有轨电车嵌入式轨道路基荷载动应力特性分析

谢宏伟; 罗强; 蒋良潍; 张良; 王腾飞; 刘钢

doi:10.3969/j.issn.0258-2724.20210303

有轨电车嵌入式轨道路基荷载动应力特性分析

doi: 10.3969/j.issn.0258-2724.20210303

谢宏伟^{1, 2,},
罗强^{1, 2, ,},
蒋良潍^{1, 2},
张良^{1, 2},
王腾飞^{1, 2},
刘钢³

1.
西南交通大学土木工程学院，四川成都 610031
2.
西南交通大学高速铁路线路工程教育部重点实验室，四川成都 610031
3.
西华大学建筑与土木工程学院，四川成都 610039

基金项目: 国家自然科学基金（52078435）；四川省科技计划（2021YJ0001）

详细信息

作者简介:
谢宏伟（1991—），男，博士研究生，研究方向为路基动力学，E-mail：hongweixie@my.swjtu.edu.cn

通讯作者:
罗强（1963—），男，教授，研究方向为土力学与路基工程，E-mail：LQrock@swjtu.edu.cn

中图分类号: U213.1
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- 被引次数: 0
出版历程
- 收稿日期: 2021-05-05
- 修回日期: 2021-08-26
- 网络出版日期: 2022-12-10
- 刊出日期: 2022-07-13

Analysis on Load Dynamic Stress Characteristics of Embedded Track Subgrade of Tram

XIE Hongwei^{1, 2
,},
LUO Qiang^{1, 2
, ,},
JIANG Liangwei^{1, 2},
ZHANG Liang^{1, 2},
WANG Tengfei^{1, 2},
LIU Gang³

1.
School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China
2.
MOE Key Laboratory of High-Speed Railway Engineering, Southwest Jiaotong University, Chengdu 610031, China
3.
School of Architecture and Civil Engineering, Xihua University, Chengdu 610039, China

摘要

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.
- 路基动应力特性 /
- 耦合动力学 /
- 有轨电车 /
- 嵌入式轨道
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.
- subgrade dynamic stress characteristics /
- coupled dynamics /
- modern tram /
- embedded track

HTML全文

图 1 有轨电车-嵌入式轨道-土质路基动力学模型

Figure 1. Tram-embedded rail track-subgrade dynamic model

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图 2 嵌入式轨道

Figure 2. Embed rail track

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图 3 高低不平顺模拟结果

Figure 3. Vertical rail irregularity sample

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图 4 路基结构三维有限元模型（单位：m）

Figure 4. Subgrade 3D FE model （unit：m）

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图 5 路基面动应力时程曲线

Figure 5. Vertical dynamic stress on the top of subgrade

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图 6 路基面动应力时程曲线

Figure 6. Vertical dynamic stress on the top of subgrade

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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

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图 8 速度对路基面动力应力影响

Figure 8. Influence of speed on subgrade dynamic stress

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图 9 路基动应力沿深度的分布

Figure 9. Subgrade dynamical stress distribution along depth

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图 10 φ_z沿深度衰减

Figure 10. Attenuation of φ_z along depth

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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
	l_co/m	1.436
	h_u/m	2.0
	h_d/m	1.5
	l_t/m	0.8
	R/m	0.31
质量/惯量	m₁，m₅/kg	11106
	m₂，m₄/kg	11979
	m₃/kg	7691
	m_t1，m_t3/kg	2231
	m_t2/kg	1291
	m_w/kg	933
	J₁，J₅/（kg·m²）	35773
	J₂，J₄/（kg·m²）	42097
	J₃/（kg·m²）	13530
	J_t1，J_t3/（kg·m²）	500
	J_t2/（kg·m²）	230
连接件	K_ux1，K_ux2，K_ux4/（N·m⁻¹）	5 × 10⁸
	K_ux3/（N·m⁻¹）	1 × 10⁵
	K_dxi/（N·m⁻¹）	5 × 10⁸
	K_dzi/（N·m⁻¹）	5 × 10⁸
	K_sz/（N·m⁻¹）	2 × 10⁶
	K_pz/（N·m⁻¹）	4 × 10⁶
	C_ux1，C_ux2，C_ux4/（N·s·m⁻¹）	3000
	C_ux3/（N·s·m⁻¹）	3000
	C_dxi/（N·s·m⁻¹）	3000
	C_dzi/（N·s·m⁻¹）	3000
	C_sz/（N·s·m⁻¹）	6 × 10⁴
	C_pz/（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	m_r/（kg·m⁻¹）	59.75
60R2 钢轨	E_rI_r/（N·m²）	6.93 × 10⁶
弹性垫板	k_p/（N·m⁻¹·m⁻¹）	1.10 × 10⁷
弹性垫板	c_p/（N·s·m⁻¹·m⁻¹）	6.12 × 10⁴
叠合梁	m_b/（kg·m⁻¹）	3316
叠合梁	E_bI_b/（ N·m²）	3.43 × 10⁶
路基	k_f/（ N·m⁻¹·m⁻¹）	1.13 × 10⁸
路基	c_f/（ N·s·m⁻¹·m⁻¹）	6.00 × 10⁴

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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

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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

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表 5 φ₀的K-S检验

Table 5. K-S test for φ₀

样本数量	统计量 D	P 值	结论（α=5%）
1659	0.019	0.583	服从正态分布（P > α）

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表 6 φ₀特征值

Table 6. Characteristic value of φ₀

均值 μ	标准差 σ	$\varphi _0^{\rm{f}}$	$\varphi _0^{\rm{l}}$
1.008	0.100	1.058	1.308

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表 7 动应力放大系数φ_z沿深度衰减方程

Table 7. Attenuation equations of φ_z in 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

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