A general analytical solution for two-dimensional plane strain consolidation of unsaturated soil incorporating lateral and vertical impeded drainage boundaries

Abstract

In most practical consolidation problems, impeded drainage boundaries are a great concern. By simultaneously introducing the impeded drainage boundaries in the horizontal and vertical directions, this study attempts to constitute a general two-dimensional (2D) plane strain consolidation system of unsaturated soil. A newly analytical solution is developed to calculate the excess pore-air and pore-water pressures and average degree of consolidation. On the basis of the eigenfunction expansion method, the developed analytical solution is given as a product of three functions, including one variable of time, horizontal and vertical dimensions only. For the impeded drainage boundaries, the eigenfunctions and eigenvalues are derived in the horizontal and vertical dimensions. The Laplace transform technique is further adopted to solve the ordinary differential system in the time domain. The developed analytical solution is verified with the existing analytical/semi-analytical solutions and finite difference solution for several typical cases. Excellent agreements are obtained so that the correctness of the developed analytical solution is validated. Moreover, two worked examples are presented to show the superiority of the developed analytical solution and to assess the influences of the drainage parameters on the 2D plane strain consolidation behavior of unsaturated soil.