Keywords: dynamic interaction, train, railway structure, contact-impact, derailment, multibody dynamics, nonlinear response analysis, finite element method.

It is very important to study the combined dynamic behavior of a high-speed train and the railway structure including post-derailment during an earthquake to design an earthquake-safe high-speed railway system. In this paper, a simple and efficient computational method to solve for the dynamic interaction of a Shinkansen train (high-speed train in Japan) and a railway structure including the post derailment behavior during an earthquake is given.

The motion of the train is modeled using multibody dynamics with nonlinear springs and dampers to connect cars at the connectors and all components in each car. Simple and efficient mechanical models to express the contact-impact behaviour between wheel and rail before derailment and between wheel and the track structure after derailment are given to solve the interaction between the wheel and track structure effectively. The criteria for the derailment of the wheel to the field and gauge sides of the track are given by the relative displacement between wheel and rail in the transverse direction.

After the derailment of wheel, the relationship of the relative displacement and force on the contact surface between wheel and track structure is given to express the contact-impact behaviour in the vertical and transverse directions. Rail and track elements have been developed to model the behaviour of long track components in the longitudinal direction such as the rail and track based on multibody dynamics and finite element method (FEM) combined, where in-plane motions of the cross-section are determined using multibody dynamics and out-of-plane motions in the rail direction are determined using the FEM to solve the interaction between wheel and long railway components effectively.

The motion of the railway structure is modeled with various finite elements such as beam, truss, shell, solid, and nonlinear spring and damper elements, and also with rail and track elements. The transient nonlinear dynamic response during an earthquake is obtained by solving the equations of motion of the train and railway structure subjected to interactions between wheel and the track structure including post-derailment behaviour.

Based on the present method a computer program, DIASTARS, has been developed for the simulation of a Shinkansen train running at high speed on the railway structure including post-derailment behavior during an earthquake. An example of the high-speed train running at high speed on a four-spanned steel-concrete hybrid bridge during an earthquake is demonstrated. The dynamic behaviour of the train and the bridge during the earthquake are shown. The simulation results of a Shinkansen car running at a speed of 300 km/h on the ladder track with guards attached to prevent the wheels deviating from the track even after derailment from the three spanned viaduct during an earthquake is demonstrated. Through applications to actual problems, the effectiveness of the method presented is discussed.

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