Long-period design response spectrum study of ultra-long-span suspension bridges
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摘要: 为了建立适用于超大跨悬索桥抗震设计的长周期设计反应谱，从中国、日本和美国的强震数据库中收集了17 574条实测地震动记录，通过对收集的地震动进行校正、滤波和频谱特性分析，提出了界定常规地震动与长周期地震动的标准和方法，并以此方法筛选出了1 084条长周期地震动；采用一种“四段式”的标准化反应谱数学模型来拟合长周期地震动的平均谱，通过遗传算法对模型参数进行标定，建立了不同工程场地的长周期设计反应谱；以一主跨为2 300 m的超大跨悬索桥为依托工程，通过分析分别由安评反应谱和长周期设计反应谱引起的结构响应，来验证所提出的长周期设计反应谱的合理性。研究结果表明：加速度反应谱周期在0.02~10.00 s范围内的平均周期大于或等于1.5 s和傅里叶谱的主频成分小于1 Hz可作为界定常规地震动和长周期地震动的2个重要标准；相对于规范反应谱，提出的长周期设计反应谱可以更全面地考虑长周期地震动的影响；E1地震作用下，长周期设计反应谱与安评反应谱引起的依托工程桥塔关键位置的地震响应差值比为1.4%~42.4%，E2地震作用下该差值比为0.3%~19.3%，长周期设计反应谱作用下桥塔和加劲梁的地震响应均大于安评反应谱对应的响应；对于E2地震作用下关键承重构件需要保持弹性的超大跨悬索桥而言，提出的长周期设计反应谱可以合理地指导其抗震设计。Abstract: To establish the long-period design response spectrum suitable for the seismic design of ultra-long-span suspension bridges, 17 574 measured ground motion records were collected from the strong earthquake databases of China, Japan, and the United States. By correcting, filtering, and analyzing the spectral characteristics of the collected records, a standard and method for defining the conventional ground motion and the long-period ground motion were proposed. Then, 1 084 long-period ground motions were selected by this method.A "four-segment" standardized response spectrum mathematical model was used to fit the average amplitude of the long-period ground motions. The model parameters were calibrated by a genetic algorithm, the long-period design response spectra for different engineering sites were established. An ultra-long-span suspension bridge with a main span of 2 300 m was taken as the support project, the rationality of the proposed spectrum was verified by analyzing the structural response caused by the safety evaluation response spectrum and the long-period design response spectrum.Analysis results show that the average period of the acceleration response spectrum in the range of 0.02-10.00 s is no less than 1.5 s, which can be used as an important criterion with the less-than-1Hz main frequency component of the Fourier spectrum to define the conventional ground motion and the long-period ground motion.Compared with the standard response spectrum, the proposed long-period design response spectra can take the effect of long-period ground motion into more comprehensive consideration. Under E1 earthquake action, the seismic response difference ratio at the key position of the bridge tower in the support project, caused by the long-period design response spectrum and the safety assessment response spectrum, is 1.4%-42.4% while the difference ratio is 0.3%-19.3% under E2 earthquake action. Additionally, under the long-period design response spectrum, the seismic responses of the bridge tower and the stiffened beam are greater than that corresponding to the safety assessment response spectrum. For an ultra-long-span suspension bridge, where key load-bearing components need to maintain elasticity under E2 earthquake action, the proposed long-period design response spectrum can rationally guide its seismic design.
