非饱和土的广义有效应力原理及其本构模型研究
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摘要
土力学发展到目前为止,其理论基础仍然很不完善,仍处于半理论、半经验的发展阶段,土力学统一和完备的理论基础仍有待于研究和发展。上世纪六七十年代发展起来的多相孔隙介质理论,为非饱和土力学的发展提供了理论基础。非饱和土是一种三相的多孔介质材料,它由固体颗粒和孔隙组成,孔隙中填充着水和气。气体的存在使得非饱和土的性质比饱和土要复杂得多,也使得影响非饱和土性质的因素变多,因此很难像饱和土那样找出非饱和土的响应(或应变)与应力状态之间的简单和唯一的关系。本文以多相孔隙介质力学理论为基础,提出了非饱和土广义有效应力原理,并建立了非饱和土的本构模型,主要研究成果为：
(1)以多相孔隙介质理论为基础,从基本的物理规律即各种平衡方程出发,建立非饱和土的基本方程,并得到了非饱和土变形功的表达式。在总变形功的具体方程基础上提出了广义有效应力原理,给出了本文建议的与土骨架位移在功上对偶的有效应力表达式。指出应当选择非饱和土有效应力,修正吸力和气压三个应力状态变量来描述非饱和土的行为,并给出了相对应的功共轭的广义变形,为建立非饱和土本构方程奠定基础。
(2)根据非饱和土的变形功表达式,推导得到了非饱和土各相的自由能和耗散势增量方程,然后采用热力学的方法来建立非饱和土的本构模型。根据广义有效应力原理选择应力变量,并选择适当的内变量来考虑非饱和土三相之间的联系,建立了固液气三相耦合的非饱和土本构模型框架。该框架将可以考虑很多复杂因素的影响,比如气相耗散对土体的影响等。
(3)在非饱和土模型框架的基础上,通过适当的假设和简化,建立三轴应力状态下固液气三相耦合的非饱和土本构模型。其最大的特点在于首次在模型中考虑了气相硬化的影响,从理论的角度,这一模型由于考虑了气相压力变化的影响,因此更加全面和更具有一般性。采用已有的实验数据对模型进行验证,结果表明不论是在低饱和度阶段还是高饱和度阶段,模型都能很好的拟合试验结果。
(4)对SFG模型进行了探讨和研究,指出其中存在的不足即无法考虑饱和度对土体性质的影响。以本文给出的有效应力为基础,提出了修正的SFG模型。该模型通过非饱和土的有效应力很自然地将SFG模型中无法考虑的饱和度对土体的影响引入进来。将修正后的模型与SFG模型进行了比较,并将模型与已有的试验数据进行了对比,结果表明本文模型在没有增加参数的同时可以考虑饱和度的影响并能反映更多的实验现象。
So far the theory basis of soil mechanics is still far from consummate and still in a semi-theoretical, semi-empirical stage. It is necessary to develop a unified theoretical basis for soil mechanics. The multiphase porous medium theory, developed from 1960s, can describe the complex interaction in each phase and their response under external pressure or in complex environment, which provides a theoretical basis for soil mechanics. An unsaturated soil is a three phase porous media, consisting of soil skeleton and pores, with water and gas filled in the pores. The existence of gas in the soil makes its properties much more complex than saturated soils. Owing to the complexity of unsaturated soils, it is difficult to predict the deformation and strength behaviour of unsaturated soil uniquely. In this thesis, based on the multiphase porous media theory, the principle of generalized effective stress is derived, and the constitutive models of unsaturated soils can be further developed. The following conclusions can be drawn:
(1) Based on the multiphase porous media theory and thermodynamics, the work and energy balance equations for unsaturated soils by using the geotechnical terminologies are derived. Then a principle of generalized effective stress for unsaturated soils is proposed, which makes preparation for constructing the constitutive models.
(2) The free energy and the dissipation equation can be derived from the work expression. Based on the principle of generalized effective stress, the constitutive equations for unsaturated soils can be established using the thermomechanical method. The choice of internal state variables is important to build the relationship among the three phases. A solid-liquid-gas coupled constitutive modeling framework is established, which can consider many complex situations, for example the influence of gas dissipation on soil behaviour.
(3) Based on the constitutive framework of unsaturated soils, a three phase coupled constitutive equations in triaxial stress state is presented with some reasonable assumption and simplification. The constitutive equations can be easy to apply in practice. The model is then used to predict the exiting experimental data, results showing the model agrees well with the test points in both low degree of saturation and high degree of saturation situation.
(4) Studying on SFG model, it is found that the model could not consider the influence of degree of saturation on the soil behaviour. Using the principle of generalized effective stress deduced from the work expression, a modified model is proposed which can take the degree of saturation into account without increasing any more parameters. The modified model is then compared with SFG model, and model predictions are also given to simulate the existing experimental results.
(1)以多相孔隙介质理论为基础,从基本的物理规律即各种平衡方程出发,建立非饱和土的基本方程,并得到了非饱和土变形功的表达式。在总变形功的具体方程基础上提出了广义有效应力原理,给出了本文建议的与土骨架位移在功上对偶的有效应力表达式。指出应当选择非饱和土有效应力,修正吸力和气压三个应力状态变量来描述非饱和土的行为,并给出了相对应的功共轭的广义变形,为建立非饱和土本构方程奠定基础。
(2)根据非饱和土的变形功表达式,推导得到了非饱和土各相的自由能和耗散势增量方程,然后采用热力学的方法来建立非饱和土的本构模型。根据广义有效应力原理选择应力变量,并选择适当的内变量来考虑非饱和土三相之间的联系,建立了固液气三相耦合的非饱和土本构模型框架。该框架将可以考虑很多复杂因素的影响,比如气相耗散对土体的影响等。
(3)在非饱和土模型框架的基础上,通过适当的假设和简化,建立三轴应力状态下固液气三相耦合的非饱和土本构模型。其最大的特点在于首次在模型中考虑了气相硬化的影响,从理论的角度,这一模型由于考虑了气相压力变化的影响,因此更加全面和更具有一般性。采用已有的实验数据对模型进行验证,结果表明不论是在低饱和度阶段还是高饱和度阶段,模型都能很好的拟合试验结果。
(4)对SFG模型进行了探讨和研究,指出其中存在的不足即无法考虑饱和度对土体性质的影响。以本文给出的有效应力为基础,提出了修正的SFG模型。该模型通过非饱和土的有效应力很自然地将SFG模型中无法考虑的饱和度对土体的影响引入进来。将修正后的模型与SFG模型进行了比较,并将模型与已有的试验数据进行了对比,结果表明本文模型在没有增加参数的同时可以考虑饱和度的影响并能反映更多的实验现象。
So far the theory basis of soil mechanics is still far from consummate and still in a semi-theoretical, semi-empirical stage. It is necessary to develop a unified theoretical basis for soil mechanics. The multiphase porous medium theory, developed from 1960s, can describe the complex interaction in each phase and their response under external pressure or in complex environment, which provides a theoretical basis for soil mechanics. An unsaturated soil is a three phase porous media, consisting of soil skeleton and pores, with water and gas filled in the pores. The existence of gas in the soil makes its properties much more complex than saturated soils. Owing to the complexity of unsaturated soils, it is difficult to predict the deformation and strength behaviour of unsaturated soil uniquely. In this thesis, based on the multiphase porous media theory, the principle of generalized effective stress is derived, and the constitutive models of unsaturated soils can be further developed. The following conclusions can be drawn:
(1) Based on the multiphase porous media theory and thermodynamics, the work and energy balance equations for unsaturated soils by using the geotechnical terminologies are derived. Then a principle of generalized effective stress for unsaturated soils is proposed, which makes preparation for constructing the constitutive models.
