橫向等向性半無限空間內之應力與位移

Abstract

傳統上，一般基礎材料受工程結構物所引致的位移、應力量之推估，大多假設此介質為均質、均向、線彈性之連體；然而，對於許多天然大地材料而言，由於受到生成過程或是生成過程後變形作用之影響，其力學性質如強度、變形性等…，均受方向性所控制而展現出異向性質，例如黏土之沈積作用與其隨後所發生的壓密特性，以及岩體受不連續性切割等…。因此，對於此類材料受外力作用後之位移、應力分佈的估計，宜考慮因異向性質所造成的影響。在工程實務上，異向性土壤╱岩石若以其明顯之地質構造或彈性對稱方向為座標軸，一般可分為正交性或橫向等向性材料。本論文係針對橫向等向性半無限空間之彈性載重問題來加以解析與探討，主要工作項目包括：（一）重新推導點荷重之位移與應力基本解；（二）推導埋置於地表下之非對稱形荷重（有限線載重、均佈與線性分佈矩形載重、均佈與線性分佈三角形載重）的位移與應力解；（三）擴充三角形荷重解，用以計算質內受不規則形荷重所引致的位移與應力；（四）製作影響圖，用以計算介質內承受不規則形地表荷重所產生的應力、內部位移及地表位移。本論文所推導出的解析解，與少數僅存的現有異向性解符合，且將解化簡成均向性的情形，亦與許多均向性解相符；由一系列的參數研究顯示，所得的位移與應力分佈深受不同荷重模式、介質種類與異向性程度之影響，且其與以傳統均向性理論所做的評估有相當大的差異；至於在估算橫向等向性半無限空間內受不規則形荷童作用下的位移與應力值方面，本文所提出的解析解法與圖解法，其計算結果於精度上均可達至工程實務的要求，且能夠有效率地成為數值方法外的多重選擇。

Conventionally, the linear elastic and isotropic theory has been extensively used for the calculation of displacements and stresses in a loaded soil or rock. However, many soils and rocks exhibit some degrees of anisotropy in their response to deformations and stresses. Anisotropic soils/rocks are often modeled as orthotropic or transversely isotropic materials. In this dissertation, several closed-form solutions and influence charts were presented for calculating the induced displacements and stresses in a horizontal transversely isotropic half-space subjected to applied loads. The major work includes (1) rederiving the displacement and stress solutions induced by a point load; (2) solving the displacements and stresses due to various buried asymmteric loads (finite line loads, uniform/linearly varying rectangular loads, and uniform/linearly varying triangular loads); (3) extending the triangular loading solutions to calculate the displacements and stresses subjected to an arbitrarily-shaped load; (4) constructing influence charts for computing the stresses and displacements induced by an arbitrarily-shaped load. A series ofparametric studies were conducted to verif/the derived closed-fonnsolutions, and investigate the effect of the loading types, and the type and degree of material anisotropy on the displacements and stresses. The results indicate that (1) the displacement and stress in a transversely isotropic half-space can be correctly calculated by these presented solutions; (2) the displacement and stress accounted for anisotropy are quite different from those by isotropic solutions. Computing the stress and displacement in a transversely isotropic half-space subjected to uniform/non-uniform loads on an irregular shape, a triangulating technique and a graphical method provide results with reasonable accuracy. The two methods are practical and can be the alternatives of numerical methods.