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覆水饱和双相介质圆弧场地P波激励下散射问题的理论解 |
A theoretical solution for the scattering of incident plane P waves by a circular-arc site in saturated double-phase media with overlying water |
投稿时间:2020-05-09 修订日期:2020-09-16 |
DOI: |
中文关键词: 地震动 理论解 波函数展开法 平面P波 饱和双相介质 |
英文关键词:earthquake motions theoretical solution wave function expansion method plane P wave saturated double-phase media |
基金项目:国家自然科学基金项目(面上项目,重点项目,重大项目) |
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中文摘要: |
为了满足工程技术水平发展的需要,保障水域长大结构在遭受重大地震灾害时的安全性,有必要进一步探究水域环境下场地因素对地震动的影响,为水域长大结构的抗震响应分析提供更加科学合理的地震动输入。本文采用波函数展开法对平面P波入射复杂水域地形的空间变异性地震动场进行研究;该地形具有覆水层、水下地基双相介质(饱和土)、场地非平坦(圆弧场地散射特性)以及第二类分层(分层界面穿越圆弧场地)等综合特征属性。首先,依据地震波反射和透射特性推导笛卡尔坐标系下的自由波场分布;然后,根据场地特点以及引入的大圆弧法拟定极坐标系下的含有待定系数的散射波场势函数;进而,结合土-水分界面和饱和土层分界面边界条件,依次求解散射波场中的待定系数;最后,通过自由波场和散射波场得到覆水饱和双相介质圆弧场地的波函数理论解。基于上述理论推导,本文通过算例验证了理论推导的合理性及可靠性,分析了地表位移在不同条件下的差异性。结果表明:相对于均匀介质而言,饱和双相介质会显著改变地表位移分布;入射波频率和角度对地震地面运动特性有着较大的影响。 |
英文摘要: |
To meet the needs of the development of engineering technology and ensure the safety of those huge and complex structures constructed in water field during major earthquake disasters, it is necessary to study the influence of site characteristics on earthquake motions. The research can provide more scientific and reasonable earthquake motion input for huge structures constructed in water field. Using the wave function expansion method, this paper mainly studies the earthquake motion field with spatial variability when incident plane P wave into a complex terrain with overlying water. The site has comprehensive attributes such as the water-covered layer, the double-phase media (saturated soil) due to the overlying water, the non-flat site (scattering by the circular-arc field), and the second type of stratification (layered boundary crossing the circular-arc field). First, based on the reflection and transmission characteristics of seismic waves, the free wave field functions in Cartesian coordinate system are derived. Then, according to the characteristics of the site and the large arc method, the scattering wave field functions with the undetermined coefficients in the polar coordinate system are derived. Furthermore, the undetermined coefficients are solved by the boundary conditions consisting of saturated soil interface and soil-water interface. Finally, a theoretical solution for the scattering by circular-arc site in saturated double-phase media under surface water is given. The rationality and reliability of theoretical solution is verified by a numerical calculation and the surface displacement at different conditions is analyzed. Numerical results show that: compared to the uniform medium, the saturated double-phase media significantly change the surface motion, and the incident wave frequency and angle have great influences on the ground vibration characteristics. |
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