岩石变形局部化及失稳破坏的理论与实验研究
|
摘要
岩石的局部化变形是岩土材料失稳的一个重要特征，是材料破坏的先兆，岩石中的局部化变形直接导致了加载过程中岩石整体强度的降低，使岩体工程的承载力下降。所以研究和预测局部化变形带的起动、演化发展及剪切带形成规律对于研究岩石材料失稳破坏具有非常重要的意义。本文应用理论研究、实验研究和数值分析相结合的方法，对软岩的局部化起动、演化、形成宏观剪切带及失稳破坏进行了深入系统的研究，得到了一些有益的研究成果：
(1) 通过重庆红色泥砂岩单向、三向受压状态下的实验研究，分析了软岩的损伤演化规律及裂纹扩展的非线性分形特征。在此基础上结合岩石强度概率分布假设，采用重正化群模型对岩石失稳破坏过程中的临界现象进行了研究，得到了岩石材料失稳破坏的理论临界点。通过实验数据与重正化群模型计算结果的对比，证明了重正化破坏模型能准确地模拟岩石的失稳破坏，并能有效地推测出破坏的临界点，建立判断岩石稳定状态的判据。
(2) 基于岩石变形局部化与失稳破坏过程中的自组织临界特征，采用“沙堆元胞自动机”模型，从新的角度对岩石变形过程中的裂纹扩展、损伤演化以及能量释放等细观尺度上的自组织临界行为进行了研究。
(3) 自行研制了平面应变加载系统，首次研究了重庆红色泥砂岩在平面应变加载条件下的变形局部化行为及失稳破坏机理。对平面应变加载过程中的弹性波速变化特征进行了研究，跟踪了岩石变形局部化的演化全过程，并根据弹性波测试结果得到了软岩变形局部化的起动点和失稳破坏的临界点。同时，还研究了平面应变条件下，加载速率、含水量及坡角的变化对软岩变形局部化发生和发展的影响规律。
(4) 采用先进的激光数字散斑光测方法，对泥砂岩和泥岩两种软岩试件进行变形局部化对比实验研究。研究了单轴压缩状态下，加载速率对软岩变形局部化的影响。经过一系列散斑干涉的相关分析，实时、定量地跟踪和测定了软岩变形局部化的变化规律，首次观测到了泥砂岩和泥岩变形局部化带的“转动”全过程，并确定了局部化起动的时刻，定量地测定了局部化带的宽度及局部化带内的变形速度。
(5) 基于岩石的弹塑性本构关系，采用滑块—弹簧组合系统研究了岩石剪切带形成的力学模型，并得出了该力学模型控制的变形局部化起动条件。
(6) 基于材料失稳破坏的分叉理论，对软岩变形局部化进行理论研究，以确定软岩变形局部化起动条件以及局部化方位角等理论模型。对弹塑性材料变形局
重庆大学博士学位论文
部化进行分叉分析。根据Maxwell不相容条件，对岩石在平面应变和平面应力状
态下的局部化准则进行了理论分析。
(7)基于材料变形破坏的梯度塑性理论，对岩石变形局部化带的理论宽度进
行了分析，并根据实验数据得到了泥砂岩的内部长度以及单轴压缩和平面应变状
态下局部化带的宽度。
(8)基于岩石微元的强度分布函数满足威布尔分布的假设，采用RFPAZD对
岩石单轴受压、等围压三轴、平面应力以及平面应变几种状态下的局部化剪切带
形成过程和失稳破坏进行了数值分析。
The deformation localization of the rock is both an important characteristic of the rock material's instability and the symptom of material failure, which directly leads to the decrease in its overall intensity during the loading process and the loading-bearing capacity of the rock project.
Therefore, the study and prediction of the initiation and evolution of the deformation localization band and the evolution rule of the shear band are very meaningful to the exploration of the rock material's instability and failure. In this paper, applying the methods of theoretical study and experimental study as well as numerical analysis, from a new point of view, the author makes a thorough and systematic study of the soft rock's deformation localization from its initiation, evolution, and taking shape into macro-shearing band and its instability as well, and yields some positive research results.
(1) Through the experimental study of red mud sand rock in Chongqing under the conditions of uniaxial and triaxial loading, the author analyzes the damage evolution law of the soft rock and the nonlinear fractal features of the crack expansion. On such a basis, the author, combing the probability distribution hypothesis of the rock strength, studies the critical phenomenon during the process of the rock's unstable failure with the adoption of renormalization model, and gains the theoretical critical point of the rock material's unstable failure and the development direction of its stability. Contrasting the experimental data with the calculative results of renormalization model, the author proves that the model can accurately simulate the rock's unstable failure and effectively predict the critical point of failure, thus, establishes the criterion of the rock's stability.
(2) According to the deformation localization of the rock and the self-organized critical action during the instability failure process, "sandpile cellular automata" model is adopted to study the microscopic self-organized critical behavior such as the crack expansion and damage evolution and energy release during the rock deformation process.
(3) A plane strain loading system is developed, then the localized deformation and the instable failure mechanism of Chongqing red mud sandstone under the plane strain condition are investigated by this loading system for the first time. Author studies the elastic wave features during the plane strain loading process, keeps track of the whole evolution process of the rock's deformation localization, and acquires the initiative
point of the soft rock's deformation localization and the critical point of instable failure. Meanwhile, he studies, under the condition of plane strain, the affection of the initiation and evolution of the soft rock's deformation localization according to the variations of loading speed, water content and slope angle.
