饱和软粘土动力本构模型研究与地铁隧道长期振陷分析
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摘要
伴随着地铁建设的迅猛发展，地铁运行荷载造成软土地基的长期沉降问题也引起了足够的重视，如何预测沉降、有效合理地控制和减小沉降成为软土地区交通建设中亟待解决的一大技术难题。但从研究现状来看，研究多集中于地震荷载分析，对长时间施加的往复荷载以及饱和软土这种反应敏感的土类研究较少，目前还未发现有合适的本构模型能够同时考虑各向异性与循环荷载作用下的复杂的变形特征，也没有建立能用于工程应用的计算方法。因此本文以临界状态理论与边界面理论为出发点，较为系统地总结了上海淤泥质饱和软粘土的各向异性以及循环加载特性，提出了循环荷载下各向异性边界面模型和基于运动硬化准则的边界面模型，可更为合理的计算饱和软土的显著各向异性以及动力特性，并建立了一个易于工程实现的预测方法来计算地铁隧道的长期沉降，从而为下一步探索控制和减少路基长期沉降的有效途径提供了可靠的理论依据和数值分析手段。因此，本课题具有重大的理论意义和工程实用价值。
本课题取得了如下创新性的研究成果：
1．鉴于以往试验研究大多不能反映土体实际固结状态，因此采用GDS土体多功能三轴试验机，对上海饱和淤泥质软粘土进行了一系列的偏压固结静力三轴压缩试验以及大数目循环次数的循环三轴试验，针对其在围压、动应力水平、排水条件影响下的变形规律进行了系统分析。试验表明，动应力水平或围压水平越大，累积变形与孔压也越大；随着循环次数达到一定数目，软粘土的累积变形与孔压增长速度逐渐缓慢直至趋于稳定；部分排水条件下的累积变形高于不排水条件。
2．基于边界面理论建立了循环荷载下的各向异性边界面模型，模型既可以反映各向异性的影响，又可以描述循环荷载条件下卸载再加载的弹塑性特性。该模型具有以下特点：其一，在修正剑桥模型屈服面中引入各向异性张量和形状参数，边界面形状灵活又可以反映初始各向异性的影响；其二，引入旋转硬化准则可较好考虑应力各向异性的影响；其三，引入运动的映射中心，将卸载再加载时的映射中心改为卸载起始点，从而改变了传统边界面模型将映射中心固定在应力空间原点以及弹性卸载的概念，这样模型可以反映出卸载的弹塑性
With a rapid development of subway construction, long-term settlements of subsoils induced by traffic loading have received much attention recently. Predicting, controlling and reducing settlements have been a great interest to geotechnical engineers. However, little effort has been made to behaviors of saturated soft clay subjected to long-term cyclic loads. Most of constitutive models in the literature are not capable of capturing both anisotropic and cyclic behaviors of soft clay simultaneously. There are no practical methods available for predicting subway train-load-induced long-term settlements under anisotropically consolidated conditions. Anisotropic and cyclic behavior of Shanghai saturated soft clays is investigated by conducting a series of cyclic triaxial tests on anisotropically consolidated samples. Based on critical state theory and bounding surface theory, two constitutive models are herein developed. One is an anisotropic bounding surface model and the other is a bounding surface model incorporating kinematic hardening, which account for anisotropic and cyclic properties of soft clays. Finally, a practical method is proposed for predicting the subway train-load-induced long-term settlements. Present research is of importance both for theoretical analysis and practical engineering.
The main achievements of this thesis are as follows:
1. A series of triaxial compression tests and cyclic triaxial compression tests on anisotropically consolidated soft clay are conducted on GDS triaxial apparatus. Response of deformation and pore pressure are compared based on tests performed with different consolidated stress, cyclic stress amplitudes and drained conditions. Results show that accumulative plastic strain increases with increasing effective mean normal stress and cyclic stress level. Moreover, accumulative deformation and pore pressure increase rapidly at early stage and attain a stable state with large cyclic numbers. In partially drained condition, accumulative axial strain and pore pressure are certainly greater than those in undrained condition.
2. Based on bounding surface theory, an anisotropic bounding surface constitutive model is developed for predicting anisotropic and cyclic behaviors of soft clay. The proposed model can take into account the initial anisotropy by introducing anisotropic tensor and shape parameter based on yield surface of MCC. Simultaneously, for anisotropic tensor, rotational hardening law is introduced to predict stress anisotropy. Unlike other simple bounding surface models, the proposed model involves a kinematic mapping centre described by the following working rules. For virgin loading, the mapping centre is located at the origin of stress space, whereas
本课题取得了如下创新性的研究成果：
1．鉴于以往试验研究大多不能反映土体实际固结状态，因此采用GDS土体多功能三轴试验机，对上海饱和淤泥质软粘土进行了一系列的偏压固结静力三轴压缩试验以及大数目循环次数的循环三轴试验，针对其在围压、动应力水平、排水条件影响下的变形规律进行了系统分析。试验表明，动应力水平或围压水平越大，累积变形与孔压也越大；随着循环次数达到一定数目，软粘土的累积变形与孔压增长速度逐渐缓慢直至趋于稳定；部分排水条件下的累积变形高于不排水条件。
2．基于边界面理论建立了循环荷载下的各向异性边界面模型，模型既可以反映各向异性的影响，又可以描述循环荷载条件下卸载再加载的弹塑性特性。该模型具有以下特点：其一，在修正剑桥模型屈服面中引入各向异性张量和形状参数，边界面形状灵活又可以反映初始各向异性的影响；其二，引入旋转硬化准则可较好考虑应力各向异性的影响；其三，引入运动的映射中心，将卸载再加载时的映射中心改为卸载起始点，从而改变了传统边界面模型将映射中心固定在应力空间原点以及弹性卸载的概念，这样模型可以反映出卸载的弹塑性
With a rapid development of subway construction, long-term settlements of subsoils induced by traffic loading have received much attention recently. Predicting, controlling and reducing settlements have been a great interest to geotechnical engineers. However, little effort has been made to behaviors of saturated soft clay subjected to long-term cyclic loads. Most of constitutive models in the literature are not capable of capturing both anisotropic and cyclic behaviors of soft clay simultaneously. There are no practical methods available for predicting subway train-load-induced long-term settlements under anisotropically consolidated conditions. Anisotropic and cyclic behavior of Shanghai saturated soft clays is investigated by conducting a series of cyclic triaxial tests on anisotropically consolidated samples. Based on critical state theory and bounding surface theory, two constitutive models are herein developed. One is an anisotropic bounding surface model and the other is a bounding surface model incorporating kinematic hardening, which account for anisotropic and cyclic properties of soft clays. Finally, a practical method is proposed for predicting the subway train-load-induced long-term settlements. Present research is of importance both for theoretical analysis and practical engineering.
The main achievements of this thesis are as follows:
1. A series of triaxial compression tests and cyclic triaxial compression tests on anisotropically consolidated soft clay are conducted on GDS triaxial apparatus. Response of deformation and pore pressure are compared based on tests performed with different consolidated stress, cyclic stress amplitudes and drained conditions. Results show that accumulative plastic strain increases with increasing effective mean normal stress and cyclic stress level. Moreover, accumulative deformation and pore pressure increase rapidly at early stage and attain a stable state with large cyclic numbers. In partially drained condition, accumulative axial strain and pore pressure are certainly greater than those in undrained condition.