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图 1 地震动的震中距和矩震级的分布
Figure 1. Distribution of epicentral distances and moment magnitudes of ground motions
图 3 处理前后的地震动时程曲线及其弹性反应谱
Figure 3. Time history curves and elastic response spectra of ground motions before and after treatment
图 4 地震动的傅里叶归一谱和加速度反应谱
Figure 4. Fourier normalized spectra and acceleration response spectra of ground motions
图 6 长周期的地震动震中距和矩震级分布
Figure 6. Distribution of epicentral distances and moment magnitudes of long-period ground motions
图 8 长周期设计β谱与地震动β谱对比
Figure 8. Comparison between long-period design β-spectrum and ground motion β-spectrum
图 13 长周期设计反应谱和安评反应谱
Figure 13. Long-period design response spectra and safety assessment response spectra
图 14 纵向地震作用下的北桥塔响应
Figure 14. Response of northern bridge tower under longitudinal seismic action
图 15 横向地震作用下的北桥塔响应
Figure 15. Response of northern bridge tower under lateral seismic action
图 16 纵向地震作用下的南桥塔响应
Figure 16. Response of southern bridge tower under longitudinal seismic action
图 17 横向地震作用下的南桥塔响应
Figure 17. Response of southern bridge tower under lateral seismic action
图 19 地震作用下的加劲梁位移响应
Figure 19. Displacement response of stiffening beam under seismic action
表 1 场地类别与Vs-30对应关系
Table 1. Correlation between site categories and Vs-30
Vs-30 /(m·s-1) >510 (260, 510] (150, 260] ≤150 场地类别 Ⅰ Ⅱ Ⅲ Ⅳ 
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表 2 地震动条数分布
Table 2. Distribution of number of ground motions
场地类别 Ⅰ Ⅱ Ⅲ Ⅳ 第1组 118 103 40 17 第2组 301 435 110 31 第3组 4 659 10 322 1 202 236 合计 5 078 10 860 1 352 284
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表 3 长周期地震动条数分布
Table 3. Distribution of number of long-period ground motions
场地类别 Ⅰ Ⅱ Ⅲ Ⅳ 第1组 1 第2组 6 32 16 第3组 170 552 288 19 合计 176 585 304 19
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表 4 参数标定结果
Table 4. Parameter calibration results
β谱参数 βmax Tg/s Tf/s γ δ Ⅰ 第1分组 Ⅰ 第2分组 2.63 0.62 4.92 0.49 2.17 Ⅰ 第3分组 2.62 0.93 7.60 0.73 2.13 Ⅱ 第1分组 Ⅱ 第2分组 2.78 1.03 4.91 0.70 1.99 Ⅱ 第3分组 2.75 1.27 5.18 0.72 1.84 Ⅲ 第1分组 Ⅲ 第2分组 2.41 1.71 5.23 0.55 2.89 Ⅲ 第3分组 2.86 1.59 5.95 0.79 2.28 Ⅳ 第1分组 Ⅳ 第2分组 Ⅳ 第3分组 3.14 2.02 6.08 1.29 2.81
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表 5 参数建议取值
Table 5. Recommended parameter values
β谱参数 βmax Tg/s Tf/s γ δ Ⅰ 第1分组 Ⅰ 第2分组 2.65 0.65 5 0.8 1.6 Ⅰ 第3分组 2.65 0.95 6 0.8 1.6 Ⅱ 第1分组 Ⅱ 第2分组 2.75 1.00 5 0.8 1.6 Ⅱ 第3分组 2.75 1.30 6 0.8 1.6 Ⅲ 第1分组 Ⅲ 第2分组 2.85 1.50 5 0.8 1.6 Ⅲ 第3分组 2.85 1.60 6 0.8 1.6 Ⅳ 第1分组 Ⅳ 第2分组 Ⅳ 第3分组 3.15 2.00 6 1.2 1.8
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表 6 基础六弹簧模型的刚度矩阵参数取值
Table 6. Stiffness matrix parameter values of six-spring foundation model
kN·m 刚度 Kx Ky Kz Krx Kry Krz 北桥塔 9.284×107 9.284×107 3.548×108 2.955×1011 6.097×1010 9.193×1010 南桥塔 1.197×108 1.197×108 3.623×108 3.019×1011 6.248×1010 1.184×1011 辅塔 2.565×107 2.540×107 7.939×107 7.943×1010 2.531×109 2.621×1010
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表 7 动力特性计算值与实测值对比
Table 7. Comparison of calculated and measured values of dynamic characteristics
阶次 有限元计算频率/Hz 风洞试验实测频率/Hz 振型特点 误差/ % 1 0.038 1 0.037 0 加劲梁一阶正对称横弯 2.97 2 0.060 5 0.061 0 加劲梁纵飘 -0.82 3 0.083 2 0.075 1 加劲梁一阶反对称横弯 10.79 4 0.085 2 0.082 0 加劲梁一阶正对称竖弯 3.90 5 0.091 7 0.094 3 加劲梁一阶反对称竖弯+纵飘 -2.76
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