Semi-analytical solutions to two-dimensional plane strain consolidation for unsaturated soils under time-dependent loading

This paper presents semi-analytical solutions of two-dimensional plane strain consolidation for unsaturated soils under time-dependent loading using Fourier sine series and Laplace transform. The consolidation equations in form of two-order partial differential equations with three variables are firstly converted to that with two variables. Then four-order ordinary differential equations about excess pore-air and pore-water pressures are presented, and the semi-analytical solutions of excess pore-air and pore-water pressures and settlement are achieved in the Laplace transform domain. Two comparisons are performed to verify the exactness of the obtained solutions, and the consolidation behavior involving three time-dependent loadings is illustrated and discussed.