# Numerical Evaluation of Structural Safety for Aged Onshore Wind Foundation to Extend Service Life
## 3 Structural Safety Evaluation for Aged Wind Foundation
### Ultimate Strength  
Using the results of the material strength evaluation for the in-service foundation concrete, it was evaluated whether or not the ultimate strength of the foundation was satisfied for the current turbine load [12; 13; 14; 15]. The ultimate strength was evaluated by numerical analysis by FE analysis program DIANA [16] reflecting the in-situ concrete compressive strength indicated in Table 2. DIANA  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Compressive Strength** & **Elastic Modulus** & **Tensile Strength** & **Fracture Energy** \\ \hline Average & 40.6 MPa & 23,673 N/mm\({}^{2}\) & 3.83 MPa & 0.143 N/mm \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of the concrete material test.  
Figure 5: Concrete material properties evaluation: (**a**) concrete cores; (**b**) compressive strength test; (**c**) ultrasonic test.  
software has advantages in the nonlinear analysis of complex concrete members such as onshore wind foundations since it has various modeling and physical property modules for the concrete members. The yield strengths of the anchor ring and reinforcing rebar were 240 and 400 N/nm\({}^{2}\), respectively. The structural members constituting the foundation such as the concrete, reinforcement, and anchor ring were modeled as realistically as possible [17], as shown in Figure 6. Concrete foundations and anchor rings were modeled as solid elements, and reinforcing bars were modeled using embedded reinforcement elements. The tower was not modeled separately, but only the extreme load acting on the bottom of the tower was applied to the top of the anchor ring, as presented in Figure 4a. For the concrete material model, the total strain crack model considering the compressive behavior and the tensile behavior (fracture energy-based) was used.  
For the evaluation of the bearing capacity of the soil layer, the soil layer of the bottom of the foundation was modeled using a compressive spring [3; 12], as presented in Figure 6, for which the reaction force is to be subjected to the foundation bottom only when the foundation and the ground are in contact with each other, as presented in Figure 4a. The ultimate turbine load for the structural safety evaluation of the foundation was provided by the turbine company, and the specifications of the foundation were provided by the authority of the wind farm.  
At first, critical points for each structural member of the concrete, reinforcement, anchor ring were selected through pre-analysis. As a result of pre-analysis, critical points of the tension part of the foundation were distributed around the concrete crushing cone resisting pull-out from the anchor ring plate, as presented in Figures 6 and 7a. Also, critical points of the compression part of the foundation were distributed around the concrete crushing cone that resists compaction under the anchor ring plate, as presented in Figures 6 and 7a. Then, the maximum stresses in these critical points were evaluated by applying the ultimate turbine load. The structural safety for the ultimate strength was evaluated by comparing the maximum stresses (f\({}_{\text{max}}\)) at critical points and the yield strengths (f\({}_{\text{y}}\)) of each material.  
\[R_{\text{f}}=f_{\text{max}}/f_{\text{y}} \tag{2}\]  
As a result of the evaluation, as indicated in Figure 7 and Table 3, the maximum stress ratios (actual strength/design strength) for each structural member such as concrete, reinforcement, anchor ring were 0.49 or less, indicating that ultimate strength safety was maintained.  
Figure 6: Concrete foundation modeling.