2. Based on bounding surface theory, an anisotropic bounding surface constitutive model is developed for predicting anisotropic and cyclic behaviors of soft clay. The proposed model can take into account the initial anisotropy by introducing anisotropic tensor and shape parameter based on yield surface of MCC. Simultaneously, for anisotropic tensor, rotational hardening law is introduced to predict stress anisotropy. Unlike other simple bounding surface models, the proposed model involves a kinematic mapping centre described by the following working rules. For virgin loading, the mapping centre is located at the origin of stress space, whereas
引文
[1] Akira Sakai, Lawalenna Samang, Norihiko Miura. Partially-drained cyclic behavior and its application to the settlement of a low embankment road on silty-clay. Japanese Geotechnical Society. 2003, 9: 33-46.
[2] Al Tabbaa A. Permeability and stress-strain response of Speswhite kaolin, PhD dissertation. University of Cambridge, 1987.
[3] Al Tabbaa A, Wood, M D. An experimentally based "bubble" model for clay, Proceedings of the 3rd International. Conference on Numerical Models in Geomechanics, Niagara Falls, 1989.
[4] Anandarajah, Dafalias, Y F. Bounding surface plasticity III: Application to anisotropic cohesive soils. Journal of Engineering Mechanics, ASCE, 1986, 112(12): 1292-1319.
[5] Atilla, M Ausai, Ayfer Erken. Undrained behavior of clay under cyclic shear stresses. Journal of Geotechnical. Engineering, ASCE, 1989, 115(7): 968-983.
[6] Baladi G Y, Renoud-Lias. An elasto-plastic constitutive model for saturated sand subjected to monotonic and/or cyclic loading. Proceedings of the 3rd International Conference on Numerical Methods in Geomechnics, Achen, 1979.
[7] Baladi, G Y. Normalized characterization model of pavement materials. ASTM special technical publication 807, ASTM, Philadelphia, Pa, 1983: 55-64.
[8] Banerjee, P K, Yousif N B. A plasticity model for the mechanical behaviour of anisotropically consolidated clay. International Journal for Numerical and Analytical Methods in Geomechanics, 1986, 10(4): 521-541.
[9] Bardet J P. Application of bounding surface plasticity to cyclic sand behavior, Proceedings of the 2nd International Conference on Soil Dynamics and Earthquake Engineering, 1985.2-16.
[10] Bardet J P. Modeling of sand behaviour with bounding surface plasticity. Proceedings of 2nd International Symposium on Numerical Models in Geomechanics, Balkema AA. 1986.79-90
[11] Baudet, B, Stallebrass, S. A constitutive model for structured clays. Geotechnique, 2004, 54(4): 269-278.
[12] Bishop, A W, Henkel D J. The measurement of soil properties in the triaxial test. Edward Arnold Ltd. 1957
[13] Borja RI. Cam-clay plasticity. Part II : Implicity integration of constitutive equation based on a nonlinear elastic stress predietor. Computer Methods in Applied Mechanics and Engineering, 1991, 88: 225-240.
[14] Brown, S F, Lashine A K F, Hyde A F L. Repeated load triaxial testing of a silty clay. Geotechnique, 1975, 25(1): 95-114.
[15] 蔡宏英．弹塑性模型积分格式的数值分析及软粘土卸载特性的研究．同济大学博士学位论文，2001．
[16] 蔡英，曹新文．重复加载下路基填土的临界动应力和永久变形初探．西南交通大学学报，1996，31(1)：1-5．
[17] Carter, J P, Booker J R, Wroth C P. A critical state soil model for cyclic loading. Soil Mechanics-Transient and Cyclic Loading. John Wiley & Sons, Chichester, 1982.219-252.
[18] Chai, J C, and Miura, N. Traffic-load-induced permanent deformation of road on soft subsoil. Journal of Geotechnical and Geoenvironmental Engineering, 2002, 128(11): 907-916.
[19] Chen W F, and Baladi G Y. Soil plasticity—theory and Implementation, Elsevier, 1985.
[20] 程斌．车致振动下地铁隧道位移规律的研究．同济大学博士学位论文，2003．
[21] Clayton C R I, Matthews M C, Simons N E. Site investigation, Blackwell Sciences Ltd., 1995.
[22] Cowin S C. Microstructural continuum model for granular materials, Continuum Mechanical and Statistical Approaches in the Mechanics of Granular materials, edited by Cowin S C and Satake M et al, Tokyo, 1978. 162.
[23] Crouch R S, Wolf J P. On a three-dimensional anisotropic plasticity model for soil. Geotechnique, 1995, 45(2):301-305.
[24] Dafalias Y F, Herrmann L R. A bounding surface soil plasticity model. International Soil under Cyclic and Transient Loading, 1980, 1: 335-346.
[25] Dafalias Y F. Anisotropic critical state soil plasticity model. Mechanics Research Communications, 1987, 13(6): 341-347
[26] Dafalias Y F, Herrmann L R. Bounding surface formulation of soil plasticity. Soil Mechanics-Transient and Cyclic Loads, edited by G N Pande and O C Zienkiewicz, John Wiley & Sons, Chichester, U. K., 1982. 153-182.
[27] Dafalias, Y F, Herrmann L R. Bounding surface plasticity Ⅱ: Application to isotropic cohesive soils. Journal of Engineering Mechanics, ASCE, 1986, 112(EM12): 1263-1291.
[28] Dafalias Y F, Popov E P. A model of nonlinearly hardening materials for complex loading. Acta Mechanica, 1975, 21: 173-192.
[29] Diaz Rodrguez J A et al. Yielding of Mexico city clay and other natural clays, Journal of Geotechnical Engineering, ASCE, 1992, 118(GT7): 981-995.
[30] France J W, Sangrey D A. Effects of drainage in repeated loading of clays. Journal of Geotechnical Engineering, ASCE, 1977, 103(7): 769-785.
[31] Fujiwara H. et al. Consolidation of alluvial clay under repeated loading. Soils and Foundations, 1985, 25(3): 19-30.
[32] Gajo A, Muir Wood D. A new approach to anisotropic, bounding surface plasticity: general formulation and simulations of natural and reconstituted clay behavior. International Journal for Numerical and Analytical Methods in Geomechanics, 2001, 25: 207-241.
[33] Gajo, A., Wood, D. M.. A new approach to anisotropic, bounding surface plasticity: general formulation and simulations of natural and reconstituted clay behaviour. International Journal for Numerical and Analytical Methods in Geomechanics, 2001, 25: 207-241.
[34] Gbaboussi J, Momen H. Plasticity model for cyclic behavior of sands. Proceedings of the 3rd International Conference on Numerical Methods in Geomechanics, Aachen, 1979.423-434.
[35] Ghaboussi J, Momen H. Modelling and inalysis of cyclic behaviour of sands. Soil Mechanics-Transient and Cyclic Loads. Constitutive Relations and Numerical Treatment, edited by G N Pande & O C Zienkiewicz, John Wiley & Sons Ltd. ,Chapter 12,1982.313-342.
