Identifying amplitude-dependent damping for vertical human-structure interaction on footbridges

Design codes for pedestrian footbridges assume predetermined walking forces and ignore the feedback between bridge motion and gait adaptation. The result is non-conservative amplitude predictions at resonance and overly cautious design margins elsewhere. We resolve this gap with a vertical human-structure interaction load model identified directly on a footbridge tuned to walking frequencies. Each pedestrian is represented as a single-degree-of-freedom system whose leg stiffness varies periodically with the gait phase. The stiffness modulation alone generates the walking force, without an externally prescribed drive. Coupling to a flexible bridge introduces a single interaction damping term that captures the net energy exchange between person and structure. Nineteen subjects walked on a treadmill mounted at the midspan of a laboratory footbridge in a vibration-prone configuration around 2 Hz and a rigid reference configuration without modal contribution at the treadmill. The per-step power flow between centre-of-mass acceleration and deck velocity yields the interaction damping for each subject. The interaction damping is amplitude-dependent. A passive part represents the human body as a mass-spring-damper and acts at any amplitude. An active part comes from the gait-phase stiffness modulation. It activates near resonance and vanishes again when bridge motion grows large enough to disrupt the gait. For nearly all of the tested subjects walking at the bridge frequency the active part dominates and pedestrians inject net energy into the structure instead of damping it. The resulting model produces a self-limiting limit-cycle amplitude at resonance. Off-resonance only the passive damping remains. The same formulation accounts for both regimes. Without recalibration the predicted amplitudes lie in the range of those reported on four published footbridges. This suggests the load model generalises beyond the calibration bridge.