jointed rockmasses. Geotechnique,1983,33(3):187.
[47]Yong Ming Tien, Ming Chuan Kuo. A failure criterion for transversely isotropic rocks. Int. J. Rock Mech.& Min. Sci.,2001,38:399～412.
[48]郑颖人,沈珠江,龚晓南.岩土塑性力学原理[M].北京：中国建筑工业出版社,2002,1～11.
[49]谢守益,徐卫亚,邵建富.多孔岩石塑性压缩本构模型研究.岩石力学与工程学报,2005,24(17)：3154～3158.
[50]褚卫江.低孔隙度岩石细观本构模型及损伤—渗流祸合研究[D].南京：河海大学,2007,5～7.
[51]袁聚云,赵锡宏,董建国.上海粘性土各向异性弹塑性模型的研究.同济大学学报,1999.27(4)：402～406.
[52]Pietruszczak S, Krucinski S. Description of anisotropic response of clays using a tensorial measure of structural disorder. J. Mech. Mater., Abstr,1989,8:237～249.
[53]Pietruszczak S, Krucinski S. Considerations on soil response to the rotation of principal stress directions. Comput. Geotech., Abstr,1989,8:89～110.
[54]Pietruszczak S. On inelastic behaviour of anisotropic frictional materials. Mech. Cohes.-Frict. Mater.,1999,4:281～293.
[55]Pietruszczaka S, Mrozb Z. Formulation of anisotropic failure criteria incorporating a microstructure tensor. Computers and Geotechnics,2000,26: 105～112.
[56]Pietruszczak S, Mroz Z. On failure criteria for anisotropic cohesive-frictional materials. Int. J. Numer. Anal. Meth. Geomech.,2001,25:509～524.
[57]Pietruszczak S, Lydzba D, Shao J F. Modelling of inherent anisotropy in sedimentary rocks. International Journal of Solids and Structures,2002,39:637～648.
[58]Poul V. Lade. Modeling failure in cross-anisotropic frictional materials. International Journal of Solids and Structures,2007,44:5146～5162.
[59]中华人民共和国水利部.水利水电工程岩石试验规程(SL264-2001).北京：中国水利水电出版社,2001.55～60.
[60]中华人民共和国国家标准编写组.工程岩体试验方法标准(GB／T50266-99).北京：中国计划出版社,1999.17～21.