非饱和土一维固结的解析解及半解析解
|
摘要
本文对Fredlund非饱和土一维固结方程进行适当简化,得到了大面积均布瞬时加荷及大面积加荷随时间指数变化两种情况,在多种边界条件下有限厚度非饱和土层一维固结的一系列解析解及半解析解,并将以上线弹性非饱和土一维固结半解析解的求解方法拓展到粘弹性非饱和土中。
论文的主要内容可以归为以下几点:
(1)对大面积均布瞬时加荷情况,由Fredlund液相及气相的控制方程、Darcy定律及Fick定律,经Laplace变换及采用Cayley-Hamilton数学方法,得到了大面积均布瞬时加荷情况,有限厚度非饱和土层任意深度状态向量与顶面状态向量之间的传递关系。
(2)基于Fredlund非饱和土一维固结理论,推导了大面积加荷随时间指数变化情况下非饱和土一维固结的液相及气相控制方程。由此控制方程及Darcy定律和Fick定律,经Laplace变换及采用Cayley-Hamilton数学方法,得到了大面积加荷随时间指数变化情况,有限厚度非饱和土层顶面状态向量与任意深度处状态向量间的传递关系。
(3)通过引入初始条件及边界条件,得到了大面积均布瞬时加荷和加荷随时间指数变化情况,在多种边界条件下Laplace变换域内的超孔隙水压力、超孔隙气压力以及土层沉降的解。
(4)采用直接Laplace逆变换方法得到了大面积均布瞬时加荷和加荷随时间指数变化情况下,顶面排水排气、底面不排水不排气边界条件下超孔隙水压力、超孔隙气压力及土层沉降的解析解表达式。应用典型算例,进行了非饱和土的固结特性分析;分析了不同气、水渗透系数比情况下土体超孔隙水压力、超孔隙气压力、土层沉降随时间的变化规律及不同深度超孔隙水压力、超孔隙气压力的消散规律。
(5)采用Crump及Durbin方法编制程序实现拉普拉斯逆变换,得到了均布瞬时加荷和加荷随时间指数变化情况下,多种边界条件下的时间域内的超孔隙水压力、超孔隙气压力的半解析解。并进行了以上情况下非饱和土的固结特性分析。将半解析解与解析解进行了比较。证明了采用Crump及Durbin方法实现Laplace逆变换的有效性。
(6)采用有限差分方法,编制Fredlund一维固结方程的计算程序,对大面积均布瞬时加荷和加荷随时间指数变化两种情况下,多种边界条件进行求解,得到了非饱和土一维固结的数值解。将得到的数值解与本文得到的解析解对比,证明了本文解析解的精确性及气相控制方程简化的合理性。
(7)将得到的解析解及半解析解退化成适用饱和土的解,并与太沙基饱和土固结理论结果比较。退化为饱和土时本文的解析解及半解析解与太沙基饱和土固结理论解一致。
(8)采用李氏比拟法,应用Merchant粘弹性模型,得到了Laplace变换域内粘弹性非饱和土地基一维固结时超孔隙水压力,超孔隙气压力以及土层沉降的解;采用Crump及Durbin方法实现Laplace逆变换,获得大面积均布瞬时加荷,在顶面排气排水,底面不排气不排水情况下粘弹性非饱和土地基一维固结时的半解析解。分析了不同气、水渗透系数比k_a/k_w,Merchant粘弹性模型的Kelvin体中弹性模量E_1和粘滞系数η等对粘弹性非饱和土地基一维固结特性的影响,揭示了粘弹性非饱和土地基的固结特性。
本文基于线性假定得到的解析解及半解析解为研究复杂的非饱和土非线性问题提供了有价值的一阶近似。线性模型通常需要相对较少的数据并且可以快速获取一个复杂的非饱和土耦合系统的的机理,分析各种材料性质和边界条件的影响。因此,面对复杂的非饱和土固结问题,对于基于线性假定的解析法的研究和发展是非常有价值的。本文的研究结果对非饱和土固结机理、固结特性的研究具有重要的学术意义,并具有较大工程应用价值。
In this paper, a series of analytical and semi-analytical solutions to one-dimensional consolidation in unsaturated soil with finite thickness are obtained under several kinds of boundary conditions under the large-area uniform instantaneous loading and loading changed exponentially with time. The semi-analytical solution to one-dimensional consolidation for linearly elastic unsaturated soils is extended to that for the viscoelastic unsaturated soils.
Main contents can be drawn as follows:
(1) For the large-area uniform instantaneous loading, based on the Fredlund's one-dimensional consolidation theory for unsaturated soil, the transfer relations between the state vectors at top surface and any depth are gained by using the Laplace transform and Cayley-Hamilton mathematical methods to the Fredlund's governing equations of water and air, Darcy's law and Fick's law.
(2) For the large-area loading changing exponentially with time, the governing equations of one-dimensional consolidation are derived based on Fredlund's one-dimensional consolidation theory for unsaturated soil. The transfer relation between the state vectors at the top surface and at arbitrary depth are gained by using the Laplace transform and Cayley-Hamilton mathematical methods to this governing equations of water and air, Darcy's law and Fick's law.
(3) The excess pore-air pressure, the excess pore-water pressure and the settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and certain boundary conditions, in the cases of the large-area uniform instantaneous loading and loading changing exponentially with time.
(4) For the large-area uniform instantaneous loading and loading changing exponentially with time, the analytical solutions of the excess pore-air pressure, the excess pore-water pressure and the soil settlement are obtained by performing the inverse Laplace transforms under the boundary conditions of the top surface permeable to water and air, and the bottom impermeable to water and air. A typical example result is given to show the changes in the excess pore-air pressure, the excess pore-water pressure and the soil settlement rate with time under different air-water coefficient rates.
