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采用波函数展开法及边界离散的方法给出了任意断面形状地下洞室在平面SH波入射下动应力的一个半解析解,并对该方法的精度进行了详细的验证。利用蒙特卡罗方法随机模拟产生了30组半径变异系数为0.05的洞室断面样本,通过对该30组断面地下洞室在平面SH波入射下洞室动应力峰值的统计分析,研究了洞室断面形状对动应力峰值大小的影响。结果表明,洞室断面形状对动应力的峰值大小有显著影响,样本峰值的最大值均显著大于相应圆形洞室的解析解的峰值,样本峰值的最大值比圆形洞室解析解峰值增大60%,样本峰值的最大值的平均增大程度也可达24%;样本动应力峰值的变异系数可达洞室半径变异系数的3.5倍。
A semi-analytic solution of dynamic stress of an underground caverns with arbitrary cross-section under incidence of plane SH waves is given by using the method of wave function expansion and boundary discretization. The accuracy of this method is verified in detail. Thirty groups of cavern samples with variation coefficient of radius of 0.05 were generated by Monte-Carlo method. Through statistical analysis of the dynamic stress peaks of the cavern in the 30 groups of cavern under the incidence of plane SH wave, Effect of section shape on the peak value of dynamic stress. The results show that the cross-sectional shape of the tunnel has a significant effect on the peak value of dynamic stress. The maximum of the peak value of the sample is significantly larger than that of the corresponding circular cavity. The maximum value of the sample peak is larger than the peak value of the analytical solution of the circular cavity 60% larger, the average peak value of the sample increases by an average of 24%. The coefficient of variation of dynamic stress peak value in sample can reach 3.5 times of the coefficient of variation of tunnel radius.