[36] 宫全美，廖彩风等．地铁行车荷载作用下地基土动孔隙水压力实验研究．岩石力学与工程学报，2001，20(增)：1154-1157．
[37] Graham J, Noonan M L, Lew K V. Yield states and stress-strain relationships in a natural plastic clay. Canadian Geotechnical Journal, 1983, 20(3): 502-516.
[38] Hau, K W. Application of a three-surface kinematic hardening model to the repeated loading of thinly surfaced pavements. PhD thesis, University of Nottingham, 2003.
[39] 黄茂松，李进军，李兴照．饱和软粘土的不排水循环累积变形特性．岩土工程学报，2006，28(7)：891-895．
[40] Hvorslev M J. Uber die Festigkeitseigenschaften gestorter bindiger Boden Ingerniorvidenshabelige Skriften, 1937, 45.
[41] Hyde, A F L, Brown S F. The plastic deformation of a silty clay under creep and repeated loading. Geotechnique, 1976, 26(1): 173-184.
[42] Hyde, A F L, Ward S J. A pore pressure and stability model for a silty clay under repeated loading. Geotechnique, 1985, 35(2): 113-125.
[43] Hyodo M, Yasuhara K, Hirao K. Prediction of clay behaviour in undrained and partially drained cyclic tests. Soils and foundations. 1992, 32(4): 117-127.
[44] Hyodo M, Yamamoto etal. Undrained cyclic shear behaviour of normally consolidated clay subjected to initial static shear stress, Soils and foundations 1994, 34(4): 1-11.
[45] Hyodo M, Yasuhara K. Analytical procedure for evaluating porewater pressure and deformation of saturated clay groud subjected to traffic loads. Proceedings of the 6th International Conference on Numerical Methods in Geomechanics. Rotterdam, Balkema, 1988. 653-658.
[46] Iwan W D. On a class of models for the yielding behavior of continuous and composite systems. Journal of Applied Mechanics, ASME, 1967, 34: 612-617.
[47] 姜宏伟，赵锡宏．K_0固结各向异性不排水抗剪强度研究．岩土力学，1997，18(2)：1-7．
[48] 蒋军．循环荷载作用下粘土及含砂芯复合试件性状试验研究．浙江大学博士学位论文，2000．
[49] 蒋军，陈龙珠．循环荷载作用下粘土应变速率试验研究．岩土工程学报．200l，24(4)：528-531
[50] Kanatani K I. Description of directional data and fabric tensor. International Journal of Engineering Science, 1984, 22: 149.
[51] Kavvadas M J. A constitutive model for clays based on non-associated anisotropic elasto-plasticity. Proceedings of the International Conference on Constitutive Laws for Engineering Materials-Theory and Application, Tuscon, Arizona, 1982.
[52] Kavvadas M, Amorosi A. A constitutive model for structured soils. Geotechnique, 2000, 50(3): 263-273.
[53] Knutson, R. M.. Materials evaluation study-ballast and foundation materials research program. Rep. No. FRA-OR&D-77-02, Univ. of Illinois, Urbana-Champaign, 111, 1977.
[54] 孔德金，苗中海．软粘土抗剪强度增长规律．岩土工程字报，1999，21(6)：757-759．
[55] 孔亮．复杂应力状态下土体弹塑性本构模型研究．后勤工程学院博士学位论文．2002．
[56] Konishi J, Oda M, Nemat-Nasser S. Inherent anisotropy and shear strength of assembly. IUTAM Conference on deformation and failure of granular materials, Delft, Netherland, Eds. Vermeer P A, Luger H J, 1982: 403-412.
[57] Koutsoftas D C, and Fisher J A. Dynamic properties of two marine clays. Journal of Geotechnical Engineering, ASCE, 1980, 106(6): 645-657.
[58] Koutsoftas, D C. Effect of cyclic loads on undrained strength of two marine clays. Journal of Geotechnical Engineering, ASCE, 1978, 104(5): 609-620.
[59] Krieg R D. A practical two-surface plasticity theory. Journal of Applied Mechanics, ASME, 1975, 42: 641-646.
[60] Kutara K etal. Settlement and countermeasures of road with low embankment on soft ground. Technical rep. of Civil Engineering, JSCE, 1996. 22(8): 13-16.
[61] Leroueil S, Tavenas F. Strain Rate Behavior of Sant-Jean-Vianney Clay, Discussion, Canadian Geotechnical Journal, 1979, 16(3): 616-620.
[62] Li D, Selig E T. Cumulative plastic deformation for fine-grained subgrade soils. Journal of Geotechnical Engineering, 1996, 122(12): 1006-1013.
[63] 李广信．高等土力学．北京：清华大学出版社，2004．
[64] 李进军．交通荷载作用下饱和软粘土长期沉降分析．同济大学博士学位论文，2005．
[65] 李进军，黄茂松，王育德．交通荷载作用下软土路基累积塑性变形分析方法．中国公路学报，2006，19(1)：1-5．
[66] 李亮，赵成刚．饱和土体动力本构模型研究进展．世界地震工程，2004，20(1)：138-148．
[67] Li, Meissner H. Two-surface plasticity model for cyclic undrained behavior of clays. Geotechnical and Geoenvironmental Engineering, ASCE, 2002, 128(7): 613-626.
[68] 李兴照．饱和软粘土的流变和循环流变特性研究．同济大学博士学位论文，2005．
[69] Liang R Y, and Ma F. Anisotropic plasticity model for undrained cyclic behavior of clays: theory. Journal of the Geotechnical Engineering, 1992, 118(2): 229-245.
[70] Ling H I, Yue D, Kaliakin V N. Anisotropic elastoplastic bounding surface model for cohensive model. Journal of Engineering Mechanics, 2002, 128(7): 748-758.
[71] 凌建明，王伟，邬洪波．行车荷载作用下湿软路基残余变形的研究．同济大学学报，2002，30(11)：1315-1320．
[72] 刘汉龙，陈生水．土体动力本构模型及动力分析研究进展．岩土工程青年专家学术论坛文集．中国建筑工业出版社，1998：29-42．
[73] 刘汉龙，余湘娟．土动力学与岩土地震工程研究进展．河海大学学报，1999，27(1)：6-15．
[74] Majidzadeh. Labortary verification of a mechanistic subgrade rutting model. Transportation Research Rec. No. 616, Transportation Research Board, Washington, D C, 1976. 34-37.
[75] Majidzadeh. Rutting evaluation of subgrade soils in Ohio. Transportation Research Rec. No. 671, Transportation Research Board, Washington, D C, 1978. 75-91.
[76] Masin D. A kinematic hardening critical state model for anisotropic clays. Proceedings of Constitutive Modeling and Analysis of Boundary Value problems in Geotechnical Engineering, Napoli, Italy, 2003: 253-263
[77] Masin D, Herle I. Numerical analyses of a tunnel in London clay using different constitutive models. Proceedings of the 5th International Symposium Geotechnical Aspects of Underground Construction in Soft Ground, Amsterdam, 2005. 595-600.
[78] Masin D. Laboratory and numerical modeling of natural clays. PhD Thesis, City University, London, 2004.