(5) For the large-area uniform instantaneous loading and loading changing exponentially with time, a computer program using the method of Crump and F. Durbin is developed to obtain the semi-analytical solutions of the excess pore-air pressure, the excess pore-water pressure and the soil settlement rate under several kinds of boundary conditions. At the same time the consolidation behavior for unsaturated soils is analyzed according to the semi- analytical solution, and the results prove that the method is of high precision.
(6) For the large-area uniform instantaneous loading and loading changing exponentially with time, a computer program is developed to obtain the numerical solutions to one-dimensional consolidation in unsaturated soils by the finite difference method under several kinds of boundary conditions. Comparisons between the numerical and analytical results indicate that the results of the two methods are almost the same.
(7) The analytical solution is compared with the Terzaghi solution for saturated soils and it is known that the two solutions are almost the same for saturated soils. Therefore, the analytical solution to one-dimensional consolidation in unsaturated soilis correct.
(8) Unsaturated soil is assumed to obey Merchant viscoelastic model. By using Lee's matching law, the excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained for one-dimensional consolidation in unsaturated soils, under the large-area uniform instantaneous loading. A computer program using the method by Crump and Durbin is developed to obtain the semi-analytical solution of the excess pore-air pressure, excess pore-water pressure and settlement under the boundary conditions of the top surface permeable to water and air and the bottom impermeable to water and air. At the same time the consolidation behavior of the viscoelastic unsaturated soils is analyzed according to the semi-analytical solution. The changes in the excess pore-air pressure, excess pore-water pressure and settlement of the viscoelastic unsaturated soil layer with thetime under different air-water coefficients k_a / k_w and E_l ,ηin the Merchantviscoelastic model are analyzed.
In this paper, some linear assumptions associated with the transport processes and constitutive equations were made, which provided useful initial approximations for unsaturated soil consolidation, and the linear models require relatively less data and it becomes possible for the models to be solved by means of analytical methods. Such analytical solutions are often used to gain a quick insight into the physics of a complex coupled system, and the influence of various material properties and boundary conditions can be investigated. Therefore, developing simplified analytical solutions is always valuable when dealing with complex problems of consolidation in unsaturated soils. The analytical solutions have a high academic value to the studies on unsaturated soils consolidation mechanism and consolidation characteristics, and also the engineering value for solving practical problems.
论文的主要内容可以归为以下几点:
(1)对大面积均布瞬时加荷情况,由Fredlund液相及气相的控制方程、Darcy定律及Fick定律,经Laplace变换及采用Cayley-Hamilton数学方法,得到了大面积均布瞬时加荷情况,有限厚度非饱和土层任意深度状态向量与顶面状态向量之间的传递关系。
(2)基于Fredlund非饱和土一维固结理论,推导了大面积加荷随时间指数变化情况下非饱和土一维固结的液相及气相控制方程。由此控制方程及Darcy定律和Fick定律,经Laplace变换及采用Cayley-Hamilton数学方法,得到了大面积加荷随时间指数变化情况,有限厚度非饱和土层顶面状态向量与任意深度处状态向量间的传递关系。
(3)通过引入初始条件及边界条件,得到了大面积均布瞬时加荷和加荷随时间指数变化情况,在多种边界条件下Laplace变换域内的超孔隙水压力、超孔隙气压力以及土层沉降的解。
(4)采用直接Laplace逆变换方法得到了大面积均布瞬时加荷和加荷随时间指数变化情况下,顶面排水排气、底面不排水不排气边界条件下超孔隙水压力、超孔隙气压力及土层沉降的解析解表达式。应用典型算例,进行了非饱和土的固结特性分析;分析了不同气、水渗透系数比情况下土体超孔隙水压力、超孔隙气压力、土层沉降随时间的变化规律及不同深度超孔隙水压力、超孔隙气压力的消散规律。
(5)采用Crump及Durbin方法编制程序实现拉普拉斯逆变换,得到了均布瞬时加荷和加荷随时间指数变化情况下,多种边界条件下的时间域内的超孔隙水压力、超孔隙气压力的半解析解。并进行了以上情况下非饱和土的固结特性分析。将半解析解与解析解进行了比较。证明了采用Crump及Durbin方法实现Laplace逆变换的有效性。
(6)采用有限差分方法,编制Fredlund一维固结方程的计算程序,对大面积均布瞬时加荷和加荷随时间指数变化两种情况下,多种边界条件进行求解,得到了非饱和土一维固结的数值解。将得到的数值解与本文得到的解析解对比,证明了本文解析解的精确性及气相控制方程简化的合理性。
(7)将得到的解析解及半解析解退化成适用饱和土的解,并与太沙基饱和土固结理论结果比较。退化为饱和土时本文的解析解及半解析解与太沙基饱和土固结理论解一致。
(8)采用李氏比拟法,应用Merchant粘弹性模型,得到了Laplace变换域内粘弹性非饱和土地基一维固结时超孔隙水压力,超孔隙气压力以及土层沉降的解;采用Crump及Durbin方法实现Laplace逆变换,获得大面积均布瞬时加荷,在顶面排气排水,底面不排气不排水情况下粘弹性非饱和土地基一维固结时的半解析解。分析了不同气、水渗透系数比k_a/k_w,Merchant粘弹性模型的Kelvin体中弹性模量E_1和粘滞系数η等对粘弹性非饱和土地基一维固结特性的影响,揭示了粘弹性非饱和土地基的固结特性。
本文基于线性假定得到的解析解及半解析解为研究复杂的非饱和土非线性问题提供了有价值的一阶近似。线性模型通常需要相对较少的数据并且可以快速获取一个复杂的非饱和土耦合系统的的机理,分析各种材料性质和边界条件的影响。因此,面对复杂的非饱和土固结问题,对于基于线性假定的解析法的研究和发展是非常有价值的。本文的研究结果对非饱和土固结机理、固结特性的研究具有重要的学术意义,并具有较大工程应用价值。
In this paper, a series of analytical and semi-analytical solutions to one-dimensional consolidation in unsaturated soil with finite thickness are obtained under several kinds of boundary conditions under the large-area uniform instantaneous loading and loading changed exponentially with time. The semi-analytical solution to one-dimensional consolidation for linearly elastic unsaturated soils is extended to that for the viscoelastic unsaturated soils.
