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以管状双椭圆高水压洞室围岩应力为研究对象,将该问题简化为混合边界的双椭圆孔平面应力计算模型。基于平面弹性复变理论,通过保角映射、Cauchy积分及留数定理等方法,求解了具有单椭圆内压孔的两个平面应力复势函数;采用Schwarz交替算法,推导了具有双椭圆内压孔无限平面内任一点的应力分量表达式。据所得表达式,编制了Matlab计算程序,研究了无限平面含双洞室或双椭圆洞室的4个算例,分析了内压及两孔相对位置对围岩应力的影响。研究结果表明:两洞室均无内压时,水平对称双椭圆洞室的左孔口0°(或右孔口180°)处有最大切向应力;各孔口的最大或最小切向应力均随内压的增大而减小;当两孔中仅一孔含内压时,两孔孔口应力随内压的增大而或增或减,具体视孔壁位置而定。
Taking the stress of surrounding rock of tubular double oval high hydraulic caverns as the research object, this problem is reduced to the calculation model of double elliptical hole plane stress of mixed boundary. Based on the plane elasticity theory, two planar stress complex functions with single ellipse internal pressure hole are solved by means of conformal mapping, Cauchy integral and residual theorem. The Schwarz alternating algorithm is used to derive the double elliptic internal pressure Stress component expression at any point in infinite hole of hole. According to the obtained expression, Matlab program was developed, and four examples of infinite-plane double-cavity or double-elliptic cavity were studied. The influence of internal pressure and relative position of two holes on surrounding rock stress was analyzed. The results show that there is maximum tangential stress at the left orifice 0 ° (or right orifice 180 °) of the horizontally symmetric double oval cavity when there is no internal pressure in both chambers and the maximum or minimum tangential stress Both decrease with the increase of internal pressure. When only one hole of two holes contains internal pressure, the stress of the two holes increases or decreases with the increase of internal pressure, depending on the position of the hole wall.