变荷载下考虑井阻随时空变化的竖井地基固结解

竖井排水固结法中井阻随时空演变（即由淤堵和弯折所引起的竖井排水能力下降）的现象已引起广泛关注，且变井阻对竖井地基固结速率的影响不容忽略。但目前能同时考虑变荷载及井阻随时间和空间变化的固结解析解还鲜有报道。考虑井阻随时空演变过程，引入实际中广泛采用的单级或多级加载模式，建立了竖井地基固结模型，并应用分离变量法获得固结模型的解析解答。通过与已有的解析解、有限差分解及工程实测值进行对比分析，充分验证了该模型的正确性。通过大量的计算，分析变井阻参数对竖井地基固结性状的影响。结果表明：竖井地基固结速率随竖井最终排水能力的增大而加快，随深度井阻参数及时间井阻参数的增大而减缓，且时间井阻参数的影响更为显著。

Analytical solution for consolidation of soft soils with vertical drains by considering variable well resistance with time and depth and time-dependent loading

The phenomenon that the well resistance changes with both time and depth (i.e., the decrease of drainage capacity caused by silting and bending) has been widely concerned during the consolidation of soft soils with vertical drains. Moreover, the influence of variable well resistance on consolidation rate of soft soils with vertical drains cannot be ignored. However, there are few analytical solutions for consolidation which can consider the time-dependent loading and the variation of well resistance with time and depth at the same time. Considering the evolution process of time-and depth-dependent well resistance, a consolidation model of soft soils with vertical drains is developed by incorporating a single stage loading or a multistage loading which is widely adopted in practice, and the analytical solution of the consolidation model is obtained by using the separation of variables method. The correctness of the model is fully verified by comparison with the existing analytical solutions, finite difference solutions and engineering measured values. Finally, the influences of variable well resistance parameters on consolidation behavior of soft soils with vertical drains are analyzed through a lot of calculations. The results show that the consolidation rate of soft soils with vertical drains increases with an increase in the final drainage capacity of vertical drains, and decreases with an increase in the value of depth resistance parameters and time resistance parameters, and influences of time resistance parameters on the rate of consolidation are more significant.