(2) The free energy and the dissipation equation can be derived from the work expression. Based on the principle of generalized effective stress, the constitutive equations for unsaturated soils can be established using the thermomechanical method. The choice of internal state variables is important to build the relationship among the three phases. A solid-liquid-gas coupled constitutive modeling framework is established, which can consider many complex situations, for example the influence of gas dissipation on soil behaviour.
(3) Based on the constitutive framework of unsaturated soils, a three phase coupled constitutive equations in triaxial stress state is presented with some reasonable assumption and simplification. The constitutive equations can be easy to apply in practice. The model is then used to predict the exiting experimental data, results showing the model agrees well with the test points in both low degree of saturation and high degree of saturation situation.
(4) Studying on SFG model, it is found that the model could not consider the influence of degree of saturation on the soil behaviour. Using the principle of generalized effective stress deduced from the work expression, a modified model is proposed which can take the degree of saturation into account without increasing any more parameters. The modified model is then compared with SFG model, and model predictions are also given to simulate the existing experimental results.
引文
[1]赵成刚.土力学的现状及其数值分析方法中某些问题的讨论.岩土力学.2006,27(8)：1361-1364.
[2]赵成刚,白冰.土力学原理修订本.北京：清华大学出版社,北京交通大学出版社,2009.
[3]Lubarda V. A. Elastoplasticity theory. New York:CRC Press,2002.
[4]黄筑平.连续介质力学基础.北京：高等教育出版社,2003.
[5]de Boer R. Theory of porous media. Berlin:Springer,2000.
[6]Hutter K., Johnk K. Continuum methods of physical modeling. Berlin:Springer,2004.
[7]赵成刚,张雪东,郭璇.土的本构方程与热力学.力学进展.2006,36(04)：611-618.
[8]赵成刚,刘艳,周贵荣,等.非饱和土本构模型研究进展.北京工业大学学报.2008,34(8)：820-829.
[9]Li X. S. Thermodynamics-based constitutive framework for unsaturated soils.1:Theory. Geotechnique.2007,57(5):411-422.
[10]陈正汉,谢定义,刘祖典.非饱和土固结的混合物理论(Ⅰ).应用数学和力学.1993,14(2)：127-137.
[11]陈正汉.非饱和土固结的混合物理论(Ⅱ).应用数学和力学.1993,14(8)：687-698.
[12]黄义,张引科.非饱和土本构关系的混合物理论(Ⅰ)--非线性本构方程和场方程.应用数学和力学.2003,24(2)：111-123.
[13]黄义,张引科.非饱和土本构关系的混合物理论(Ⅱ)--线性本构方程和场方程.应用数学和力学.2003,24(2)：124-137.
[14]牛永红,苗天德.混合物理论中的体积分数约束.中国科学A辑.2002,32(2)：76-82.
[15]杨松岩,俞茂宏.多相孔隙介质的本构描述.力学学报.2000,32(1)：11-24.
[16]包承纲,詹良通.非饱和土性状及其与工程问题的联系.岩土工程学报.2006,28(2)：129-136.
[17]殷宗泽等.土工原理水利水电出版社,2007.
[18]Fredlund D. G., Morgenstern N. R.非饱和土力学中国建筑工业出版社,1997.
[19]Gens A. Soil-environment interactions in geotechnical engineering. Geotechnique.2010, 60(1):3-74.
[20]谢定义,冯志焱.对非饱和土有效应力研究中若干基本观点的思辨.岩土工程学报.2006,28(2)：170-173.
[21]周建.非饱和土本构模型中应力变量选择研究.岩石力学与工程学报.2009,28(6).
[22]杨庆,张传庆,栾茂田.基于微结构定量分析的非饱和土广义有效应力原理.大连理工大学学报.2004,44(4)：556-559.
[23]包承纲.非饱和土的性状及膨胀土边坡稳定问题.岩土工程学报.2004,26(1)：1-15.
[24]汤连生,颜波,张鹏程,等.非饱和土中有效应力及有关概念的解说与辨析.岩土工程学报.2006,28(2)：216-220.
[25]赵成刚,蔡国庆.非饱和土广义有效应力原理.岩土力学.2009,30(11)：3232-3236.
[26]Bishop A. W. The principle of effective stress. Teknisk Ukeblad.1959,106:859-863.
[27]Aitchison G. D. Relationship of moisture and effective stress functions in unsaturated soils. Proc.4th Int. Conf. Soil Mech. Found. Eng. London:Butterworths,1961.47-52.
[28]Jennings J. E. B. A revised effective stress law for use in the prediction of the behaviour of unsaturated soils. London:Butterworth,1961.26-30.
[29]Bishop A. W., Donald I. B. The experimental study of partly saturated soils in triaxial apparatus. Proc.5 Int. Conf. Soil Mech. Found. Eng. Paris:1961.13-21.
[30]Khalili N., Khabbaz M. H. A unique A unique relationship for x for the determination of shear strength of unsaturated soils. Geotechnique.1998,48(5):681-688.
[31]Jennings J. E. B., Burland J. B. Limitations to the use of effective stresses in unsaturated soils. Geotechnique.1962,12:125-144.
[32]Burland J. B. Some aspects of the mechanical behaviour of partly saturated soils. Moisture Equilibria and Moisture Changes in Soils Beneath Covered Areas. Butterworth, Sydeny, Australia:1965.270-278.
[33]Aitchison G. D. Soils properties, shear strength, and consolidation. Proc.,6th Int. Conf. SMFE. Toronto:University of Toronto Press,1965.319-321.
[34]Matyas E. L., Radhakrishna H. S. Volume change characteristics of partially saturated soils. Geotechnique.1968,18:432-448.
[35]Brackley I. J. A. Partial collapse in unsaturated expansive clay. Proc.5th Regional Conf. SMFE. South Africa:1971.23-30.
[36]Fredlund D. G., Morgenstern N. R. Stress state variables for unsaturated soils. Journal of the Geotechanical Engineering Division (ASCE).1977,103:447-466.
[37]Khalili N., Geiser F., Blight G. E. Effective stress in unsaturated soils:review with new evidence. Inernational Journal of Geomechanics.2004,4(2):115-126.
[38]Loret Benjamin, Khalili Nasser. A three-phase model for unsaturated soils. Int. J. Numer. Anal. Meth. Geomech.2000,24:893-927.
[39]Coleman J. D. Stress-strain relations for partly saturated soils. Geotechnique.1962,12(4): 348-350.
[40]Bishop A. W., Blight G. E. Some aspects of the effective stress in saturated and partially saturated soils. Geotechnique.1963,13(3):177-197.
[41]Blight G. E. Effective stress evaluation for unsaturated soils. J.Soil Mech. Found. Div. Am. Soc. Civ. Engrs.1967,93:125-148.
[42]Fredlund D. G., Morgenstern N. R. Stress state variables for unsaturated soils. Journal of the Geotechanical Engineering Division (ASCE).1977,103:447-466.
[43]Geiser F., Laloui L., Vulliet L. Modelling the behaviour of unsaturated silt. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema,2000.155-175.
[44]Bocking Ka, Fredlund D. G. Limitations of the asix translation technique. Proceedings of the 4th international conference on expansive soils. Denver:1980.117-135.
