基于非达西渗流的软土一维非线性固结半解析解

在土中渗流遵循非达西渗流定律的前提下，考虑软土在固结过程中的非线性固结特性，根据饱和土体一维固结的连续条件，推导出基于非达西渗流的软土一维非线性固结控制方程。利用半解析方法对其进行求解，并与差分计算结果进行对比，验证半解析方法的可靠性。最后，着重分析非达西渗流与达西定律之间非线性固结性状的差别，以及不同自重应力分布方式对固结速率的影响。结果表明，考虑非达西渗流下的非线性固结速率比达西定律下要慢，且指数和临界水力坡降越大，非线性固结速率越慢。而且，作用的外荷载越小、地基土层越厚，非达西渗流下非线性固结速率的减慢愈明显。自重应力均匀分布下的非线性固结速率要比自重应力线性分布下慢，但随着荷载的增大、土层的变薄，两者之间的差别会越来越小。

Semi-analytical solution of one-dimensional nonlinear consolidation with non-Darcian flow

Based on the non-Darcian flow in soft soil and nonlinearity during the process of consolidation, the governing equation of one-dimensional nonlinear consolidation was derived according to continuity condition of one-dimensional consolidation. Solutions for this question were obtained by adopting a semi-analytical method, and were verified by comparing with the results by finite difference method. Finally, the difference of consolidation behavior between non-Darcian flow and Darcy’s law and influence of distribution types of dead-weight stress on consolidation rate were emphatically analyzed. The results show that the rate of nonlinear consolidation will be slowed down when non-Darcian flow is considered; and the larger the exponent and threshold hydraulic gradient are, the slower the rate of nonlinear consolidation is. Furthermore, this retardation of nonlinear consolidation with non-Darcian flow will be more noticeable with an increase of thickness of soil layer and a decrease of external loading. The rate of nonlinear consolidation with linear distribution of dead-weight stress is faster than that with uniform distribution; and the difference between them will diminish with increasing the external loading and decreasing the thickness of a soil layer.