Semianalytical Solutions to the Axisymmetric Free Strain Consolidation Problem of Unsaturated Soils under the Homogeneous and Mixed Boundary Conditions

Abstract

Since the wide applicability of axisymmetric consolidation model, the axisymmetric consolidation problem of unsaturated soils has gradually become a hot issue. However, the mixed boundary conditions of axisymmetric free strain consolidation of unsaturated soils have not been fully considered. The boundary condition is the main factor affecting the consolidation process with the determined consolidation model and related parameters. In this paper, the governing equations of water and air in the polar coordinate were given according to two stress state variables theory of unsaturated soils, Darcy’s law, and Fick’s law under the axisymmetric condition. Based on the free strain hypothesis, a series of semianalytical solutions of the axisymmetric consolidation for unsaturated soil grounds under four different boundary conditions are proposed by using the Laplace transform and the finite Hankel transform. After the correctness of the proposed governing equations and semianalytical solutions is verified by degeneration verification, the parametric consolidation characteristics of unsaturated soils under different parameters through numerical examples and parametric studies are analyzed. Combining the four boundary conditions, the entire consolidation process under homogeneous boundary will be overestimated compared to that under the mixed boundary. In other words, the time required to complete consolidation will be extended accordingly if the boundary condition is not homogeneous. It is clear that the study on the axisymmetric consolidation of unsaturated soils considering multiple boundary conditions is conducive to a more comprehensive understanding of unsaturated soils and provides strong theoretical support for engineering practice.