The Analytical Solution for Consolidation of Vertical Drain with Vacuum Preloading Based on Equivalent Annular Drain

Abstract

Based on the equivalent annular band-shaped drain, and considering the vacuum preloading and the variation of radial permeability coefficient of the smeared soil zone, the mathematical model is established. An analytic method is used to derive the general solution for the consolidation of vertical drain based on equivalent annular and arbitrary variation of load with time. Based on the general solutions, the detailed closed-form solutions are further derived for the cases of instantaneously loading and linear loading. Based on the closed solution, the calculation program is compiled and the consolidation curves of the vacuum preloading shaft foundation based on the annular equivalent are drawn. The results show that the equivalent annular consolidation rate is less than that given by the equivalent circumference. With the increase of the area reduction coefficient, the consolidation rate of the equivalent annular approaches to the consolidation rate of the equivalent circumference. With the decrease of the permeability coefficient of the vertical drain, the influence of the permeability coefficient on the consolidation rate is weakened. The dissipation rate of pore water under instantaneous load is greater than that of linear pore water dissipation.