Bayesian model updating in ballasted tracks with the consideration of non-linear ballast stiffness

The nonlinear behaviour of granular engineering materials is widely known; and railway ballast has no exception. Under large amplitude vibrations, the behaviour of ballast becomes non-linear. Therefore, to reduce modelling errors in the detection of ballast damage, most importantly, under the sleeper; the nonlinear elastic behaviour of the ballast must be considered. Non-linear modelling is usually synonymous with discrete element modelling (DEM), in which the time constraint and the computational cost hinder applicability in large scale analysis. This paper reports the development of a methodology for model updating of the rail-ballast-sleeper system based on the Bayesian stsatistical framework, by incorporating non-linear ballast stiffness into finite element models. Instead of calculating the ballast stiffness, the proposed methodology estimate the marginal posterior (updated) probability density function (PDF) of various nonlinear ballast stiffness parameters utilizing a set of measured vibration data. To avoid the limitations identified with modal parameters, time-domain vibration data were utilized in the methodology. The applicability and effectiveness of the proposed model updating methodology were verified using simulated impact hammer vibration data. Different case studies with different simulated noise levels and different amount of measured data were also considered to investigate the robustness of the methodology. The analysis results are very encouraging showing possible extension of the proposed methodology in ballast damage identification.