Reliability Analysis of Uncertain Correlation During the Construction Period of a Cantilevered Arch Considering Temperature Effects

To investigate the influence of temperature effects on the reliability of cantilever-cast arch bridges during construction, and to comprehensively account for uncertain correlations among multiple variables, this paper proposes a time-varying reliability analysis framework for cantilever-cast reinforced concrete arch bridges during construction, with explicit consideration of temperature effects and uncertain correlations among multiple random variables. The framework integrates Copula functions with Bayesian Dynamic Models (BDMs) to overcome two key limitations of conventional reliability approaches: the common assumption of variable independence and the inability to dynamically update reliability estimates using field monitoring data. The Gaussian Copula is adopted to characterize the nonlinear dependence structures among construction-stage variables—including cable forces, material properties, and ambient temperature—while the AR(1)-based BDM enables recursive state prediction and real-time reliability updating. To ensure computational tractability for large-scale finite element models, an XGBoost surrogate model (R2 = 0.97, RMSE = 0.76 MPa), selected through systematic comparison against six alternative methods, is coupled with an improved Non-dominated Sorting Genetic Algorithm II (NSGA-II) optimization algorithm for efficient computation of component and system reliability indices. The proposed framework is validated through three independent exercises: Monte Carlo simulation using the surrogate model with 106 samples (relative errors < 3.2%), comparison with FORM and independent-assumption approaches, and an analytical benchmark (relative error 1.2%). Application to the Shatuo Bridge—a 240 m span reinforced concrete deck arch bridge constructed by the cantilever casting method—demonstrates that temperature effects reduce the arch rib stress reliability index from β = 4.25 under ideal conditions to β = 3.98 under actual construction conditions, a reduction of approximately 6.3%. The system reliability index, accounting for failure-mode correlations via the Gaussian Copula, is β = 3.921, which is lower than the independent-failure prediction (β = 4.11) but still exceeds the target reliability of 3.5 specified in Chinese code JTG 2120-2020. Quantification of epistemic uncertainties—surrogate-model error (1.1%), model-form uncertainty (4.2%), and parameter-estimation uncertainty (1.5%)—yields a reliability index range of β = 3.81–3.97, confirming the robustness of the safety assessment. Global sensitivity analysis using Sobol indices identifies the arch rib elastic modulus (38% variance contribution), unit weight (21%), cable forces (15% combined), temperature (12%), and thermal expansion coefficient (8%) as the dominant factors governing structural safety. The proposed Gaussian-Copula-BDM framework provides a theoretically sound and computationally efficient tool for dynamic safety control during arch bridge construction, enabling proactive risk management through continuous updating with monitoring data.