非饱和土水力全耦合模型与数值模拟方法研究
|
摘要
无论是300m级高坝,还是高陡边坡、大型地下工程建设,均无一例外地涉及复杂赋存环境下岩土体渗流、变形与稳定控制问题。岩土体渗流与变形的耦合作用以及多场多相耦合过程既是近30年来国际岩土力学领域的前沿研究热点,也是大型水利水电工程、深部岩体工程、核废料地质处置工程等建设中迫切需要解决的关键科学技术难题。本文以非饱和土为主要研究对象,以土体细观结构及其演化为基础,紧密围绕非饱和土水力耦合机理的量化描述、耦合过程的精细模拟、耦合效应的工程控制这一核心科学问题,重点开展了非饱和土水力全耦合本构模型及数值模拟方法等内容的研究。主要研究成果如下：
(1)建立了考虑颗粒黏结效应的非饱和土弹塑性本构模型
大量研究表明,非饱和状态下土体颗粒间的黏结效应对其变形具有显著影响。采用单位接触面积上弯液面引起的黏结力,定义了黏结因子这一具有严格物理意义的独立变量,用以表征颗粒黏结效应对非饱和土力学特性的影响。基于试验成果,建立了黏结因子与孔隙比的内在联系,推导了加载一湿陷屈服方程,并在修正剑桥模型的框架下建立了三轴应力状态下非饱和土的弹塑性本构模型。与经典的巴塞罗那模型(Barcelona Basic Model, BBM)相比,该模型仅采用单一屈服面(BBM有2个),模型参数较少(8个,较BBM少4个参数),且物理意义明确,均可通过常规试验确定。试验验证结果表明,该模型不仅具备BBM模型所有的描述能力,还能够描述脱湿引起的弹塑性变形等复杂力学特性。
(2)建立了考虑变形效应的土水特性与渗透特性演化模型
在水力耦合过程中,土体变形及孔隙分布演化对其土水特性具有显著影响。尽管土体孔隙分布的演化模式较为复杂,但试验研究表明,土体在变形过程中,孔隙分布的基本形态未发生显著变化、统计分布特征基本不变。以参考状态孔隙分布函数为基础,经平移和缩放给岀了变形条件下土体的孔隙分布函数,进而建立了考虑变形和滞回效应的土水特征曲线模型。由于变形对土水特性的影响是通过孔隙分布这一细观结构特征表征的,因此模型参数具有明确的物理意义,且可通过常规室内试验确定。采用14组试验数据对该模型进行了验证,很好地揭示了不同加载路径、不同应力状态下,土体的主吸湿、主脱湿、干湿循环和扫描曲线等水力特性。
另一方面,土体的非饱和渗透系数也与土体变形及孔隙结构演化密切相关。传统的Mualem统计模型尽管应用广泛,但该模型假定土体具有刚性的孔隙结构,因而无法考虑变形对土体非饱和渗透特性的影响。通过引入与饱和度相对应的饱水平均孔隙半径这一参量,对传统Mualem统计模型进行了修正,进而与上述土水特征曲线模型相结合,建立了考虑变形效应的土体非饱和渗透系数模型。采用4组试验数据对模型进行了验证,表明修正模型对变形条件下土体的渗透特性演化具有更强的描述能力。
(3)建立了非饱和土水力全耦合热力学一致性本构模型
基于上述非饱和土弹塑性本构模型与土水特征曲线模型,在热力学框架下建立了非饱和土固液气三相系统热力学势的一般形式,导岀了土体骨架变形、毛细滞回和水体流动耗散能的具体表达式,建立了考虑非饱和土上骨架弹塑性变形与毛细滞回效应的水力全耦合热力学一致性本构模型,详细论述了变形过程与毛细滞回过程的耦合机理,采用复杂应力路径下的非饱和土室内试验成果对全耦合本构模型进行了系统验证,表明该模型能够很好地反映非饱和土弹塑性变形与毛细滞回的耦合行为。
(4)建立了土体固液气三相全耦合数学模型与数值模拟方法
基于连续介质力学原理和混合体理论,建立了土体固液气三相耦合数学模型及有限元数位模拟方法。研发了非饱和土固液气三相全耦合数位分析平台,给岀了弹塑性变形与毛细滞回全耦合模型本构积分的全隐式折返-映射(Return-mapping)算法,利用砂柱排水试验成果验证了耦合模型和计算程序的正确性与可靠性。在此基础上,研究了土质边坡在降雨入渗过程中的地下水渗流、气体迁移以及变形和稳定性演化过程,揭示了孔隙气体迁移过程和土体变形过程对边坡湿润锋面的推进以及稳定性变化的阻滞和延缓作用。
(5)依托水布垭工程,开展了高堆石坝非稳定渗流与非线性变形耦合分析
研究了土体固液气三相耦合模型的退化形式,针对水位涨落与骤变条件下具有复杂渗控结构的非稳定渗流问题,建立了与PDE提法完全等价的非稳定性渗流分析抛物Signorini型变分不等式(PVI)提法及有限元数值模拟方法。通过开展矩形砂槽排水试验,验证了PVI方法的正确性与可靠性。依托水布垭工程,对坝体、坝基和地下厂房开展了非稳定渗流与非线性变形耦合分析研究,数位模拟结果与现场实测数据吻合,较好地揭示了水布垭面板堆石坝及地下厂房渗流场与变形场演化的基本特征,为大坝蓄水与安全运行决策提供了理论依据。
Characterization of the coupled stress-strain, water flow and gas transport pro-cesses in gcomaterials is a fundamental issue for performance/safety assessment and optimization design in large-scale hydropowcr engineering, slope engineering and large scale underground space engineering, and in recent decades, there has been an increasing interest in the analysis of coupled hydro-mechanical (HM) phenomena in gcomaterials. In this thesis, a coupled solid-liquid-gas mathematical model for skeleton deformation, water flow and gas transport was developed for unsaturated soils based on the principles of the continuum mechanics and the averaging approach of the mixture theory. On the basis of soil's microstructural observations, a constitutive model for fully coupled stress-strain and hydraulic hysteresis behaviors was proposed in a thermodynamic consistent framework. The proposed model was implemented in a finite element code, and was applied to modeling of coupled deformation, water flow and gas transport in a soil slope subjected to rain infiltration, and modeling of coupled processes of non-steady seepage flow and non-linear deformation in Shuibuya concrete-faced rockfill dam. The major achievements obtained in this study arc summarized as follows:
(1) An elastoplastic constitutive model accounting for the inter-particle bonding effect was proposed for unsaturated soil
Starting from the experimental observation that the inter-particle bonding effect induced by water menisci has a significant influence on the stress-strain behavior of unsaturated soils, an inter-particle bonding factor of rigorous physical meaning, defined as the bonding force per unit cross-sectional area that the force acts on, has been used as an independent variable in our model to represent the magnitude of equivalent bonding stress. Based on an empirical relationship between the bonding factor and the void ratio, a new loading-collapse yield function was proposed, and then a constitutive model in triaxial stress states was presented within the framework of Modified Cam-Clay Model. Compared with the classic Barcelona Basic Model (BBM), which contains two yield surfaces and twelve parameters, the proposed model only consists of one yield surface and eight parameters. All of the model parameters have clean physical meanings and can be obtained through standard triaxial and suction-controlled laboratory tests. Comparisons between experimental data and model results show that in most cases, the proposed model is not only able to reproduce the stress-strain behaviors that can be described by BBM, but also able to model the drying-induced elastoplastic deformation.
(2) A deformation-dependent hysteretic water retention curve and hy-draulic conductivity model were proposed for unsaturated soils
It has been well recognized that the deformation of soil skeleton and the change in pore size distribution (PSD) have a significant effect on water retention behavior of unsaturated soils. Although the PSD evolves rather complicatedly during deformation, experimental data showed that the overall shapes and the distribution characteristics of the PSD function are not significantly altered. Based on these findings, the PSD function at a deformed state was obtained by horizontal shifting and vertical scaling of the corresponding PSD function at a reference state. On this basis, a hysteretic water retention curve model was formulated to account for the influences of deformation and hysteresis on the variation of saturation. Since the effect of deformation on water retention curve is represented by the change in PSD, all of the model parameters have clear physical meanings and can be calibrated by standard laboratory tests. Fourteen experimental data sets were used to validate the proposed model, showing that the model can reasonably capture important features of retention properties for deformable soils under different loading paths and different stress states, including main wetting, main drying, drying-wetting cycles and scanning curves.
On the other hand, the permeability of soils is also dependent on soil deformation and PSD evolution. Although Mualem statistical model is widely used to determine un-saturated hydraulic conductivity, Mualem model is not adequate for describing the un-saturated hydraulic conductivity in deformable soils. In this thesis, the original Mualem model was modified by incorporating a new variable defined as the mean radius of pores completely filled by water in a given degree of saturation to account for the effects of soil deformation on the unsaturated hydraulic conductivity. An unsaturated hydraulic conductivity model was then proposed by combining our water retention curve model and the modified Mualem model to account for the effect of deformation on permeability evolution. Experimental data of four types of soils were used to evaluate the modified model, which indicated that the modified model is able to describe the permeability for deformable soils with higher accuracy.
(3) A therrnodynamic consistent model for fully coupled hydromechani-cal behaviors of unsaturated soils was proposed
Within the framework of therrnodynamic, a general therrnodynamic potential was defined for the three phases in unsaturated soils, and then the expression of dissipation energy for solid deformation, capillary hysteresis and water flow were derived. Based on the proposed models mentioned in (1) and (2), the constitutive model for fully cou-pled stress-strain and hydraulic hysteresis were proposed in a thermodynamie consistent framework, and the coupling mechanism between deformation and capillary hystere-sis was discussed in details. Laboratory tests with complex stress paths were used to evaluate the coupled model, showing that in most cases, the proposed model can rea-sonably capture the important features of coupled stress-strain and hydraulic hysteresis behaviors in unsaturated soils.
(4) A numerical model for coupled solid deformation, water flow and gas transport in unsaturated soils was proposed
A coupled solid-liquid-gas mathematical model for unsaturated soils was developed based on the principles of the continuum mechanics and the averaging approach of the mixture theory. A three dimensional computer code was developed, in which a fully implicit return-mapping algorithm was adopted to integrate the stress-strain and water retention relations. The computer code was validated by Liakopoulos' draining test. On this basis, the coupled processes of unsaturated flow, gas transport and soil deformation were simulated with the proposed coupled solid-liquid-gas model, and the numerical results demonstrate the delaying effects and impacts of gas transport and soil deformation on the propagation of the wetting front and the evolution of slope stability.
(5) Coupled analysis of non-steady seepage flow and non-linear deforma-tion processes in Shuibuya concrete-faced rockfill dam was performed
As for the non-steady seepage flow problem subjected to variable water head condi-tions, a new parabolic variation inequality (PVI) formulation mathematically equivalent to the PDE formulation was proposed, and the corresponding discretized FEM formu-lation was established and validated by laboratory tests. The proposed method was used to model the coupled processes of non-steady seepage flow and non-linear defor-mation in Shuibuya concrete-faced rockfill dam. Comparison of model predictions with in-situ measurements shows that the presented model has an acceptable performance for capturing the main features of non-steady seepage and non-linear deformation behav-iors, which provides a theoretical basis for dam impounding decision and safe operation management.
