A Social Force Model Considering Falls and Injuries of Pedestrian Counterflow on Slopes
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摘要:
行人在斜坡上运动时，其受力情况、运动速度及心理状态均与在平地运动时不同，难以应用现有社会力模型进行有效仿真. 为此，考虑斜坡上行人的运动特征，提出一个改进的社会力模型，此模型基于过往实证数据对行人在斜坡上的期望速度进行了校准，并提出了推搡行为下行人摔倒的概率计算方法，同时，结合行人体重、运动加速度、承受压力及等待时间等实时状态实现了对行人摔倒、受伤及不耐烦心理的模拟. 斜坡相向行人流场景仿真结果表明：坡度、行人初始密度的升高会延长人群运动时间，使人均意外发生率上升最高至38.0%；不耐烦心理有助于车道效应的形成，但会降低人群运动效率；行人流基本图中，高坡度下流量-密度关系趋势不如平地明显，各坡度行人平均速度比较接近.
Abstract:When pedestrians move on the slope, their force condition, speed, and mental states are different from those on the flat road, so it is difficult to apply the existing social force model for effective simulation. Therefore, the social force model was improved by considering the movement characteristics of pedestrians on slopes. The improved model calibrated pedestrian speed on slopes based on previous empirical data to a desired value, and the probability calculation method of pedestrian falls under the pushing behavior was proposed. Meanwhile, pedestrian falls, injuries, and impatience were simulated according to their weight, acceleration, body pressure, and waiting time in real time. The simulation results of pedestrian counterflow on slopes show that the increase in slope gradient and initial pedestrian density prolongs the movement time and increases the per capita accident rate of the crowd to 38.0%. Pedestrian impatience contributes to the formation of lane effects but reduces the movement efficiency of the crowd. In the fundamental pedestrian flow diagram, the trend of the flow-density relationship under high slopes is not as obvious as that under a flat road, and the average speed of pedestrians under different slopes is relatively close.
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Key words:
- slopes /
- pedestrian counterflow /
- social force model /
- falls and injuries /
- impatience
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图 2 不同文献斜坡行人速率对比
Figure 2. Comparison of pedestrian speeds on slopes in different literature
图 9 经典模型与改进模型对比（t=18 s）
Figure 9. Comparison of traditional model and improved model (t=18 s)
图 10 不同密度、不同坡度下的行人平均运动时间
Figure 10. Average movement time of pedestrians under different densities and slopes
图 11 不同坡度下的行人平均运动时间统计
Figure 11. Average movement time of pedestrians under different slopes
图 12 不同行人初始密度下的受伤情况统计
Figure 12. Injured pedestrians under different initial densities
图 13 各不耐烦因子下的人群运动效率及人均意外发生率
Figure 13. Movement efficiency and per capita accident rate of the crowd under different impatience factors
表 1 模型各参数取值
Table 1. Parameter values of the model
参数 取值 τi/s 0.5 Ai/N 2 × 103 Bi/m 0.08 σ1 0.1 σ2 0 vi0 根据式（5）取值 k/（kg•s−2） 1.2 × 105 κ/（kg•m−1•s−1） 2.4 × 105 mi [50,80] ri 根据式（6）取值 Ts/s 2 Tim/s 2 Pi 根据式（7）取值 Qi 根据式（9）取值 kim 1 qs 0.8 
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表 2 分析指标及含义
Table 2. Analysis indicators and meanings
分析指标 含义 行人初始密度 仿真开始时刻在坡顶和坡底平台下的行人密度 平均运动时间 每个行人离开斜坡的平均时长 轻伤人数 运动过程中受轻伤的人数 重伤人数 运动过程中受重伤的人数 人群运动效率 30 s 内完成离开斜坡人数占总人数的比例 人均意外发生率 运动过程中人均受伤或摔倒次数，摔倒并受伤按 2 次意外计
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