## 1 Introduction  
Reinforced concrete aqueducs are critical structures in water transportation systems, playing a vital role in delivering water efficiently across regions [1, 2]. The demand for reliable water supply systems has grown globally due to urbanization, climate change, and the increasing need for efficient resource management. Aqueducs, as essential infrastructure for transporting water, face significant challenges related to environmental degradation, particularly carbonation, which affects their long-term reliability. Therefore, it is critical to evaluate the structural integrity of these systems to ensure their continued functionality in meeting current and future water demands. Over their service life, carbon dioxide from the atmosphere penetrates the concrete of these structures and reacts with calcium hydroxide to form calcium carbonate [3]. This reaction lowers the pH of concrete that is exposed to various environmental factors, leading to deterioration. Among these, carbonation is one of the most prevalent and damaging issues [4]. Carbonation is a chemical process in concrete, diminishing its alkalinity and the protective oxide layer around the steel reinforcement. As a result, the reinforcing steel becomes susceptible to corrosion, which can lead to cracking, spalling, and, ultimately, structural failure [5; 6]. Given the significant impact of carbonation on the durability and safety of aquducts, it is essential to evaluate the structural reliability of these systems over time [7]. Reliability analysis [8; 9] helps in understanding the likelihood of failure and the progression of deterioration, thus providing critical insights for maintenance and intervention strategies. By assessing the reliability of aquducts while considering carbonation effects, engineers can develop more effective and timely maintenance plans, ensuring the longevity and safety of these structures. Traditional reliability analysis methods often assume static conditions [10], which do not account for the progressive nature of deterioration mechanisms such as carbonation. In reality, the performance and safety of aquducts are influenced by multiple time-varying factors, including environmental exposure [11], material degradation [12], and dynamic load conditions [13]. Time-dependent reliability analysis [14] addresses this by incorporating the temporal evolution of these factors, providing a comprehensive assessment of structural reliability. Extensive research has been conducted on the reliability analysis of reinforced concrete structures, employing various probabilistic and deterministic methods. For aquducts, specific studies have explored the impacts of environmental degradation [15], load variations [16], and material properties [17] on structural performance. Finite element analysis (FEA) [18; 19] has emerged as a powerful tool for simulating complex structural behaviors and assessing reliability under diverse conditions. However, there is a notable gap in the literature regarding the application of FEA to the time-dependent reliability analysis of aquducts considering carbonation effects. Most existing studies [20; 21] focus on static reliability assessments or use simplified models that do not fully capture the intricate interactions between carbonation processes and structural responses over time. Considering the progressive nature of carbonation and its significant impact on structural performance, there is a clear need for robust time-dependent reliability analysis [22] specifically tailored for aquducts. On the other hand, several methodologies have been developed for time-dependent reliability analysis, including Monte Carlo simulation (MCS) [23; 24; 25], the FORM or SORM method [26; 27; 28], the surrogate-based reliability method [29], the high-order moment method (such as the fourth-moment method) [30; 31], etc. The MCS method is a widely adopted technique for computing time-dependent reliability indices.