Equivalent method for designed earthquake-induced track geometric irregularities on high-speed railway bridges
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摘要: 为解决考虑结构随机的设计震致轨道几何不平顺等效问题，建立了高速铁路轨道-桥梁系统的数值仿真模型，基于短时傅里叶变换和假设检验原理构造了设计震致轨道几何不平顺，建立了设计震致轨道几何不平顺的等效拟合模型和等效幅值反应谱，提出了考虑结构随机的等效幅值反应谱修正方法，结合震后实测轨道几何不平顺对设计震致轨道几何不平顺等效方法的合理性展开了评价。分析结果表明：在不同墩高条件下，采用正弦函数和一次函数的组合作为等效拟合模型可将设计震致轨道几何不平顺的拟合误差控制在10%以内；在设防地震和罕遇地震作用下，当修正系数分别取为3.0和1.5时，等效拟合模型与修正系数相乘得到的修正拟合模型可以满足随机结构的适用性需求；地震前后实测轨道几何不平顺形状和幅值均无明显差异，对应的横向车体加速度幅值误差小于5%，当地震强度较小时列车可正常运行，无需大幅度减速；与震后实测轨道几何不平顺相比，设计震致轨道几何不平顺使横向车体加速度幅值提升了近50%，基于设计震致轨道几何不平顺计算得到的震后行车速度阈值具有合理安全余量；建立的高速铁路桥上设计震致轨道几何不平顺等效方法可为高速铁路震后行车速度阈值确定与基于震后行车性能的抗震设计提供快速准确的手算方法。Abstract: In order to solve the equivalent problem of designed earthquake-induced track geometric irregularities considering structural randomness, a numerical simulation model of high-speed railway track-bridge system was established. Based on the short-time Fourier transform and the hypothesis testing principle, designed earthquake-induced track geometric irregularities were constructed. The equivalent fitting models and equivalent amplitude response spectra of designed earthquake-induced track geometric irregularities were established. A method for correcting the equivalent amplitude response spectrum considering structural randomness was proposed, and the rationality of the equivalent method for designed earthquake-induced track geometric irregularities was evaluated by comparing to measured geometric track irregularities after earthquake. Analysis results show that the fitting errors of designed earthquake-induced track geometric irregularities can be controlled below 10% under different pier height conditions by the combination of sine function and linear function. When the correction coefficients under seismic fortification and rare earthquakes are set to 3.0 and 1.5, the applicability of the modified fitting model obtained by multiplying the equivalent fitting model and the correction coefficient to random structures can meet the requirements. There is not significant difference in the shape and amplitude of measured geometric track irregularities before and after earthquake, and the corresponding amplitude error of lateral vehicle body acceleration is less than 5%. When the earthquake intensity is low, train can operate normally without significant deceleration. Compared with the measured geometric track irregularities after earthquakes, designed earthquake-induced track geometric irregularities increase the amplitude of lateral vehicle body acceleration by nearly 50%, and the driving speed threshold after earthquake calculated based on designed earthquake-induced geometric track irregularities has a reasonable safety margin. The established equivalent method for designed earthquake-induced track geometric irregularities on high-speed railway bridges can provide a fast and accurate manual calculation method for determining the driving speed threshold after earthquake and earthquake-resistant design based on driving performance after earthquake.
