Based on past earthquake events, bridges are the most critical and most vulnerable component of road and rail transport systems, while bridge damage is related to substantial direct and indirect losses. For the case of railway bridges, the estimation of seismic fragility is a rather complex and computationally demanding procedure given the real-time interaction of the train movement and the bridge and the different failure modes of subsystems. Considering vehicle-bridge interaction (VBI) in the frame of railway bridge fragility analysis is rather challenging, requiring analysis of the bridge and the vehicle at every time step. Partitioning of the coupled VBI problem proposing a weak formulation scheme and a set of second-order ordinary differential equations (ODEs) is performed in a way that allows for independent subsystem (vehicle and bridge) analysis. Several methodologies are available in the literature to estimate the seismic fragility of train-bridge systems that ignore the nonlinear behavior of the bridge during earthquake loading, the step-by-step VBI, and the different failure modes of critical components. The scope of this research paper is to propose a real-time component-based methodology for estimating bridge fragility curves, considering all critical components and failure modes of subsystems. The two subsystems are incorporated in a uniform software platform using the co-simulation approach and a Gauss-Seidel communication pattern. The vehicle-rail system is solved using a C++ tailor-made code, including a mathematical formulation that is based on the description of the constrained problem with a set of pure ODEs, avoiding issues related to differential-algebraic equations, constraint violation, drifts, energy loss, stability, and convergence. The vehicle subsystem is solved using multibody dynamics (MBD), while the bridge subsystem is modeled and solved using OpenSees.py. An ad-hoc software for the implementation of the probabilistic framework and the derivation of fragility curves is developed in Python. A novel methodological procedure is proposed, dully tailored to the demanding estimation of fragility curves of the coupled vehicle-bridge problem. The step-by-step solution of subsystems is performed using the co-simulation technique. Real-time interaction is allowed, considering a rational transfer of force, velocity, and displacement between subsystems. The methodology along with the software developed is described and applied to two representative reinforced concrete (RC) bridges of the Greek railway network (v <= 200 m/sec), providing fragility curves (i.e., the seismic performance for various levels of earthquake intensity) for the coupled system. The results are discussed and assessed.