Main contents can be drawn as follows:
(1) For the large-area uniform instantaneous loading, based on the Fredlund's one-dimensional consolidation theory for unsaturated soil, the transfer relations between the state vectors at top surface and any depth are gained by using the Laplace transform and Cayley-Hamilton mathematical methods to the Fredlund's governing equations of water and air, Darcy's law and Fick's law.
(2) For the large-area loading changing exponentially with time, the governing equations of one-dimensional consolidation are derived based on Fredlund's one-dimensional consolidation theory for unsaturated soil. The transfer relation between the state vectors at the top surface and at arbitrary depth are gained by using the Laplace transform and Cayley-Hamilton mathematical methods to this governing equations of water and air, Darcy's law and Fick's law.
(3) The excess pore-air pressure, the excess pore-water pressure and the settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and certain boundary conditions, in the cases of the large-area uniform instantaneous loading and loading changing exponentially with time.
(4) For the large-area uniform instantaneous loading and loading changing exponentially with time, the analytical solutions of the excess pore-air pressure, the excess pore-water pressure and the soil settlement are obtained by performing the inverse Laplace transforms under the boundary conditions of the top surface permeable to water and air, and the bottom impermeable to water and air. A typical example result is given to show the changes in the excess pore-air pressure, the excess pore-water pressure and the soil settlement rate with time under different air-water coefficient rates.
(5) For the large-area uniform instantaneous loading and loading changing exponentially with time, a computer program using the method of Crump and F. Durbin is developed to obtain the semi-analytical solutions of the excess pore-air pressure, the excess pore-water pressure and the soil settlement rate under several kinds of boundary conditions. At the same time the consolidation behavior for unsaturated soils is analyzed according to the semi- analytical solution, and the results prove that the method is of high precision.
(6) For the large-area uniform instantaneous loading and loading changing exponentially with time, a computer program is developed to obtain the numerical solutions to one-dimensional consolidation in unsaturated soils by the finite difference method under several kinds of boundary conditions. Comparisons between the numerical and analytical results indicate that the results of the two methods are almost the same.
(7) The analytical solution is compared with the Terzaghi solution for saturated soils and it is known that the two solutions are almost the same for saturated soils. Therefore, the analytical solution to one-dimensional consolidation in unsaturated soilis correct.
(8) Unsaturated soil is assumed to obey Merchant viscoelastic model. By using Lee's matching law, the excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained for one-dimensional consolidation in unsaturated soils, under the large-area uniform instantaneous loading. A computer program using the method by Crump and Durbin is developed to obtain the semi-analytical solution of the excess pore-air pressure, excess pore-water pressure and settlement under the boundary conditions of the top surface permeable to water and air and the bottom impermeable to water and air. At the same time the consolidation behavior of the viscoelastic unsaturated soils is analyzed according to the semi-analytical solution. The changes in the excess pore-air pressure, excess pore-water pressure and settlement of the viscoelastic unsaturated soil layer with thetime under different air-water coefficients k_a / k_w and E_l ,ηin the Merchantviscoelastic model are analyzed.
In this paper, some linear assumptions associated with the transport processes and constitutive equations were made, which provided useful initial approximations for unsaturated soil consolidation, and the linear models require relatively less data and it becomes possible for the models to be solved by means of analytical methods. Such analytical solutions are often used to gain a quick insight into the physics of a complex coupled system, and the influence of various material properties and boundary conditions can be investigated. Therefore, developing simplified analytical solutions is always valuable when dealing with complex problems of consolidation in unsaturated soils. The analytical solutions have a high academic value to the studies on unsaturated soils consolidation mechanism and consolidation characteristics, and also the engineering value for solving practical problems.
引文
[1].Terzaghi,K.Erdbaumechanik auf Bodenphysikalischer Grundlage[M].Leipzig Deuticke,Vienna,1925.
[2].Biot,M.A.General theory of three-dimensional consolidation[J].Journal of Applied Physics,1941,12(2):155-164.
[3].殷宗泽等.土工原理[M],北京:中国水利水电出版社,2007,350-364.
[4].李广信.高等土力学[M],北京:清华大学出版社,2004,268-303.
[5].Bishop,A.W.The principle of effective stress[J].Tek.Ukeblad,1959,39:859-863.
[6].Jennings,J.E.B.and Burland,J.B.Limitation to the use of effective stress in partly saturated soils[J].Geotechnique,1961,12(2):125-144.
[7].Fredlund,D.G.and Morgenstem,N.R.Stress state variable for unsaturated soils [J].Journal of Geotechnical Engineering ASCE,1977,103(5):447-466.
[8].Fredlund,D.G.,Morgenstem,N.R.and Widger,R.S.The shear strength of unsaturated soils,Canadian Geotechnical Journal,1978,15(3):313-321.
[9].Fredlund,D.G.Appropriate concepts and technology for unsaturated soils[J].Canadian Geotechnical Journal,1979,16:121-139.
[10].Lloret A.and Alonso,E.E.State surfaces for partially saturated soils[C].Proceedings of 11th International Conference on Soil Mechanics and Foundation Engineering,San Franciso,International Society of Soil Mechanics and Foundation Engineering,A.A.Balkmema,1985,2:557-562.
