Probabilistic evaluation of railway vehicle?s safety on bridges under random earthquake and track irregularity excitations

With the rapid expansion of high-speed rail networks, the safety of vehicles against derailment on bridges during earthquakes has become a significant concern in bridge design. The vehicle's responses are the combined effect of earthquakes and track irregularities, both random processes. But few studies exist on the combination rule of derailment indexes from the two random excitations. In addition, the seismic fragility analysis commonly used in structural engineering was rarely seen in the derailment analysis. In this paper, the probability density evolution method (PDEM) was used to obtain the probability density function (PDF) of wheel unloading extremes by treating the earthquake and track irregularity as random processes. The combination rule of extremes of wheel unloading ratio from the two excitation sources was investigated by comparing the PDFs of combined results with direct simulation. It is shown that the extreme values of wheel unloading under earthquakes and track irregularities approximately satisfy the SRSS formula. In addition, the seismic fragility analysis using the incremental dynamic analysis (IDA) was introduced into the vehicle-bridge interaction (VBI) system to simplify the probabilistic derailment assessment. By comparing with the fragility curve from the PDEM (it can be seen as an accurate solution), the IDA-based seismic fragility curve estimated by twenty or more earthquake samples was found to have adequate accuracy for engineering application.