Characteristics of sudden cable fracture and train-bridge coupled vibration of highway-railway cable-stayed bridge
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摘要:
为研究公铁两用斜拉索在运营状态下发生突然断索事故对桥梁结构安全性与桥上列车行驶安全性的影响，开发了基于显式非线性有限元动力算法的列车-桥梁耦合振动计算程序；以实际大跨度公铁两用斜拉桥为研究对象，构建了全桥三维有限元模型；使用静力非线性有限元法计算了桥梁在恒载下的成桥状态；使用显式非线性有限元法，计算了多根斜拉索连续断索时桥梁结构的动力响应，对斜拉索断索下坠与主梁接触碰撞后的位置进行了计算分析，计算了不同工况列车-桥梁耦合振动作用下突发断索时桥梁与列车的动力响应。研究结果表明：显式有限元法能简便直观地模拟斜拉桥断索破坏，在列车-桥梁耦合振动计算中兼具精度与效率优势，具有更好的技术适用性；斜拉桥结构安全冗余度高，断索后剩余拉索可有效分担荷载，在单侧连续断索超10根的极端情况下，主梁才可能发生垮塌；在风速达到30 m·s-1的横向风作用下，斜拉索断索容易坠入主梁上层桥面；单根斜拉索断索后，列车可保持通行；跨中最长拉索34#断索瞬间，主梁竖向与横向位移突变显著，主梁竖向加速度突变至约20 m·s-2；当列车以200 km·h-1的速度在桥上行驶时，中跨右侧最长拉索34#突发断索，极端工况下，短时间内，轮重减载率最大达到约0.91，脱轨系数最大达到约2.73，断索产生的主梁振动使列车面临明显的脱轨风险。研究结果可以为斜拉桥发生断索时的安全评估提供参考。
Abstract:To investigate the impact of sudden cable fracture accidents on the safety of bridge structures and running trains under operational conditions for highway-railway cable-stayed bridges, a train-bridge coupled vibration calculation program based on the explicit nonlinear finite element dynamic algorithm was developed. A three-dimensional full-bridge finite element model of an actual long-span highway-railway cable-stayed bridge was constructed. The completed bridge state under dead load was calculated by using the static nonlinear finite element method. By using the explicit nonlinear finite element method, the dynamic response of the bridge structure under continuous fractures of multiple stay cables was calculated. The positions of the fractured stay cables after falling and colliding with the main girder were calculated and analyzed. Furthermore, the dynamic responses of the bridge and train under a sudden cable fracture were calculated under different train-bridge coupled vibration conditions. The results indicate that the explicit finite element method can simply and intuitively simulate the cable fracture damage of cable-stayed bridges, possesses advantages in both accuracy and efficiency in the calculation of train-bridge coupled vibration, and has better technical applicability. The cable-stayed bridge structure has a high safety redundancy, and the remaining cables can effectively share the load after a cable fracture. The main girder may collapse only in an extreme case where more than 10 continuous stay cables fracture on one side. Under the action of a transverse wind with a speed of 30 m·s-1, the fractured stay cable is prone to fall onto the upper deck of the main girder. After the fracture of a single stay cable, trains can maintain passage. At the moment of fracture of the longest stay cable 34# at the mid-span, the vertical and transverse displacements of the main girder change abruptly and significantly, and the vertical acceleration of the main girder jumps to approximately 20 m·s-2. When a train travels on the bridge at a speed of 200 km·h-1, and the longest stay cable 34# on the right side of the mid-span suddenly fractures, under extreme conditions, the maximum wheel load reduction rate reaches approximately 0.91, and the maximum derailment coefficient reaches approximately 2.73 within a short period of time. The main girder vibration caused by the cable fracture exposes the train to an obvious derailment risk. The research results can provide a reference for the safety assessment of cable-stayed bridges when cable fracture accidents occur.
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图 3 基于显式有限元法的列车-桥梁耦合振动计算流程
Figure 3. Calculation flow of train-bridge coupling vibration based on EFEM
图 5 斜拉桥前4阶模态计算结果
Figure 5. Calculation results of the first 4 modes of cable-stayed bridge
图 8 简支梁列车-桥梁耦合振动计算结果
Figure 8. Calculation results of simply supported beam train-bridge coupled vibration
图 9 右侧拉索34#断索后桥梁结构动力响应（不计碰撞）
Figure 9. Dynamic response of bridge structure after fracture of right side cable 34# (without considering the collision)
图 10 右侧拉索34#至25#发生连续断索极限状态计算结果（不计碰撞）
Figure 10. Calculation results for continuous cable fracture limit state of right side cables 34# to 25# (without considering the collision)
图 11 石家庄滹沱河大桥断索事故
Figure 11. Cable fracture accident of Hutuo River Bridge in Shijiazhuang
图 12 不同风速下拉索34#断索下坠轨迹
Figure 12. Falling trajectory of cable 34# when it fractures under different wind speeds
图 13 横向风速30 m·s-1作用下拉索34#下坠与桥面碰撞接触计算结果
Figure 13. Calculation results of collision and contact between the falling 34# cable and the bridge deck under the action of a transverse wind speed of 30 m·s-1
图 16 工况1、4、5下桥梁位移与加速度响应
Figure 16. Bridge displacement and acceleration responses under working conditions 1, 4 and 5
表 1 列车作用下发生断索时各个计算工况
Table 1. Calculation conditions with cable fracture occurring under train effects
工况 列车信息 断索时第1轮对位置 突发断索编号 1 1列（8节） 无断索 2 1列（16节） 无断索 3 1列（16节） 右侧拉索34#已断索，桥梁处于静止状态 4 1列（8节） 主梁位移最大时 右侧拉索34# 5 1列（8节） 拉索34#锚固点位置 右侧拉索34# 
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