Seepage analysis based on weak finite element method

In the design and operation management of hydraulic structures such as dams, gates and embankments, the seepage calculation plays a very important role. The current methods for seepage analysis are mainly based on the general finite element method. It is often hoped, by refining the mesh, to pursue the calculated results with higher-precision in the seepage analysis. However, the general finite element method, which belongs to the coordinated finite element method, cannot handle hybrid grids, and the refined mesh may lead to unstable calculation formats and the divergence of the calculated results. The weak finite element method is a non-coordinated one, which replaces the classical gradient operator in the variational formula for the general finite element method with the weak gradient operator of the weak function, and adds a stable sub-term in the variational formula, to obtain an absolute stability of the calculation format, and it can handle hybrid grids. For the same mesh grid, the degree of freedom of the overall algebraic equations for the weak finite element method is much larger than that of the general finite element method. In order to reduce the degree of freedom of the weak finite element method, the targeted mixed meshing grid is used to establish the weak finite element method which is used to solve the free surface of seepage and to analyze the seepage field of the gate foundation with anti-seepage curtain. The numerical simulation shows that the weak finite element method can be used to process flexibly hybrid grids, and it is of high accuracy.