Abstract: The soft soil usually exhibits obvious nonlinear compressibility and permeability characteristics during the consolidation process. At the same time, the clogging effect of vertical drains often causes the well resistance to change with depth and time during the consolidation process. However, the analytical solution for nonlinear consolidation of soils with vertical drain, in which the variation of well resistance over time and depth can be considered, is still rarely reported in the literature. In this study, semi-logarithmic models between the void ratio and the effective stress, and between the void ratio and the permeability coefficient are introduced to describe the nonlinear consolidation characteristics of soils, and a nonlinear consolidation model of soils with vertical drain, which can simultaneously consider the time- and depth-variation of well resistance and the influence of smearing, is developed, then the analytical solution of this consolidation model is obtained by the method of separated variables. The consolidation calculation results derived here under specific parameters are compared with the laboratory tests data, and the existing vertical drains consolidation solutions to verify its reliability. Finally, a large number of calculations and analyses have been carried out on the nonlinear consolidation behavior. The results show that the more obvious the linear decay of the vertical drain permeability coefficient with depth is, the slower the consolidation rate of soils with vertical drain is. Considering the exponential decrement of the vertical drain permeability coefficient with time, the consolidation rate of soils with vertical drain is much slower than that with consideration of the vertical drain permeability coefficient remaining constant over time. When the external load is constant, the consolidation rate of the vertical drain foundation decreases with the ratio of the soft soil compression index (cc) to the permeability index (ck) increases. When the value of cc/ck remains constant, the consolidation rate of the vertical drain foundation increases with the external load increases. Among the three variations related with horizontal permeability in smear zone, the vertical drain consolidation rate is the fastest under the parabolic variation mode, the next is the linear variation mode, and the vertical drain consolidation rate under the constant variation mode is the slowest. The influences of smear zone on consolidation behavior are not affected by the change of well resistance and the nonlinear consolidation characteristics of soils.

Key words: vertical drain, variable well resistance, nonlinear consolidation, smearing, analytical solution