Seismic response of ballastless track system with Ⅲ-type slab on bridge considering traveling wave effect
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摘要: 为分析考虑行波效应的El-Centro地震波对轨道桥梁结构动力响应的影响，探究行波效应下扣件纵向阻力、固定支座墩/台顶纵向刚度变化时桥梁构件的受力和变形规律，以简支梁桥为研究对象，基于有限元法和梁-板-轨相互作用原理，在ABAQUS平台建立了11~32 m简支梁桥Ⅲ型板式无砟轨道模型，采用直接加速度法模拟行波效应，根据动力响应分析结果，给出了相应影响因素的建议值。研究结果表明：考虑地震行波效应时，不同工况下的桥梁结构沿纵桥向的受力和变形规律基本一致，但考虑行波效应的地震激励使轨道桥梁结构沿行波传播方向发生位移；随着视波速的增大，各构件纵向最大应力/力变化规律不一致，需要结合视波速进行分析；构件纵向最大位移随着视波速的减小而增加，其中墩/台顶纵向位移变化最显著，增幅达49.8%；采用15.0 kN·组-1或10.0 kN·组-1扣件时，构件的受力与变形基本相同，其中构件最大位移差均小于5.0%；使用4.1 kN·组-1小阻力扣件时，增加了除钢轨外其余构件31.6%以上的拉应力，增加了236.0%的构件位移和948.0%的轨板相对位移，因此，建议选择纵向阻力高于10.0 kN·组-1的扣件；固定支座墩/台顶纵向刚度与构件最大受力/变形呈正相关关系，其中轨道板纵向位移增幅最大，为87.2%，因此，桥上采用小于1.0倍系数值的支座纵向刚度。研究成果可为震区桥上Ⅲ型板式无砟轨道结构的抗震设计提供理论参考。Abstract: To analyze the influence of the El-Centro seismic wave considering the traveling wave effect on the dynamic response of the track-bridge structure, and investigate the force and deformation laws of bridge components when the longitudinal resistance of fasteners and the longitudinal stiffness of the top of the fixed bearing pier/abutment were changed under the traveling wave effect, a simply supported beam bridge was selected as the research object. Based on the finite element method and the principle of beam-slab-rail interaction, a ballastless track model with a Ⅲ-type slab for a simply supported beam bridge of 11-32 m was established on the ABAQUS platform. The direct acceleration method was used to simulate the traveling wave effect. According to the results of dynamic response analysis, recommended values for corresponding influencing factors were proposed. Research results show that when the seismic traveling wave effect is considered, the force and deformation laws along the longitudinal direction of the bridge structure remain basically consistent under different operating conditions. However, seismic excitation considering traveling wave effect causes the displacement of the track-bridge structure along the traveling wave propagation direction. With the increase in the apparent wave velocity, the variation laws of maximum longitudinal stress/force in components differ and should be analyzed in conjunction with apparent wave velocity. The maximum longitudinal displacement of components increases as apparent wave velocity decreases, with the most significant change observed in the longitudinal displacement of the top of the fixed bearing pier/abutment, with an increase of 49.8%. When fasteners with longitudinal resistance of 15.0 kN·set-1 or 10.0 kN·set-1 are used, the force and deformation of components are nearly the same, and the difference in maximum displacement is less than 5.0%. When low-resistance fasteners with 4.1 kN·set-1 are used, the tensile stress in components other than the rail increases by over 31.6%; component displacement increases by 236.0%, and the relative displacement of the track slab increases by 948.0%. Therefore, fasteners with longitudinal resistance of higher than 10.0 kN·set-1 are recommended. The longitudinal stiffness at the top of the fixed bearing pier/abutment is positively correlated with the maximum stress/deformation of components, with the greatest increase found in the longitudinal displacement of the track slab, reaching 87.2%. Therefore, it is suggested that the longitudinal stiffness at bearing on the bridge should not exceed a coefficient value of 1.0. The above research results can provide a theoretical reference for the seismic design of ballastless track structures with a Ⅲ-type slab on bridges in earthquake-prone areas.
