# Numerical Evaluation of Structural Safety for Aged Onshore Wind Foundation to Extend Service Life
## 3 Structural Safety Evaluation for Aged Wind Foundation
### Fatigue Life  
Fatigue life was evaluated by performing fatigue analysis by FE analysis program ANSYS [18], which is widely used for fatigue analysis of various structures including the concrete members, using the equivalent fatigue load of the in-service wind turbine. In the DNV-GL guidelines [19] for fatigue life, it is recommended to use a fatigue load corresponding to negative inverse slope m = 3 of the S-N curve when the number of fatigue load cycles is \(10^{7}\) or less. Also, it is recommended to use a fatigue load corresponding to negative inverse slope m = 5.0 of the S-N curve when the number of fatigue load cycles exceeds \(10^{7}\)[19]. The purpose of this section is to evaluate the overall fatigue life of the in-service foundation. Therefore, it was evaluated by applying a fatigue load corresponding to negative inverse slope m = 3.0 until 20 years because it was subjected to a cycle fatigue load of \(10^{7}\) or less until 20 years. Fatigue life after 20 years was evaluated by applying a fatigue load corresponding to the negative inverse slope m = 5.0, as indicated in Table 4. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Concrete (MPa)**} & \multicolumn{3}{c}{**Reinforcement (MPa)**} & \multicolumn{3}{c}{**Anchor Ring (MPa)**} \\  & **C1** & **C2** & **R1** & **R2** & **R3** & **R4** & **S1** & **S2** \\ \hline FE & 13.4 & 10.7 & 16.1 & 25.4 & 28.0 & 93.2 & 115.4 & 117.0 \\ Design & 40.6 & & & 400 & & & 240 & \\ Ratio & 0.33 & 0.26 & 0.04 & 0.06 & 0.07 & 0.23 & 0.48 & 0.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: FE results for ultimate strength. Figure 7: FE analysis results: (**a**) critical points; (**b**) concrete; (**c**) reinforcement. The S-N curve for each material used in fatigue life evaluation is provided in Figure 8. In the case of concrete, the S-N curve of the FIB model [18; 20] was applied, and in the case of steel, the S-N curve of A36 steel with a yield strength of 40 MPa, which is the same as the reinforcing bar (HD25 to 29) applied to the aged concrete foundation, was applied [18]. The average fatigue stress theory for each structural member to evaluate fatigue life is as follows. For the steel, [PERSON]'s theory [18; 21] is applied to obtain stable results for low-ductility metals. For the concrete, the [PERSON] theory [18; 22; 23] is applied, which is known to be more conservative than the [PERSON] theory and suitable for brittle materials such as the concrete. In this paper, fatigue life was evaluated using the concept of the \"Fatigue Safety Index [18]\" in the corresponding year, represented by the following equation, where if the fatigue safety index is 1.0 or over, it means that it is safe for fatigue life. \[\text{Fatigue Safety Index = Fatigue allow stress/Fatigue stress} \tag{3}\]  
The service life used for fatigue life evaluation was targeted at two cases: the service life to now (16 years) and the service life up to 40 years. The fatigue load corresponding to m = 3 was applied in the fatigue life evaluation for the service life up to now, and the fatigue load corresponding to m = 5 was applied to the fatigue life evaluation up to service life 40 years. The fatigue safety index of the foundation was evaluated for each of the most critical areas for tension and compression for each structural member, respectively, as presented in Figure 9. As a result of fatigue life evaluation, the minimum fatigue safety indexes of steel and concrete for the equivalent fatigue load of m = 3.0 were 2.93 and 1.88, respectively, as presented in Figure 10. The minimum fatigue safety indexes for the equivalent fatigue load of m = 5.0 were 1.76 and 1.21, respectively, as presented in Figure 11. In summary, the in-service foundation showed that the fatigue safety index of up to 40 years of service life was 1.0 or higher for the in-service turbine fatigue load, thereby securing a fatigue life of 40 years or more.