## 1 Introduction
However, MCS suffers from the interactable disadvantage of being computationally prohibitive, especially for large-scale and complex structures. FORM and SORM [32] are efficient for high-dimensional problems but may face challenges with highly nonlinear and complex failure surfaces. Among these, the fourth-moment method [33] is of great interest in this study, as its advantage lies in better handling non-normal distributions by capturing skewness and kurtosis. Despite the advancements in these methods, accurately computing large reliability indices remains a significant challenge [8]. It is noted that large reliability indices correspond to low probabilities of failure, requiring precise and efficient computational techniques to avoid excessive resource consumption and ensure accuracy. Therefore, integrating these methods with FEA to account for carbonation effects in aquducts introduces additional complexities that need to be addressed. This study aims to develop and validate a robust methodology for the time-dependent reliability analysis of reinforced concrete aqueducts, specifically accounting for carbonation effects, which are a significant factor influencing the long-term performance of these structures. While considerable research has been conducted on the reliability analysis of reinforced concrete structures, existing studies often overlook the influence of environmental factors such as carbonation over time and fail to address the challenges in accurately assessing small failure probabilities in time-dependent reliability analysis. To fill this gap, this work integrates several advanced methods, including the fourth-moment method, dual power transformation, and Yeo-Johnson transformation, to enhance the accuracy of small failure probability calculations. By combining these techniques, the study provides a more comprehensive and accurate approach to assessing the time-dependent reliability of reinforced concrete aqueducts under carbonation effects. The structure of the study is as follows: Section 2 introduces the carbonation function for reinforced concrete structures, detailing the calculation of carbonation depth and the derivation of the reliability function. Section 3 establishes a finite-element-based framework for the time-dependent reliability analysis of aqueducts while considering the carbonation process. This section outlines the detailed steps involved in the model setup, simulation, and reliability assessment. Section 4 presents a case study to demonstrate the application of the proposed method, including a comprehensive analysis of the results and validation of the proposed method's effectiveness. After fitting the reliable index data calculated in the above section, a formula is obtained to predict the life of an aqueduct in Section 5. The last part, Section 6, offers the key findings of the study and future research. By following this structure, the study aims to provide a thorough and practical approach to assessing and managing the long-term reliability of reinforced concrete aqueducts under the influence of carbonation, thereby contributing to the advancement of structural engineering and maintenance strategies. Time-Varying Performance Function of Concrete Carbonization and the Statistical Moments of Its Random Variables