高速公路混合交通流圆曲线半径可靠性设计

张航; 胡颖鹏; 彭翔; 孙煜; 吕能超

doi:10.3963/j.jssn.1674-4861.2025.04.005

高速公路混合交通流圆曲线半径可靠性设计

doi: 10.3963/j.jssn.1674-4861.2025.04.005

张航^1,,
胡颖鹏¹,
彭翔¹,
孙煜¹,
吕能超^2, ,

1.
武汉理工大学交通与物流工程学院武汉 430063
2.
武汉理工大学智能交通系统研究中心武汉 430063

基金项目:

国家自然科学基金项目 52472366

湖北省自然科学基金项目 2025AFD759

详细信息

作者简介:
张航（1967—），博士，副教授. 研究方向：道路工程规划设计. E-mail：zhanghang1999@sina.com

通讯作者:
吕能超（1982—），博士，研究员. 研究方向：交通安全、驾驶行为研究. E-mail：lnc@whut.edu.com

中图分类号: U412.3
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出版历程
- 收稿日期: 2025-02-25

A Reliability Design of Circular Curve Radius of Highway Under Mixed Traffic Flow

1.
School of Transportation and Logistics Engineering, Wuhan University of Technology, Wuhan 430063, China
2.
Intelligent Transportation Systems Research Center, Wuhan University of Technology, Wuhan 430063, China

摘要

摘要: 针对自动驾驶汽车（autonomous vehicles，AVs）与人工驾驶车辆（human-drive vehicles，HDVs）组成的混合交通流在高速公路圆曲线路段因路侧设施遮挡等原因导致的停车视距不足问题，以及传统确定性方法计算模型的局限性，研究保障混合交通流视距安全的高速公路最小圆曲线半径。基于防抱死制动系统（anti-lock braking system，ABS）制动过程、横净距法，将汽车制动过程分为3个阶段，并考虑不同偏向、不同车道的有效视距，分别建立停车视距和有效视距计算模型，量化最不利情况的视距需求与供给。基于可靠度理论，考虑不同的AVs渗透率，以及驾驶人或自动驾驶系统在运行速度和制动反应时间上的随机性，使用不确定性的方法建立圆曲线半径对应的停车视距可靠性计算模型，计算《公路路线设计规范》中圆曲线一般最小半径（以下简称规范值）的停车视距可靠概率。使用95%作为目标可靠概率，提出满足视距安全的最小圆曲线半径推荐值和不同圆曲线半径下的安全车速推荐值，通过SUMO仿真验证推荐值的合理性。结果表明：AVs渗透率为0%、圆曲线半径取规范值时左偏最内侧车道的可靠概率均小于95%；随着AVs渗透率增大，可靠概率随之增大；AVs渗透率越高，满足停车视距可靠性要求的最小圆曲线半径越小、安全车速越高；与规范值相比，采用推荐值时仿真试验的交通冲突率平均降低了71.1%、交通流功率平均提高了27.3%，且进一步增大圆曲线半径无显著效益。
- 道路工程 /
- 圆曲线半径 /
- 停车视距 /
- 可靠度理论 /
- 高速公路 /
- 自动驾驶
Abstract: The insufficiency of stopping sight distance (SSD) on highway curves due to roadside obstructions is a critical issue for mixed traffic flow composed of autonomous vehicles (AVs) and human-drive vehicles (HDVs). Traditional deterministic models for addressing this have limitations. Therefore, the minimum circular curve radius ensuring sight distance safety for this mixed traffic flow is investigated. The vehicle braking process is modeled in three stages, incorporating anti-lock braking system (ABS) and the lateral clearance method. Calculation models for SSD and available sight distance (ASD) are developed for various lanes and curve directions. This quantifies sight distance supply and demand under the most critical conditions. A reliability-based model is developed to assess sight distance for given curve radii. This model accounts for random variations in operating speed and braking reaction time of both drivers and autonomous systems, across different AVs penetration rates. The probability of SSD for the general minimum radius specified in the Design Specification for Highway Alignment (hereinafter referred to as standard values) is calculated. Using 95% as the target reliability probability, the recommended values for the minimum radius of circular curves and corresponding safe speed limits under various radii scenarios are proposed. The rationality of these recommended values is verified through SUMO simulations. Results indicate that when the AVs penetration rate is 0%, the reliability probability for the innermost lane of left-turning curves is lower than 95% when using the standard values. Higher AVs penetration increases the reliability probability, allowing for smaller minimum curve radii and higher safe speeds. SUMO simulations verify that the recommended values reduce traffic conflicts by 71.1% and improve traffic efficiency by 27.3% on average, compared to the standard values. Further increasing the curve radius provides no significant benefit.
- road engineering /
- radius of circular curve /
- stopping sight distance /
- reliability theory /
- highway /
- autonomous driving

HTML全文

图 1 汽车制动过程示意图

Figure 1. Car braking process diagram

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图 2 圆曲线有效视距示意图

Figure 2. Schematic diagram of circular curve available sight distance

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图 3 右偏圆曲线横净距法计算模型示意图

Figure 3. Schematic diagram of calculation model of right-turning circular curve with horizontal clear distance method

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图 4 右偏圆曲线横净距示意图

Figure 4. Schematic diagram of horizontal clear distance for the right-turning circular curve

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图 5 左偏圆曲线横净距法计算模型示意图

Figure 5. Schematic diagram of calculation model of left-turning circular curve with horizontal clear distance method

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图 6 左偏圆曲线横净距示意图

Figure 6. Schematic diagram of horizontal clear distance for the left-turning circular curve

