Abstract
A FEM for unsaturated transient seepage is established by using a quadrilateral isoparametric element, considering the fact that the main permeability does not coincide with the axis situation. It creates a function by using the element’s node hydraulic head and shape function instead of the real head in the Richard seepage control equation. With the help of the Galerkin weighted residual method, a FEM equation is given for analyzing 2-dimensional transient seepage problem. Further, based on the Jacobi matrix and Gauss numerical integral, it determines the elements of stiffness and capacitance matrices. This FEM equation considers not only the anisotropic of soil but also the uncoincidence between permeability and the axis. It is a common form of transient seepage. In the end, two examples illustrate the node accuracy of the quadrilateral element and the correctness of this FEM equation.
Highlights
Transient seepage of unsaturated soils is a hot issue of research currently [1,2,3], For instance, dam seepage [4, 5], subgrade moisture field, the steadiness of rainfall side slope [6], and other unsaturated seepage problems can be considered according to two-dimensional seepage problems. e finite element method (FEM) is a highly valued analysis method
Due to the anisotropy and heterogeneity of soils, the phenomenon of the main seepage coefficient not coinciding with the coordinate axis often appears
Two examples are given: one is to illustrate the difference between triangular element and quadrilateral element and the other one gives a calculation of certain dam seepage to clarify the accuracy of the proposed method in seepage flow
Summary
Transient seepage of unsaturated soils is a hot issue of research currently [1,2,3], For instance, dam seepage [4, 5], subgrade moisture field, the steadiness of rainfall side slope [6], and other unsaturated seepage problems can be considered according to two-dimensional seepage problems. e finite element method (FEM) is a highly valued analysis method. This paper attempts to consider the phenomenon of the anisotropy of soils and main seepage coefficient not coinciding with the coordinate axis and adopt one-dimensional quadrilateral isoparametric element to research on establishing the calculating method of the finite element for transient seepage of unsaturated soils. On this basis, by using the Galerkin weighted residual method, this paper establishes a transient seepage finite element calculation method of unsaturated soils. Two examples are given: one is to illustrate the difference between triangular element and quadrilateral element and the other one gives a calculation of certain dam seepage to clarify the accuracy of the proposed method in seepage flow
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