## 3 Evaluation of Service Life Using Different Design Approaches
### Service Life Variation with Activation Energy-Deterministic Methods  
The design parameters like mean and COV for service life evaluation are listed in Table 4 with the related references [15; 16; 17], and the target RC culvert is shown in Figure 9, which was constructed in UAE Barakah [34; 35].  
In Table 4, the average sulfate ion concentration was set to 200 ppm, which amounts to 96.06 g/L (mol of SO4\({}^{2-}\)) since the annual average was reported to be low due to rainfall drainage [36]. The elastic modulus and Poisson's ratio were assumed to be at the normal level, referring to ACI 318-95 and KS F 2438. The parameters of roughness, fracture energy, and linear parameter (B) are adopted from the previous results [17; 37]. In the model, high-strength concrete may have a relatively rapid deteriorating rate due to the high elasticity and low Poisson's ratio, but it has a very low diffusion coefficient of sulfate ions due to the dense pore structure. The concrete with GGBFS (ground-granulated blast furnace slag), which is very efficient for chemical erosion control, has a very low diffusion coefficient,  
Figure 8: Activation energy of sulfate ions with the previous studies on chloride ions.  
Figure 7: Probability distributions of measured diffusion coefficients.  
but it has lots of Al2O3, over 10.0%. For controlling sulfate erosion, the effect of design parameters on the deteriorating rate should be considered comprehensively.  
Through Equations (1)-(3), the deterioration depth with period was evaluated, which showed the service life was evaluated as being shortened due to enlarged diffusion with rising temperature. The environmental load factor (1.1) and reduction factor (0.94) were adopted, referring to the related codes. The results are shown in Figure 10, where, with increasing temperature from 20 \({}^{\circ}\)C to 50 \({}^{\circ}\)C, the service life was reduced to 9.57 years, which amounts to 29.4%. The enlarged diffusion coefficient with temperature was utilized in Equation (1) and linearly considered for the deterioration coefficient and service life.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Types**} & \multirow{2}{*}{\
\begin{tabular}{c} **Deterioration** \\ **Depth Method** \\ \end{tabular} } & \multicolumn{2}{c}{**Probabilistic Method**} \\ \cline{3-4}  & & **Mean** & \multicolumn{2}{c}{**Normal**} \\ \hline Cover depth (mm) & 50 & 50 & 0.12 \\ \hline Al2O3 (\%) & 0.05 & 0.05 & 0.15 \\ \hline Average sulfate concentration (ppm) & 200 & 200 & 0.25 \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Diffusion coefficient \\ (10\({}^{-12}\cdot\)m\({}^{2}\)/s) \\ \end{tabular} } & \multirow{4}{*}{1.95} & 20 \({}^{\circ}\)C 1.95 & 0.04 \\ \cline{3-4}  & & 30 \({}^{\circ}\)C 3.38 & 0.02 \\ \cline{3-4}  & & 40 \({}^{\circ}\)C 4.35 & 0.08 \\ \cline{3-4}  & & 50 \({}^{\circ}\)C 6.63 & 0.15 \\ \hline Elastic modulus (Mpa) & 26,000 & 26,000 & - \\ \hline Poisson’s ratio (-) & 0.17 & 0.17 & - \\ \hline Roughness coefficient (-) & 0.25 & 0.25 & - \\ \hline Concrete fracture energy (J/m\({}^{2}\)) & 10 & 10 & - \\ \hline B \(\left(10^{-6}\)m\({}^{3}\)/mol\(\right)\) & 1.8 & 1.8 & - \\ \hline \hline \end{tabular}
\end{table}
Table 4: Durability design parameters for two evaluation methods.  
Figure 9: Schematic diagram of RC culvert under sulfate attack.