[45]Tarantino A., Mongiovi L. Experimental investigations on the stress variables governing unsaturated soil behaviour at medium to high degrees of saturation. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema,2000.1-20.
[46]Tarantino A. Direct measurement of soil water tension. Proc.3th International Conference on unsaturated soils. Recife:2004.1005-1017.
[47]Wheeler S. J., Sharma R. S., Buisson M. S. R. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Geotechnique.2003,53(1):41-54.
[48]Houlsby G. T. The work input to an unsaturated granular material. Geotechnique.1997,47(1): 193-196.
[49]Dean E. T., Houlsby Gt. Editorial. Geotechnique.2005,55(2):415-417.
[50]Jommi C. Remarks on the constitutive modelling of unsaturated soils. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema,2000.139-154.
[51]Vaunat J., Romero E., Jommi C. An elastoplastic hydro-mechanical model for unsaturated soils. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema, 2000.121-138.
[52]赵成刚,张雪东.非饱和土中功的表述以及有效应力与相分离原理的讨论.中国科学(E辑：技术科学).2008,38(09)：1453-1463.
[53]Zhao C. G., Liu Y., Gao F. P. Work and energy equations and the principle of generalized effective stress for unsaturated soils. International Journal for Numerical and Analytical Methods in Geomechanics.2010,34(9):920-936.
[54]Sheng D., Sloan S. W., Gens A. A constitutive model for unsaturated soils:thermomechanical and computational aspects. Computational Mechanics.2004,33(6):453-465.
[55]Li X. S. Thermodynamics-based constitutive framework for unsaturated soils.1:Theory. Geotechnique.2007,57(5):411-422.
[56]Li X. S. Thermodynamics-based constitutive framework for unsaturated soils 2:a basic triaxial model. Geotechnique.2007,57(5):423-435.
[57]Alonso E. E., Gens A., Josa A. A constitutive model for partially saturated soils. Geotechnique. 1990,40(3):405-430.
[58]Wheeler S. J., Sivakumar V. An elasto-plastic critical state framework for unsaturated soil. Geotechnique.1995,45(1):35-53.
[59]Chiu C. F., Ng C. W. W. A state-dependent elasto-plastic model for saturated and unsaturated soils. Geotechnique.2003,53(9):809-829.
[60]Nuth Mathieu. Constitutive modelling of unsaturated soils with hydro-geomechanical couplings. Lausanne:Ecole Polytechnique Federale de Lausanne (EPFL),2009.
[61]Vassallo Roberto, Mancuso C. Soil behaviour in the small and large strain range under controlled suction conditions. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema,2000.75-89.
[62]Chen R. Experimental study and constitutive modeling of stress-dependent coupled hydraulic hysteresis and mechanical behaviour of an unsaturated soil. Hong Kong:Hong Kong University,2007.
[63]Wheeler S. J., Gallipoli D., Karstunen M. Comments on use of the Barcelona Basic Model for unsaturated soils. International Journal for Numerical and Analytical Methods in Geomechanics.2002,26(15):1561-1571.
[64]Sheng Daichao, Fredlund Delwyn G., Gens Antonio. A new modelling approach for unsaturated soils using independent stress variables. Canadian Geotechnical Journal.2008,45: 511-534.
[65]Loret Benjamin, Khalili Nasser. A three-phase model for unsaturated soils. Int. J. Numer. Anal. Meth. Geomech.2000,24:893-927.
[66]Wei Changfu, Kong Lingwei, Wang Jili. A comprehensive approach to modeling the constitutive behavior of unsaturated soils. Dalian:Dalian University of Technology Press, 2006.
[67]Khalili N., Geiser F., Blight G. E. Effective stress in unsaturated soils:review with new evidence. Inernational Journal of Geomechanics.2004,4(2):115-126.
[68]Tamagnini R. An extended Cam-clay model for unsaturated soils with hydraulic hysteresis. Geotechnique.2004,54(3):223-228.
[69]Jommi C. Remarks on the constitutive modelling of unsaturated soils. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema,2000.139-154.
[70]Li X. S. Thermodynamics-based constitutive framework for unsaturated soils 2:a basic triaxial model. Geotechnique.2007,57(5):423-435.
[71]Wheeler S. J., Sharma R. S., Buisson M. S. R. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Geotechnique.2003,53(1):41-54.
[72]Gallipoli D., Gens A., Sharma R., et al. An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Geotechnique.2003,53(1):123-135.
[73]Sheng D., Sloan S. W., Gens A. A constitutive model for unsaturated soils:thermomechanical and computational aspects. Computational Mechanics.2004,33(6):453-465.
[74]张雪东.土水特征曲线及其在非饱和土力学中应用的基本问题研究.北京：北京交通大学,2010.
[75]孙德安.非饱和土的水力和力学特性及其弹塑性描述.岩土力学.2009(11)：3217-3231.
[76]方祥卫,陈正汉,申春妮,等.剪切对非饱和土土水特征曲线影响的探讨.岩土力学.2004,25(9)：1451-1454.
[77]龚壁卫,吴宏伟,王斌.应力状态对膨胀土SWCC的影响研究.岩土力学.2004,25(12)：1915-1918.
[78]李志清,胡瑞林,王立朝,等.非饱和膨胀土SWCC研究.岩土力学.2006,27(5)：730-734.
[79]Miao Linchang, Jing Fei, Houston Sandra L. Soil-Water Characteristic Curve of Remolded Expansive Soils. Carefree, Arizona, USA:ASCE,2006.
[80]张文杰.城市生活垃圾填埋场中水分运移规律研究.杭州：浙江大学,2007.
[81]王铁行,卢靖,岳彩坤.考虑温度和密度影响的非饱和土土-水特征曲线研究.岩土力学.2008,29(1)：1-5.
[82]Huang Shangyan, Barbour S. L., Fredlund D. G. Development and verification of a coefficient of permeability function for a deformable unsaturated soil. Canadian Geotechnical Journal. 1998,35(3):411-425.
[83]Brooks R. H., Corey A. T. Hydraulic properties of porous media. Hydrology paper number 3. Colorado State University,1964.
[84]Gallipoli D., Wheeler S. J., Karstunen M. Modelling the variation of degree of saturation in a deformable unsaturated soil. Geotechnique.2003,53(1):105-112.
[85]van Genuchten M. T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soil. Soil Science Society of America Journal.1980,44:892-898.
[86]Nitao J. J., Bear J. Potentials and their role in transport in porous media. Water Resources Research.1996,32(2):225-250.
[87]Fredlund D. G. The implementation of unsaturated soil mechanics into geotechnical engineering. Canadian Geotechnical Journal.2000,37(5):963-986.
[88]Scott P. S., Farquhar G. J., Kouwen N. Hysteretic effects on net infiltration.In Advances in infiltration. St. Joseph, Mich:ASCE,1983.163-170.
[89]Kawai K., Karube D., Kato S. The model of water retention curve considering effects of void ratio. Proceedings of Asian Conference on Unsaturated Soils. Singapore:Balkema,2000. 329-334.
[90]Karube D., Kawai K. The role of pore water in the mechanical behaviour of unsaturated soils. Geotechnical and Geological Engineering.2001,19(3/4):211-241.
[91]Feng M., Fredlund D. G. Hysteretic influence associated with thermal conductivity sensor Measurements. Proceedings from Theory to the Practice of Unsaturated Soil Mechanics in Association with the 52nd Canadian Geotechnical Conference and the Unsaturated Soil Group. Regina, Sask:Canadian Geotechnical Society,1999.14-20.
