A semi-analytical solution to consolidation of unsaturated soils with the free drainage well
Based on Fredlunds one-dimensional consolidation equation for unsaturated soil, Darcys law and Ficks law, a semi-analytical solution was presented to the free drainage well with a finite thickness under application of uniform vertical loading and the boundary of the top and bottom surfaces impermeable to water and air. According to the polar governing equations of water and air phases and the boundary and initial conditions, the excess pore-air and pore-water pressures and the soil layer settlement in the Laplace transformed domain are obtained by performing the Laplace transform and utilizing the Bessel functions. Crumps method is used to perform the inversion of Laplace transform in order to obtain numerical solutions in the real time domain. Finally, a typical example is given to illustrate the changes in the excess pore-air and pore-water pressures and soil layer settlement with time factor at different ratios of airwater permeability coefficient and/or different distances from the well.
semi-analytical solution unsaturated soil free drainage well excess pore-air pressure excess pore-water pressure