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图 7 双向4车道设计速度100 km/h下可靠概率分布曲线

Figure 7. Probability distribution curve for two-way four-lane design speed of 100 km/h

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图 8 AVs加速度调整规则

Figure 8. AVs acceleration adjustment rules

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图 9 不同渗透率、不同圆曲线半径下的交通冲突率

Figure 9. Traffic conflict rate under different penetration rates and radius of circular curve

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图 10 不同渗透率、不同圆曲线半径下的交通流功率

Figure 10. Traffic flow efficiency under different penetration rates and radius of circular curve

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表 1 圆曲线路段线形设计值

Table 1. The design value of circular curve alignment

设计参数	线形设计值
设计速度V_d /（km/h）	120	100	80
圆曲线一般最小半径R / m	1 000	700	400
中央分隔带宽度B_m / m	3.0	2.0	2.0
左侧路缘带宽度B_L / m	0.75	0.75	0.5
车道宽度B_X / m	3.75	3.75	3.75
右侧硬路肩宽度B_R / m	3.0	3.0	3.0
侧向余宽C / m	0.5	0.25	0.25

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表 2 自由流速度K-S检验结果

Table 2. K-S test results of vehicle speed

检验参数		检验结果
检验参数		双向4车道			双向6车道
V_d /（km/h）		120	100	80	120	100	80
速度采集路段		G4	S1	S18	G0422	S7	S19
	样本量	752	683	430	769	604	486
最内侧车道/（km/h）	均值	108.64	93.84	78.46	113.10	92.49	75.91
	标准差	9.87	9.44	9.18	9.20	10.17	9.13
	精确显著性水平（双侧）	0.897	0.834	0.751	0.860	0.599	0.770
	样本量	683	658	468	702	529	398
最外侧车道/（km/h）	均值	101.45	89.21	72.39	105.38	87.30	71.74
	标准差	10.49	11.49	11.93	10.69	12.42	10.38
	精确显著性水平（双侧）	0.573	0.761	0.850	0.676	0.751	0.649

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表 3 可靠概率计算结果

Table 3. Results of probability

V_d /（km/h）	规范值/m	p /%	可靠概率/%
			双向4车道		双向6车道
			右偏最外侧车道	左偏最内侧车道	右偏最外侧车道	左偏最内侧车道
120	1 000	0	98.02	25.83	96.04	26.99
		20	98.37	38.89	96.89	39.39
		40	98.83	51.55	97.49	52.91
		60	99.21	64.18	98.24	65.95
		80	99.54	77.09	99.02	79.14
		100	99.96	89.98	99.75	92.00
100	700	0	97.17	30.03	97.37	35.06
		20	97.79	42.06	97.86	46.61
		40	98.34	55.02	98.32	58.13
		60	98.81	67.67	98.84	69.68
		80	99.32	80.00	99.32	81.30
		100	99.83	92.46	99.81	93.12
80	400	0	96.53	26.38	97.85	33.48
		20	97.17	38.44	98.25	45.33
		40	97.84	50.98	98.73	57.66
		60	98.50	63.36	99.08	69.48
		80	99.12	76.01	99.47	81.50
		100	99.73	88.14	99.93	93.79

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表 4 最小圆曲线半径推荐值

Table 4. Recommended minimum radius of circular curves

V_d /（km/h）	规范值/m	p /%	圆曲线最小半径推荐值/m
V_d /（km/h）	规范值/m	p /%	双向4车道	双向6车道
120	1 000	0	2 320	2 230
		20	2 220	2 140
		40	2 100	2 030
		60	1 930	1 860
		80	1 640	1 580
		100	1 120	1 070
100	700	0	1 660	1 650
		20	1 600	1 570
		40	1 490	1 470
		60	1 360	1 330
		80	1 140	1 110
		100	750	740
80	400	0	1 150	1 020
		20	1 100	970
		40	1 030	920
		60	930	820
		80	760	670
		100	470	410

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表 5 安全车速推荐值（左偏圆曲线最内侧车道）

Table 5. Recommended safe speed (innermost lane of left curve)

V_d /（km/h）	规范值/m	p /%	安全车速推荐值/（km/h）
V_d /（km/h）	规范值/m	p /%	双向4车道	双向6车道
120	1 000	0	89	88
		20	90	89
		40	91	91
		60	93	93
		80	98	96
		100	117	118
100	700	0	76	77
		20	77	77
		40	78	78
		60	82	81
		80	84	84
		100	100	100
80	400	0	60	60
		20	62	61
		40	63	64
		60	64	65
		80	67	68
		100	80	80

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表 6 交通冲突率平均变化率计算结果

Table 6. Calculation result of average change rate of traffic conflict rate

p /%	平均变化率/%		推荐值前后平均变化率比值
p /%	1 000 m~推荐值	推荐值~3 000 m	推荐值前后平均变化率比值
0	-2.056	-0.528	3.89
20	-1.505	-0.448	3.36
40	-1.781	-0.252	7.06
60	-1.000	-0.080	12.51
80	-0.038	-0.012	3.05
100	-0.04	-0.001	81.47
注：推荐值见表 4。

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表 7 交通流功率平均变化率计算结果

Table 7. Calculation result of average change rate of traffic flow efficiency

p /%	平均变化率/%		推荐值前后平均变化率比值
p /%	1 000 m~推荐值	推荐值~3 000 m	推荐值前后平均变化率比值
0	46.30	13.64	3.39
20	58.19	17.97	3.24
40	62.94	18.09	3.48
60	65.69	18.32	3.59
80	72.65	20.77	3.50
100	4.98	0.61	8.15
注：推荐值见表 4。

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