Macroscopic wall pressure and microscopic contact load in crowds without egress: social-group cohesion and boundary buffering

Abstract

Crowd safety in confined venues is usually evaluated through evacuation performance or pre-collision avoidance, while direct mechanical hazards in dense gatherings without egress remain poorly understood. We study an Elastic Reorientation Model (ERM), a Social Force Model (SFM), and their coupled dynamics. Post-collision behavior is represented by social-group cohesion (${\hat{I}}_g^3$) and wall buffering (${\hat{I}}_w^3$), while risk is quantified by the macroscopic wall line pressure ($P_{\text{wall}}$) and the microscopic maximum per-agent collision impulse ($\hat{I}´p_{\text{max}}$). In the ERM, cohesion and wall buffering generally reduce $P_{\text{wall}}$ by retaining agents in the bulk, but large groups exhibit a high-$\hat{I}´p_{\text{max}}$ hazard window at intermediate cohesion. As ${\hat{I}}_g^3\to 1$, local pairing suppresses cluster growth and shifts kinetic energy from relative to center-of-mass motion, reducing $\hat{I}´p_{\text{max}}$. SFM pushing and sliding amplify $\hat{I}´p_{\text{max}}$, especially when agent-agent and agent-wall interactions coexist, while active driving raises $P_{\text{wall}}$ through near-wall accumulation. The coupled dynamics produces a wall-pressure/contact-load ($P$-$p$) trade-off. Finite-size scaling reveals an independent-agent-induced phase boundary at ${\hat{I}}_w^3=0.5$, characterized by a susceptibility discontinuity, and a grouped-agent-induced continuous phase boundary along a finite segment of $(1-{\hat{I}}_w^3)(1-{\hat{I}}_g^3)=0.5$, characterized by divergent susceptibility and terminating at a critical point. Both disappear in the social-force-free ERM, showing that they emerge from the coupled ERM+SFM dynamics. These results provide mechanistic guidance for crowd-risk mitigation and safety planning in high-density venues without egress.

16 pages, 8 figures

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