Seismic Response and Damage Analysis of High-speed Railway Continuous Rigid Frame Bridge under Near-fault Ground Motion
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摘要: 为研究考虑轨道约束效应对高速铁路连续刚构桥的地震反应及损伤状态的影响，本文以一座跨径为256（48+2×80+48）m的连续刚构桥为对象进行研究。通过模拟连续刚构桥的施工过程获得成桥时的真实内力状态，然后基于等效荷载法得到内力等效荷载，并将其施加于OpenSees动力分析模型中，使其处于等效内力状态。输入三维近断层脉冲型地震动进行非线性时程分析。本文首先分析了是否考虑无砟轨道约束对高墩连续刚构桥主梁和桥墩的地震响应，其次分别以曲率延性系数和支座位移作为桥墩和支座的损伤评价指标，对是否考虑轨道约束的连续刚构桥进行损伤分析。结果表明：无砟轨道为连续刚构桥提供了很大的纵向约束，会明显降低主梁各部位（梁端和跨中）沿纵桥向的位移响应，在梁端处最大可降低约1.3倍，在跨中处最大降低约1.25倍；同时沿横桥向轨道约束会降低梁端地震响应，在横桥向可降低55.3%～66.3%，在竖向可降低0.7%～4.2%，但是轨道约束会放大跨中地震峰值位移（1.04倍～1.5倍）。此外，轨道约束在一定程度上也会降低桥墩和桥台处支座的损伤。Abstract: In order to study the effects of track restraint on the seismic response and damage state of high-speed railway continuous rigid frame bridges, a continuous rigid frame bridge with a span of 256 (48+2×80+48) m is taken as the research background. First, the actual internal force state when the bridge is completed is obtained by simulating the construction process of the continuous rigid frame bridge, and then the internal force equivalent load is obtained based on the equivalent load method and applied to the OpenSees dynamic analysis model to make it in the equivalent internal force state. The nonlinear time-history analysis is carried out by inputting three-dimensional near-fault pulse-type ground motions. Firstly, the seismic response of the continuous rigid frame bridge with high pier is analyzed whether the ballastless track constraint is considered or not. Secondly, the curvature ductility coefficient and the displacement of the support are used as the damage evaluation index of the pier and the support. The results show that the ballastless track provides great longitudinal restraint for the continuous rigid frame bridge, which will significantly reduce the displacement response of each part of the main beam (beam end and middle span) along the longitudinal bridge direction; At the beam ends, the maximum reduction can be approximately 1.3 times, and at the mid-span, the maximum reduction is about 1.25 times. Meanwhile, along the transverse bridge direction, track constraints can reduce the seismic response at the beam ends by approximately 55.3% to 66.3% in the transverse direction and by 0.7% to 4.2% in the vertical direction. However, track constraints amplify the mid-span seismic response by 1.04 to 1.5 times; in addition, the track constraint will also reduce the damage of the piers and abutments to a certain extent.
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图 5 桥梁-轨道系统连接件力-位移关系
Figure 5. Force-displacement relationship of bridge-rail system connectors
图 9 主梁沿纵桥向位移时程曲线
Figure 9. Time history curve of main girder displacement along longitudinal bridge
图 10 主梁沿纵桥向峰值位移比
Figure 10. Peak displacement ratio of main girder along longitudinal bridge
图 11 主梁沿横桥向位移时程曲线
Figure 11. Time history curve of main girder displacement along cross bridge
图 13 各桥墩墩顶沿纵桥向位移时程曲线及峰值位移比
Figure 13. Time history curve and peak displacement ratio of pier top displacement along longitudinal bridge
图 14 各桥墩墩顶沿横桥向位移时程曲线及峰值位移比
Figure 14. Time history curve and peak displacement ratio of pier top displacement along cross bridge
图 16 主梁沿纵桥向位移分布
Figure 16. Displacement distribution of main girder along longitudinal bridge
表 1 施工阶段分析表
Table 1. Construction phase analysis table
