地下洞室断面形状对动应力峰值大小影响的统计分析

Statistical Analysis of the Effect of Underground Cavity Cross-section Shape on Dynamic Stress Peaks

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-analytical solution of dynamic stress of arbitrary cross-section underground cav- ity in half-space for incident plane SH waves is presented using wave functions expansion method combined with boundary discrete method, and the numerical precision is validated in detail. Monte Carlo method is used to randomly generate 30 samples of variation coefficient 0.05 for cross-section shape of the cavity, and the effect of cross-section shape on the dynamic stress peak （DSP） is studied by statistical analysis. It is shown that, cross-section shape has significant effect on the DSP around cavities in half-space. The maxima of the DSPs are much larger than those of its relevant peaks of the analytical solutions of the circular cavity, with the maximal value being increased by 60%, and the averaged value being increased by 24% the variation coefficient of the DSP may be up to 3.5 times greater than the variation coefficient of the cavity radius.