The smoothness of the high-speed railway (HSR) on the bridge may exceed the allowable standard when an earthquake causes vibrations for HSR bridges, which may threaten the safety of running trains. Indeed, few studies have evaluated the exceeding probability of rail displacement exceeding the allowable standard. The purposes of this article are to provide a method for investigating the exceeding probability of the rail displacement of HSRs under seismic excitation and to calculate the exceeding probability.

In order to investigate the exceeding probability of the rail displacement under different seismic excitations, the workflow of analyzing the smoothness of the rail based on incremental dynamic analysis (IDA) is proposed, and the intensity measure and limit state for the exceeding probability analysis of HSRs are defined. Then a finite element model (FEM) of an assumed HSR track-bridge system is constructed, which comprises a five-span simply-supported girder bridge supporting a finite length CRTS II ballastless track. Under different seismic excitations, the seismic displacement response of the rail is calculated; the character of the rail displacement is analyzed; and the exceeding probability of the rail vertical displacement exceeding the allowable standard (2mm) is investigated.

The results show that: (1) The bridge-abutment joint position may form a step-like under seismic excitation, threatening the running safety of high-speed trains under seismic excitations, and the rail displacements at mid-span positions are bigger than that at other positions on the bridge. (2) The exceeding probability of rail displacement is up to about 44% when PGA = 0.01g, which is the level-five risk probability and can be described as 'very likely to happen'. (3) The exceeding probability of the rail at the mid-span positions is bigger than that above other positions of the bridge, and the mid-span positions of the track-bridge system above the bridge may be the most hazardous area for the running safety of trains under seismic excitation when high-speed trains run on bridges.

The work extends the seismic hazardous analysis of HSRs and would lead to a better understanding of the exceeding probability for the rail of HSRs under seismic excitations and better references for the alert of the HSR operation.