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图 4 不同视波速下构件纵向受力包络图
Figure 4. Longitudinal stress/force envelope diagram of components under different apparent wave velocities
图 5 不同视波速下构件纵向位移包络图
Figure 5. Longitudinal displacement envelope diagram of components under different apparent wave velocities
图 6 不同扣件纵向阻力下构件纵向受力包络图
Figure 6. Longitudinal stress/force envelope diagram of components under different longitudinal resistance of fasteners
图 7 不同扣件纵向阻力下构件纵向位移包络图
Figure 7. Longitudinal displacement envelope diagram of components under different longitudinal resistance of fasteners
图 8 不同支座纵向刚度下构件纵向受力包络图
Figure 8. Longitudinal stress/force envelope diagram of components under different longitudinal stiffness of support
图 9 不同支座纵向刚度下构件纵向位移包络图
Figure 9. Longitudinal displacement envelope diagram of components under different longitudinal stiffness of support
表 1 各结构材料参数
Table 1. Individual structural material parameters
结构名称 钢轨 轨道板 自密实混凝土层 凸台 弹性垫层 底座板 梁体 混凝土强度 C60 C40 C40 C40 C50 弹性模量/Pa 2.10×1011 3.65×1010 3.40×1010 3.40×1010 2.50×107 3.40×1010 3.55×1010 密度/(kg·m-3) 7 830 2 500 2 500 2 500 1 900 2 500 2 500 泊松比 0.3 0.2 0.2 0.2 0.2 0.2 0.2 
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表 2 不同视波速下构件纵向受力最值
Table 2. Minimum/maximum longitudinal stress/force of components under different apparent wave velocities
视波速/(m·s-1) 钢轨应力/MPa 轨道板应力/MPa 自密实混凝土层应力/MPa 底座板应力/MPa 墩/台顶力/MN 540 -166.066/124.607 -0.164/0.067 -0.102/0.077 -0.705/0.239 3.089 800 -131.099/109.477 -0.128/0.104 -0.086/0.085 -0.533/0.420 1.867 1 600 -125.506/112.762 -0.122/0.113 -0.091/0.089 -0.501/0.460 1.417 3 200 -124.064/113.713 -0.125/0.115 -0.094/0.090 -0.518/0.471 1.353 +∞ -122.915/114.828 -0.127/0.117 -0.089/0.090 -0.526/0.479 1.291
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表 3 不同视波速下构件纵向位移绝对值最大值
Table 3. Maximum absolute values of longitudinal displacement of components under different apparent wave velocities
视波速/(m·s-1) 钢轨位移/mm 轨道板位移/mm 自密实混凝土层位移/mm 底座板位移/mm 墩/台顶位移/mm 轨板相对位移/mm 540 71.426 72.179 72.165 72.172 72.782 21.988 800 52.031 52.469 52.460 52.467 52.783 16.328 1 600 49.241 49.718 49.710 49.716 49.980 15.401 3 200 48.449 48.931 48.923 48.929 49.180 15.152 +∞ 47.866 48.350 48.342 48.348 48.586 14.957
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表 4 不同扣件纵向阻力下构件纵向受力最值
Table 4. Minimum/maximum longitudinal stress/force of components under different longitudinal resistance of fasteners
扣件纵向阻力/(kN·组-1) 15.0 10.0 4.1 扣件力/kN -15.0/15.0 -10.0/10.0 -4.1/4.1 钢轨应力/MPa -166.066/124.607 -150.304/120.079 -82.721/80.686 轨道板应力/MPa -0.164/0.067 -0.148/0.057 -0.120/0.075 自密实混凝土层应力/MPa -0.102/0.077 -0.084/0.050 -0.061/0.370 底座板应力/MPa -0.705/0.239 -0.654/0.222 -0.550/0.360
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表 5 不同扣件纵向阻力下构件纵向位移绝对值最大值
Table 5. Maximum absolute values of longitudinal displacement of components under different longitudinal resistance of fasteners
扣件纵向阻力/(kN·组-1) 15.0 10.0 4.1 钢轨位移/mm 71.426 72.791 46.260 轨道板位移/mm 72.179 73.918 242.300 自密实混凝土层位移/mm 72.165 73.905 242.284 底座板位移/mm 72.172 73.911 242.310 轨板相对位移/mm 21.988 20.916 230.380
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表 6 不同支座纵向刚度构件纵向受力最值
Table 6. Minimum/maximum longitudinal stress/force of components under different longitudinal stiffness of support
支座纵向刚度 0.5k0 1.0k0 2.0k0 扣件力/kN -15/15 -15/15 -15/15 钢轨应力/MPa -118.970/ 78.824 -166.066/ 124.607 -227.466/ 182.005 轨道板应力/MPa -0.150/ 0.056 -0.164/ 0.067 -0.253/ 0.095 自密实混凝土层应力/MPa -0.096/ 0.070 -0.102/ 0.077 -0.141/ 0.080 底座板应力/MPa -0.635/ 0.136 -0.704/ 0.238 -1.127/ 0.430 墩/台顶力/MN 2.729 3.089 3.603
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表 7 不同支座纵向刚度下构件纵向位移绝对值最大值
Table 7. Maximum absolute values of longitudinal displacement of components under different longitudinal stiffness of support
支座纵向刚度 0.5k0 1.0k0 2.0k0 钢轨位移/mm 42.241 71.427 109.040 轨道板位移/mm 42.740 72.179 110.146 自密实混凝土层位移/mm 42.729 72.165 110.125 底座板位移/mm 42.735 72.172 110.137 墩/台顶位移/mm 43.152 72.782 110.833 轨板相对位移/mm 14.282 21.988 31.746
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