The probability of an instant rail break, initiated at a single pre-existing rail foot crack due to a severe wheel impact loading, is predicted using statistical methods and a time-domain model for the simulation of dynamic vehicle–track interaction. A linear elastic fracture mechanics approach is employed to calculate the stress intensity at the crack in a continuously welded rail subjected to combined bending and temperature loading. Based on long-term field measurements in a wayside wheel load detector, a three-parameter probability distribution of the dynamic wheel load is determined. For a faster numerical assessment of the probability of failure, a thin plate spline regression is implemented to develop a meta-model of the performance function quantifying the stress intensity at the crack. The methodology is demonstrated by investigating the influence of initial crack length, fracture toughness and rail temperature difference on the risk for an instant rail break
