用弹性力学的复变函数法求解矩形硐室周边应力  

Solution for Perimeter Stresses of Rocks Around a Rectangular Chamber Using the Complex Function of Elastic Mechanics

作　　者：赵凯[1] 刘长武[1] 张国良[1] 

机构地区：[1]四川大学水利水电学院,四川成都610065

出　　处：《采矿与安全工程学报》2007年第3期361-365,共5页Journal of Mining & Safety Engineering

基　　金：国家自然科学基金资助项目(50574064;50074029)

摘　　要：针对目前地下硐室围岩应力分布的解析解仅仅限于圆形和椭圆形等简单形状的情况,本文采用复变函数法计算矩形硐室的周边应力.采用保角变换法将Z平面上的硐室几何边界映射到ζ平面上的单位中心圆上,用多角形法求解矩形硐室的映射函数,定义了一个仅仅和硐室高宽比有关的系数,通过对硐室高宽比和这个系数的试算,可以得到映射函数的逼近解,得到了复变理论求解矩形硐室周边应力的基本公式.在给定硐室的高度和宽度的情况下,可获得硐室周边应力分布。通过算例表明,此法求解矩形、方形硐室周边应力是可行的,实用性强.The analytical solutions for stress distribution of rocks around underground chambers are simply circular and oval in shape. Aiming at this problem, the complex function was used to calculate the surrounding stress of the rectangular chambers. The coefficient only related to the height-width ratio of the chamber was defined by using the conformal transformation to map the geometric boundaries of the chamber on Z-plane to the central circle on ξ plane and by using the polygonal method to find the mapping function of the rectangular chamber. Through the trial calculation of the height-width ratio, the approximation solution of the mapping function may be obtained. Thus, the basic formula based on complex function for solving the perimeter stress of a rectangular chamber was obtained, making it possible for us to calculate the perimeter stress of a rectangular chamber when only the height and width are given. The case study shows that this method is feasible for calculating perimeter stresses of rock masses around a rectangular underground chamber.

关 键 词：矩形硐室 保角变换 映射函数 复变理论 围岩应力 

分 类 号：TD322[矿业工程—矿井建设]