(1)建立了考虑颗粒黏结效应的非饱和土弹塑性本构模型
大量研究表明,非饱和状态下土体颗粒间的黏结效应对其变形具有显著影响。采用单位接触面积上弯液面引起的黏结力,定义了黏结因子这一具有严格物理意义的独立变量,用以表征颗粒黏结效应对非饱和土力学特性的影响。基于试验成果,建立了黏结因子与孔隙比的内在联系,推导了加载一湿陷屈服方程,并在修正剑桥模型的框架下建立了三轴应力状态下非饱和土的弹塑性本构模型。与经典的巴塞罗那模型(Barcelona Basic Model, BBM)相比,该模型仅采用单一屈服面(BBM有2个),模型参数较少(8个,较BBM少4个参数),且物理意义明确,均可通过常规试验确定。试验验证结果表明,该模型不仅具备BBM模型所有的描述能力,还能够描述脱湿引起的弹塑性变形等复杂力学特性。
(2)建立了考虑变形效应的土水特性与渗透特性演化模型
在水力耦合过程中,土体变形及孔隙分布演化对其土水特性具有显著影响。尽管土体孔隙分布的演化模式较为复杂,但试验研究表明,土体在变形过程中,孔隙分布的基本形态未发生显著变化、统计分布特征基本不变。以参考状态孔隙分布函数为基础,经平移和缩放给岀了变形条件下土体的孔隙分布函数,进而建立了考虑变形和滞回效应的土水特征曲线模型。由于变形对土水特性的影响是通过孔隙分布这一细观结构特征表征的,因此模型参数具有明确的物理意义,且可通过常规室内试验确定。采用14组试验数据对该模型进行了验证,很好地揭示了不同加载路径、不同应力状态下,土体的主吸湿、主脱湿、干湿循环和扫描曲线等水力特性。
另一方面,土体的非饱和渗透系数也与土体变形及孔隙结构演化密切相关。传统的Mualem统计模型尽管应用广泛,但该模型假定土体具有刚性的孔隙结构,因而无法考虑变形对土体非饱和渗透特性的影响。通过引入与饱和度相对应的饱水平均孔隙半径这一参量,对传统Mualem统计模型进行了修正,进而与上述土水特征曲线模型相结合,建立了考虑变形效应的土体非饱和渗透系数模型。采用4组试验数据对模型进行了验证,表明修正模型对变形条件下土体的渗透特性演化具有更强的描述能力。
(3)建立了非饱和土水力全耦合热力学一致性本构模型
基于上述非饱和土弹塑性本构模型与土水特征曲线模型,在热力学框架下建立了非饱和土固液气三相系统热力学势的一般形式,导岀了土体骨架变形、毛细滞回和水体流动耗散能的具体表达式,建立了考虑非饱和土上骨架弹塑性变形与毛细滞回效应的水力全耦合热力学一致性本构模型,详细论述了变形过程与毛细滞回过程的耦合机理,采用复杂应力路径下的非饱和土室内试验成果对全耦合本构模型进行了系统验证,表明该模型能够很好地反映非饱和土弹塑性变形与毛细滞回的耦合行为。
(4)建立了土体固液气三相全耦合数学模型与数值模拟方法
基于连续介质力学原理和混合体理论,建立了土体固液气三相耦合数学模型及有限元数位模拟方法。研发了非饱和土固液气三相全耦合数位分析平台,给岀了弹塑性变形与毛细滞回全耦合模型本构积分的全隐式折返-映射(Return-mapping)算法,利用砂柱排水试验成果验证了耦合模型和计算程序的正确性与可靠性。在此基础上,研究了土质边坡在降雨入渗过程中的地下水渗流、气体迁移以及变形和稳定性演化过程,揭示了孔隙气体迁移过程和土体变形过程对边坡湿润锋面的推进以及稳定性变化的阻滞和延缓作用。
(5)依托水布垭工程,开展了高堆石坝非稳定渗流与非线性变形耦合分析
研究了土体固液气三相耦合模型的退化形式,针对水位涨落与骤变条件下具有复杂渗控结构的非稳定渗流问题,建立了与PDE提法完全等价的非稳定性渗流分析抛物Signorini型变分不等式(PVI)提法及有限元数值模拟方法。通过开展矩形砂槽排水试验,验证了PVI方法的正确性与可靠性。依托水布垭工程,对坝体、坝基和地下厂房开展了非稳定渗流与非线性变形耦合分析研究,数位模拟结果与现场实测数据吻合,较好地揭示了水布垭面板堆石坝及地下厂房渗流场与变形场演化的基本特征,为大坝蓄水与安全运行决策提供了理论依据。
Characterization of the coupled stress-strain, water flow and gas transport pro-cesses in gcomaterials is a fundamental issue for performance/safety assessment and optimization design in large-scale hydropowcr engineering, slope engineering and large scale underground space engineering, and in recent decades, there has been an increasing interest in the analysis of coupled hydro-mechanical (HM) phenomena in gcomaterials. In this thesis, a coupled solid-liquid-gas mathematical model for skeleton deformation, water flow and gas transport was developed for unsaturated soils based on the principles of the continuum mechanics and the averaging approach of the mixture theory. On the basis of soil's microstructural observations, a constitutive model for fully coupled stress-strain and hydraulic hysteresis behaviors was proposed in a thermodynamic consistent framework. The proposed model was implemented in a finite element code, and was applied to modeling of coupled deformation, water flow and gas transport in a soil slope subjected to rain infiltration, and modeling of coupled processes of non-steady seepage flow and non-linear deformation in Shuibuya concrete-faced rockfill dam. The major achievements obtained in this study arc summarized as follows:
(1) An elastoplastic constitutive model accounting for the inter-particle bonding effect was proposed for unsaturated soil
Starting from the experimental observation that the inter-particle bonding effect induced by water menisci has a significant influence on the stress-strain behavior of unsaturated soils, an inter-particle bonding factor of rigorous physical meaning, defined as the bonding force per unit cross-sectional area that the force acts on, has been used as an independent variable in our model to represent the magnitude of equivalent bonding stress. Based on an empirical relationship between the bonding factor and the void ratio, a new loading-collapse yield function was proposed, and then a constitutive model in triaxial stress states was presented within the framework of Modified Cam-Clay Model. Compared with the classic Barcelona Basic Model (BBM), which contains two yield surfaces and twelve parameters, the proposed model only consists of one yield surface and eight parameters. All of the model parameters have clean physical meanings and can be obtained through standard triaxial and suction-controlled laboratory tests. Comparisons between experimental data and model results show that in most cases, the proposed model is not only able to reproduce the stress-strain behaviors that can be described by BBM, but also able to model the drying-induced elastoplastic deformation.
(2) A deformation-dependent hysteretic water retention curve and hy-draulic conductivity model were proposed for unsaturated soils
It has been well recognized that the deformation of soil skeleton and the change in pore size distribution (PSD) have a significant effect on water retention behavior of unsaturated soils. Although the PSD evolves rather complicatedly during deformation, experimental data showed that the overall shapes and the distribution characteristics of the PSD function are not significantly altered. Based on these findings, the PSD function at a deformed state was obtained by horizontal shifting and vertical scaling of the corresponding PSD function at a reference state. On this basis, a hysteretic water retention curve model was formulated to account for the influences of deformation and hysteresis on the variation of saturation. Since the effect of deformation on water retention curve is represented by the change in PSD, all of the model parameters have clear physical meanings and can be calibrated by standard laboratory tests. Fourteen experimental data sets were used to validate the proposed model, showing that the model can reasonably capture important features of retention properties for deformable soils under different loading paths and different stress states, including main wetting, main drying, drying-wetting cycles and scanning curves.
On the other hand, the permeability of soils is also dependent on soil deformation and PSD evolution. Although Mualem statistical model is widely used to determine un-saturated hydraulic conductivity, Mualem model is not adequate for describing the un-saturated hydraulic conductivity in deformable soils. In this thesis, the original Mualem model was modified by incorporating a new variable defined as the mean radius of pores completely filled by water in a given degree of saturation to account for the effects of soil deformation on the unsaturated hydraulic conductivity. An unsaturated hydraulic conductivity model was then proposed by combining our water retention curve model and the modified Mualem model to account for the effect of deformation on permeability evolution. Experimental data of four types of soils were used to evaluate the modified model, which indicated that the modified model is able to describe the permeability for deformable soils with higher accuracy.
(3) A therrnodynamic consistent model for fully coupled hydromechani-cal behaviors of unsaturated soils was proposed
Within the framework of therrnodynamic, a general therrnodynamic potential was defined for the three phases in unsaturated soils, and then the expression of dissipation energy for solid deformation, capillary hysteresis and water flow were derived. Based on the proposed models mentioned in (1) and (2), the constitutive model for fully cou-pled stress-strain and hydraulic hysteresis were proposed in a thermodynamie consistent framework, and the coupling mechanism between deformation and capillary hystere-sis was discussed in details. Laboratory tests with complex stress paths were used to evaluate the coupled model, showing that in most cases, the proposed model can rea-sonably capture the important features of coupled stress-strain and hydraulic hysteresis behaviors in unsaturated soils.
(4) A numerical model for coupled solid deformation, water flow and gas transport in unsaturated soils was proposed
A coupled solid-liquid-gas mathematical model for unsaturated soils was developed based on the principles of the continuum mechanics and the averaging approach of the mixture theory. A three dimensional computer code was developed, in which a fully implicit return-mapping algorithm was adopted to integrate the stress-strain and water retention relations. The computer code was validated by Liakopoulos' draining test. On this basis, the coupled processes of unsaturated flow, gas transport and soil deformation were simulated with the proposed coupled solid-liquid-gas model, and the numerical results demonstrate the delaying effects and impacts of gas transport and soil deformation on the propagation of the wetting front and the evolution of slope stability.
(5) Coupled analysis of non-steady seepage flow and non-linear deforma-tion processes in Shuibuya concrete-faced rockfill dam was performed
As for the non-steady seepage flow problem subjected to variable water head condi-tions, a new parabolic variation inequality (PVI) formulation mathematically equivalent to the PDE formulation was proposed, and the corresponding discretized FEM formu-lation was established and validated by laboratory tests. The proposed method was used to model the coupled processes of non-steady seepage flow and non-linear defor-mation in Shuibuya concrete-faced rockfill dam. Comparison of model predictions with in-situ measurements shows that the presented model has an acceptable performance for capturing the main features of non-steady seepage and non-linear deformation behav-iors, which provides a theoretical basis for dam impounding decision and safe operation management.
引文
[1]王驹,郑华铃,徐国庆,等.我国高放废物地质处置研究十年进展[M].北京：原子能岀版社,2004.
[2]Gens A. Soil environment interactions in geotechnical engineering[J]. Geotechnique,2010, 60(1):3-74.
[3]Dai Fuchu, Lee CF, Wang Sijing. Analysis of rainstorm-induced slide-debris flows on natural terrain of lantau island, Hong Kong[J]. Engineering Geology,1999,51(4):279-290.
[4]Hu R, Chen Y, Zhou C. Modeling of coupled deformation, water flow and gas transport in soil slopes subjected to rain infiltration[J]. Sci China Tech Sci,2011,54(10):2561-2575.
[5]史斗,郑军卫.世界天然气水合物研究开发现状和前景.地球科学进展[J],1999,14(4)：330-339.
[6]Raveendiraraj A. Coupling of mechanical behaviour and water retention behaviour in un-saturated soils[D]. Scotland:University of Glasgow,2009.
[7]Sun DA, Sun WJ, Li X. Effect of degree of saturation on mechanical behaviour of unsaturated soils and its elastoplastic simulation[J]. Computers and Geotechnics,2010,37(5):678-688.
[8]Terzaghi K. Principles of soil mechanics, iv-settlement and consolidation of clay [J]. Engi-neering News-Record,1925,95(3):874-878.
[9]Biot MA. General theory of three-dimensional consolidation. Journal of applied physics [J], 1941,12(2):155-164.
[10]Lloret A, Romero E, Villar MV. FEBEX II Project Final report on thermo-hydro-mechanical laboratory tests[R]. Publicacion tecnica. (Empresa Nacional de Residuos Radi-activos),2004,10,11-165.
[11]Sten Bjurstrom. Storage of nuclear waste in sweden[J]. Tunnelling and Underground Space Technology,1989,4(2):139-142.
[12]Neerdael B, Boyazis,JP. The belgium underground research facility:Status on the demon-stration issues for radioactive waste disposal in clay[J]. Nuclear engineering and design,1997, 176(1):89-96.
[13]Rummery TE, Rosinger E. The Canadian nuclear fuel waste management program[R]. Whiteshell Nuclear Research Establishment,1984.
[14]Iwasaki Y. Reassessment of the effective stress coefficient x in unsaturated soils[D]. Japan: Kobe University, 1978.
[15]Wlieeler S, Sivakumar V. An elasto plastic critical state framework for unsatnrated soil[J]. Geotechnique 1995; 45(1): 35-53.
[16]Sharma R. Mechanical behaviour of unsaturated highly expansive clays[D]. United Kingdom: University of Oxford, 1998.
[17]Sivakumar, R. Effects of anisotropy on the behaviour of unsaturated compacted clay[D]. United Kingdom: The Queen's University of Belfast, 2005.
[18]Gallipoli D, Toll D, Augarde C, et al. The MUSE Network: sharing research expertise on unsaturated soils across Europe[J]. Geotechnical Special Publication, 2006; 147(2): 2075.
[19]Josa A, Alonso EE, Lloret A, et al.Stress strain behaviour or partially saturated soils[C]. In Proceedings 9th European Conference on Soil Mechanics and oundation Engineering, 561-564, 1987.
[20]Alonso EE, Gens A, Josa A. A Constitutive Model for Partially Saturated Soils[J]. Geotechnique 1990; 40(3): 405-430.
[21]Cui YJ, Delage P. Yielding and plastic behaviour of an unsaturated compacted silt[J]. Geotechnique, 1996,46(2): 291-311.
[22]Gallipoli D, Wheeler SJ, Karstunen K. Modelling the variation of degree of saturation in a defornable unsaturated soil[J]. Geotechnique, 2003, 53(1): 105-112.
[2,3]Wheeler SJ, Sharma RS, Buisson MSR. Coupling of hydraulic hysteresis and stress strain behaviour in unsa.turated soils[J]. Geotechnique, 2003, 53(1): 41-54.
[24]Chen ZH, Fredhmd DC, KM G J. Overall volume change, water volume change, and yield associated with an unsaturated compacted loess[J]. Canadian Geotechnical Journal, 1999, 36(2): 321-329.
[25]Sivakumar V. A critical state framework for unsaturated soil[D]. United Kingdom: Univer-sity of Sheffield. 1993.
[26]Nimmo JR, Miller EE. The temperature dependence of isothermal moisture vs. potential characteristics of soils[J]. Soil Science Society of America Journal, 1986, 50(5): 1 105-1113.
[27]Huang S, Harbour SL,Fredlund DG. Development and verification of a. coefficient of perme ability function for a deformable unsaturated soil[J]. Canadian Geotechnical Journal, 1998, 35(3):411-425.
[28]Romero, E. Characterisation and thermo-hydro-mechanical behavior of unsaturated Boom clay:an experimental study[D]. Spain:Universitat Politecnica de Catalunya,1999.
[29]Vanapalli S, Fredlund D, Pufahl D. The influence of soil structure and stress history on the soil-water characteristics of a compacted till[J]. Geotechnique,1999,49(2):143-160.
[30]WW Ng C,Pang YW. Experimental investigations of the soil water characteristics of a volcanic soil[J]. Canadian Geotechnical Journal,2000,37(6):1252-1264.
[31]Romero E, Vaunat J. Retention curves of deformable clays[M]. Experimental evidence and theoretical approaches in unsaturated soils,2000:91-106.
[32]Barrera M. Estudio experimental del comportamiento hidro mecanico de suelos co-lapsables[D]. Spain:Universitat Politecnica de Catalunya,2002.
[33]Villar M, Romero E, Lloret A. Thermo-mechanical and geochemical effects on the perme-ability of high-density clays[C]. Proceedings of the international symposium on large scale field tests in granite Advances in understanding engineered clay barriers In:Alonso EE, Ledesma A (eds) AA Balkema Publishers, Leiden,2005, p.177-191.
[34]Delage P, Marcial D, Cui Y, et al. Ageing effects in a compacted bentonite:a microstructure approach [J]. Geotechnique,2006,56(5):291-304.
[35]Olivella S. Alonso E. Gas flow through clay barriers. Geotechnique [J],2008,58(3):157-176.
[36]Gallage C, Uchimura T. Effects of dry density and grain size distribution on soil-water characteristic curves of sandy soils[J]. Soils and Foundations,2010,50(1):161-172.
[37]Tarantino A. A water retention model for deformable soils[J]. Geotechnique,2009,59(9): 751-762.