[11].Coleman,J.D.Stress-strain relations for partly saturated siol[J].Geotechnique,1962,12(4):348-350.
[12].Matyas,E.L.and Radhakrishna,H.S.Volume change characteristics of partially saturated soils[J].Geotechnique,1968,18(4):432-448.
[13].Alonso,E.E,Gens,A.and Josa,A.A constitutive model for partially saturated soils[J].Geotechnique,1990,40(3):405-430.
[14].Gens,A.,Alonso,E.E.A framework for the behaviour of unsaturated expansive clays [J] .Canadian Geotechnique Journal, 1992,29:1013-1032.
[15]. Cui, Y. J., Delage, P. Yielding and plastic behaviour of an unsaturated compacted silt [J] .Geotechnique, 1996,46(2): 291-311 .
[16]. Bolzon, G., Schrefler, B. A. and Zienkiewicz , O. C. Elastoplastic soil constitutive laws generalised to partially saturated states [J] .Geotechnique, 1996, 46(2): 279-289.
[17].Wheeler, S.J. and Sivakumar, V. An elastoplastic critical state framework for unsaturated soil [J], Geotechnique, 1995, 45(1): 35-53.
[18].Sun, D.A., Matsuoka, H. and Yao, Y.P. An elastoplastic model for unsaturated soil in three-dimensional stresses [J], Soils and Foundations, 2000, 40(3): 17-28.
[19]. Sun, D.A., Matsuoka, H, Cui H.B., Xu, Y. F. Three-dimensional elastoplastic model for unsaturated compacted soils with different initial densities [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2003,27(10): 1079-1098.
[20]. Sun, D.A., Matsuoka, H. and Xu, Y.F. Collapse behavior of compacted clays by suction-controlled triaxial tests [J]. ASTM Geotechnical Testing Journal, 2004, 27(4): 362-370.
[21]. Brooks, R.H.and Corey, A.T. Hydraulic properties of porous media [C], Hydrology Papers, 3: 1-24, Colorado State University, Fort Collins.
[22]. Van Genuchten, M.T.H. and Nielsen, D.R. On describing and predicting the hydraulic properties of unsaturated soils [J]. Annual Geophysics, 1985, 3: 615-628.
[23]. Fredlund, D.G. and Xing, A. Equations for the soil-water characteristics curves [J], Canadian Geotechnicla Journal, 1994, 31: 533-546.
[24]. Wheeler, S.J, Sharma, R.S. and Buisson, M.S.R. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils [J]. Geotechnique, 2003, 53(1): 41-54.
[25]. Gallipoli, D., Gens, A.,Vaunat, J. et al. Role of degree of saturation on the normally consolidated behaviour of unsaturated soils. Proceedings 3rd International Conference on Unsaturated Soils [C]. Recife, Brazil: A.A.Balkema Publishers, 2002, 113-120.
[26]. Gallipoli, D., Wheeler, S. J., and Karstunen, M. Modelling the variation of degree of saturation in a deformable unsaturated soil [J].Geotechnique, 2003, 53(2):105-112.
[27]. Sun, D.A, Sheng, D.C and Sloan, S.W. Elastoplastic modelling of hydraulic and stress-strain behaviour of unsaturated compacted soils [J]. Mechanics of Material, 2007, 39(3): 212-221.
[28]. Sun, D.A., Cui, H.B. Matsuoka, H, and Sheng, D.C. A three-dimensional elastoplastic model for unsaturated compacted soil with hysteresis [J]. Soils and Foundations, 2007, 47(2): 253-264.
[29]. Sun, D.A., Sheng, D.C., Xiang, L. and Sloan, S.W. Elastoplastic prediction of hydro-mechanical behaviour of unsaturated soils under undrained conditions [J], Computers and Geotechnics, 2008, 35(6), 845-852.
[30]. Barden, L. Consolidation of compacted and unsaturated clays [J]. Geotechnique, 1965, 15(3): 267-286.
[31]. Scott R F. Principles of soil mechanics [M]. Addison Wesley Publishing Company, 1963.
[32]. Olson, R.E. State-of-the-art: consolidation testing. Consolidation of soils, testing and evaluation [C]. Edited by R.N. Yong and F.C. Townsend. American Society for Testing and Materials, Philadelphia, Pa., ASTM STP 892,1986.
[33]. Chang, C.S, and Duncan, J.M. Consolidation analysis for partly saturated clay by using an elastic-plastic effective stress-strain model [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1983, 7(1): 39-55.
[34]. Fredlund, D.G. and Morgenstern, N.R. Constitutive relations for volume change in unsaturated soils [J]. Canadian Geotechnical Journal, 1976, 13(2): 386-396.
[35]. Fredlund, D.G. and Hasan J.U. One-dimensional consolidation theory unsaturated soils [J]. Canadian Geotechnical Journal, 1979,17 (3): 521-531.
[36]. Lloret, A. and Alonso, E.E. Consolidation of unsaturated soils including swelling and collapse behavior [J]. Geotechnique, 1980, 30 (4): 449-477.
[37]. Dakshanamurthy, V. and Fredlund, D.G. Moisture and air flow in an unsaturated soil [C]. Proceedings of the 4th International Conference on Expansive Soils, Denver, Colorado. American Society of Civil Engineering, 1980,1: 514-532.
[38]. Dakshanamurthy,V., Fredlund,D.G., and Rahardjo,H. Coupled three- dimensional consolidation theory of unsaturated porous media [C]. In Proceedings of the 5th International Conference on Expansive Soils, Adelaide, South Australia, 1984, 99-103.
[39]. Wong Tai T, Fredlund D.G. and Krahn J. Numerical study of coupled consolidation in unsaturated soils [J].Canadian Geotechnical Journal, 1998, 35(6): 926-937.
