A general analytical solution for axisymmetric electro‐osmotic consolidation of unsaturated soil with semi‐permeable boundary

Abstract This study proposes a closed‐form solution for axisymmetric electro‐osmotic consolidation of unsaturated soil under semi‐permeable boundary conditions. The governing equations are formulated to allow for vertical and radial flows of liquid and air phases. The techniques of eigenfunction expansion and Laplace transformation are employed to develop the exact solution for excess pore‐air (EPAP) and pore‐water pressures (EPWP). The proposed solution is first validated by comparing it to an existing solution, followed by verification through finite element simulations. Both methods of validation confirm the accuracy of the analytical solution. Then, based on the obtained solution, the effects of vertical flow, semi‐permeable boundary conditions, electrical voltage, electro‐osmosis conductivity and spacing ratio r e / r w on the consolidation profile have been further investigated. Parametric studies show that the EPWP at the steady state depends on the electro‐osmosis conductivity and applied electricity gradient. In addition, the dissipation rates of EPWP and EPAP in the axisymmetric electro‐osmotic consolidation would be underestimated if the vertical flows are neglected. The semi‐permeable boundary conditions have great influences on the dissipation rate and the steady‐state solution. The proposed solution could serve as a theoretical basis for axisymmetric electro‐osmotic consolidation of unsaturated soil.