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沉积盆地和山体对地震动的显著影响已被地震观测和理论证实,但两者的复合作用尚需予以定量分析。本文基于单层位势理论,在散射体表面施加虚拟荷载构造散射波场;然后由边界条件建立方程求解得到虚拟荷载密度,由散射波场和自由波场叠加得到总波场,并进行了详细的参数(入射频率、入射角度、山体高度等)分析。结果表明:在SH波水平入射情况下,山体主要表现为“屏障”作用,其后方盆地中位移幅值可降低30%左右;在垂直入射情况下,盆地内部地震响应反而会增大,如当η=0.5时,其放大程度超过50%;整体上看,随着山体高度增大,对盆地内部地震响应的影响增大。本文研究结论可为复杂地形条件下长大桥梁、高坝等大型工程结构抗震设计提供部分科学依据。
The significant effects of sedimentary basins and mountains on earthquakes have been confirmed by the earthquakes and theories. However, the combined effects of the two have yet to be quantitatively analyzed. In this paper, based on the theory of single-layer potential, the scattering wave field is constructed by applying the virtual load on the surface of the scatterer. Then the virtual load density is obtained by establishing the boundary conditions, and the total wave field is obtained by superposition of the scattering wave field and the free wave field. The parameters (incident frequency, angle of incidence, altitude, etc.) are analyzed. The results show that under the condition of horizontal incidence of SH wave, the main body of the mountain is “barrier”, and the amplitude of the rearward basin can be reduced by about 30%. Under vertical incidence, the seismic response inside the basin will increase, For example, when η = 0.5, the magnification is more than 50%. On the whole, as the height of the mountain increases, the influence on the seismic response inside the basin increases. The conclusions of this paper can provide some scientific basis for the aseismic design of large-scale engineering structures such as bridges and high dam under complex terrain conditions.