An optimized 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 the explicit format, resulting in high computational costs and error rates due to conditional stability and low-order truncation errors. To tackle this issue, this study develops an efficient and accurate implicit difference (ID) numerical solution. The ID scheme and virtual mesh method are used to discretize the consolidation equations and boundary conditions. The final iterative format is obtained by assembly of matrices. Under von Neumann’s theorem, the numerical method has been verified to be unconditionally stable. A series of comparison and verification examples is conducted to demonstrate the advantages of the ID solution. The results show that the ID method has higher computational efficiency and accuracy compared to the explicit difference method. Furthermore, the ID solution is used to verify the accuracy of analytical and semi-analytical solutions.