Existing solutions for analyzing one‐dimensional (1‐D) consolidation of unsaturated soil are only derived to cater to two extreme drainage conditions (fully drained and undrained). This study presents a new explicit solution for 1‐D consolidation of unsaturated soil with semi‐permeable drainage boundary. Based on the assumptions of two independent stress variables and the governing equations proposed by Fredlund, the eigenfunction expansion method is adopted to develop an explicit analytical solution to calculate excess pore‐water and pore‐air pressures in an unsaturated soil when it is subjected to external loads. The developed general solutions are expressed in terms of depth, z, and time, t. For the semi‐permeable drainage boundary, eigenvalues and eigenfunctions in the space domain are developed. The technique of Laplace transform is used to solve the coupled ordinary differential equations in the time domain. The newly derived explicit solution is verified with the existing semi‐analytical method in the literature, and an excellent agreement is obtained. Compared with the semi‐analytical solution, the newly derived analytical solution is more straightforward and explicit so that this solution is relatively easier to be implemented into a computer program to carry out a preliminary assessment of 1‐D consolidation of unsaturated soil.

中文翻译：

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具有半渗透性排水边界的非饱和土一维固结显式解

现有的分析非饱和土壤一维（一维）固结的解决方案只能满足两种极端的排水条件（完全排水和不排水）。这项研究为具有半渗透性排水边界的非饱和土的一维固结提供了一种新的显式解决方案。基于两个独立应力变量的假设和Fredlund提出的控制方程，采用本征函数展开法来开发一种显式解析解决方案，以计算非饱和土壤在受到外部压力时的多余孔隙水和孔隙空气压力负载。所开发的一般解决方案以深度z和时间t表示。对于半渗透性排水边界，开发了空间域的特征值和特征函数。拉普拉斯变换技术用于在时域中求解耦合的常微分方程。用文献中现有的半分析方法对新推导的显式解进行了验证，并获得了很好的一致性。与半解析解相比，新导出的解析解更加直接和明确，因此该解相对易于实施到计算机程序中，以对非饱和土的一维固结进行初步评估。