A Simple Analytical Solution for One-Dimensional Consolidation of Unsaturated Soil under Local Surcharge Load

Abstract

This paper presents an exact analytical solution of one-dimensional consolidation for unsaturated soils under the local surcharge load using the mode superposition method. Based on the solution to Boussinesq’s problem, the distribution of total normal stress is considered in the consolidation equations. Then, the excess pore-air and pore-water pressures are expressed in a series of products of eigenfunctions concerning depth and normal coordinates concerning time, respectively. After matrix algebraic manipulation, the normal coordinates can be determined by the initial conditions and the loading function, and the final solutions for the unsaturated consolidation are obtained. This solution can avoid inconvenient Laplace transform and inverse Laplace transform and can be degenerated to the existing formulation. Through calculating two classic examples, the validations of the proposed analytical solution are verified against other analytical solutions and the developed finite difference solution. According to the proposed solutions, the consolidation behaviors involving three loading patterns and two loading histories are graphically demonstrated and discussed.