## 5 Dynamic Compressive Strength Model of FCC
### Dynamic Compressive Strength Model for FCHC  
Figure 13 shows the relationship between the FRP actual confining stress and the dynamic compressive strength of FCHC. It can be seen from Figure 13 that the dynamic compressive strength is influenced by the actual FRP confining stress and the dynamic compressive strength of FCHC is proportional to the actual confining stress. The actual axial capacity contribution of the FRP can be estimated by subtracting the axial dynamic capacity of the unconfined concrete from the corresponding axial dynamic capacity of FCHC. The dynamic compressive strength of FCHC can be estimated by the following formula:  
Among them, \(f^{\prime}_{cc,d}\) and \(f^{\prime}_{o,d}\) are FCC's dynamic compressive strength and unconfined concrete dynamic compressive strength, respectively; \(k\) is the constraint validity coefficient formulated by experimental data; and \(f_{l}\) is the nominal maximum confining stress provided by the FRP. The relationship between the strain rate and the DIF of NSC, which can be used for design and analysis, is given by the International Federation for Structural Concrete (_fib_) [60]. However, the inevitable structural effects, such as the transverse inertia effect and the end friction restraint effect, will occur in the high-speed impact test of concrete materials. [PERSON] and [PERSON] [61] used the numerical simulation method to remove the influence of transverse inertia and the end friction constraint from the relationship of CEB and obtained an exact equation for the DIF of concrete as follows:  
\[\left\{ \begin{array}{c}\mathrm{DIF}=\frac{f^{\prime}_{o,d}}{f_{o}}=0.0419 \big{(}log\dot{\varepsilon_{d}}\big{)}+1.2165,\ \dot{\varepsilon_{d}}\leq 30\mathrm{s}^{-1}\\ \mathrm{DIF}=\frac{f^{\prime}_{o,d}}{f^{\prime}_{o}}=0.8988\big{(}log\dot{ \varepsilon_{d}}\big{)}^{2}-2.8255\big{(}log\dot{\varepsilon_{d}}\big{)}+3.49 07,\ \dot{\varepsilon_{d}}>30\mathrm{s}^{-1}.\end{array} \right. \tag{9}\]  
It is assumed that whether the specimens are subjected to static or dynamic pressure, the confinement mechanism of the FRP remains unchanged. Referring to the compressive strength model of FCC proposed by [PERSON] and [PERSON] [57], which has been widely accepted, the following formula is used to determine the static compressive strength of FCC:  
\[\frac{f^{\prime}_{cc}}{f^{\prime}_{o}}=1+3.3\frac{f_{l}}{f^{\prime}_{co}}, \tag{10}\]  
where \(f_{l}\) is determined by the following formula:  
\[f_{l}=k_{\epsilon}\frac{2f_{f\!r}t}{d}, \tag{11}\]  
where \(f^{\prime}_{cc}\) is the compressive strength of concrete confined by the FRP; \(f^{\prime}_{cc}\) is the compressive strength of unconfined concrete;\(f_{f\!r}\) and \(t\) are the tensile strength and thickness of the FRP, respectively; \(d\) is the diameter of the confined concrete; and \(k_{\epsilon}\) is the hoop strain effective coefficient of the FRP [57], that is, the ratio of the actual fracture strain of the FRP to the fracture strain of the FRP measured by the tensile test. Equation 10 includes all the material properties of the FRP and takes the influence of the diameter of the circular section specimen on the confinement stress into account. Figure 13: Relationship between the FRP confining stress and the dynamic compressive strength of FCHC. [PERSON] et al. [56] improved the FCC model in 2009, where the revised model was demonstrated to be capable for FCHC under static compression [59]. The compressive strength of FCC specified in [PERSON] et al. [56] is evaluated by the following equations:  
\[\left\{ \begin{array}{c}\frac{f_{\varepsilon\varepsilon}^{\sigma}}{f_{ \varepsilon\omega}}=1+3.5(\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.