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图 1 高速铁路轨道-桥梁系统数值仿真模型
Figure 1. Numerical simulation model of high-speed railway track-bridge system
图 4 震致轨道几何不平顺集和设计震致轨道几何不平顺
Figure 4. Earthquake-induced track geometric irregularity set and designed earthquake-induced track geometric irregularity
图 5 设计震致轨道几何不平顺激励下的横向车体加速度曲线
Figure 5. Lateral vehicle body acceleration curve under excitation of designed earthquake-induced track geometric irregularity
图 6 震致轨道几何不平顺集激励下的横向车体加速度峰值
Figure 6. Peak lateral vehicle body accelerations under excitation of earthquake-induced track geometric irregularity set
图 7 不同跨数条件下的设计震致轨道几何不平顺
Figure 7. Designed earthquake-induced track geometric irregularities under different span conditions
图 8 不同跨数条件下的横向车体加速度曲线
Figure 8. Lateral vehicle body acceleration curves under different span conditions
图 9 设计震致轨道几何不平顺与其等效拟合模型
Figure 9. Designed earthquake-induced track geometric irregularity and its equivalent fitting model
图 10 设计震致轨道几何不平顺与其等效拟合模型激励下横向车体加速度曲线
Figure 10. Lateral vehicle body acceleration curves under excitations of designed earthquake-induced track geometric irregularities and their equivalent fitting models
图 11 设计震致轨道几何不平顺的等效幅值反应谱
Figure 11. Equivalent amplitude response spectra of designed earthquake-induced track geometric irregularity
图 12 设计震致轨道几何不平顺的等效横向车体加速度谱
Figure 12. Equivalent lateral vehicle body acceleration spectra of designed earthquake-induced track geometric irregularity
图 13 具有明显局部折角的设计震致轨道几何不平顺
Figure 13. Designed earthquake-induced track geometric irregularities with significant local bending angles
图 14 不同地震强度下横向车体加速度峰值的比值集合
Figure 14. Ratio sets of peak lateral vehicle body acceleration under different earthquake intensities
图 15 不同样本量下比值元素的样本均值和样本标准差
Figure 15. Sample means and sample standard deviations of ratio element under different sample sizes
图 16 不同修正系数下的比值上界
Figure 16. Ratio upper bounds under different correction coefficients
图 18 地震前后实测轨道不平顺激励下的横向车体加速度曲线
Figure 18. Lateral vehicle body acceleration curves under excitations of measured track irregularities before and after earthquake
图 19 初始轨道几何不平顺和设计震致轨道几何不平顺激励下的横向车体加速度
Figure 19. Lateral accelerations of vehicle body under excitations of initial track geometric irregularity and designed post-earthquake track geometric irregularity
表 1 非线性弹簧单元的水平向力-位移关系
Table 1. Horizontal force-displacement relationship of nonlinear spring elements
构件 屈服力/kN 屈服位移/mm 横向 纵向 横向 纵向 剪力齿槽 1 465 1 465 0.12 0.12 固定支座 1 000 1 000 2.00 2.00 滑动支座 100 100 2.00 2.00 侧向挡块 453 0 2.00 0.00 水泥沥青砂浆层 42 42 0.50 0.50 钢轨扣件 24 9 2.00 2.00 剪切钢筋 23 23 0.08 0.08 滑动层 6 6 0.50 0.50 
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表 2 Yd与Yf下横向车体加速度峰值与误差
Table 2. Peak lateral vehicle body accelerations and errors under Yd and Yf
墩高/m 设防地震 罕遇地震 Yd下加速度峰值/(m·s-2) Yf下加速度峰值/(m·s-2) 误差/% Yd下加速度峰值/(m·s-2) Yf下加速度峰值/(m·s-2) 误差/% 5 0.022 0.023 4 0.143 0.133 -8 6 0.023 0.024 4 0.141 0.140 -1 7 0.024 0.025 4 0.140 0.133 -5 8 0.024 0.026 8 0.139 0.132 -5 9 0.024 0.025 4 0.140 0.150 7 10 0.027 0.028 4 0.145 0.152 5 11 0.027 0.028 4 0.153 0.148 -3 12 0.030 0.031 3 0.156 0.144 -8 13 0.030 0.031 3 0.171 0.159 -8 14 0.031 0.032 3 0.174 0.165 -5 15 0.037 0.037 0 0.178 0.175 -2 16 0.041 0.042 2 0.190 0.197 4 17 0.046 0.047 2 0.232 0.252 8 18 0.053 0.055 4 0.220 0.221 0 19 0.061 0.060 -2 0.212 0.228 7 20 0.069 0.073 5 0.212 0.228 7
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