Smoothness Estimation of Super-large Bridges in Railway Line Based on Fitting Railway Plane and Profile
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摘要: 合理评价大跨度桥梁挠曲变形是保障桥上铁路行车平稳和舒适的基本前提. 针对当前大跨度桥梁挠曲变形重要评价指标挠跨比的不足，如忽略了挠曲变形对线路平纵断面的影响，本文基于桥梁挠曲变形曲线的规律以及铁路线路线型的特点，采用最小二乘法分别在平纵断面上将桥梁的挠曲变形曲线拟合成线路的标准线型，并依据铁路线路设计规范对其进行评价. 结合国内某特大桥的工程实例，研究发现：在考虑系统振动的最不利荷载工况下，该特大桥的最小竖曲线和平面曲线半径分别为29.3 km和54 km，符合规范要求；设置垂向预拱可以在一定程度上抵消桥梁竖向挠曲，有利于保持轨道结构的平顺性；本方法能从桥上线路平顺性的角度对桥梁的挠曲变形进行合理评价，可用于指导大跨度桥梁设计以保障铁路行车安全.Abstract: Reasonable evaluation of the flexural deformation of long-span bridges is the basic precondition of guaranteeing service stability and comfort of trains. Considering the limitations of the current evaluation index, the deflection-span ratio, such as the effects of deflection on railway plane and profile being ignored, a new methodology that uses the least-square method to fit the deformation curve into the standard railway line in plane and profile first and then evaluates the smoothness of railway super-large bridge by the Code for Design of Railway Line, was proposed. This method was applied to the engineering example of Wufeng Mountain super-large bridge for validation. Results show that under the worst load conditions of system vibration, the minimum radii of the vertical curve and plane circular curve are 29.3 km and 54 km, respectively, which conform to specification requirements. Setting up a vertical arch can neutralize the vertical deformation to some extent, and is beneficial to keep the regularity of track. The proposed method could evaluate the deformation of bridges properly from the aspect of railway smoothness and is applicable to instruct the design of long-span bridges and ensure the safety of railway operation.
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Key words:
- long-span bridges /
- line smoothness /
- plane and profile /
- the least-square method
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图 3 列车荷载作用下挠曲增加（包含预拱）与梁体曲率的变化规律
Figure 3. Relationship between bridge’s deflection (including the vertical arch) and beam curvature under train load
图 4 桥梁竖向挠曲与最小竖曲线半径关系
Figure 4. Relationship between bridge’s vertical deflection and minimum radius of vertical curve
图 6 横向风荷载作用下挠曲增加与梁体曲率变化规律
Figure 6. Relationship between bridge’s deflection and beam curvature under the lateral loads of wind
图 7 桥梁横向挠曲与最小平面曲线半径关系
Figure 7. Relationship between bridge’s lateral deflection and the minimum radius of plane curve
图 8 横向风荷载作用下桥梁平面曲线段拟合结果
Figure 8. Bridge’s plane curve fitting under the lateral loads of wind
表 1 竖曲线半径限值与挠曲变形峰值的关系
Table 1. Relationship between the limit value of vertical curve radius and the peak value of deflection
竖曲线半径/km 桥梁挠曲变形峰值（不设预拱）/m 桥梁挠曲变形峰值（设置预拱）/m 25 2.25 2.94 20 2.80 3.67 15 3.41 4.87 10 5.61 7.24 
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表 2 竖曲线段评价结果
Table 2. Evaluation of vertical curve
竖曲线（阴影区域） 曲线长度/m 曲率/(×10−5 m−1) 曲线半径/(×104 m) 半径规范最低限值/(×104 m) （1） 40 3.481 2.93 2.5 （2） 20 3.209 3.12 2.5 （3） 15 0.284 3.52 2.5 （4） 15 0.252 3.97 2.5 （5） 20 3.292 3.04 2.5 （6） 40 3.263 3.06 2.5
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表 3 平面曲线段评价结果
Table 3. Evaluation of plane curve
平面曲线（阴影区域） 曲线长度/m 曲率/(×10−5 m−1) 曲线半径/(× 104 m) 半径规范最低限值(× 104 m) (1) 10 1.839 5.4 0.7 (2) 350 −0.356 28.1 0.7 (3) 10 1.839 5.4 0.7
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