Abstract
Crowding force is an important index in evaluating the safety of those within high density crowds. However, studies on high density crowd simulation models have not been sufficiently developed, and related experimental studies are not sufficiently detailed to guide modeling research. Models that can reproduce real high density crowds and enable calibration of key parameters are lacking. In this study, we improved the typical social force model to simulate high density crowd motion with the calculation of crowding forces. To simulate high density crowds, pedestrians were modeled using the three-circle model, and an agent-based pedestrian model was formulated that can regulate the psychological force automatically according to crowd density. An individual crowd density calculation method is proposed that is more suitable for high density crowds. To calculate real crowding force, body stiffness was formulated and the corresponding parameters were calibrated by a series of experiments. Field experiments show that passengers bear greater force on their backs than the force on each shoulder in metro carriage. The modified model was verified by comparing the simulation results with observed data. We applied this model to the Beijing subway, and the theoretical maximum crowd densities in different seasons were calculated from the perspective of crowding force to ensure the safety of passengers, which are 7.2 people/m2 in winter and 10.3 people/m2 in summer. Therefore, to ensure passenger safety, the subway operation department should arrange more trains during winter peak hours.
Highlights
With the increasing urban population, high density crowds in public places have been recognized as potential hazards [1], and tragedies have occurred on different occasions [2], [3] such as the Hajj crush in Mecca, the crowd stampede during the Lantern Festival in China, the Houphouët-Boigny Arena stampede during a football game in Côte d’Ivoire, and passenger injury caused by metro carriage crowding in Beijing and Tokyo
CROWDING FORCE IMPROVEMENT In a typical social force model, physical force or crowding force is calculated using linear elasticity models with constant stiffness, which does not conform to reality; these stiffness values differ in different studies [5], [41]
The maximum density in the simulation is 8.60 people/m2. These results show that the modified model can reproduce high density crowd motion and can simulate the density attained in reality
Summary
With the increasing urban population, high density crowds in public places have been recognized as potential hazards [1], and tragedies have occurred on different occasions [2], [3] such as the Hajj crush in Mecca, the crowd stampede during the Lantern Festival in China, the Houphouët-Boigny Arena stampede during a football game in Côte d’Ivoire, and passenger injury caused by metro carriage crowding in Beijing and Tokyo. Previous studies [4]–[7] mainly focused on parameter calibration and model modification based on the social force model to simulate high density crowds under specific situations. Because passengers’ crowd density in the Beijing subway system can reach 8.23 people/m2 during morning peak hours [11], a field investigation on the metro system was conducted to measure crowding forces and the model parameters were calibrated based on experimental data. The comfort space is the distance necessary for the individual to react and adjust their behavior unhurriedly when meeting an exceptional condition; safety space is the distance necessary to ensure that the individual can react quickly and avoid emergencies under exceptional conditions In accordance with these definitions, we analyzed pedestrian walking records in transfer channels of the Beijing subway to build a new calculation method of the psychological repulsive force. A can be formulated based on interaction range, as shown in (2):
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