土的细观损伤本构模型
|
摘要
基于连续损伤力学所建立的损伤模型,只求预计的宏观力学行为符合某种实验结果,而不细察损伤的细观物理与力学过程,因而其适用性受到较大的限制。目前对土的细观损伤研究,仅停留对CT扫描试验中所观测到的现象进行描述和结果的简单归纳上,未能有效地将这些试验现象和成果纳入到土的本构模型中。
本文尝试将土的细观损伤机制与唯象损伤理论结合起来,为此,在以下两个方面进行了有益的探索:
(1)认为土体骨架在损伤阶段是由完好骨架和破损骨架两相材料组成的复合体,完好骨架的破损遵循Mohr-Coulomb准则,根据应力圆与破损强度包络线的相对位置,计算出破损骨架的体积分数;视完好骨架为复合体中的完善联结夹杂,视破损骨架为复合体中的非完善联结夹杂,运用细观力学中的夹杂理论,给出了求解复合体剪切模量的非线性方程组。与试验结果的对比表明,本文提出的细观力学模型能较好地反映无明显剪胀的土的剪切变形行为。可以适用于复杂应力状态和复杂的应力路径。
(2)在工程荷载范围内,忽略骨架颗粒的变形,认为土体骨架的变形是颗粒接触面变形的总和,并且在围压不变的条件下,骨架变形的非线性是源于颗粒接触面之间的滑动。不同的应力水平,会导致不同取向范围内的接触面产生滑动。假定颗粒接触面的滑动遵循Mohr-Coulomb准则,根据应力圆与颗粒滑动包络线的相对位置,计算出该应力状态下滑动接触面的取向范围;并将该取向范围的值与其所能达到的最大值(由骨架整体破坏时的应力圆计算得到)定义为损伤比,然后按照两种接触面的剪切模量进行加权平均得到复合体的剪切模量。复合体的体积变形由两个部分组成,一部分与体积应力相关,另一部分由塑性剪应变引起。选取了排水剪胀砂土和不排水粘土在不同围压,不同固结方式、多种应力路径下的试验数据,验证本文所提出的基于颗粒细观滑动机制的损伤模型。并归纳了损伤比与剪应力、应力比、本文提出的广义应力比之间的关联,结果发现本文提出的损伤比与广义应力比之间有着一一对应的关系,即也可以用广义应力比作为描述损伤状态的参数,颗粒滑动的取向范围的比值与广义应力比只是分别从不同的角度来解释损伤状态,两者给出的结果是一致的。
Because the damage constitutive model based on continuum damage mechanics does not concern the physical mechanism of microscopic damage, it seems to only provide an estimate of the macroscopic deformation of soil and its applicability is limited to the particular stress conditions or stress paths. In the present studies for microscopic damage of soil, only the descriptions about the phenomena and the result obtained from the CT test, rather than the constitutive models that can reflect the influence of microscopic damage, are given.
This paper explores two methods to establish the microscopic damage constitutive model of soil:
(1) Assuming the skeleton of soil is composed of perfect skeleton and damage skeleton in the damage deformation phase, and the conversion from perfect skeleton to damage skeleton obeys Mohr-Coulomb law, a calculation of the volume fraction of damage skeleton is conducted according to the relative distance from the stress circle to the initial damage line. Regarding the perfect skeleton as perfectly bonded impurity and the damage skeleton as imperfectly bonded impurity, the nonlinear functions for calculating the composing modulus are obtained by using micromechanics method. To evaluate the performance of the proposed constitutive model, comparisons between simulated deformation and the actual deformation were conducted. The consequence indicates that the proposed micromechanics model was capable of simulating the nonlinear shear deformation behavior for the soil which has not significant amount of shear dilation.
(2) A hypothesis that the skeleton deformation is only the deformation of the interfaces of grains, and the deformation characteristics including nonlinearity, plastic deformation and shear dilation are controlled by the sliding of interfaces of grains within soil skeleton, is presented in this paper. According to the relative distance from the stress circle to the initial sliding envelope line, direction-range value of the sliding interfaces can be determined. The damage ratio is defined as the ratio of the previous direction-range values to its maximum value (determined by failure stress circle). The overall shear modulus is the weighting average of the perfect contact shear modulus and sliding contact shear modulus. The volumetric strain is made up of two parts: the one induced by hydrostatic stress, the other one induced by plastic shear strain. Test on the versatility of the proposed damage model based on the micro-sliding mechanism, including varying hydrostatic stresses, consolidation methods and stress paths, indicate that the proposed micro-sliding damage model is capable of describing deformation characteristics for various conditions. In addition, the relations between damage ration and shear stress, stress ratio and generalized stress ratio proposed in this paper are illustrated and compared. The result reveals that the damage ration has a one-to-one relation with the generalized stress ratio, namely, the generalized stress ratio proposed in this paper can be also used to describe the damage state.
