非饱和土固结的混合物理论(Ⅱ)*
Consolidation Theory of Unsaturated Soil Based on the Theory of Mixture (Ⅱ)
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摘要: 本文应用文[1]建立的非饱和土固结的数学模型求解边值问题.借助Laplace变换和有限Fourier变换求得了一维问题的解析解,从控制方程同时解出了竖向位移、孔隙水压力和孔隙气压力,并给出了固结系数和固结度的理论公式.应用Galerkin权余法导出了二维固结问题的有限元方程,编制了8结点等参元FORTRAN程序CSU8,求解了平面应变固结问题,揭示了非饱和土固结的若干规律及数值分析的某些特点.这些成果为把本文的理论应用于工程实际提供了方便.Abstract: The present paper uses the mathematics model for consolidation of unsaturated soil developed in ref.[I] to solve boundary value problems.The analytical solutions for one-dimensional consolidation problem are gained by making use of Laplace transform and finite Fourier transform.The displacement and the pore water pressure as well as the pore gas pressure are found from governing equations simul taneously.The theoretical formulae of coefficient and degree of consolidation are also given in the paper.With the help of the method of Galerkin Weighted Residuals,the finite element equations for two-dimensional consolidation problem are derived.A FORTRAN program named CSU8 using 8-node isoparameter element is designed.A plane strain consol idation problem is solved using the program,and some distinguishing features on consolidation of unsaturated soil and certain peculiarities on numerical analysis are revealed.These achievements make it convenient to apply the theory proposed by the author in engineering practice.
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[1] 陈正汉等,非饱和土固结的混合物理论(I),应用数学和力学,14(2)(1993).127-137. [2] 陈正汉等,非饱和土的水气运动规律与吸力、孔压特性的试验研究,岩土工程学报,14(3)(1993). [3] 陈正汉等,非饱和土的有效应力探讨.岩土工程学报.15(1)(1994),(待发表). [4] Fredlund,D.G.,et al.,One-dimensional consolidation theory:Unsaturated soils,Canadian Geotechnical Journal,16,3(1979),521-531. [5] Fredlund,D.G.,Consolidation of unsaturated porous media,Proc.of NATO Advanced Study Institute on Mechanics of Fluids in Porous Media,Newark,Delaware,USA(1982),525-578. [6] Fredlund,D.G.,Soil mechanics principles that embrace unsaturated soils,Proc.11-stInternational Conference of Soil Mechanics and Foundation Engineering,San Francisco,USA(1985),313-321. [7] 朱伯芳,《有限单元法的原理及其应用》,水利电力出版社(1979). [8] Booker,J.R.and J.C.Small,An investigation of the stability of numerical solutions of Biot's equations of consolidation,Int.J.Solids and Structures,11,(1975),907-917. [9] Wilson,R.K.and E.C.Aifantis,On the theory of consolidation with double porosity,Int.J.Engng.Sci.,20(1982),1009-1035． -
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