Complete statistical approach to modelling variable pedestrian forces induced on rigid surfaces

This study presents a stochastic model of near-periodic walking force signals featuring variable walking speed on the step-by-step basis as the key input modelling parameter. This is a notable departure from traditional deterministic and periodic Fourier series models where the key modelling parameter is the average pacing rate in a walking trial. Walking speed instead of pacing rate is a more natural choice since human nervous system adopts speed of successive steps to the surrounding environment, including vibrations of the supporting structure. Starting from the previously developed models of variable walking speed and spatiotemporal parameters in a walking trial, this study derived a complementary model of variable dynamic loading factors (DLFs) corresponding to the first five dominant harmonics and subharmonics of the walking force. Both the mean and coefficient of variation of DLFs are described as the products of two factors. The first represents the deterministic dependence on the step speed and is modelled as a second-order polynomial. The second factor reproduces the random inter-pedestrian variability of the DLFs which is defined by a Beta distribution. Extensive vibration simulations of virtual footbridges due to measured and simulated walking forces showed a reliable performance of the model. Moreover, the results provided a strong evidence that the step-by-step variability of gait in a single-pedestrian walking trial yields up to 22% relative error in the simulated vibration response.