## 5 Case Study  
Figure 14 shows the non-uniform patterns of the locations of stagnant water (30 cases) at the top surface of studied RC deck. The relation of the wetting rate at the top surface (WR) expressed in Equation (4), and the computed fatigue lives is shown in Figure 15, where their detailed remaining fatigue lives, normalized fatigue life by the fully dry condition, and WR indices are listed in Table 3. The simulation results prove the wide range of fatigue life despite of the same WR aiming at the significance of wetting patterns on the fatigue life. It is clear that the fatigue life is significantly reduced when the wetting locations are at the central zone of the wheel loading path as the following cases: (3), (13), (16), (20), (27), and (29). On the other hand, the impact of stagnant water is significantly reduced, when the wetting locations are near the sides of the deck, away from the wheel loading path, as the following cases: (4-9), (17-19), and (26). It is demonstrated that the negative impact of the stagnant water on the fatigue life is reduced as the wetting locations start to be farther from the central zone of the wheel-loading path, as shown in Figure 16, where X is the longitudinal distance of the central wetting location to the center of the RC deck. \[\mathrm{WR\%}=\frac{\sum_{k=1}^{k=n}\left(E_{k}\right)}{n}\times 100, \tag{4}\]  
where WR% is the wetting rate among the top mesh layer of the RC deck, k is the k\({}^{\mathrm{th}}\) element at the top surface, E\({}_{k}\) is environmental condition of the k\({}^{\mathrm{th}}\) element (0 for dry, 1 for wet), and n is the total number of elements at the top surface of the deck (336 is this study). Figure 12: Load cycles and the top compressive stresses of the transverse direction of the central zone of the RC deck. Figure 13: Load cycles and the bottom-steel tensile stresses of the central zone of the RC deck. For further investigation for the wetting pattern, a comparison has been made between case (5) that has low water impact and case (16) that has high impact, where the difference in their fatigue lives is around 1.6 times despite of the quite close value of WR. Figure 17 shows the development of the central live load deflection with loading cycles for cases (5) and (16), where their remaining fatigue lives are 160.0 and 99.8 million cycles, respectively. By investigating the rate of erosion of the concrete at the wetting locations for both cases (see Figure 18), it is obvious that the erosion starts earlier in case (16) than case (5). This is also clear in the rise of the pore water pressure for each case at the same particular time of reaching full erosion (K = 0), as shown in Figure 19. This can be explained by checking the average principal strains at the bottom surface of the RC deck just below their wetting locations, as shown in Figure 20.  
Figure 14: Location patterns of stagnant water. Figure 15: Relation of wetting rate at the top layer of RC deck and the fatigue life. Figure 16: Effect of wetting locations on the fatigue life of RC decks. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{\ \begin{tabular}{c} **Life** \\ **\"Million Cycles\"** \\ \end{tabular}  } & \multicolumn{1}{c}{**Normalized**} & \multirow{2}{*}{**WR\%**} & \multirow{2}{*}{**Case**} & \multirow{2}{*}{** \begin{tabular}{c} **Life** \\ **\"Million Cycles\"** \\ \end{tabular}  } & \multirow{2}{*}{**Normalized**} & \multirow{2}{*}{**WR\%**} \\  & & & & & & & \\ \hline
1 & 171.7 & 0.78 & 2.4 & 16 & 99.8 & 0.45 & 4.8 \\  
Figure 19: Load cycles and the pore water pressure of the upper zone of cases (5) and (16) at their wetting locations. Figure 20: Load cycles and the average principal strains of the bottom zone of cases (5) and (16) at their wetting locations. It is found that the amplitude of the principal strains for case (16) is higher than that of case (5), since it is the location of maximum bending moment, where the flexure cracks occur with great strain.