何玲丽,田东方. 基于混合格式Richards方程的非均质土体渗流模拟[J]. 水利水运工程学报,2022(3):59-65. doi: 10.12170/20201209002
引用本文: 何玲丽,田东方. 基于混合格式Richards方程的非均质土体渗流模拟[J]. 水利水运工程学报,2022(3):59-65. doi: 10.12170/20201209002
(HE Lingli, TIAN Dongfang. Seepage simulation for heterogeneous soil based on the mixed form of Richards’ equation[J]. Hydro-Science and Engineering, 2022(3): 59-65. (in Chinese)). doi: 10.12170/20201209002
Citation: (HE Lingli, TIAN Dongfang. Seepage simulation for heterogeneous soil based on the mixed form of Richards’ equation[J]. Hydro-Science and Engineering, 2022(3): 59-65. (in Chinese)). doi: 10.12170/20201209002

基于混合格式Richards方程的非均质土体渗流模拟

Seepage simulation for heterogeneous soil based on the mixed form of Richards’ equation

  • 摘要: 基于混合格式Richards方程的数值模拟能保证质量守恒,可模拟饱和-非饱和渗流。采用有限元模拟时,需知节点处的体积含水率,但由于体积含水率在材料分界面不连续,模拟非均质土体渗流时存在一定困难。为实现基于混合格式Richards方程的非均质土体饱和-非饱和渗流有限元模拟,将材料分界面的节点赋予两个编号,从而分界面上节点的体积含水率分别根据不同材料参数按压力水头泰勒展开;同时应用拉格朗日乘子法保证总水头在材料分界面的连续性。根据所建模型的有限元格式,编制了Matlab数值模拟程序,并用于模拟一维层状土入渗和脱湿过程及二维层状土入渗过程。所得结果与一维解析解、二维其他学者研究结果吻合较好,同时所建模型满足质量守恒。

     

    Abstract: The numerical simulation based on the mixed form of Richards’ equation has the mass conservative property, and can be used to simulate the variably saturated seepage which is prior to other forms of equations. However, on material interface, the distribution of moisture content which is required for the FEM numerical simulation is discontinuous, thus the mixed form of Richards’ equation cannot be utilized in the FEM simulation for heterogeneous soil. In this research, a numerical method was proposed to simulate the variably saturated water flow in heterogeneous soil based on the mixed form of the equation. In the proposed method, two nodal numbers are assigned to each node which locates on the material interface so that the moisture content of each node can be expanded in a truncated Taylor series with respect to pressure head with different material properties. The continuity of the total head is imposed by the Lagrange multiplier method. The proposed method and program based on Matlab were validated against two examples stemmed from other literature. One example was a 1 d problem for the infiltration and draining process of a two layered soil column, and another example was a 2 d infiltration problem for a two layered soil column. And the verification indicated a good agreement between our modeling results and analytical solution for 1 d problem as well as the numerical results for 2 d problem.

     

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