(4) Adopting advanced laser digital speckle method, the author first conducts the contrasting experiments of deformation localization between the mud sandstone and muddy rock and studies the effects of loading speed on the soft rock's deformation localization under uniaxial pressure. Through a range of correlation analyses of speckle interference, and the temporal and quantitative pursuit and determination of the variation laws of the soft rock's deformation localization, he observes the whole "revolving" process of the deformation localization area of the mud sandstone and the muddy rock. Also, he determines the starting moment of localization and quantitatively surveys the width and the deformation speed of the localization area.
(5) Based on elastic-plastic constitutive model of the rocks, the author, adopting the sliding block - spring combination system, studies the mechanics model of the shear band and obtains the starting conditions of deformation localization controlled by such a mechanics model.
(6) According to the bifurcation theory of material instable failure, the author makes a theoretical study of the soft rock's deformation localization in order to d
(1) 通过重庆红色泥砂岩单向、三向受压状态下的实验研究，分析了软岩的损伤演化规律及裂纹扩展的非线性分形特征。在此基础上结合岩石强度概率分布假设，采用重正化群模型对岩石失稳破坏过程中的临界现象进行了研究，得到了岩石材料失稳破坏的理论临界点。通过实验数据与重正化群模型计算结果的对比，证明了重正化破坏模型能准确地模拟岩石的失稳破坏，并能有效地推测出破坏的临界点，建立判断岩石稳定状态的判据。
(2) 基于岩石变形局部化与失稳破坏过程中的自组织临界特征，采用“沙堆元胞自动机”模型，从新的角度对岩石变形过程中的裂纹扩展、损伤演化以及能量释放等细观尺度上的自组织临界行为进行了研究。
(3) 自行研制了平面应变加载系统，首次研究了重庆红色泥砂岩在平面应变加载条件下的变形局部化行为及失稳破坏机理。对平面应变加载过程中的弹性波速变化特征进行了研究，跟踪了岩石变形局部化的演化全过程，并根据弹性波测试结果得到了软岩变形局部化的起动点和失稳破坏的临界点。同时，还研究了平面应变条件下，加载速率、含水量及坡角的变化对软岩变形局部化发生和发展的影响规律。
(4) 采用先进的激光数字散斑光测方法，对泥砂岩和泥岩两种软岩试件进行变形局部化对比实验研究。研究了单轴压缩状态下，加载速率对软岩变形局部化的影响。经过一系列散斑干涉的相关分析，实时、定量地跟踪和测定了软岩变形局部化的变化规律，首次观测到了泥砂岩和泥岩变形局部化带的“转动”全过程，并确定了局部化起动的时刻，定量地测定了局部化带的宽度及局部化带内的变形速度。
(5) 基于岩石的弹塑性本构关系，采用滑块—弹簧组合系统研究了岩石剪切带形成的力学模型，并得出了该力学模型控制的变形局部化起动条件。
(6) 基于材料失稳破坏的分叉理论，对软岩变形局部化进行理论研究，以确定软岩变形局部化起动条件以及局部化方位角等理论模型。对弹塑性材料变形局
重庆大学博士学位论文
部化进行分叉分析。根据Maxwell不相容条件，对岩石在平面应变和平面应力状
态下的局部化准则进行了理论分析。
(7)基于材料变形破坏的梯度塑性理论，对岩石变形局部化带的理论宽度进
行了分析，并根据实验数据得到了泥砂岩的内部长度以及单轴压缩和平面应变状
态下局部化带的宽度。
(8)基于岩石微元的强度分布函数满足威布尔分布的假设，采用RFPAZD对
岩石单轴受压、等围压三轴、平面应力以及平面应变几种状态下的局部化剪切带
形成过程和失稳破坏进行了数值分析。
The deformation localization of the rock is both an important characteristic of the rock material's instability and the symptom of material failure, which directly leads to the decrease in its overall intensity during the loading process and the loading-bearing capacity of the rock project.
Therefore, the study and prediction of the initiation and evolution of the deformation localization band and the evolution rule of the shear band are very meaningful to the exploration of the rock material's instability and failure. In this paper, applying the methods of theoretical study and experimental study as well as numerical analysis, from a new point of view, the author makes a thorough and systematic study of the soft rock's deformation localization from its initiation, evolution, and taking shape into macro-shearing band and its instability as well, and yields some positive research results.
(1) Through the experimental study of red mud sand rock in Chongqing under the conditions of uniaxial and triaxial loading, the author analyzes the damage evolution law of the soft rock and the nonlinear fractal features of the crack expansion. On such a basis, the author, combing the probability distribution hypothesis of the rock strength, studies the critical phenomenon during the process of the rock's unstable failure with the adoption of renormalization model, and gains the theoretical critical point of the rock material's unstable failure and the development direction of its stability. Contrasting the experimental data with the calculative results of renormalization model, the author proves that the model can accurately simulate the rock's unstable failure and effectively predict the critical point of failure, thus, establishes the criterion of the rock's stability.
(2) According to the deformation localization of the rock and the self-organized critical action during the instability failure process, "sandpile cellular automata" model is adopted to study the microscopic self-organized critical behavior such as the crack expansion and damage evolution and energy release during the rock deformation process.
(3) A plane strain loading system is developed, then the localized deformation and the instable failure mechanism of Chongqing red mud sandstone under the plane strain condition are investigated by this loading system for the first time. Author studies the elastic wave features during the plane strain loading process, keeps track of the whole evolution process of the rock's deformation localization, and acquires the initiative
point of the soft rock's deformation localization and the critical point of instable failure. Meanwhile, he studies, under the condition of plane strain, the affection of the initiation and evolution of the soft rock's deformation localization according to the variations of loading speed, water content and slope angle.