本文尝试将土的细观损伤机制与唯象损伤理论结合起来,为此,在以下两个方面进行了有益的探索:
(1)认为土体骨架在损伤阶段是由完好骨架和破损骨架两相材料组成的复合体,完好骨架的破损遵循Mohr-Coulomb准则,根据应力圆与破损强度包络线的相对位置,计算出破损骨架的体积分数;视完好骨架为复合体中的完善联结夹杂,视破损骨架为复合体中的非完善联结夹杂,运用细观力学中的夹杂理论,给出了求解复合体剪切模量的非线性方程组。与试验结果的对比表明,本文提出的细观力学模型能较好地反映无明显剪胀的土的剪切变形行为。可以适用于复杂应力状态和复杂的应力路径。
(2)在工程荷载范围内,忽略骨架颗粒的变形,认为土体骨架的变形是颗粒接触面变形的总和,并且在围压不变的条件下,骨架变形的非线性是源于颗粒接触面之间的滑动。不同的应力水平,会导致不同取向范围内的接触面产生滑动。假定颗粒接触面的滑动遵循Mohr-Coulomb准则,根据应力圆与颗粒滑动包络线的相对位置,计算出该应力状态下滑动接触面的取向范围;并将该取向范围的值与其所能达到的最大值(由骨架整体破坏时的应力圆计算得到)定义为损伤比,然后按照两种接触面的剪切模量进行加权平均得到复合体的剪切模量。复合体的体积变形由两个部分组成,一部分与体积应力相关,另一部分由塑性剪应变引起。选取了排水剪胀砂土和不排水粘土在不同围压,不同固结方式、多种应力路径下的试验数据,验证本文所提出的基于颗粒细观滑动机制的损伤模型。并归纳了损伤比与剪应力、应力比、本文提出的广义应力比之间的关联,结果发现本文提出的损伤比与广义应力比之间有着一一对应的关系,即也可以用广义应力比作为描述损伤状态的参数,颗粒滑动的取向范围的比值与广义应力比只是分别从不同的角度来解释损伤状态,两者给出的结果是一致的。
Because the damage constitutive model based on continuum damage mechanics does not concern the physical mechanism of microscopic damage, it seems to only provide an estimate of the macroscopic deformation of soil and its applicability is limited to the particular stress conditions or stress paths. In the present studies for microscopic damage of soil, only the descriptions about the phenomena and the result obtained from the CT test, rather than the constitutive models that can reflect the influence of microscopic damage, are given.
This paper explores two methods to establish the microscopic damage constitutive model of soil:
(1) Assuming the skeleton of soil is composed of perfect skeleton and damage skeleton in the damage deformation phase, and the conversion from perfect skeleton to damage skeleton obeys Mohr-Coulomb law, a calculation of the volume fraction of damage skeleton is conducted according to the relative distance from the stress circle to the initial damage line. Regarding the perfect skeleton as perfectly bonded impurity and the damage skeleton as imperfectly bonded impurity, the nonlinear functions for calculating the composing modulus are obtained by using micromechanics method. To evaluate the performance of the proposed constitutive model, comparisons between simulated deformation and the actual deformation were conducted. The consequence indicates that the proposed micromechanics model was capable of simulating the nonlinear shear deformation behavior for the soil which has not significant amount of shear dilation.
(2) A hypothesis that the skeleton deformation is only the deformation of the interfaces of grains, and the deformation characteristics including nonlinearity, plastic deformation and shear dilation are controlled by the sliding of interfaces of grains within soil skeleton, is presented in this paper. According to the relative distance from the stress circle to the initial sliding envelope line, direction-range value of the sliding interfaces can be determined. The damage ratio is defined as the ratio of the previous direction-range values to its maximum value (determined by failure stress circle). The overall shear modulus is the weighting average of the perfect contact shear modulus and sliding contact shear modulus. The volumetric strain is made up of two parts: the one induced by hydrostatic stress, the other one induced by plastic shear strain. Test on the versatility of the proposed damage model based on the micro-sliding mechanism, including varying hydrostatic stresses, consolidation methods and stress paths, indicate that the proposed micro-sliding damage model is capable of describing deformation characteristics for various conditions. In addition, the relations between damage ration and shear stress, stress ratio and generalized stress ratio proposed in this paper are illustrated and compared. The result reveals that the damage ration has a one-to-one relation with the generalized stress ratio, namely, the generalized stress ratio proposed in this paper can be also used to describe the damage state.
