Physics-based provisions against pedestrian-induced lateral structural instability

This paper presents probabilistic criteria for assessing the lateral dynamic stability of structures subjected to pedestrian loading, derived from the calibrated and generalised inverted pendulum pedestrian model (IPM). The model captures the key mechanism of pedestrian–structure interaction associated with the legged nature of human locomotion and was calibrated using experimental data from pedestrians walking on a laterally oscillating instrumented treadmill. This calibration led to a generalised foot placement control law expressed in terms of anthropometric and gait parameters. Closed-form analytical solutions of the IPM were used to determine the equivalent added damping and added mass introduced by pedestrians. These quantities form the basis for probabilistic structural stability criteria expressed in terms of the pedestrian Scruton number. To account for variability within the pedestrian population, a statistical model of anthropometric parameters representative of the British population was developed, allowing stability boundaries to be defined for different confidence levels and pedestrian distribution scenarios. For practical application, simplified piecewise-linear envelopes of the critical equivalent added damping and its variability were proposed as functions of structural natural frequency and pedestrian-to-structure mass ratio. The framework is demonstrated through a case study of the Clifton Suspension Bridge in the UK, showing that the proposed criteria provide realistic estimates of critical pedestrian numbers and required damping levels while maintaining a clear physical interpretation of the underlying interaction mechanisms.