3D scattering by an alluvial valley embedded in a layered half-space for obliquely incident Rayleigh waves
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摘要: 针对层状半空间中沉积谷地对斜入射瑞雷波的三维散射问题， 采用直接刚度法计算自由场波场， 以层状半空间中移动斜线均布荷载动力格林影响函数求解三维散射波场， 建立了求解该问题的间接边界元方法. 通过与已有结果的比较， 验证了该方法的正确性， 并以均匀半空间以及弹性基岩上单一土层场地中沉积谷地为例进行了计算分析. 研究结果表明： 层状半空间与均匀半空间中沉积谷地对瑞雷波的散射存在显著差别； 层状半空间中瑞雷波的振动模态对沉积附近位移幅值有着重要影响； 土层刚度和厚度等参数也对沉积附近位移幅值大小及空间分布有着显著的影响.Abstract: Aiming at solving the problem of 3D scattering by an alluvial valley embedded in a layered half-space, the indirect boundary element method (IBEM) is established based on the free wave field calculated by using the direct stiffness method, and 3D scattering wave field simulated by using the Green’s functions of moving distributed loads in the layered half-space. The method is validated by comparison with known results, and numerical analyses are performed by examples of a valley embedded in a uniform half-space and in a single soil layer over elastic bedrock. The results show that the wave scattering around the valley embedded in a uniform half-pace are distinctively different from that in a layered half-space, the modals of the Rayleigh waves in a layered half-space have important effects on the displacement amplitudes around the valley, and also the stiffness and depth of the soil layer have important influence on the amplitudes and distribution of the displacement.
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Keywords:
- 3D scattering /
- alluvial valley /
- Rayleigh wave /
- moving Green’s function /
- layered half-space
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图 1 计算模型
(a) 瑞雷波入射方位图； (b) 沉积谷地截面图
Figure 1. Calculation model
(a) Azimuth of incident Rayleigh wave； (b) Cross section of the alluvial valley
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图 2 本文计算结果与Dravinski和Mossessian (1987)结果的比较
Figure 2. Comparison of results given by the present method with those by Dravinski and Mossessian (1987)
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图 3 水平入射角度φ不同时沉积谷地附近地表位移幅值
Figure 3. Displacement amplitudes around the alluvial valley for different horizontal incident angles
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图 4 水平入射角度不同时沉积谷地附近位移幅值云图
Figure 4. Contours of displacement amplitudes near the alluvial vally for different horizontal incident angles φ
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图 5 层状半空间基岩单一土层场地频散曲线
Figure 5. Dispersion curves of a single soil layer overlaid on bedrock in half-space
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图 6 沉积谷地附近位移幅值云图(场地1和场地2)
Figure 6. Contours of displacement amplitudes around the alluvial valley (site 1 and site 2)
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