Axisymmetric Consolidation of Unsaturated Soils by Differential Quadrature Method

Axisymmetric consolidation in a sand drain foundation is a common problem in foundation engineering. In unsaturated soils, the excess pore-water and pore-air pressures simultaneously change during the consolidation procedure; and the solutions are not easy to obtain. The present paper uses the differential quadrature method (DQM) for axisymmetric consolidation of unsaturated soils in a sand drain foundation. The radial seepage of sand drain foundation is considered based on the framework of Fredlund's one-dimensional consolidation theory in unsaturated soils. With the use of Darcy's law and Fick's law, the polar governing equations of excess pore-air and pore-water pressures of axisymmetric consolidation are derived. By using DQM, the two governing equations are transformed into two sets of ordinary differential equations. Then the solutions of excess pore-water and pore-air pressures can be obtained by Rong-Kutta method. The DQM solution can be used to deal with the case of nonuniform initial pore-air and pore-water distributions. Finally, case studies are presented to investigate the behavior of axisymmetric consolidation of unsaturated soils. The convergence analysis and average degree of consolidation, the settlements in radial and vertical direction, and the effects of different initial excess pore pressure distributions are presented, and discussed in this paper.