关键词: seismic response, response spectrum, convex set, extreme value, one-dimensional consolidation, homogeneous boundary condition, semi-analytical solution, unsaturated soil, time-dependent loading

Abstract:

This paper presents general semi-analytical solutions to Fredlund and Hasan's one-dimensional (1D) consolidation equations for unsaturated soils subject to different initial conditions, homogeneous boundaries and time-dependent loadings. Two variables are introduced to transform the two-coupled governing equations of pore-water and pore-air pressures into an equivalent set of partial differential equations (PDEs), which are solved with the Laplace transform method. The pore-water and pore-air pressures and settlement are obtained in the Laplace transform domain. The Crump's method is used to perform inverse Laplace transform to obtain the solutions in the time domain. The present solutions are more general in practical applications and show good agreement with the previous solutions in the literature.

Key words: seismic response, response spectrum, convex set, extreme value, unsaturated soil, homogeneous boundary condition, semi-analytical solution, time-dependent loading, one-dimensional consolidation