高山-峡谷复合地形对入射平面P-SV波的散射  

Scattering and Diffraction by the Hill⁃Canyon Composite Topography for Incident Plane P⁃and SV⁃Waves

作　　者：巴振宁[1,2] 吴孟桃 梁建文[1,2] 喻志颖 BA Zhenning;WU Mengtao;LIANG Jianwen;YU Zhiying(Department of Civil Engineering,Tianjin University,Tianjin 300350,P.R.China;Laboratory of Earthquake Engineering Simulation and Seismic Resilience of China Earthquake Administration,Tianjin University,Tianjin 300350,P.R.China)

机构地区：[1]天津大学土木工程系,天津300350 [2]天津大学中国地震局地震工程综合模拟与城乡抗震韧性重点实验室,天津300350

出　　处：《应用数学和力学》2020年第7期695-712,共18页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51778413,51578373,51578372)。

摘　　要：高山峡谷地形作为一种常见的复合场地,其对地震波散射相干效应十分复杂,然而,目前相关的研究成果还十分有限.为此,提出了一种用于求解平面内多域弹性波散射的多域间接边界元法,研究了高山峡谷地形对平面P-SV波的散射问题.该方法充分利用全空间Green函数与半空间Green函数在构造独立闭合域和半空间开口域中散射波场方面的优势,结合辅助函数法给出了高山峡谷场地的地震波场解答,在保证计算精度的同时显著提高了求解效率.该文通过与已有结果的比较验证了方法的正确性,并以半空间中Gauss型高山峡谷为例,分别在频域和时域内进行了数值计算分析.研究表明:高山峡谷地形附近地表位移幅值的分布非常复杂,山体与峡谷之间存在显著的动力相互作用,频域响应依赖于入射波的频率和角度;地震波垂直入射时,山体的存在对峡谷地震动有一定的抑制作用,显著改变了峡谷内部的加速度峰值及反应谱特性;高山峡谷地形两侧山体高宽比的改变将引起地震效应的改变,基岩的存在也将显著放大地形的地震效应.As a common composite site,the hill⁃canyon topography has complex coherence effects on seismic wave scattering.However,the publications of related research are still very limited.Therefore,a multi⁃domain indirect boundary element method was proposed to solve the scattering of in⁃plane elastic waves,and the scattering and diffraction of plane P⁃SV waves by hill⁃canyon topography were studied.The method takes advantages of both full⁃space Green’s function and half⁃space Green’s function to construct the scattered field in the independent closed region and the half⁃space open region,respectively.Combined with the auxiliary func⁃tion method,dynamic wavefield solutions for the hill⁃canyon site were given,with the calcula⁃tion accuracy ensured and the solution efficiency improved.The proposed method was verified through comparison of the results with published ones,and numerical calculations were per⁃formed in the frequency domain and time domain in the case of a Gaussian hill⁃canyon site.Re⁃sults show that,the distribution of the surface displacement amplitude is very complex.There is significant dynamic interaction between the hill and the canyon,and the frequency⁃domain response depends on the frequency and angle of the incident wave.The presence of hills has an inhibition effect on the canyon for vertically incident waves,which significantly changes the peak acceleration and spectrum characteristics inside the canyon.Different height⁃to⁃width rati⁃os of hills will cause changes in the seismic effect,and the presence of bedrock will also obvi⁃ously amplify the seismic effect of the overall terrain.

关 键 词：高山峡谷 地震波散射 多域间接边界元法 场地效应 动力相互作用 

分 类 号：TU435[建筑科学—岩土工程] O343.1[建筑科学—土工工程]