[38]Chapuis RP. Predicting the saturated hydraulic conductivity of soils:a review[J]. Bulletin of Engineering Geology and the Environment,2012,71(3):401-434.
[39]Bishop A. The principle of effective stress[J]. Teknisk Ukeblad,1959,106(39):859-863.
[40]Blight G. Effective stress evaluation for unsaturated soils[J]. Journal of the Soil Mechanics and Foundations Division:proceedings of the American Society of Civil Engineers,1967, 93:125-148. Journal of the Soil Mechanics and Foundations Division
[41]Kohgo Y, Nakano M, Miyazaki T. Theoretical aspects of constitutive modelling for unsat-urated soils[J]. Soils and Foundations,1993,33(4):49-63.
[42]Karube D. An ideal unsaturated soil and the Bishop's soil[C]. Proceeding in 13th Interna-tional Conference SMFE,1994, pp.43-46.
[43]Karube D, Kawai K. The role of pore water in the mechanical behavior of unsaturated soils Geotechnical and Geological Engineering[J], 2001, 19(3): 211-241.
[44]Burland J. Some aspects of the mechanical behaviour of partly saturated soils[M]. Moisture Equilibria and Moisture Change in Soils Beneath Covered Areas, 1965, 270: 10-20.
[45]Morgenstern N. Properties of compacted soils[C]. Contribution to panel discussion, Session IV, Proceeding 6th Panamerican Conf on Soil Mechanics and Foundation Engineering, 1979, pp. 349-354.
[46]Aitchison, GD, Donald TB. Some- preliminary studies of unsa.turat.ed soils, (b) Effective stress-es in unsaturated soils[C]. The 2nd Australia New Zealand Conference on Soil Mechanics and Foundation Engineering, Christchurch, 1956, 192-199.
[47]Bishop A, Blight G. Some aspects of effective stress in saturated and partly saturated soils[J]. Geoteehnique, 1963, 13(3): 177-197.
[48]Fredlund DG, Morgenstern NR. Stress state variables for unsaturated soils[J]. Journal of Geotechnical and Geoenvironmental Engineering, 1977, 103(5): 447-466.
[49]Sun DA, Matsuoka H, Yao YP, et al. An elasto pla.stic model for unsaturated soil in three dimensional stresses [J]. Soils and Foundations, 2000, 40(3): 17-28.
[50]Loret B, Khalili N. An effective stress elastic -plastic model for unsaturated porous media[J]. Mechanics of Materials 2002, 34(2): 97-116.
[51]姚仰平,牛雷,崔文杰,等.超固结非饱和土的本构关系[J].岩土工程学报,2011,33(6)：833-839.
[52]Yao YP. Hou W, Zhou AX. UH model: three-dimensional unified hardening model for overconsolidated clays[J]. Geotechnique, 2009, 59(5): 451-469.
[53]Wheeler S. Inclusion of specific water volume within an elasto plastic model for unsaturated soil [J]. Canadian Geotechnical Journal, 1996; 33(1): 42-57.
[54]Dangla P, Malinsky L, Coussy O. Plasticity and imbibition drainage curves for unsaturated soils: a unified approach[C]. Proceeding 6th International Symposium Numerical Models in Geomechanics (NUMOGVI), Montreal, 1997, pp. 141-146.
[55]Vaunat J, Romero E, Jonimi C. An elastopla.stic hydromechanical model for unsaturated soils[C]. In Proceedings of the international workshop on unsat.urated soils, Trento, 2000, pp. 121-138.
[56]Tarnagnini R. An extended Cam clay model for unsaturated soils with hydraulic hystere-sis[J]. Geotechnique, 2004, 54(3), 223-228.
[57]Sun DA, Sheng D, Sloan SW. Elastoplastic modelling of hydraulic and stress-strain be-haviour of unsaturated soils[J]. Mechanics Of Materials,2007,39(3):212-221.
[58]Nuth M, Laloui L. Effective stress concept in unsaturated soils:clarification and validation of a unified framework[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2008,32(7):771-801.
[59]Romero E, Jommi C. An insight into the role of hydraulic history on the volume changes of anisotropic clayey soils[J]. Water Resources Research,2008,44(12):W12412.
[60]Sheng D, Fredlund DG, Gens A. A new modelling approach for unsaturated soils using independent stress variables [J]. Canadian Geotechnical Journal,2008,45(4):511-534.
[61]Muraleetharan KK, Liu C, Wei C, et al. An elastoplatic framework for coupling hydraulic and mechanical behavior of unsaturated soils [J]. International Journal of Plasticity,2009, 25(3):473-490.
[62]Arairo W, Prunier F, Djeran MI, et al. A new insight into modelling the behaviour of unsatu-rated soils[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2012, DOI:10.1002/nag.2151
[63]Khosravi A, McCartney JS. Impact of Hydraulic Hysteresis on the Small-Strain Shear Mod-ulus of Low Plasticity Soils[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2012,138(11):1326-1333.
[64]Liu C, Muraleetharan KK. Coupled hydro-mechanical elastoplastic constitutive model for unsaturated sands and silts. I:Formulation [J]. International Journal of Geomechanics,2012, 12(3):239-247.
[65]沈珠江.土体变形特征的损伤力学模拟[C].第5届全国土力学数值分析与解析方法讨论会议论文集.重庆,1994：1-8.
[66]缪林昌.非饱和土的本构模型研究[J].岩土力学,2007,28(5)：855-860.
[67]李广信,司韦,张其光.非饱和土的清华弹塑性模型[J].岩土力学,2008,29(8)：2033-2062.
[68]Sun D, Sheng D, Cui H, et al. A density-dependent elastoplastic hydro-mechanical model for unsaturated compacted soils [J]. International Journal for Numerical and Analytical Methods in Geomechanics,2007,31(11):1257-1279.
[69]孙德安.非饱和土的水力和力学特性及其弹塑性描述[J].岩土力学,2009,30(11)：3217-3231.
[70]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[J].岩土工程学报,2009,31(9)：1324-1335.
[71]Gray WG, Schrefler BA. Thermodynamic approach to effective stress in partially saturated porous media[J]. European Journal of Mechanics A/Solids, 2001, 20(4): 521-538.
[72]Sheng D, Sloan S, Gens A. A constitutive model for unsaturated soils: thermomechanical and computational aspects[J]. Computational Mechanics, 2004, 33(6): 453-465.
[73]Santagiuliana R, Schrefler B. Enhancing the Bolzon - Schrefler - Zienkiewicz constitutive model for partially saturated soil[J]. Transport in Porous Media, 2006, 65(1): 1-30.
[74]Li X. Thermodynamics based constitutive framework for unsaturated soils[J]. 1: Theory. Geotechnique, 2007, 57(5): 411-422.
[75]Li X. Thermodynamics based constitutive framework for unsaturated soils[J]. 2. A basic triaxial model. Geoteehnique, 2007, 57(5): 423-435.
[76]Coussy O, Pereira JM, Vaunat J. Revisiting the thermodynamics of hardening plasticity for unsaturated soils[J]. Computers and Geoteclmics, 2010, 37(1): 207-215.
[77]Zhao C, Liu Y, Gao F. Work and energy equations and the principle of generalized effective stress for unsaturated soils[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2010, 34(9): 920-936.
[78]Mroginski JL, Etse G, Vreeh SM. A thermodynamical gradient theory for deformation and strain localization of porous media[J]. International Journal of Plasticity, 2011, 27(4): 620-634.
[79]Nikooee E, Habibagahi G, Hassanizadeh SM, et al. Effective Stress in Unsaturated Soils: A Thermodynamic Approach Based on the Interfacial Energy and Hydrorneehanieal Con-pling[J]. Transport, in Porous Media, 2013, 96(2): 369-396.
[80]Gallipoli D, Gens A, Sharma R, et, al. An elasto plastic model for unsaturated soil in-corporating the effects of suction and degree of saturation on mechanical behaviour[J]. Geotechnique, 2003, 53(1): 123-136.
[81]Brooks R H, Corny A T. Hydraulic properties of porous media. Fort Collins, CO: Colorado State University[R]. Hydrology Paper, 1964, No. 3.
[82]van Genuchten MT. A closed form equation for predicting the hydraulic conductivity of unsaturated soils[J]. Soil Science Society of America Journal, 1980, 44(5): 892-898.
[83]Berkowitz B, Ewing RP. Percolation theory and network modeling applications in soil physic-s[J]. Surveys in Geophysics, 1998, 19(1): 23-72.
[84]Fredlund D, Xing A. Equations for the soil water characteristic eurve[J]. Canadian Geotech-nical Journal, 1994, 31(4): 521-532.
[85]Assouline S. Modeling the relationship between soil bulk density and the water retention curve[J]. Vadose Zone Journal,2006,5(2):554-563.
[86]Nuth M, Laloui L. Advances in modelling hysteretic water retention curve in dcformable soils[J]. Computers and Geotechnics,2008,35(6):835-844.
[87]Masin D. Predicting the dependency of a degree of saturation on void ratio and suction using effective stress principle for unsaturated soils[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2010,34(1):73-90.
[88]Gallipoli D. A hysteretic soil-water retention model accounting for cyclic variations of suc-tion and void ratio[J]. Geotechnique,2012,62(7):605-616.
[89]Zhou A, Sheng D, Carter J. Modelling the effect of initial density on soil-water characteristic curves [J]. Geotechnique,2012,62(8):669-680.
[90]Morvan M, Wong H, Branque D. Incorporating porosity-dependent hysteretic water reten-tion behavior into a new constitutive model of unsaturated soils[J]. Canadian Geotechnical Journal,2011,48(12):1855-1869.
[91]Assouline S, Tessier D, Bruand A. A conceptual model of the soil water retention curve[J]. Water Resources Research,1998,34(2):223-231.
[92]周葆春,孔令伟.考虑体积变化的非饱和膨胀土土水特征[J].水利学报,2011,42(10)：1152-1160.
[93]Simms P, Yanful E. Predicting soil-water characteristic curves of compacted plastic soils from measured pore-size distributions [J]. Geotechnique,2002,52(4):269-278.
[94]Cuisinier O, Laloui L. Fabric evolution during hydromechanical loading of a compacted silt[J]. International Journal For Numerical and Analytical Methods in Geomechanics,2004, 28(6):483-499.
[95]Simms P, Yanful E. A pore-network model for hydromechanical coupling in unsaturated compacted clayey soils[J]. Canadian Geotechnical Journal,2005,42(2):499-514.
[96]张雪东,赵成刚,刘艳,等.变形对土水特征曲线影响规律模拟研究[J].土木工程学报,2011,44(7)：119-126.
[97]Mualem Y, Klute A. Hydraulic conductivity of unsaturated soils:prediction and formu-las[M]. Methods of soil analysis Part 1:Physical and mineralogical methods,1986:799-823.
[98]Richards LA. Capillary conduction of liquids through porous mediums[J]. Physics,1931, 1(5):318-333.
[99]Wind G. A field experiment concerning capillary rise of moisture in a heavy clay soil[J]. Netherlands Journal of Agricultural Science, 1955, 3: 60-69.
[100]Weeks L, Richards S. Soil-water properties computed from transient, flow data[J]. Soil Sci-ence Society of America Journal, 1967,31(6): 721-725.
[101]Gardner W, Fireman M. Laboratory studies of evaporation from soil columns in the presence of a water table[J]. Soil Science, 1958, 85(5): 244-249.
[102]Arbhabhirama A. Kridakorn C. Steady downward flow to a water table[.I]. Wafer Resources Research, 1968, 4(6): 1249-1257.
[103]Gardner W. Some steady-state solutions of the unsaturafed moisture flow equation with application to evaporation from a water table[J]. Soil Science, 1958, 85(4): 228-232.
[104]Philip J. Linearized unsteady multidimensional infiltration [J]. Water Resources Research, 1986, 22(12): 1717-1727.
[105]Davidson J, Stone L, Nielsen D, et al. Field measurement and use of soil water properties[J]. Wafer Resources Research, 1969,5(6): 1312-1321.
[106]Dane J, Klufe A. Salt effects on the hydraulic properties of a swelling soil[J]. Soil Science Society of America Journal, 1977,41(6): 1043-1049.
[107]Zaclnnann D, Duchatean P, Klute A. The calibration of the Richards flow equation for draining column by parameter identification[J]. Soil Science Society of America Journal, 1981, 45(6): 1012-1015.
[108]Hillel D. Introduction to soil physics[M]. Academic press, New York, 1982.
[109]Averjanov S. About permeability of subsurface soils in ease of incomplete saturation [J]. English collection, 1950, 7:19-21.
[110]Irmay S. On the hydraulic: conductivity of unsaturafed soils[J]. Transactions, American Geophysical Union, 1954, 35: 463-467.
[111]Mualern Y. Hydraulic: conductivity of unsafurated porous media: generalized macroscopic approach[J]. Water Resources Research, 1978, 14(2): 325-334.
[112]Childs EC, Collis George N. The permeability of porous materials[J]. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 1950, 201(1066): 392-405.
[113]Laliberte GE, Corey AT, Brooks R. Properties of unsaturatecl porous media[R], Colorado State University Fort Collins, Colorado, 1966.
[114]Huang Sliangyan. Evaluation and Laboratory Measurement of the Coefficient of Permeabil-ity in Deformable[D]. Canada:University of Saskatchewan,1994.
[115]Burdine N, Gournay L, Reichertz P. Pore size distribution of petroleum reservoir rocks[J]. Journal of Petroleum Technology,1950,2(7):195-204.
[116]Purcell W. Capillary pressures-their measurement using mercury and the calculation of permeability thcrefrom[J]. Journal of Petroleum Technology,1949,1(2):39-48.
[117]Fatt I, Dykstra H. Relative permeability studies[J]. Journal of Petroleum Technology,3(9): 249-256,1951.
[118]Burdine NT. Relative permeability calculations from pore size distribution data[J]. Journal of Petroleum Technology,5(3):71-78,1953.
[119]Wyllie MRJ, Gardne GHF. The generalized Kozeny-Carman equation:A novel approach to problems of fluid flow[J]. World Oil Prod Sect,1958,146:210-228.