(4) Adopting advanced laser digital speckle method, the author first conducts the contrasting experiments of deformation localization between the mud sandstone and muddy rock and studies the effects of loading speed on the soft rock's deformation localization under uniaxial pressure. Through a range of correlation analyses of speckle interference, and the temporal and quantitative pursuit and determination of the variation laws of the soft rock's deformation localization, he observes the whole "revolving" process of the deformation localization area of the mud sandstone and the muddy rock. Also, he determines the starting moment of localization and quantitatively surveys the width and the deformation speed of the localization area.
(5) Based on elastic-plastic constitutive model of the rocks, the author, adopting the sliding block - spring combination system, studies the mechanics model of the shear band and obtains the starting conditions of deformation localization controlled by such a mechanics model.
(6) According to the bifurcation theory of material instable failure, the author makes a theoretical study of the soft rock's deformation localization in order to d
引文
[1] 郑捷等．岩石变形局部化的实验研究[J]．地球物理学报，1983，26(6)
[2] 周维垣．高等岩石力学[M]．北京：水利电力出版社，1990
[3] Muhlaus, H.B. Shear-band analysis in granular material by Cosserat theory. Ing. Arch., Berlin, Germany, 1986(56) 389～399
[4] Aifanitis, E.C. On the microstructural origin of certain inelastic models. J. Engrg. Mater. Tech. Trans. Of ASME, 1987(106), 326～330
[5] 谢和平．岩石混凝土损伤力学[M]．徐州：中国矿业大学出版社，1990
[6] 余寿文，冯西桥．损伤力学．北京：清华大学出版社，1997
[7] Vardoulakis, I. Shear band inclination and shear modulus of sand in biaxial tests. Int. J. Numer. Anal. Methods. In Geomech., 1980(40), 103～119
[8] 尹光志等．岩石在平面应变条件下剪切带的分叉分析[J]，煤炭学报，1999，24(4)：364～367
[9] 潘一山等．岩土材料变形局部化的实验研究[J]，煤炭学报，2002，27(3)：281～284
[10] 徐永波，白以龙等．钢中剪切变形局部化的形成与发展[J]，金属学报，1995，31(11)：485～492
[11] 胡平．高分子材料平面应变拉伸变形局部化[J]，力学学报，1996，28(5)：565～574 1)
[12] 胡平．预延伸非晶聚合物材料各向异性变形局部化[J]，力学学报，1998，30(3)：354～361
[13] 蒋明镜，沈珠江．结构性粘土剪切带的微观分析[J]，岩土工程学报，1998，20(2)：102～108
[14] 张我华，煤／瓦斯突出过程中煤介质局部化破坏的损伤机理[J]，岩土工程学报，1999，21 (6)：731～736
[15] 张启辉，赵锡宏．主应力轴旋转对剪切带形成的影响分析[J]，岩土力学，2000，21(1)：32～35
[16] 徐松林等．三轴压缩大理岩局部化变形的试验研究及其分岔行为[J]，岩土工程学报，2001，23(3)：296～301
[17] 王学滨，潘一山．地质灾害中的应变局部化现象[J]，地质灾害与环境保护，2001，12(4)
[18] 王学滨，潘一山等．岩体假三轴压缩及变形局部化剪切带数值模拟[J]，岩土力学，2001，22(3)，323～326
[19] 潘一山，杨小彬．岩土材料变形局部化的实验研究[J]，煤炭学报，2002，27(3)：281～284
[20] 赵吉东，周维垣．基于应变梯度的损伤局部化研究及应用[J]，力学学报 2002，3
[21] Piertuszczak S, Niu X. On the descriptio of localized deformation[J]. Int J Numer Analyt Meth Geomech, 1993, 17: 791-805.
