Semianalytical Solutions to the Consolidation of Drainage Well Foundations in Unsaturated Soils with Radial Semipermeable Drainage Boundary under Time-Dependent Loading

Abstract

This paper presents semianalytical solutions to the consolidation of drainage well foundations in unsaturated soils with radial semipermeable drainage boundary subjected to time-dependent loading, and radial boundary condition is employed to illustrate the smear effect. First, the governing equations of excess pore-air and pore-water pressures are transformed into equivalent partial differential equations. Afterwards, the final semianalytical solutions of the equations based on the free strain assumption are obtained by introducing the Bessel functions and Laplace transform techniques. The inverse Laplace transform is performed to derive the solutions in the time domain by means of Crump's method. Furthermore, the solutions are verified to be reliable by the regressive solutions and the numerical solutions by finite difference method (FDM). Finally, instantaneous loading, ramp loading, exponential loading, and sinusoidal loading are adopted to illustrate the changing regularity of excess pore-air and pore-water pressures against the ratios of air-water permeability, radial semipermeability coefficient parameters, and loading parameters.