Substructure simulation of inhomogeneous track and layered ground dynamic interaction under train passage

The vibrations in track and ground induced by train passages are investigated by the substructure method with due consideration to dynamic interaction between an inhomogeneous track system comprising continuous rails and discrete sleepers, and the underlying viscoelastic layered half space ground. Initially, the total system is divided into two separately formulated substructures, i.e., the track and the ground. The rail is described by introducing the Green function for an infinite long Euler beam both for moving axle loads action from a train and for reactions from sleepers. The ground is formulated by the layer transfer matrix approach for wave propagation along the depth. Subsequently, these substructures are integrated to meet the displacement compatibility and force equilibrium via inertia of sleepers and stiffness of railpad springs. The dynamic equations are solved in the frequency-wave-number domain by applying the Fourier transform procedure. Based on the assumption of a constant train speed, the time domain response is evaluated from the inverse Fourier transform computation. The dispersive characteristics of the layered ground and the moving axle loads lead to significantly different response features, depending on the train speed. The response is classified as quasistatic for a low speed, whereas it is dynamic for a high-speed situation. An illustrative case study is presented for Swedish X-2000 train track properties and ground profile.