Reliability-Based Modelling of Reinforced Concrete Structural Deterioration under Coupled Chloride-Induced Corrosion and Mechanical Loading

Abstract

Reinforced concrete (RC) structures exposed to chlorides while carrying sustained load deteriorate through interacting processes that are usually modelled separately. This study develops a time-dependent probabilistic framework in which chloride-induced corrosion and mechanical damage are coupled explicitly. A one-dimensional Fickian chloride ingress model with lognormal parameters defines the distribution of corrosion initiation time. After initiation, corrosion penetration is amplified by a mechanical damage index (one-way coupling), while the same damage index independently reduces flexural resistance. Resistance is compared with a time-growing bending-moment demand through the limit-state function g(t) = M_R(t) − M_E(t), and Monte Carlo simulation (MCS) in MATLAB gives the probability of failure P_f(t) = P[g(t) ≤ 0] and the reliability index β(t) = −Φ⁻¹(P_f(t)) over 50 years. For a simply supported 5.0 m beam, mean chloride concentration at the reinforcement rises to about 1.45 kg/m³ at 50 years and passes the 0.60 kg/m³ threshold at 19–20 years (5th–95th percentile at 50 years: 0.83–2.15 kg/m³). Bar diameter falls from 20.0 mm to 18.92 mm (−5.4%) for corrosion only and to 18.55 mm (−7.25%) for the coupled model, which is about 34% more diameter loss. Mean resistance falls from 67.5 to 39.5 kN·m (−41.5%) while mean demand rises from 80 to 89 kN·m (+11.3%), widening the resistance–demand gap from 12.5 to 49.5 kN·m. Because mean demand already exceeds mean resistance at t = 0, P_f starts near 0.85 (β ≈ −1.0); under coupled deterioration β falls to about −3.4 and P_f approaches 1.0 by 30–35 years. The corrosion-attributable reliability difference reaches about 1.38 at 50 years. Neglecting corrosion–mechanical interaction therefore underestimates long-term deterioration in the case studied.