Transverse Seismic Response Analysis of Small and Medium-span Highway Bridges in Service Considering Time-varying Characteristics of Materials
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摘要: 构件材料性能会随服役时间的增加而退化，并导致桥梁结构抗震性能存在时变性。为探讨不同服役期下中小跨径桥梁抗震性能变化规律，以3跨预应力混凝土连续桥梁为例，通过分析材料力学性能指标时变性，量化不同服役期构件力学分析模型参数，并考虑桥墩、挡块及支座等构件力学性能退化,采用OpenSees软件建立桥梁有限元分析模型。基于非线性时程分析结果，揭示服役中小跨径桥梁横桥向地震响应时变性。研究结果表明，随着服役时间的增加，材料力学性能发生退化，使中小跨径桥梁各构件抗震能力下降；相同水平地震作用下，中小跨径桥梁主梁及挡块位移响应随服役时间的增加而降低，而桥墩损伤程度加剧，构件震害程度与不考虑构件力学性能时变性时相差较大，其中板式橡胶支座刚度及摩擦系数时变性是关键。因此，在服役中小跨径桥梁抗震分析中，有必要同时考虑桥墩、挡块及支座力学性能退化。Abstract: As the service time of bridge components increases, their material properties degrade, leading to a time-dependent reduction in the seismic performance of the bridge. To investigate the variation in seismic performance of small- and medium-span highway bridges over time, a finite element analysis (FEA) was conducted using a three-span prestressed concrete continuous girder bridge as a case study. This study quantifies the time-varying mechanical properties of components, such as piers, shear keys, and laminated rubber bearings, by incorporating degradation effects into a mechanical analysis model. The bridge FEA model was developed using OpenSees, accounting for the deterioration of key structural elements over time. The analysis reveals that, as service time increases, the degradation of material properties results in a reduced seismic capacity for various components. Under the same seismic event, the displacement response of the main girder and shear key decreases with time, while the damage to the piers becomes more severe. The seismic damage patterns of these components, when accounting for time-varying mechanical properties, differ significantly from those observed without considering such degradation. One critical finding is that the time-dependent variation in stiffness and friction coefficient of laminated rubber bearings plays a crucial role in the overall seismic response. Therefore, in the seismic analysis of small- and medium-span highway bridges, it is essential to consider the concurrent degradation of mechanical properties in piers, shear keys, and laminated rubber bearings to accurately assess their long-term seismic performance.
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图 2 桥墩钢筋锈胀及混凝土剥落
Figure 2. Steel bar rust expansion and concrete spalling of bridge pier
图 11 不同服役期主梁最大位移
Figure 11. Maximum displacement of the main girder with different service time
图 13 不同服役期下D1挡块力-位移曲线
Figure 13. Force-displacement curve of D1 shear key with different service time
图 14 不考虑支座退化时挡块力-位移曲线
Figure 14. Force-displacement curve of D1 shear key without considering degradation of laminated rubber bearing
图 15 考虑桥墩-挡块-支座共同退化后桥墩曲率变化规律
Figure 15. The variation law of pier curvature after co-degradation
表 1 不同服役时间钢筋及混凝土强度
Table 1. Strength of rebar and concrete with different service time
项目 服役时间T/a 0（初始时间） 20 30 40 50 fy/MPa 335 334 332 329 325 fc/MPa 30.0 23.8 20.7 17.8 16.2 
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表 2 不同服役时间挡块强度
Table 2. Strength value of shear key with different service time
项目 强度/kN 服役0年 服役20年 服役30年 服役40年 服役50年 V1y（A点） 469.91 463.58 458.25 451.65 444.95 V1n（B点） 532.86 519.67 510.56 500.16 491.23 V1d（C点） 423.36 422.10 419.56 415.78 410.44
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表 3 不同服役时间挡块位移
Table 3. Displacement value of shear key with different service time
项目 位移/mm 服役0年 服役20年 服役30年 服役40年 服役50年 $ {\varDelta _{1 {\mathrm{y}}}} $（A点） 7.44 7.42 7.37 7.30 7.21 $ {\varDelta _{1 {\mathrm{n}}}} $（B点） 17.5 17.5 17.5 17.5 17.5 $ {\varDelta _{1 {\mathrm{d}}}} $（C点） 70.0 70.0 70.0 70.0 70.0 $ {\varDelta _{1 {\mathrm{u}}}} $（D点） 117.70 117.70 116.35 115.50 113.75
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表 4 不同服时间支座力学性能参数
Table 4. Mechanical property parameters of bearing at different service times
项目 服役时间T/a 0（初始时间） 10 20 30 40 50 剪切模量G/MPa 1.20 1.37 1.49 1.61 1.76 1.88 水平刚度K/MPa 1 293 1 792 2 247 2 914 3 471 3 707 摩擦系数μ 0.2 0.257 0.259 0.259 0.259 0.259
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表 5 桥墩损伤状态划分
Table 5. Pier damage status division
损伤状态 对应曲率/m−1 服役0年 服役20年 服役30年 服役40年 服役50年 无损伤 0≤Φ<1.28×10−3 0≤Φ<1.24×10−3 0≤Φ<1.21×10−3 0≤Φ<1.18×10−3 0≤Φ<1.15×10−3 轻微损伤 1.28×10−3≤Φ<2.14×10−3 1.24×10−3≤Φ<2.07×10−3 1.21×10−3≤Φ<2.03×10−3 1.18×10−3≤Φ<1.98×10−3 1.15×10−3≤Φ<1.95×10−3 中等损伤 2.14×10−3≤Φ<14.12×10−3 2.07×10−3≤Φ<13.24×10−3 2.03×10−3≤Φ<12.71×10−3 1.98×10−3≤Φ<10.96×10−3 1.95×10−3≤Φ<10.64×10−3 严重损伤 14.12×10−3≤Φ<35.58×10−3 13.24×10−3≤Φ<35.69×10−3 12.71×10−3≤Φ<36.72×10−3 10.96×10−3≤Φ<36.84×10−3 10.64×10−3≤Φ<36.95×10−3 完全破坏 Φ≥35.58×10−3 Φ≥35.69×10−3 Φ≥36.72×10−3 Φ≥36.84×10−3 Φ≥36.95×10−3
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表 6 钢筋混凝土挡块损伤状态划分及判断准则
Table 6. Criterion for damage status division and judgment of reinforced concrete shear key
判断准则 损伤状态描述 损伤状态 $ \varDelta \leqslant {\varDelta _{1 {\mathrm{y}}}} $ 钢筋混凝土挡块出现细小裂缝，钢筋不发生屈服。 无损伤 $ {\varDelta _{1 {\mathrm{y}}}}{\text{ < }}\varDelta \leqslant {\varDelta _{1{\text{n}}}} $ 细小裂缝扩大并连成一线，形成主裂缝，挡块内部部分钢筋发生屈服。 轻微损伤 $ {\varDelta _{1 {\mathrm{n}}}}{\text{ < }}\varDelta \leqslant {\varDelta _{1{\text{d}}}} $ 主裂缝由上至下贯穿挡块，且裂缝宽度扩大，同时开始产生新的主裂缝。 中等损伤 $ {\varDelta _{1 {\mathrm{d}}}}{\text{ < }}\varDelta \leqslant {\varDelta _{1{\text{u}}}} $ 数条主裂缝贯穿挡块，且宽度较大，部分钢筋暴露，混凝土大面积破坏。 严重损伤 $ \varDelta {\text{ > }}{\varDelta _{1{\text{u}}}} $ 挡块位移明显，钢筋被拉断，挡块甚至完全脱落。 挡块破坏
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