彈性常數隨深度呈指數變化之橫向等向性半無限空間承受點荷重後之位移與應力

Abstract

本文係根據異向性彈性力學理論，解析出有關承受點荷重後，無限與半無限空間之非均質且橫向等向性岩體之位移與應力解；所分析的橫向等向性岩體之彈性對稱面與水平受力面平行，而五個彈性常數（E、 、 、n、 ）中的水平楊氏係數（E）、垂直楊氏係數（ ）及垂直剪力模數（ ）係假設隨著覆土（岩）深度之增加而呈指數函數增加；其所推導出的解透過數值積分運算，可與水平之均質橫向等向性岩體之特例相互比較，以檢視其異質性與異向性的程度造成橫向等向性岩體內位移與應力分佈之影響。

Based on the theory of anisotropic elasticity, the solutions of displacements and stresses in nonhomogrneous and transversely isotropic full/half spaces subjected to a point load are presented in this thesis. The plane of transversely isotropy is assumed to be parallel to the horizontal loading surface. Three elastic constants 、 、 in the form of exponential increase with the increase of depth. The derved solutions can be simplified to campare with those existed solutions of homogeneous and transversely isotropic full/half spaces. Besides, a series of parametric study was conducted to investigate the degree of nonhomogeneity on the distributions of displacements and stresses induced by the applied point load in the isotropic/transversely isotropic full/half spaces.