Time-Variant Reliability Model for Parallel-Wire Stay Cables Incorporating Corrosion Evolution and Local Stress Amplification

The long-term reliability of stay cables is essential to the structural integrity of cable-stayed bridges, particularly under the coupled effects of high stress ratios, progressive corrosion, and local stress concentrations. Conventional fatigue formulations—such as S–N curves or static Weibull models—are inadequate for representing the nonlinear and stochastic nature of corrosion-fatigue deterioration. This study develops a time-dependent reliability model formulated within a four-parameter Weibull framework, where the shape and scale parameters evolve as functions of the corrosion rate and stress ratio. The corrosion evolution is modeled by an exponential function of exposure time, establishing a temporal coupling between mechanical loading and environmental degradation. Analytical derivations yield closed-form expressions for the time-dependent hazard function ℎ(t) and survival function R(t), providing explicit reliability evaluation without iterative computation. At the system level, a series–parallel reliability model is constructed by integrating wire-level degradation with a load redistribution function that captures sequential wire failures. Model parameters are estimated using a maximum-likelihood method based on 99 experimental datasets, and Monte Carlo simulations are performed to assess stochastic reliability evolution under varying corrosion intensities. The findings show that models incorporating corrosion evolution and stress-amplification effects consistently predict earlier fatigue failure than those based on the conventional assumption of constant corrosion, thereby offering a more conservative and realistic representation of structural degradation. The proposed framework is mathematically tractable and broadly applicable, enabling rigorous corrosion–fatigue reliability assessment for cable-stayed structures and other complex multi-component systems.