引文
[1] Colliat-Dangus J L, Desrues J, Foray P. Triaxial testing of granular soil under elevated cell pressure. In: Donaghe R T, Chaney R C, Silver M L, ed. Advanced Triaxial Testing for Soil and Rocks. Philadelphia, 1988 STP977: 290-310
[2] Mokni M. Relations entre deformations en masse et deformations localisees dans les materiaux granulaires. Ph. D thesis, Universite J. Fourier de Grenoble, Fance, 1992
[3] Tillard-Ngan D, Desrues J, Raynaud S, et al. Strain localization in the Beaucaire marl. In: Geotechnical engineering of hard soils-soft rocks. Rotterdam: Balkema, 1992: 1679-1686
[4] Desrues J, Chambon R, Mokni M, et al. Void ratio evolution inside shear bands in triaxial and specimens studied by computed tomography. Geotechnique, 1996, 46(3): 529-546
[5] Finno R J, Harris W W, Mooney M A, et al. Shear bands in plane strain compre- ssion of loose sand. Geotechnique, 1997, 47(1): 149-165
[6] Kruse G A M, Bezuijen A. The use of CT scans to evaluate soil models. Proc. Of Centrifuge’98. Balkema, 1998: 79-84
[7] Otani J, Mukunoki T, Obara Y. Application of X-ray CT method for characteri- zation of failure in soils. Soils and Foundations, 2000, 40(2): 111-118
[8] Otani J, Mukunoki T, Obara Y. Computer methods and Advances in geomechanics. Fesai et al. ed. Balkema, Rotterdam, 2001: 977-980
[9]吴紫汪,蒲毅彬,马巍等.冻土蠕变过程体积变化的CT分析.冰川冻土, 1995. l7(增刊): 41-46
[10]马巍,吴紫汪,蒲毅彬等.冻土三轴蠕变过程中结构变化的CT勃态监测冰川冻土, 1997, 19(1): 52-57
[11]蒲毅彬,陈万业,廖全荣.陇东黄土湿陷过程的CT结构变化研究.岩土工程学报, 2000, 22(1): 49-54
[12]李晓军,张登良.路基填土单轴受压细观结构CT监测分析.岩土工程学报,2000, 22(20): 205-209
[13]沈珠江.结构性粘土的非线性损伤力学模型.水利水运科学研究, 1993, 3: 247-255
[14]沈珠江.结构性粘土的弹塑性损伤模型.岩土工程学报, 1993, 15(3)
[15]沈珠江.土体变形特性的损伤力学模拟.第五界全国岩土力学数值分析与解析方法讨论会论文集, 1994: 1-8
[16]沈珠江岩土力学理论的某些进展.江苏力学, 1994: 35-36
[17]沈珠江.土体结构性的数学模型——21世纪土力学的核心问题.岩土工程学报, 1996, 18(1): 95-97
[18] Frantziskonis G, Desai C S. Constitutive model with strain softening. Int. J. Solids, 1987, 23(6): 133-150
[19] Frantziskonis G, Desai C S. Analysis of a strain softening constitutive model. Int. J. Solids, 1987, 23(6): 751-767
[20]施建勇,赵维炳,顾吉等.考虑损伤的软土地基变形分析.岩土工程学报, 1998, 20(2): 2-5
[21]胡黎明,濮家骝.土与结构物接触面损伤本构模型.岩土力学, 2002, 3(1): 6-11
[22]沈珠江.软土工程特性和软土地基设计.岩土工程学报, 1998, 20(1): 100-111
[23]何开胜.结构性粘土的微观变形机理和弹粘塑性损伤模型研究.南京水利科学研究院博士学位论文, 2001
[24]陈铁林.结构性粘土本构模型与参数测定研究.南京水利科学研究院博士学位论文, 2001
[25] Zhang W, Valliappan S. Analysis of random anisotropic damage mechanics problems of rock mass. Part 1-probabistic simulation. Rock Mechanics and Rock Engineering, 1990, 23: 91-112
[26]刘祖德,王士恩.结构性土体破损的力学描述.土工基础, 1996, 10(3): 1-6
[27]郑永来,周澄,夏颂佑.岩土材料粘弹性连续损伤本构模型探讨.河海大学学报, 1997, 25 (2): 114-116
[28] Al-Shamrani M A, Sture S. A time-dependent bounding surface model for anisotropic cohesive soils. Soils and Foundations, 1998, 38(1): 61-67
[29]杨松岩,余茂宏.一种基于混合物理论的非饱和岩土类材料的弹塑性损伤模型,岩土工程学报, 1998, 20(5): 58-63
[30]孙红,赵锡宏.结构性软土的损伤及其对地基沉降的影响.岩土力学, 1999, 20(1): 19-21
[31]孙红,赵锡宏.软土的弹塑性各向异性损伤分析.岩土力学, 1999, 20(3): 7-12
[32] Mitchell J K. Fundamentals of Soil Behavior(Second Edition). New York: John Wiley & Sons Inc. Printed in USA, 1993
[33]黄文熙主编.土的工程性质.北京:水利水电出版社, 1983
[34]钱家欢,殷宗泽主编,土工原理与计算(第2版).北京:中国水利水电出版社, 1996
[35] G Bianchini, A Seada, P Puccini (et al). Complex Stress Paths and Validation of Constitutive Models. Geotechnical Testing Journal, 1991, 14(1): 13-25
