Failure Mode of Isolated Beam Bridge by Weighted Rank Sum Ratio Method
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摘要: 为了综合评价桥梁在地震作用下失效模式的信息，考虑地震动中存在的不确定性影响，对实际工程中的某6跨隔震连续梁桥的失效模式进行了分析.基于IDA法，选用16条足够反映地震动中存在的不确定性且PDA分布在一个较宽强度范围内的地震动，对桥梁中支座、桥墩墩底这两个最容易失效的部位分别基于位移和修正的Park-Ang损伤理论判断其失效，引用加权秩和比法综合了16条地震动作用下的桥梁失效模式的评价信息，分析给出具有统计意义的失效模式，并找出了桥梁的最弱失效模式.研究结果表明：该隔震连续梁桥的失效模式为该桥梁中墩的隔震支座先失效，然后是桥梁过渡墩支座失效，最后是边墩底部和边墩的支座失效；桥梁的最弱失效模式为桥梁所有隔震支座先失效，其次是边墩底部失效，然后是中墩失效，最后是过渡墩失效.Abstract: To estimate the failure modes of seismically isolated continuous girder bridges, a practical engineering with six spans was analyzed considering the uncertainty of seismic ground motions. Sixteen ground motion records were selected to be used in IDA method, which could provide sufficient accuracy of seismic analysis demands, and the PGA of these records were distributed in a wide range. Bearings and the bottom of piers were the most vulnerable parts of the bridge, of which failure criteria were estimated by displacement and modified Park-Ang damage theory, respectively. And weighted rank sum ratio method was adopted to analyze evaluation information of the bridge under sixteen ground motion records, then the statistically significant failure modes and the weakest failure mode of the bridge were identified. The results show that the final failure mode of the isolation continuous girder bridge arises at the isolation bearings of the middle piers, at the isolation bearings of the transition piers, and at the bottom of side piers and bearings. The weakest failure mode of this bridge happens with all isolation bearings cease to be effective first, then it comes to the bottom of the side piers and the middle piers, and finally the transitional piers.
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Key words:
- isolation /
- failure mode /
- IDA method /
- continuous girder bridge
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表 1 LRB支座的参数
Table 1. Details of LRB
支座类型 布置位置 竖向承载力/kN 横向刚度
/(kN·mm-1)竖向刚度Kv
/(kN·mm-1)屈服力
Qy/kN屈服前刚度K1
/(kN·mm-1)屈服后刚度K2
/(kN·mm-1)LRB1250 1#、7#(边墩) 12 500 4.4 2 000 848 18.2 2.8 LRB2750 2#、6#(过渡墩) 27 500 10.0 4 922 965 50.9 7.9 LRB2500 3#、4#、5#(中墩) 25 000 9.2 4 357 877 46.5 7.2 
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表 2 选取的地震动参数
Table 2. Details of ground movements
序号 地震动 PGA/(×g) 年份 GM-1 El Centro 0.357 1940 GM-2 Northridge 0.416 1994 GM-3 人工波1 0.150 — GM-4 Loma Prieta 0.220 1989 GM-5 Taft Lincoln 0.156 1952 GM-6 James RD 0.550 1979 GM-7 Hollywood Storage 0.059 1952 GM-8 kobe 0.370 1995 GM-9 MIYAGI-Coast 0.325 1978 GM-10 HOKKAIDO-SW_Coast 0.330 1993 GM-11 HYUGANADA-Coast 0.392 1968 GM-12 NIHONKAI-Central 0.432 1983 GM-13 HOKKAIDO-EastCoast 0.447 1994 GM-14 HYOUGOKEN_South 0.828 1995 GM-15 San Fernando 0.315 1971 GM-16 人工波2 0.319 —
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表 3 修正Park-Ang构件损伤分级及参数
Table 3. Structural member classification and parameters of amendatory Park-Ang
序号 损伤等级 损伤描述 量化指标 1 无损伤 无损伤或仅在局部产生微细裂缝 Ds＜0.1 2 可修复损坏 裂缝扩展明显并伴有局部表层混凝土剥落, 刚度依旧保持 Ds=0.1＜0.4 3 不可修复损坏 虽然维持有一定的竖向承载力, 但遗留下永久损伤 Ds=0.4＜0.77 4 倒塌 Ds=0.77 注:本文Ds=0.75时, 认为构件失效.