[120]Mualem Y. A new model for predicting the hydraulic conductivity of unsaturated porous media[J]. Water Resources Research,1976,12(3):513-522.
[121]Lai WM, Rubin DH, Rubin D, et al. Introduction to continuum mechanics[M.]Butterworth Heinemann,2009.
[122]Biot M. General solutions of the equations of elasticity and consolidation for a porous material [J]. Journal of Applied Mechanics,1956,23(1):91-96.
[123]De Boer R. Theory of porous media-past and present[J]. ZAMM-Journal of Applied Math-ematics and Mechanics/Zeitschrift fUr Angewandte Mathematik und Mechanik,1998,78(7): 441-466.
[124]Morland L. A simple constitutive theory for a fluid-saturated porous solid[J]. Journal of Geophysical Research,1972,77(5):890-900.
[125]Bowen RM. Compressible porous media models by use of the theory of mixtures[J]. Inter-national Journal of Engineering Science,1982,20(6):697-735.
[126]Hassanizadeh SM, Gray WG. Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries [J]. Advances in Water Resources,1990,13(4):169-186.
[127]Achanta S, Cushman J, Okos M. On multicomponent, multiphase thermomechanics with interfaccs[J]. International Journal of Engineering Science,1994,32(11):1717-1738.
[128]Zienkiewicz OC. Basic formulation of static: and dynamic: behavior of soil and other porous media[M]. Numerical Methods in Geornechanics. D. Reidl, 1982.
[129]Zienkiewicz OC. Dynamic: behavior of saturated porous media: the generalized Riot's formu-lation and its finite element solution[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1984, 8: 71-96.
[130]Zienkiewiez OC, Xie Y, Schrefler B, et al. Static and dynamic behaviour of soils: a rational approach to quantitative solutions. Ⅱ. Semi saturated problems[J]. Proceedings of the I loyal Society of London A Mathematical and Physical Sciences, 1990, 429(1877): 311-321.
[131]Li XK. Finite-element analysis for immiscible two phase fluid flow in deforming porous media and an unconditionally stable staggered solution [J]. Communications in applied nu-merical methods, 1990, 6(2): 125-135.
[132]Li XK, Zienkiewiez OC. Multiphase flow in deforming porous media and finite element solutions[J]. Computers & Structures, 1992,45(2): 211-227.
[133]杨代泉.非饱和土二维广义固结非线性数值模型[J].岩土工程学报,1992,14(A09)：2-12.
[134]Schrefler B, Xiaoyong Z. A fully coupled model for water flow and airflow in deformable porous media[J]. Wafer Resources Research, 1993,29(1): 155-167.
[135]Gawin D, Baggio P, Schrefler BA. Coupled heat, water and gas flow in deformable porous media[J]. International Journal for Numerical Methods in Fluids, .1995, 20(8 9): 969-987.
[136]Schrefler BA, Zhan X. Sitnoni L. A coupled model for wafer flow, airflow and heat flow in deformable porous media[J]. International Journal of Numerical Methods for Heat and Fluid Flow, 1995, 5(6): 531-547.
137] Gawin D, Schrefler BA. Galindo M. Thermo hydro mechanical analysis of partially satu-rated porous materials[J]. Engineering Computations, 1996, 13(7): 113-143.
[138]Mroginski JL, Rado D, Ariel IT. et al. A finite element approach for multiphase fluid flow in porous mcdia[J]. Mathematics and Computers in Simulation, 2010, 81(1): 76-91.
[139]Schreflcr BA. Scotta. R. A fully coupled dynamic: model for two phase fluid flow in de formable porous media[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(24): 3223-3246.
[140]Wu YS, Forsyth PA. On the selection of primary variables in numerical formulation for modeling multiphase flow in porous media [J]. Journal of Contaminant Hydrology, 2001, 48(3): 277-304.
[141]Laloui L, Klubertanz G, Vulliet L. Solid-liquid-air coupling in multiphase porous medi-a[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2003, 27(3):183-206.
[142]Oettl G, Stark R, Hofstetter G. Numerical simulation of geotechnical problems based on a multi-phase finite element approach[J]. Computers and Geotechnics,2004,31(8):643-664.
[143]Stelzer R, Hofstetter G. Adaptive finite element analysis of multi-phase problems in geotech-nics[J]. Computers and Geotechnics,2005,32(6):458-481.
[144]徐炎兵,韦昌富,李幻,等.非饱和土渗流与变形耦合问题的有限元分析[J].岩土力学,2009,30(5)：1490-1496.
[145]Khoei A, Mohammadnejad T. Numerical modeling of multiphase fluid flow in deforming porous media:A comparison between two and three-phase models for seismic analysis of earth and rockfill dams[J]. Computers and Geotechnics,2011,38(2):142-166.
[146]Mohammadnejad T, Khoei A. Hydra-mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2012, DOI:10.1002/nag.2079.
[147]Sheng D, Sloan SW, Gens A, et al. Finite element formulation and algorithms for unsaturated soils. Part Ⅰ:Theory[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2003,27(9):745-765.
[148]Sheng D, Gens A, Fredlund DG, et al. Unsaturated soils:from constitutive modelling to numerical algorithms [J]. Computers and Geotechnics,2008,35(6):810-824.
[149]Wang W, Kosakowski G, Kolditz O. A parallel finite element scheme for thermo-hydro-mechanical (THM) coupled problems in porous media[J]. Computers & Geosciences,2009, 35(8):1631-1641.
[150]Callari C, Abati A. Finite element methods for unsaturated porous solids and their appli-cation to dam engineering problems[J]. Computers and Structures,2009,87(7):485-501.
[151]Nagel F, Meschke G. An elasto-plastic three phase model for partially saturated soil for the finite element simulation of compressed air support in tunnelling[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2010,34(6):605-625.
[152]Pertl M, Hofmann M, Hofstetter G. Coupled FE Analysis Involving Partially Saturated Soils[J]. Proceedings in Applied Mathematics and Mechanics,2010,10(1):207-208.
[153]Rutqvist J, Ijiri Y, Yamamoto H. Implementation of the Barcelona Basic Model into TOUGH-FLAC for simulations of the geomechanical behavior of unsaturated soils [J]. Com-puters and Geosciences,2011,37(6):751-762.
[154]Costa L, Pontes I, Guimaraes L, et, al. Numerical modelling of hydro mechanical behaviour of collapsible soils[J]. Communications in Numerical Methods in Engineering,2008,24(12): 1839-1852.
[155]Zhang H, Zhou L. Implicit integration of a chemo plastic constitutive model for partially saturated soils[J]. International Journal for Numerical and Analytical Methods in Geome-chanics,2008,32(14):1715-1735.
[156]Khoshghalb A. Khalili N. A meshfree method for fully coupled analysis of flow and defor-mation in unsaturated porous media[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2012, DOI:10.1002/nag.1120.
[157]廖红建,姬建.深基坑开挖中饱和非饱和土体渗流 沉降的耦合分析[J].应用力学学报,2008,25(4)：637-640.
[158]张玉军.核废料处置概念库近场热、水应力耦合模型及数值分析[J].岩土力学,2007,28(1)：17-22.
[159]张玉军.核废物地质处置中热、水应力耦合对迁移影响的三维有限元模拟[J].岩土力学,2009,30(7)：2126-2132.
[160]秦爱芳,赵飞,赵小龙.缓冲材料参数对核废料处置库近场影响的二维有限元分析[J].上海大学学报：自然科学版,2012,18(5)：539-544.
[161]黄润秋,戚国庆.饱和渗流基质吸力对边坡稳定性的影响[J].工程地质学报,2002,10(4)：343-348.
[162]Cai F, Ugai K. Numerical analysis of rainfall effects on slope stability[J]. International Journal of Geomeehanies,2004,4(2):69-78.
[163]荣冠,张伟,周创兵.降雨入渗条件下边坡岩体饱和非饱和渗流计算[J].岩土力学,2005,26(10)：1545-1550.
[164]孙冬梅,冯平,张明进.考虑气相作用的降雨入渗对非饱和土坡稳定性的影响[J].天津大学学报,2009,42(9)：777-783.
[165]Sanavia L. Numerical modelling of a slope stability test by means of porous media mechan-ics[J]. Engineering Computations,2009,26(3):245-266.
[166]Borja R.I, White JA, Liu X, et al. Factor of safety in a partially saturated slope inferred from hydro mechanical contimunn modeling[J]. International Journal for Numerical and Analytical Methods in Geomechanies,2012,36(2):236-248.
[167]朱文彬,刘宝琛.降雨条件下上体滑坡的有限元数值分析[J].岩石力学与工程学报,2002,21(4)：509-512.
[168]Cho SE, Lee SR. Instability of unsaturated soil slopes due to infiltration [J]. Computers and Geotechnics,2001,28(3):185-208.
[169]王协群,张有祥,邹维列,等.降雨入渗条件下非饱和路堤变形与边坡的稳定数值模拟[J].岩土力学,2010,31(11)：3640-3655.
[170]吴李泉,张锋,凌贤长,等.强降雨条件下浙江武义平头村山体高边坡稳定性分析[J].岩石力学与工程学报,2009,28(6)：1193-1199.
[171]田东方,刘德富,王世梅,等.土质边坡非饱和渗流场与应力场耦合数值分析[J].岩土力学,2009,30(3)：810-814.
[172]Ehlers W, Graf T, Ammann M. Deformation and localization analysis of partially saturated soil[J]. Computer Methods in Applied Mechanics and Engineering,2004,193(27):2885-2910.
[173]Zheng H, Liu D, Lee C, et al. A new formulation of Signorini's type for seepage problems with free surfaces[J]. International Journal for Numerical Methods in Engineering,2005, 64(1):1-16.
[174]Chen Y, Zhou C, Zheng H. A numerical solution to seepage problems with complex drainage systems[J]. Computers and Geotechnics,2008,35(3):383-393.
[175]陈益峰,周创兵,郑宏.含复杂渗控结构渗流问题数值模拟的SVA方法[J].水力发电学报,2009,28(2)：89-95.
[176]Vanorio T, Prasad M, Nur A. Elastic properties of dry clay mineral aggregates, suspensions and sandstones [J]. Geophysical Journal International,2003,155(1):319-326.
[177]Simmer K. Bodenmechanik. Erdstatische Berechnungen[M], Grundbau Teil,1987,1.
[178]Gvirtzman H, Magaritz M, Klein E, et al. A scanning electron microscopy study of water in soil[J]. Transport in Porous Media,1987,2(1):83-93.
[179]Vogel H-J, Roth K. Quantitative morphology and network representation of soil pore struc-ture[J]. Advances in Water Resources,2001,24(3):233-242.
[180]Schrefler B, Lewis R. The finite element method in the static and dynamic deformation and consolidation of porous media[M]. Wiley, Chichester,1998.
[181]Whitaker S. The transport equations for multi-phase systems [J]. Chemical Engineering Science,1973,28(1):139-147.
[182]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[J].中国科学：E辑,2008,38(9)：1453-1463.
[183]Yeh G.3DFEMWATER:A three-dimensional finite element model of water flow through saturated-unsaturated media[R]. Oak Ridge National Lab., TN (USA),1987.
[184]朱岳明,龚道勇.三维饱和一非饱和渗流场求解舣其逸岀面边界条件处理[J].水科学进展,2003,14(1)：67-71.
[185]Borsi I, Farina A, Fasano A. On the infiltration of rain water through the soil with runoff of the excess water[J]. Nonlinear analysis:real world applications,2004,5(5):763800.
[186]Borsi I, Farina A, Priniicerio M. A rain water infiltration model with unilateral boundary condition:qualitative analysis and numerical simulafcions[J]. Mathematical Methods in the Applied Sciences,2006,29(17):2047-2077.
[187]陈益峰,周创兵,胡冉,等.大型水电工程渗流分析的若干关键问题研究[J],岩土工程学报,2010,32(9)：1448-1454.
[188]Dcsai C, Li G. A residual flow procedure and application for free surface flow in porous media[J]. Advances in Water Resources,1983,6(1):27-35.
[189]Bathe. K.J, Khoshgoftaar MR. Finite element free surface seepage analysis without, mesh iteration [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1979,3(1):13-22.
[190]张有天,陈平,王镭.有自由面渗流分析的初流量法[J].水利学报,1988,8(1)：18-26.
[191]周创兵,熊文林,梁业国.求解无压渗流流场的一种新方法[J].水动力学研究与进展,1996,11(5)：528-534.
[192]速宝玉,朱岳明.不变网格确定渗流自由面的节点虚流量法[J].河海大学学报,1991,19(5)：113-117.
[193]Chen SH, Wang WM, She CX, el. al. Unconfined seepage analysis of discontinuous rock slopc[J). Journal of Hydrodynamics, Sor. B,2000,12(3):75-86.
[194]Jiang QH, Deng SS, Zhou CB, et al. Modeling unconfined seepage flow using three dimensional numerical manifold method [J]. Journal of Hydrodynamics, Ser B,2010,22(4): 554-561.
[195]Alt HW. Numerical solution of steady-state porous flow free boundary probletns[J]. Nu-merische Mathematik,1980,36(1):73-98.
[196]陈益峰,卢礼顺,周创兵,等Signorini型变分不等式方法在实际工程渗流问题中的应用[J].岩土力学,2007,28(supp)：178-182.
[197]Coussy O. Poromechanics[M]. New York:Wiley,2004.
[198]Cho GC, Santamarina JC. Unsaturated particulate materials-particle-level studies. Journal of Geotechnical and Gcoenvironmental Engineering[J],2001,127(1):84-96.
[199]Mitarai N, Nori F. Wet granular materials[J]. Advances in Physics,2006,55(1-2):1-45.
[200]Soulie F, Cherblanc F, El Youssoufi MS, et al. Influence of liquid bridges on the mechanical behaviour of polydisperse granular materials [J]. International Journal for Numerical and Analytical Methods in Geomechanics,2006,30(3):213-228.
[201]Scholtes L, Hicher PY, Nicot F, et al. On the capillary stress tensor in wet granular materi-als. International Journal for Numerical and Analytical Methods in Geomechanics [J],2009, 33(10):1289-1313.
