Semianalytical Solution for One-Dimensional Consolidation in a Multilayered Unsaturated Soil System with Exponentially Time-Growing Permeable Boundary

Abstract

This paper proposes new semianalytical solutions to one-dimensional consolidation of unsaturated soils with a multilayered system under the partially permeable boundary condition, in which a time-decaying exponential function is applied to represent the variations of excess pore pressures for both water and air at the boundary. The general solutions are explicitly presented by the aid of the Laplace transform. Based on the general solutions, interfacial continuity between layers, and boundary conditions, the transfer matrix approach is adopted to deduce the analytical solutions of the multilayered unsaturated soil consolidation in the Laplace space, and the numerical inverse computations of Laplace transform in terms of Crump’s technique are carried out to obtain the final analytical solutions. Then, the existing solution for single-layered soils and the numerical solutions for two-layered unsaturated soils performed by finite-difference methods are utilized to demonstrate the validity of the present methodology as well as semianalytical solutions. Finally, a case study considering two distinct soil profiles is implemented to illustrate the influence of the impeded boundary parameters on the settlement of two-layered unsaturated soils.