[92]Mualem Y. Modified approach to capillary hysteresis based on a similarity hypothesis. Water Resources Research.1973,9(5):1324-1331.
[93]Mualem Y. A concept model of hysteresis. Water Resources Research. Water Resources Research.1974,9(5):1324-1331.
[94]Mualem Y. Extension of the similarity hypothesis used for modeling the soil water characterist ics. Water Resources Research.1977,13(4):773-780.
[95]Topp G. C. Soil-water hysteresis:The domain theory extended to pore interaction conditions. Soil Science Society of America Journal.1971,35:219-225.
[96]Parlange Jean Yves. Capillary Hysteresis and the Relationship Between Drying and Wetting Curves. Water Resources Research.1976,12(2):224-228.
[97]Hogarth W. L., Hopmans J., Parlange J. Y. Application of a simple soil-water hysteresis model. Journal of Hydrology.1988,98(1/2):21-29.
[98]Liu Y., Parlange J. Y., Steenhuis T. S. A soil water hysteresis model for fingered flow data. Water Resources Research.1995,31(9):2263-2266.
[99]Dafalias Yannis F. Bounding Surface Plasticity.Ⅰ:Mathematical Foundation and Hypoplasticity. Journal of Engineering Mechanics.1986,112(9):966-987.
[100]Dafalias Yannis F., Herrmann Leonard R. Bounding Surface Plasticity. Ⅱ:Application to Isotropic Cohesive Soils. Journal of Engineering Mechanics.1986,112(12):1263-1291.
[101]Li X. S. Modelling of hysteresis response for arbitrary wetting/drying paths. Computers and Geotechnics.2005,32(2):133-137.
[102]Wei C. F., Dewoolkar M. M. Formulation of capillary hysteresis with internal state variables. Water Resources Research.2006, vol.42(no.7).
[103]俞培基,陈愈炯.非饱和土的水一气形态及其与力学性质的关系.水利学报.1965(1)：16-23.
[104]包承纲.非饱和压实土的气相形态及其裂隙压力消散的关系.第三届全国土力学与基础工程会议论文集.北京：中国建筑工程出版社,1979.129-135.
[105]Wroth C. P., Houlsby G. T. Soil mechanics:Property characterization and analysis procedures. Proc 11th Int. Conf. Soil Mech. Found Eng. San Francisco:1985.1-55.
[106]汤连生,王思敬.吸湿力及非饱和土的有效应力原理探讨.岩土工程学报.2001,22(1)：83-88.
[107]Kogho Y. Elastoplastic models for unsaturated soils with two suction effects and unsaturated soil behavior. Proc.3rd international conference on unsaturated soils. Recife, Brazil:2002.
[108]Fredlund D. G. The scope of unsaturated soil mechanics:an overview. Proc.1st international conference on unsaturated soils. Pairs, France:1995.1155-1177.
[109]Terzaghi K. Theoretical soil mechanics. London:Wiley,1944.
[110]Klausner Y. Fundamentals of continuum mechanics of soilsSpringer-Verlag,1990.
[111]Wheeler S. J. The undrained shear strength of soils containing large gas bubbles. Geotechnique.1988,38(3):399-413.
[112]Nageswaran S. Effect of gas bubbles on the sea-bed behaviorOxford University,1983.
[113]Thomas S. D. The consolidation behavior of gassy soilOxford University,1987.
[114]Sham W. K. The undrained shear strength of soils containing large gas bubbles. United Kingdom:Queen's University of Belfast,1989.
[115]Pietruszczak S.,Pande G. N. Constitutive Relations for Partially Saturated Soils Containing Gas Inclusions. Journal of Geotechnical Engineering.1996,122(1):50-59.
[116]陈正汉,周海清,Fredlund D. G.,等.非饱和土的非线性模型及其应用.岩土工程学报.1999,21(5)：603-608.
[117]陈正汉,孙树国,方祥位,等.非饱和土与特殊土测试技术新进展.岩土工程学报.2006,28(2)：147-169.
[118]殷宗泽,周建,赵仲辉,等.非饱和土本构关系及变形计算.岩土工程学报.2006,28(2)：137-146.
[119]谢定义.对非饱和土基本特性的学习与思考.第二届全国非饱和土学术研讨会.杭州：2005.
[120]Josa A., Balmaceda A., Gens A., et al. An elasto-plastic model for partially saturated soils exhibiting a maximum of collapse. Proc.3rd Int. Conf. Computational Plasticity. Barcelona: 1992.815-826.
[121]Yudhbir B. Collapsing behaviour of residual soils. Proc.7th SE Asian Geotech Conf. Hong Kong:1982.915-930.
[122]Sun De'an, Sheng Daichao, Xiang Li, et al. Elastoplastic prediction of hydro-mechanical behaviour of unsaturated soils under undrained conditions. Computers and Geotechnics.2008, 35(6):845-852.
[123]Wheeler S. J., Karube D. Constitutive modeling. Proc.1st Int. Conf. Unsaturated Soils. Paris: Balkema,1995.1323-1356.
[124]Sun D. A., Sheng D. C., Cui H. B., et al. A density-dependent elastoplastic hydro-mechanical model for unsaturated compacted soils. International Journal for Numerical and Analytical Methods in Geomechanics.2007,31(11):1257-1279.
[125]陈正汉,谢定义,王永胜.非饱和土的水气运动规律及其工程性质研究.岩土工程学报.1993,15(3)：9-20.
[126]赵成刚,刘艳.连续孔隙介质土力学及其在非饱和土本构关系中的应用.岩土工程学报.2009,31(9)：1324-1335.
[127]刘艳,赵成刚,蔡国庆,等.考虑气相压力变化和偏应力影响的非饱和土本构模型.岩土工程学报.2011,已录用.
[128]Hassanizadeh M., Gray W. G. General conservation equations for multi-phase systems: 1.averaging procedure. Advance in Water Resources.1979,2(9):131-144.
[129]Schrefler B. A. Mechanics and thermodynamics of saturated/unsaturated porous materials and quantitative solutions. Applied Mechanics reviews.2002,55(4):351-388.
[130]Bowen R. M. Incompressible porous media models by use of the theory of mixtures. Int J Eng Sci.1980,18(9):1129-1148.
[131]Bowen R. M. Compressible porous media models by use of the theory of mixtures. Int J Eng Sci.1982,20(6):679-735.
[132]de Boer R. Highlights in the historical development of the porous media:toward a consistent macroscopic theory. Applied Mechanics Reviews.1996,49(4):201-262.
[133]Hassanizadeh M., Gray W. G. General conservation equations for multi-phase systems:2. Mass, momenta, energy, and entropy equations. Advance in Water Resources.1979,2(12): 191-203.
[134]Hassanizadeh M., Gray W. G. General conservation equations for multi-phase systems:3. Constitutive theory for porous media flow. Advance in Water Resources.1980,3(3):25-40.
[135]Achanta S., Cushman J. H. On multicomponent, multiphase thermomechanics with interfaces. Int J Eng Sci.1994,32(11):1717-1738.
[136]Truesdell C. Rational Thermodynamics.2nd ed. New York:Springer-Verlag,1984.
[137]Hutter K., Johnk K. Continuum methods of physical modeling. Berlin:Springer,2004.
[138]Hansen A. C. Reexamining some basic definitions of modern mixture theory. Int J Engineering Science.1989,27(12):1531-1544.
