Consolidation theory of soft foundation with partially penetrating vertical drains under surcharge-vacuum preloading

Due to the limitations of the existing methods, a simplified method for calculating the consolidation degree for the soft foundation with partially penetrating vertical drains is devised, in which the soil is divided into two layers: an upper layer with vertical drain and a lower layer without vertical drain. The proposed method accounts for the continuity of pore-water pressure between the upper and lower soil layers using the continuous drainage boundary condition. Under a surcharge-vacuum combined load, the analytical solutions to the excess pore-water pressure and consolidation degree are derived based on pervious top with pervious bottom (PTPB) and pervious top with impervious bottom (PTIB) conditions, respectively. The rationality of the present solution is verified by comparing it with the existing simplified methods and semi-analytical solutions. On basis of the present solution, the consolidation behaviors of soft foundation with partially penetrating vertical drains under surcharge-vacuum preloading are investigated. The results show that the whole consolidation rate becomes quick with the increase of penetration degree. When considering the vacuum preloading under PTPB condition, the vacuum negative pressure has attenuation along depth in the lower soil layer.