[202]Fleureau JM, Hadiwardoyo S, Correia AG. Generalised effective stress analysis of strength and small strains behaviour of a silty sand, from dry to saturated state[J]. Soils and Foun-dations,2003,43(4):21-33.
[203]Justo J L, Vazquez M. A model for capillary pressure in unsaturated granular soils within the pendular saturation regime[C]. In:Alonso EE, Gens A, editors. Unsaturated soils, vol. 3, CRC Press,2011,151-156.
[204]Toll D. A framework for unsaturated soil behaviour[J]. Geotechnique,1990,40(1):31-44.
[205]Jaky J. Pressure in silos[C]. Proceedings 2nd International Conference Soil Mechanics and Foundation Engineering,1948,1:103-107.
[206]Liu HH, Wei MY, Rutqvist J. Normal-stress dependence of fracture hydraulic properties including two-phase flow properties[J]. Hydrogeology Journal,2012,21:371-382.
[207]Kosugi K. Lognormal distribution model for unsaturated soil hydraulic properties [J]. Water Resources Research,1996,32(9):2697-2703.
[208]Diamond S. Pore size distributions in clays[J]. Clays and Clay Minerals,1970,18(1):7-23.
[209]Delage P, Lefebvre G. Study of the structure of a sensitive Champlain clay and of its evo-lution during consolidation[J]. Canadian Geotechnical Journal,1984,21(1):21-35.
[210]Coulon E, Bruand A. Effects of compaction on the pore space geometry in sandy soils[J]. Soil and Tillage Research,1989,15(1):137-151.
[211]Griffiths F. Joshi R. Change in pore size distribution due to consolidation of clays[J]. Geoteclnique,1989,39(1):159-167.
[212]Penumadu D, Dean J. Compressibility effect in evaluating the pore-size distribution of kaolin clay using mercury intrusion porosimetry[J]. Canadian Geotechnical Journal,2000,37(2): 393-405.
[213]Sivakumar V, Wheeler S. Influence of compaction procedure on the mechanical behaviour of an unsaturated compacted clay. Part, 1: Wetting and isotropic compression[J]. Geoteehnique, 2000, 50(4): 359-368.
[214]Koliji A, Vulliet L, Laloui L. Structural characterization of unsatnrated aggregated soil[J]. Canadian Gcotechnical Journal, 2010, 47(3): 297-311.
[215]Li X, Zhang LM. Characterization of dual structure pore size distribution of soil[J]. Cana-dian Geotechnical Journal, 2009, 46(2): 129-141.
[216]Lapicrre C, Leroucil S, Locat J. Mercury intrusion and permeability of Louiseville clay[J]. Canadian Geotechnical Journal, 1990, 27(6): 761-773.
[217]Tanaka H, Shiwakoti DR., Omukai N, et al. Pore size distribution of clayey soils measured by mercury intrusion porosimetry and its relation to hydraulic conductivity [J]. Soils and Foundations, 2003, 43(6): 63-73.
[218]Ninjgarav E, Chung SG, Jang WY, et al. Pore size distribution of Pusan clay measured by mercury intrusion porosimetry[J], KSCE Journal of Civil Engineering, 2007, 11(3): 133-139.
[219]Monroy R, Zdravkovic L, Ridley A. Evolution of microstructure in compacted London Clay during wetting and loa.ding[J]. Geotechnique, 2010, 60(2): 105-119.
[220]Tarantino A. Unsaturated soils: Compacted versus reconstituted stntes[C]. In 5th Interna-tional Conference on Unsaturated Soil, Barcelona, September 6 8, 2010, 113-136.
[221]Nowamooz II, Masrouri V. Suction variations and soil fabric of swelling compacted soils[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2010, 2:129-134.
[222]Croney D, Coleman JD. Pore pressure and suction in soils[C]. In Proceedings of the Con-ference on Pore Pressure; and Suction in Soils. Butterworths, London, 1961, pp. 31-37.
223] Kayadelen C. The consolidation characteristics of an unsaturated compacted soil[J]. Envi-ronmental Geology, 2008, 54(2): 325-334.
[224]Sugii T, Yamada K, Kondou T. Relationship between soil water characteristic curve and void ratio[C]. In: Recife, editor. In UNSAT 2002, Proc 3rd Unsaturated Soils Conference, de Campos and Marinho, 2002, pp. 209-214.
[225]Tarantino A, De Col E. Compaction behaviour of cla,y[J]. Geotechnique, 2008, 58(3): 199-213.
[226]Tombolato S. Resistenza a taglio di un argil la costipata non satura: Risultati sperimentali modellazione[C]. Italy: Universita' degli Studi di Trento, 2003.
[227]D'Onza F, Gallipoli D, Wheeler S, et al. Benchmark of constitutive models for unsaturated soils[J]. Geotechnique,2011,61(4):283-302
[228]Chen Y, Zhou C, Jing L. Modeling coupled THM processes of geological porous media with multiphase flow:Theory and validation against laboratory and field scale experiments[J]. Computers and Geotechnics,2009,36(8):1308-1329.
[229]Assouline S. A model for soil relative hydraulic conductivity based on the water retention characteristic curve[J]. Water Resources Research,2001,37(2):265-271.
[230]Fredlund D, Xing A, Huang S. Predicting the permeability function for unsaturated soils using the soil water characteristic curve[J]. Canadian Geotechnical Journal,1994,31(4): 533-546.
[231]Leij FJ, Russel WB, Lesch SM. The UNSODA unsaturated soil hydraulic database, version 1.0. Report EPA/600/R-96/095 [R]. National Risk Management Research Laboratory, US Environmental Protection Agency, Cincinnati, Ohio,1996.
[232]Malvern LE. Introduction to the Mechanics of a Continuous Medium[M]. Prentice-Hall Inc, New Jersey,1969.
[233]Lemaitre J, Chaboche JL. Mechanics of solid materials[M]. Cambridge University Press, Cambridge, UK,1994.
[234]Olivier Coussy. Mechanics and physics of porous solids[M]. New York:Wiley,2011.
[235]Voyiadjis GZ, Dorgan RJ. Framework using functional forms of hardening internal state variables in modeling elasto-plastic-damage behavior[J]. International Journal of Plasticity, 2007,23(10):1826-1859.
[236]Houlsby GT. The work input to an unsaturated granular material [J]. Geotechnique,1997, 47(1):193-196.
[237]Kuhn H, Tucker A. Nonlinear programming. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probabilistics[M]. University of California Press,1951, pp. 481-492.
[238]Collins IF, Kelly PA. A thermomechanical analysis of a family of soil models[J]. Geotechnique,2002,52(7):507-518.
[239]Collins IF, Hilder T. A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2002,26(13):1313-1347,2002.
[240]Zienkiewicz OC, Taylor RL. The Finite Element Method: Solid Mechanics[M]. New York: Butterworth heinemanri, 2000.
[241]Hughes TJ. Franca LP, Balestra M. A new finite clement formulation for computational fluid dynamics: V. Circumventing the Balmska Brezzi condition: A stable Petrov- Galerkin formulation of the Stokes problem accommodating equal order interpolations[J]. Computer Methods in Applied Mechanics and Engineering, 1986, 59(1): 85-99.
[242]Simo JC, Hughes TJR. Computational Inelasticity[M]. New York: Springer, 1998.
[243]Rutqvist .J, Borgesson L, Chijirnatsu M, et al. Thermohydromechanics of partially saturated geological media: governing equations and formulation of four finite element models[J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(1): 105-127.
[244]Liakopoulos AC. Transient, flow through unsatunited porous media[D]. USA: University of California, 1964.
[245]Brooks RH. Properties of porous media affecting fluid flow. Journal of the Irrigation and Drainage Division[C]. Proceedings of the American Society of Civil Engineers, 1906, pp. 61-88.
[246]Rathfelder K, Abriola LM. Mass conservative numerical solutions of the head based R.ichard-s equation[J]. Water Resources Rescarch, 1994, 30(9): 2579-2586.
[247]郑铁生,李立,许庆余.一类椭圆型变分不等式离散问题迭代算法[J].应用数学和力学1995,16(4)：351-358.
[248]Tracy FT. Clean two and three dimensional analytical solutions of Richards' equation for testing numerical solvers[J]. Water Resources Research, 2006, 42(8): W08503.
[249]Vauclin M, Khanji D, Vachaud C. Experimental and numerical study of a transient, two dimensional unsaturated saturated water table recharge problem[J]. Water Resources Re-search, 1979, 15(5): 1089-1101.
[250]Haverkamp R, Vauclin M, Touma J, et al. A comparison of numerical simulation models for one-dimensional infiltra.tion[J]. Soil Science Society of America Journal. 1977, 41(2): 285-294.
[251]Akai K, Ohnishi Y, Nishigaki M. Finite element analysis of three dimensional flow in saturated unsaturated soils[C]. In Proceedings of the 3rd Int. Conf. Numerical Methods in Georneehanics — Aachen, 1979, pp. 227-239.
[252]Chen Y, Hu R, Zhou C, el, al. A new parabolic variational inequality formulation of Signori-ni's condition for non steady seepage problems with complex seepage control systems[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2011,35(9): 1034-1058.
[253]毛昶熙.渗流计算分析与控制[M].北京：水利电力出版社,1990.
[254]Zhou W. Chang X, Zhou C, et, al. Creep analysis of high concrete-faced rockfill dam[J]. In-ternational Journal for Numerical Methods in Biomedical Engineering,2010,26(11):1477-1492.
[255]钱纪芸,张嘎,张建民.降雨条件下土坡变形机制的离心模型试验研究[J].岩土力学,2011,32(2)：398-402.
[256]郭明伟,李春光,葛修润,等.基于矢量和分析方法的边坡滑而搜索[J].岩土力学,2009,30(6)：1775-1781.
[257]Morgenstern N, Price VE. The analysis of the stability of general slip surfaces[J]. Geotechnique,1965,15(1):79-93.
[258]Fredlund D, Morgenstern N, Widger R. The shear strength of unsaturated soils[J]. Canadian Geotechnical Journal,1978,15(3):313-321.
[259]SVanapalli S, Fredlund D. Comparison of different procedures to predict unsaturated soil shear strength [J]. Geotechnical Special Publication,2000, pp.195-209.
[260]程展林,左永振,丁红顺,等.堆石料湿化特性试验研究[J].岩土：工程学报,2010,32(2)：243-247.
[261]Desai C, Zaman M, Lightner J, et al. Thin-layer element for interfaces and joints[J]. In-ternational Journal for Numerical and Analytical Methods in Geomechanics,1984,8(1): 19-43.
[262]周创兵,陈益峰,毛新莹.水布垭防渗工程渗流场-应力场耦合分析研究报告[R].武汉：武汉大学,2009.
[263]Gangi AF. Variation of whole and fractured porous rock permeability with confining pres-sure[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1978,15(5):249-257
[264]陈益峰,周创兵,毛新莹,等.水布垭地下厂房围岩渗控效应数值模拟与评价[J].岩石力学与工程学报,2010,29(2)：308-318.
[2]Gens A. Soil environment interactions in geotechnical engineering[J]. Geotechnique,2010, 60(1):3-74.
[3]Dai Fuchu, Lee CF, Wang Sijing. Analysis of rainstorm-induced slide-debris flows on natural terrain of lantau island, Hong Kong[J]. Engineering Geology,1999,51(4):279-290.
[4]Hu R, Chen Y, Zhou C. Modeling of coupled deformation, water flow and gas transport in soil slopes subjected to rain infiltration[J]. Sci China Tech Sci,2011,54(10):2561-2575.
[5]史斗,郑军卫.世界天然气水合物研究开发现状和前景.地球科学进展[J],1999,14(4)：330-339.
[6]Raveendiraraj A. Coupling of mechanical behaviour and water retention behaviour in un-saturated soils[D]. Scotland:University of Glasgow,2009.
[7]Sun DA, Sun WJ, Li X. Effect of degree of saturation on mechanical behaviour of unsaturated soils and its elastoplastic simulation[J]. Computers and Geotechnics,2010,37(5):678-688.
[8]Terzaghi K. Principles of soil mechanics, iv-settlement and consolidation of clay [J]. Engi-neering News-Record,1925,95(3):874-878.
[9]Biot MA. General theory of three-dimensional consolidation. Journal of applied physics [J], 1941,12(2):155-164.
[10]Lloret A, Romero E, Villar MV. FEBEX II Project Final report on thermo-hydro-mechanical laboratory tests[R]. Publicacion tecnica. (Empresa Nacional de Residuos Radi-activos),2004,10,11-165.
[11]Sten Bjurstrom. Storage of nuclear waste in sweden[J]. Tunnelling and Underground Space Technology,1989,4(2):139-142.
[12]Neerdael B, Boyazis,JP. The belgium underground research facility:Status on the demon-stration issues for radioactive waste disposal in clay[J]. Nuclear engineering and design,1997, 176(1):89-96.
[13]Rummery TE, Rosinger E. The Canadian nuclear fuel waste management program[R]. Whiteshell Nuclear Research Establishment,1984.
[14]Iwasaki Y. Reassessment of the effective stress coefficient x in unsaturated soils[D]. Japan: Kobe University, 1978.
[15]Wlieeler S, Sivakumar V. An elasto plastic critical state framework for unsatnrated soil[J]. Geotechnique 1995; 45(1): 35-53.
[16]Sharma R. Mechanical behaviour of unsaturated highly expansive clays[D]. United Kingdom: University of Oxford, 1998.
[17]Sivakumar, R. Effects of anisotropy on the behaviour of unsaturated compacted clay[D]. United Kingdom: The Queen's University of Belfast, 2005.
[18]Gallipoli D, Toll D, Augarde C, et al. The MUSE Network: sharing research expertise on unsaturated soils across Europe[J]. Geotechnical Special Publication, 2006; 147(2): 2075.
[19]Josa A, Alonso EE, Lloret A, et al.Stress strain behaviour or partially saturated soils[C]. In Proceedings 9th European Conference on Soil Mechanics and oundation Engineering, 561-564, 1987.
[20]Alonso EE, Gens A, Josa A. A Constitutive Model for Partially Saturated Soils[J]. Geotechnique 1990; 40(3): 405-430.
