Bayesian Modeling of Axial Strain-Hardening Behaviour in Railway Ballast

The heterogeneity, irregularity and unbounded nature of railway ballast particles are believed to be responsible for certain intrinsic behaviors of ballast, among which is strain-hardening property. Hence, for ballast modeling studies involving settlement, stress, stiffness, etc., inclusion of this phenomenon is pertinent. Developing models that incorporate strain-hardening from triaxial test data are plagued by numerous parameters and inconsistencies amongst others, thus necessitating an empirical approach. In this study, a best fitting axial stress-strain model for capturing the behavior of ballast is investigated, based on vertical acceleration data collected from impact hammer test on an indoor track panel with simulated ballast damage. A simple beam on an elastic foundation model (BOEF) of the track, with the ballast modeled as elastic-plastic spring series was developed. To cater for the uncertainties and errors rife with empirical models as well as from measurement, an adaptive Markov Chain Monte Carlo Bayesian Scheme was developed in the time domain and used in calibrating the parameters of the investigated models. Five strain hardening power laws, which are variations of the Ludwik model are examined, and the Bayesian model selection method was utilized in determining the most plausible calibrated model conditional on the measured vibration data. Afterward, the applicability of the proposed methodology in effective detection of ballast damage location and severity beneath a sleeper is demonstrated.