Multidirectional seismic performance evaluation of concrete-filled steel tube pier-continuous beam bridges based on endurance time method
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摘要:
针对多跨连续梁桥在多向地震动作用下的强非线性响应，提出了一种基于耐震时程法的钢管混凝土桥墩抗震性能评估方法；采用高精度有限元软件ABAQUS，基于混合强化-韧性损伤模型与约束混凝土三轴塑性-损伤模型，利用实体-壳单元构建了两跨连续梁桥的精细有限元模型，并通过双向振动台试验数据进行了验证，以确保模型的准确性；引入耐震时程法分析技术，利用人工合成的多维耐震时程曲线，模拟不同地震强度和方向下钢管混凝土桥墩的非线性动力响应与损伤演化过程，量化了桥墩在各工况下的位移响应及损伤程度，并评估了传统组合方法在多向地震输入下的适用性与准确性。研究结果表明：试验与有限元分析结果的一致性验证了模型的可靠性；以控制墩P2为例，多向地震作用下横桥向最大位移由约26 mm增大至32~40 mm，对应位移角为3.99%~5.02%，部分工况超过4%的关键性能限值；此外，与耐震时程分析结果相比，传统的平方和开平方根与100%/30%组合方法在典型双向工况下将P2墩轴向力由316.69~320.39 kN保守放大至407.19~440.55 kN，高估幅度为27%~39%，主要是由于地震动各方向存在相位差及结构的非线性响应，导致传统方法难以充分考虑多向耦合效应和真实动力特性，从而影响抗震性能的准确评估。在实际工程设计中，关键构件的抗震设计应结合时程分析，充分考虑地震动的相位差与耦合效应，综合运用多种评估方法，在安全性与经济性之间取得更优平衡。
Abstract:To address the strongly nonlinear response of multi-span continuous girder bridges under multi-directional seismic excitation, this paper proposes an endurance time method (ETM)-based approach for assessing the seismic performance of concrete-filled steel tube (CFST) bridge piers. A refined finite element model of a two-span continuous girder bridge is developed using the high-fidelity FE software ABAQUS with solid-shell elements, incorporating a combined hardening-ductile damage model and a triaxial plastic-damage model for confined concrete. The model is validated against bidirectional shaking-table test data to ensure its accuracy. Subsequently, the ETM analysis technique is introduced. Artificially generated multi-component endurance time acceleration functions are employed to simulate the nonlinear dynamic response and damage evolution of CFST piers under different seismic intensities and directions, to quantify the displacement response and damage level of the piers under various scenarios, and to evaluate the applicability and accuracy of conventional combination rules under multi-directional seismic inputs. The results show that the good agreement between the experimental and numerical responses confirms the reliability of the proposed model. Taking the controlling pier P2 as an example, under multi-directional seismic excitation, its maximum transverse displacement increases from approximately 26 mm to 32-40 mm, corresponding to drift ratios of 3.99%-5.02%, and in some cases exceeds the critical performance limit of 4%. Furthermore, compared with the ETM-based time-history analysis, the traditional square-root-of-sum-of-squares (SRSS) and 100%/30% combination rules conservatively amplify the axial force of pier P2 from 316.69-320.39 kN to 407.19-440.55 kN under typical bidirectional loading, resulting in an overestimation of approximately 27%-39%. This discrepancy mainly arises from the phase differences among ground-motion components and the nonlinear structural response, which make it difficult for the conventional rules to adequately capture multi-directional coupling effects and the actual dynamic characteristics, thereby compromising the accuracy of seismic performance evaluation. In practical bridge design, it is recommended that the seismic design of critical components be supplemented by time-history analysis that explicitly accounts for ground-motion phase differences and coupling effects. An integrated application of multiple assessment approaches should be adopted to achieve an improved balance between safety and economy.
