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针对实际工程中遇到的斜坡边界下圆形孔扩张问题,提出了相应的计算方法。在考虑坡体自重应力的情况下,通过坐标变换将其转为水平边界半无限体中圆孔扩张,采用复变函数共形映射的方法得到应力解析。当圆形孔埋置较深时,将问题简化为无限体中圆孔的扩张,通过弹性力学的基本叠加得到最终应力解答。以一斜坡边界下圆形孔洞扩张为例,求解了圆孔周围径向正应力σr、环向正应力σφ与切应力τrφ的分布。计算结果表明:斜坡倾角对坡体中应力分布影响显著,某点应力随距圆心距离的增大而减小,超过约4倍圆孔半径远处逐渐趋于稳定,其值接近于初始地应力场。当圆孔为深埋的情况时,与简化为无限平面的情况进行了对比,两种方法计算结果接近,距圆心2.5R远处岩体径向正应力σr和环向正应力σφ均为负值,而切应力τrφ正负值间隔分布,各应力极值分布与斜坡倾向呈一定的相关性。
In order to solve the problem of circular hole expansion under the slope boundary encountered in practical engineering, a corresponding calculation method is proposed. Considering the self-weight stress of the slope, the hole is transformed into a semi-infinite horizontal hole by coordinate transformation, and the stress analysis is obtained by conformal mapping of complex functions. When the circular hole is buried deeply, the problem is simplified as the expansion of the circular hole in the infinite body, and the final stress solution is obtained through the basic superposition of elasticity. Taking the expansion of a circular hole under a slope boundary as an example, the distribution of radial normal stress σr, circumferential normal stress σφ and shear stress τrφ is solved. The calculated results show that the slope inclination has a significant influence on the stress distribution in the slope, and the stress at one point decreases with the increase of the distance from the center of the slope. When the radius of the circular hole is more than about 4 times, the stress tends to be stable at a distance close to the initial ground stress field. When the circular hole is deep buried, compared with the simplified case of infinite plane, the results of the two methods are close to each other, and the radial normal stress σr and annular normal stress σφ of the rock mass at the distance of 2.5R from the center are all negative Value, and shear stress τrφ positive and negative interval distribution, the stress distribution and slope inclination of a certain correlation.