连续排水边界条件下土体一维非线性固结解析解

An analytical solution for one-dimensional nonlinear consolidation of soils with continuous drainage boundary

基于Davis和Raymond土体一维非线性固结的假设,通过引入连续排水边界条件研究瞬时荷载下的土体一维非线性固结问题。利用变量代换、分离变量法及Laplace变换得到连续排水边界下土体一维非线性固结问题的解析解,通过退化为Davis双面排水解答初步验证本文解析解的正确性。基于所得解析解,对不同界面参数以及非线性参数对土体固结特性的影响进行分析。结果表明:基于连续排水边界条件的土体一维非线性固结理论的边界条件能严格满足其初始条件,并且其退化结果表明固结方程是适定的,且所得解是连续的。连续排水边界条件下按沉降定义的平均固结度Us随非线性参数Nσ值的增大而增大,而按孔压定义的平均固结度Up随Nσ值的增大而减小。对比土层界面参数对土体固结的影响与非线性参数Nσ对土体固结的影响可知,土层界面参数对土体固结的影响更大。

Based on the assumptions of one-dimensional nonlinear consolidation proposed by Davis and Raymond,one-dimensional nonlinear consolidation of soils under instant loading was investigated by introducing the continuous drainage boundary. An analytical solution of the one-dimensional nonlinear consolidation problem of soils was derived by utilizing variable substitution,variable separation and Laplace transform,and the reasonableness of the solution was verified compared with Davis solution. Influence of different interface parameters or nonlinear parameters on consolidation behavior of soils was analyzed in detail. The results show that the boundary conditions of the presented solution can strictly meet the initial conditions,and that the consolidation equation is well-posed and its solution is continuous. The average consolidation degree,Us,defined by the settlement,increases with increasing the nonlinear parameter Nσ ,but the average consolidation degree, Up,defined by the pore pressure, decreases with ascending Nσ . Comparisons indicate that the interface parameters have more marked influence on soil consolidation than the nonlinear parameter Nσ .