Probability-based estimation of vibration for pedestrian structures due to walking.

Modern civil engineering structures exposed to human-induced dynamic loading due to walking, such as footbridges and long-span floors, are becoming increasingly slender and therefore more prone to vibrations generated by people. As a consequence, the vibration serviceability of these structures is becoming their governing design criterion. Currently, the design procedures for the vibration serviceability check used in practice are mainly of a deterministic nature. This means that the walking force is modelled via a unique set of parameters, such as walking frequency, step length and force amplitude assumed to be representative for all pedestrians. Therefore, the natural inter-subject variability that exists in these parameters generated by different people is neglected. Moreover, these parameters vary with each step even in the force time history of a single person (intra-subject variability). This implies that the walking force is a narrow-band random process rather than a deterministic force. As a result of these shortcomings, current design procedures based on deterministic forces do not predict reliably the vibration responses to single person walking across as-built slender structures. To improve design procedures, it is necessary to take into account the both inter- and intrasubject variabilities in the walking force. This implies that a probability-based approach, whereby the probability of occurrence of various walking parameters can be taken into account, might be more appropriate to model the walking excitation. In this thesis, a probability-based framework for a vibration serviceability check due to a single person walking is developed. For this, the probability density functions for walking frequencies, step lengths, magnitude of walking force and imperfections in human walking are proposed. They are used as building blocks to develop a design procedure that can estimate the probability of occurrence of a certain level of vibration response. Based on this result, a probability that the vibration response will not exceed certain predefined limiting values can be found. Moreover, a methodology for finding a reasonable limiting vibration level, based on the assumption that some human-structure dynamic interaction takes place when walking across perceptibly moving bridge, is suggested. A provisional value of 0.35 m/s2 is identified for two footbridges investigated. The probability-based design procedure developed in this thesis can be used for vibration serviceability check of footbridges responding in one or more vibration modes to excitation induced by a single walker. The method has potential to be used for vibration serviceability check of other slender structure