[139]Houlsby G. T., Puzrin A. M. A thermomechanical framework for constitutive models for rate-independent dissipative materials. International Journal of Plasticity.2000,16: 1017-1047.
[140]Dean E. T., Houlsby Gt. Editorial. Geotechnique.2005,55(2):415-417.
[141]Houlsby G. T. The work input to an unsaturated granular material. Geotechnique.1997,47(1): 193-196.
[142]Ziegler H., Wehrli C. The derivation of constitutive relations from the free energy and the dissipation function. Advances in Applied Mechanics.1987,25:183-238.
[143]Collins I. F., Houlsby G. T. A thermomechanical framework for rate-independent dissipative materials with internal functions. International Journal of Plasticity.2001,17:1147-1165.
[144]Collins I. F., Hilder T. A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests. International Journal for Numerical and Analytical Methods in Geomechanics.2002,26(13):1313-1347.
[145]Tarantino A., Mongiovi L. Experimental investigations on the stress variables governing unsaturated soil behaviour at medium to high degrees of saturation. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema,2000.1-20.
[146]Zhang X., Lytton R. L. Stress State Variables for Saturated and Unsaturated Soils. Proceedings of the Fourth International Conference on Unsaturated Soils. Carefree, Arizona, USA:ASCE, 2006.2380-2391.
[147]Collins I. F. The concept of stored plastic work for frozen elastic energy in soil mechanics. Geotechnique.2005,55(5):373-382.
[148]Collins Ian F., Hilder Tamsyn. A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests. International Journal for Numerical and Analytical Methods in Geomechanics.2002,26(13):1313-1347.
[149]Loret B., Khalili N. An effective stress elastic-plastic model for unsaturated porous media. Mechanics of Materials.2002,34:97-116.
[150]Laloui L., Nuth M. On the use of the generalised effective stress in the constitutive modelling of unsaturated soils. Computer and Geotechnics.2009,36(1-2):20-23.
[151]Giuseppe B., Roberto N. An elastoplastic strainhardening model for soil allowing for hydraulic bonding debounding effects. Internatioinal journal for numerical and analytical methods in geomechanics.2009,33:1055-1086.
[152]刘艳,赵成刚.土水特征曲线滞后模型的研究.岩土工程学报.2008,30(03)：399-405.
[153]Sun D. A., Sheng D.C., Cui H. B., et al. A density-dependent elastoplastic hydro-mechanical model for unsaturated compacted soils. International Journal for Numerical and Analytical Methods in Geomechanics.2007,31(11):1257-1279.
[154]Nuth Mathieu, Laloui Lyesse. Advances in modelling hysteretic water retention curve in deformable soils. Computers and Geotechnics.2008,35(6):835-844.
[155]Pham Hung Q., Fredlund Delwyn G., Barbour S. L. A study of hysteresis models for soil-water characteristic curves. Canadian Geotechnical Journal.2005,42(6):1548-1568.
[156]Raveendiraraj A. Coupling of mechanical behaviour and water retention behaviour in unsaturated soils. Glasgow, United Kingdom:University of Glasgow,2009.
[157]Collins I. F., Kelley P. A. A thermomechanical analysisi of a family of soil models. Geotechnique.2002,52(7):506-518.
[158]Butterfield R. A. Natural compression law of soils (an advance on e-logp'). Geotechnique. 1979,29:469-480.
[159]Hashiguchi K. On the linear relations of v-lnp and lnv-lnp for isotropic consolidation of soils. International Journal for Numerical and Analytical Methods in Geomechanics.1995,19(3): 367-376.
[160]Cunningham M. R., Ridley A. M., Dineen K., et al. The mechanical behaviour of a reconstituted unsaturated silty clay. Geotechnique.2003,53(2):183-194.
[161]Sun D. A., Matsuoka H., Cui H. B., et al. Three-dimensional elasto-plastic model for unsaturated compacted soils with different initial densities. International Journal for Numerical and Analytical Methods in Geomechanics.2003,27(12):1079-1098.
[162]Sun D. A., Sheng Daichao, Xu Yongfu. Collapse behaviour of unsaturated compacted soil with different initial densities. Canadian Geotechnical Journal.2007,44:673-686.
[163]Sun D. A., Cui H. B., Matsuoka Hajime,et al. A three-dimensional elastoplastic model for unsaturated compacted soils with hydraulic hysteresis. Soil and foundation.2007,47(2): 253-264.
[2]赵成刚,白冰.土力学原理修订本.北京：清华大学出版社,北京交通大学出版社,2009.
[3]Lubarda V. A. Elastoplasticity theory. New York:CRC Press,2002.
[4]黄筑平.连续介质力学基础.北京：高等教育出版社,2003.
[5]de Boer R. Theory of porous media. Berlin:Springer,2000.
[6]Hutter K., Johnk K. Continuum methods of physical modeling. Berlin:Springer,2004.
[7]赵成刚,张雪东,郭璇.土的本构方程与热力学.力学进展.2006,36(04)：611-618.
[8]赵成刚,刘艳,周贵荣,等.非饱和土本构模型研究进展.北京工业大学学报.2008,34(8)：820-829.
[9]Li X. S. Thermodynamics-based constitutive framework for unsaturated soils.1:Theory. Geotechnique.2007,57(5):411-422.
[10]陈正汉,谢定义,刘祖典.非饱和土固结的混合物理论(Ⅰ).应用数学和力学.1993,14(2)：127-137.
[11]陈正汉.非饱和土固结的混合物理论(Ⅱ).应用数学和力学.1993,14(8)：687-698.
[12]黄义,张引科.非饱和土本构关系的混合物理论(Ⅰ)--非线性本构方程和场方程.应用数学和力学.2003,24(2)：111-123.
[13]黄义,张引科.非饱和土本构关系的混合物理论(Ⅱ)--线性本构方程和场方程.应用数学和力学.2003,24(2)：124-137.
[14]牛永红,苗天德.混合物理论中的体积分数约束.中国科学A辑.2002,32(2)：76-82.
[15]杨松岩,俞茂宏.多相孔隙介质的本构描述.力学学报.2000,32(1)：11-24.
[16]包承纲,詹良通.非饱和土性状及其与工程问题的联系.岩土工程学报.2006,28(2)：129-136.
[17]殷宗泽等.土工原理水利水电出版社,2007.
[18]Fredlund D. G., Morgenstern N. R.非饱和土力学中国建筑工业出版社,1997.
[19]Gens A. Soil-environment interactions in geotechnical engineering. Geotechnique.2010, 60(1):3-74.
[20]谢定义,冯志焱.对非饱和土有效应力研究中若干基本观点的思辨.岩土工程学报.2006,28(2)：170-173.
[21]周建.非饱和土本构模型中应力变量选择研究.岩石力学与工程学报.2009,28(6).
[22]杨庆,张传庆,栾茂田.基于微结构定量分析的非饱和土广义有效应力原理.大连理工大学学报.2004,44(4)：556-559.
[23]包承纲.非饱和土的性状及膨胀土边坡稳定问题.岩土工程学报.2004,26(1)：1-15.
[24]汤连生,颜波,张鹏程,等.非饱和土中有效应力及有关概念的解说与辨析.岩土工程学报.2006,28(2)：216-220.
[25]赵成刚,蔡国庆.非饱和土广义有效应力原理.岩土力学.2009,30(11)：3232-3236.
[26]Bishop A. W. The principle of effective stress. Teknisk Ukeblad.1959,106:859-863.