[79] Monismith C L. Rutting prediction in asphalt concrete pavements: A state of the art Annu. Meeting of the TRB, Transportation Research Board, Washington, D C, 1976.
[80] Mroz Z. On the description of anisotropic hardening. Journal of Mechanical Physics. Solids, 1967, 15: 163-175.
[81] Mroz Z, Norris V A, Zienkiewicz O C. An anisotropic hardening model for soils and its application to cyclic loading. International Journal for Numerical and Analytical Methods in Geomechanics, 1978, 2: 203-221.
[82] Mroz Z, Norris V A, Zienkiewicz O C. Application of an anisotropic hardening model in the analysis of elasto-plastic deformation of soils. Geotechnique, 1979, 29(1): 1-34.
[83] Mroz Z, Norris V A, Zienkiewicz O C. An anisotropic, critical state model for soils subject to cyclic loading. Geotechnique, 1981, 31(4): 451-469.
[84] Mroz Z, Norris V A. Elastoplastic and viscoplastic constitutive models for soils with application to cyclic loading. Soil Mechanics-Transient and Cyclic Loads, edited by G. N. Pande and O C Zienkiewicz, John Wiley & Sons Ltd, 1982.
[85] Mroz Z, Zienkiewicz O C. Uniform formulation of constitutive equations for clays and sands. Mechanics of Engineering Materials, edited by C S Desai and R H Gallagher, John Wiley and Sons Ltd., Chapter22, 1984. 415-449.
[86] Mroz Z, Zienkiewicz O C. Generalized plasticity formulation and applications to geomechanics. Mechanics of Engineering Materials, edited by C S Desai and R H Gallagher, John Wiley and Sons Ltd., Chapter33, 1984. 655-679.
[87] Muhanna A S. A testing procedure and a model for resilient modulus and accumulated plastic strain of cohesive subgrade soils. PhD. Dissertation, North Carolina State University, 1994.
[88] Muir Wood D. True triaxial tests on Boston Blue clay, Proceedings of the 10th International Conference on Soil Mechanics and Foundation Engineering, Stockholm, Sweden, 1981, session 4. 825-830.
[89] Muir Wood D M. Soil behaviour and critical soil mechanics. Cambridge University Press, 1990.
[90] Pestana J M, Whittle A J. Formulation of a unified constitutive model for clays and sands. International Journal for Numerical and Analytical Methods in Geomechanics, 1999,23(12): 1215-1243.
[91] Pestana J M, Whittle A J. Formulation of a unified constitutive model for clays and sands. International Journal for Numerical and Analytical Methods in Geomechanics, 1999,23(12): 1215-1243
[92] Pietruszczak S T, Krucinski S. Description of anisotropic response of clays using a tensorial measure of structural disorder. Mechanics of materials, 1989(8): 237-249.
[93] Prevest J H. A simple plastic theory for frictional cohenionless soils. Soil Dynamic and Earthquake Engineering, 1985, 4(1): 9-17.
[94] Prevest J H. Anisotropic undrained stress-strain behavior of clay. Journal of the Geotechnical Engineering Division, ASCE, 1978a, 104(8): 1075-1090.
[95] Prevest J H. Mathematical modeling of monotonic and cyclic undrained clay behaviour. International Journal for Numerical and Analytical Methods in Geomechanics, 1977, 1: 195-216.
[96] Prevest J H. Plasticity theory for soil stress-strain behavior. ASCE, EM Division, 1978b, 104: 1177-1194.
[97] Roscoe K H, Burland J B. On the generalized stress-strain behaviour of 'wet' clay, Engineering Plasticity, Cambridge University, 1968. 535-608.
[98] Roscoe K H, Schofield A N, Thurairajah A. Yielding of clays in the state wetter than critical. Geotechnique, 1963, 13(3): 211-240.
[99] Rouainia M, Muir Wood D. A kinematic hardening constitutive model for natural clays with loss of structure. Geotechnique, 2000, 50(2): 153-164.
[100] Rouainia M, Muir Wood D. Implicit numerical integration for a kinematic hardening soil plasticity model. Geotechnique, 2001, 25(2): 1305-1325.
[101] Sangrey, D A, Henkel D J. The effective stress response of a saturated clay soil to repeated loading. Canadian Geotechnical Journal, 1969, 6(3): 241-252.
[102] Seed H B, Chart C K. Effect of duration of stress application on soil deformation under repeated loading. Proceedings of the 5th International Congress on Soil Mechanics and Foundations, Pairs, Dunod, 1961. 341-345.
[103] 沈珠江．理论土力学．北京：中国水利水电出版社，2000．
[104] Smith P R, Jardine R J, Hight D W. On the yielding of Bothnkennar clay. Geotechnique, 1992, 42(2): 257-274.
[105] Stallebrass S E, Taylor R N. The development and evaluation of constitutive model for the prediction of ground movements in overconsolidated clay. Geotechnique, 1997, 47(2): 235-253.
[106] Stallebrass S E. The effect of recent stress history on the deformation of overconsolidated soils: PhD thesis, City University, 1990.
[107] 孙德安，姚仰平，殷宗泽．初始应力各向异性土的弹塑性模型．岩土力学，2000，21(3)：222-226．
[108] Tavenas F, Leroueil S. Effects of stress and time of yielding of clays, the 9th International Conference of CSMFE, Tokyo, 1977, 1. 319-326.
[109] Thiers G R etal. Strength and stress-strain characteristics of clays subjected to seismic loading conditions. Vibration Effects of Earthquakes on Soils and Foundations, ASTM, 1969.
[110] 王炳龙．高速铁路软土路基沉降预测与控制．同济大学博士学位论文．2003．
[111] 王建华，刘振纹等．原状海滩粘土不固结不排水循环特性．天津大学学报，2001，34(2)：236-240．
[112] 王建华，要明伦．软粘土不排水循环特性的弹塑性模拟．岩土工程学报，1996，18(3)：11-18．
[113] 王立忠，叶盛华，沈恺伦，胡亚元．K_0固结软土不排水抗剪强度．岩土工程学报，2006，28(8)：970-977．
[114] 王志良，王余庆，韩清宇．不规则循环剪切荷载作用下土的粘弹性模型．岩土工程学报，1980，2(3)：10-20．
[115] 魏汝龙．软粘土的强度和变形，北京：人民交通出版社，1987．
[116] 魏星．黄茂松．黏土的各向异性边界面模型．水利学报，2006，37(7)：831-837．
[117] 魏星．天然粘土的各向异性与结构性本构模型研究．同济大学博士学位论文，2005．
[118] Wheeler S J, Karstunen M. Discussion of Finite strain, anisotropic Modefied Cam Clay Model with plastic spin Ⅰ: Theory. edited by George Z. Voyiadjis and Chung R. Song. Journal of Engineering Mechanics, 2002, 4: 497-498.
[119] Wheeler S J, Naatanen A, Karstunen M, Lojander M. An anisotropic elastoplastic model for soft clays. Canadian Geotechnical Journal, 2003, 40: 403-418.
