## 5 Theoretical Model of Accelerated Factor
### Model Validation and Discussions  
In this study, the ageing accelerated method was taking the BFRP specimen with the thickness \(h=4\) mm as the standard specimen. The \(AF\)s of BFRP specimens with \(h=1\) mm, \(h=2\) mm, and \(h=4\) mm are calculated by Equation (10) and the results are shown in Table 3. The obtaining of accelerated ageing days is transformed by multiplying the actual ageing days of the thicker specimen by the corresponding \(AF\) based on the two thicknesses of the thicker specimen and the standard specimen. According to the existing test results, the accelerated time is up to eight years on the water absorption trend and tensile strength retention of BFRP specimen with \(h=4\) mm. It should be noted that the transformed results of the specimens with 1 and 2 mm represent the predicted results of the standard specimen \(h=4\) mm. Figure 16 shows the long-term prediction of water absorption of BFRP specimens with \(h=4\) mm according to the transformed results of 1 and 2 mm specimens in deionized water and alkaline solution. The predicted curves were fitted by using Matlab (2018a Version, MathWorks, Inc., Massachusetts, USA, 2018). It can be seen from Figure 16 that the predicted curves are fitted well with a Two-stage model in whole. It reveals that the predicted law of water absorption in deionized water was better with Two-stage model than that in alkaline solution. Figure 17 shows the long-term prediction of tensile strength retention of BFRP specimens with \(h=4\) mm according to the transformed results of 1 and 2 mm specimens in deionized water and alkaline solution, which is also fitted well with [PERSON]'s model [55] in whole.  
Compared with the traditional temperature-dependent accelerated ageing method, there are two main advantages of the proposed new specimen thickness-dependent accelerated ageing method in this study. First, the proposed thickness-dependent accelerated ageing method is easy to apply because this method does not need the activation energy, which must be required in the temperature-dependent method. In order to obtain the activation energy in the temperature-dependent method, at least three different temperature environment tests must be conducted [56], which increases the test difficulty. In contrast, the accelerated factor calculating in the proposed method is only dependent on specimen thickness, which would be easy to be conducted. Second, the \(AF\) of the temperature-dependent accelerated ageing method is limited due to the limitation of \(T_{\text{g}}\) of FRP composites, leading to the acceleration times being relatively small. The \(AF\) of the proposed method is only dependent on specimen thickness and thus eliminates the limitation of \(T_{\text{g}}\). Therefore, greater \(AF\) can be obtained in the proposed method.  
Figure 16: Accelerated ageing results of water absorption based on specimen thickness in (**a**) deionized water and (**b**) alkaline solution.  
Figure 17: Accelerated ageing results of tensile strength retention based on specimen thickness: (**a**) deionized water and (**b**) alkaline solution.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Specimen Thickness**} \\ \cline{2-4}  & **1 mm** & **2 mm** & **4 mm** \\ \hline
**Accelerated factor (\(AF\))** & \(16\) & \(4\) & \(1\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The accelerated factor \(AF\) of BFRP laminates with different thicknesses.