[36]孙岳崧,濮家骝,李广信.不同应力路径对砂土应力应变关系影响.岩土工程学报, 1987, VoI. 9(6): 78-87
[37] Duncan J M, Chang C Y. Nonlinear analysis of stress and strain in soils. Proc. ASCE, JSMFD 1970, 96(SM5): 1629-1633
[38] Domaschuk, L. and Valliappan, P. ( 1975 ), Nonlinear settlement analysis by finite element, Journal of Geotechnical Engineering Div. ASCE. 101 (GT7), July
[39]李广信,高等土力学.北京:清华大学出版社, 2004
[40]沈珠江,理论土力学.北京:中国水利水电出版社, 2000
[41] Lade P V, Duncan J M. Elasto-plastic stress-strain theory for cohesionless soils. Proc ASCE, JGTD, 1975, 10l(GT10): 1037-1053
[42] Lade P V, Duncan J M. Elasto-plastic stress-strain theory for cohesionless solils with curved yield surface. Int. J. solidsand structure, 1977, 13(11): 1019-1035
[43]黄文熙,濮家骝,陈愈炯.土的硬化规律和屈服函数.岩土工程学报, 1981, 3(3): 19-26
[44] Roscoe K. H. and Burland J. B.. On the Generalized stress strain Behavior of“wet”Clay, Engineering Plasticity. Ed, by J. Hoyman and F. A. Leekie, Cambridge Univ. Press, 1968
[45] Roscoe K. H. and Schofield A. W.. Mechanical behavior of an idealized“wet”c1ay, Proc, 2nd European Conference on soil Mech. And Foundation Eng. 1, 1963
[46] Roscoe K. H. , Schofield A. N. and Thurairajah. Yielding of clays in states wetter than critical, Geotechnique, 1963,13
[47] Roscoe K. H. , Schofield A. N. and Wroth C. P.. On the Yielding of soils, Geotechnique, 1958, 8(1)
[48] Desai C S, Toth J. Disturbed state constitutive modeling based on stress-strain and nondestructive behavior [J] . International Journal of Solids and Structures, 1996, 33(11): 1619-1650
[49] Nemat-Nasser S and Hori M. Micromechanics: Overall properties of heterogeneous materials. Elsevier. The Netherlands, 1993
[50] Tvergaard V. Material Failure by Void Growth to Coalescence. The Danish Center for Applied Mathematics and Mechanics, Report No. S45, The Technical University of Denmark, 1988
[51] Gilormini P. Licht C and Suquet P. Growth of voids in a ductile matrix: a review. Arch. Mech, 1988, 400: 43-80
[52] Krajcinovic D. Damage mechanics. Mech. Mater, 1989, 8, 117-197
[53] Yang W and Lee W. B. Mesoplasticity and its Applications. Springer-Verlag, Berlin, 1993
[54] Kachanov M. Effective elastic properties of crack solids, critical review of some basic concepts. Appl. Mech. Review, 1992, 45(7): 304-335
[55] Bazant Z P. Mechanics of distributed cracking. Appl. Mech. Review, 1986, 39(1): 675-705
[56]冯西桥.脆性材料的细观损伤理论和损伤结构的安定分析.清华大学博士学位论文, 1995
[57] Eshelby, J. D.: The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Roc. Soc. , A24, 1957: 376-396
[58] Eshelby, J. D.: The elastic field outside an ellipsoidal inclusion, Proc. Roc. Soc. , A252, 1959: 561-569
[59] Esh Eshelby, J. D.: Elastic inclusion and inhomogeneities, in Progress in solid Mechanics 2, eds. Sneddon, 1. N. and Hill, R. , North-Holland, Amsterdam, 1961:222-246
[60] Mura, T.: Micromechanics of defects in solids, Martinus Nijhoff, Dordrecht, 1987
[61] Routh, E. J.: Theorems on the attraction of ellipsoids for certain laws of force other than the inverse space, Phil. Trans. Roy. Soc., 186-Ⅱ, 1895: 897-950
[62]仲政,杨卫,黄克智.考虑晶界滑动的多晶体塑性大变形本构关系.塑性力学和细观力学文集[M].北京大学出版社, 1993
[63] Christensen R M and Lo K H. Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids, 1979, 27: 315-330
[64] Aboudi J and Benvensite Y. The effective moduli of cracked bodies in phase deformations. Eng. Fract. Mech. , 1987, 26: 171-184
