不同地表形態下橫向等向性岩石基礎承載力解析解

Abstract

傳統上，在分析計算岩石淺基礎之承載力時，常視岩石為均質、均向性、 彈、塑、脆性材料。實際上，甚多岩石由於受到生成過程或後來變形作用 之影響，大都呈現異向性，如板岩、頁岩、片岩等，致使現存考慮岩石為 均向性材料之基礎承載力分析方法無法適用。本文研究的對象為具異向性 強度之橫向等向性岩石，利用滑動線法( Slip Line Method)及修正後適 用於具有單一組平行弱面之Hoek-Brown強度破壞準則，提出可適用於具橫 向等向性軟弱岩石之淺基礎承載力理論解析解。本文之理論解析解因係採 用平面應變條件下之塑性理論推導而得，故僅適用於具理想剛塑性性質之 橫向等向性岩石，且岩層走向與分析平面垂直；惟對具有理想剛塑性性質 之橫向等向性土壤同樣亦可適用。本解析解可求出具不同層面傾角、坡面 角及坡頂上不同退縮(Setback)距離之各種不同地表形態下之岩石淺基礎 承載力及破壞滑動線。經一系列數例分析得知，在不同地表形態下，由於 弱面存在及邊坡坡度之影響，致使岩石基礎承載力會隨弱面傾角方向及坡 度大小而變化。由本文中例子可知，當基礎係座落在水平地表面上時，承 載力最大值出現於層面傾角為90°時，而層面傾角為45°時，承載力有最 小值，承載力最大值與最小值相差約有2∼3倍。若基礎係座落在坡頂平地 上時，則承載力受岩石層面傾角、坡面角、基礎與坡面退縮(Setback)距 離等因素影響。此外，Hoek-Brown破壞準則中當參數s<0.001時，參數s對 承載力影響並不顯著，另以Hoek-Brown破壞準則及Mohr-Coulomb破壞準則 為屈伏函數所計算得基礎承載力相當接近，其平均誤差約在百分之十至五 十左右。 When attempting to predict the bearing capacity of foundation rocks, it is usually to assume the rocks are ideally homogeneous, isotropic, elasto-plastic and brittle geomaterials. In fact, anisotropy is common in many rocks because of preferred orientations of mineral grains or directional stress history, such as slates, shales, schists, etc.. Therefore, isotropic solutions for the bearing capacity in foundation rocks cannot be used for rocks that exhisit strength anisotropy. A few analytical solutions for the bearing capacity of anisotropic foundation rocks were proposed. These solutions are limited to rock masses with strength anisotropy because of one set of weak planes and placed on level ground. For the bearing capacity of anisotropic foundation rocks located on sloping ground or at the crest of a slope, analytical solutions were not considered for rocks with strength anisotripy in the literature. The thesis describes a new analytical solution using slip line method for bearing capacity and slip line in foundation rocks with strength anisotropy on level ground and at the crest of a slope. In the solutions, the foundation rocks are transversely isotropy, modelled as rigid-plastic materials and satisfied associated flow rule and modified Hoek-Brown failure criterion. The analytical solution is not only applied to transversely isotropic rocks, but also transversely isotropic soils. Numerical examples are conducted to investigate the effect of the dip direction and angle of strata, the slope angle, and the location of foundation placed at the crest of a slope on the bearing capacity of the rocks with strength anisotropy.