[22] 黄茂松，钱建固，吴世明．饱和土体应变局部化的复合体理论[J]，土工程学报，2002，24(1)：21～25
[23] 李国琛，耶那．塑性大变形微结构力学[M]，北京：科学出版社，1993
[24] 李国琛．剪切带状分叉的力学条件[J]，力学学报，1988，20(4)
[25] 李国琛．韧性材料的剪切带状分叉[J]，力学学报，1987，19(1)
[26] 张启辉，赵锡宏．主应力轴旋转对剪切带形成的影响分析[J]，岩土力学，2000，21(1)：32～35
[27] 孙红，赵锡宏．软土的损伤对剪切带形成的影响[J]，同济大学学报，2001，29(3)：278～282
[28] 冯吉利，韩国城．损伤剪切带的稳定状态与路径——大变形非局部化分析[J]，大连理工大学学报，1996，7，483～487
[29] 李蓓，赵锡宏等．上海粘性土剪切带倾角的试验研究[J]，岩土力学，2002，23(4)：424～427
[30] 黄克智．损伤与断裂[M]．见：王仁，黄克智，朱兆祥主编．塑性力学进展．铁道出版社，1988
[31] 李国琛等．材料分叉的数值分析[J]，力学学报，1996，28(2)：165～170
[32] 李国琛．非均匀性对材料分叉的作用[J]，固体力学学报，1996，17(2)：135～139
[33] 尚新春，程昌钧．超弹性材料中的球形空穴分叉[J]，第28卷第6期1996年11月752～755 1)
[34] 尹光志等．岩石在平面应变条件下剪切带的分叉分析[J]，煤炭学报，1999，24(4)：364～367
[35] 尹光志，鲜学福．岩石细观断裂过程的分叉与混沌特征[J]，重庆大学学报，2000，23(2)：56～59
[36] 张永强，俞茂宏．金属材料的平面应力非连续分叉[J]，机械工程学报，2001，37(4)：83～88
[37] 张永强，俞茂宏．弹塑性材料的平面应力非连续分岔[J]，力学学报，2001，33(5)：706～713
[38] 陈忠辉，唐春安等．岩石微破裂损伤演化诱致突变的数值模拟[J]，岩土工程学报，1998，20 (6)
[39] 黄克智．损伤与断裂[M]．见：王仁，黄克智，朱兆祥主编．塑性力学进展．铁道出版社，1988，31～36．
[40] 李灏．损伤力学基础[M]．山东科学技术出版社，1992
[41] Dougill J.W., Lau J.C. and Burt N.J. Mechanics in Engineering[J], ASCE, EMD, 1976, 333～355
[42] 卢应发，葛修润．岩石损伤本构理论[J]．岩土力学，1989，10(2)：67～71
[43] 孙红，赵锡宏．软土的弹塑性各向异性损伤分析[J]，岩土力学，1999，20(3)：7～12
[44] 赵爱红，虞吉林．准脆性材料的细观损伤演化模型[J]，清华大学学报(自然科学版)，2000，40(5)：88～91
[45] 杨小林，王树仁．岩石爆破损伤断裂的细观机理[J]，爆炸与冲击，2000，20(3)：247～252
[46] 李浩，郭应桐．岩石在复杂荷载下的细观损伤模型[J]，岩土力学，2001，22(2)：159～162
[47] 孙红，赵锡宏．软土初始损伤门槛值的真三轴试验研究[J]，水利学报，2002，7：93～97，
[48] 孙红，赵锡宏．各向异性损伤对土压力强度的影响分析[J]，同济大学学报，2002，30(8)
[49] 叶黔元．岩石的内时损伤本构模型[C]，见：袁建新主编，第四届全国岩土力学数值分析与解析方法讨论会论文集，武汉：武汉测绘科技大学出版社，1991，85～90
[50] Hill R, Hutchinson J.W., Bifurcation phenomena in the plane tension test[J], J Mech. Phys.
Solids, 1975 (23) 239-264
[51] Yatomi C, Yashima A, Sano I. General theory of shear bands formation by a non coaxial Camclay model[J]. soil and Foundations, 1989, 29(3): 41-53.
[52] Marsal R.J., Large scale testing of rockfill materials, J. Soil Mech. Fdn Engng Div. Am. Soc. Civ. Engrs. 93, 1967, SM2, 27-34
[53] Charles J.A., Watts K.S., The influence of confining pressure on the shear strength of compacted rockfill, Géotechnique 30, No.4, 353-367
[54] Lee Y.H., Strength and deformation characteristics of rockfill, PhD thesis, Asian Institute of Technology, Bangkok, 1986
[55] Leps T.M., Review of shearing strength of rockfill, J. Soil Mech. Fdn Engng Div. Am. Soc. Civ. Engrs 96, 1970, SM4, 1159-1170
[56] Chang C.S., Strain tensor and deformation for granular material, Journal of Engineering Mechanics, Vol.116 No.4, April. 1988, 790-804
[55] Mindlin R.D. et al, Elastic Sphere in contact under varying oblique forces, J. Appl. Mech. Engns. Vol.20 No.3, 327-344, 1953
[56] Cundall P.A., A computer model for simulating progressive large scale movements in blocky systems, Proceeding of the Symposium of the International Society of Rock Mechanics, Nancy, France, Vol.1 No.2, 1971
[57] Cundall P.A., The measurement and analysis of acceleration in rock slopes, Ph.D Dissertation, University of London, Imperial College of Science and Technology, 1971
[58] Cundall P.A., Ball-a program to model granular media using the distinct element method, Dames & Moore Advanced Technology Group, London, 1978
[59] 李伟．不连续散粒体的离散单元法[J]，南京航空航天大学学报，Vol．31 No．1，1999，85-91
[60] 蒋鹏．离散元法用于块石土强夯过程模拟[J]，岩土力学，Vol．20 No．3，1999，29-34
[61] Sia Nemat-Nasser, A micromechanically-based constitutive model for frictional deformation of granular materials, Journal of the Mechanics of Solids 48, 2000, 1541-1563
[62] Ali Daouadji, An elastoplastic model for granular materials taking into account grain breakage. Eur. J. Mech. A/Solids 20(2001), 113-117
[63] Steen Krenk, Characteristic state plasticity for granular materials, International Jour of Solids and Structures 37(2000), 9643-9360
[64] 王自强，段祝平．塑性细观力学[M]，北京：科学出版社
[65] L.Anand & W.A.Spizig, Initiation of localization shear bands in plane strain, J.Mech.Phys.Solids vol.28, 113～128
[66] A.Needleman. Non-normality and bifurcation in plane strain tension and compression,
J.Mech.Phys.Solids vol.27.231～254
[67] Vardoulakis, I., Goldscheider, M., & Gudehus, G. Formation of shear bands in sand bodies as a bifurcation problem, Int. J. Num. Anal. Meth. Geomech. 1978, Vol(2), 99～128
[68] Vardoulakis, I. Bifurcation analysis of the triaxial test on sand samples, Acta Mechanica vol32, 35～54
[69] H.B.Muhlhaus & I.Vardoulakis. The thickness of shear band in granular materials, Geoteclmique vol37, No.3, 271～283
[70] J.W.Rudnicki & J.r.Rice, Conditions for the localization of deformation in pressure-sensitive dilatant materials, J.Mech.Phys.Solids, 1975, vol23, 371～394
[71] Drescher J., Lanier J. Localization of the deformation in tests on sand sample. Engng Fracture Mech. 1985, vol21, No.4, 909～911
[72] Toupin, R.A., 1962. Elastic materials with couple stresses. Arch. Radonal Mech. Anal. 11, 385-414.
