岩土体三维非线性渗流有限元数值分析

3D NONLINEAR SEEPAGE ANALYSIS FOR ROCK-SOILS WITH FINITE ELEMENT METHOD

从渗流机理的角度研究了在达西定律不适用的情况下岩土体三维非线性渗流问题,讨论了非线性渗流的影响因素和表达公式。进行了岩土体的三维非线性渗流有限元数值分析,根据试验确定的非线性渗流关系式,运用伽辽金有限元法导出了非线性的控制方程组,并用直接迭代法进行求解,讨论了迭代收敛标准以及提高计算精度和加速收敛的技术等问题。所给出的算例,其计算结果与理论解十分吻合。初步研究表明,本方法具有编程简单、计算效率高和收敛速度快等优点。

From the point of seepage mechanism, 3D nonlinear seepage analysis is made for the case in which Darcy law is not available. The controlling factor and formula representation of nonlinear seepage are discussed. 3D nonlinear seepage analysis is carried out on rock-soils with FEM, based on an empirical nonlinear relation between seepage velocity and hydraulic gradient. The nonlinear seepage controlling equations are derived by using Galerkin FEM, and numerically solved by direct iteration. Some issues, including the criteria of iteration convergence, improvement of the calculation precision, and acceleration of convergence, are discussed. An explanatory example is given, and the numerical result is very close to theoretical solution. The study result shows that the presented approach is of simplicity for programming, high computational efficiency and fast convergence.