地下透镜体断面形状随机性对地表动力响应极值的影响

Effect of Randomness in the Cross-section Shape of Underground Lenticles on the Extreme of the Surface Dynamic Response

摘要:

采用波函数展开法及边界离散的方法给出任意断面形状的地下透镜体对平面SH波散射的半解析解,利用蒙特卡罗方法随机模拟产生30组透镜体断面样本,通过对30组具有同一统计特征的任意断面地下透镜体在平面SH波入射下地表动力响应极值的统计分析并与相应椭圆透镜体解答比较,研究透镜体断面形状随机性对平面SH波散射的影响。研究表明,透镜体断面形状随机性对地表动力响应极值具有重要影响。以长短轴比为4的椭圆形透镜体为例,当断面矢径的变异系数为0.1时,样本地表位移响应极值的最大值远大于对应椭圆透镜体解的极值,平均可达47.46%。且增加幅度随着透镜体介质与半空间介质波速差距增大而增大。透镜体埋深越小,增加幅度越大。

Abstract:

The semi-analytical solution of SH-waves scattering by an arbitrary cross-section of an underground lenticle in half space is presented using the wave functions expansion method combined with the boundary discrete method. The Monte Carlo method was used to randomly generate 30 samples of the cross-section shape of the lenticle, and the effect of randomness in the cross-section shape on the surface dynamic response was studied by statistical analysis. It was observed that the randomness of the cross-section shape has a significant effect on the surface dynamic response around a lenticle in half space. When the variation coefficient of the inclusion radius is equal to 0.1 for a lenticle of elliptical shape, the maximum of the surface displacement amplitude is larger than that of the peak values observed for the elliptic solution with an average of 47.46%. The difference increases as the inclusion rigidity decreases, whereas the difference decreases as the inclusion depth increases.