[73] Fleck, N.A. and Hutchinson, J. W. An assessment of a class of strain gradient plasticity theories. To appear in J. Mech. Phys. Solids. 2001
[74] N.A. Fleck, J.W.Hutchinson. A reformulation of swain gradient plasticity. Journal of the Mechanics and Physics of Solids. 49(2001), 2245～2271
[75] Shu, J.Y., Fleck, N.A., 1998. The prediction of a size e4ect in micro-indentation. Int. J. Solids Struet. 35, 1363-1383.
[76] Nix, W.D., Gao, H., 1998. Indentation size e4ects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411-425.
[77] Aifantis, E.C., 1984. On the microstructural origin of certain inelastic models. Trans. ASME J. Eng. Mat.Tech. 106, 326-330.
[78] Aifantis, E.C., 1999. Strain gradient interpretation of size e4ects. Int. J. Fracture 95, 299-314.
[79] Chen S, Wang T C. A new hardening law for strain gradient plasticity. Acta Mater, 2000, 48: 3997～4005
[80] Zhang Y, Huang J, Wang R. Technical note real-time SEM observation of the micro-fractureing process in during a compression test[J].Int. J. Rock mech, Min. Sci and Geomech. Abstr, 1993, 30(6): 643～652
[81] Zhu, H., Zbib, H.M. and Aifantis, E.C., On the Effect of Anisotropy and Inertia on ShearBanding: Stability of Biaxial Stretching, ASME J. Appl. Mech. Rev, 1992, 45, 110-117, .
[82] R. de Borst and H.B. Muhlhaus, Gradient-dependent plasticity: Formulation and algorithmic aspects, International Journal for Numerical Methods in Engineering 35 (1992) 521～539.
[83] Tejchman, J., Bauer, E., Numerical simulation of shear band formation with a polar hypoplastic
constitutive model. Computers and Geotechnics, Vol. 19, 1996, No. 3, 221-244.
[84] Y.Berthaud, S.Calloch, F.Collin, F.Hild et, Analysis of the degradation mechanisms in Composite Materials through a Correlation Technique in White Light.In Advanced Optical Methods and Applications in Solid Mechanics, A.Lagarde(Edt.), Kluwer, Dordrecht(Pays Bas), pp.627～634
[85] Hettler A. and Vardoulakis I.(1984). Behavior of dry sand tested in a large triaxial apparatus. Geotechnique, 34, 183-198.
[86] 尹光志．砚石台煤矿特殊动力现象定性分析及定量指标与防治措施研究报告，重庆：重庆大学，1995
[87] 纪连帮．用激光散斑测金属的杨氏模量[J]，长春光学精密机械学院学报，1989．012(2)．74～78
[88] 张晶瑶，朱林．激光散斑法对岩柱变形规律的探讨[J]，金属矿山，1990．019(005)，28-30
[89] 张晶瑶，激光散斑法测岩石悬臂梁的位移[J] 有色矿冶．1994．010(003)．1-5
[90] 吴瑞琪，杨光群．用激光散斑法研究岩土力学性质[J] 成都科技大学学报．1991．000(001)．39-44
[91] 王淑琴，魏恩生．用激光散斑法测量碳复合材料的弹性模量[J] 无损检测．1992．014(009) 249-251
[92] 谢和平．岩土介质的分形孔隙和分形粒子[J]．力学进展，1993，23(2)：145～164
[93] 谢和平．分形力学研究进展[J]．力学与实践，1996，18(2)：10～18
[94] 董聪，何庆芝．微裂纹演化过程中分岔与混沌现象的描述及若干问题探讨[J]．力学进展，1994，24(1)：106～116
[95] 王金龙，林卓英，吴玉山，袁建新．脆性岩石的损伤与裂隙扩展[J]．岩土力学，1990，11(3)：1～8
[96] 李庆斌，郝军保．岩石三轴损伤本构模型[C]．见：朱维申编．中国青年学者岩土工程力学及其应用讨论会论文集，北京：科学出版社．1994，149～155
[97] 周光泉，陈德华，席道联．岩石连续损伤本构方程[J]．岩石力学与工程学报，1995，1(3)：229～235
[98] 李广平，陶振宇．真三轴条件下的岩石细观损伤力学模型[J]，岩土工程学报，1995，17(1)：24～31
[99] 吴政，张承娟．单向荷载作用下岩石损伤模型及其力学特性研究[J]．岩石力学与工程学报，1996，15(1)，55～61
[100] 李皓．岩石细观损伤理论及其力学过程模型的研究[博士学位论文] [D]．武汉：武汉水利电力大学，1997
[101] 杨友卿．岩石强度的损伤力学分析．岩石力学与工程学报[J]，1999，18(1)：23～27
[102] 朱建明，徐秉业，任天贵等．基于三轴压缩试验的破裂岩损伤演化方程的建立[J]．工程地质学报，2000，8(2)：175～179
[103] 刘立等．复合岩石损伤本构方程与实验[J]．重庆大学学报(自然科学版)，2000，23(3)：57～60
[104] 吴玉山．大理岩卸载力学特性的研究[J]，岩土力学．1984，5(1)：28～36
