Augmented Gauss Points Method For Steady-State Seepage Analysis With Free Surface

In hydraulic and hydropower engineering, the unconfined seepage problem with free surface is often confronted. Because the position of free surface and overflow boundaries are both unknown in advance, an iterative process is consequently required, it is a boundary nonlinear problem. At all times, how to locate the free surface and overflow boundaries reliably and efficiently is where the shoe pinches for the unconfined seepage field analysis. Currently, Finite Element Method (FEM) is the primary means for numerical analysis of seepage. Fixed Mesh Method (FMM), one of the FEM, owing to advantages of itself, has a very broad application, and is taking the place gradually of?the Altered Mesh Method (AMM), the traditional finite element method in this realm which need to modify the mesh when the free surface changes during the iteration process. Augmented Gauss Points Method proposed in this paper is an improved Gauss Points Method, and it is a FMM.First, the basic principle of seepage and FEM for seepage calculation has been described briefly. And then several methods common in use were introduced, including AMM, Residual Schemes Method, Bathe Method and Initial Flow Method. The Bathe Method suggests divide the whole domain by free surface into two parts, saturated region and unsaturated region under and beyond the free surface, the element coefficient of permeability within the unsaturated region is discounted to a very small value while keeps unchanged within the saturated region. Because that FEM adopt the Gaussian integrating formula to calculate the element conductivity matrix approximately, Gauss Points Method suggests adjust the permeability coefficient at Gaussian integrating point according to the relation between its hydraulic head and elevation, as a result, the calculation for the position of free surface is avoided. In order to raise the calculation precision of element conductivity matrix of the compound elements, Augmented Gauss Points Method has been adopted in this paper. According to this method, the number of Gaussian integrating points increases within the compound elements while keeps invariable within the others. At the same time, the treatment for the overflow boundary conditions was introduced in this paper. In the end, the program MESeep for steady-state seepage analysis has been coded in C++ language. And the planning and developing processes of software MESeep were described. Employing the software MESeep, steady-state seepage analysis for cases of confined and unconfined, 2-D and 3-D, homogeneous and unhomogeneous, isotropic and anisotropic have been carried out. And the results demonstrate that Augmented Gauss Points Method and software MESeep are feasible.