考虑井阻时空变化的竖井地基非线性固结解析解

软土固结过程中展现出明显的非线性压缩和渗透特性，同时竖井的淤堵效应常导致井阻在固结过程中随深度和时间不断演化，但目前能考虑井阻随时空演化的竖井地基非线性固结解析解还很鲜见。通过引入孔隙比与有效应力及孔隙比与渗透系数间的半对数模型描述了土体的非线性固结特性，建立了能同时考虑井阻随时空变化和涂抹影响的竖井地基非线性固结模型，并采用分离变量法获得了固结模型的解析解。将特定参数下固结解的计算结果与实测数据、已有的竖井地基固结解答进行了对比分析以验证其可靠性。最后，对竖井地基的非线性固结性状开展了大量计算分析。结果表明：竖井渗透系数随深度线性衰减越明显则地基固结速率越慢；外荷载一定时，随着软土压缩指数c_c与渗透率指数c_k之比的增大，竖井地基固结速度减慢；在c_c /c_k值不变的情况下，外荷载增加，地基固结速率加快。在涂抹区的3种径向渗透系数变化模式中，抛物线变化模式下的地基固结速度最快，线性变化模式下的地基固结速度次之，恒定模式下的地基固结速度最慢，且这种性状并不因为考虑井阻变化或土体非线性固结特性而发生改变。

Analytical solution for nonlinear consolidation of soft soil with vertical drains by considering time- and depth-variation of well resistance

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.