中文摘要 本研究使用「元素釋放法」(element-free method, EFM)來處理地下水滲流的問題，並推導出三維滲流之控制方程式來進行數值分析，在其基本原理上合乎元素釋放法之理論，而程式架構上則建造為三維。在邊界處理的部分，則施加Lagrangian乘子法於二維之邊界網格，來建立整體的控制方程式(governing equation)之擴增矩陣。 由於元素釋放法的基本理論，是建立於「移動式最小平方」(moving least-squares, MLS)內差的觀念，處理定義域內節點資料之一種無網格(meshless)的數值分析方法，只需考慮各離散節點的資料，故消除了節點與元素間之關係限制。因此，可節省大量人為前置作業的時間。但由於MLS並不滿足Kronecker delta criterion的性質，故於邊界的部分，引用前人建議精確度較高的Lagrangian乘子法作以邊界條件之施加。本文以程式自動建構出三維的矩形積分網格體，而基於滲流問題只考慮總水頭Ht一個方向之自由度，故在邊界上則是以建立矩形二維網格的方式施加，所形成之擴增矩陣只有一個自由度(degree of freedom)但含有四個節點分量。 對於加入非滲透性結構物後，使得節點影響範圍因而改變，而於三維中其影響範圍將形成一影響球。判斷之方式為採用前人所研究之「通視原則」，以進行節點搜尋範圍的修正。而對於積分網格體被幾何邊界跨越之情形，則利用權重影響之體積分配來做修正。本文以侷限流(confined flow)之問題做參數研究，驗證三維程式之正確性。並於後加入非透水地下結構物，繪出等勢能線及流線並分析其合理性。 ABSTRACT In this paper, applications of element free method (EFM)on the simulation of 3D seepage problems are presented. The 3D integral meshes are builded automatically and the governing equation of seepage in 3D satisfied. To deal with the essential boundary conditions, the extantion matrix employed by Lagragian multipliers method is set to be the instrument. The theory of EFM is based on the moving least-square (MLS) interpolation technique used in construct the shape functions. Based on the concept of MLS, the connection between elements and nodes is eliminated. However, for the MLS does not satisfy the property of Kronecker delta criterion, Lagragian multipliers method is used to deal with the boundary conditions. In this paper, only one degree-of-freedom(the total head Ht) exists for solving the seepage problems. For the 2D boundary, four nodes are distributed in each boundary integral mesh. The influent zone of a node is changed due to an existing impervious structure. The 3D influence zone in 3-D is a sphere. The so-called “optical see-through” method is used to adjust the influence zone. Only 2D analysis is done to show the accuracy of the newly developed 3D EFM code and both the streamlines and equipotential lines are computed to form a flow net.