[27]Aitchison G. D. Relationship of moisture and effective stress functions in unsaturated soils. Proc.4th Int. Conf. Soil Mech. Found. Eng. London:Butterworths,1961.47-52.
[28]Jennings J. E. B. A revised effective stress law for use in the prediction of the behaviour of unsaturated soils. London:Butterworth,1961.26-30.
[29]Bishop A. W., Donald I. B. The experimental study of partly saturated soils in triaxial apparatus. Proc.5 Int. Conf. Soil Mech. Found. Eng. Paris:1961.13-21.
[30]Khalili N., Khabbaz M. H. A unique A unique relationship for x for the determination of shear strength of unsaturated soils. Geotechnique.1998,48(5):681-688.
[31]Jennings J. E. B., Burland J. B. Limitations to the use of effective stresses in unsaturated soils. Geotechnique.1962,12:125-144.
[32]Burland J. B. Some aspects of the mechanical behaviour of partly saturated soils. Moisture Equilibria and Moisture Changes in Soils Beneath Covered Areas. Butterworth, Sydeny, Australia:1965.270-278.
[33]Aitchison G. D. Soils properties, shear strength, and consolidation. Proc.,6th Int. Conf. SMFE. Toronto:University of Toronto Press,1965.319-321.
[34]Matyas E. L., Radhakrishna H. S. Volume change characteristics of partially saturated soils. Geotechnique.1968,18:432-448.
[35]Brackley I. J. A. Partial collapse in unsaturated expansive clay. Proc.5th Regional Conf. SMFE. South Africa:1971.23-30.
[36]Fredlund D. G., Morgenstern N. R. Stress state variables for unsaturated soils. Journal of the Geotechanical Engineering Division (ASCE).1977,103:447-466.
[37]Khalili N., Geiser F., Blight G. E. Effective stress in unsaturated soils:review with new evidence. Inernational Journal of Geomechanics.2004,4(2):115-126.
[38]Loret Benjamin, Khalili Nasser. A three-phase model for unsaturated soils. Int. J. Numer. Anal. Meth. Geomech.2000,24:893-927.
[39]Coleman J. D. Stress-strain relations for partly saturated soils. Geotechnique.1962,12(4): 348-350.
[40]Bishop A. W., Blight G. E. Some aspects of the effective stress in saturated and partially saturated soils. Geotechnique.1963,13(3):177-197.
[41]Blight G. E. Effective stress evaluation for unsaturated soils. J.Soil Mech. Found. Div. Am. Soc. Civ. Engrs.1967,93:125-148.
[42]Fredlund D. G., Morgenstern N. R. Stress state variables for unsaturated soils. Journal of the Geotechanical Engineering Division (ASCE).1977,103:447-466.
[43]Geiser F., Laloui L., Vulliet L. Modelling the behaviour of unsaturated silt. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema,2000.155-175.
[44]Bocking Ka, Fredlund D. G. Limitations of the asix translation technique. Proceedings of the 4th international conference on expansive soils. Denver:1980.117-135.
[45]Tarantino A., Mongiovi L. Experimental investigations on the stress variables governing unsaturated soil behaviour at medium to high degrees of saturation. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema,2000.1-20.
[46]Tarantino A. Direct measurement of soil water tension. Proc.3th International Conference on unsaturated soils. Recife:2004.1005-1017.
[47]Wheeler S. J., Sharma R. S., Buisson M. S. R. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Geotechnique.2003,53(1):41-54.
[48]Houlsby G. T. The work input to an unsaturated granular material. Geotechnique.1997,47(1): 193-196.
[49]Dean E. T., Houlsby Gt. Editorial. Geotechnique.2005,55(2):415-417.
[50]Jommi C. Remarks on the constitutive modelling of unsaturated soils. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema,2000.139-154.
[51]Vaunat J., Romero E., Jommi C. An elastoplastic hydro-mechanical model for unsaturated soils. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema, 2000.121-138.
[52]赵成刚,张雪东.非饱和土中功的表述以及有效应力与相分离原理的讨论.中国科学(E辑：技术科学).2008,38(09)：1453-1463.
[53]Zhao C. G., Liu Y., Gao F. P. Work and energy equations and the principle of generalized effective stress for unsaturated soils. International Journal for Numerical and Analytical Methods in Geomechanics.2010,34(9):920-936.
[54]Sheng D., Sloan S. W., Gens A. A constitutive model for unsaturated soils:thermomechanical and computational aspects. Computational Mechanics.2004,33(6):453-465.
[55]Li X. S. Thermodynamics-based constitutive framework for unsaturated soils.1:Theory. Geotechnique.2007,57(5):411-422.
[56]Li X. S. Thermodynamics-based constitutive framework for unsaturated soils 2:a basic triaxial model. Geotechnique.2007,57(5):423-435.
[57]Alonso E. E., Gens A., Josa A. A constitutive model for partially saturated soils. Geotechnique. 1990,40(3):405-430.
[58]Wheeler S. J., Sivakumar V. An elasto-plastic critical state framework for unsaturated soil. Geotechnique.1995,45(1):35-53.
[59]Chiu C. F., Ng C. W. W. A state-dependent elasto-plastic model for saturated and unsaturated soils. Geotechnique.2003,53(9):809-829.
[60]Nuth Mathieu. Constitutive modelling of unsaturated soils with hydro-geomechanical couplings. Lausanne:Ecole Polytechnique Federale de Lausanne (EPFL),2009.
[61]Vassallo Roberto, Mancuso C. Soil behaviour in the small and large strain range under controlled suction conditions. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema,2000.75-89.
[62]Chen R. Experimental study and constitutive modeling of stress-dependent coupled hydraulic hysteresis and mechanical behaviour of an unsaturated soil. Hong Kong:Hong Kong University,2007.
[63]Wheeler S. J., Gallipoli D., Karstunen M. Comments on use of the Barcelona Basic Model for unsaturated soils. International Journal for Numerical and Analytical Methods in Geomechanics.2002,26(15):1561-1571.
[64]Sheng Daichao, Fredlund Delwyn G., Gens Antonio. A new modelling approach for unsaturated soils using independent stress variables. Canadian Geotechnical Journal.2008,45: 511-534.
[65]Loret Benjamin, Khalili Nasser. A three-phase model for unsaturated soils. Int. J. Numer. Anal. Meth. Geomech.2000,24:893-927.
[66]Wei Changfu, Kong Lingwei, Wang Jili. A comprehensive approach to modeling the constitutive behavior of unsaturated soils. Dalian:Dalian University of Technology Press, 2006.
[67]Khalili N., Geiser F., Blight G. E. Effective stress in unsaturated soils:review with new evidence. Inernational Journal of Geomechanics.2004,4(2):115-126.
[68]Tamagnini R. An extended Cam-clay model for unsaturated soils with hydraulic hysteresis. Geotechnique.2004,54(3):223-228.
[69]Jommi C. Remarks on the constitutive modelling of unsaturated soils. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema,2000.139-154.
[70]Li X. S. Thermodynamics-based constitutive framework for unsaturated soils 2:a basic triaxial model. Geotechnique.2007,57(5):423-435.
[71]Wheeler S. J., Sharma R. S., Buisson M. S. R. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Geotechnique.2003,53(1):41-54.
[72]Gallipoli D., Gens A., Sharma R., et al. An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Geotechnique.2003,53(1):123-135.
