An Analysis of the Reliability of Radius Parameters of Circular Curves on Super-speed Highways
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摘要: 为探究超高速公路路线设计确保车辆行车安全的圆曲线最小半径值，引入可靠度理论，以汽车在圆曲线路段行驶时不产生横向滑移为约束条件构建动力学模型，利用该模型对圆曲线半径进行分析，并提出圆曲线半径的可靠度功能函数。对功能函数中的车辆运行速度、路面横向摩擦系数、道路超高值等相关参数进行统计，并分析其分布规律。求解设计速度分别为100，120，140，160 km/h时超高速公路圆曲线的最小半径值，取整后用蒙特卡洛法仿真估计各设计速度对应最小半径的失效概率。结合公众心理承受度，以失效概率小于0.01%为基准，对各设计速度下的圆曲线半径进行可靠性设计，得到超高速公路圆曲线最小半径推荐值在潮湿的路面条件下分别为920，1 000，1 100，1 220 m；在积雪的路面条件下分别为1 380，1 400，1 420，1 450 m。实证结果表明：在事故率较高的路段，各段圆曲线半径对应的失效概率最小值为0.019 5%，大于最小圆曲线半径的失效概率值0.01%。采用0.01%的失效概率设计超高速公路圆曲线半径，可保证其安全性高于现有标准。Abstract: The design of super-speed highways should consider the minimum radius parameters of circular curves that ensures the safety of vehicles operating at a high speed. In this paper, a reliability theory is proposed, and a mechanical model is developed in order to study an appropriate radius of circular curves, which will ensure that the vehicles running over the curves will not create any lateral slip. Based on this principle, the radius of circular curves is analyzed, and a reliability function is proposed. In the proposed reliability function, a number of parameters are computed and analyzed, including the vehicle speed, friction coefficient of the transverse surface, superelevation, etc. Under the design speed of 100, 120, 140 and 160 km/h, the minimum radius of the circular curve is calculated and rounded. A Monte Carlo simulation method is used to calculate the failure probability of the minimum radius corresponding to each design speed. Combined with psychological tolerance of the public, a reliability design for the radius of circle curve at each design speed should ensure the failure probability is less than 0.01%. The recommended value of the minimum radius of circular curve at each design speed is 920, 1 000, 1 100 and 1 220 m under a condition of wet pavement; The minimum radius of circular curve is 1 380, 1 400, 1 420 and 1 450 m under a condition of snow-covered pavement. Study results show that in the sections with high accident rate, the minimum failure probability corresponding to the radius of circular curve for each segment is 0.019 5%. It is greater than the failure probability of 0.01% for the minimum radius of circular curve. The safety level of super-speed highway is higher than current standards when the radius of circular curve is designed with the failure probability of 0.01%.
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图 1 车辆在曲线路段上行驶受力分析图
Figure 1. Force analysis diagram of vehicle driving on curve section
图 2 圆曲线路段事故率和半径失效概率关系图
Figure 2. Relationship between accident rate and radius failure probability of circular curve
表 1 高速公路分级
Table 1. Classification of highway
公路等级 设计速度/(km/h) 超高速公路 超一级高速 160/140/120/100 超二级高速 200/180/160/140 超三级高速 240/220/200/180 普通高速公路 120/100/80/60 
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表 2 车辆运行速度K-S检验结果表
Table 2. K-S test results of vehicle running speed
设计速度/ (km/h) 样本数 正态参数 最极端差别 K-SZ 渐进显著性 均值 标准差 120 83 115.096 11.696 0.031 0.739 0.761 100 78 96.332 8.570 0.030 0.502 0.678 80 75 79.445 10.466 0.041 0.811 0.593
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表 3 不同状态路面在不同速度下的路面摩擦系数
