超高速公路圆曲线半径参数的可靠性分析

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。 

An Analysis of the Reliability of Radius Parameters of Circular Curves on Super-speed Highways

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%.