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2023年第3卷第10期《计算力学学报》Vol.4 No.10

摘要：本文重点发展和实现了V形非均匀多层介质峡谷的多点地震动场模拟，其理论依据是在长期假设均匀介质峡谷场地的基础上引入了分层效应模型，其优点是考虑了地下土层分布不均匀对地震动的影响。具体理论包括：，稳态波场被分为封闭区和开放区，同时引入波函数展开法和大圆弧法，经推导得到了V形峡谷在SH波入射激励下稳态波场的分布频域解析解，进而得到分布于V形峡谷表面的频域谱；然后，简述导出的基于V形峡谷地形的“平-凹”相干函数模型；进而，利用两步骤传递函数法（水平自由表面→V形峡谷表面→峡谷地下）推导得到地下频域谱；由此，形成并阐明了非均匀多层介质V形峡谷表面和地下的多点地震动具体模拟方法；最后，开发了依据上述途径的V形场地多点地震动模拟程序，实现其可视化，验证了计算结果的合理性和可靠性。同时表明：波场幅值在两侧水平场地与峡谷底部具有明显差异，峡谷效应的多点相干性因各土层分界面与峡谷边界稳态波场中的散射成分存在而被降底。本文内容成果可应用于后续文章关于V形峡谷桥梁的多点地震分析。

关键词：桥梁工程；多点地震动；波函数；V形峡谷；非均匀介质；地震动模拟

中图分类号：P315.9;U442   文献标识码：A     文章编号：

Abstract： A simulation approach of multi-support earthquake was proposed and developed based on the theory of spatial variable seismic motions in a multi-layered V-shaped canyon. The homogeneous-media canyon model was improved by the layer model and the effects of inhomogeneous media were taken into account. Firstly, the steady-state wave field was separated into two regions which are the open region and the enclosed region. The wave function expansion method and big-arc boundary method were adopted to obtain the analytical solution of seismic wave field in the V-shaped canyon by a train of plane SH waves. A flat-sunken coherence function model of a V-shape canyon was illuminated. Moreover, the underground power spectral density functions were obtained by a two-step transfer function method. Then the simulation approach of spatially variable seismic motions in a multi-layered V-shaped canyon was illuminated. Finally, a visual program was developed for the simulation, and tested for the rationality of calculation results. Numerical results showed great differences of the wave displacement amplitudes between flat terrain and canyon bottom. The scattering wave components were increased by the layer interface boundary and the canyon surface boundary, lowering the coherence of seismic waves. The simulation results can be referenced as inputs for the bridge dynamic response analysis in the subsequent paper.