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表 4 桥墩的能力参数
Table 4. Capacity parameters of the pier
状态 弯矩/
(MN·m)曲率/
(1·m-1)屈服(纵桥向) 186 0.008 8 极限(纵桥向) 191 0.015 0 屈服(横桥向) 498 0.003 0 极限(横桥向) 505 0.005 3
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表 5 各地震动作用下桥梁各单元的失效次序
Table 5. Failure sequence of bridge element in every ground movement
序号 地震动 失效秩序 1 2 3 4 5 6 7 8 9 GM-1 El Centro ⑤ ④ ③ ② ⑥ ⑦ ① ⑧ ⑭ GM-2 Northridge ⑤ ④ ③ ② ⑥ ⑦ ① ⑧ ⑭ GM-3 人工波1 ⑧ ⑤ ④ ③ ② ⑥ ⑦ ① ⑭ GM-4 Loma Prieta ④ ③ ⑤ ⑥ ② ① ⑦ ⑧ ⑭ GM-5 Taft Lincoln ⑧ ④ ③ ⑤ ⑥ ② ① ⑦ ⑭ GM-6 James RD ③ ⑤ ④ ⑥ ② ① ⑦ ⑧ ⑭ GM-7 Hollywood Storage ④ ③ ⑤ ⑥ ② ① ⑦ ⑧ ⑭ GM-8 kobe ⑧ ③ ④ ⑤ ⑥ ② ① ⑦ ⑭ GM-9 MIYAGI-Coast ③ ④ ⑤ ⑥ ② ① ⑦ ⑧ ⑭ GM-10 Hokkaido-SW Coast ⑤ ④ ③ ② ⑥ ⑦ ① ⑧ ⑭ GM-11 Hyuganada-Coast ⑧ ⑭ ⑤ ④ ③ ② ⑥ ⑦ ① GM-12 Nihonkai-Centrall ⑤ ③ ④ ② ⑥ ⑦ ① ⑧ ⑭ GM-13 Hokkaido-East Coast ③ ④ ⑤ ⑥ ② ① ⑦ ⑧ ⑭ GM-14 Hyougoken South ⑤ ③ ④ ② ⑥ ⑦ ① ⑧ ⑭ GM-15 San Fernando ④ ⑤ ③ ② ⑥ ⑦ ① ⑧ ⑭ GM-16 人工波2 ③ ⑤ ④ ⑥ ② ① ⑦ ⑧ ⑭
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表 6 失效单元的加权秩和比
Table 6. Rank-sum ratio of failure element
秩R 单元 ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑭ 1 7 4 3 2 1 5 6 8 9 2 7 4 3 2 1 5 6 8 9 3 8 5 4 3 2 6 7 1 9 4 6 5 2 1 3 4 7 8 9 5 7 6 3 2 4 5 8 1 9 6 6 5 1 3 2 4 8 7 9 7 6 5 2 1 3 4 7 8 9 8 7 6 2 3 4 5 8 1 9 9 6 5 1 2 3 4 7 8 9 10 7 4 3 2 1 5 6 8 9 11 9 6 5 4 3 7 8 1 2 12 7 4 2 3 1 5 6 8 9 13 6 5 1 2 3 4 7 8 9 14 7 4 2 3 1 5 6 8 9 15 7 4 2 1 3 5 6 8 9 16 6 5 1 2 3 4 7 8 9 WRSR 0.748 7 0.551 2 0.254 2 0.250 7 0.277 3 0.524 9 0.790 1 0.695 7 0.990 2 失效顺序 7 5 2 1 3 4 8 6 9
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