Effect of Ground Motion Spatial Variations on Pounding Response of High-Pier Railway Bridge
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摘要: 为了研究不同地震动参数对高墩铁路桥碰撞的影响，以一座典型高墩铁路桥为例，基于OpenSees平台采用弹塑性动力时程分析方法对其在一致激励及多点激励下的碰撞响应进行了理论分析.首先，采用Hertz-damp模型充分考虑了结构在碰撞过程中的能量耗散和刚度变化；其次，依据中国桥梁抗震规范并基于"谱兼容"的方法选取了符合不同场地条件的天然地震记录；最后，在此基础上完成了考虑行波效应和场地效应的高墩桥碰撞响应对比分析.研究结果表明：地震动的空间变化性不但会对桥梁结构的内力产生显著影响，还会增大结构的振幅或加剧相邻结构之间的不同步振动，从而显著增大碰撞发生的概率和碰撞力的大小，在桥梁的抗震设计中应考虑其对桥梁结构碰撞产生的影响，否则会错误的估计结构的响应；行波效应会改变地震动的相位角，对梁-梁处的碰撞影响更为显著，特别是视波速较小时，而场地效应会增大地震动的幅值，对梁-桥台处的碰撞影响更为显著，在进行防撞减撞设计时不但要考虑地震动的空间效应，还应充分考虑导致结构不同部位发生碰撞的主要因素，以便采取合适的减撞措施和设计方法.Abstract: The authors present a theoretical analysis for a typical HPRB under synchronous and asynchronous excitations, using nonlinear dynamic analysis based on OpenSees, to investigate the effect of ground motion spatial variations (GMSVs) on the pounding response of high-pier railway bridges (HPRBs). The Hertz-damp model was adopted to simulate energy dissipation and the change in stiffness during pounding. In accordance with the Chinese seismic code of bridges, actual ground motion records were selected for each site condition by using the spectrum match method, and then, a comparative analysis was conducted considering both the wave-path and local site effects. The results show that GMSVs not only increases the seismic responses of the bridge structure but also increases the amplitude and non-synchronous vibration of adjacent structures, which will result in more pounding. Therefore, special attention should be paid on the effect of GMSVs on the seismic design of high-pier bridges. Otherwise, the responses of the bridge structure will be incorrectly estimated. Moreover, the wave-path effect may become more evident for beam-beam pounding by changing the phase angle of ground motions, especially, for a lower apparent velocity, while the local site effect may become more evident for beam-abutment pounding by increasing the amplitude of ground motions. It is suggested that both GMSVs and the leading cause of pounding at different locations should be considered for adopting an appropriate seismic design method and measures to mitigate or prevent pounding.
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Key words:
- high-pier bridges /
- pounding /
- ground motion spatial variations /
- wave-path effect /
- site conditions
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图 3 各场地条件下地震动反应谱与目标反应谱比较
Figure 3. Comparison of the target spectrums and the spectrum of selected ground motions for different site condition
图 6 桥梁结构响应峰值对比图
Figure 6. Comparison of peak seismic responses of bridge structure under different conditions
表 1 混凝土本构模型各参数取值
Table 1. Parameters of concrete material model
特征参数 无约束混凝土 约束混凝土 弹性模量E0/GPa 32.5 32.5 最大压应力fpc/MPa 26.8 34.8 最大压应变εc0 0.003 0.002 极限压应力fpcU/MPa 5.36 6.96 极限压应变εU 0.010 0.042 最大拉应力ft/MPa 3.75 4.87 
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表 2 钢筋本构模型各参数取值
Table 2. Parameters of steel material model
弹性模量Es0/GPa 屈服强度fps 应变硬化系数b 200 330 0.01
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表 3 Hertz-damp简化模型特征参数
Table 3. Properties of Simplified Hertz-damp model
特征参数 取值 Hertz-damp理论模型的碰撞刚度Kh/(kip·in-3/2) 25 000 Hertz系数n 3/2 回归系数e 0.8 最大入侵位移δm/mm 16 屈服参数a 0.1 屈服位移δy/mm 1.6 等效刚度Keff/(kN·mm-1) 3 472 初始刚度Kt1/(kN·mm-1) 8 472 应变硬化刚度Kt2/(kN·mm-1) 2 916 初始间隙gp/mm 100
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表 4 支座参数取值
Table 4. Values of bearing parameters
参数 支座1 支座3 支座4 支座5 支座6 滑动摩擦因数μd 0.02 0.02 0.02 0.02 0.02 上部结构重力R/kN 9 582.2 9 575.7 3 250.9 8 647.4 3 260.6 临界滑动摩擦力Fmax/kN 191.64 191.51 65.02 172.95 65.21 屈服位移xy/m 0.004 0.004 0.004 0.004 0.004 初始刚度k/(kN·m-1) 47 911.0 47 878.5 16 254.5 43 237.0 16 302.6
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表 5 不同场地条件下目标反应谱参数
Table 5. Parameters of target spectra under different site conditions
参数 硬场 中硬场 软场 特征周期Tg/s 0.25 0.35 0.45 场地系数Cs 0.9 1.0 1.0 抗震重要系数Ci 1.7 阻尼调整系数Cd 1.0 基本加速度峰值A/(×g) 0.3
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表 6 所选地震动详细信息
Table 6. Detail of selected ground motions
编号 地震名称 年份 记录点 场地类型 PGA/(×g) MSE f RSN1614 Duzce Turkey 1999年 Lamont 1061 硬场 0.20 0.104 1 1.98 中硬场 0.29 0.096 6 2.85 软场 0.34 0.137 2 3.40 RSN1633 Manjil Iran 1990年 Abbar 硬场 0.22 0.087 2 0.45 中硬场 0.32 0.097 7 0.64 软场 0.38 0.133 3 0.77 RSN3750 Cape Mendocino 1992年 Loleta Fire Station 硬场 0.18 0.132 6 0.68 中硬场 0.26 0.082 7 0.98 软场 0.31 0.068 5 1.17
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表 7 多点激励工况
Table 7. Cases for multiple-excitation
计算内容 地震编号 场地条件 视波速/(m·s-1) 一致激励 RSN1614
RSN1633
RSN3750中硬场 无穷大 行波效应 RSN1614
RSN1633
RSN3750中硬场 300
800场地效应 RSN1614
RSN1633
RSN3750F-M-S-F-M-S-F
F-M-S-F-M-S-F
F-M-S-F-M-S-F无穷大 注: F-M-S-F-M-S-F依次表示桥台1、桥墩1~5以及桥台2墩底处的场地条件, F表示硬场, M表示中硬场, S表示软场.
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表 8 结构动力特性
Table 8. Dynamic characteristics of bridge structure
结构形式 振动频率fFq/Hz 振型 连续刚构桥 0.8 纵漂 连续梁桥 1.2 纵漂
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