[21]Cui YJ, Delage P. Yielding and plastic behaviour of an unsaturated compacted silt[J]. Geotechnique, 1996,46(2): 291-311.
[22]Gallipoli D, Wheeler SJ, Karstunen K. Modelling the variation of degree of saturation in a defornable unsaturated soil[J]. Geotechnique, 2003, 53(1): 105-112.
[2,3]Wheeler SJ, Sharma RS, Buisson MSR. Coupling of hydraulic hysteresis and stress strain behaviour in unsa.turated soils[J]. Geotechnique, 2003, 53(1): 41-54.
[24]Chen ZH, Fredhmd DC, KM G J. Overall volume change, water volume change, and yield associated with an unsaturated compacted loess[J]. Canadian Geotechnical Journal, 1999, 36(2): 321-329.
[25]Sivakumar V. A critical state framework for unsaturated soil[D]. United Kingdom: Univer-sity of Sheffield. 1993.
[26]Nimmo JR, Miller EE. The temperature dependence of isothermal moisture vs. potential characteristics of soils[J]. Soil Science Society of America Journal, 1986, 50(5): 1 105-1113.
[27]Huang S, Harbour SL,Fredlund DG. Development and verification of a. coefficient of perme ability function for a deformable unsaturated soil[J]. Canadian Geotechnical Journal, 1998, 35(3):411-425.
[28]Romero, E. Characterisation and thermo-hydro-mechanical behavior of unsaturated Boom clay:an experimental study[D]. Spain:Universitat Politecnica de Catalunya,1999.
[29]Vanapalli S, Fredlund D, Pufahl D. The influence of soil structure and stress history on the soil-water characteristics of a compacted till[J]. Geotechnique,1999,49(2):143-160.
[30]WW Ng C,Pang YW. Experimental investigations of the soil water characteristics of a volcanic soil[J]. Canadian Geotechnical Journal,2000,37(6):1252-1264.
[31]Romero E, Vaunat J. Retention curves of deformable clays[M]. Experimental evidence and theoretical approaches in unsaturated soils,2000:91-106.
[32]Barrera M. Estudio experimental del comportamiento hidro mecanico de suelos co-lapsables[D]. Spain:Universitat Politecnica de Catalunya,2002.
[33]Villar M, Romero E, Lloret A. Thermo-mechanical and geochemical effects on the perme-ability of high-density clays[C]. Proceedings of the international symposium on large scale field tests in granite Advances in understanding engineered clay barriers In:Alonso EE, Ledesma A (eds) AA Balkema Publishers, Leiden,2005, p.177-191.
[34]Delage P, Marcial D, Cui Y, et al. Ageing effects in a compacted bentonite:a microstructure approach [J]. Geotechnique,2006,56(5):291-304.
[35]Olivella S. Alonso E. Gas flow through clay barriers. Geotechnique [J],2008,58(3):157-176.
[36]Gallage C, Uchimura T. Effects of dry density and grain size distribution on soil-water characteristic curves of sandy soils[J]. Soils and Foundations,2010,50(1):161-172.
[37]Tarantino A. A water retention model for deformable soils[J]. Geotechnique,2009,59(9): 751-762.
[38]Chapuis RP. Predicting the saturated hydraulic conductivity of soils:a review[J]. Bulletin of Engineering Geology and the Environment,2012,71(3):401-434.
[39]Bishop A. The principle of effective stress[J]. Teknisk Ukeblad,1959,106(39):859-863.
[40]Blight G. Effective stress evaluation for unsaturated soils[J]. Journal of the Soil Mechanics and Foundations Division:proceedings of the American Society of Civil Engineers,1967, 93:125-148. Journal of the Soil Mechanics and Foundations Division
[41]Kohgo Y, Nakano M, Miyazaki T. Theoretical aspects of constitutive modelling for unsat-urated soils[J]. Soils and Foundations,1993,33(4):49-63.
[42]Karube D. An ideal unsaturated soil and the Bishop's soil[C]. Proceeding in 13th Interna-tional Conference SMFE,1994, pp.43-46.
[43]Karube D, Kawai K. The role of pore water in the mechanical behavior of unsaturated soils Geotechnical and Geological Engineering[J], 2001, 19(3): 211-241.
[44]Burland J. Some aspects of the mechanical behaviour of partly saturated soils[M]. Moisture Equilibria and Moisture Change in Soils Beneath Covered Areas, 1965, 270: 10-20.
[45]Morgenstern N. Properties of compacted soils[C]. Contribution to panel discussion, Session IV, Proceeding 6th Panamerican Conf on Soil Mechanics and Foundation Engineering, 1979, pp. 349-354.
[46]Aitchison, GD, Donald TB. Some- preliminary studies of unsa.turat.ed soils, (b) Effective stress-es in unsaturated soils[C]. The 2nd Australia New Zealand Conference on Soil Mechanics and Foundation Engineering, Christchurch, 1956, 192-199.
[47]Bishop A, Blight G. Some aspects of effective stress in saturated and partly saturated soils[J]. Geoteehnique, 1963, 13(3): 177-197.
[48]Fredlund DG, Morgenstern NR. Stress state variables for unsaturated soils[J]. Journal of Geotechnical and Geoenvironmental Engineering, 1977, 103(5): 447-466.
[49]Sun DA, Matsuoka H, Yao YP, et al. An elasto pla.stic model for unsaturated soil in three dimensional stresses [J]. Soils and Foundations, 2000, 40(3): 17-28.
[50]Loret B, Khalili N. An effective stress elastic -plastic model for unsaturated porous media[J]. Mechanics of Materials 2002, 34(2): 97-116.
[51]姚仰平,牛雷,崔文杰,等.超固结非饱和土的本构关系[J].岩土工程学报,2011,33(6)：833-839.
[52]Yao YP. Hou W, Zhou AX. UH model: three-dimensional unified hardening model for overconsolidated clays[J]. Geotechnique, 2009, 59(5): 451-469.
[53]Wheeler S. Inclusion of specific water volume within an elasto plastic model for unsaturated soil [J]. Canadian Geotechnical Journal, 1996; 33(1): 42-57.
[54]Dangla P, Malinsky L, Coussy O. Plasticity and imbibition drainage curves for unsaturated soils: a unified approach[C]. Proceeding 6th International Symposium Numerical Models in Geomechanics (NUMOGVI), Montreal, 1997, pp. 141-146.
[55]Vaunat J, Romero E, Jonimi C. An elastopla.stic hydromechanical model for unsaturated soils[C]. In Proceedings of the international workshop on unsat.urated soils, Trento, 2000, pp. 121-138.
[56]Tarnagnini R. An extended Cam clay model for unsaturated soils with hydraulic hystere-sis[J]. Geotechnique, 2004, 54(3), 223-228.
[57]Sun DA, Sheng D, Sloan SW. Elastoplastic modelling of hydraulic and stress-strain be-haviour of unsaturated soils[J]. Mechanics Of Materials,2007,39(3):212-221.
[58]Nuth M, Laloui L. Effective stress concept in unsaturated soils:clarification and validation of a unified framework[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2008,32(7):771-801.
[59]Romero E, Jommi C. An insight into the role of hydraulic history on the volume changes of anisotropic clayey soils[J]. Water Resources Research,2008,44(12):W12412.
[60]Sheng D, Fredlund DG, Gens A. A new modelling approach for unsaturated soils using independent stress variables [J]. Canadian Geotechnical Journal,2008,45(4):511-534.
[61]Muraleetharan KK, Liu C, Wei C, et al. An elastoplatic framework for coupling hydraulic and mechanical behavior of unsaturated soils [J]. International Journal of Plasticity,2009, 25(3):473-490.
[62]Arairo W, Prunier F, Djeran MI, et al. A new insight into modelling the behaviour of unsatu-rated soils[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2012, DOI:10.1002/nag.2151
[63]Khosravi A, McCartney JS. Impact of Hydraulic Hysteresis on the Small-Strain Shear Mod-ulus of Low Plasticity Soils[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2012,138(11):1326-1333.
[64]Liu C, Muraleetharan KK. Coupled hydro-mechanical elastoplastic constitutive model for unsaturated sands and silts. I:Formulation [J]. International Journal of Geomechanics,2012, 12(3):239-247.
[65]沈珠江.土体变形特征的损伤力学模拟[C].第5届全国土力学数值分析与解析方法讨论会议论文集.重庆,1994：1-8.
[66]缪林昌.非饱和土的本构模型研究[J].岩土力学,2007,28(5)：855-860.
[67]李广信,司韦,张其光.非饱和土的清华弹塑性模型[J].岩土力学,2008,29(8)：2033-2062.
[68]Sun D, Sheng D, Cui H, et al. A density-dependent elastoplastic hydro-mechanical model for unsaturated compacted soils [J]. International Journal for Numerical and Analytical Methods in Geomechanics,2007,31(11):1257-1279.
[69]孙德安.非饱和土的水力和力学特性及其弹塑性描述[J].岩土力学,2009,30(11)：3217-3231.
[70]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[J].岩土工程学报,2009,31(9)：1324-1335.
[71]Gray WG, Schrefler BA. Thermodynamic approach to effective stress in partially saturated porous media[J]. European Journal of Mechanics A/Solids, 2001, 20(4): 521-538.
[72]Sheng D, Sloan S, Gens A. A constitutive model for unsaturated soils: thermomechanical and computational aspects[J]. Computational Mechanics, 2004, 33(6): 453-465.
[73]Santagiuliana R, Schrefler B. Enhancing the Bolzon - Schrefler - Zienkiewicz constitutive model for partially saturated soil[J]. Transport in Porous Media, 2006, 65(1): 1-30.
[74]Li X. Thermodynamics based constitutive framework for unsaturated soils[J]. 1: Theory. Geotechnique, 2007, 57(5): 411-422.
[75]Li X. Thermodynamics based constitutive framework for unsaturated soils[J]. 2. A basic triaxial model. Geoteehnique, 2007, 57(5): 423-435.
[76]Coussy O, Pereira JM, Vaunat J. Revisiting the thermodynamics of hardening plasticity for unsaturated soils[J]. Computers and Geoteclmics, 2010, 37(1): 207-215.
[77]Zhao C, Liu Y, Gao F. Work and energy equations and the principle of generalized effective stress for unsaturated soils[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2010, 34(9): 920-936.
[78]Mroginski JL, Etse G, Vreeh SM. A thermodynamical gradient theory for deformation and strain localization of porous media[J]. International Journal of Plasticity, 2011, 27(4): 620-634.
[79]Nikooee E, Habibagahi G, Hassanizadeh SM, et al. Effective Stress in Unsaturated Soils: A Thermodynamic Approach Based on the Interfacial Energy and Hydrorneehanieal Con-pling[J]. Transport, in Porous Media, 2013, 96(2): 369-396.
[80]Gallipoli D, Gens A, Sharma R, et, al. An elasto plastic model for unsaturated soil in-corporating the effects of suction and degree of saturation on mechanical behaviour[J]. Geotechnique, 2003, 53(1): 123-136.
[81]Brooks R H, Corny A T. Hydraulic properties of porous media. Fort Collins, CO: Colorado State University[R]. Hydrology Paper, 1964, No. 3.
[82]van Genuchten MT. A closed form equation for predicting the hydraulic conductivity of unsaturated soils[J]. Soil Science Society of America Journal, 1980, 44(5): 892-898.
[83]Berkowitz B, Ewing RP. Percolation theory and network modeling applications in soil physic-s[J]. Surveys in Geophysics, 1998, 19(1): 23-72.
[84]Fredlund D, Xing A. Equations for the soil water characteristic eurve[J]. Canadian Geotech-nical Journal, 1994, 31(4): 521-532.
[85]Assouline S. Modeling the relationship between soil bulk density and the water retention curve[J]. Vadose Zone Journal,2006,5(2):554-563.
[86]Nuth M, Laloui L. Advances in modelling hysteretic water retention curve in dcformable soils[J]. Computers and Geotechnics,2008,35(6):835-844.
[87]Masin D. Predicting the dependency of a degree of saturation on void ratio and suction using effective stress principle for unsaturated soils[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2010,34(1):73-90.
[88]Gallipoli D. A hysteretic soil-water retention model accounting for cyclic variations of suc-tion and void ratio[J]. Geotechnique,2012,62(7):605-616.
[89]Zhou A, Sheng D, Carter J. Modelling the effect of initial density on soil-water characteristic curves [J]. Geotechnique,2012,62(8):669-680.
[90]Morvan M, Wong H, Branque D. Incorporating porosity-dependent hysteretic water reten-tion behavior into a new constitutive model of unsaturated soils[J]. Canadian Geotechnical Journal,2011,48(12):1855-1869.
[91]Assouline S, Tessier D, Bruand A. A conceptual model of the soil water retention curve[J]. Water Resources Research,1998,34(2):223-231.
[92]周葆春,孔令伟.考虑体积变化的非饱和膨胀土土水特征[J].水利学报,2011,42(10)：1152-1160.
[93]Simms P, Yanful E. Predicting soil-water characteristic curves of compacted plastic soils from measured pore-size distributions [J]. Geotechnique,2002,52(4):269-278.
[94]Cuisinier O, Laloui L. Fabric evolution during hydromechanical loading of a compacted silt[J]. International Journal For Numerical and Analytical Methods in Geomechanics,2004, 28(6):483-499.
[95]Simms P, Yanful E. A pore-network model for hydromechanical coupling in unsaturated compacted clayey soils[J]. Canadian Geotechnical Journal,2005,42(2):499-514.
[96]张雪东,赵成刚,刘艳,等.变形对土水特征曲线影响规律模拟研究[J].土木工程学报,2011,44(7)：119-126.
[97]Mualem Y, Klute A. Hydraulic conductivity of unsaturated soils:prediction and formu-las[M]. Methods of soil analysis Part 1:Physical and mineralogical methods,1986:799-823.
[98]Richards LA. Capillary conduction of liquids through porous mediums[J]. Physics,1931, 1(5):318-333.
[99]Wind G. A field experiment concerning capillary rise of moisture in a heavy clay soil[J]. Netherlands Journal of Agricultural Science, 1955, 3: 60-69.