[73]Sheng D., Sloan S. W., Gens A. A constitutive model for unsaturated soils:thermomechanical and computational aspects. Computational Mechanics.2004,33(6):453-465.
[74]张雪东.土水特征曲线及其在非饱和土力学中应用的基本问题研究.北京：北京交通大学,2010.
[75]孙德安.非饱和土的水力和力学特性及其弹塑性描述.岩土力学.2009(11)：3217-3231.
[76]方祥卫,陈正汉,申春妮,等.剪切对非饱和土土水特征曲线影响的探讨.岩土力学.2004,25(9)：1451-1454.
[77]龚壁卫,吴宏伟,王斌.应力状态对膨胀土SWCC的影响研究.岩土力学.2004,25(12)：1915-1918.
[78]李志清,胡瑞林,王立朝,等.非饱和膨胀土SWCC研究.岩土力学.2006,27(5)：730-734.
[79]Miao Linchang, Jing Fei, Houston Sandra L. Soil-Water Characteristic Curve of Remolded Expansive Soils. Carefree, Arizona, USA:ASCE,2006.
[80]张文杰.城市生活垃圾填埋场中水分运移规律研究.杭州：浙江大学,2007.
[81]王铁行,卢靖,岳彩坤.考虑温度和密度影响的非饱和土土-水特征曲线研究.岩土力学.2008,29(1)：1-5.
[82]Huang Shangyan, Barbour S. L., Fredlund D. G. Development and verification of a coefficient of permeability function for a deformable unsaturated soil. Canadian Geotechnical Journal. 1998,35(3):411-425.
[83]Brooks R. H., Corey A. T. Hydraulic properties of porous media. Hydrology paper number 3. Colorado State University,1964.
[84]Gallipoli D., Wheeler S. J., Karstunen M. Modelling the variation of degree of saturation in a deformable unsaturated soil. Geotechnique.2003,53(1):105-112.
[85]van Genuchten M. T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soil. Soil Science Society of America Journal.1980,44:892-898.
[86]Nitao J. J., Bear J. Potentials and their role in transport in porous media. Water Resources Research.1996,32(2):225-250.
[87]Fredlund D. G. The implementation of unsaturated soil mechanics into geotechnical engineering. Canadian Geotechnical Journal.2000,37(5):963-986.
[88]Scott P. S., Farquhar G. J., Kouwen N. Hysteretic effects on net infiltration.In Advances in infiltration. St. Joseph, Mich:ASCE,1983.163-170.
[89]Kawai K., Karube D., Kato S. The model of water retention curve considering effects of void ratio. Proceedings of Asian Conference on Unsaturated Soils. Singapore:Balkema,2000. 329-334.
[90]Karube D., Kawai K. The role of pore water in the mechanical behaviour of unsaturated soils. Geotechnical and Geological Engineering.2001,19(3/4):211-241.
[91]Feng M., Fredlund D. G. Hysteretic influence associated with thermal conductivity sensor Measurements. Proceedings from Theory to the Practice of Unsaturated Soil Mechanics in Association with the 52nd Canadian Geotechnical Conference and the Unsaturated Soil Group. Regina, Sask:Canadian Geotechnical Society,1999.14-20.
[92]Mualem Y. Modified approach to capillary hysteresis based on a similarity hypothesis. Water Resources Research.1973,9(5):1324-1331.
[93]Mualem Y. A concept model of hysteresis. Water Resources Research. Water Resources Research.1974,9(5):1324-1331.
[94]Mualem Y. Extension of the similarity hypothesis used for modeling the soil water characterist ics. Water Resources Research.1977,13(4):773-780.
[95]Topp G. C. Soil-water hysteresis:The domain theory extended to pore interaction conditions. Soil Science Society of America Journal.1971,35:219-225.
[96]Parlange Jean Yves. Capillary Hysteresis and the Relationship Between Drying and Wetting Curves. Water Resources Research.1976,12(2):224-228.
[97]Hogarth W. L., Hopmans J., Parlange J. Y. Application of a simple soil-water hysteresis model. Journal of Hydrology.1988,98(1/2):21-29.
[98]Liu Y., Parlange J. Y., Steenhuis T. S. A soil water hysteresis model for fingered flow data. Water Resources Research.1995,31(9):2263-2266.
[99]Dafalias Yannis F. Bounding Surface Plasticity.Ⅰ:Mathematical Foundation and Hypoplasticity. Journal of Engineering Mechanics.1986,112(9):966-987.
[100]Dafalias Yannis F., Herrmann Leonard R. Bounding Surface Plasticity. Ⅱ:Application to Isotropic Cohesive Soils. Journal of Engineering Mechanics.1986,112(12):1263-1291.
[101]Li X. S. Modelling of hysteresis response for arbitrary wetting/drying paths. Computers and Geotechnics.2005,32(2):133-137.
[102]Wei C. F., Dewoolkar M. M. Formulation of capillary hysteresis with internal state variables. Water Resources Research.2006, vol.42(no.7).
[103]俞培基,陈愈炯.非饱和土的水一气形态及其与力学性质的关系.水利学报.1965(1)：16-23.
[104]包承纲.非饱和压实土的气相形态及其裂隙压力消散的关系.第三届全国土力学与基础工程会议论文集.北京：中国建筑工程出版社,1979.129-135.
[105]Wroth C. P., Houlsby G. T. Soil mechanics:Property characterization and analysis procedures. Proc 11th Int. Conf. Soil Mech. Found Eng. San Francisco:1985.1-55.
[106]汤连生,王思敬.吸湿力及非饱和土的有效应力原理探讨.岩土工程学报.2001,22(1)：83-88.
[107]Kogho Y. Elastoplastic models for unsaturated soils with two suction effects and unsaturated soil behavior. Proc.3rd international conference on unsaturated soils. Recife, Brazil:2002.
[108]Fredlund D. G. The scope of unsaturated soil mechanics:an overview. Proc.1st international conference on unsaturated soils. Pairs, France:1995.1155-1177.
[109]Terzaghi K. Theoretical soil mechanics. London:Wiley,1944.
[110]Klausner Y. Fundamentals of continuum mechanics of soilsSpringer-Verlag,1990.
[111]Wheeler S. J. The undrained shear strength of soils containing large gas bubbles. Geotechnique.1988,38(3):399-413.
[112]Nageswaran S. Effect of gas bubbles on the sea-bed behaviorOxford University,1983.
[113]Thomas S. D. The consolidation behavior of gassy soilOxford University,1987.
[114]Sham W. K. The undrained shear strength of soils containing large gas bubbles. United Kingdom:Queen's University of Belfast,1989.
[115]Pietruszczak S.,Pande G. N. Constitutive Relations for Partially Saturated Soils Containing Gas Inclusions. Journal of Geotechnical Engineering.1996,122(1):50-59.
[116]陈正汉,周海清,Fredlund D. G.,等.非饱和土的非线性模型及其应用.岩土工程学报.1999,21(5)：603-608.
[117]陈正汉,孙树国,方祥位,等.非饱和土与特殊土测试技术新进展.岩土工程学报.2006,28(2)：147-169.
[118]殷宗泽,周建,赵仲辉,等.非饱和土本构关系及变形计算.岩土工程学报.2006,28(2)：137-146.
[119]谢定义.对非饱和土基本特性的学习与思考.第二届全国非饱和土学术研讨会.杭州：2005.
[120]Josa A., Balmaceda A., Gens A., et al. An elasto-plastic model for partially saturated soils exhibiting a maximum of collapse. Proc.3rd Int. Conf. Computational Plasticity. Barcelona: 1992.815-826.