[65] Huang Y. Hu K and Chandra A. A generalized self-consistent mechanics method for microcracked solids. J. Mech. Phys. Solids, 1994, 42(8): 1273-1291
[66] Hashin Z. The differential scheme and its application to cracked materials. J. Mech. Phys. Solids, 1988, 36: 719-734
[67] Budiansky B and O’Connell R J. Elastic moduli of a cracked solids. Int. J. Solid Struct. , 1976, 12(1): 81-95
[68] Benvensite Y. On the Mori-Tanaka’s method in cracked solids. Mech. Res. Comm. , 1986, 13(4): 193-201
[69] Krajcinovic D. Constitutive Theories for Solids with Defective Micro-structure, Damage Mechanics and Continuum Modeling. Stubks N, Krajcinovic D eds. New York: ASCE, 1985: 39-56
[70] Krajcinovic D, Sumaral D. A Mecsomechanical Model for Brittle Deformation Processes: Part I and PartⅡ, ASME J Appl. Mech. , 1989, 56: 51-62
[71] Krajcinovic D, Basista M, Sumaral D. Micromechnically Inspired Phenomenological Damage Model, ASME J Appl. Mech. , 1991, 58: 305-310
[72] Hult] . Effect of Voids on Creep Rate and Strength, Damage Mechanics and Continuum Modeling. Stubbs N, Krajcinovic Deds. New York: ASCE, 1985: 13-24
[73] Atkinson B K, Meredith P G. The Theory of Subcritical crock Growth with Applications to Minerals and Rocks. Fracture Mechanics of Rock. Atkinson B Ked.London: Academic Press, 1987: 111-166
[74]杨光松.损伤力学与复合材料损伤.北京:国防工业出版社, 1995
[75]余寿文,冯西桥编著.损伤力学,北京:清华大学出版社, 1997
[76]余寿文.断裂损伤与细观力学.力学与实践, 1988, 10(6): 12-18
[77]吕运水,陈幸福.关于损伤张量的阶次.应用数学与力学, 1989, 10(3)
[78] Murakami S. Anisotropic Aspects of Matertal Damage and Application of Continuum Damage Mechanics, Continuum Damage Mechanics. Theory and Applications. Krajcinovic D, Lemaitre J Leds. Springer-Verlay Wien-New York, 1987: 9l-134
[79] Shen W, Peng L H, Yue Y G, Shen Z, Tang X D. Elastic Damage and Energy Dissipation in Anisotropic Sold Material Engng. Fracture Mech. , 1987, 33(2)
[80] Chen X F, Lu Y B, Lee H. AnEndochronic Plastic Theory with Anisatropic Damage, Engng. Fracture Mech. , 1989, 32(4)
[81] Tzou D Y, Chen E P. Mesocrack Damage Induced by A Macro-crack in Heterogeneous Materials. Engng. Fracture Mech. , 1991, 39(2)
[82] Dougill J W, Lau J C, Burt N J. Toward A Theoretical Model for Progressive Failure and softening in Rock, Concrete and Similar Materials. Mech in Engng. , ASCE-END, 1976: 335-355
[83] Costin L S. Time-Dependent Damage and creep of Brittle Rock. Damage Mechanics and Continuum Modeling. Stubbs N, Krajcinovic Deds. New York: ASCE, 1985: 25-38
[84]谢和平.大理岩微观断裂的分形模型研究.科学通报, 1989, 34(5)
[85]谢和平,高峰.岩石类材料损伤演化的分形特征.岩石力学与工程学报, 1991, 10(1): 1-9
[86]谢和平, D. J. Sanderson, D. C. P. Peacock.雁型断裂分形模型和能量耗散.岩土工程学报, 1994, 16(1): 1-7
[87]凌建明.节理岩体损伤力学及时效损伤特征的研究.上海:同济大学博士学位论文, 1992, 11
[88]叶黔元.岩石的内时损伤本构模型.第四届全国岩土力学数值方法与解析方法会议论文集,武汉:武汉测绘科技大学出版社, 1991: 85-90
[89]李广平,陶振字.真三轴条件下的岩石细观损伤力学模型.岩土工程学报, 1995, 17(1): 24-31
[90] Hult J, Janson J. Fracture Mechanics and Damage Mechanics-A. Combined Approach. J. Me canique Appliq ee, 1977, (1): 69-84
[91] Leglndra D, Mazars J.混凝土的损伤力学和断裂力学(一个联合方法),张彦秋译,岩石泪凝土断裂与强度, 1985(1): 51-58
[92]邢修三.脆性断裂的微观机理和非平衡统计特性.力学进展, 1986, 16(4): 495-510
[93]邢修三.损伤与断裂的统一.力学学报, 1991, 23(1): 123-127
[94] Bai Y L et al. A statistical Evolution Model from Damage to Failure Proceedings of Aop93, Beijing: 185-191
