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Title: Numerical simulation of unsaturated flow using modified transformation methods
Keywords: Unsaturated soils, seepage, finite element method, under-relaxation, transformation, temporal adaptive scheme
Issue Date: 20-Sep-2008
Citation: CHENG YONGGANG (2008-09-20). Numerical simulation of unsaturated flow using modified transformation methods. ScholarBank@NUS Repository.
Abstract: The finite element method provides an effective means for solving problems of seepage in unsaturated soils. However, convergence difficulties exist in such numerical simulations because of the high nonlinearity of the soil hydraulic properties. This thesis presents a combination approach TUR1 consisting of a rational function transformation and a common under-relaxation technique to solve the h-based form of Richards equation. Numerical studies show that TUR1 can use larger time step and mesh size to produce acceptable results and also converge to a stable solution quickly in each time step.Automatic time stepping scheme with embedded error control has recently been developed. The combination of proposed TUR1 approach and such adaptive scheme (ATUR1) is shown to be a more practical method, as it provides the most efficient solution at minimal computational cost, and temporal errors are constrained proportionally to user prescribed tolerances.Several multi-dimensional examples with both homogeneous and heterogeneous materials are analyzed to show the robustness and efficiency of the proposed TUR1 and ATUR1 methods. It is shown that these improved approaches are efficient in complex problems with both very dry and variably saturated conditions.The proposed methods are then applied to solve the rainfall-induced slope failure problem. It is showed that these methods can predict the wetting front accurately with coarse mesh and hence more accurate computation of the slope safety factor can be obtained.
Appears in Collections:Ph.D Theses (Open)

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