摘要
地形对地震波传播路径及能量分布具有重要影响。为研究地形对地震波传播的调制效应,采用波函数展开法研究均匀半无限介质中等腰三角形山体受到水平剪切波(horizontal shear wave,SH波)作用时山体的动力响应。基于已有的散射频域解,引入地形地震动传递因子,并结合Laplace及Fourier变换求得山体位移的时域解析解答,研究SH波与三角形地形相互作用下山体的地震动时空分布特征及能量分布规律。结果表明:(1)SH波入射下山体表面点的波动程度显著高于平地表点,受频率成分影响更强,特定频率下表现出显著的放大效应和衰减效应。入射角度对共振频率及地形地震动传递因子的幅值具有重要影响。(2)地震波在山体边界和尖端处发生多次反射与折射,形成复杂的干涉波场。单位幅值脉冲垂直入射时山顶点位移幅值达2.65,随入射角度增加,位移幅值极大值减小并由山体顶点向山体右侧移动,水平入射时位移幅值极大值为2.12。(3)三角形山体地形与地震波的相互作用导致地震波能量在山体特定区域发生聚焦。垂直入射时能量集中在山顶及斜坡附近;斜入射和水平入射时,能量更多分布在山体背坡面,且几何聚焦效应更为显著,局部能量汇聚更加明显。
Topography plays a crucial role in shaping the propagation paths and energy distribution of seismic waves.To investigate the modulation effect of topography on seismic wave propagation,the dynamic response of isosceles triangular mountain subjected to horizontal shear wave(SH wave)in a homogeneous semi-infinite medium was studied by the wave function expansion method.Based on the existing frequency-domain scattering solution,the topographic ground motion transfer factor was introduced,and the time-domain analytical solution of mountain displacement was obtained by combining Laplace and Fourier transform.The spatiotemporal and energy distribution characteristics of mountain ground motion under the interaction of SH wave and triangular topography were studied.This solution allows for a comprehensive study of the spatiotemporal and energy distribution characteristics of ground motion when SH waves interact with triangular topography.The results show that:(1)Under SH wave incidence,the surface points of the mountain exhibit significantly greater fluctuations compared to flat ground points,with a stronger influence from frequency components.At specific frequencies,notable amplification and attenuation effects are observed.The incident angle has a significant impact on the resonance frequency and the amplitude of the topographic ground motion transfer factor.(2)Seismic waves undergo multiple reflections and refractions at the mountain’s boundaries and apex,forming a complex interference wave field.Under vertical incidence,the displacement amplitude at the mountain apex reaches 2.65.As the incident angle increases,the maximum displacement amplitude decreases and shifts from the apex to the right slope,with a maximum value of 2.12 under horizontal incidence.(3)The interaction between the triangular mountain topography and seismic waves causes energy to focus on specific areas of the mountain.Under vertical incidence,energy is concentrated near the apex and slopes.Under oblique and horizontal incidence,energy tends to be distributed more on the right side of the mountain.The geometric focusing effect is more pronounced under oblique and horizontal incidence,leading to more significant energy convergence in localized areas.
作者
余小越
许明
谢强
蔡宇
刘先珊
甘峰帆
YU Xiao-yue;XU Ming;XIE Qiang;CAI Yu;LIU Xian-shan;GAN Feng-fan(School of Civil Engineering,Chongqing University,Chongqing 400045,China;National Joint Engineering Research Center of Geologic Hazards Prevention in the Reservoir Areas,Chongqing University,Chongqing 400045,China;Chongqing Design Group Co.,Ltd.,Chongqing 401120,China;China Railway Eryuan Engineering Group Co.,Ltd.,Chengdu,Sichuan 610031,China)
出处
《岩土力学》
北大核心
2025年第8期2639-2649,2660,共12页
Rock and Soil Mechanics
基金
国家自然科学基金(No.52279094,No.52478328)
广西重点研发计划(桂科AB20238036)。
关键词
地形效应
三角形山体地形
波函数展开法
地震动时空分布
能量分布
topographic effect
triangular mountain topography
wave function expansion method
spatiotemporal distribution of ground motion
energy distribution
