轴对称平衡分布载荷作用下弹性半空间体力学分析

SURFACE AND INNER OF A HALF-SPACE BODY SUBJECTED TO AXIAL SYMMETERICAL DISTRIBUTION LOAD

根据实际工程项目和现场岩体力学试验的需要 ,研究了弹性半空间体承受轴对称平衡分布载荷的问题。利用弹性力学的基本理论和位移解法 ,借助位移矢量的 Stokes分解 ,首次得到了弹性半空间体承受轴对称平衡分布载荷的位移解和应力解。结果表明 ,半空间边界应力对应竖直向下的轴对称分布载荷 ,并且展布在整个边界上 ,边界剪应力不等于零 ,但满足积分意义上为零的条件。该结果可以直接用于土木工程、水电工程等领域的岩体力学分析 。

This paper studies the surface and inner of an elastic half space body subjected to axial symmetrical distribution load in order to meet the demand of an actual project and experiment of the rock strength on the spot. By means of the linear theory of elasticity, Lamé equations and Stokes decomposition of displacement vector, the formulae of the displacement and stress field of an elastic half space body under the action of axial symmetrical and balanced distribution load are derived for the first time. The result shows that the half space boundary stress is in correspondence with the vertically downward axial symmetrical distribution load and is applied on the entire boundary. And shearing stress does not be equal to zero on boundary; fortunately it satisfies the condition of zero in integral meaning. The result of this paper can be directly used in stress analysis of rock mass in civil engineering and the fields such as the project of hydroelectricity. At the same time, it can offer new analyzing and testing means for getting mechanical parameters of rock mass on the spot.