On the use of dispersion curves to determine the critical speed of railway tracks. Application to case studies

Abstract

Trains may reach a so-called critical speed at which, in the absence of damping, the dynamic response of the entire railway infrastructure would grow without any bound. A train will have less impact on the track the more its speed is lower than the critical speed. Therefore, in terms of track maintenance, it is of vital importance to know the critical speed along the track before its construction.Following the results mathematically proved by Kausel et al. (2020), we present a procedure —referred to as the “CSC method”— to determine the critical speed of railway tracks. It is based on the dispersive characteristics of the railway track system, which consists of the track bed layers (including the ballast, subballast and form layers among others), the embankment and the foundation ground (which can be arbitrarily layered). We validate the CSC method by using measurements from the well-known real case of Ledsgard (Sweeden). This method is easier to be implemented than dynamic FEM models and requires less geotechnical parameters and computational time.The CSC method is applied to some case studies: We use it to estimate the critical speed of a typical high-speed line and to study the influence on the critical speed of (i) the height of the embankment and (ii) the presence and thickness of an upper ground layer with low shear wave velocity. In addition, the critical speed inferred for the typical high-speed line is corroborated with experimental results from a railway testing facility at 1:1 scale, which can be interpreted as further validation of the CSC method. Moreover, the robustness of this method is demonstrated by the fact that the trend of results from the latter calculations (cases i and ii) agrees with the expected ones.