Stochastic analysis and dynamic reliability of the heavy-haul train-bridge system based on direct probability integral method

In this paper, a heavy-haul ballasted track-bridge interaction model is established by the finite element method in matrix representations, and their interaction to the train is achieved by the wheel-rail contact. A new direct probability integral method (DPIM) is introduced to achieve the stochastic analysis and reliability assessment of the train-ballasted track-bridge interaction (TTBI) system. Besides, the accuracy of the train-ballasted track-bridge model is validated by the field measurement. The probability characteristics of the dynamic behavior of the system are compared between DPIM and sophisticated PDEM, to show the accuracy and efficiency of the stochastic analysis method. The results demonstrated that the efficiency is improved by 1-2 orders of magnitude in terms of stochastic post-processing. Furthermore, the influences of random factors, e.g., track irregularity, axle loads and bridge parameters, etc., on the dynamic behavior of system are investigated by the proposed method, and the time-dependent reliability is presented with the aid of the extreme distribution events. The results indicate that the train axle load, running speed and variability of parameters have remarkable effects on dynamic performance. Besides, the failure probability of the bridge is very small attribution to the higher allowable threshold (e.g., mid-span displacement), but the safety of train operation decreases with the increase of vehicle speed especially under the critical speed of resonance.