Vehicle-bridge interaction analysis modeling derailment during earthquakes

A realistic simulation of train derailment is crucial when assessing the safety of a train running over a bridge during earthquake excitation. This paper presents a seismic vehicle-bridge interaction analysis that simulates directly different wheel-rail contact states including flange contact, detachment, uplifting, wheel-rail climbing-up, recontact, and ultimately, derailment. The proposed model determines the contact point and the direction of the contact forces over practical nonlinear profiles of wheels and rails. It then classifies the wheel-rail contact, as double contact, single contact or double detachment, and tackles accordingly the kinematics. The modeling of the wheel-rail contact along the normal direction hinges upon the principles of nonsmooth dynamics and accounts for continuous contacts of finite duration, impacts (instantaneous duration) and transitions from continuous contacts to detachments. The modeling of the tangential contact forces follows the nonlinear creep theory. The results verify that well-known force-based metrics such as derailment factor and offload factor yield conservative estimations of train operational safety. The analysis stresses the key role of flange contact under a large contact angle that could lead to the detachment of the other wheel of the same wheelset, and underlines the importance of a more realistic train-bridge interaction modeling during earthquakes. For the examples examined, which involve a complete three-dimensional vehicle running on simply supported bridge units, derailment occurs when a wheel rolls over the rail head (wheel-rail climbing-up). The results unveil that both the amplitude and the frequency of the earthquakes are important to the safety of trains running over bridges.