IBEM simulation of seismic wave scattering by valley topography with fluid layer
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摘要: 结合单相介质动力格林函数和流体域格林函数，将间接边界元方法拓展到含流体层河谷对地震波散射的求解，并结合具体算例进行大量参数分析。研究结果表明，含流体层河谷地形对平面P波、SV波入射时的地震响应受控于入射波频率、入射波角度及流体深度等多种因素。总体来看：① 在低频域内，含流体河谷底部及附近地表的频谱特性与不含流体的河谷反应基本一致；② P波入射时在水层体系共振频率处，河谷底部位移缩小效应显著，而此频率处流体表面位移达到最大；③ 流体层具有吸收地震波能量的作用，流体深度越大，河谷表面及附近地表的地震动位移越小。研究成果可在一定程度上为河谷地形附近地震动效应的评估及防震减灾工作提供理论依据。Abstract: Combined with the dynamic Green’s function of single-phase medium and the Green’s function in the fluid domain, the indirect boundary element method is developed to solve the scattering of valley topography with fluid on plane P and SV waves, and the parameter analysis is carried out in combination with specific examples. The results show that the seismic response of valley topography with fluid layer to plane P and SV waves is controlled by many factors, such as incident wave frequency, incident wave angle and the depth of fluid. Generally speaking: ① In the low frequency domain, the frequency spectrum characteristics of the valley bottom and the nearby surface are basically the same in the valley with or without water. ② When P wave incidents, at the resonance frequency of this aquifer system, the displacement at the bottom of the valley decreases significantly, but the displacement of fluid surface reaches the maximum. ③ The fluid layer has the function of absorbing seismic wave energy. The larger the fluid depth is, the smaller the ground motion displacement of the valley surface and nearby ground is. The results can provide a theoretical basis for the evaluation of the ground motion effect near the valley terrain and the work of earthquake prevention and mitigation.
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图 1 含流体层沉积河谷对地震波的散射计算模型
（a） 含流体河谷计算模型；（b） 单元离散
Figure 1. Calculation model of seismic wave scattering by sedimentary valley with fluid layer
（a） Calculation model of the valley with fluid layer；（b） Element discretization
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图 3 平面SV波入射下本文含水河谷退化位移与文献结果对比 （引自Sánchez-Sesma，Campillo，1991）
Figure 3. Comparison between the degradation displacement of water bearing valley of this paper and the results of literature induced by plane SV waves （after Sánchez-Sesma，Campillo，1991）
（a） η＝2.0，θβ＝0°；（b） η＝2.0，θβ＝30°
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图 4 平面P波入射下不含流体的河谷与充满流体的河谷竖向位移放大系数对比
Figure 4. Comparison of vertical displacement amplification factors between the valley without fluid and the valley full of fluid induced by plane P waves
（a） η＝0.5，θα＝0°；（b） η＝2.0，θα＝0°；（c） η＝5.0，θα＝0°；（d） η＝0.5，θα＝30°；（e） η＝2.0，θα＝30°；（f） η＝5.0，θα＝30°
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图 5 平面SV波入射下不含流体的河谷与充满流体的河谷水平位移放大系数对比
Figure 5. Comparison of horizontal displacement amplification factors between the valley without fluid and the valley full of fluid induced by plane SV waves
（a） η＝0.5，θα＝0°；（b） η＝2.0，θα＝0°；（c） η＝5.0，θα＝0°；（d） η＝0.5，θα＝30°；（e） η＝2.0，θα＝30°；（f） η＝5.0，θα＝30°
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图 6 平面P波入射下充满流体的河谷表面和流体表面位移放大系数谱
Figure 6. Displacement amplification factor spectrum of the valley surface with full of fluid and that of the fluid surface induced by plane P waves
（a） x/a＝0，θα＝0°；（b） x/a＝0.5，θα＝0°；（c） x/a＝0，θα＝30°；（d） x/a＝0.5，θα＝30°
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图 7 平面P波入射下不含流体的河谷与充满流体的河谷竖向位移放大系数谱
Figure 7. Amplification factor spectrum of vertical displacement for the valley without fluid and the valley full of fluid induced by plane P waves
（a） x/a＝0，θα＝0°；（b） x/a＝0.5，θα＝0°；（c） x/a＝1.5，θα＝0°；（d） x/a＝0，θα＝30°；（e） x/a＝0.5，θα＝30°；（f） x/a＝1.5，θα＝30°
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图 8 平面SV波入射下不含流体的河谷与充满流体的河谷水平位移放大系数谱
Figure 8. Amplification factor spectrum of horizontal displacement for the valley without fluid and the valley full of fluid induced by plane SV waves
（a） x/a＝0，θα＝0°；（b） x/a＝0.5，θα＝0°；（c） x/a＝1.5，θα＝0°；（d） x/a＝0，θα＝30°；（e） x/a＝0.5，θα＝30°；（f） x/a＝1.5，θα＝30°
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图 9 平面P波入射下流体深度不同时河谷表面的竖向位移放大系数
Figure 9. Vertical displacement amplification factor of the valley surface with different fluid depth induced by P waves
（a） η＝0.5，θα＝0°；（b） η＝2.0，θα＝0°；（c） η＝5.0，θα＝0°；（d） η＝0.5，θα＝30°；（e） η＝2.0，θα＝30°；（f） η＝5.0，θα＝30°
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图 10 平面SV波入射下流体深度不同时河谷表面的水平位移放大系数
Figure 10. Horizontal displacement amplification factor of the valley surface with different fluid depth induced by plane SV waves
（a） η＝0.5，θα＝0°；（b） η＝2.0，θα＝0°；（c） η＝5.0，θα＝0°；（d） η＝0.5，θα＝30°；（e） η＝2.0，θα＝30°；（f） η＝5.0，θα＝30°
表 1 含流体层河谷地形对平面P波、SV波的地震响应计算参数
Table 1 Calculation parameters of seismic response of valley terrain with fluid layer for plane P wave and SV wave
P波波速cα/（m·s−1） SV波波速cβ/（m·s−1） 密度ρ/（kg·m−3） 空气 330 — 1.29 流体 1 501 — 1 000 弹性土体 2 670 1 090 2 200 
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