[40]. Ausilio, E., Conte, E. Settlement rate of foundations on unsaturated soils [J]. Canadian Geotechnical Journal, 1999,36(5): 940-946.
[41]. Ausilio, E., Conte, E. and Dente G. An analysis of the consolidation of unsaturated soils [C]. Proceeding of the 3rd International Conference on Unsaturated Soils, Recife, Brazil, 2002,1: 239-251.
[42]. Conte E. Consolidation analysis for unsaturated soils [J]. Canadian Geotechnical Journal, 2004,41(4): 599-612.
[43]. Conte E. Plane Strain and Axially Symmetric Consolidation in Unsaturated Soils [J]. International Journal of Geomechanics, 2006,6(2): 131-135.
[44]. Blight G E. Strength and consolidation characteristics of compacted soils [D]. PhD dissertation, England: University of London, 1961.
[45]. Rahardjo H. The study of undrained and drained behavior of unsaturated soils [D] Canada: University of Saskatchewan, 1990.
[46]. Kitamura, R. Constitutive model for consolidation based on microscopic consideration by probability theory[C]. Proceedings of the International Offshore and Polar Engineering Conference, Colorado: Golden, 1996,1:456-459.
[47]. Saix, C, Devillers, P. and EI Youssoufi M S. Elements of thermomechanical coupling in the consolidation of unsaturated soils [J]. Canadian Geotechnical Journal, 2000,37(2): 308-317.
[48]. Rahardjo, H., and Fredlund, D.G. Experimental verification of the theory of consolidation for unsaturated soils [J]. Canadian Geotechnical Journal, 1995, 32(5):749-766.
[49].蒋彭年.非饱和土工程性质简介[J].岩土工程学报,1989,11(6):39-59.
[50].陈正汉.非饱和土固结的混合物理论.数学模型、试验研究、边值问题[D].陕西:陕西机械学院,1991.
[51].Cheng Zheng-han,Xie Ding-yi,and Lu Zou-dian.The consolidation of unsaturated soil.Proceedings of 7th International Conference on Computer Methods and Advances in Geomechanics[C].Australias:Beer G,Carter J P,eds.1991,1617-1621.
[52].陈正汉.非饱和土固结的混合物理论(Ⅰ)[J].应用数学和力学,1993,14(2):127-137.
[53].陈正汉.非饱和土固结的混合物理论(Ⅱ).[J].应用数学和力学,1993,14(8):687-698.
[54].杨代泉.非饱和土广义固结理论及其数值模拟与试验研究[D],南京:南京水科院,1990.
[55].杨代泉,非饱和土一维固结简化计算[J].岩土工程学报,1991,13(5):70-78.
[56].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(9):2-12.
[57].卢廷浩.非饱和土三维固结问题探讨[J].成都科技大学学报,1996,1,21-28.
[58].张庆华,丁学福.非饱和土固结一维半解析解[J].水道港口,1996,17(1):33-41.
[59].梁燕,孟学清.太沙基渗透固结理论在近饱和土中的应用[J].土工基础,1996,11(2):40-48.
[60].YIN Zong-ze,SUN Chang-long L,MIAO Ling-chang.Consolidation of unsaturated expansive soils[C].2nd Intemational Conference on Unsaturated Soils.1998:533-537.
[61].陈正汉,周海清.非饱和土的非线性模型及其应用[J].岩土工程学报,1999,21(5):603-608.
[62].陈正汉,黄海,卢再华.非饱和土的非线性固结模型和弹塑模性固结模型及其应用[J].应用数学和力学,2001,22(1):93-103.
[63].唐益群,吕少伟.浅气层高孔压非饱和土固结规律研究[J].土木工程学报,2001,34(6):100-104.
[64].殷宗泽,凌华.非饱和土一维固结简化计算[J].岩土工程学报,2007,29(5):633-637.
[65].卢再华.非饱和膨胀土的弹塑性损伤模型及其在土坡多场耦合分析中的应用[D].重庆:解放军后勤工程学院,2001.
[66].沈珠江.非饱和土简化固结理论及其应用[J].水利水运工程学报,2003,25(4):1-6.
[67].魏海云,詹良通,陈云敏.高饱和度非饱和土的压缩和固结特性及其运用[J].岩土工程学报,2006,28(2):264-269.
[68].凌华,殷宗泽.非饱和土二、三维固结方程简化计算方法[J].水利水电科学进展,2007,27(2):18-21.
[69].凌华,殷宗泽.非饱和土受荷后的单向初期变形和固结变形[J],河海大学学报,2007,35(1):47-50
[70].曹雪山,殷宗泽,凌华.非饱和土受压变形的简化计算研究[J].岩土工程学报,2008,31(8):61-65.
[71].陈宗基.固结及时间效应的单维固结问题[J].土木工程学报,1958,5(1):1-10.
[72].Lo,K.Y.Secondary compression of clays[J].ASCE,JSMFD,1961,87(SM4):61-86.
[73].门福录.粘土固结与次时间效应单维问题的近似解[J].水利学报,1963,(1):44-63.
[74].Komamura,F.and Huang R.J.New rheological model for soil behavior[J].ASCE,JGED,1974,100(GT7):807-824.
[75].赵维炳.广义Voigt模型模拟的饱和土体轴对称固结理论解[J].河海大学学报(工学版),1988,16(5):47-56.
[76].Xie,K.H,Li,B.H.and Li,Q.L.A nonlinear theory of consolideration under time-dependent loading[C].Proc.2th International Conference on Soft Soil Engineering.Nanjing,1996
[77].Xie,K.H.,Li,G.S.,Li,B.H and Zeng,G.X.A theory of consolideration for soils exhibiting rheological characteristics under cyclic loading[C].Proc.of the 9th Int.Conference on computer Methods and Advances in Geomechanics.Wuhan.1997(2):1053-1058.