[100]Weeks L, Richards S. Soil-water properties computed from transient, flow data[J]. Soil Sci-ence Society of America Journal, 1967,31(6): 721-725.
[101]Gardner W, Fireman M. Laboratory studies of evaporation from soil columns in the presence of a water table[J]. Soil Science, 1958, 85(5): 244-249.
[102]Arbhabhirama A. Kridakorn C. Steady downward flow to a water table[.I]. Wafer Resources Research, 1968, 4(6): 1249-1257.
[103]Gardner W. Some steady-state solutions of the unsaturafed moisture flow equation with application to evaporation from a water table[J]. Soil Science, 1958, 85(4): 228-232.
[104]Philip J. Linearized unsteady multidimensional infiltration [J]. Water Resources Research, 1986, 22(12): 1717-1727.
[105]Davidson J, Stone L, Nielsen D, et al. Field measurement and use of soil water properties[J]. Wafer Resources Research, 1969,5(6): 1312-1321.
[106]Dane J, Klufe A. Salt effects on the hydraulic properties of a swelling soil[J]. Soil Science Society of America Journal, 1977,41(6): 1043-1049.
[107]Zaclnnann D, Duchatean P, Klute A. The calibration of the Richards flow equation for draining column by parameter identification[J]. Soil Science Society of America Journal, 1981, 45(6): 1012-1015.
[108]Hillel D. Introduction to soil physics[M]. Academic press, New York, 1982.
[109]Averjanov S. About permeability of subsurface soils in ease of incomplete saturation [J]. English collection, 1950, 7:19-21.
[110]Irmay S. On the hydraulic: conductivity of unsaturafed soils[J]. Transactions, American Geophysical Union, 1954, 35: 463-467.
[111]Mualern Y. Hydraulic: conductivity of unsafurated porous media: generalized macroscopic approach[J]. Water Resources Research, 1978, 14(2): 325-334.
[112]Childs EC, Collis George N. The permeability of porous materials[J]. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 1950, 201(1066): 392-405.
[113]Laliberte GE, Corey AT, Brooks R. Properties of unsaturatecl porous media[R], Colorado State University Fort Collins, Colorado, 1966.
[114]Huang Sliangyan. Evaluation and Laboratory Measurement of the Coefficient of Permeabil-ity in Deformable[D]. Canada:University of Saskatchewan,1994.
[115]Burdine N, Gournay L, Reichertz P. Pore size distribution of petroleum reservoir rocks[J]. Journal of Petroleum Technology,1950,2(7):195-204.
[116]Purcell W. Capillary pressures-their measurement using mercury and the calculation of permeability thcrefrom[J]. Journal of Petroleum Technology,1949,1(2):39-48.
[117]Fatt I, Dykstra H. Relative permeability studies[J]. Journal of Petroleum Technology,3(9): 249-256,1951.
[118]Burdine NT. Relative permeability calculations from pore size distribution data[J]. Journal of Petroleum Technology,5(3):71-78,1953.
[119]Wyllie MRJ, Gardne GHF. The generalized Kozeny-Carman equation:A novel approach to problems of fluid flow[J]. World Oil Prod Sect,1958,146:210-228.
[120]Mualem Y. A new model for predicting the hydraulic conductivity of unsaturated porous media[J]. Water Resources Research,1976,12(3):513-522.
[121]Lai WM, Rubin DH, Rubin D, et al. Introduction to continuum mechanics[M.]Butterworth Heinemann,2009.
[122]Biot M. General solutions of the equations of elasticity and consolidation for a porous material [J]. Journal of Applied Mechanics,1956,23(1):91-96.
[123]De Boer R. Theory of porous media-past and present[J]. ZAMM-Journal of Applied Math-ematics and Mechanics/Zeitschrift fUr Angewandte Mathematik und Mechanik,1998,78(7): 441-466.
[124]Morland L. A simple constitutive theory for a fluid-saturated porous solid[J]. Journal of Geophysical Research,1972,77(5):890-900.
[125]Bowen RM. Compressible porous media models by use of the theory of mixtures[J]. Inter-national Journal of Engineering Science,1982,20(6):697-735.
[126]Hassanizadeh SM, Gray WG. Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries [J]. Advances in Water Resources,1990,13(4):169-186.
[127]Achanta S, Cushman J, Okos M. On multicomponent, multiphase thermomechanics with interfaccs[J]. International Journal of Engineering Science,1994,32(11):1717-1738.
[128]Zienkiewicz OC. Basic formulation of static: and dynamic: behavior of soil and other porous media[M]. Numerical Methods in Geornechanics. D. Reidl, 1982.
[129]Zienkiewicz OC. Dynamic: behavior of saturated porous media: the generalized Riot's formu-lation and its finite element solution[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1984, 8: 71-96.
[130]Zienkiewiez OC, Xie Y, Schrefler B, et al. Static and dynamic behaviour of soils: a rational approach to quantitative solutions. Ⅱ. Semi saturated problems[J]. Proceedings of the I loyal Society of London A Mathematical and Physical Sciences, 1990, 429(1877): 311-321.
[131]Li XK. Finite-element analysis for immiscible two phase fluid flow in deforming porous media and an unconditionally stable staggered solution [J]. Communications in applied nu-merical methods, 1990, 6(2): 125-135.
[132]Li XK, Zienkiewiez OC. Multiphase flow in deforming porous media and finite element solutions[J]. Computers & Structures, 1992,45(2): 211-227.
[133]杨代泉.非饱和土二维广义固结非线性数值模型[J].岩土工程学报,1992,14(A09)：2-12.
[134]Schrefler B, Xiaoyong Z. A fully coupled model for water flow and airflow in deformable porous media[J]. Wafer Resources Research, 1993,29(1): 155-167.
[135]Gawin D, Baggio P, Schrefler BA. Coupled heat, water and gas flow in deformable porous media[J]. International Journal for Numerical Methods in Fluids, .1995, 20(8 9): 969-987.
[136]Schrefler BA, Zhan X. Sitnoni L. A coupled model for wafer flow, airflow and heat flow in deformable porous media[J]. International Journal of Numerical Methods for Heat and Fluid Flow, 1995, 5(6): 531-547.
137] Gawin D, Schrefler BA. Galindo M. Thermo hydro mechanical analysis of partially satu-rated porous materials[J]. Engineering Computations, 1996, 13(7): 113-143.
[138]Mroginski JL, Rado D, Ariel IT. et al. A finite element approach for multiphase fluid flow in porous mcdia[J]. Mathematics and Computers in Simulation, 2010, 81(1): 76-91.
[139]Schreflcr BA. Scotta. R. A fully coupled dynamic: model for two phase fluid flow in de formable porous media[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(24): 3223-3246.
[140]Wu YS, Forsyth PA. On the selection of primary variables in numerical formulation for modeling multiphase flow in porous media [J]. Journal of Contaminant Hydrology, 2001, 48(3): 277-304.
[141]Laloui L, Klubertanz G, Vulliet L. Solid-liquid-air coupling in multiphase porous medi-a[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2003, 27(3):183-206.
[142]Oettl G, Stark R, Hofstetter G. Numerical simulation of geotechnical problems based on a multi-phase finite element approach[J]. Computers and Geotechnics,2004,31(8):643-664.
[143]Stelzer R, Hofstetter G. Adaptive finite element analysis of multi-phase problems in geotech-nics[J]. Computers and Geotechnics,2005,32(6):458-481.
[144]徐炎兵,韦昌富,李幻,等.非饱和土渗流与变形耦合问题的有限元分析[J].岩土力学,2009,30(5)：1490-1496.
[145]Khoei A, Mohammadnejad T. Numerical modeling of multiphase fluid flow in deforming porous media:A comparison between two and three-phase models for seismic analysis of earth and rockfill dams[J]. Computers and Geotechnics,2011,38(2):142-166.
[146]Mohammadnejad T, Khoei A. Hydra-mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2012, DOI:10.1002/nag.2079.
[147]Sheng D, Sloan SW, Gens A, et al. Finite element formulation and algorithms for unsaturated soils. Part Ⅰ:Theory[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2003,27(9):745-765.
[148]Sheng D, Gens A, Fredlund DG, et al. Unsaturated soils:from constitutive modelling to numerical algorithms [J]. Computers and Geotechnics,2008,35(6):810-824.
[149]Wang W, Kosakowski G, Kolditz O. A parallel finite element scheme for thermo-hydro-mechanical (THM) coupled problems in porous media[J]. Computers & Geosciences,2009, 35(8):1631-1641.
[150]Callari C, Abati A. Finite element methods for unsaturated porous solids and their appli-cation to dam engineering problems[J]. Computers and Structures,2009,87(7):485-501.
[151]Nagel F, Meschke G. An elasto-plastic three phase model for partially saturated soil for the finite element simulation of compressed air support in tunnelling[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2010,34(6):605-625.
[152]Pertl M, Hofmann M, Hofstetter G. Coupled FE Analysis Involving Partially Saturated Soils[J]. Proceedings in Applied Mathematics and Mechanics,2010,10(1):207-208.
[153]Rutqvist J, Ijiri Y, Yamamoto H. Implementation of the Barcelona Basic Model into TOUGH-FLAC for simulations of the geomechanical behavior of unsaturated soils [J]. Com-puters and Geosciences,2011,37(6):751-762.
[154]Costa L, Pontes I, Guimaraes L, et, al. Numerical modelling of hydro mechanical behaviour of collapsible soils[J]. Communications in Numerical Methods in Engineering,2008,24(12): 1839-1852.
[155]Zhang H, Zhou L. Implicit integration of a chemo plastic constitutive model for partially saturated soils[J]. International Journal for Numerical and Analytical Methods in Geome-chanics,2008,32(14):1715-1735.
[156]Khoshghalb A. Khalili N. A meshfree method for fully coupled analysis of flow and defor-mation in unsaturated porous media[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2012, DOI:10.1002/nag.1120.
[157]廖红建,姬建.深基坑开挖中饱和非饱和土体渗流 沉降的耦合分析[J].应用力学学报,2008,25(4)：637-640.
[158]张玉军.核废料处置概念库近场热、水应力耦合模型及数值分析[J].岩土力学,2007,28(1)：17-22.
[159]张玉军.核废物地质处置中热、水应力耦合对迁移影响的三维有限元模拟[J].岩土力学,2009,30(7)：2126-2132.
[160]秦爱芳,赵飞,赵小龙.缓冲材料参数对核废料处置库近场影响的二维有限元分析[J].上海大学学报：自然科学版,2012,18(5)：539-544.
[161]黄润秋,戚国庆.饱和渗流基质吸力对边坡稳定性的影响[J].工程地质学报,2002,10(4)：343-348.
[162]Cai F, Ugai K. Numerical analysis of rainfall effects on slope stability[J]. International Journal of Geomeehanies,2004,4(2):69-78.
[163]荣冠,张伟,周创兵.降雨入渗条件下边坡岩体饱和非饱和渗流计算[J].岩土力学,2005,26(10)：1545-1550.
[164]孙冬梅,冯平,张明进.考虑气相作用的降雨入渗对非饱和土坡稳定性的影响[J].天津大学学报,2009,42(9)：777-783.
[165]Sanavia L. Numerical modelling of a slope stability test by means of porous media mechan-ics[J]. Engineering Computations,2009,26(3):245-266.
[166]Borja R.I, White JA, Liu X, et al. Factor of safety in a partially saturated slope inferred from hydro mechanical contimunn modeling[J]. International Journal for Numerical and Analytical Methods in Geomechanies,2012,36(2):236-248.
[167]朱文彬,刘宝琛.降雨条件下上体滑坡的有限元数值分析[J].岩石力学与工程学报,2002,21(4)：509-512.
[168]Cho SE, Lee SR. Instability of unsaturated soil slopes due to infiltration [J]. Computers and Geotechnics,2001,28(3):185-208.
[169]王协群,张有祥,邹维列,等.降雨入渗条件下非饱和路堤变形与边坡的稳定数值模拟[J].岩土力学,2010,31(11)：3640-3655.
[170]吴李泉,张锋,凌贤长,等.强降雨条件下浙江武义平头村山体高边坡稳定性分析[J].岩石力学与工程学报,2009,28(6)：1193-1199.
[171]田东方,刘德富,王世梅,等.土质边坡非饱和渗流场与应力场耦合数值分析[J].岩土力学,2009,30(3)：810-814.
[172]Ehlers W, Graf T, Ammann M. Deformation and localization analysis of partially saturated soil[J]. Computer Methods in Applied Mechanics and Engineering,2004,193(27):2885-2910.
[173]Zheng H, Liu D, Lee C, et al. A new formulation of Signorini's type for seepage problems with free surfaces[J]. International Journal for Numerical Methods in Engineering,2005, 64(1):1-16.
[174]Chen Y, Zhou C, Zheng H. A numerical solution to seepage problems with complex drainage systems[J]. Computers and Geotechnics,2008,35(3):383-393.
[175]陈益峰,周创兵,郑宏.含复杂渗控结构渗流问题数值模拟的SVA方法[J].水力发电学报,2009,28(2)：89-95.
[176]Vanorio T, Prasad M, Nur A. Elastic properties of dry clay mineral aggregates, suspensions and sandstones [J]. Geophysical Journal International,2003,155(1):319-326.
[177]Simmer K. Bodenmechanik. Erdstatische Berechnungen[M], Grundbau Teil,1987,1.
[178]Gvirtzman H, Magaritz M, Klein E, et al. A scanning electron microscopy study of water in soil[J]. Transport in Porous Media,1987,2(1):83-93.
[179]Vogel H-J, Roth K. Quantitative morphology and network representation of soil pore struc-ture[J]. Advances in Water Resources,2001,24(3):233-242.
[180]Schrefler B, Lewis R. The finite element method in the static and dynamic deformation and consolidation of porous media[M]. Wiley, Chichester,1998.
[181]Whitaker S. The transport equations for multi-phase systems [J]. Chemical Engineering Science,1973,28(1):139-147.
[182]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[J].中国科学：E辑,2008,38(9)：1453-1463.
