## 4 Conclusions  
In this study, the service life of RC structures affected by sulfate ingress was analyzed with a temperature-dependent diffusion coefficient and patterns of design parameters. Through obtaining activation energy based on the diffusion test results, two different design techniques were applied to the RC drainage structure, and the effects of design parameters (cover depth, component of cement, exterior sulfate concentration, and diffusion coefficient) and their variations were analyzed in terms of service life variation. The conclusions drawn from this work are as follows.  
Through a natural diffusion cell test from 20 \({}^{\circ}\)C to 50 \({}^{\circ}\)C, the diffusion coefficient of sulfate ions was obtained, and the activation energy, which can be used for the temperature parameter, was derived based on the Arrhenius equation. With the increasing temperature to 50 \({}^{\circ}\)C, the service life of RC culvert was greatly reduced due to the enlarged diffusion coefficient and constant cover depth. The probabilistic pattern of the diffusion coefficient (mean and COV) showed higher mean and COV with increasing temperature due to unstable ion transport and the dissociation of bound ions. The service life from the probabilistic technique considering the temperature effect showed similar results to the deterministic technique since the design parameters have a reasonable level of COV and no consideration of the use period. When considering more marginal cover depth in the deterministic technique based on the design code, more conservative results were evaluated in the deterministic technique.  
Among the four design parameters of cover depth, content of Al\({}_{2}\)O\({}_{3}\), sulfate concentration, and diffusion coefficient, the cover depth greatly affected the service life since the three parameters, except for cover depth, in the governing equation were linearly proportional to the deteriorated depth due to sulfate penetration. Through the probabilistic simulation based on normal distribution, the COV over 0.2 yielded a large reduction in service life, and it was remarkably observed in the case of small cover depth.  
In this study, a limited number of samples were tested in the different temperature conditions, and simple normal distributions of design parameters were assumed. For more reasonable durability design through the probabilistic approach, several further studies are required for the definition of time-dependent diffusion for sulfate ions, reasonable database construction for design parameters, and quantitative definition of exterior conditions, such as sulfate ion concentration, saturation, and temperature.  
Conceptualization, S.-J.K. and A.K.A.; methodology, S.-J.K. and A.K.A.; formal analysis, S.-J.K. and H.-W.L.; investigation, S.-J.K. and K.-H.Y.; resources, S.-J.K.; data curation, S.-J.K. and H.-W.L.; writing--original draft preparation, S.-J.K. and H.-W.L.; writing--review and editing, S.-J.K. and K.-H.Y.; supervision, S.-J.K. and K.-H.Y.; funding acquisition, S.-J.K. and A.K.A. All authors have read and agreed to the published version of the manuscript.  
National Research Foundation of Korea (NRF), grant funded by the Korean government.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
**Acknowledgments:** This work was supported by the National Research Foundation of Korea (NRF), grant funded by the Korean government (MSIT) (No. RS-2024-00415881 and NRF-2022M2E9A3091898).  
**Conflicts of Interest:** The authors declare no conflicts of interest.