Experiment Calibrated Simulation Modeling of Crowding Forces in High Density Crowd

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.