[183]Yeh G.3DFEMWATER:A three-dimensional finite element model of water flow through saturated-unsaturated media[R]. Oak Ridge National Lab., TN (USA),1987.
[184]朱岳明,龚道勇.三维饱和一非饱和渗流场求解舣其逸岀面边界条件处理[J].水科学进展,2003,14(1)：67-71.
[185]Borsi I, Farina A, Fasano A. On the infiltration of rain water through the soil with runoff of the excess water[J]. Nonlinear analysis:real world applications,2004,5(5):763800.
[186]Borsi I, Farina A, Priniicerio M. A rain water infiltration model with unilateral boundary condition:qualitative analysis and numerical simulafcions[J]. Mathematical Methods in the Applied Sciences,2006,29(17):2047-2077.
[187]陈益峰,周创兵,胡冉,等.大型水电工程渗流分析的若干关键问题研究[J],岩土工程学报,2010,32(9)：1448-1454.
[188]Dcsai C, Li G. A residual flow procedure and application for free surface flow in porous media[J]. Advances in Water Resources,1983,6(1):27-35.
[189]Bathe. K.J, Khoshgoftaar MR. Finite element free surface seepage analysis without, mesh iteration [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1979,3(1):13-22.
[190]张有天,陈平,王镭.有自由面渗流分析的初流量法[J].水利学报,1988,8(1)：18-26.
[191]周创兵,熊文林,梁业国.求解无压渗流流场的一种新方法[J].水动力学研究与进展,1996,11(5)：528-534.
[192]速宝玉,朱岳明.不变网格确定渗流自由面的节点虚流量法[J].河海大学学报,1991,19(5)：113-117.
[193]Chen SH, Wang WM, She CX, el. al. Unconfined seepage analysis of discontinuous rock slopc[J). Journal of Hydrodynamics, Sor. B,2000,12(3):75-86.
[194]Jiang QH, Deng SS, Zhou CB, et al. Modeling unconfined seepage flow using three dimensional numerical manifold method [J]. Journal of Hydrodynamics, Ser B,2010,22(4): 554-561.
[195]Alt HW. Numerical solution of steady-state porous flow free boundary probletns[J]. Nu-merische Mathematik,1980,36(1):73-98.
[196]陈益峰,卢礼顺,周创兵,等Signorini型变分不等式方法在实际工程渗流问题中的应用[J].岩土力学,2007,28(supp)：178-182.
[197]Coussy O. Poromechanics[M]. New York:Wiley,2004.
[198]Cho GC, Santamarina JC. Unsaturated particulate materials-particle-level studies. Journal of Geotechnical and Gcoenvironmental Engineering[J],2001,127(1):84-96.
[199]Mitarai N, Nori F. Wet granular materials[J]. Advances in Physics,2006,55(1-2):1-45.
[200]Soulie F, Cherblanc F, El Youssoufi MS, et al. Influence of liquid bridges on the mechanical behaviour of polydisperse granular materials [J]. International Journal for Numerical and Analytical Methods in Geomechanics,2006,30(3):213-228.
[201]Scholtes L, Hicher PY, Nicot F, et al. On the capillary stress tensor in wet granular materi-als. International Journal for Numerical and Analytical Methods in Geomechanics [J],2009, 33(10):1289-1313.
[202]Fleureau JM, Hadiwardoyo S, Correia AG. Generalised effective stress analysis of strength and small strains behaviour of a silty sand, from dry to saturated state[J]. Soils and Foun-dations,2003,43(4):21-33.
[203]Justo J L, Vazquez M. A model for capillary pressure in unsaturated granular soils within the pendular saturation regime[C]. In:Alonso EE, Gens A, editors. Unsaturated soils, vol. 3, CRC Press,2011,151-156.
[204]Toll D. A framework for unsaturated soil behaviour[J]. Geotechnique,1990,40(1):31-44.
[205]Jaky J. Pressure in silos[C]. Proceedings 2nd International Conference Soil Mechanics and Foundation Engineering,1948,1:103-107.
[206]Liu HH, Wei MY, Rutqvist J. Normal-stress dependence of fracture hydraulic properties including two-phase flow properties[J]. Hydrogeology Journal,2012,21:371-382.
[207]Kosugi K. Lognormal distribution model for unsaturated soil hydraulic properties [J]. Water Resources Research,1996,32(9):2697-2703.
[208]Diamond S. Pore size distributions in clays[J]. Clays and Clay Minerals,1970,18(1):7-23.
[209]Delage P, Lefebvre G. Study of the structure of a sensitive Champlain clay and of its evo-lution during consolidation[J]. Canadian Geotechnical Journal,1984,21(1):21-35.
[210]Coulon E, Bruand A. Effects of compaction on the pore space geometry in sandy soils[J]. Soil and Tillage Research,1989,15(1):137-151.
[211]Griffiths F. Joshi R. Change in pore size distribution due to consolidation of clays[J]. Geoteclnique,1989,39(1):159-167.
[212]Penumadu D, Dean J. Compressibility effect in evaluating the pore-size distribution of kaolin clay using mercury intrusion porosimetry[J]. Canadian Geotechnical Journal,2000,37(2): 393-405.
[213]Sivakumar V, Wheeler S. Influence of compaction procedure on the mechanical behaviour of an unsaturated compacted clay. Part, 1: Wetting and isotropic compression[J]. Geoteehnique, 2000, 50(4): 359-368.
[214]Koliji A, Vulliet L, Laloui L. Structural characterization of unsatnrated aggregated soil[J]. Canadian Gcotechnical Journal, 2010, 47(3): 297-311.
[215]Li X, Zhang LM. Characterization of dual structure pore size distribution of soil[J]. Cana-dian Geotechnical Journal, 2009, 46(2): 129-141.
[216]Lapicrre C, Leroucil S, Locat J. Mercury intrusion and permeability of Louiseville clay[J]. Canadian Geotechnical Journal, 1990, 27(6): 761-773.
[217]Tanaka H, Shiwakoti DR., Omukai N, et al. Pore size distribution of clayey soils measured by mercury intrusion porosimetry and its relation to hydraulic conductivity [J]. Soils and Foundations, 2003, 43(6): 63-73.
[218]Ninjgarav E, Chung SG, Jang WY, et al. Pore size distribution of Pusan clay measured by mercury intrusion porosimetry[J], KSCE Journal of Civil Engineering, 2007, 11(3): 133-139.
[219]Monroy R, Zdravkovic L, Ridley A. Evolution of microstructure in compacted London Clay during wetting and loa.ding[J]. Geotechnique, 2010, 60(2): 105-119.
[220]Tarantino A. Unsaturated soils: Compacted versus reconstituted stntes[C]. In 5th Interna-tional Conference on Unsaturated Soil, Barcelona, September 6 8, 2010, 113-136.
[221]Nowamooz II, Masrouri V. Suction variations and soil fabric of swelling compacted soils[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2010, 2:129-134.
[222]Croney D, Coleman JD. Pore pressure and suction in soils[C]. In Proceedings of the Con-ference on Pore Pressure; and Suction in Soils. Butterworths, London, 1961, pp. 31-37.
223] Kayadelen C. The consolidation characteristics of an unsaturated compacted soil[J]. Envi-ronmental Geology, 2008, 54(2): 325-334.
[224]Sugii T, Yamada K, Kondou T. Relationship between soil water characteristic curve and void ratio[C]. In: Recife, editor. In UNSAT 2002, Proc 3rd Unsaturated Soils Conference, de Campos and Marinho, 2002, pp. 209-214.
[225]Tarantino A, De Col E. Compaction behaviour of cla,y[J]. Geotechnique, 2008, 58(3): 199-213.
[226]Tombolato S. Resistenza a taglio di un argil la costipata non satura: Risultati sperimentali modellazione[C]. Italy: Universita' degli Studi di Trento, 2003.
[227]D'Onza F, Gallipoli D, Wheeler S, et al. Benchmark of constitutive models for unsaturated soils[J]. Geotechnique,2011,61(4):283-302
[228]Chen Y, Zhou C, Jing L. Modeling coupled THM processes of geological porous media with multiphase flow:Theory and validation against laboratory and field scale experiments[J]. Computers and Geotechnics,2009,36(8):1308-1329.
[229]Assouline S. A model for soil relative hydraulic conductivity based on the water retention characteristic curve[J]. Water Resources Research,2001,37(2):265-271.
[230]Fredlund D, Xing A, Huang S. Predicting the permeability function for unsaturated soils using the soil water characteristic curve[J]. Canadian Geotechnical Journal,1994,31(4): 533-546.
[231]Leij FJ, Russel WB, Lesch SM. The UNSODA unsaturated soil hydraulic database, version 1.0. Report EPA/600/R-96/095 [R]. National Risk Management Research Laboratory, US Environmental Protection Agency, Cincinnati, Ohio,1996.
[232]Malvern LE. Introduction to the Mechanics of a Continuous Medium[M]. Prentice-Hall Inc, New Jersey,1969.
[233]Lemaitre J, Chaboche JL. Mechanics of solid materials[M]. Cambridge University Press, Cambridge, UK,1994.
[234]Olivier Coussy. Mechanics and physics of porous solids[M]. New York:Wiley,2011.
[235]Voyiadjis GZ, Dorgan RJ. Framework using functional forms of hardening internal state variables in modeling elasto-plastic-damage behavior[J]. International Journal of Plasticity, 2007,23(10):1826-1859.
[236]Houlsby GT. The work input to an unsaturated granular material [J]. Geotechnique,1997, 47(1):193-196.
[237]Kuhn H, Tucker A. Nonlinear programming. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probabilistics[M]. University of California Press,1951, pp. 481-492.
[238]Collins IF, Kelly PA. A thermomechanical analysis of a family of soil models[J]. Geotechnique,2002,52(7):507-518.
[239]Collins IF, Hilder T. A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2002,26(13):1313-1347,2002.
[240]Zienkiewicz OC, Taylor RL. The Finite Element Method: Solid Mechanics[M]. New York: Butterworth heinemanri, 2000.
[241]Hughes TJ. Franca LP, Balestra M. A new finite clement formulation for computational fluid dynamics: V. Circumventing the Balmska Brezzi condition: A stable Petrov- Galerkin formulation of the Stokes problem accommodating equal order interpolations[J]. Computer Methods in Applied Mechanics and Engineering, 1986, 59(1): 85-99.
[242]Simo JC, Hughes TJR. Computational Inelasticity[M]. New York: Springer, 1998.
[243]Rutqvist .J, Borgesson L, Chijirnatsu M, et al. Thermohydromechanics of partially saturated geological media: governing equations and formulation of four finite element models[J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(1): 105-127.
[244]Liakopoulos AC. Transient, flow through unsatunited porous media[D]. USA: University of California, 1964.
[245]Brooks RH. Properties of porous media affecting fluid flow. Journal of the Irrigation and Drainage Division[C]. Proceedings of the American Society of Civil Engineers, 1906, pp. 61-88.
[246]Rathfelder K, Abriola LM. Mass conservative numerical solutions of the head based R.ichard-s equation[J]. Water Resources Rescarch, 1994, 30(9): 2579-2586.
[247]郑铁生,李立,许庆余.一类椭圆型变分不等式离散问题迭代算法[J].应用数学和力学1995,16(4)：351-358.
[248]Tracy FT. Clean two and three dimensional analytical solutions of Richards' equation for testing numerical solvers[J]. Water Resources Research, 2006, 42(8): W08503.
[249]Vauclin M, Khanji D, Vachaud C. Experimental and numerical study of a transient, two dimensional unsaturated saturated water table recharge problem[J]. Water Resources Re-search, 1979, 15(5): 1089-1101.
[250]Haverkamp R, Vauclin M, Touma J, et al. A comparison of numerical simulation models for one-dimensional infiltra.tion[J]. Soil Science Society of America Journal. 1977, 41(2): 285-294.
[251]Akai K, Ohnishi Y, Nishigaki M. Finite element analysis of three dimensional flow in saturated unsaturated soils[C]. In Proceedings of the 3rd Int. Conf. Numerical Methods in Georneehanics — Aachen, 1979, pp. 227-239.
[252]Chen Y, Hu R, Zhou C, el, al. A new parabolic variational inequality formulation of Signori-ni's condition for non steady seepage problems with complex seepage control systems[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2011,35(9): 1034-1058.
[253]毛昶熙.渗流计算分析与控制[M].北京：水利电力出版社,1990.
[254]Zhou W. Chang X, Zhou C, et, al. Creep analysis of high concrete-faced rockfill dam[J]. In-ternational Journal for Numerical Methods in Biomedical Engineering,2010,26(11):1477-1492.
[255]钱纪芸,张嘎,张建民.降雨条件下土坡变形机制的离心模型试验研究[J].岩土力学,2011,32(2)：398-402.
[256]郭明伟,李春光,葛修润,等.基于矢量和分析方法的边坡滑而搜索[J].岩土力学,2009,30(6)：1775-1781.
[257]Morgenstern N, Price VE. The analysis of the stability of general slip surfaces[J]. Geotechnique,1965,15(1):79-93.
[258]Fredlund D, Morgenstern N, Widger R. The shear strength of unsaturated soils[J]. Canadian Geotechnical Journal,1978,15(3):313-321.
[259]SVanapalli S, Fredlund D. Comparison of different procedures to predict unsaturated soil shear strength [J]. Geotechnical Special Publication,2000, pp.195-209.
[260]程展林,左永振,丁红顺,等.堆石料湿化特性试验研究[J].岩土：工程学报,2010,32(2)：243-247.
[261]Desai C, Zaman M, Lightner J, et al. Thin-layer element for interfaces and joints[J]. In-ternational Journal for Numerical and Analytical Methods in Geomechanics,1984,8(1): 19-43.
[262]周创兵,陈益峰,毛新莹.水布垭防渗工程渗流场-应力场耦合分析研究报告[R].武汉：武汉大学,2009.
[263]Gangi AF. Variation of whole and fractured porous rock permeability with confining pres-sure[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1978,15(5):249-257
[264]陈益峰,周创兵,毛新莹,等.水布垭地下厂房围岩渗控效应数值模拟与评价[J].岩石力学与工程学报,2010,29(2)：308-318.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |