Semi-analytical solutions to consolidation for unsaturated soils by vertical drains under arbitrary time-dependent loading

Abstract

This paper presents general semi-analytical solutions to equal strain consolidation for unsaturated soil layer by vertical drains, and the well resistance is considered. Firstly, the coupled governing equations are transformed into ordinary differential equations (ODEs) by Laplace transform and introducing two new variables, and combined with boundary conditions to obtain solutions. On this basis, the semi-analytical solutions in the time domain are achieved by performing inverse Laplace transform with Crump’s method. Secondly, the correctness of the semi-analytical solutions are verified by comparison with the existing analytical solutions of radial consolidation for unsaturated soils under constant loading. Finally, the effect of well resistance factor, permeability coefficient ratio ka/kw and load parameter on the average degree of consolidation was analyzed under exponential loading.