A Hansbo's consolidation solution of sand-drained ground with impeded boundaries under vacuum and surcharge preloading

The top and bottom boundaries of sand-drained ground were visualized as impeded boundaries to investigate the effects of the pervious behaviors of the cushion above the top and the substratum below the bottom during the consolidation process of sand-drained ground. Based on the axisymmetric consolidation equations and the equal strain assumption, the consolidation solution of sand-drained ground with impeded boundaries was obtained using Hansbo's method for vacuum and surcharge preloading. The effects of the pervious coefficients of top and bottom boundaries on the consolidation degrees and settlements of vacuum preloading and surcharge preloading were analyzed. The similarities and differences between the solution and Indraratna et al.,'s solution and Zhou et al.,'s solution were compared under vacuum preloading alone. The results reveal the following:(1) for either vacuum or surcharge preloading, the consolidation degree of the ground increases with the increasing pervious coefficients of the boundaries when the consolidation time factor is the same; (2) for vacuum preloading, the larger the pervious coefficient of the bottom boundary is, the smaller the final settlement of the ground is, and the smaller is the settlement at the same time factor during the consolidation process; the larger the pervious coefficient of the top boundary is, the greater is the settlement at the same time factor during the consolidation process; (3) for surcharge preloading, the larger the pervious coefficient of the bottom or top boundary is, the larger is the settlement at the same time factor during the consolidation process while the final settlement remains constant; (4) when the top boundary is permeable during vacuum preloading, the consolidation degree of Zhou et al's solution is higher than the consolidation degree of the proposed solution, and the consolidation degree of the solution is higher than the consolidation degree of Indraratna et al's solution. The level of perviousness of the bottom boundary of ground should be reduced to increase the final consolidation settlement under vacuum preloading.