[105] 陈忠辉等．岩石破裂声发射过程的围压效应[J]．岩石力学与工程学报，1997，16(2)：65～70
[106] 肖洪天，周维垣，杨若琼．岩石裂纹流变扩展的细观机理分析[J]．岩石力学与工程学报，1999，18(6)：623～626
[2] 周维垣．高等岩石力学[M]．北京：水利电力出版社，1990
[3] Muhlaus, H.B. Shear-band analysis in granular material by Cosserat theory. Ing. Arch., Berlin, Germany, 1986(56) 389～399
[4] Aifanitis, E.C. On the microstructural origin of certain inelastic models. J. Engrg. Mater. Tech. Trans. Of ASME, 1987(106), 326～330
[5] 谢和平．岩石混凝土损伤力学[M]．徐州：中国矿业大学出版社，1990
[6] 余寿文，冯西桥．损伤力学．北京：清华大学出版社，1997
[7] Vardoulakis, I. Shear band inclination and shear modulus of sand in biaxial tests. Int. J. Numer. Anal. Methods. In Geomech., 1980(40), 103～119
[8] 尹光志等．岩石在平面应变条件下剪切带的分叉分析[J]，煤炭学报，1999，24(4)：364～367
[9] 潘一山等．岩土材料变形局部化的实验研究[J]，煤炭学报，2002，27(3)：281～284
[10] 徐永波，白以龙等．钢中剪切变形局部化的形成与发展[J]，金属学报，1995，31(11)：485～492
[11] 胡平．高分子材料平面应变拉伸变形局部化[J]，力学学报，1996，28(5)：565～574 1)
[12] 胡平．预延伸非晶聚合物材料各向异性变形局部化[J]，力学学报，1998，30(3)：354～361
[13] 蒋明镜，沈珠江．结构性粘土剪切带的微观分析[J]，岩土工程学报，1998，20(2)：102～108
[14] 张我华，煤／瓦斯突出过程中煤介质局部化破坏的损伤机理[J]，岩土工程学报，1999，21 (6)：731～736
[15] 张启辉，赵锡宏．主应力轴旋转对剪切带形成的影响分析[J]，岩土力学，2000，21(1)：32～35
[16] 徐松林等．三轴压缩大理岩局部化变形的试验研究及其分岔行为[J]，岩土工程学报，2001，23(3)：296～301
[17] 王学滨，潘一山．地质灾害中的应变局部化现象[J]，地质灾害与环境保护，2001，12(4)
[18] 王学滨，潘一山等．岩体假三轴压缩及变形局部化剪切带数值模拟[J]，岩土力学，2001，22(3)，323～326
[19] 潘一山，杨小彬．岩土材料变形局部化的实验研究[J]，煤炭学报，2002，27(3)：281～284
[20] 赵吉东，周维垣．基于应变梯度的损伤局部化研究及应用[J]，力学学报 2002，3
[21] Piertuszczak S, Niu X. On the descriptio of localized deformation[J]. Int J Numer Analyt Meth Geomech, 1993, 17: 791-805.
[22] 黄茂松，钱建固，吴世明．饱和土体应变局部化的复合体理论[J]，土工程学报，2002，24(1)：21～25
[23] 李国琛，耶那．塑性大变形微结构力学[M]，北京：科学出版社，1993
[24] 李国琛．剪切带状分叉的力学条件[J]，力学学报，1988，20(4)
[25] 李国琛．韧性材料的剪切带状分叉[J]，力学学报，1987，19(1)
[26] 张启辉，赵锡宏．主应力轴旋转对剪切带形成的影响分析[J]，岩土力学，2000，21(1)：32～35
[27] 孙红，赵锡宏．软土的损伤对剪切带形成的影响[J]，同济大学学报，2001，29(3)：278～282
[28] 冯吉利，韩国城．损伤剪切带的稳定状态与路径——大变形非局部化分析[J]，大连理工大学学报，1996，7，483～487
[29] 李蓓，赵锡宏等．上海粘性土剪切带倾角的试验研究[J]，岩土力学，2002，23(4)：424～427
[30] 黄克智．损伤与断裂[M]．见：王仁，黄克智，朱兆祥主编．塑性力学进展．铁道出版社，1988
[31] 李国琛等．材料分叉的数值分析[J]，力学学报，1996，28(2)：165～170
[32] 李国琛．非均匀性对材料分叉的作用[J]，固体力学学报，1996，17(2)：135～139
[33] 尚新春，程昌钧．超弹性材料中的球形空穴分叉[J]，第28卷第6期1996年11月752～755 1)
[34] 尹光志等．岩石在平面应变条件下剪切带的分叉分析[J]，煤炭学报，1999，24(4)：364～367
[35] 尹光志，鲜学福．岩石细观断裂过程的分叉与混沌特征[J]，重庆大学学报，2000，23(2)：56～59
[36] 张永强，俞茂宏．金属材料的平面应力非连续分叉[J]，机械工程学报，2001，37(4)：83～88
[37] 张永强，俞茂宏．弹塑性材料的平面应力非连续分岔[J]，力学学报，2001，33(5)：706～713
[38] 陈忠辉，唐春安等．岩石微破裂损伤演化诱致突变的数值模拟[J]，岩土工程学报，1998，20 (6)
[39] 黄克智．损伤与断裂[M]．见：王仁，黄克智，朱兆祥主编．塑性力学进展．铁道出版社，1988，31～36．
[40] 李灏．损伤力学基础[M]．山东科学技术出版社，1992
[41] Dougill J.W., Lau J.C. and Burt N.J. Mechanics in Engineering[J], ASCE, EMD, 1976, 333～355
[42] 卢应发，葛修润．岩石损伤本构理论[J]．岩土力学，1989，10(2)：67～71
[43] 孙红，赵锡宏．软土的弹塑性各向异性损伤分析[J]，岩土力学，1999，20(3)：7～12
[44] 赵爱红，虞吉林．准脆性材料的细观损伤演化模型[J]，清华大学学报(自然科学版)，2000，40(5)：88～91
[45] 杨小林，王树仁．岩石爆破损伤断裂的细观机理[J]，爆炸与冲击，2000，20(3)：247～252
[46] 李浩，郭应桐．岩石在复杂荷载下的细观损伤模型[J]，岩土力学，2001，22(2)：159～162
[47] 孙红，赵锡宏．软土初始损伤门槛值的真三轴试验研究[J]，水利学报，2002，7：93～97，
[48] 孙红，赵锡宏．各向异性损伤对土压力强度的影响分析[J]，同济大学学报，2002，30(8)
[49] 叶黔元．岩石的内时损伤本构模型[C]，见：袁建新主编，第四届全国岩土力学数值分析与解析方法讨论会论文集，武汉：武汉测绘科技大学出版社，1991，85～90
[50] Hill R, Hutchinson J.W., Bifurcation phenomena in the plane tension test[J], J Mech. Phys.
