Calculation of the dynamic responses of a railway track on a non-uniform foundation

The dynamic response of a railway track has been investigated by analytical or numerical models. When rail supports (sleepers) or foundation contain defects, the damage reduces stiffness and the track becomes non-uniform. This paper presents a new analytical model to calculate the dynamic responses of a railway track on a non-uniform foundation. In this model, the rail is considered as an infinite beam resting on equidistant supports and subjected to moving forces. The sleepers responses are stable provided that there is a sufficiently large distance between the applied forces and the defective area. By combining this condition and the dynamic equation of the beam, we can deduce a relation between the reaction forces in the supports and the displacement of the beam. This relation does not depend on supports and foundation behaviors. Hence, we can calculate the dynamic response of the track by using the constitutive laws of the supports. The responses can be obtained finally with direct or with iterative techniques. The numerical examples show that a defective zone causes an increase in the rail displacement at the defective zone and overloads the neighbor supports.