[120] Wheeler S, Karstunen M, Naatanen A. Anisotropy hardening model for normally Consolidated Soft Clays. Proceedings of the 7th International Symposium on Numerical Models in Gcomechanics(NUMOG Ⅶ), Graz, 1999. 33-40.
[121] Whittle A J. A constitutive model for overconsolidated clays with application to the cyclic loading of friction piles. PhD. Thesis, Massachusetts Institute of Technology, 1987.
[122] Whittle A J. Evaluation of a constitutive model for overconsolidated clays, Geotcchnique, 1993, 43(2): 289-313.
[123] Wood D M. Soil bchaviour and critical soil mechanics. Cambridge University Press, 1990.
[124] Wroth C P, Houlsby G T. Soil mechanics - property characterization and analysis procedures, the 11th International Conference of Soil Mechanics and Foundation Engineering, San Francisco, 1985. 1-55.
[125] 吴世明等．土动力学．北京：中国建筑工业出版社，2000．
[126] 谢定义．土动力学．西安交通大学出版社，1988．
[127] 徐干成，谢定义，郑颖人．饱和砂土循环动应力应变特性的弹塑性模拟研究．岩土工程学报，1995，17(2)：1-12．
[128] 徐日庆．土的边界面应力应变本构关系．同济大学学报，1997，25(1)：29-33．
[129] 阎澎旺．往复荷载作用下重塑软粘土的变形特性．岩土工程学报，199l，13(1)：48-53．
[130] Yasuhara K, Yamanouchi T et al. Approximate prediction of soil deformation under drained-repeated loading. Soils and Foundations, 1983, 23(2): 13-24.
[131] Yasuhara K, and Yamanouchi T et al. Approximate prediction of soil deformation under drained-repeated loading. Soils and Foundations, 1983, 23(2): 13-24.
[132] Yasuhara K, Yamanouchi T, Hirao K. Cyclic strength and deformation of normally consolidation clay. Soils and Foundations, 1982, 22(3): 77-91.
[133] 叶耀东．地铁振动对隧道周围软粘土动力性状及微结构影响试验研究．同济大学硕士学位论文，2003．
[134] 袁聚云．软土各向异性性状的试验研究及其在工程中的应用．同济大学博士学位论文，1995．
[135] Yue D. A anisotropic and time dependent bounding surface model for clays and its application to a containment system constructed over a soft foundation. PhD. Thesis, Columbia University, 2001.
[136] Zenter R, Karstunen M, Schweiger C et al. Compare of two approaches for modeling anisotropy of soft clays. Proceedings of the 8th International Symposium on Numerical Models in Geomechanics(NUMOG Ⅷ), Rome, 2002. 115-121.
[137] Zhang wei, Per ullidtz, Macdonald Robin. Pavement Subgrade Performance Study: Part Ⅱ: Modeling Pavement Response and Predicting Pavement Performance. 1998, 87: 135.
[138] 郑大同，王惠昌．循环荷载作用下土的非线性应力应变模型．岩土工程学报，1983，5(1)：65-76．
[139] 郑颖人，沈珠江，龚晓南．广义塑性力学—岩土塑性力学原理，北京：中国建筑工业出版社，2002
[140] 郑颖人，严德俊．基于试验拟合的土的多重屈服面模型．见：第五届全国岩土力学数值分析与解析方法讨论会论文集．武汉测绘大学出版社，1994：9-14．
[141] Zienkiewicz O C, Leung K H, Hinton E, Chang C T. Liquefaction and permanent deformation under dynamic conditions - numerical solution and constitutive relations. Soil Mechanics - Transient and Cyclic Loading, edited by Pande G N and Zienkiewicz O C, UK, John Wiley & Son, 1982. 71-103
[142] 钟辉虹，黄茂松等．循环荷载作用下软粘土变形特性研究．岩土工程学报，2002，24(5)：629-632．
[143] 钟辉虹．软土结构性及蠕变特性理论研究．同济大学博士学位论文，2004．
[144] 周建．循环荷载作用下饱和软粘土特性研究．浙江大学博士学位论文，1998．
[145] 周健，孙吉主，吴世明．往复荷载下软土的边界面广义弹塑性模型．岩石力学与工程学报，2002，2l(2)：200-214．
[2] Al Tabbaa A. Permeability and stress-strain response of Speswhite kaolin, PhD dissertation. University of Cambridge, 1987.
[3] Al Tabbaa A, Wood, M D. An experimentally based "bubble" model for clay, Proceedings of the 3rd International. Conference on Numerical Models in Geomechanics, Niagara Falls, 1989.
[4] Anandarajah, Dafalias, Y F. Bounding surface plasticity III: Application to anisotropic cohesive soils. Journal of Engineering Mechanics, ASCE, 1986, 112(12): 1292-1319.
[5] Atilla, M Ausai, Ayfer Erken. Undrained behavior of clay under cyclic shear stresses. Journal of Geotechnical. Engineering, ASCE, 1989, 115(7): 968-983.
[6] Baladi G Y, Renoud-Lias. An elasto-plastic constitutive model for saturated sand subjected to monotonic and/or cyclic loading. Proceedings of the 3rd International Conference on Numerical Methods in Geomechnics, Achen, 1979.
[7] Baladi, G Y. Normalized characterization model of pavement materials. ASTM special technical publication 807, ASTM, Philadelphia, Pa, 1983: 55-64.
[8] Banerjee, P K, Yousif N B. A plasticity model for the mechanical behaviour of anisotropically consolidated clay. International Journal for Numerical and Analytical Methods in Geomechanics, 1986, 10(4): 521-541.
[9] Bardet J P. Application of bounding surface plasticity to cyclic sand behavior, Proceedings of the 2nd International Conference on Soil Dynamics and Earthquake Engineering, 1985.2-16.
[10] Bardet J P. Modeling of sand behaviour with bounding surface plasticity. Proceedings of 2nd International Symposium on Numerical Models in Geomechanics, Balkema AA. 1986.79-90
[11] Baudet, B, Stallebrass, S. A constitutive model for structured clays. Geotechnique, 2004, 54(4): 269-278.
[12] Bishop, A W, Henkel D J. The measurement of soil properties in the triaxial test. Edward Arnold Ltd. 1957
[13] Borja RI. Cam-clay plasticity. Part II : Implicity integration of constitutive equation based on a nonlinear elastic stress predietor. Computer Methods in Applied Mechanics and Engineering, 1991, 88: 225-240.
[14] Brown, S F, Lashine A K F, Hyde A F L. Repeated load triaxial testing of a silty clay. Geotechnique, 1975, 25(1): 95-114.
[15] 蔡宏英．弹塑性模型积分格式的数值分析及软粘土卸载特性的研究．同济大学博士学位论文，2001．
[16] 蔡英，曹新文．重复加载下路基填土的临界动应力和永久变形初探．西南交通大学学报，1996，31(1)：1-5．
[17] Carter, J P, Booker J R, Wroth C P. A critical state soil model for cyclic loading. Soil Mechanics-Transient and Cyclic Loading. John Wiley & Sons, Chichester, 1982.219-252.
[18] Chai, J C, and Miura, N. Traffic-load-induced permanent deformation of road on soft subsoil. Journal of Geotechnical and Geoenvironmental Engineering, 2002, 128(11): 907-916.
