大地工程問題的數值分析法的有很多種，主要分為將岩石視為連續體的數值計算方法如:有限元素法(Finite Element Method, FEM)；把岩石視為非連續體的數值分析計算方法如:非連續變形分析法(Discontinuous Deformation Analysis, DDA)。本論文研究之數值流形法(Manifold Method, MM)乃是結合有限元素法的位移函數與非連續體變形分析法的接觸理論，在分析過程中可以同時處理塊體內連續部分與塊體間的接觸情形。
本研究主要探討節理岩體基礎的承載特性與邊坡受到振動時之行為。分析節理岩體基礎承載時，顯示流形法元素密度越密模擬結果越佳，且在深層的應力模擬結果與解析解一致。另一方面，在振動邊坡的討論時則建立數值流形法模擬振動問題的方法，即設定塊體內各元素節點為束制點然後將依時性位移施加於節點上，藉由水平振動問題與斜面振動問題的解析解與流形法數值解之比較，確定數值流形法能模擬震動邊坡的問題。

There are many numerical analysis methods applied to geotechnical engineering problems. They can be classified as following categories. One takes the rock mass to be a continuous material, such as Finite Element Method (FEM). The other one takes the rock mass to be a discontinuous material, such as Discontinuous Deformation Analysis (DDA). Manifold method (MM), investigated in this study, consists of the displacement function of finite element method and the contact theory of Discontinuous Deformation Analysis. MM can describe the behaviors of the continuous blocks as wall as the contact between blocks during simulation.
The major objective of this study is to investigate the stress distribution of the jointed rock mass loaded by a foundation and the behavior of a seismic slope. In the loaded foundation on a jointed rock mass, we conclude that the high density of element has better answers than low density. In addition, the numerical solution in the depth agrees with the analytical solution. On the other hand, we developed an algorithm for MM to simulate the behavior of seismic slope. The algorithm is that takes the nodes of all elements of the block to be constrained point then inputs time-dependent displacements on the nodes. Compare the analytical solutions to numerical ones of horizontal and inclined plane seismic problems, we validate the correctness of using new seismic MM on seismic slope analysis.

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