阶段编号 施工阶段 主要施工内容 加载与边界条件 1 桥墩浇筑阶段 1#～3#桥墩分段浇筑，采用滑模、翻模或组合模施工。 桥墩墩底采用固结，不考虑桩土相互作用；加载自重和二期恒载。 2 0#块浇筑 在墩顶托架上浇注0#块，形成悬臂梁施工起点。 激活0#块结构单元并加载自重和二期恒载；维持边界条件不变。 3 悬臂梁段施工 依次对称悬浇A1～A10及A1'～A10'段，使用轻型挂篮。 逐段激活新浇段的单元并加载自重、预应力荷载。 4 中跨合拢 安装中跨合拢撑架，浇筑合拢段。 加载合拢梁段的自重与二期恒载，激活对应结构单元。 5 边跨合拢 依次浇注两侧边跨的A11、A12段，完成边跨悬浇施工。 激活边跨A11、A12段单元并加载自重、二期恒载和预应力荷载。 6 边跨支架现浇 在0#桥台和4#桥台处搭建施工托架，现浇边跨A13段，完成桥梁施工。 激活A13段结构单元，加载自重和二期恒载。 
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表 2 单个纵向连续构件力学参数
Table 2. Mechanical parameters of a single longitudinal continuous member
部件 截面面积/m2 弹性模量/(N·m−2) J/m4 Iy/m4 Iz/m4 密度/(kg·m−3) 摩擦板 3.6 3.00× 1010 0.18 662 0.048 24.3 9 360 底座板 0.561 3.00× 1010 0.00 647 0.00 169 0.406 1 496.85 轨道板 0.51 3.55× 1010 0.00 646 0.0 017 0.276 1 370.6 轨道 0.00 775 2.06× 1011 0.0 000 025 0.0 000 325 0.00 026 60.64
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表 3 BM与BTM中主梁的峰值位移表（单位：厘米）
Table 3. Peak displacement table of main beam in BM and BTM （Unit: cm）
地震动编号 主梁沿纵桥向 [1] 地震动编号 主梁沿纵桥向 梁端 跨中 梁端 跨中 DBM DBTM D DBM DBTM D DBM DBTM D DBM DBTM D E01 31.05 29.51 1.54 30.94 29.46 1.48 E21 29.86 28.11 1.75 30.01 28.22 1.79 E02 49.66 43.83 5.83 49.69 43.83 5.86 E22 18.54 16.55 2.00 18.59 16.47 2.12 E03 29.18 26.29 2.90 29.15 26.24 2.92 E23 22.23 21.95 0.28 22.35 22.05 0.30 E04 23.46 21.24 2.22 23.43 21.24 2.19 E24 15.38 12.23 3.15 15.50 12.35 3.15 E05 27.67 25.06 2.61 27.67 25.11 2.55 E25 13.49 12.92 0.57 13.56 12.95 0.61 E06 24.99 23.92 1.06 24.96 23.93 1.03 E26 13.49 13.08 0.41 13.56 13.13 0.43 E07 9.18 9.64 -0.46 9.19 9.67 -0.48 E27 21.06 20.91 0.15 21.08 20.98 0.11 E08 17.64 15.63 2.01 17.67 15.66 2.01 E28 59.11 63.38 -4.27 58.88 62.98 -4.10 E09 7.42 6.15 1.27 7.38 6.12 1.27 E29 15.39 16.33 -0.94 15.33 16.28 -0.95 E10 12.24 9.84 2.40 12.28 9.87 2.41 E30 26.71 24.82 1.89 26.71 24.82 1.89 E11 21.52 19.66 1.86 21.51 19.64 1.87 E31 46.66 40.12 6.54 46.63 40.12 6.52 E12 15.92 13.13 2.79 15.96 13.16 2.80 E32 27.76 29.60 -1.83 27.83 29.66 -1.83 E13 42.48 39.03 3.45 42.42 39.02 3.40 E33 21.06 19.70 1.36 21.04 19.71 1.34 E14 19.85 18.23 1.62 19.78 18.20 1.57 E34 25.25 22.09 3.16 25.27 22.09 3.18 E15 19.83 18.29 1.54 19.76 18.29 1.47 E35 32.43 27.99 4.44 32.43 27.99 4.44 E16 22.76 20.89 1.87 22.60 20.79 1.81 E36 41.21 36.65 4.57 41.23 36.61 4.62 E17 38.02 41.39 -3.37 37.87 41.56 -3.69 E37 53.26 52.78 0.49 53.04 52.59 0.44 E18 29.93 28.78 1.15 29.80 28.54 1.26 E38 52.80 54.99 -2.19 52.64 54.78 -2.14 E19 25.49 26.48 -0.99 25.53 26.55 -1.02 E39 22.01 19.36 2.65 21.82 19.47 2.34 E20 12.88 10.54 2.34 12.97 10.56 2.41 E40 26.53 28.00 -1.46 26.56 28.01 -1.45 注：D=DBM-DBTM
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表 4 不同破坏状态的描述及损伤指标
Table 4. Description and damage index of different failure states
破坏状态 无损伤 轻微损伤 中等损伤 严重损伤 完全破坏 破坏准则 $ 0 \lt {\mu }_{\phi }\leqslant \mu _{\phi \text{y}}^{\prime} $ $ \mu _{\phi \text{y}}^{\prime} \lt {\mu }_{\phi }\leqslant {\mu }_{\phi \text{y}} $ $ {\mu }_{\phi \text{y}} \lt {\mu }_{\phi }\leqslant {\mu }_{\phi \text{4}} $ $ {\mu }_{\phi \text{4}} \lt {\mu }_{\phi }\leqslant {\mu }_{\phi \text{max}} $ $ {\mu }_{\phi \text{max}} \lt {\mu }_{\phi } $
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表 5 各桥墩在不同损伤状态下的曲率指标
Table 5. Curvature index of each pier under different damage conditions
位置 方向 $ \phi _{\text{y}}^{\prime} $/m−1 $ \phi _{\text{y}}^{} $/m−1 $ \phi _{\text{c4}}^{} $/m−1 $ \phi _{\text{m}}^{} $/m−1 1#墩 纵向 0.00030 0.00034 0.00687 0.00912 横向 0.00014 0.00016 0.00288 0.00412 2#墩 纵向 0.00030 0.00034 0.00681 0.00907 横向 0.00012 0.00014 0.00237 0.00323 3#墩 纵向 0.00030 0.00034 0.00681 0.00910 横向 0.00012 0.00014 0.00246 0.00335
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