基于两向设计地震动的二维自由场构建
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摘要
针对在设计地震动基础上构建平面半空间自由场的问题,在综合考虑水平向与竖直向设计地震动基础上获得平面半空间自由场,实现了将设计地震动与以任意角度组合入射的P波、SV波构成的自由场相联系。首先在已有成果的基础上,研究了以任意角度入射情况下P波及其反射波、SV波及其反射波对水平向和竖直向设计地震动的贡献;然后在假设入射P波、SV波与两向设计地震动具有相同频率组成的基础上,获得了以特定角度组合入射条件下P波、SV波的频谱和相位信息;进而通过傅里叶逆变换获得入射P波、SV波的时间序列;最后依据P波、SV波及其反射波在平面半空间的传播情况获得自由场条件下平面半空间内任意点的水平向和竖直向地震动。该文所采用的波场构建方法可实现对包含任意频谱和相位信息的两向设计地震动所对应的平面半空间自由场的构建,所获得的斜入射P波和SV波也具有各自的频谱和相位信息。最终得到的平面半空间自由场任意点水平向和竖直向地震动时间序列具有非一致性;根据入射P波、SV波结合地基边界条件确定的空间点地震动时间序列可用于结构的非一致地震动输入。
To study the free field wave motions of plane half-space based on design earthquake, a new approach synthetically considering the horizontal and vertical design earthquake ground motions is proposed. This approach can connect the design earthquake and free field wave motions based on oblique incident P, SV waves with arbitrary angles. Firstly, on the basis of previous researchers' works, the contribution of oblique incident P, SV and their reflected waves to the two components of design earthquake is discussed. Then, based on the assumption that the P and SV waves have the same frequencies with design earthquakes, the amplitude and phase spectrum of P and SV waves are obtained. The time history of P and SV wave is obtained by inverse Fourier transform. Finally, the horizontal and vertical motions of any points in plane half-space are obtained by studying the propagation of P and SV waves and their reflections. The method proposed in this paper could be applied on horizontal and vertical design earthquake ground motions with arbitrary amplitude and phase information. The obtained P and SV waves have respective spectrum information. And the motions in the plane half-space are non-uniform. The motions of points obtained by incident P and SV waves considering ground boundary conditions could be used in structure analysis for multiple-support excitation.
引文
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