An analytical solution for consolidation of soils with stone columns and vertical drains by considering the deformation of stone columns

The composite foundation reinforced by stone columns and vertical drains is widely used in various projects. However, available calculation methods for such consolidation are rarely reported in the literature. Firstly, a set of basic equations are proposed to describe the seepage relations among stone columns, vertical drains, and soft soils in this study. Then, the governing consolidation equation, in which the average total excess pore water pressure (EPWP) serves as a variable, is derived by considering the deformation of stone columns during consolidation under the assumption of equal strain conditions. Moreover, the analytical solution for the consolidation equation is obtained by the method of separation of variables, and its reliability is verified by degenerating into the solution for the consolidation of composite foundations reinforced by stone columns and comparing it with the field measurements. Finally, a parametric study is performed to investigate the consolidation behavior. The results show that the consolidation rate can be significantly increased by installing vertical drains between the stone columns compared to reducing the column spacing; for some composite foundations reinforced by stone columns with a high ratio of replacement, the deformation of columns during consolidation cannot be ignored; the smear effect caused by vertical drains can be ignored in such composite foundations.