Analysis on Load Dynamic Stress Characteristics of Embedded Track Subgrade of Tram
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摘要:
掌握有轨电车交通荷载下路基动力响应特性是设计嵌入式轨道路基结构的关键技术前提. 首先，考虑车体间铰接形式、轨道支承特点与路基阻尼影响，构建有轨电车-嵌入式轨道-土质路基耦合动力学模型；然后，以中国普通干线铁路轨道谱为激励，进行动力学仿真；最后，分析路基面承受车辆荷载特点，并讨论动应力放大系数的概率分布特征与沿深度衰减规律. 研究表明：嵌入式轨道结构路基面动应力的幅值受轨道随机不平顺影响服从正态分布规律；在有轨电车轴重11 t、设计速度100 km/h、90%干线轨道谱条件下，路基面动应力放大系数服从正态分布
N (1.008, 0.1002)，超越概率30%的常遇动力系数为1.058，保证率为99.9%的极限动力系数为1.308；受路基材料阻尼影响，动应力放大系数沿深度线性衰减，阻尼增大，衰减趋势加剧；随着深度增加，动应力放大系数均值逐渐减小，由动力作用增大区略大于1过渡到动力作用减弱区小于1.Abstract:Determining the dynamic response characteristics of a subgrade under tram traffic loads is a key technical prerequisite for the design of embedded rail roadbed structures. First, a tram-embedded track-soil subgrade coupling dynamics model is established by considering the articulation forms between the car bodies, track support conditions, and damping effect of the subgrade. Then, dynamics simulations are performed using the track irregularity PSD of the China railway (CR) as excitation. Finally, the vehicle load characteristics on the subgrade surface are analyzed and the probability distribution characteristics of the dynamic stress amplification factor and its decay law with depth are discussed. The results show that the dynamic stress amplitude on the embedded track subgrade surface is subject to a normal distribution resulting from random track irregularities. Under the conditions of a tram with an 11 t axle, a design speed of 100 km/h, and a 90% CR track spectrum, the dynamic stress amplification factor on the subgrade surface obeys a normal distribution
N (1.008, 0.1002), the frequent dynamic factor with a 30% exceedance probability is 1.058, and the limit dynamic factor with a 99.9% guarantee rate is 1.308. Influenced by the damping of the subgrade material, the dynamic stress amplification factor decays linearly with depth, and when the damping increases, the decay trend accelerates. With increasing depth, the mean dynamic stress amplification factor gradually decreases, from the dynamic action increasing zone slightly greater than 1, and to the dynamic action weakening zone less than 1. -
图 7路基面动力应力直方图与Q-Q图
Figure 7.Histogram and Q-Q plot of dynamic stress on subgrade surface
表 1有轨电车模型参数
Table 1.Parameters of modern tram
类别 参数 数值 几何 l1，l5/m 3.728 l2，l4/m 3.282 l3/m 2.289 lco/m 1.436 hu/m 2.0 hd/m 1.5 lt/m 0.8 R/m 0.31 质量/惯量 m1，m5/kg 11106 m2，m4/kg 11979 m3/kg 7691 mt1，mt3/kg 2231 mt2/kg 1291 mw/kg 933 J1，J5/（kg·m2） 35773 J2，J4/（kg·m2） 42097 J3/（kg·m2） 13530 Jt1，Jt3/（kg·m2） 500 Jt2/（kg·m2） 230 连接件 Kux1，Kux2，Kux4/（N·m−1） 5 × 108 Kux3/（N·m−1） 1 × 105 Kdxi/（N·m−1） 5 × 108 Kdzi/（N·m−1） 5 × 108 Ksz/（N·m−1） 2 × 106 Kpz/（N·m−1） 4 × 106 Cux1，Cux2，Cux4/（N·s·m−1） 3000 Cux3/（N·s·m−1） 3000 Cdxi/（N·s·m−1） 3000 Cdzi/（N·s·m−1） 3000 Csz/（N·s·m−1） 6 × 104 Cpz/（N·s·m−1） 1.872 × 104 
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表 2线路结构参数
Table 2.Parameters of track
层位 参数 数值 60R2 钢轨 mr/（kg·m−1） 59.75 ErIr/（N·m2） 6.93 × 106 弹性垫板 kp/（N·m−1·m−1） 1.10 × 107 cp/（N·s·m−1·m−1） 6.12 × 104 叠合梁 mb/（kg·m−1） 3316 EbIb/（ N·m2） 3.43 × 106 路基 kf/（ N·m−1·m−1） 1.13 × 108 cf/（ N·s·m−1·m−1） 6.00 × 104 下载:
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表 3轨道谱高低不平顺特征参数
Table 3.Vertical parameters of CR track spectrum
轨道 A1 A2 A3 A4 A5 A6 A7 左轨 1.1029 −1.4709 0.5941 0.8480 3.8016 −0.2500 0.0112 右轨 0.8581 −1.4607 0.5848 0.0407 2.8428 −0.1989 0.0094 下载:
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表 4路基材料参数
Table 4.Material Parameters of Subgrade
结构
层位密度/
（kg·m−3）弹性模量/
MPa泊松比 阻尼比 自振
频率/Hz碎石类 2000 140 0.30 0.04 29.8 砾石类 1900 120 0.30 0.04 24.2 黏土 1890 40 0.35 0.04 20.4 下载:
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表 6φ0特征值
Table 6.Characteristic value ofφ0
均值μ 标准差σ $\varphi _0^{\rm{f}}$ $\varphi _0^{\rm{l}}$ 1.008 0.100 1.058 1.308 下载:
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表 7动应力放大系数φz沿深度衰减方程
Table 7.Attenuation equations ofφzin depth
$ \zeta $ ${\bar \varphi _{\textit{z}}}$ $\varphi _{\textit{z}}^{\rm{f}}$ $\varphi _{\textit{z}}^{\rm{l}}$ 0.04 1.018−0.0258z 1.069−0.0258z 1.324−0.0257z 0.08 1.017−0.0260z 1.068−0.0263z 1.322−0.0279z 0.12 1.016−0.0262z 1.067−0.0269z 1.320−0.0300z 0.15 1.015−0.0265z 1.066−0.0273z 1.319−0.0315z 下载:
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