Synthesis of Non-Stationary Seismic Waves Based on Phase Difference Spectrum and Its Application
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摘要: 为了模拟地震动的非平稳性和多维性并克服传统三角级数法在合成地震波中选择包络函数具有任意性和不能表征频率非平稳性的缺点，提出了基于相位差谱法的多维多点非平稳人工地震波合成. 首先，基于随机场理论模拟地震动的行波效应、相干效应、场地效应和多维性；其次，确定能表征地震动的强度非平稳和频率非平稳性的相位差谱；最后，将合成的非平稳地震波和当量反应谱应用到实际桥梁抗震分析中进行分析对比. 研究结果表明：相位差谱法合成多维多点非平稳地震动不需要包络函数控制地震波的波形，排除人工选择强度包络函数的任意性，且考虑了地震动的空间相关性和多维性，优于传统的三角级数法；本文方法与传统反应谱法计算结果基本一致，采用反应谱法计算的两处墩底的剪力值和弯矩值分别相差在10%和17%以内，本文方法分别在9%和12%以内.Abstract: A synthetic method of multi-dimensional and multi-point non-stationary seismic waves (MMNSWs) based on phase difference spectrum is proposed to simulate the non-stationarity and multi-dimensionality of real ground motions in hope to overcome the deficiencies of the traditional trigonometric series method, such as the arbitrariness in selection of the envelope function and loss of non-stationarity feature in frequency domain. First, the traveling wave effect, coherence effect, local site effect and multi-dimensional property of ground motions are modelled using the random field theory. Then, the phase difference spectrum is determined and used to characterize the non-stationarity of intensity and frequency of ground motions. Finally, the synthetic non-stationary ground motions are applied to an actual bridge for seismic analysis, and the generated dynamic responses are compared with the equivalent response spectrum obtained by response spectrum method. Results show that the MMNSWs generated based on phase difference spectrum does not need the envelope function to control the waveform of seismic waves, and hence can exclude the arbitrariness of artificial selection of the intensity envelope function. Since it has taken into account the relevance and multidimensionality of seismic ground motions, the proposed method is better than the traditional trigonometric series method for synthesis of ground motions. In addition, the results generated by the proposed method are basically consistent with those by the traditional response spectrum method. The difference between the values of shear force and bending moment at two pier bottoms, calculated by the response spectrum method, is in the range of 10% and 17%, respectively, while the difference is less than 9% and 12%, respectively, by the proposed method.
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图 2 连续刚构桥示意（单位：m）
Figure 2. Schematic diagram of continuous rigid frame bridge (unit：m)
图 6 拟合反应谱和设计反应谱（未修正）
Figure 6. Fitting response spectrum and design response spectrum（uncorrected）
图 4 y方向非平稳地震动时程（未修正）
Figure 4. Non-stationary ground motion at y direction（uncorrected）
图 7 x方向的非平稳人工地震时程（修正）
Figure 7. Non-stationary ground motion at x direction（corrected）
图 8 拟合反应谱和目标设计反应谱（修正）
Figure 8. Non-stationary fitting response spectrum and target design response spectrum（corrected）
图 10 一致激励与多点激励的墩底剪力弯矩（相位差谱法）
Figure 10. Shearing and moment at the bottom of the piers under UE and ME（phase difference spectrum method）
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