Quantifying live bending moments in rail using train-mounted vertical track deflection measurements and track modulus estimations

This paper presents a new methodology to quantify the vertical bending moments that generate in rail under the passage of train wheels. In this method, the rail-bending moments are quantified from track modulus estimated using train-mounted vertical track deflection (VTD) measurements. This provides a practical approach for quantifying the rail-bending moments along large railway networks. The method requires the mathematical correlations between VTD, track modulus and rail-bending moments. Hence, a detailed finite element model was developed to investigate and quantify the mathematical correlations between these parameters. Various track modulus distributions were simulated and the resultant VTD and rail-bending moments were calculated. The mathematical correlation between inputted track modulus, and modelled VTD and rail-bending moments were then quantified using statistical approaches. From the results, track modulus average and standard deviation can be estimated over track windows using the VTD measurements. These estimations can be then employed to quantify the average and peak for the envelope of the maximum vertical bending moment in rail over the same track window. The accuracy of the method was verified using a numerical case study for which a random track modulus distribution was considered and artificial noise was added to the modelled VTD.