本研究的目的為將特殊九節點四邊形元素應用在離散未開裂邊界以及異向性岩石性質的矩形體與圓柱體試體中的雙/單裂縫，使用FORTRAN語言撰寫程式，利用三維單域邊界元素法(或稱對偶邊界元素法)探討三維情況下異向性岩石的混合模態應力強度因子。

在本文中，對於異向性岩石性質的矩形體雙裂縫、圓柱體單裂縫試體，模擬在受到垂直張力加載情況下，分別提出三種不同的案例情況加以探討分析。首先，在矩形體雙裂縫案例中，可看到當裂縫垂直距離越來越靠近時，應力強度因子的數值趨勢會越來越小。再來是圓柱體內部矩形裂縫案例，可以發現到當裂縫旋轉角度增加時，沿著裂縫前緣的模態I型正規化應力強度因子數值會有減少的下降趨勢。最後，在圓柱體邊緣裂縫案例中，可發現到當裂縫開裂越深時，模態I型的應力強度因子會有增加的上升趨勢。此外，當裂縫旋轉至45度時，相對於其他角度，模態I-II-III的應力強度因子會有較大程度的變化情況。

本研究之主要特色與貢獻，為與以往研究單一裂縫情況相比，探討了解多裂縫在異向性岩石性質下的情況，以及將其應用於圓柱形試體的模擬建立。

The purpose of this study is to present the nine-node quadrilateral elements to discretize the un-cracked boundary and the dual/single -crack in an anisotropic cuboid/cylinder rocks. The FORTRAN program developed is to determine the three-dimensional(3D) mixed–mode stress intensity factors(SIFs) by using 3D single-domain boundary element method(BEM) or dual-BEM.

Three cases are presented for dual-cracked cuboid or single-cracked cylinder which are transversely isotropic under a uniform vertical traction. The first cases of the dual-cracked cuboid show that the SIF values are smaller when the vertical distance of two cracks becomes closer. The second cases of a rectangular crack within the cylinder observe that the variation of the normalized mode-I SIF along the crack front decreases with increasing crack orientation angles. In the final cases, a edge crack within the cylinder show that the variation of the normalized mode-I SIF increases with increasing crack depth. Furthermore, the magnitude of the maximum in mode I-II-III SIF when the crack orientation equal to 45 degree is larger than otherwise angles.

The first characteristic of this thesis knows the dual-crack of the anisotropic rocks with compared previous research of the single-crack. The second characteristic is applied to construction of cylindrical specimens.

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