Solids, 1975 (23) 239-264
[51] Yatomi C, Yashima A, Sano I. General theory of shear bands formation by a non coaxial Camclay model[J]. soil and Foundations, 1989, 29(3): 41-53.
[52] Marsal R.J., Large scale testing of rockfill materials, J. Soil Mech. Fdn Engng Div. Am. Soc. Civ. Engrs. 93, 1967, SM2, 27-34
[53] Charles J.A., Watts K.S., The influence of confining pressure on the shear strength of compacted rockfill, Géotechnique 30, No.4, 353-367
[54] Lee Y.H., Strength and deformation characteristics of rockfill, PhD thesis, Asian Institute of Technology, Bangkok, 1986
[55] Leps T.M., Review of shearing strength of rockfill, J. Soil Mech. Fdn Engng Div. Am. Soc. Civ. Engrs 96, 1970, SM4, 1159-1170
[56] Chang C.S., Strain tensor and deformation for granular material, Journal of Engineering Mechanics, Vol.116 No.4, April. 1988, 790-804
[55] Mindlin R.D. et al, Elastic Sphere in contact under varying oblique forces, J. Appl. Mech. Engns. Vol.20 No.3, 327-344, 1953
[56] Cundall P.A., A computer model for simulating progressive large scale movements in blocky systems, Proceeding of the Symposium of the International Society of Rock Mechanics, Nancy, France, Vol.1 No.2, 1971
[57] Cundall P.A., The measurement and analysis of acceleration in rock slopes, Ph.D Dissertation, University of London, Imperial College of Science and Technology, 1971
[58] Cundall P.A., Ball-a program to model granular media using the distinct element method, Dames & Moore Advanced Technology Group, London, 1978
[59] 李伟．不连续散粒体的离散单元法[J]，南京航空航天大学学报，Vol．31 No．1，1999，85-91
[60] 蒋鹏．离散元法用于块石土强夯过程模拟[J]，岩土力学，Vol．20 No．3，1999，29-34
[61] Sia Nemat-Nasser, A micromechanically-based constitutive model for frictional deformation of granular materials, Journal of the Mechanics of Solids 48, 2000, 1541-1563
[62] Ali Daouadji, An elastoplastic model for granular materials taking into account grain breakage. Eur. J. Mech. A/Solids 20(2001), 113-117
[63] Steen Krenk, Characteristic state plasticity for granular materials, International Jour of Solids and Structures 37(2000), 9643-9360
[64] 王自强，段祝平．塑性细观力学[M]，北京：科学出版社
[65] L.Anand & W.A.Spizig, Initiation of localization shear bands in plane strain, J.Mech.Phys.Solids vol.28, 113～128
[66] A.Needleman. Non-normality and bifurcation in plane strain tension and compression,
J.Mech.Phys.Solids vol.27.231～254
[67] Vardoulakis, I., Goldscheider, M., & Gudehus, G. Formation of shear bands in sand bodies as a bifurcation problem, Int. J. Num. Anal. Meth. Geomech. 1978, Vol(2), 99～128
[68] Vardoulakis, I. Bifurcation analysis of the triaxial test on sand samples, Acta Mechanica vol32, 35～54
[69] H.B.Muhlhaus & I.Vardoulakis. The thickness of shear band in granular materials, Geoteclmique vol37, No.3, 271～283
[70] J.W.Rudnicki & J.r.Rice, Conditions for the localization of deformation in pressure-sensitive dilatant materials, J.Mech.Phys.Solids, 1975, vol23, 371～394
[71] Drescher J., Lanier J. Localization of the deformation in tests on sand sample. Engng Fracture Mech. 1985, vol21, No.4, 909～911
[72] Toupin, R.A., 1962. Elastic materials with couple stresses. Arch. Radonal Mech. Anal. 11, 385-414.