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图 4 基于三维实体-壳单元的精细有限元模型在整体桥梁系统中的应用(单位：mm)
Figure 4. Application of 3D solid-shell element-based refined finite element model in the overall bridge system (unit: mm)
图 5 试验结果与有限元结果的时程曲线对比
Figure 5. Comparison of time-history curves between experimental results and finite element results
图 6 试验与有限元墩底屈曲形态对比
Figure 6. Comparison of the pier base buckling modes between experimental and finite element results
图 7 x方向时程曲线及累计最大位移曲线
Figure 7. Time history curves and cumulative maximum displacement curves in the x direction
图 8 y方向时程曲线及累计最大位移曲线
Figure 8. Time history curves and cumulative maximum displacement curves in the y direction
图 10 性能水准判定随时间曲线
Figure 10. Performance level determination as a function of time curves
表 1 两跨连续梁桥x方向峰值位移
Table 1. Peak displacement in x-direction of two span continuous beam bridge
桥墩 P1 P2 P3 正向 负向 正向 负向 正向 负向 有限元结果/m 0.013 09 -0.014 87 0.015 89 -0.017 15 0.015 384 -0.017 52 试验结果/m 0.013 70 -0.014 56 0.013 42 -0.014 64 0.017 010 -0.018 49 误差/% 4.45 2.12 15.54 14.64 10.57 5.54 
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表 2 两跨连续梁桥y方向峰值位移
Table 2. Peak displacement in y-direction of two span continuous beam bridge
桥墩 P1 P2 P3 正向 负向 正向 负向 正向 负向 有限元结果/m 0.018 24 -0.019 47 0.018 68 -0.020 83 0.020 917 -0.025 467 试验结果/m 0.020 71 -0.021 30 0.018 43 -0.019 21 0.023 380 -0.023 140 误差/% 11.92 8.59 1.34 7.78 11.78 9.14
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表 3 加载维度和方向
Table 3. Loading dimensions and directions
工况 维度 主方向 输入地震波 1 1 x gx 2 1 y gy 3 2 x gx+0.85gy 4 2 y 0.85gx+gy 5 3 x gx+0.85gy+0.65z 6 3 y 0.85gx+gy+0.65z 7 1 z gz 8 2 x gx+0.85gz 9 2 y gy+0.85gz
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表 4 P2墩最大位移及轴向力
Table 4. Maximum displacements and axial forces of pier P2
工况 输入地震波 x-最大位移/mm y-最大位移/mm z-轴向力/kN 1 gx 13.64 0.00 301.66 2 gy 0.00 25.95 311.27 3 gx+0.85gy 16.06 32.41 316.69 4 0.85gx+gy 14.63 40.19 320.39 5 gx+0.85gy+0.65z 16.46 31.93 674.36 6 0.85gx+gy+0.65z 14.84 39.35 697.73 7 gz 0.00 0.00 988.90 8 gx+0.85gz 15.77 0.00 810.59 9 gy+0.85gz 0.00 25.48 849.49
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表 5 IO、LS以及CP对应的位移角
Table 5. Drift ratio corresponding to IO, LS, and CP
阶段 IO LS CP 位移角θ/% 1 2 4
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表 6 各工况下x、y方向最大位移及性能水准判定
Table 6. Displacements in x and y directions and performance level assessment for each load case
工况 x方向位移角 y方向位移角 性能水准判定 1 13.64/801≈1.70% 介于IO(1%)与LS(2%)之间 2 25.95/801≈3.24% 介于LS(2%)与CP(4%)之间 3 16.06/801≈2.00% 32.41/801≈4.05% y方向已大于4%, 超CP 4 14.63/801≈1.83% 40.19/801≈5.02% y方向大于4%, 超CP 5 16.46/801≈2.06% 31.93/801≈3.99% x超2%(达LS)，y接近4%(临近CP) 6 14.84/801≈1.85% 39.35/801≈4.91% y方向大于4%，超CP 7 0 0 不涉及水平位移(纯竖向) 8 15.77/801≈1.97% 介于IO(1%)与LS(2%)之间 9 13.12/801≈1.64% 介于IO(1%)与LS(2%)之间 10 25.48/801≈3.18% 介于LS(2%)与CP(4%)之间 11 23.76/801≈2.96% 介于LS(2%)与CP(4%)之间
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表 7 SRSS与100%/30%准则组合方法的轴向力
Table 7. Axial force based on the srss and 100%/30% combination method
工况 Fz/kN FSRSS/kN F100%/30%/kN (FSRSS-Fz)/Fz/% (F100%/30%-Fz)/Fz/% 1 301.66 2 311.27 3 316.69 440.55 407.19 39.11 28.58 4 320.39 440.55 407.19 3 750 27.09
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