## 4 Experimental Test Results
### Life Estimation of Fatigue of GFRP-Reinforced Precast FDDP
Non-linear damage theories proposed \(D=\sum\left(n_{i}/N_{fi}\right)^{\alpha_{l}}\) where \(\alpha_{l}\) depends on the load level. When considering the change of load level to be \(P/P_{u}\), the authors propose the non-linearity of the damaging effect on the step loading through Equation (2) as a result of the observed stiffness degradations, keeping the linearity of \(D=1\) and solving for the \(\eta\) using the non-linear least square regression analysis (NLREG). Figure 15: Degradation of the precast FDDPs with different joints details under CAF and VAF loading. \[N_{f}=e^{\eta(1-P/P_{u})} \tag{2}\]  
where \(\eta\) equals 25.86, 24.32, and 25.609 for the A-Joint, C-Joint, and Z-Joint, respectively. Tables 7-10 illustrate the fatigue data where \(D=1\) for all types of joints of the precast FDDPs. The proposed model to determine the P-N effect is shown in Equation (3), where \(K\) equals 0.039, 0.041, and 0.039 for the A-Joint, C-Joint, and Z-Joint, respectively. For static failure \(N=1\), the model yields to \(P/P_{u}=1\). \[\frac{P}{P_{u}}=-K\text{ln}\Big{(}N_{f}\Big{)}+1 \tag{3}\]  
Figure 17 shows the P-N fatigue curves for the developed model compared to the recently developed models on log-scale graphs compared to other fatigue models [46; 47; 62; 63]. Equations (4)-(11) summarize the recent fatigue models. [PERSON]'s model [46]  
\[\frac{P}{P_{u}}=1-\frac{\text{ln}(N)}{29} \tag{4}\]  
\[N=e^{-29(P/P_{u})+29} \tag{5}\]  
[PERSON] et al. 's model [47]  
\[\frac{P}{P_{u}}=0.0034(\log{(N)})^{2}-0.1187\text{log}\left(N\right)+1.0752 \tag{6}\]  
\[N=e^{40.19-0.0147\sqrt{-2.826\times 10^{5}+7.21\times 10^{6}(P/P_{u})}} \tag{7}\]  
[PERSON]'s model [62]  
\[LogN=5.737\sqrt{\frac{1-R}{R}} \tag{8}\]  
\[N=10^{5.737\sqrt{\frac{1-R}{R}}} \tag{9}\]  
[PERSON] et al. 's model [63]  
Figure 15:0  
Figure 15:1  
Figure 15:2 Comparison among degradation of the precast FDDPs under CAF and VAF loading. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Joint Pattern** & **H** & **K** \\ \hline A-Jointed Precast FDDP & 25.86 & 0.039 \\ \hline C-Jointed Precast FDDP & 24.32 & 0.041 \\ \hline Z-Jointed Precast FDDP & 25.61 & 0.039 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Fatigue parameters. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Segment**} & \multirow{2}{*}{**P\({}_{\mathbf{u}}\)**} & \multicolumn{4}{c}{**FLS**} & \multirow{2}{*}{**P\({}_{\mathbf{min}}\)**} & \multirow{2}{*}{**P\({}_{\mathbf{max}}\)**} & \multirow{2}{*}{**P\({}_{\mathbf{empty}}\)**} & \multirow{2}{*}{**P\({}_{\mathbf{mean}}\)**} & \multirow{2}{*}{**R**} & \multirow{2}{*}{**A**} & \multirow{2}{*}{**P\({}_{\mathbf{max}}\)/P\({}_{\mathbf{a}}\)**} & \multirow{2}{*}{**n**} & \multirow{2}{*}{**N\({}_{\mathbf{f}}\)**} & \multirow{2}{*}{**n/N\({}_{\mathbf{f}}\)**} \\ \cline{3-3} \cline{5-12}  & **MF** & & **WL** & **FLS1** & & & & & & & & & & & \\ \hline
1 & 930.92 & 1.0 & 87.5 & 122.5 & 15 & 137.50 & 61.25 & 76.25 & 0.109 & 0.803 & 0.148 & 100,000 & 3740,491,266 & \(2.673\times 10^{-5}\) \\ \hline
2 & 930.92 & 1.5 & 87.5 & 183.8 & 15 & 198.75 & 91.88 & 106.88 & 0.075 & 0.860 & 0.213 & 100,000 & 682,217,686 & 0.0001466 \\ \hline
3 & 930.92 & 2.0 & 87.5 & 245.0 & 15 & 260.00 & 122.50 & 137.50 & 0.057 & 0.891 & 0.279 & 100,000 & 124,427,776 & 0.0008037 \\ \hline
4 & 930.92 & 2.5 & 87.5 & 306.3 & 15 & 321.25 & 153.13 & 168.13 & 0.046 & 0.911 & 0.345 & 100,000 & 22,694,030 & 0.0044064 \\ \hline
5 & 930.92 & 3.0 & 87.5 & 367.5 & 15 & 382.50 & 183.75 & 198.75 & 0.039 & 0.925 & 0.411 & 100,000 & 4.139,100 & 0.0241596 \\ \hline
6 & 930.92 & 3.5 & 87.5 & 428.8 & 15 & 443.75 & 214.38 & 229.38 & 0.034 & 0.935 & 0.477 & 100,000 & 754,919 & 0.1324646 \\ \hline
7 & 930.92 & 4.0 & 87.5 & 490.0 & 15 & 505.00 & 245.00 & 260.00 & 0.030 & 0.942 & 0.542 & 115,381 & 137,688 & 0.8379916 \\ \hline
8 & 930.92 & 4.0 & 87.5 & 490.0 & 15 & 505.00 & 245.00 & 260.00 & 0.030 & 0.942 & 0.542 & 94,112 & 137,688 & 0.8635187 \\ \hline \hline \end{tabular}
\end{table}