Probabilistic reliability assessment of a reinforced concrete beam under uncertainty and climate-driven deterioration: Monte Carlo, FORM and metamodel-based evidence for a tropical urban exposure in Kinshasa

Introduction:

The long-term performance of reinforced concrete structures in tropical urban environments is governed not only by initial resistance, but also by deterioration processes accelerated by climate and environmental exposure. This study investigates the reliability of a reinforced concrete beam under uncertainties in material properties, loading and degradation, with a code-oriented interpretation based on a tropical urban exposure representative of Kinshasa, Democratic Republic of the Congo.

Methods:

A probabilistic framework was developed to assess flexural, shear and durability-related limit states. The analysis combined Monte Carlo simulation, the First-Order Reliability Method (FORM), and metamodel-based approximations. A time-dependent carbonation–corrosion model was introduced to represent deterioration under three scenarios: current tropical urban exposure, intensified climate exposure, and climate-resilient design adaptation. Reliability was interpreted against the common target benchmark of β = 3.8 for structural members over a 50-year reference period.

Results:

The results show that flexure governs at the initial stage, whereas durability becomes the governing criterion over time in all scenarios. The median corrosion initiation time was approximately 25.8 years for the current scenario, 17.5 years for the intensified scenario, and 69.0 years for the resilient scenario. At 50 years, the resilient design markedly improved performance relative to the other scenarios and achieved a flexural reliability index close to or slightly above the target level, whereas the governing reliability remained below target because durability controlled the long-term response. Among the surrogate models tested, the quadratic response surface remained the most stable and accurate after tuning and repeated cross-validation.

Conclusions:

The findings indicate that, for a tropical urban exposure such as Kinshasa, durability-driven design measures are more influential than simply increasing initial structural resistance. Increasing cover, improving concrete quality and reducing permeability appear to be the most effective strategies for enhancing long-term reliability and climate resilience.