[19] Chen W F, and Baladi G Y. Soil plasticity—theory and Implementation, Elsevier, 1985.
[20] 程斌．车致振动下地铁隧道位移规律的研究．同济大学博士学位论文，2003．
[21] Clayton C R I, Matthews M C, Simons N E. Site investigation, Blackwell Sciences Ltd., 1995.
[22] Cowin S C. Microstructural continuum model for granular materials, Continuum Mechanical and Statistical Approaches in the Mechanics of Granular materials, edited by Cowin S C and Satake M et al, Tokyo, 1978. 162.
[23] Crouch R S, Wolf J P. On a three-dimensional anisotropic plasticity model for soil. Geotechnique, 1995, 45(2):301-305.
[24] Dafalias Y F, Herrmann L R. A bounding surface soil plasticity model. International Soil under Cyclic and Transient Loading, 1980, 1: 335-346.
[25] Dafalias Y F. Anisotropic critical state soil plasticity model. Mechanics Research Communications, 1987, 13(6): 341-347
[26] Dafalias Y F, Herrmann L R. Bounding surface formulation of soil plasticity. Soil Mechanics-Transient and Cyclic Loads, edited by G N Pande and O C Zienkiewicz, John Wiley & Sons, Chichester, U. K., 1982. 153-182.
[27] Dafalias, Y F, Herrmann L R. Bounding surface plasticity Ⅱ: Application to isotropic cohesive soils. Journal of Engineering Mechanics, ASCE, 1986, 112(EM12): 1263-1291.
[28] Dafalias Y F, Popov E P. A model of nonlinearly hardening materials for complex loading. Acta Mechanica, 1975, 21: 173-192.
[29] Diaz Rodrguez J A et al. Yielding of Mexico city clay and other natural clays, Journal of Geotechnical Engineering, ASCE, 1992, 118(GT7): 981-995.
[30] France J W, Sangrey D A. Effects of drainage in repeated loading of clays. Journal of Geotechnical Engineering, ASCE, 1977, 103(7): 769-785.
[31] Fujiwara H. et al. Consolidation of alluvial clay under repeated loading. Soils and Foundations, 1985, 25(3): 19-30.
[32] Gajo A, Muir Wood D. A new approach to anisotropic, bounding surface plasticity: general formulation and simulations of natural and reconstituted clay behavior. International Journal for Numerical and Analytical Methods in Geomechanics, 2001, 25: 207-241.
[33] Gajo, A., Wood, D. M.. A new approach to anisotropic, bounding surface plasticity: general formulation and simulations of natural and reconstituted clay behaviour. International Journal for Numerical and Analytical Methods in Geomechanics, 2001, 25: 207-241.
[34] Gbaboussi J, Momen H. Plasticity model for cyclic behavior of sands. Proceedings of the 3rd International Conference on Numerical Methods in Geomechanics, Aachen, 1979.423-434.
[35] Ghaboussi J, Momen H. Modelling and inalysis of cyclic behaviour of sands. Soil Mechanics-Transient and Cyclic Loads. Constitutive Relations and Numerical Treatment, edited by G N Pande & O C Zienkiewicz, John Wiley & Sons Ltd. ,Chapter 12,1982.313-342.
[36] 宫全美，廖彩风等．地铁行车荷载作用下地基土动孔隙水压力实验研究．岩石力学与工程学报，2001，20(增)：1154-1157．
[37] Graham J, Noonan M L, Lew K V. Yield states and stress-strain relationships in a natural plastic clay. Canadian Geotechnical Journal, 1983, 20(3): 502-516.
[38] Hau, K W. Application of a three-surface kinematic hardening model to the repeated loading of thinly surfaced pavements. PhD thesis, University of Nottingham, 2003.
[39] 黄茂松，李进军，李兴照．饱和软粘土的不排水循环累积变形特性．岩土工程学报，2006，28(7)：891-895．
[40] Hvorslev M J. Uber die Festigkeitseigenschaften gestorter bindiger Boden Ingerniorvidenshabelige Skriften, 1937, 45.
[41] Hyde, A F L, Brown S F. The plastic deformation of a silty clay under creep and repeated loading. Geotechnique, 1976, 26(1): 173-184.
[42] Hyde, A F L, Ward S J. A pore pressure and stability model for a silty clay under repeated loading. Geotechnique, 1985, 35(2): 113-125.
[43] Hyodo M, Yasuhara K, Hirao K. Prediction of clay behaviour in undrained and partially drained cyclic tests. Soils and foundations. 1992, 32(4): 117-127.
[44] Hyodo M, Yamamoto etal. Undrained cyclic shear behaviour of normally consolidated clay subjected to initial static shear stress, Soils and foundations 1994, 34(4): 1-11.
[45] Hyodo M, Yasuhara K. Analytical procedure for evaluating porewater pressure and deformation of saturated clay groud subjected to traffic loads. Proceedings of the 6th International Conference on Numerical Methods in Geomechanics. Rotterdam, Balkema, 1988. 653-658.
[46] Iwan W D. On a class of models for the yielding behavior of continuous and composite systems. Journal of Applied Mechanics, ASME, 1967, 34: 612-617.
[47] 姜宏伟，赵锡宏．K_0固结各向异性不排水抗剪强度研究．岩土力学，1997，18(2)：1-7．
[48] 蒋军．循环荷载作用下粘土及含砂芯复合试件性状试验研究．浙江大学博士学位论文，2000．
[49] 蒋军，陈龙珠．循环荷载作用下粘土应变速率试验研究．岩土工程学报．200l，24(4)：528-531
[50] Kanatani K I. Description of directional data and fabric tensor. International Journal of Engineering Science, 1984, 22: 149.
[51] Kavvadas M J. A constitutive model for clays based on non-associated anisotropic elasto-plasticity. Proceedings of the International Conference on Constitutive Laws for Engineering Materials-Theory and Application, Tuscon, Arizona, 1982.
[52] Kavvadas M, Amorosi A. A constitutive model for structured soils. Geotechnique, 2000, 50(3): 263-273.
[53] Knutson, R. M.. Materials evaluation study-ballast and foundation materials research program. Rep. No. FRA-OR&D-77-02, Univ. of Illinois, Urbana-Champaign, 111, 1977.
[54] 孔德金，苗中海．软粘土抗剪强度增长规律．岩土工程字报，1999，21(6)：757-759．
[55] 孔亮．复杂应力状态下土体弹塑性本构模型研究．后勤工程学院博士学位论文．2002．
[56] Konishi J, Oda M, Nemat-Nasser S. Inherent anisotropy and shear strength of assembly. IUTAM Conference on deformation and failure of granular materials, Delft, Netherland, Eds. Vermeer P A, Luger H J, 1982: 403-412.
[57] Koutsoftas D C, and Fisher J A. Dynamic properties of two marine clays. Journal of Geotechnical Engineering, ASCE, 1980, 106(6): 645-657.
[58] Koutsoftas, D C. Effect of cyclic loads on undrained strength of two marine clays. Journal of Geotechnical Engineering, ASCE, 1978, 104(5): 609-620.
[59] Krieg R D. A practical two-surface plasticity theory. Journal of Applied Mechanics, ASME, 1975, 42: 641-646.
