## 3 Results and Discussions
### Application of 1D Norton-Bailey Time-Hardening Power Law
Thus, this study enables the time-dependent analysis of the structures to compute the time-dependent deformation attributable to a constant applied load, so that it can be included in the computation of the total deformation of the structures when one the design methods is conducted. The 10-year long-term axial deformation (strain) at the struts adjacent to the hanging points (Figure 4C) were reported in Figure 5. As a creep phenomenon, the applied stress should be constant during the creep duration. However, a reduction in the applied creep stress was observed from the beginning of load application to the end of load application. This descending behavior in the creep stress (constant stress) is believed to be attributable to the mesh refinement and the time step \begin{table}
\begin{tabular}{c c} \hline \hline \(\epsilon_{\sigma 2,b}\) (mm/mm) & 0.0015 \\ \(\epsilon_{\sigma 1,a}\) (mm/mm) & 0.0013 \\ \(t_{\sigma 2,b}\) (day) & 78.6 \\ \(t_{\sigma 1,a}\) (day) & 14 \\ \(\sigma_{2}\) (Mpa) & 5.09 \\ \(\sigma_{1}\) (MPa) & 3 \\ \(\epsilon_{\sigma 3,c}\) (mm/mm) & 0.0035 \\ \(t_{\sigma 3,c}\) (day) & 187.5 \\ \(\sigma_{3}\) (Mpa) & 11.8 \\ A (MPa\({}^{-n}\)day\({}^{-m}\)) & \(2.414\times 10^{-7}\) \\ n & 2.2 \\ m & \(-0.8\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental results and the computed parameters of Norton-Bailey power law model. selected to minimize the computational efforts [51; 52]. To characterize the long-term deformation of the aquacultural geodesic spherical rigid frame structure, a convergence study was conducted and reported in Table 2 based on the mesh (number of elements) refinement and the time-stem intervals and their effects on the axial deformation and the axial stress in the strut adjacent to the hanging point. An approximately 7% reduction in the applied stress was observed during the 10 years FEA modeling. However, there was a similarity in the resulted axial strain at the strut adjacent to the hanging position for the FEA model with the lowest number of elements (2676 beam element) at the time increment t = 0.125 day and the FEA model with 51,552 beam element at the time step (increment) t = 1 day as shown in Table 2. It is computationally not possible to have a finer mesh with a smaller time step to conduct such a long-term FEA study for this structure. Thus, the FEA model was conducted using 51,552 beam elements and at time step t = 1 day. To comply with the acceptance criteria of the creep behavior of the material mentioned in the ASTM D6815, the creep rate should be decreasing during the service life of the structure. The strain rate was selected for one-year intervals and was reported for four intervals as shown in Table 3. The strain rate of the axial strain at the struts adjacent to the hanging point showed a descending pattern which means the axial long-term deformation is accepted. Figure 4: A 10-year Abaqus FEA time-dependent deformation of a 20-m-diameter aquacultural rigid frame structure made from WPC struts. (**A**) Non-deformed structure in four-point hanging position, and (**B**) deformed shape after ten years. (**C**) the strut adjacent to the hanging point.