A Fast Algorithm for Axisymmetric Consolidation of Unsaturated Soil Considering Permeable and Impermeable Columns

Abstract

Most existing finite difference methods for solving unsaturated soil consolidation problems are based on explicit schemes, which lead to high computational costs and notable errors due to conditional stability and low-order truncation errors. To address this issue, the present study proposes an efficient and accurate implicit difference (ID) numerical solution. The consolidation equations and boundary conditions are discretized using the ID scheme combined with the virtual mesh method, and the final iterative formulation is obtained through matrix assembly. The proposed method is verified to be unconditionally stable under von Neumann’s theorem. A series of comparative and verification examples is conducted to demonstrate the advantages of the ID solution. The results indicate that the ID method achieves higher computational efficiency and accuracy than the explicit difference method. Furthermore, the ID solution can also be used to validate the accuracy of analytical and semi-analytical solutions.