Probabilistic characterisation of transition points in three-stage permanent deformation curves using Bayesian inference approach

Abstract

ABSTRACT Multiple specimens are tested to evaluate their rutting propensity by applying static and dynamic creep loads until a three-stage permanent deformation curve is obtained. This three-stage curve consists of two transition points, i.e. one from the primary to the secondary stage and the other one from the secondary to the tertiary stage of deformation. Due to replication, these transition points behave like random variables rather than deterministic. This stochasticity in the transition points is characterised by the Probabilistic -Stress-Number of cycles (P-S-N) approach. A power law model is used to describe the trajectory of transition points with respect to the input stress level. The probabilistic nature of these power law parameters is characterised by the Bayesian approach rather than the classical approach because the latter considers distribution parameters to be constant and does not reflect the replicate stochasticity. Posterior distributions are determined based on data translated likelihood method. Based on the posterior distributions of the data sets, obtained power law trajectories at various reliability levels, ranging from highest to lowest, are constructed. One advantage of this approach is its capability to extrapolate secondary transition points (Flow number or Flow time) when they cannot be readily obtained under desired testing conditions.