考虑井阻与涂抹的非饱和土竖井地基固结分析

基于等应变假设与 Fredlund 非饱和土固结理论, 得到了考虑井阻与涂抹的非饱和土竖井地基固结半解析解. 首先, 引入两个新的变量, 通过 Laplace 变换将控制方程组转化为易于求解的常微分方程组; 然后, 考虑井阻与涂抹条件, 并将 Laplace 变换下的解用 Crump 方法编程实现 Laplace 逆变换, 得到地基内任一深度的平均超孔隙气压力、平均超孔隙水压力和整个深度范围内的平均固结度在时间域内的解;最后, 将所求解退化为饱和土中考虑井阻与涂抹的等应变固结解进行验证, 并与非饱和土中自由应变假设下理想井固结解进行对比, 验证了半解析解的可靠性. 通过分析发现:井阻因子、涂抹系数和涂抹区半径比任何一个值增大, 固结都将变慢;考虑井阻与涂抹能更加准确地预测非饱和土竖井地基的固结度.

Analysis of radial consolidation of unsaturated soil with vertical drains considering drain resistance and the smear effect

Based on the equal-strain hypothesis and Fredlund's consolidation theory of unsaturated soil mechanics, a semi-analytical solution to consolidation of unsaturated soil with vertical drains considering drain resistance and the smear effect is proposed. Firstly, the governing equations are transformed into easy-to-solve equivalent linear partial differential equations by introducing new variables and the Laplace transform, with both drain resistance and smear effect conditions in the solution derivation taken into account. By utilizing Crump's method, the inverse Laplace transform is then used to obtain the average excess pore-air and pore-water pressures and the average consolidation degree in the time domain. Moreover, the validity of the solution is verified by degenerating and comparing with the existing solution to the foundation with ideal boundary conditions of unsaturated soil based on the free-strain assumption. The results show that an increase in the drain resistance factor, smear coefficient, or smear zone radius ratio will extend the consolidation time. Drain resistance and the smear effect are considered useful for more reasonably predicting the consolidation degree of unsaturated soil with vertical drains.