[78].刘兴旺,谢康和,潘秋元.竖向排水井地基粘弹性固结解析理论[J].土木工程学报,1998,31(1):10-19.
[79].李冰河,谢康和.变荷载下软粘土非线性一维固结半解析解[J].岩土工程学报,1999,21(3):288-293.
[80].李冰河,谢康和.初始有效应力沿深度变化的非线性一维固结半解析解[J].土木工程学报,1999,32(6):47-55.
[81].蔡袁强,徐长节,袁海明.任意荷载下成层粘弹性地基的一维固结[J].应用数学和力学,2001,22(3):307-313.
[82].王瑞春,谢康和.考虑半透水边界的竖向排水井地基粘弹性固结解析分析[J].长江科学院院报,2001,18(6):33-36.
[83].蓝柳和,谢康和.成层软粘土地基粘弹性一维固结半解析解[J].土木工程学报,2003,36(4):105-110.
[84].Gennaro,V.D.,Delage,P.,Cui,Y.J.,Schroeder,C.and Collin,F.Time-dependent behaviour of oil reservoir chalk:A multiphase approach[J]..Soils and Foundations,43(4):131-147.
[85].刘加才,赵维炳,明经平,黄家清.均质未贯穿竖井地基粘弹性固结分析[J].岩石力学与工程学报,2005,24(11):1972-1977.
[86].Korn,G.A.,Kom,T.M.Mathematical handbook for scientists and engineerings [M].McGraw-Hill Inc,1968.
[87].汪德新.数学物理方法(第二版)[M].武汉:华中科技大学出版社,2001.
[88].Durbin,F.Numerical inversion of the Laplace transforms:an efficient improvement to Dubner and Abate's method[J].Computational Journal,1974,17:371-376.
[89].Fredlund,D.G.and Rahardjo,H.Soil Mechanics for Unsaturated Soil[M].New York:John Wiley and Sons,1993.陈仲颐等译.
[90].张志红,赵成刚,邓敏.非饱和土固结理论新进展[J].岩土力学,2005,26(4):667-672.
[2].Biot,M.A.General theory of three-dimensional consolidation[J].Journal of Applied Physics,1941,12(2):155-164.
[3].殷宗泽等.土工原理[M],北京:中国水利水电出版社,2007,350-364.
[4].李广信.高等土力学[M],北京:清华大学出版社,2004,268-303.
[5].Bishop,A.W.The principle of effective stress[J].Tek.Ukeblad,1959,39:859-863.
[6].Jennings,J.E.B.and Burland,J.B.Limitation to the use of effective stress in partly saturated soils[J].Geotechnique,1961,12(2):125-144.
[7].Fredlund,D.G.and Morgenstem,N.R.Stress state variable for unsaturated soils [J].Journal of Geotechnical Engineering ASCE,1977,103(5):447-466.
[8].Fredlund,D.G.,Morgenstem,N.R.and Widger,R.S.The shear strength of unsaturated soils,Canadian Geotechnical Journal,1978,15(3):313-321.
[9].Fredlund,D.G.Appropriate concepts and technology for unsaturated soils[J].Canadian Geotechnical Journal,1979,16:121-139.
[10].Lloret A.and Alonso,E.E.State surfaces for partially saturated soils[C].Proceedings of 11th International Conference on Soil Mechanics and Foundation Engineering,San Franciso,International Society of Soil Mechanics and Foundation Engineering,A.A.Balkmema,1985,2:557-562.
[11].Coleman,J.D.Stress-strain relations for partly saturated siol[J].Geotechnique,1962,12(4):348-350.
[12].Matyas,E.L.and Radhakrishna,H.S.Volume change characteristics of partially saturated soils[J].Geotechnique,1968,18(4):432-448.
[13].Alonso,E.E,Gens,A.and Josa,A.A constitutive model for partially saturated soils[J].Geotechnique,1990,40(3):405-430.
[14].Gens,A.,Alonso,E.E.A framework for the behaviour of unsaturated expansive clays [J] .Canadian Geotechnique Journal, 1992,29:1013-1032.
[15]. Cui, Y. J., Delage, P. Yielding and plastic behaviour of an unsaturated compacted silt [J] .Geotechnique, 1996,46(2): 291-311 .
[16]. Bolzon, G., Schrefler, B. A. and Zienkiewicz , O. C. Elastoplastic soil constitutive laws generalised to partially saturated states [J] .Geotechnique, 1996, 46(2): 279-289.
[17].Wheeler, S.J. and Sivakumar, V. An elastoplastic critical state framework for unsaturated soil [J], Geotechnique, 1995, 45(1): 35-53.
[18].Sun, D.A., Matsuoka, H. and Yao, Y.P. An elastoplastic model for unsaturated soil in three-dimensional stresses [J], Soils and Foundations, 2000, 40(3): 17-28.
[19]. Sun, D.A., Matsuoka, H, Cui H.B., Xu, Y. F. Three-dimensional elastoplastic model for unsaturated compacted soils with different initial densities [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2003,27(10): 1079-1098.
[20]. Sun, D.A., Matsuoka, H. and Xu, Y.F. Collapse behavior of compacted clays by suction-controlled triaxial tests [J]. ASTM Geotechnical Testing Journal, 2004, 27(4): 362-370.
[21]. Brooks, R.H.and Corey, A.T. Hydraulic properties of porous media [C], Hydrology Papers, 3: 1-24, Colorado State University, Fort Collins.
[22]. Van Genuchten, M.T.H. and Nielsen, D.R. On describing and predicting the hydraulic properties of unsaturated soils [J]. Annual Geophysics, 1985, 3: 615-628.
