Analytical solution for consolidation of unsaturated composite foundation improved by permeable and impermeable columns considering depth-dependent initial stress

The combination of permeable and impermeable columns is commonly employed to enhance the stability of natural ground and expedite the consolidation process while effectively reducing foundation settlement. This study presents a comprehensive investigation of the consolidation characteristics of unsaturated composite foundations (USCF) using various methods. Firstly, a mathematical model is developed under the assumption of equal strain, considering depth-dependent initial stress. To obtain more generalized analytical solutions for excess pore pressures and foundation settlement, separation of variables, Laplace transformation, and inversion Laplace transformation are employed. Secondly, the accuracy of the proposed analytical solutions is validated by comparing them with two specific cases reported in the existing literature, achieved by reducing the compression modulus of columns. Lastly, a series of parameters are investigated to examine the consolidation characteristics of USCF considering depth-dependent initial stress. The results demonstrate that the final settlement of the foundation will be overestimated while the variation of vertical stress along the depth is neglected. Furthermore, adjusting the values of area replacement ratios proves to be more effective and straightforward than modifying the compression modulus of columns in the reinforcement treatment of USCF.