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Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with symmetric semi-permeable drainage boundary

机译：具有半渗透性对称边界的非饱和土一维固结的半解析解

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This paper presents semi-analytical solutions to Fredlund and Hasan's one-dimensional consolidation for unsaturated soils under symmetric semi-permeable drainage boundary conditions. Two variables are introduced to transform two coupled governing equations of pore-air and pore-water pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. Then, the pore-air and pore-water pressures, and soil settlement are obtained in the Laplace domain. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi analytical solutions in time domain. It is shown that the present solution is more applicable to various types of drainage boundary conditions, and in a good agreement with existing solutions from the literature. Furthermore, several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with traditional drainage boundary (single or double), and single-sided and double-sided semi-permeable drainage boundaries. Finally, it illustrates the changes in pore-air and pore-water pressures and soil settlement with time at different values of symmetric semipermeable drainage boundary conditions parameters. In addition, parametric studies are conducted by the variations of pore-air and pore-water pressures at different ratios of air-water permeability coefficient and the depth. (C) 2017 Elsevier Ltd. All rights reserved.
机译：本文提出了对称半透水排水边界条件下Fredlund和Hasan一维固结非饱和土的半解析解。引入了两个变量，以将孔隙空气压力和孔隙水压力的两个耦合控制方程式转换为等价的偏微分方程组，这可以通过拉普拉斯变换轻松解决。然后，在拉普拉斯地区获得了孔隙空气和孔隙水的压力以及土壤沉降。采用Crump方法进行拉普拉斯逆变换，以获得时域的半解析解。结果表明，本解决方案更适用于各种类型的排水边界条件，并且与文献中的现有解决方案非常吻合。此外，提供了几个数值示例来研究具有传统排水边界（单或双），单面和双面半透水排水边界的非饱和单层土的固结特性。最后，它说明了在对称半透水排水边界条件参数的不同值下，孔隙空气和孔隙水压力以及土壤沉降随时间的变化。另外，通过不同的空气-水渗透系数和深度比来改变孔隙空气压力和孔隙水压力，进行参数研究。 （C）2017 Elsevier Ltd.保留所有权利。

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