Analytic Solution for Diffraction of Plane P Waves by a Circular Alluvial Valley in Wedge-shaped Space
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摘要: 基于大圆弧假定，利用傅立叶-贝塞尔（Fourier-Bessel）级数波函数展开法，给出了含圆弧形沉积的楔形空间对平面P波的散射解析解。为方便构造地表面引起的散射波场，本文利用2个大圆弧面来模拟地表面，由连续性边界条件建立方程并求解得出该问题的解析解。算例结果表明，楔形空间沉积附近地表的动力响应特征依赖于入射波频率、入射角度、沉积内外介质特性与楔形夹角等因素，且位移放大效应较半空间情况更为显著。Abstract: An analytical solution was derived in this paper to study the diffraction of plane P waves by a circular alluvial valley in wedge-shaped space on the basis of large circle assumption with Fourier-Bessel series expansion. In order to construct the scattering field, the ground surface was simulated with two large curved surfaces. An equation was established with continuous boundary conditions and the analytic solution was derived. The numerical results indicate that the surface displacement characteristics around the alluvial valley in wedge-shaped space depend on the frequency of the incident wave, the angle of incidence, the material properties of the media and the angle of the wedge. The displacement amplification effect on ground motion is more significant than that of the half space.
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Key words:
- Wedge-shaped space /
- Alluvial valley /
- Plane P-Waves /
- Scattering /
- Analytical solution
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图 2 沉积附近地表位移幅值（θ0＝0°）
Figure 2. Surface displacement amplitude around the alluvial valley (θ0＝0°)
图 3 沉积附近地表位移幅值（θ0＝60°）
Figure 3. Surface displacement amplitude around the alluvial valley (θ0＝60°)
图 4 沉积附近地表位移幅值（θ0＝90°）
Figure 4. Surface displacement amplitude around the alluvial valley (θ0＝90°)
图 5 沉积附近地表位移幅值（θ0＝0°，η＝5.0）
Figure 5. Surface displacement amplitude around the alluvial valley (θ0＝0°, η＝5.0)
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