平面P波入射半无限介质空间域划分及运动偏振特征

doi:10.13722/j.cnki.jrme.2018.0970

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摘要针对地震动空间差异问题，基于波动理论和叠加原理，通过解析方法研究入射地震波在场址内形成地震动的空间差异及运动偏振特征。以平面P波在半无限介质内倾斜入射为例开展研究。首先依据质点运动的叠加模式差异将半无限介质空间域划分为叠加区和分离区，并给出分界线的解析表达式。然后以无量纲量叠加区范围系数为基础研究P波倾斜入射情况下分界线的控制参数。最后对自由面、叠加区和分离区特征质点的运动空间差异和偏振特征进行研究。结果显示，在P波倾斜入射时，叠加区与分离区的分界线可能由入射P波(PI)、反射P波(PR)和反射SV波(SR)中任意两条地震波的分离线控制。得到临界角的隐式解析表达式，当入射角小于临界角时分界线由PR和SR的分离线控制；当入射角大于临界角时分界线由PI和PR的分离线控制；当PR幅值系数为0时，分界线由PI和SR的分离线控制。平面P波倾斜入射时，自由面质点运动偏振特征与入射波偏振特征存在一一对应关系；在叠加区和分离区，单波贡献时段质点运动的偏振特征与对应地震波偏振特征一致，多波贡献时段质点运动偏振特征表现出复杂的时变特征。

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关键词 ：水利工程, 平面P波, 半无限空间, 空间域划分, 偏振特征

Abstract：Based on wave theory and superposition principle，the spatial variation of motions caused by incident seismic waves was investigated by taking the oblique incident plane primary wave in semi-infinite space as a study object in this paper. According to the wave superposition pattern of particle motion，the half-infinite space was divided into superposition and separation domains. An analytical expression of the border line of two spaces was given and the control parameters of the border line were studied based on the dimensionless superposition range coefficient. The spatial variation and polarization characteristics of particle motion in different spaces were studied. The result shows that the border of two domains is determined by separation lines of arbitrary two waves of incident P wave(PI)，reflected P wave(PR) and reflected SV wave(SR). An implicit equation was given to obtain the critical angle which controls the border. It is shown that the border is respectively determined by the separation lines of PR and SR，PI and PR，and PI and SR in the cases of the incident angle less than the critical angle，the incident angle larger than the critical angle and the amplitude of PR equal to zero. There is a one-to-one correspondence between the polarization angle of particle motion on the surface and the incident angle. In superposition and separation domains，the polarization characteristic of particle motion is in consistent with the seismic wave when the particle motion is contributed by one single wave，but changes with time when particle motion is contributed by different waves.

Key words： hydraulic engineering plane primary wave semi-infinite space division of space polarization characteristic of motion

引用本文:

何卫平1，2，周宜红1，2，赵春菊1，2. 平面P波入射半无限介质空间域划分及运动偏振特征[J]. 岩石力学与工程学报, 2019, 38(2): 321-331.
HE Weiping1，2，ZHOU Yihong1，2，ZHAO Chunju1，2. Spatial division of semi-infinite space and polarization characteristics of particle motion for incident plane primary wave#br#. , 2019, 38(2): 321-331.

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http://www.rockmech.org/CN/10.13722/j.cnki.jrme.2018.0970 或 http://www.rockmech.org/CN/Y2019/V38/I2/321

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