[95] Yao YP, Luo T, Sun DA. A simple 3-D constitutive model for both clay and sand. Chinese Journal of Geotechnical Engineering, 2002, 24(2): 240-246
[2] Mokni M. Relations entre deformations en masse et deformations localisees dans les materiaux granulaires. Ph. D thesis, Universite J. Fourier de Grenoble, Fance, 1992
[3] Tillard-Ngan D, Desrues J, Raynaud S, et al. Strain localization in the Beaucaire marl. In: Geotechnical engineering of hard soils-soft rocks. Rotterdam: Balkema, 1992: 1679-1686
[4] Desrues J, Chambon R, Mokni M, et al. Void ratio evolution inside shear bands in triaxial and specimens studied by computed tomography. Geotechnique, 1996, 46(3): 529-546
[5] Finno R J, Harris W W, Mooney M A, et al. Shear bands in plane strain compre- ssion of loose sand. Geotechnique, 1997, 47(1): 149-165
[6] Kruse G A M, Bezuijen A. The use of CT scans to evaluate soil models. Proc. Of Centrifuge’98. Balkema, 1998: 79-84
[7] Otani J, Mukunoki T, Obara Y. Application of X-ray CT method for characteri- zation of failure in soils. Soils and Foundations, 2000, 40(2): 111-118
[8] Otani J, Mukunoki T, Obara Y. Computer methods and Advances in geomechanics. Fesai et al. ed. Balkema, Rotterdam, 2001: 977-980
[9]吴紫汪,蒲毅彬,马巍等.冻土蠕变过程体积变化的CT分析.冰川冻土, 1995. l7(增刊): 41-46
[10]马巍,吴紫汪,蒲毅彬等.冻土三轴蠕变过程中结构变化的CT勃态监测冰川冻土, 1997, 19(1): 52-57
[11]蒲毅彬,陈万业,廖全荣.陇东黄土湿陷过程的CT结构变化研究.岩土工程学报, 2000, 22(1): 49-54
[12]李晓军,张登良.路基填土单轴受压细观结构CT监测分析.岩土工程学报,2000, 22(20): 205-209
[13]沈珠江.结构性粘土的非线性损伤力学模型.水利水运科学研究, 1993, 3: 247-255
[14]沈珠江.结构性粘土的弹塑性损伤模型.岩土工程学报, 1993, 15(3)
[15]沈珠江.土体变形特性的损伤力学模拟.第五界全国岩土力学数值分析与解析方法讨论会论文集, 1994: 1-8
[16]沈珠江岩土力学理论的某些进展.江苏力学, 1994: 35-36
[17]沈珠江.土体结构性的数学模型——21世纪土力学的核心问题.岩土工程学报, 1996, 18(1): 95-97
[18] Frantziskonis G, Desai C S. Constitutive model with strain softening. Int. J. Solids, 1987, 23(6): 133-150
[19] Frantziskonis G, Desai C S. Analysis of a strain softening constitutive model. Int. J. Solids, 1987, 23(6): 751-767
[20]施建勇,赵维炳,顾吉等.考虑损伤的软土地基变形分析.岩土工程学报, 1998, 20(2): 2-5
[21]胡黎明,濮家骝.土与结构物接触面损伤本构模型.岩土力学, 2002, 3(1): 6-11
[22]沈珠江.软土工程特性和软土地基设计.岩土工程学报, 1998, 20(1): 100-111
[23]何开胜.结构性粘土的微观变形机理和弹粘塑性损伤模型研究.南京水利科学研究院博士学位论文, 2001
[24]陈铁林.结构性粘土本构模型与参数测定研究.南京水利科学研究院博士学位论文, 2001
[25] Zhang W, Valliappan S. Analysis of random anisotropic damage mechanics problems of rock mass. Part 1-probabistic simulation. Rock Mechanics and Rock Engineering, 1990, 23: 91-112
[26]刘祖德,王士恩.结构性土体破损的力学描述.土工基础, 1996, 10(3): 1-6
[27]郑永来,周澄,夏颂佑.岩土材料粘弹性连续损伤本构模型探讨.河海大学学报, 1997, 25 (2): 114-116
[28] Al-Shamrani M A, Sture S. A time-dependent bounding surface model for anisotropic cohesive soils. Soils and Foundations, 1998, 38(1): 61-67
[29]杨松岩,余茂宏.一种基于混合物理论的非饱和岩土类材料的弹塑性损伤模型,岩土工程学报, 1998, 20(5): 58-63
[30]孙红,赵锡宏.结构性软土的损伤及其对地基沉降的影响.岩土力学, 1999, 20(1): 19-21
[31]孙红,赵锡宏.软土的弹塑性各向异性损伤分析.岩土力学, 1999, 20(3): 7-12
[32] Mitchell J K. Fundamentals of Soil Behavior(Second Edition). New York: John Wiley & Sons Inc. Printed in USA, 1993
[33]黄文熙主编.土的工程性质.北京:水利水电出版社, 1983
[34]钱家欢,殷宗泽主编,土工原理与计算(第2版).北京:中国水利水电出版社, 1996
[35] G Bianchini, A Seada, P Puccini (et al). Complex Stress Paths and Validation of Constitutive Models. Geotechnical Testing Journal, 1991, 14(1): 13-25
[36]孙岳崧,濮家骝,李广信.不同应力路径对砂土应力应变关系影响.岩土工程学报, 1987, VoI. 9(6): 78-87
[37] Duncan J M, Chang C Y. Nonlinear analysis of stress and strain in soils. Proc. ASCE, JSMFD 1970, 96(SM5): 1629-1633