[23]. Fredlund, D.G. and Xing, A. Equations for the soil-water characteristics curves [J], Canadian Geotechnicla Journal, 1994, 31: 533-546.
[24]. Wheeler, S.J, Sharma, R.S. and Buisson, M.S.R. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils [J]. Geotechnique, 2003, 53(1): 41-54.
[25]. Gallipoli, D., Gens, A.,Vaunat, J. et al. Role of degree of saturation on the normally consolidated behaviour of unsaturated soils. Proceedings 3rd International Conference on Unsaturated Soils [C]. Recife, Brazil: A.A.Balkema Publishers, 2002, 113-120.
[26]. Gallipoli, D., Wheeler, S. J., and Karstunen, M. Modelling the variation of degree of saturation in a deformable unsaturated soil [J].Geotechnique, 2003, 53(2):105-112.
[27]. Sun, D.A, Sheng, D.C and Sloan, S.W. Elastoplastic modelling of hydraulic and stress-strain behaviour of unsaturated compacted soils [J]. Mechanics of Material, 2007, 39(3): 212-221.
[28]. Sun, D.A., Cui, H.B. Matsuoka, H, and Sheng, D.C. A three-dimensional elastoplastic model for unsaturated compacted soil with hysteresis [J]. Soils and Foundations, 2007, 47(2): 253-264.
[29]. Sun, D.A., Sheng, D.C., Xiang, L. and Sloan, S.W. Elastoplastic prediction of hydro-mechanical behaviour of unsaturated soils under undrained conditions [J], Computers and Geotechnics, 2008, 35(6), 845-852.
[30]. Barden, L. Consolidation of compacted and unsaturated clays [J]. Geotechnique, 1965, 15(3): 267-286.
[31]. Scott R F. Principles of soil mechanics [M]. Addison Wesley Publishing Company, 1963.
[32]. Olson, R.E. State-of-the-art: consolidation testing. Consolidation of soils, testing and evaluation [C]. Edited by R.N. Yong and F.C. Townsend. American Society for Testing and Materials, Philadelphia, Pa., ASTM STP 892,1986.
[33]. Chang, C.S, and Duncan, J.M. Consolidation analysis for partly saturated clay by using an elastic-plastic effective stress-strain model [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1983, 7(1): 39-55.
[34]. Fredlund, D.G. and Morgenstern, N.R. Constitutive relations for volume change in unsaturated soils [J]. Canadian Geotechnical Journal, 1976, 13(2): 386-396.
[35]. Fredlund, D.G. and Hasan J.U. One-dimensional consolidation theory unsaturated soils [J]. Canadian Geotechnical Journal, 1979,17 (3): 521-531.
[36]. Lloret, A. and Alonso, E.E. Consolidation of unsaturated soils including swelling and collapse behavior [J]. Geotechnique, 1980, 30 (4): 449-477.
[37]. Dakshanamurthy, V. and Fredlund, D.G. Moisture and air flow in an unsaturated soil [C]. Proceedings of the 4th International Conference on Expansive Soils, Denver, Colorado. American Society of Civil Engineering, 1980,1: 514-532.
[38]. Dakshanamurthy,V., Fredlund,D.G., and Rahardjo,H. Coupled three- dimensional consolidation theory of unsaturated porous media [C]. In Proceedings of the 5th International Conference on Expansive Soils, Adelaide, South Australia, 1984, 99-103.
[39]. Wong Tai T, Fredlund D.G. and Krahn J. Numerical study of coupled consolidation in unsaturated soils [J].Canadian Geotechnical Journal, 1998, 35(6): 926-937.
[40]. Ausilio, E., Conte, E. Settlement rate of foundations on unsaturated soils [J]. Canadian Geotechnical Journal, 1999,36(5): 940-946.
[41]. Ausilio, E., Conte, E. and Dente G. An analysis of the consolidation of unsaturated soils [C]. Proceeding of the 3rd International Conference on Unsaturated Soils, Recife, Brazil, 2002,1: 239-251.
[42]. Conte E. Consolidation analysis for unsaturated soils [J]. Canadian Geotechnical Journal, 2004,41(4): 599-612.
[43]. Conte E. Plane Strain and Axially Symmetric Consolidation in Unsaturated Soils [J]. International Journal of Geomechanics, 2006,6(2): 131-135.
[44]. Blight G E. Strength and consolidation characteristics of compacted soils [D]. PhD dissertation, England: University of London, 1961.
[45]. Rahardjo H. The study of undrained and drained behavior of unsaturated soils [D] Canada: University of Saskatchewan, 1990.
[46]. Kitamura, R. Constitutive model for consolidation based on microscopic consideration by probability theory[C]. Proceedings of the International Offshore and Polar Engineering Conference, Colorado: Golden, 1996,1:456-459.
[47]. Saix, C, Devillers, P. and EI Youssoufi M S. Elements of thermomechanical coupling in the consolidation of unsaturated soils [J]. Canadian Geotechnical Journal, 2000,37(2): 308-317.
[48]. Rahardjo, H., and Fredlund, D.G. Experimental verification of the theory of consolidation for unsaturated soils [J]. Canadian Geotechnical Journal, 1995, 32(5):749-766.
[49].蒋彭年.非饱和土工程性质简介[J].岩土工程学报,1989,11(6):39-59.
[50].陈正汉.非饱和土固结的混合物理论.数学模型、试验研究、边值问题[D].陕西:陕西机械学院,1991.
[51].Cheng Zheng-han,Xie Ding-yi,and Lu Zou-dian.The consolidation of unsaturated soil.Proceedings of 7th International Conference on Computer Methods and Advances in Geomechanics[C].Australias:Beer G,Carter J P,eds.1991,1617-1621.
