Stochastic Collision Probability Assessment of Vessels with Padma Bridge Piers under Random Initial Conditions

Abstract Ship-bridge collisions remain a persistent global safety concern, often leading to severe structural damage, vessel losses, and risks to passenger safety. The Padma Multipurpose Bridge in Bangladesh, a 6.15 km long structure supported by 42 piers, has experienced several vessel impacts during and after construction, mainly involving ferries. While the structural damage has been minor, the repeated incidents underscore the urgent need for a quantitative risk assessment in this critical waterway. This study presents a probabilistic framework for evaluating the collision risks of small cargo vessels with Padma Bridge piers, focusing on the influence of vessel manoeuvrability under random initial conditions. Ship dynamics were modelled using Nomoto's K–T manoeuvring equations, with trajectories stochastically simulated via the Runge–Kutta fourth-order method. A total of sixty-two million simulations were performed across varying rudder angles (–15° to +15°) and speeds (6–10 knots), with the navigation domain divided into 14 subregions around piers 9 to 18. The simulation typically takes approximately 50 hours to complete on a standard laptop computer. Results show that collision probability increases significantly with larger rudder angles and higher speeds, with piers 9, 10, 16, and 17 identified as high-risk zones. Conversely, central courses were found to minimise collision likelihood, offering safer navigation pathways. The findings are consistent with historical incidents, demonstrating the model's validity and underscoring the importance of manoeuvring discipline in confined waterways. Beyond the Padma Bridge case, the proposed stochastic framework provides a transferable methodology for assessing ship–structure collision risks in complex riverine or coastal environments, supporting both navigational safety management and bridge protection strategies