车路耦合荷载下沥青混凝土路面振动响应

董倩; 程少锋; 张献民; 包伊婷

doi:10.13700/j.bh.1001-5965.2021.0654

车路耦合荷载下沥青混凝土路面振动响应

doi: 10.13700/j.bh.1001-5965.2021.0654

董倩^{1, 2},
程少锋¹,
张献民^{1, 3, ,},
包伊婷¹

1.
中国民航大学交通科学与工程学院，天津 300300
2.
天津大学建筑工程学院，天津 300072
3.
南京航空航天大学民航学院，南京 210016

基金项目: 国家自然科学基金(51178456)；中央高校基本科研业务费(3122017039)

详细信息

通讯作者:
E-mail：xmzhang@cauc.edu.cn

中图分类号: U411
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出版历程
- 收稿日期: 2021-11-01
- 录用日期: 2022-01-21
- 网络出版日期: 2022-02-15
- 整期出版日期: 2023-10-01

Vibration response of asphalt concrete pavement under vehicle-road coupled load

DONG Qian^{1, 2},
CHENG Shaofeng¹,
ZHANG Xianmin^{1, 3
, ,},
BAO Yiting¹

1.
College of Transportation Science and Engineering，Civil Aviation University of China，Tianjin 300300，China
2.
School of Civil Engineering，Tianjin University，Tianjin 300072，China
3.
College of Civil Aviation，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China

Funds: National Natural Science Foundation of China (51178456); The Fundamental Research Funds for the Central Universities (3122017039)

More Information

Corresponding author: E-mail：xmzhang@cauc.edu.cn

摘要

摘要:
为研究沥青混凝土路面的振动特性，采用滤波白噪声法拟合出路面平整度时域模型，基于1/4车辆模型，考虑车辆–道路的耦合作用，分析不同车辆速度、不同路面平整度等级时，车辆对路面的实时动荷载；建立道路三维有限元模型，研究车辆随机动荷载作用下道路的振动响应，分析道路各结构层参数对道路表面中心振动基频的影响。结果表明：路面平整度等级、车辆行驶速度对车–路耦合系统影响显著，当路面平整度等级由A级变化至C级时，同一行驶速度下的车辆动荷载增大了20%；道路振动基频随土基动模量呈对数关系增加，土基动模量由60 MPa增大至260 MPa，道路振动基频由5.61 Hz增大至10.80 Hz，振动基频增幅高达48.06%；在常用动模量变化范围内，面层、基层、垫层的动模量对基频的影响较小；随着面层、基层与垫层厚度的增加，道路基频呈线性减小的趋势，面层厚度对振动频率影响的敏感性大于基层厚度，基层厚度对振动频率影响的敏感性大于垫层厚度；在常用结构层厚度变化范围内，振动基频分别减小9.28%、18.05%与12.75%。试验结果证明：振动基频计算较正确，计算结果可为道路承载力快速测试提供理论支持。
- 沥青混凝土路面 /
- 车辆动荷载 /
- 有限元 /
- 结构层厚度 /
- 结构层弹性模量 /
- 振动基频
Abstract:
To study the vibration characteristics of asphalt concrete pavement, the time domain model of road roughness was simulated by the white noise filtering method, the coupling effect of vehicle and road with different vehicle speeds and different road roughness levels was analyzed based on the quarter vehicle mode, and the real-time dynamic load of vehicle on the road surface was determined to study the vibration characteristics of Tarmac pavements. The three-dimensional finite element model of the road is established, the vibration response of the road under the action of the vehicle random dynamic load is analyzed, and the influence of the road structure-layer parameters on the fundamental vibrational frequency of the road surface center is analyzed. The results show that the pavement roughness level and vehicle speed have significant influence on the vehicle-road coupling system. When the pavement roughness level changes from class A to class C, the dynamic load of vehicles under the same speed increases by 20%; the fundamental vibrational frequency of the road increases with the logarithmic relation of dynamic subgrade modulus, the subgrade modulus increases from 60 MPa to 260 MPa, the fundamental vibrational frequency of the road increases from 5.61 Hz to 10.80 Hz, with an increase of 48.06%. The dynamic modulus of the surface layer, base layer and cushion have little influence on the fundamental frequency, which are almost negligible. As the thickness of surface layer, base layer and cushion increases, the fundamental frequency of road shows a linear decrease trend. Within the commonly used variation range of the thickness of structure layer, the fundamental vibrational frequency decreases by 9.28%, 18.05% and 12.75% respectively.
- asphalt concrete pavement /
- vehicle dynamic load /
- finite-element /
- thickness of structural layer /
- elastic modulus of structural layer /
- fundamental frequency

