Application Of Sub-domain Integration Method And Composite Grid Method In Unconfined Seepage Analysis

Since the necessity for the assembly and decomposition of the conduction matrix is needed only one time, the Initial Flow Method has been widely used in steady unconfined seepage analysis. However, because of the "jump" of permeability between the upside and underside of the free surface, the integrand of nodal initial flow is discontinuous in elements that intersect with the free surface in this method. If traditional Gaussian integral method is adopted in numerical integration, the contribution of some domain in these elements to the nodal initial flow may be ignored, exaggerated or mutation of nodal initial flow might appear when slight movement of the free surface from the underside of the integration point to the upside, reducing the convergence and stability of numerical simulation.There are also discontinuous intgrands related to the "jump" of permeability and specific storage coefficient around the free surface in the Initial Flow Method when it is adopted in the unconfined transient seepage analysis. Once again, the existence of these two discontinuous terms greatly reduced the convergence rate and stability of numerical simulation as large integration error may be caused. Improvement for the integration of these discontinuous terms is of great value to improvement of the algorithom’s stability and convergence and of great importance for the further application of Initial Flow Method.In unconfined steady seepage analysis,"line-style structure" that has a very small size in some direction compared with the whole domain is often encountered. When the flow in these structures can not be ignored, they have to be finely discreted. However, the thickness of these structures may be up to the centimeter or millimeter level, this inevitably leads to the fine discretization also in other regions so as to maintain accuracy, greatly increasing the difficulty and the workload of discretization as well as computation and degrading the precision and convergence of Finite Element simulation. To solve these problems, it is of great significance that a reasonable and feasible approach for reducing the discretization, deserving the seepage characteristics in these structures and improving the caculation speed and accuracy is presented.Theoretical study is carried out on the problems mentioned above in this paper. The application of the subdomain integration theory, the composite grid method in the unconfined seepage analysis and the extension of Initial Flow Method to unconfiend transient seepage analysis is presented., the initial flow method extended to the non-steady seepage calculation. Corresponding computer programs writen with FORTRAN language is coed accordingly to verify their validation.The main content and innovative achievements include the following three aspects: (1) The Initial Flow Method is improved based on the sub-domain integration method. The elements intersecting with the free surface are divided into two parts, one part is below the free surface while the other not. Then these two parts are refined to standard finer regions named sub-domains according to their specific shape. Thereafter, each sub-domain is treated as if it is a "conventional element" and Gaussian integration points are arranged in each sub-domain as in the standard Gaussian integration points sampling process. By this means, the integrand of nodal initial flow is continuous within the control volme/area of each integration points. Exaggeration/ignorance of some domain of the element’s contribution to nodal initial flow and mutation of nodal initial flow that might appear when slight movement of the free surface from the underside of the integration point to its upside is avoided. Therefore, stability and convergence of the Initial Flow Method is improved. The basic types of quadrilateral and hexahedron that intersect with the free surface are given and their detailed modes of sub-domain subdivision is presented in the case of two-dimension and three-dimensional seepage analysis. The transformation between these basic types of elements and others is also listed in this paper. The programs IIFM2DS (Improved Initial Flow Method2D with sub-domain improvement, S stands for steady) and IIFM3DS are coded for two-dimensional and three-dimensional unconfined steady seepage analysis seperately.(2)Drawing lessons from saturated-unsaturated seepage theory and research of Desai et al., the Initial Flow Method is extended to unconfined transient seepage analysis from steady case. The Finite Element discretization scheme is derived base on virtual displacement principle and the discontinuous terms are still improved by sub-domain integration method as in the steady case. The2D program IIFM2DT and3D program IIFM3DT are developed independently.(3) Composite Grid Method is applied in unconfined steady seepage analysis. Two sets of grid are used in numerical simulation, with the coarse grid of larger size simulating the entire region without consideration of "line-style structure" while the fine grid of relatively small size simulating the "line-style structure". Solution in coarse grid is adjusted by the one from fine grid through discharge correction and iterations are carried out between the two sets of grids and until desired convergence precision is achieved. The Composite Grid Method can be adapted to non-regular grid. In other words, the coaser grid and fine grid can be generated independently without any restriction from each other. A three-dimensional unconfined steady seepage analysis program named IIFM3DS-CGM is developed accordingly. Finally, numerical examples and practical application in engineering are taken advantage to verify the validity and reliability of these theory and programs. The results show that the theory is reasonable and the programs are reliable.