## 5 Dynamic Compressive Strength Model of FCC
### Dynamic Compressive Strength Model for FCHC
\tag{12}\]  
\[\rho_{k}=\frac{2E_{frp}t}{\left(\frac{f_{\varepsilon\varepsilon}^{\alpha}}{ \varepsilon_{\alpha}}\right)D}, \tag{13}\]  
\[\rho_{\varepsilon}=\frac{\varepsilon_{h,rup}}{\varepsilon_{\alpha}}, \tag{14}\]  
where \(\rho_{k}\) is the confined stiffness of FCC; \(\rho_{\varepsilon}\) is the strain ratio; \(E_{frp}\) and \(t\) are the elastic modulus and thickness of the FRP, respectively; \(D\) is the diameter of the confined concrete; \(\varepsilon_{h,rup}\) is the hoop fracture strain of FRP; and \(\varepsilon_{\alpha}\) is the axial strain of unconfined concrete. On the basis of this model, the compressive strength in Equation 10 can be replaced by the corresponding dynamic compressive strength and the coefficient 3.5 can be modified by a number of dynamic compression tests on FCHC. Therefore, the dynamic compressive strength of FCHC can be predicted by the following equation:  
\[\left\{ \begin{array}{c}\frac{f_{\varepsilon\varepsilon}^{\sigma}}{f_{ \varepsilon\omega}}=1+\alpha\ (\rho_{k}-0.01)\rho_{\varepsilon},\ \rho_{k}\geq 0.01\\ \frac{f_{\varepsilon\varepsilon}^{\sigma}}{f_{\varepsilon\omega}}=1,\ \rho_{k}<0.01, \end{array} \right. \tag{15}\]  
where \(\alpha\) is a constant to be identified. Based on a regression analysis against the test data of Tables 4 and 5, \(\alpha\) = 3.95 was obtained. Note that the test results shown in Table 5 are collected from [PERSON] et al. [32], in which an experimental program including the dynamic compression tests on the FCHC is presented. To verify the accuracy of the model, the experimental values are compared with the predicted values. As shown in Figure 14, the predicted values from the proposed model are in close agreement with the test results. Finally, the experimental results are compared with the predictions from the existing models [31; 52], namely, [PERSON] and [PERSON]'s model [31] and [PERSON] and [PERSON]'s model [52]. The standard deviation (SD) and the average absolute error (AAE) of these models are shown to be calculated in the figure to identify the accuracy. The comparisons are shown in Figure 14, which indicates that the proposed model is more accurate than the existing models [31; 52]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Specimen Size** & **FRP** & **FRP** & **Impact Pressure** & **Strain Rate** & \(f_{\varepsilon\varepsilon\varepsilon}\)**(MPa)** & \(f_{\varepsilon\varepsilon\varepsilon}\)**(MPa)** & \(f_{\varepsilon\varepsilon\varepsilon}\)**(MPa)** & \(\frac{f_{\varepsilon\varepsilon}}{f_{\varepsilon\varepsilon\varepsilon}}\) \\ \cline{1-1} \cline{5-7} d \(\times\) h/mm & **Type** & **Thickness** & **(MPa)** & **(\(s^{-1}\))** & **(\(s^{-1}\))** & **(\(s^{-1}\))** & **(\(s^{-1}\))** \\ \hline
150 \(\times\) 75 & - & 0 & 0.3 & 22.9 & 76.9 & 62.2 & 0.8 \\
150 \(\times\) 75 & - & 0 & 0.3 & 20.4 & 76.9 & 72.7 & 0.9 \\
150 \(\times\) 75 & - & 0 & 0.3 & 20.2 & 76.9 & 69.1 & 0.9 \\
150 \(\times\) 75 & - & 0 & 0.7 & 50.3 & 76.9 & 82 & 1.1 \\
150 \(\times\) 75 & - & 0 & 0.7 & 43.5 & 76.9 & 82.4 & 1.1 \\
150 \(\times\) 75 & - & 0 & 0.7 & 45.3 & 76.9 & 87.6 & 1.1 \\
150 \(\times\) 75 & - & 0 & 1.0 & 76.6 & 76.9 & 96.3 & 1.3 \\
150 \(\times\) 75 & - & 0 & 1.0 & 72.3 & 76.9 & 86.8 & 1.1 \\
150 \(\times\) 75 & - & 0 & 1.0 & 70.3 & 76.9 & 98.1 & 1.3 \\
150 \(\times\) 75 & CFRP & 0.167 & 0.3 & 4.2 & 110.4 & 92.6 & 0.8 \\
150 \(\times\) 75 & CFRP & 0.167 & 0.3 & 4 & 110.4 & 96.5 & 0.9 \\
150 \(\times\) 75 & CFRP & 0.167 & 0.3 & 4.4 & 110.4 & 95.9 & 0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental database of FRP-confined high-strength concrete specimens under dynamic compression loadings.