Estimating Exceedance Probabilities of Railway Bridge Vibrations in the Presence of Random Rail Irregularities

This contribution addresses the estimation of exceedance probabilities of the dynamic random response of railway bridges subjected to high-speed trains in the presence of random rail irregularities. The random nature of the irregular rail track is described by a spatial ergodic stochastic process, and consequently the dynamic bridge response becomes a stochastic process in time with generally unknown distributions. Using numerical simulation methods, the response thresholds for bridge deflection and acceleration are estimated to obtain small exceedance probabilities. Combining these limits with the response at perfect rail geometry provides an estimate of the dynamic response amplification due to random rail irregularities. This is in line with the semi-probabilistic safety concept of modern civil engineering, where critical response thresholds for structures are associated with small exceedance probabilities. It is shown that modeling the maximum bridge deflection as a normally distributed random variable with parameters fitted to the results of a Monte Carlo simulation with small sample size is a computationally efficient approach for estimating the amplified deflection. In contrast, the random maximum bridge acceleration is better captured by a lognormal distribution. As an efficient alternative, the subset simulation method provides accurate predictions for very small exceedance probabilities. If the amplitudes of the rail irregularities at discrete spatial coordinates along the rail axis are considered as random variables, the stability of subset simulation increases.