任意多个沉积谷地对平面SV波的散射

Scattering of arbitrary alluvial valleys to incident plane SV waves

采用间接边界元法研究了入射平面SV波在层状半空间中多个沉积谷地周围的散射问题。该方法将整体模型分解为各个沉积闭合域和开口的层状半空间域。通过在各沉积闭合边界上施加虚拟均布荷载模拟各闭合域内散射波场,通过在层状半空间开口域所有开口边界上施加虚拟荷载模拟开口域内散射波场,通过引入各沉积与层状半空间的连续条件确定所有施加虚拟荷载的密度。验证了该方法的正确性,并对均匀半空间中不同间距和不同数量的半圆沉积为例进行了数值计算分析,数值结果表明,多个沉积与单一沉积对应的位移幅值及其放大谱均显不同,沉积间的动力相互作用,使得多个沉积情况对应位移幅值显著大于单一沉积情况。沉积间距的改变导致了沉积间动力相互作用机制的改变,进而改变了放大谱的峰值及峰值周期。沉积个数影响主要体现在增强或减弱沉积间的动力相互作用上,而对相互作用机制影响较小,因而不同沉积个数对应的放大谱峰值差异明显而峰值周期较为接近。

Wave scattering of arbitrary alluvial valleys in a layered half-space to incident plane SV waves was studied using the indirection boundary element method(IBEM).The model was divided into multiple independent closed regions and an open layered half-space region.Scattering wave fields of closed regions were simulated with fictitious distributed loads acting on closed boundaries,and scattering wave field of the open layered half-space region was simulated with fictitious distributed loads acting on open boundaries.Then,the densities of distributed loads were determined according to the continuity boundary conditions.The validity of the proposed method was verified by comparing the results using this method with those using the published method.Numerical analyses were performed for semi-cylindrical valleys with different separation distances and different numbers in an uniformly half-space.The numerical results showed that both surface displacement and amplification spectrum of the observed points are influenced by the above two factors,also frequency and angle of incident SV waves and observation points;the distance between valleys and the number of valleys have a larger influence on surface displacement amplitudes and peak values of amplification spectrum when SV waves propagate with oblique angle;with increase in frequency,the above two factors have a weaker influence on surface displacement amplitudes;displacement amplitudes are influenced severely with decrease in distance between valleys;due to the dynamic interaction among valleys,displacement amplitudes of multiple valleys are bigger than those of a single valley.