[121]Yudhbir B. Collapsing behaviour of residual soils. Proc.7th SE Asian Geotech Conf. Hong Kong:1982.915-930.
[122]Sun De'an, Sheng Daichao, Xiang Li, et al. Elastoplastic prediction of hydro-mechanical behaviour of unsaturated soils under undrained conditions. Computers and Geotechnics.2008, 35(6):845-852.
[123]Wheeler S. J., Karube D. Constitutive modeling. Proc.1st Int. Conf. Unsaturated Soils. Paris: Balkema,1995.1323-1356.
[124]Sun D. A., Sheng D. C., Cui H. B., et al. A density-dependent elastoplastic hydro-mechanical model for unsaturated compacted soils. International Journal for Numerical and Analytical Methods in Geomechanics.2007,31(11):1257-1279.
[125]陈正汉,谢定义,王永胜.非饱和土的水气运动规律及其工程性质研究.岩土工程学报.1993,15(3)：9-20.
[126]赵成刚,刘艳.连续孔隙介质土力学及其在非饱和土本构关系中的应用.岩土工程学报.2009,31(9)：1324-1335.
[127]刘艳,赵成刚,蔡国庆,等.考虑气相压力变化和偏应力影响的非饱和土本构模型.岩土工程学报.2011,已录用.
[128]Hassanizadeh M., Gray W. G. General conservation equations for multi-phase systems: 1.averaging procedure. Advance in Water Resources.1979,2(9):131-144.
[129]Schrefler B. A. Mechanics and thermodynamics of saturated/unsaturated porous materials and quantitative solutions. Applied Mechanics reviews.2002,55(4):351-388.
[130]Bowen R. M. Incompressible porous media models by use of the theory of mixtures. Int J Eng Sci.1980,18(9):1129-1148.
[131]Bowen R. M. Compressible porous media models by use of the theory of mixtures. Int J Eng Sci.1982,20(6):679-735.
[132]de Boer R. Highlights in the historical development of the porous media:toward a consistent macroscopic theory. Applied Mechanics Reviews.1996,49(4):201-262.
[133]Hassanizadeh M., Gray W. G. General conservation equations for multi-phase systems:2. Mass, momenta, energy, and entropy equations. Advance in Water Resources.1979,2(12): 191-203.
[134]Hassanizadeh M., Gray W. G. General conservation equations for multi-phase systems:3. Constitutive theory for porous media flow. Advance in Water Resources.1980,3(3):25-40.
[135]Achanta S., Cushman J. H. On multicomponent, multiphase thermomechanics with interfaces. Int J Eng Sci.1994,32(11):1717-1738.
[136]Truesdell C. Rational Thermodynamics.2nd ed. New York:Springer-Verlag,1984.
[137]Hutter K., Johnk K. Continuum methods of physical modeling. Berlin:Springer,2004.
[138]Hansen A. C. Reexamining some basic definitions of modern mixture theory. Int J Engineering Science.1989,27(12):1531-1544.
[139]Houlsby G. T., Puzrin A. M. A thermomechanical framework for constitutive models for rate-independent dissipative materials. International Journal of Plasticity.2000,16: 1017-1047.
[140]Dean E. T., Houlsby Gt. Editorial. Geotechnique.2005,55(2):415-417.
[141]Houlsby G. T. The work input to an unsaturated granular material. Geotechnique.1997,47(1): 193-196.
[142]Ziegler H., Wehrli C. The derivation of constitutive relations from the free energy and the dissipation function. Advances in Applied Mechanics.1987,25:183-238.
[143]Collins I. F., Houlsby G. T. A thermomechanical framework for rate-independent dissipative materials with internal functions. International Journal of Plasticity.2001,17:1147-1165.
[144]Collins I. F., Hilder T. A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests. International Journal for Numerical and Analytical Methods in Geomechanics.2002,26(13):1313-1347.
[145]Tarantino A., Mongiovi L. Experimental investigations on the stress variables governing unsaturated soil behaviour at medium to high degrees of saturation. Proceedings of an international workshop on unsaturated soils. Trento, Italy:Balkema,2000.1-20.
[146]Zhang X., Lytton R. L. Stress State Variables for Saturated and Unsaturated Soils. Proceedings of the Fourth International Conference on Unsaturated Soils. Carefree, Arizona, USA:ASCE, 2006.2380-2391.
[147]Collins I. F. The concept of stored plastic work for frozen elastic energy in soil mechanics. Geotechnique.2005,55(5):373-382.
[148]Collins Ian F., Hilder Tamsyn. A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests. International Journal for Numerical and Analytical Methods in Geomechanics.2002,26(13):1313-1347.
[149]Loret B., Khalili N. An effective stress elastic-plastic model for unsaturated porous media. Mechanics of Materials.2002,34:97-116.
[150]Laloui L., Nuth M. On the use of the generalised effective stress in the constitutive modelling of unsaturated soils. Computer and Geotechnics.2009,36(1-2):20-23.
[151]Giuseppe B., Roberto N. An elastoplastic strainhardening model for soil allowing for hydraulic bonding debounding effects. Internatioinal journal for numerical and analytical methods in geomechanics.2009,33:1055-1086.
[152]刘艳,赵成刚.土水特征曲线滞后模型的研究.岩土工程学报.2008,30(03)：399-405.
[153]Sun D. A., Sheng D.C., Cui H. B., et al. A density-dependent elastoplastic hydro-mechanical model for unsaturated compacted soils. International Journal for Numerical and Analytical Methods in Geomechanics.2007,31(11):1257-1279.
[154]Nuth Mathieu, Laloui Lyesse. Advances in modelling hysteretic water retention curve in deformable soils. Computers and Geotechnics.2008,35(6):835-844.
[155]Pham Hung Q., Fredlund Delwyn G., Barbour S. L. A study of hysteresis models for soil-water characteristic curves. Canadian Geotechnical Journal.2005,42(6):1548-1568.
[156]Raveendiraraj A. Coupling of mechanical behaviour and water retention behaviour in unsaturated soils. Glasgow, United Kingdom:University of Glasgow,2009.
[157]Collins I. F., Kelley P. A. A thermomechanical analysisi of a family of soil models. Geotechnique.2002,52(7):506-518.
[158]Butterfield R. A. Natural compression law of soils (an advance on e-logp'). Geotechnique. 1979,29:469-480.
[159]Hashiguchi K. On the linear relations of v-lnp and lnv-lnp for isotropic consolidation of soils. International Journal for Numerical and Analytical Methods in Geomechanics.1995,19(3): 367-376.
[160]Cunningham M. R., Ridley A. M., Dineen K., et al. The mechanical behaviour of a reconstituted unsaturated silty clay. Geotechnique.2003,53(2):183-194.
[161]Sun D. A., Matsuoka H., Cui H. B., et al. Three-dimensional elasto-plastic model for unsaturated compacted soils with different initial densities. International Journal for Numerical and Analytical Methods in Geomechanics.2003,27(12):1079-1098.
[162]Sun D. A., Sheng Daichao, Xu Yongfu. Collapse behaviour of unsaturated compacted soil with different initial densities. Canadian Geotechnical Journal.2007,44:673-686.
[163]Sun D. A., Cui H. B., Matsuoka Hajime,et al. A three-dimensional elastoplastic model for unsaturated compacted soils with hydraulic hysteresis. Soil and foundation.2007,47(2): 253-264.
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