[73] Fleck, N.A. and Hutchinson, J. W. An assessment of a class of strain gradient plasticity theories. To appear in J. Mech. Phys. Solids. 2001
[74] N.A. Fleck, J.W.Hutchinson. A reformulation of swain gradient plasticity. Journal of the Mechanics and Physics of Solids. 49(2001), 2245～2271
[75] Shu, J.Y., Fleck, N.A., 1998. The prediction of a size e4ect in micro-indentation. Int. J. Solids Struet. 35, 1363-1383.
[76] Nix, W.D., Gao, H., 1998. Indentation size e4ects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411-425.
[77] Aifantis, E.C., 1984. On the microstructural origin of certain inelastic models. Trans. ASME J. Eng. Mat.Tech. 106, 326-330.
[78] Aifantis, E.C., 1999. Strain gradient interpretation of size e4ects. Int. J. Fracture 95, 299-314.
[79] Chen S, Wang T C. A new hardening law for strain gradient plasticity. Acta Mater, 2000, 48: 3997～4005
[80] Zhang Y, Huang J, Wang R. Technical note real-time SEM observation of the micro-fractureing process in during a compression test[J].Int. J. Rock mech, Min. Sci and Geomech. Abstr, 1993, 30(6): 643～652
[81] Zhu, H., Zbib, H.M. and Aifantis, E.C., On the Effect of Anisotropy and Inertia on ShearBanding: Stability of Biaxial Stretching, ASME J. Appl. Mech. Rev, 1992, 45, 110-117, .
[82] R. de Borst and H.B. Muhlhaus, Gradient-dependent plasticity: Formulation and algorithmic aspects, International Journal for Numerical Methods in Engineering 35 (1992) 521～539.
[83] Tejchman, J., Bauer, E., Numerical simulation of shear band formation with a polar hypoplastic
constitutive model. Computers and Geotechnics, Vol. 19, 1996, No. 3, 221-244.
[84] Y.Berthaud, S.Calloch, F.Collin, F.Hild et, Analysis of the degradation mechanisms in Composite Materials through a Correlation Technique in White Light.In Advanced Optical Methods and Applications in Solid Mechanics, A.Lagarde(Edt.), Kluwer, Dordrecht(Pays Bas), pp.627～634
[85] Hettler A. and Vardoulakis I.(1984). Behavior of dry sand tested in a large triaxial apparatus. Geotechnique, 34, 183-198.
[86] 尹光志．砚石台煤矿特殊动力现象定性分析及定量指标与防治措施研究报告，重庆：重庆大学，1995
[87] 纪连帮．用激光散斑测金属的杨氏模量[J]，长春光学精密机械学院学报，1989．012(2)．74～78
[88] 张晶瑶，朱林．激光散斑法对岩柱变形规律的探讨[J]，金属矿山，1990．019(005)，28-30
[89] 张晶瑶，激光散斑法测岩石悬臂梁的位移[J] 有色矿冶．1994．010(003)．1-5
[90] 吴瑞琪，杨光群．用激光散斑法研究岩土力学性质[J] 成都科技大学学报．1991．000(001)．39-44
[91] 王淑琴，魏恩生．用激光散斑法测量碳复合材料的弹性模量[J] 无损检测．1992．014(009) 249-251
[92] 谢和平．岩土介质的分形孔隙和分形粒子[J]．力学进展，1993，23(2)：145～164
[93] 谢和平．分形力学研究进展[J]．力学与实践，1996，18(2)：10～18
[94] 董聪，何庆芝．微裂纹演化过程中分岔与混沌现象的描述及若干问题探讨[J]．力学进展，1994，24(1)：106～116
[95] 王金龙，林卓英，吴玉山，袁建新．脆性岩石的损伤与裂隙扩展[J]．岩土力学，1990，11(3)：1～8
[96] 李庆斌，郝军保．岩石三轴损伤本构模型[C]．见：朱维申编．中国青年学者岩土工程力学及其应用讨论会论文集，北京：科学出版社．1994，149～155
[97] 周光泉，陈德华，席道联．岩石连续损伤本构方程[J]．岩石力学与工程学报，1995，1(3)：229～235
[98] 李广平，陶振宇．真三轴条件下的岩石细观损伤力学模型[J]，岩土工程学报，1995，17(1)：24～31
[99] 吴政，张承娟．单向荷载作用下岩石损伤模型及其力学特性研究[J]．岩石力学与工程学报，1996，15(1)，55～61
[100] 李皓．岩石细观损伤理论及其力学过程模型的研究[博士学位论文] [D]．武汉：武汉水利电力大学，1997
[101] 杨友卿．岩石强度的损伤力学分析．岩石力学与工程学报[J]，1999，18(1)：23～27
[102] 朱建明，徐秉业，任天贵等．基于三轴压缩试验的破裂岩损伤演化方程的建立[J]．工程地质学报，2000，8(2)：175～179
[103] 刘立等．复合岩石损伤本构方程与实验[J]．重庆大学学报(自然科学版)，2000，23(3)：57～60
[104] 吴玉山．大理岩卸载力学特性的研究[J]，岩土力学．1984，5(1)：28～36
[105] 陈忠辉等．岩石破裂声发射过程的围压效应[J]．岩石力学与工程学报，1997，16(2)：65～70
[106] 肖洪天，周维垣，杨若琼．岩石裂纹流变扩展的细观机理分析[J]．岩石力学与工程学报，1999，18(6)：623～626