边坡下伏地下圆形洞室的弹性应力解析

根据洞室与边坡的相对位置,将其分为深埋地下洞室与浅埋地下洞室,并分别建立了计算模型。将浅埋圆形洞室视为分布荷载作用下半无限体表面附近的孔洞的应力分析问题,采取复变函数的保角映射得到了浅埋洞室的应力解析解。将深埋洞室视为一个双向受压无限板孔应力集中问题,得到了边坡下伏深埋圆形洞室的应力解析解。以某填筑边坡下地下圆形洞室为例,计算得到了浅埋圆形洞室周边的径向应力与环向应力分布,计算结果表明洞室圆心水平线上的环向压应力随着与洞周距离的增加逐渐减小,但径向压应力却是首先增加,然后才逐步减小。洞顶圆周出现环向拉应力,随着越来越接近地表,环向应力逐步转变为压应力并且越来越大,而径向应力逐渐变大。洞周环向拉应力在洞顶与洞底数值最大,洞室左右两端洞周环向压应力数值最大;洞周径向应力在洞顶、洞底数值较小,左右两端洞周应力最大。

Elastic stress analytic solution of the round and underground cavern under slope

The underground rock caverns were divided into deep-buried and shallow-buried cavern according to the spatial location of slope and cavern.The calculation models of caverns were built.The shallow-buried cavern’s stress analytic solution was derived by elasticity theory and complex function method and the deep-buried cavern was regarded as a stress concentration problem of biaxial compression infinite plate pole and the analytic solution of stress was gotten.Taken a round cavern under earth bank for example,the distributions of radial and hoop stress are obtained from calculation.The calculation results show that the circumferential compression stress of the horizontal line through circle centre decreases,but the radial compression stress firstly increases and then decreases with the increase of distance to the hole’s periphery.The circumferential tensile stress appears on the roof and the tensile stress transfers into compression stress and becomes bigger from roof to earth surface.The circumferential tensile stress is the biggest on the roof and bottom of cavern.The circumferential compression stress is the biggest on the side of cavern.The radial compression stress is smaller on the roof and bottom of cavern and it is biggest on the side of cavern.