ProbabilisticSeismic Risk Assessment of Bridge Retrofit with BRB Based on Cloud Method
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摘要: 排架墩在中小跨径公路桥梁和城市高架桥中应用广泛，历次破坏性地震中也暴露出了其显著的震害问题。为了提升排架墩桥梁的整体抗震能力，本研究采用防屈曲支撑（Buckling-Restrained Braces, BRB）作为保险丝构件，以实现对排架墩的地震损伤控制。选取一座典型的五跨连续梁桥作为研究对象，对4组不同排架墩进行基于位移的抗震性能提升设计，并使用OpenSees软件建立全桥动力分析模型。选取特定地震动记录，以桥墩位移延性系数和支座剪应变为损伤指标，通过云图法对安装BRB前后桥梁进行概率地震需求分析，对比其概率地震需求模型、易损性曲线和危险性曲线，重点研究关键承重构件的易损性曲面随初始刚度比和屈服位移比的变化情况。结果表明，安装BRB后，各个桥墩的损伤得到了明显控制，且初始刚度比和屈服位移比对损伤控制起到了关键作用。同时，安装BRB对各个支座的损伤也产生了一定影响，在轻微损伤状态下，其影响不大，但在完全破坏状态下则存在明显差异。在相同损伤状态下，桥墩的地震损伤超越概率随初始刚度比的增加而减少，且随屈服位移比的增加而下降，并逐渐趋于稳定。Abstract: Bridge bents are extensively used in urban viaducts and small and medium-span highway bridges. However, significant damage to them has been frequently observed in recent devastating earthquakes. Buckling-restrained braces (BRB) are used as fuse members to control the seismic damage of bridge bents and enhance the seismic performance of the entire bridge supported by bridge bents. The displacement-based seismic design method is applied to enhance the seismic performance of four sets of bridge bents in a standard five-span continuous girder bridge. A dynamic analysis model of the entire bridge is created using OpenSees and nonlinear time-history analysis is conducted under a set of ground motions. The displacement ductility factor of the bridge bents and the shear strain of the bearings are used as damage indices and the cloud diagram method is applied to perform a probabilistic seismic demand analysis of the bridge before and after retrofitting with BRBs. The probabilistic seismic demand models, fragility curves, and hazard curves are compared and the change of fragility surfaces of the key load-bearing members with the initial stiffness ratio and the yield displacement ratio is primarily focused on. The results demonstrate that the damage to each bridge bent is effectively controlled with the BRB incorporation and the initial stiffness ratio and yield displacement ratio play a crucial role in controlling effect. Meanwhile, the incorporation of BRB has a certain effect on the damage to each bearing, and the difference of the effect is not significant under the slight damage state, while there is a wide difference under the complete damage state. In the same damage state, the exceedance probability of seismic damage for bridge bents decreases as the initial stiffness ratio and the yield displacement ratio increase.
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图 1 全桥动力分析有限元模型
Figure 1. Finite element model for dynamic analysis of the entire bridge
图 3 选取地震动记录Mw-R分布和反应谱
Figure 3. Distribution of selected ground motion records （Mw-R） and response spectra
图 5 设置BRB与否桥墩易损性曲线对比
Figure 5. Comparison of bents fragility curves with and without BRB
图 6 1#桥墩易损性随α变化情况
Figure 6. Variation of fragility of bents 1# with respect to changes in α
图 7 2#桥墩易损性随α变化情况
Figure 7. Variation of fragility of bents 2# with respect to Changes in α
图 8 1#桥墩易损性随β变化情况
Figure 8. Variation of fragility of bents 1# with respect to changes in β
图 9 2#桥墩易损性随β变化情况
Figure 9. Variation of fragility of bents 2# with respect to changes in β
表 1 铅芯橡胶支座（LRB）性能参数
Table 1. Performance parameters of lead rubber bearings （LRB）
构件 型号 FN/kN Fy/kN Ke/(kN·m−1) Kd/(kN·m−1) 桥台 Y4 Q620×229 2 700 142 7 100 1 100 桥墩 Y4 Q670×232 3 200 162 8 600 1 300 
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表 2 桥墩基本设计参数
Table 2. Basic design parameters of pier
关键参数 1#墩、4#墩 2#墩、3#墩 墩高/m 9 16 设计位移xd /m 0.0348 0.0590 设计地震力Fd /kN 2.48 2.8 屈服位移比α 1.9 2.5
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表 3 前5阶周期和振型
Table 3. The first five orders of periods and vibration modes
阶数 周期/s 振型描述 振型图 1阶 0.87 主梁沿纵桥向1阶振动 
2阶 0.85 主梁沿横桥向1阶振动 
3阶 0.68 主梁沿横桥向2阶振动 
4阶 0.42 主梁沿横桥向3阶振动 
5阶 0.26 主梁沿纵桥向2阶振动和桥墩纵向振动 
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表 4 BRB具体设计参数
Table 4. Specific design parameters of BRB
布置形式 单斜式 单斜式（双层） 位移放大系数f1 0.591 0.625 轴向屈服强度FRy/kN 1427 496 轴向屈服位移ΔRy/mm 5.35 7.45 轴向初始刚度KRi/(kN·m−1) 2.7×105 6.7×104 轴向设计强度FRd/kN 1512 536 轴向设计位移ΔRd/mm 21.4 37.2 核心段长度LRC/m 4.55 6.34 设计长度比ϕ 0.408 0.611 长度比允许范围 0.318<ϕ<1.0 0.49<ϕ<1.0 截面有效面积AR/m2 5.8×10−3 2.05×10−3
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表 5 各桥墩损伤指标计算结果
Table 5. Calculation results of damage indices for each bridge bents
桥墩 墩高/m μcy1 μcy μc4 μcmax 1#墩 9 1.00 1.36 4.02 7.02 2#墩 16 1.00 1.18 4.35 7.35 3#墩 9 1.00 1.36 4.02 7.02 4#墩 16 1.00 1.18 4.35 7.35
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表 7 桥墩地震反应回归分析
Table 7. Regression analysis of bridge bents seismic response
位置 方程 $ {R}^{2} $ $ {\beta }_{\mathrm{D}} $ 1#桥墩（原桥） y= 0.59853 x+0.36956 0.80907 0.21947 1#桥墩（设置BRB） y= 0.45854 x−0.44464 0.77880 0.18446 2#桥墩（原桥） y= 0.75474 x+1.11335 0.86042 0.22946 2#桥墩（设置BRB） y= 0.63247 x+0.75290 0.84892 0.20140
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表 8 支座地震反应回归分析
Table 8. Regression analysis of bearing seismic response
位置 方程 $ {R}^{2} $ $ {\beta }_{\mathrm{D}} $ 桥台处支座（原桥） y= 1.07422 x+0.61171 0.8393 0.3548 桥台处支座（设置BRB） y= 1.07349 x+0.54506 0.85338 0.33586 1#桥墩处支座（原桥） y= 1.08723 x+0.51508 0.85599 0.33661 1#桥墩处支座（设置BRB） y= 0.99210 x+0.52897 0.86477 0.29613 2#桥墩处支座（原桥） y= 0.96618 x−0.12621 0.77819 0.38936 2#桥墩处支座（设置BRB） y= 1.00716 x+0.18282 0.84231 0.32893 注：R2为相关系数；βD为地震需求D的对数标准差。
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