[38] Domaschuk, L. and Valliappan, P. ( 1975 ), Nonlinear settlement analysis by finite element, Journal of Geotechnical Engineering Div. ASCE. 101 (GT7), July
[39]李广信,高等土力学.北京:清华大学出版社, 2004
[40]沈珠江,理论土力学.北京:中国水利水电出版社, 2000
[41] Lade P V, Duncan J M. Elasto-plastic stress-strain theory for cohesionless soils. Proc ASCE, JGTD, 1975, 10l(GT10): 1037-1053
[42] Lade P V, Duncan J M. Elasto-plastic stress-strain theory for cohesionless solils with curved yield surface. Int. J. solidsand structure, 1977, 13(11): 1019-1035
[43]黄文熙,濮家骝,陈愈炯.土的硬化规律和屈服函数.岩土工程学报, 1981, 3(3): 19-26
[44] Roscoe K. H. and Burland J. B.. On the Generalized stress strain Behavior of“wet”Clay, Engineering Plasticity. Ed, by J. Hoyman and F. A. Leekie, Cambridge Univ. Press, 1968
[45] Roscoe K. H. and Schofield A. W.. Mechanical behavior of an idealized“wet”c1ay, Proc, 2nd European Conference on soil Mech. And Foundation Eng. 1, 1963
[46] Roscoe K. H. , Schofield A. N. and Thurairajah. Yielding of clays in states wetter than critical, Geotechnique, 1963,13
[47] Roscoe K. H. , Schofield A. N. and Wroth C. P.. On the Yielding of soils, Geotechnique, 1958, 8(1)
[48] Desai C S, Toth J. Disturbed state constitutive modeling based on stress-strain and nondestructive behavior [J] . International Journal of Solids and Structures, 1996, 33(11): 1619-1650
[49] Nemat-Nasser S and Hori M. Micromechanics: Overall properties of heterogeneous materials. Elsevier. The Netherlands, 1993
[50] Tvergaard V. Material Failure by Void Growth to Coalescence. The Danish Center for Applied Mathematics and Mechanics, Report No. S45, The Technical University of Denmark, 1988
[51] Gilormini P. Licht C and Suquet P. Growth of voids in a ductile matrix: a review. Arch. Mech, 1988, 400: 43-80
[52] Krajcinovic D. Damage mechanics. Mech. Mater, 1989, 8, 117-197
[53] Yang W and Lee W. B. Mesoplasticity and its Applications. Springer-Verlag, Berlin, 1993
[54] Kachanov M. Effective elastic properties of crack solids, critical review of some basic concepts. Appl. Mech. Review, 1992, 45(7): 304-335
[55] Bazant Z P. Mechanics of distributed cracking. Appl. Mech. Review, 1986, 39(1): 675-705
[56]冯西桥.脆性材料的细观损伤理论和损伤结构的安定分析.清华大学博士学位论文, 1995
[57] Eshelby, J. D.: The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Roc. Soc. , A24, 1957: 376-396
[58] Eshelby, J. D.: The elastic field outside an ellipsoidal inclusion, Proc. Roc. Soc. , A252, 1959: 561-569
[59] Esh Eshelby, J. D.: Elastic inclusion and inhomogeneities, in Progress in solid Mechanics 2, eds. Sneddon, 1. N. and Hill, R. , North-Holland, Amsterdam, 1961:222-246
[60] Mura, T.: Micromechanics of defects in solids, Martinus Nijhoff, Dordrecht, 1987
[61] Routh, E. J.: Theorems on the attraction of ellipsoids for certain laws of force other than the inverse space, Phil. Trans. Roy. Soc., 186-Ⅱ, 1895: 897-950
[62]仲政,杨卫,黄克智.考虑晶界滑动的多晶体塑性大变形本构关系.塑性力学和细观力学文集[M].北京大学出版社, 1993
[63] Christensen R M and Lo K H. Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids, 1979, 27: 315-330
[64] Aboudi J and Benvensite Y. The effective moduli of cracked bodies in phase deformations. Eng. Fract. Mech. , 1987, 26: 171-184
[65] Huang Y. Hu K and Chandra A. A generalized self-consistent mechanics method for microcracked solids. J. Mech. Phys. Solids, 1994, 42(8): 1273-1291