[60] Kutara K etal. Settlement and countermeasures of road with low embankment on soft ground. Technical rep. of Civil Engineering, JSCE, 1996. 22(8): 13-16.
[61] Leroueil S, Tavenas F. Strain Rate Behavior of Sant-Jean-Vianney Clay, Discussion, Canadian Geotechnical Journal, 1979, 16(3): 616-620.
[62] Li D, Selig E T. Cumulative plastic deformation for fine-grained subgrade soils. Journal of Geotechnical Engineering, 1996, 122(12): 1006-1013.
[63] 李广信．高等土力学．北京：清华大学出版社，2004．
[64] 李进军．交通荷载作用下饱和软粘土长期沉降分析．同济大学博士学位论文，2005．
[65] 李进军，黄茂松，王育德．交通荷载作用下软土路基累积塑性变形分析方法．中国公路学报，2006，19(1)：1-5．
[66] 李亮，赵成刚．饱和土体动力本构模型研究进展．世界地震工程，2004，20(1)：138-148．
[67] Li, Meissner H. Two-surface plasticity model for cyclic undrained behavior of clays. Geotechnical and Geoenvironmental Engineering, ASCE, 2002, 128(7): 613-626.
[68] 李兴照．饱和软粘土的流变和循环流变特性研究．同济大学博士学位论文，2005．
[69] Liang R Y, and Ma F. Anisotropic plasticity model for undrained cyclic behavior of clays: theory. Journal of the Geotechnical Engineering, 1992, 118(2): 229-245.
[70] Ling H I, Yue D, Kaliakin V N. Anisotropic elastoplastic bounding surface model for cohensive model. Journal of Engineering Mechanics, 2002, 128(7): 748-758.
[71] 凌建明，王伟，邬洪波．行车荷载作用下湿软路基残余变形的研究．同济大学学报，2002，30(11)：1315-1320．
[72] 刘汉龙，陈生水．土体动力本构模型及动力分析研究进展．岩土工程青年专家学术论坛文集．中国建筑工业出版社，1998：29-42．
[73] 刘汉龙，余湘娟．土动力学与岩土地震工程研究进展．河海大学学报，1999，27(1)：6-15．
[74] Majidzadeh. Labortary verification of a mechanistic subgrade rutting model. Transportation Research Rec. No. 616, Transportation Research Board, Washington, D C, 1976. 34-37.
[75] Majidzadeh. Rutting evaluation of subgrade soils in Ohio. Transportation Research Rec. No. 671, Transportation Research Board, Washington, D C, 1978. 75-91.
[76] Masin D. A kinematic hardening critical state model for anisotropic clays. Proceedings of Constitutive Modeling and Analysis of Boundary Value problems in Geotechnical Engineering, Napoli, Italy, 2003: 253-263
[77] Masin D, Herle I. Numerical analyses of a tunnel in London clay using different constitutive models. Proceedings of the 5th International Symposium Geotechnical Aspects of Underground Construction in Soft Ground, Amsterdam, 2005. 595-600.
[78] Masin D. Laboratory and numerical modeling of natural clays. PhD Thesis, City University, London, 2004.
[79] Monismith C L. Rutting prediction in asphalt concrete pavements: A state of the art Annu. Meeting of the TRB, Transportation Research Board, Washington, D C, 1976.
[80] Mroz Z. On the description of anisotropic hardening. Journal of Mechanical Physics. Solids, 1967, 15: 163-175.
[81] Mroz Z, Norris V A, Zienkiewicz O C. An anisotropic hardening model for soils and its application to cyclic loading. International Journal for Numerical and Analytical Methods in Geomechanics, 1978, 2: 203-221.
[82] Mroz Z, Norris V A, Zienkiewicz O C. Application of an anisotropic hardening model in the analysis of elasto-plastic deformation of soils. Geotechnique, 1979, 29(1): 1-34.
[83] Mroz Z, Norris V A, Zienkiewicz O C. An anisotropic, critical state model for soils subject to cyclic loading. Geotechnique, 1981, 31(4): 451-469.
[84] Mroz Z, Norris V A. Elastoplastic and viscoplastic constitutive models for soils with application to cyclic loading. Soil Mechanics-Transient and Cyclic Loads, edited by G. N. Pande and O C Zienkiewicz, John Wiley & Sons Ltd, 1982.
[85] Mroz Z, Zienkiewicz O C. Uniform formulation of constitutive equations for clays and sands. Mechanics of Engineering Materials, edited by C S Desai and R H Gallagher, John Wiley and Sons Ltd., Chapter22, 1984. 415-449.
[86] Mroz Z, Zienkiewicz O C. Generalized plasticity formulation and applications to geomechanics. Mechanics of Engineering Materials, edited by C S Desai and R H Gallagher, John Wiley and Sons Ltd., Chapter33, 1984. 655-679.
[87] Muhanna A S. A testing procedure and a model for resilient modulus and accumulated plastic strain of cohesive subgrade soils. PhD. Dissertation, North Carolina State University, 1994.
[88] Muir Wood D. True triaxial tests on Boston Blue clay, Proceedings of the 10th International Conference on Soil Mechanics and Foundation Engineering, Stockholm, Sweden, 1981, session 4. 825-830.
[89] Muir Wood D M. Soil behaviour and critical soil mechanics. Cambridge University Press, 1990.
[90] Pestana J M, Whittle A J. Formulation of a unified constitutive model for clays and sands. International Journal for Numerical and Analytical Methods in Geomechanics, 1999,23(12): 1215-1243.
[91] Pestana J M, Whittle A J. Formulation of a unified constitutive model for clays and sands. International Journal for Numerical and Analytical Methods in Geomechanics, 1999,23(12): 1215-1243
[92] Pietruszczak S T, Krucinski S. Description of anisotropic response of clays using a tensorial measure of structural disorder. Mechanics of materials, 1989(8): 237-249.
[93] Prevest J H. A simple plastic theory for frictional cohenionless soils. Soil Dynamic and Earthquake Engineering, 1985, 4(1): 9-17.
[94] Prevest J H. Anisotropic undrained stress-strain behavior of clay. Journal of the Geotechnical Engineering Division, ASCE, 1978a, 104(8): 1075-1090.
[95] Prevest J H. Mathematical modeling of monotonic and cyclic undrained clay behaviour. International Journal for Numerical and Analytical Methods in Geomechanics, 1977, 1: 195-216.
[96] Prevest J H. Plasticity theory for soil stress-strain behavior. ASCE, EM Division, 1978b, 104: 1177-1194.
[97] Roscoe K H, Burland J B. On the generalized stress-strain behaviour of 'wet' clay, Engineering Plasticity, Cambridge University, 1968. 535-608.
[98] Roscoe K H, Schofield A N, Thurairajah A. Yielding of clays in the state wetter than critical. Geotechnique, 1963, 13(3): 211-240.
[99] Rouainia M, Muir Wood D. A kinematic hardening constitutive model for natural clays with loss of structure. Geotechnique, 2000, 50(2): 153-164.
[100] Rouainia M, Muir Wood D. Implicit numerical integration for a kinematic hardening soil plasticity model. Geotechnique, 2001, 25(2): 1305-1325.
