Random Seismic and Reliability Analysis of Bridges Based on an Improved Frozen Soil-Pile-Cap Interaction Model
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摘要: 在季节冻土区，桥梁结构的抗震设计面临复杂挑战，主要原因在于地震动的不确定性以及冻融效应对土体-桩-桥梁相互作用的影响。本文改进并验证了现有的桩-土相互作用模型，并基于该模型分析了在Ⅷ度随机地震作用下桩基础公路桥梁的动力响应与抗震可靠度。采用概率密度演化方法和等价极值分布理论，选取水平相对位移转角作为桥墩动力性能评价指标，对100次随机地震样本进行结构动力响应分析。结果表明，不同地震时程下桥墩的水平位移差异显著，1号桥墩的位移大于2号桥墩，表明1号桥墩更易受到地震损害，这主要是由于两者的结构形式和几何尺寸不同。此外，季节冻土层对桥梁的位移响应影响较大，通常能减小桥墩的水平位移，但在特定情况下则可能增加位移。2号桥墩在随机地震作用下表现出较小的位移转角，抗震性能优于1号桥墩。抗震可靠度分析结果表明，季节冻土层对桥梁的抗震性能具有积极作用，为季节冻土区桩基础公路桥梁的抗震设计提供了理论依据。Abstract: The seismic design of bridge structures in seasonal frozen soil regions faces significant challenges, primarily due to the uncertainty of ground motion, and the influence of soil freeze-thaw effects on soil-pile-bridge interaction. This study improves and validates an existing pile-soil interaction model, and then, based on this model, analyzes the dynamic response and seismic reliability of pile-supported highway bridges under random earthquakes with an intensity of VIII. Using the probability density evolution method and equivalent extreme value distribution theory, the horizontal relative displacement angle is selected as the dynamic performance evaluation index for the bridge piers. The bridge dynamic responses to 100 random seismic samples are analyzed. The results show that Pier No. 1 has a larger horizontal displacement than Pier No. 2, indicating that Pier No. 1 is more susceptible to earthquake damage. Furthermore, the seasonal frozen soil layer significantly impacts the bridge's displacement response, typically reducing the horizontal displacement of the bridge pier, though it may increase the displacement under certain conditions. Pier No. 2 demonstrates smaller displacement under random earthquake actions, indicating better seismic performance compared to that of Pier No. 1. Seismic reliability analysis reveals that the seasonal frozen soil layer positively affects the seismic performance of the bridge, offering a theoretical foundation for the seismic design of pile-supported highway bridges in seasonal frozen soil regions.
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图 9 原型桥梁三维有限元示意图
Figure 9. Three-dimensional finite element diagram of a prototype bridge
图 11 100条代表性时程样本下桥墩水平相对位移极值
Figure 11. Peak value of pier relative horizontal displacement under 100 representative time-history samples
图 12 第46条代表性样本作用下桥墩水平相对位移时程
Figure 12. Time-history of relative horizontal displacement of pier under the representative sample Article 46
图 13 非冻土情况下不同时刻桥墩相对位移转角的概率分布
Figure 13. Probability distribution of displacement Angle of bridge pier at different time under unfrozen soil condition
图 14 冻土情况下不同时刻桥墩相对位移转角的概率分布
Figure 14. Probability distribution of displacement Angle of bridge pier at different time under frozen soil condition
表 1 t-z 和q-z 曲线对照关系
Table 1. Relationship between t-z and q-z curves
t-z曲线 q-z曲线 z/d t/tmax z/d Q/Qp 0.0016 0.30 0.002 0.25 0.0031 0.50 0.013 0.50 0.0057 0.75 0.042 0.75 0.0080 0.90 0.073 0.90 0.0100 1.00 0.100 1 0.0200 0.70～0.90 0.200 1 — 0.70～0.90 — 1 
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表 2 钢筋混凝土本构参数
Table 2. Constitutive parameters of reinforced concrete material
混凝土 钢筋 参数 约束层 非约束层 参数 纵筋 箍筋 密度/(kg·m−3) 2.5×103 2.5×103 密度/(kg·m−3) 7.85×103 7.85×103 弹模/kPa 3.5×107 3.5×107 弹模/MPa 2.0×105 2.1×105 泊松比 0.2 0.2 应变硬化率 0.01 0.01 抗压强度/kPa 5.4×104 5.0×104 泊松比 0.3 0.3 峰值压应变 0.0025 0.002 屈服强度/MPa 400 300 抗拉强度/kPa 5.1×103 4.4×103 极限强度/MPa 570 420
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表 3 不同抗震可靠度下桥墩相对位移转角阈值（单位：%）
Table 3. Threshold values of pier relative displacement Angle under different seismic reliability（Unit：%）
桥墩 抗震可靠度95% 抗震可靠度85% 抗震可靠度75% 非冻土条件 冻土条件 非冻土条件 冻土条件 非冻土条件 冻土条件 1号墩 4.42 4.34 3.92 3.78 3.64 3.51 2号墩 2.24 2.28 1.98 1.99 1.84 1.85
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