有限解析法於飽和坡地穩態破壞潛能計算之應用

Abstract

本研究根據多孔彈性介質理論(poro-elastic media theory)以及摩爾-庫倫(Mohr-Coulomb)破壞準則，利用有限解析法(finite analytic method)配合對角線卡氏座標(diagonal Cartesian coordinates)系統，模擬飽和坡地之穩態破壞潛能。有限解析法乃是利用局部解析解(local analytic solution)建構離散方程式(discritization equations)，較有限差分法(finite difference method)準確。此外，有限解析法更可以在卡氏座標下，簡單地處理不規則模擬邊界之計算問題，較有限元素法(finite element method)容易建構。但傳統有限解析法並無法於此直接應用，本研究提出變數轉換及內插技巧，將其擴展至更通用之形式。首先藉由具有解析解之案例，驗證程式正確性，再探討不同坡面形狀、波松比、孔隙率以及非均質土層分布對坡地破壞潛能之影響。

In this study, based on poro-elastic media theory and Mohr-Coulomb failure criteria, the steady failure potential of saturated hillslope is modeling by using finite analytic method integrated with diagonal Cartesian coordinates system. Due to the use of the local analytic solution for discritization, the analytic method is more accurate than the finite difference method. In addition, with Cartesian coordinates system the analytic method could easily tackle the simulation problems with irregular boundaries, so that the framework of the finite analytic method is simpler than that of the finite element method. However, the convectional finite analytic method can not be directly used herein. A variable transformation and interpolation technique is proposed in this study to extend the conventional finite analytic method to the more general form. The influences of different shapes of hillslope, porosity, possion’s ratio, and the homogeneity of soil on steady failure potential of saturated hillslope are examined after the developed numerical program is verified by the exact solutions.