# Time-varying reliability analysis of the main arch ring in reinforced concrete arch bridges considering non-stationary degradation

## TL;DR

This paper introduces a new method to assess the reliability of reinforced concrete arch bridges under changing degradation conditions over time.

## Contribution

A novel ISSA-Kriging surrogate model is proposed for non-stationary degradation analysis in reinforced concrete arch bridges.

## Key findings

- The ISSA-Kriging model achieves 60% higher accuracy than standard Kriging models in reliability prediction.
- Non-stationary degradation accelerates reliability decay by 20%-30% compared to stationary degradation.
- The model reveals a 'unimodal' reliability distribution across the main arch ring after 50 years of service.

## Abstract

Reinforced concrete arch bridges are susceptible to non-stationary degradation under combined environmental and load effects, rendering traditional reliability assessments based on stationary assumptions inadequate. To address this gap, this study first derived a reliability calculation method tailored for non-stationary degradation scenarios. Subsequently, an ISSA-Kriging surrogate model was proposed for the reliability evaluation of reinforced concrete arch bridges, with validation and analysis conducted using the Shuiluo River Bridge as an engineering case. Results indicate that the ISSA-Kriging model achieves high prediction accuracy: its sample response error is controlled within 4% in repeated random sampling tests, and its accuracy is approximately 60% higher than that of the standard Kriging model. The model reliably fits the time-varying reliability curve of the main arch ring, confirming its suitability for large-scale parametric analysis and engineering optimization. Compared with stationary degradation, non-stationary degradation accelerates the decay rate of the main arch ring’s reliability index by 20%–30%. After 50 years of service, the reliability reduction rates of the arch springing, arch crown, and mid-span (1/2 arch ring) under non-stationary degradation reach 90.8%, 97.8%, and 52.7%, respectively, leading to an obvious “unimodal” reliability distribution across the semi-structure of the main arch ring. Additionally, non-stationary load fluctuations exacerbate structural damage accumulation, emphasizing the need for targeted durability protection of key components. A limitation of this study is that the proposed non-stationary degradation model, while theoretically consistent with non-stationary deterioration laws and validated via numerical simulation, lacks direct calibration with long-term on-site monitoring data. Future research will focus on integrating structural health monitoring data to dynamically revise the model, narrowing the gap between numerical simulation and actual structural performance, and thereby enhancing the engineering practical value of non-stationary reliability assessment results. This study provides a robust technical tool for the non-stationary reliability assessment of reinforced concrete arch bridges and offers guidance for durability design and maintenance optimization.