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图 1 路面平整度时域仿真模型

Figure 1. Time domain model of pavement roughness

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图 2 不同等级路面的平整度曲线

Figure 2. Pavement roughness of three grades

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图 3 二自由度车辆模型

Figure 3. Vehicle model with two-degree-of-freedom

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图 4 A、B、C级路面随机荷载

Figure 4. Random load of grade A, B and C

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图 5 道路有限元模型

Figure 5. Finite element model of pavement

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图 6 车辆移动荷载加载轨迹

Figure 6. loading path of vehicle load

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图 7 路面中心位置处加速度与振动基频

Figure 7. Acceleration and fundamental frequency at center of road surface

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图 8 基层厚度H₂和动态模量E_d2对基频的影响

Figure 8. Effect of base thickness H₂ and modulus E_d2 on fundamental frequency

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图 9 垫层厚度H₃和动态模量E_d3对基频的影响

Figure 9. Effect of cushion thickness H₃ and modulus E_d3 on fundamental frequency

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图 10 各结构层厚度-基频回归曲线

Figure 10. Thickness-fundamental frequency regression curve of each structural layer

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图 11 不同土基动态模量时频谱曲线

Figure 11. Spectrum curve with different dynamic modulus of soil foundation

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图 12 振动基频-土基动态模量回归曲线

Figure 12. Regression curve of fundamental frequency-dynamic modulus of soil foundation

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图 13 传感器布置

Figure 13. Layout of sensors

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图 14 A1传感器的加速度响应曲线

Figure 14. Acceleration response curve at A1 sensor

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表 1 不同等级路面功率谱密度^[18]

Table 1. Grading standard of road roughness by PSD^[18] m²/m⁻¹

等级	下限值	几何平均值	上限值
A	8	16	32
B	32	64	128
C	128	256	512
D	512	1 024	2 048
E	2 048	4 096	8 192
F	8 192	16 384	32 768
G	32 768	65 536	131 072
H	131 072	262 144	524 288

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表 2 10 t加载车辆参数

Table 2. Parameters of truck with 10 tons’ weight

参数	数值
簧载部分质量m₁/kg	4450
非簧载部分质量m₂/kg	550
簧载部分刚度系数k₁/(N·m⁻¹)	1000000
非簧载部分刚度系数k₂/(N·m⁻¹)	1750000
簧载部分阻尼系数c₁/(N·s·m⁻¹)	15000000
非簧载部分阻尼系数c₂/(N·s·m⁻¹)	2000000

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表 3 路面结构和材料参数

Table 3. Structural and material parameters of road

结构层	厚度/m	动态模量/MPa	泊松比	密度/(kg.m⁻³)
沥青混凝土	0.20	4000	0.30	2400
水泥稳定碎石	0.40	8000	0.25	2200
二灰稳定碎石	0.30	2000	0.30	2000
土基	9	140	0.35	1900

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表 4 不同深度处振动基频及幅值

Table 4. Fundamental frequencies and amplitudes at different depths

y/m	振动基频 /Hz	幅值/0.1g
9.9	6.08	0.014
9.7	6.08	0.013
9.3	6.08	0.013
9.0	6.08	0.013
7.0	6.08	0.010
5.0	6.08	0.009
3.0	6.08	0.007
1.0	6.08	0.004

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表 5 不同道面参数时的振动基频

Table 5. Fundamental frequencies under different pavement parameters

面层厚度 /m	面层模量 /MPa	振动基频 /Hz	面层厚度 /m	面层模量 /MPa	振动基频 /Hz
0.14	3 500	6.57	0.20	3 500	6.08
	4 000	6.58		4 000	6.08
	4 500	6.58		4 500	6.08
	5 000	6.58		5 000	6.09
	5 500	6.59		5 500	6.09
0.16	3 500	6.40	0.22	3 500	5.96
	4 000	6.40		4 000	5.96
	4 500	6.40		4 500	5.97
	5 000	6.40		5 000	5.98
	5 500	6.41		5 500	5.98
0.18	3 500	6.26
	4 000	6.26
	4 500	6.27
	5 000	6.27
	5 500	6.27

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表 6 不同土基动态模量下道路基频

Table 6. Fundamental frequency under different soil foundation dynamic moduli

土基动态模量/MPa	基频/Hz	土基动态模量/MPa	基频/Hz
60	5.61	180	9.10
100	7.01	220	9.88
140	8.19	260	10.80

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表 7 道路结构及参数

Table 7. Structures and Parameters of road

结构层	静态模量 /MPa	动态模量 /MPa	厚度 /m	密度 / （kg·m⁻³）
沥青混凝土面层	2000	4890	0.2	2400
水泥稳定碎石基层	5000	7893.03	0.4	2200
二灰稳定碎石底基层	800	1098	0.3	2000
土基	55	167	∞	1900

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表 8 道路振动基频

Table 8. Fundamental frequencies of test road

传感器	振动基频/Hz	传感器	振动基频/Hz
A1	8.74	A4	8.64
A2	8.64	A5	8.64
A3	8.74	A6	8.74

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