含峭壁V形峡谷对地震SH波散射的解析解

张宁, 潘家琐, 代登辉, 高玉峰. 2021. 含峭壁V形峡谷对地震SH波散射的解析解. 地球物理学报, 64(3): 896-906, doi: 10.6038/cjg2021O0041
引用本文: 张宁, 潘家琐, 代登辉, 高玉峰. 2021. 含峭壁V形峡谷对地震SH波散射的解析解. 地球物理学报, 64(3): 896-906, doi: 10.6038/cjg2021O0041
ZHANG Ning, PAN JiaSuo, DAI DengHui, GAO YuFeng. 2021. An analytical solution to the scattering of plane SH waves by a V-shaped canyon with cliffs. Chinese Journal of Geophysics (in Chinese), 64(3): 896-906, doi: 10.6038/cjg2021O0041
Citation: ZHANG Ning, PAN JiaSuo, DAI DengHui, GAO YuFeng. 2021. An analytical solution to the scattering of plane SH waves by a V-shaped canyon with cliffs. Chinese Journal of Geophysics (in Chinese), 64(3): 896-906, doi: 10.6038/cjg2021O0041

含峭壁V形峡谷对地震SH波散射的解析解

  • 基金项目:

    国家自然科学基金面上项目(52078184)和国家自然科学基金重点项目(41630638)资助

详细信息
    作者简介:

    张宁, 男, 1985年生, 博士, 教授, 主要从事岩土地震工程研究.E-mail: ningzhanghhu@163.com

    通讯作者: 高玉峰, 男, 1966年生, 博士, 教授, 主要从事岩土地震工程研究.E-mail: yfgao66@163.com
  • 中图分类号: P315

An analytical solution to the scattering of plane SH waves by a V-shaped canyon with cliffs

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  • 地表地形常引起地震动的局部放大,这是由于地震波传播至局部地形时产生了散射现象.本文利用波函数展开方法和区域匹配技术,提出了含峭壁V形峡谷对平面SH波散射问题的解析解,并进行了退化验证.通过频域内的参数分析,揭示了峭壁深度、入射波频率和角度等因素对峡谷场地地面运动的影响规律,发现上部峭壁会增强峡谷对地震动的地形放大效应.研究结果不仅为数值方法提供了验证基准,还可为含峭壁峡谷周边建筑物的抗震设计提供顺河向地震动输入.

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  • 图 1 

    含峭壁V形峡谷示例:亚利桑那州北部Glen峡谷

    Figure 1. 

    An example of V-shaped canyon with cliffs: Glen canyon in northern Arizona

    图 2 

    平面SH波作用下含峭壁V形峡谷的二维模型

    Figure 2. 

    2D model of a V-shaped canyon with cliffs subjected to a plane SH waves

    图 3 

    峡谷表面五个代表性位置的地表位移收敛测试图(α=30°, h1/b=h2/b=1/3, η=4)

    Figure 3. 

    Convergence tests at five representative positions on the canyon surface (α=30°, h1/b=h2/b=1/3, η=4)

    图 4 

    本文结果(实线,对应参数:h2/b=0,h2/b=1/2,η=1)与Tsaur和Chang(2008)中无峭壁V形峡谷相应结果(点线)的比较

    Figure 4. 

    Comparison between the solution of this study (solid lines) when h1/b=0, h2/b=1/2, η=1 and the corresponding results (dotted lines) of the V-shaped canyon without steep cliffs given by Tsaur and Chang (2008)

    图 5 

    本文结果(实线,对应参数h2/b=1/2,h2/b=0,η=1)与Tsaur和Chang(2009)中去底半圆形峡谷的相应结果(虚线)的比较

    Figure 5. 

    Comparison between the solution of this study (solid lines) when h1/b=1/2, h2/b=0, η=1 and the corresponding results (dotted lines) of truncated semicircular canyon given by Tsaur and Chang (2009)

    图 6 

    本文方法对中国台湾翡翠河谷地震动的模拟

    Figure 6. 

    Simulation of the ground motions for the Feitsui Canyon, Taiwan, China

    图 7 

    对应η=0.5和不同入射角度的地表位移幅值结果

    Figure 7. 

    Surface displacement amplitudes at four different incident angles and η=0.5

    图 8 

    对应η=1和不同入射角度的地表位移幅值结果

    Figure 8. 

    Surface displacement amplitudes at four different incident angles and η=1

    图 9 

    对应η=4和不同入射角度的地表位移幅值结果

    Figure 9. 

    Surface displacement amplitudes at four different incident angles and η=4

    图 10 

    不同角度下含峭壁和不含峭壁峡谷地表位移幅值随位置x/b和无量纲频率η的变化图

    Figure 10. 

    Ground surface displacement amplitudes as a function of position x/b and dimensionless frequency η for canyons with and without steep cliffs at four different incident angles

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收稿日期:  2020-02-04
修回日期:  2020-11-06
上线日期:  2021-03-10

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