[66] Hashin Z. The differential scheme and its application to cracked materials. J. Mech. Phys. Solids, 1988, 36: 719-734
[67] Budiansky B and O’Connell R J. Elastic moduli of a cracked solids. Int. J. Solid Struct. , 1976, 12(1): 81-95
[68] Benvensite Y. On the Mori-Tanaka’s method in cracked solids. Mech. Res. Comm. , 1986, 13(4): 193-201
[69] Krajcinovic D. Constitutive Theories for Solids with Defective Micro-structure, Damage Mechanics and Continuum Modeling. Stubks N, Krajcinovic D eds. New York: ASCE, 1985: 39-56
[70] Krajcinovic D, Sumaral D. A Mecsomechanical Model for Brittle Deformation Processes: Part I and PartⅡ, ASME J Appl. Mech. , 1989, 56: 51-62
[71] Krajcinovic D, Basista M, Sumaral D. Micromechnically Inspired Phenomenological Damage Model, ASME J Appl. Mech. , 1991, 58: 305-310
[72] Hult] . Effect of Voids on Creep Rate and Strength, Damage Mechanics and Continuum Modeling. Stubbs N, Krajcinovic Deds. New York: ASCE, 1985: 13-24
[73] Atkinson B K, Meredith P G. The Theory of Subcritical crock Growth with Applications to Minerals and Rocks. Fracture Mechanics of Rock. Atkinson B Ked.London: Academic Press, 1987: 111-166
[74]杨光松.损伤力学与复合材料损伤.北京:国防工业出版社, 1995
[75]余寿文,冯西桥编著.损伤力学,北京:清华大学出版社, 1997
[76]余寿文.断裂损伤与细观力学.力学与实践, 1988, 10(6): 12-18
[77]吕运水,陈幸福.关于损伤张量的阶次.应用数学与力学, 1989, 10(3)
[78] Murakami S. Anisotropic Aspects of Matertal Damage and Application of Continuum Damage Mechanics, Continuum Damage Mechanics. Theory and Applications. Krajcinovic D, Lemaitre J Leds. Springer-Verlay Wien-New York, 1987: 9l-134
[79] Shen W, Peng L H, Yue Y G, Shen Z, Tang X D. Elastic Damage and Energy Dissipation in Anisotropic Sold Material Engng. Fracture Mech. , 1987, 33(2)
[80] Chen X F, Lu Y B, Lee H. AnEndochronic Plastic Theory with Anisatropic Damage, Engng. Fracture Mech. , 1989, 32(4)
[81] Tzou D Y, Chen E P. Mesocrack Damage Induced by A Macro-crack in Heterogeneous Materials. Engng. Fracture Mech. , 1991, 39(2)
[82] Dougill J W, Lau J C, Burt N J. Toward A Theoretical Model for Progressive Failure and softening in Rock, Concrete and Similar Materials. Mech in Engng. , ASCE-END, 1976: 335-355
[83] Costin L S. Time-Dependent Damage and creep of Brittle Rock. Damage Mechanics and Continuum Modeling. Stubbs N, Krajcinovic Deds. New York: ASCE, 1985: 25-38
[84]谢和平.大理岩微观断裂的分形模型研究.科学通报, 1989, 34(5)
[85]谢和平,高峰.岩石类材料损伤演化的分形特征.岩石力学与工程学报, 1991, 10(1): 1-9
[86]谢和平, D. J. Sanderson, D. C. P. Peacock.雁型断裂分形模型和能量耗散.岩土工程学报, 1994, 16(1): 1-7
[87]凌建明.节理岩体损伤力学及时效损伤特征的研究.上海:同济大学博士学位论文, 1992, 11
[88]叶黔元.岩石的内时损伤本构模型.第四届全国岩土力学数值方法与解析方法会议论文集,武汉:武汉测绘科技大学出版社, 1991: 85-90
[89]李广平,陶振字.真三轴条件下的岩石细观损伤力学模型.岩土工程学报, 1995, 17(1): 24-31
[90] Hult J, Janson J. Fracture Mechanics and Damage Mechanics-A. Combined Approach. J. Me canique Appliq ee, 1977, (1): 69-84
[91] Leglndra D, Mazars J.混凝土的损伤力学和断裂力学(一个联合方法),张彦秋译,岩石泪凝土断裂与强度, 1985(1): 51-58
[92]邢修三.脆性断裂的微观机理和非平衡统计特性.力学进展, 1986, 16(4): 495-510
[93]邢修三.损伤与断裂的统一.力学学报, 1991, 23(1): 123-127
[94] Bai Y L et al. A statistical Evolution Model from Damage to Failure Proceedings of Aop93, Beijing: 185-191
[95] Yao YP, Luo T, Sun DA. A simple 3-D constitutive model for both clay and sand. Chinese Journal of Geotechnical Engineering, 2002, 24(2): 240-246