[101] Sangrey, D A, Henkel D J. The effective stress response of a saturated clay soil to repeated loading. Canadian Geotechnical Journal, 1969, 6(3): 241-252.
[102] Seed H B, Chart C K. Effect of duration of stress application on soil deformation under repeated loading. Proceedings of the 5th International Congress on Soil Mechanics and Foundations, Pairs, Dunod, 1961. 341-345.
[103] 沈珠江．理论土力学．北京：中国水利水电出版社，2000．
[104] Smith P R, Jardine R J, Hight D W. On the yielding of Bothnkennar clay. Geotechnique, 1992, 42(2): 257-274.
[105] Stallebrass S E, Taylor R N. The development and evaluation of constitutive model for the prediction of ground movements in overconsolidated clay. Geotechnique, 1997, 47(2): 235-253.
[106] Stallebrass S E. The effect of recent stress history on the deformation of overconsolidated soils: PhD thesis, City University, 1990.
[107] 孙德安，姚仰平，殷宗泽．初始应力各向异性土的弹塑性模型．岩土力学，2000，21(3)：222-226．
[108] Tavenas F, Leroueil S. Effects of stress and time of yielding of clays, the 9th International Conference of CSMFE, Tokyo, 1977, 1. 319-326.
[109] Thiers G R etal. Strength and stress-strain characteristics of clays subjected to seismic loading conditions. Vibration Effects of Earthquakes on Soils and Foundations, ASTM, 1969.
[110] 王炳龙．高速铁路软土路基沉降预测与控制．同济大学博士学位论文．2003．
[111] 王建华，刘振纹等．原状海滩粘土不固结不排水循环特性．天津大学学报，2001，34(2)：236-240．
[112] 王建华，要明伦．软粘土不排水循环特性的弹塑性模拟．岩土工程学报，1996，18(3)：11-18．
[113] 王立忠，叶盛华，沈恺伦，胡亚元．K_0固结软土不排水抗剪强度．岩土工程学报，2006，28(8)：970-977．
[114] 王志良，王余庆，韩清宇．不规则循环剪切荷载作用下土的粘弹性模型．岩土工程学报，1980，2(3)：10-20．
[115] 魏汝龙．软粘土的强度和变形，北京：人民交通出版社，1987．
[116] 魏星．黄茂松．黏土的各向异性边界面模型．水利学报，2006，37(7)：831-837．
[117] 魏星．天然粘土的各向异性与结构性本构模型研究．同济大学博士学位论文，2005．
[118] Wheeler S J, Karstunen M. Discussion of Finite strain, anisotropic Modefied Cam Clay Model with plastic spin Ⅰ: Theory. edited by George Z. Voyiadjis and Chung R. Song. Journal of Engineering Mechanics, 2002, 4: 497-498.
[119] Wheeler S J, Naatanen A, Karstunen M, Lojander M. An anisotropic elastoplastic model for soft clays. Canadian Geotechnical Journal, 2003, 40: 403-418.
[120] Wheeler S, Karstunen M, Naatanen A. Anisotropy hardening model for normally Consolidated Soft Clays. Proceedings of the 7th International Symposium on Numerical Models in Gcomechanics(NUMOG Ⅶ), Graz, 1999. 33-40.
[121] Whittle A J. A constitutive model for overconsolidated clays with application to the cyclic loading of friction piles. PhD. Thesis, Massachusetts Institute of Technology, 1987.
[122] Whittle A J. Evaluation of a constitutive model for overconsolidated clays, Geotcchnique, 1993, 43(2): 289-313.
[123] Wood D M. Soil bchaviour and critical soil mechanics. Cambridge University Press, 1990.
[124] Wroth C P, Houlsby G T. Soil mechanics - property characterization and analysis procedures, the 11th International Conference of Soil Mechanics and Foundation Engineering, San Francisco, 1985. 1-55.
[125] 吴世明等．土动力学．北京：中国建筑工业出版社，2000．
[126] 谢定义．土动力学．西安交通大学出版社，1988．
[127] 徐干成，谢定义，郑颖人．饱和砂土循环动应力应变特性的弹塑性模拟研究．岩土工程学报，1995，17(2)：1-12．
[128] 徐日庆．土的边界面应力应变本构关系．同济大学学报，1997，25(1)：29-33．
[129] 阎澎旺．往复荷载作用下重塑软粘土的变形特性．岩土工程学报，199l，13(1)：48-53．
[130] Yasuhara K, Yamanouchi T et al. Approximate prediction of soil deformation under drained-repeated loading. Soils and Foundations, 1983, 23(2): 13-24.
[131] Yasuhara K, and Yamanouchi T et al. Approximate prediction of soil deformation under drained-repeated loading. Soils and Foundations, 1983, 23(2): 13-24.
[132] Yasuhara K, Yamanouchi T, Hirao K. Cyclic strength and deformation of normally consolidation clay. Soils and Foundations, 1982, 22(3): 77-91.
[133] 叶耀东．地铁振动对隧道周围软粘土动力性状及微结构影响试验研究．同济大学硕士学位论文，2003．
[134] 袁聚云．软土各向异性性状的试验研究及其在工程中的应用．同济大学博士学位论文，1995．
[135] Yue D. A anisotropic and time dependent bounding surface model for clays and its application to a containment system constructed over a soft foundation. PhD. Thesis, Columbia University, 2001.
[136] Zenter R, Karstunen M, Schweiger C et al. Compare of two approaches for modeling anisotropy of soft clays. Proceedings of the 8th International Symposium on Numerical Models in Geomechanics(NUMOG Ⅷ), Rome, 2002. 115-121.
[137] Zhang wei, Per ullidtz, Macdonald Robin. Pavement Subgrade Performance Study: Part Ⅱ: Modeling Pavement Response and Predicting Pavement Performance. 1998, 87: 135.
[138] 郑大同，王惠昌．循环荷载作用下土的非线性应力应变模型．岩土工程学报，1983，5(1)：65-76．
[139] 郑颖人，沈珠江，龚晓南．广义塑性力学—岩土塑性力学原理，北京：中国建筑工业出版社，2002
[140] 郑颖人，严德俊．基于试验拟合的土的多重屈服面模型．见：第五届全国岩土力学数值分析与解析方法讨论会论文集．武汉测绘大学出版社，1994：9-14．
[141] Zienkiewicz O C, Leung K H, Hinton E, Chang C T. Liquefaction and permanent deformation under dynamic conditions - numerical solution and constitutive relations. Soil Mechanics - Transient and Cyclic Loading, edited by Pande G N and Zienkiewicz O C, UK, John Wiley & Son, 1982. 71-103
[142] 钟辉虹，黄茂松等．循环荷载作用下软粘土变形特性研究．岩土工程学报，2002，24(5)：629-632．
[143] 钟辉虹．软土结构性及蠕变特性理论研究．同济大学博士学位论文，2004．
[144] 周建．循环荷载作用下饱和软粘土特性研究．浙江大学博士学位论文，1998．
[145] 周健，孙吉主，吴世明．往复荷载下软土的边界面广义弹塑性模型．岩石力学与工程学报，2002，2l(2)：200-214．