| Summary: | 碩士 === 國立臺灣海洋大學 === 河海工程學系 === 107 === Landslide is a great natural disaster that is life-threatening and causes property loss. The existence and change of groundwater level is the main cause of slope instability. Therefore, analyzing the seepage mechanism of groundwater and calculating the stability of slopes have important practical significance for ensuring production and construction and people's property safety.In this paper, the Trefftz method wich is a kind of meshless method is used to solve the groundwater seepage problem. The T-complete basis function
of the free surface is derived under the condition of after-teeming and evaporation. The Combination of the Trefftz basis function for saturated and unsaturated soil are adopted to solve the seepage mechanism and slope stability of groundwater. This findings and conclusion remarks are listed as follows.
(1)The governing equation of the free surface is the Dupuit-Boussinesq equation. The proposed method is to derive the general solutions using the method of separation of variables in the case of recharge and evaporation. The Dirichlet and Neumann boundary conditions for steady-state and transient free surface problems are considered. Furthermore, we adopt the characteristic length to reduce the ill-conditioned system.
(2)Several numerical examples including different boundary conditions in steady-state and transient free surface problems are carried out to verify the proposed method .The free surface with homogenous soil under different boundary conditions is then compared with the analytical solution. The results show that the maximum absolute error can reach the order of 10-10. It is found that the proposed method may provide promising numerical results for seepage problems with the free surface.
(3)Groundwater from unsaturated soil layer through the free surface into the in the process of the stability of saturated soil seepage its flow rate constant.The free surface of the continuous seepage condition is solved by The T-complete basis function of the free surface, and the soil layer is divided into the saturated soil layer and the unsaturated soil layer by the free liquid surface. This method reduces the difficulty of solving the continuous seepage problem. Research results showed that the groundwater is charging, the hydraulic gradient decreases from the high potential energy to the low side, and the pore water pressure of the unsaturated soil increases from the top to the bottom in the unsaturated soil layer; when the groundwater evaporates, the result is opposite to that of the charging.
(4)According to the water exchange between the groundwater and the atmosphere in the free aquifer and the boundary conditions, the free liquid surface in the three-dimensional space was calculated by using The T-complete basis function of the free surface.Useing the The T-complete basis function of the three-dimensional Laplacian calculate the steady-state seepage flow of the saturated soil layer in the three-dimensional free aquifer under the conditions of recharge and evaporation and the free surface are used as the top boundary. The research results show that the surrounding is Dirichlet boundary conditions. In the case of charging, the free liquid surface has a convex phenomenon, and the water flow gradually changes from vertical to horizontal flow from the center to the periphery. Under evaporation conditions, the results are the opposite of when charged.
(5)The Trefftz space-time collocation method is used to solve the transient state seepage problem under the changing water level and rainfall infiltration condition. The calculated transient state seepage uses STABL software to analyze the real-time stability of the slope. The research results show that under the condition of rainfall infiltration, the greater the hydraulic gradient in the slope is, the more unstable it is.
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