[52].陈正汉.非饱和土固结的混合物理论(Ⅰ)[J].应用数学和力学,1993,14(2):127-137.
[53].陈正汉.非饱和土固结的混合物理论(Ⅱ).[J].应用数学和力学,1993,14(8):687-698.
[54].杨代泉.非饱和土广义固结理论及其数值模拟与试验研究[D],南京:南京水科院,1990.
[55].杨代泉,非饱和土一维固结简化计算[J].岩土工程学报,1991,13(5):70-78.
[56].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(9):2-12.
[57].卢廷浩.非饱和土三维固结问题探讨[J].成都科技大学学报,1996,1,21-28.
[58].张庆华,丁学福.非饱和土固结一维半解析解[J].水道港口,1996,17(1):33-41.
[59].梁燕,孟学清.太沙基渗透固结理论在近饱和土中的应用[J].土工基础,1996,11(2):40-48.
[60].YIN Zong-ze,SUN Chang-long L,MIAO Ling-chang.Consolidation of unsaturated expansive soils[C].2nd Intemational Conference on Unsaturated Soils.1998:533-537.
[61].陈正汉,周海清.非饱和土的非线性模型及其应用[J].岩土工程学报,1999,21(5):603-608.
[62].陈正汉,黄海,卢再华.非饱和土的非线性固结模型和弹塑模性固结模型及其应用[J].应用数学和力学,2001,22(1):93-103.
[63].唐益群,吕少伟.浅气层高孔压非饱和土固结规律研究[J].土木工程学报,2001,34(6):100-104.
[64].殷宗泽,凌华.非饱和土一维固结简化计算[J].岩土工程学报,2007,29(5):633-637.
[65].卢再华.非饱和膨胀土的弹塑性损伤模型及其在土坡多场耦合分析中的应用[D].重庆:解放军后勤工程学院,2001.
[66].沈珠江.非饱和土简化固结理论及其应用[J].水利水运工程学报,2003,25(4):1-6.
[67].魏海云,詹良通,陈云敏.高饱和度非饱和土的压缩和固结特性及其运用[J].岩土工程学报,2006,28(2):264-269.
[68].凌华,殷宗泽.非饱和土二、三维固结方程简化计算方法[J].水利水电科学进展,2007,27(2):18-21.
[69].凌华,殷宗泽.非饱和土受荷后的单向初期变形和固结变形[J],河海大学学报,2007,35(1):47-50
[70].曹雪山,殷宗泽,凌华.非饱和土受压变形的简化计算研究[J].岩土工程学报,2008,31(8):61-65.
[71].陈宗基.固结及时间效应的单维固结问题[J].土木工程学报,1958,5(1):1-10.
[72].Lo,K.Y.Secondary compression of clays[J].ASCE,JSMFD,1961,87(SM4):61-86.
[73].门福录.粘土固结与次时间效应单维问题的近似解[J].水利学报,1963,(1):44-63.
[74].Komamura,F.and Huang R.J.New rheological model for soil behavior[J].ASCE,JGED,1974,100(GT7):807-824.
[75].赵维炳.广义Voigt模型模拟的饱和土体轴对称固结理论解[J].河海大学学报(工学版),1988,16(5):47-56.
[76].Xie,K.H,Li,B.H.and Li,Q.L.A nonlinear theory of consolideration under time-dependent loading[C].Proc.2th International Conference on Soft Soil Engineering.Nanjing,1996
[77].Xie,K.H.,Li,G.S.,Li,B.H and Zeng,G.X.A theory of consolideration for soils exhibiting rheological characteristics under cyclic loading[C].Proc.of the 9th Int.Conference on computer Methods and Advances in Geomechanics.Wuhan.1997(2):1053-1058.
[78].刘兴旺,谢康和,潘秋元.竖向排水井地基粘弹性固结解析理论[J].土木工程学报,1998,31(1):10-19.
[79].李冰河,谢康和.变荷载下软粘土非线性一维固结半解析解[J].岩土工程学报,1999,21(3):288-293.
[80].李冰河,谢康和.初始有效应力沿深度变化的非线性一维固结半解析解[J].土木工程学报,1999,32(6):47-55.
[81].蔡袁强,徐长节,袁海明.任意荷载下成层粘弹性地基的一维固结[J].应用数学和力学,2001,22(3):307-313.
[82].王瑞春,谢康和.考虑半透水边界的竖向排水井地基粘弹性固结解析分析[J].长江科学院院报,2001,18(6):33-36.
[83].蓝柳和,谢康和.成层软粘土地基粘弹性一维固结半解析解[J].土木工程学报,2003,36(4):105-110.
[84].Gennaro,V.D.,Delage,P.,Cui,Y.J.,Schroeder,C.and Collin,F.Time-dependent behaviour of oil reservoir chalk:A multiphase approach[J]..Soils and Foundations,43(4):131-147.
[85].刘加才,赵维炳,明经平,黄家清.均质未贯穿竖井地基粘弹性固结分析[J].岩石力学与工程学报,2005,24(11):1972-1977.
[86].Korn,G.A.,Kom,T.M.Mathematical handbook for scientists and engineerings [M].McGraw-Hill Inc,1968.
[87].汪德新.数学物理方法(第二版)[M].武汉:华中科技大学出版社,2001.
[88].Durbin,F.Numerical inversion of the Laplace transforms:an efficient improvement to Dubner and Abate's method[J].Computational Journal,1974,17:371-376.
[89].Fredlund,D.G.and Rahardjo,H.Soil Mechanics for Unsaturated Soil[M].New York:John Wiley and Sons,1993.陈仲颐等译.
[90].张志红,赵成刚,邓敏.非饱和土固结理论新进展[J].岩土力学,2005,26(4):667-672.