Table 3. Friction coefficient of pavement under different conditions and different speeds
路面状况 速度(km/h) 摩擦系数均值 摩擦系数标准差 潮湿 80.4 0.419 0.091 潮湿 85 0.401 0.091 潮湿 90 0.383 0.091 潮湿 95 0.357 0.091 潮湿 99.8 0.350 0.091 干燥 任意速度 0.885 0.095
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表 4 摩擦系数影响因子
Table 4. Influencing factors of friction coefficient
路面状况 影响因子 干燥、养护较好 1.0 干燥、磨光 0.9 潮湿、养护较好 0.7 潮湿、磨光 0.4 积雪 0.3
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表 5 其他国家高速公路最大超高值
Table 5. Maximum superelevation of highway in other countries
国家 超高/% 不受冰雪影响 考虑冰雪影响 受冰雪影响较大 美国 10(12) 8 6 日本 10 8 6 德国 8 8 8
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表 6 超一级高速公路最大超高值
Table 6. Maximum superelevation of super-speed highway class 1
设计速度/(km/h) 超高值/% 100 10 120 10 140 12 160 12
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表 7 超一级高速公路的最大超高值
Table 7. Maximum superelevation of super-speed highway class 1
设计速度/(km/h) 超高值/% 不受冰雪影响 考虑冰雪影响 100 10 8 120 10 8 140 12 8 160 12 8
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表 8 最大横向摩擦系数均值
Table 8. Mean value of maximum transverse friction coefficient
路面环境类型 路面养护较好 路面磨光 干燥 0.885 0.797 潮湿 0.225 0.140 积雪 0.105 0.105
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表 9 最小半径值
Table 9. Theoretical minimum radius
公路等级 设计速度/(km/h) 路面状况 超高值/% 折算后的最大横向摩擦系数 最小半径/m 超一级高速公路 100 潮湿 10 0.14 328.084 积雪 8 0.10 437.445 120 潮湿 10 0.14 472.441 积雪 8 0.10 629.921 140 潮湿 12 0.14 593.580 积雪 8 0.10 857.393 160 潮湿 12 0.14 775.288 积雪 8 0.10 1 119.860
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表 10 最小设计半径值及其可靠度结果
Table 10. Theoretical minimum design radius and reliability results
公路等级 设计速度/(km/h) 路面条件 最小设计半径/m 运行速度均值/ (km/h) 运行速度标准差/ (km/h) 可靠指标 失效概率/% 超一级高速公路 100 潮湿 350 88.03 12.32 2.820 0.24 积雪 450 92.05 12.89 2.400 0.82 120 潮湿 500 93.74 13.12 2.911 0.18 积雪 630 97.44 13.64 2.473 0.67 140 潮湿 600 96.65 13.53 3.036 0.12 积雪 860 102.42 14.34 2.536 0.56 160 潮湿 800 101.26 14.17 2.948 0.16 积雪 1 120 106.65 14.93 2.612 0.45
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表 11 设计半径推荐最小安全值
Table 11. Recommended minimum safety value of radius
公路等级 设计速度/ (km/h) 路面 安全半径/m 可靠指标 失效概率/% 超一级高速公路 100 潮湿 920 3.719 0.01 积雪 1 380 3.719 0.01 120 潮湿 1 000 3.719 0.01 积雪 1 400 3.719 0.01 140 潮湿 1 100 3.719 0.01 积雪 1 420 3.719 0.01 160 潮湿 1 220 3.719 0.01 积雪 1 450 3.719 0.01
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表 12 圆曲线路段事故率及失效概率
Table 12. Accident rate and failure probability of circular curve
起点 终点 设计速度/(km/h) 事故率/[次/(年• km)] 运行速度/(km/h) 半径/m 超高值/% 半径失效概率/% K169+240 K169+720 120 10.42 121.35 2 802 3 4.23x10-6 K169+720 K171+050 120 5.26 121.35 2 802 3 4.23x10-6 K171+050 K171+450 120 12.5 121.35 2 802 3 4.23x10-6 K173+500 K173+860 120 22.22 118.81 1 800 4 0.0195 K184+280 K184+550 120 22.22 118.81 1 800 4 0.0195 K192+208 K192+700 120 6.1 121.91 3 093 3 1.78x10-7 K192+700 K193+299 120 10.02 121.91 3 093 3 1.78x10-7 K193+299 K194+020 120 9.71 121.91 3 093 3 1.78x10-7 K194+020 K194+540 120 3.85 121.91 3 093 3 1.78x10-7 K195+716 K196+400 120 5.85 120.69 2 500 3 1.00x10-4 K196+400 K197+400 120 4 120.69 2 500 3 1.00x10-4 K197+400 K198+312 120 7.68 120.69 2 500 3 1.00x10-4 K198+981 K199+700 120 9.74 120.69 2 500 3 1.00x10-4 K199+700 K200+000 120 10 120.69 2 500 3 1.00x10-4
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