Quantification of dynamic excitation potential of pedestrian population crossing footbridges

Due to their slenderness, many modern footbridges may vibrate significantly under pedestrian traffic. Consequently, the vibration serviceability of these structures under human-induced dynamic loading is becoming their governing design criterion. Many current vibration serviceability design guidelines, concerned with prediction of the vibration in the vertical direction, estimate a single response level that corresponds to an "average" person crossing the bridge with the step frequency that matches a footbridge natural frequency. However, different pedestrians have different dynamic excitation potential, and therefore could generate significantly different vibration response of the bridge structure. This paper aims to quantify this potential by estimating the range of structural vibrations (in the vertical direction) that could be induced by different individuals and the probability of occurrence of any particular vibration level. This is done by introducing the inter-and intra-subject variability in the walking force modelling. The former term refers to inability of a pedestrian to induce an exactly the same force with each step while the latter refers to different forces (in terms of their magnitude, frequency and crossing speed) induced by different people. Both types of variability are modelled using the appropriate probability density functions. The probability distributions were then implemented into a framework procedure for vibration response prediction under a single person excitation. Instead of a single response value obtained using currently available design guidelines, this new framework yields a range of possible acceleration responses induced by different people and a distribution function for these responses. The acceleration ranges estimated are then compared with experimental data from two real-life footbridges. The substantial differences in the dynamic response induced by different people are obtained in both the numerical and the experimental results presented. These results therefore confirm huge variability in different people's dynamic potential to excite the structure. The proposed approach for quantifying this variability could be used as a sound basis for development of new probability-based vibration serviceability assessment procedures for pedestrian bridges.