Examination of occurrence probability of vortex-induced vibration of long-span bridge decks by Fokker-Planck-Kolmogorov equation

Vortex-induced vibration (VIV) is a major concern for long-span bridge decks, which may happen especially for closed-box girders under certain environmental wind conditions. Traditionally, sustained VIV is observed as long as the wind speed falls within the lock-in region in wind tunnel tests. However, structural vibration monitoring of long-span bridges has indicated that frequency of VIV events may exhibit a probabilistic pattern. This paper proposes an analytical framework to evaluate the probability of VIV occurrence. First, a nonlinear aeroelastic model with multi-stability limit cycles is used to simulate the bridge deck VIV response within the VIV-triggering wind conditions. The first structural dynamic equilibrium point is usually unstable; the bridge deck instantaneous oscillation amplitude, which is excited by external environmental loads, must exceed this fixed point to trigger the VIV event. The external environmental excitation applied on bridge can be identified from the deck vibration without VIV occurring, then the VIV occurrence probability can be evaluated by Fokker-Planck-Kolmogorov equation. This study utilizes the field measurement data from the Humen Bridge, on which VIV event occurred the first time after 23-year servicing period, because water-filled barriers were placed along the two edges of bridge deck. Afterwards, VIV occurred frequently for over one month. The bridge deck VIV occurrence probability is evaluated by combining environmental wind information, stochastic deck excitation magnitude and a nonlinear aeroelastic VIV model. The results suggest that the proposed methods can approximate the VIV occurrence probability in comparison with empirical estimations using field measurements.