Hybrid Finite Element Formulation For Seepage Analysis In Dam Foundation And Dam Body

Due to that the seepage problem will directly influence the security of dams, the seepage problemis always a hot research subject in civil engineering field, especially the seepage problem with free surface. The location of free surface is unknown, so it increases the difficulty of solving seepage problem.This thesis develops the fundamental solution-based hybrid finite element method(HFS-FEM), which is used for calculating two-dimensional steady-state seepage analysis. In the thesis, the seepage analysis includes linear seepage analysis of orthotropic dam foundation and nonlinear seepage analysis with the presence of free surface in isotropic dam body.As a new numerical method, the present hybrid finite element method, which is developed in recent years and based on the fundamental solution interpolations, is a kind of domain-type numerical methods. Owning to that the linear combination of fundamental solutions is used to satisfy the fundamental solution of governing equations, the hybrid finite element method needs only element boundary integrations. Moreover, the element shape can be arbitrary polygon element, which is very suitable for computing problems with composite material and moving boundaries. The arbitrary polygon element can also significantly reduce the difficulty of mesh structure and the number of meshes.In this thesis, fundamental solutions for orthotropic and isotropic seepage problems are employed to construct the element interior hydraulic head field, while the conventional shape functions are used for the element frame hydraulic head field. The element interior hydraulic head field and the element frame hydraulilc head field are connected by a double-variable hybrid functional, and then it can use the functional extremum to produce the final solving equations. According to physical definition of fundamental solutions, the elemental interior fieldcan naturally satisfy the seepage governing equation and as a result, all two-dimensional element domain integrals in the present algorithm can reduce to one-dimensional element boundary integrals. In addition, the polygon elements are constructed for computing the area nearby free surface, which can simplify remesh during the interation process and reduce the amount of calculation.In the thesis, the present hybrid finite element with fundamental solution kernels method is firstly verified by way of analytical solutions. Afterwards, linear seepage problem of orthotropic dam foundation and nonlinear seepage problem with the presence of free surface in isotropic dam body are computed, and the results of calculation are discussed in the paper.