## 3 Experimental Results and Discussion  
### Compression Strength  
The experimental results of the compressive strength for FRC at different strain rates are shown in Figures 3 and 4. In general, the compressive strength of FRC increases with the increase of strain rate, showing an obvious rate sensitivity, which agrees with the existing research [13; 14; 16; 17; 18]. At the quasi-static strain rate (i.e., a strain rate of \(10^{-5}\) s\({}^{-1}\)), the strength of the two kinds of plain concrete meet the design requirements. The addition of PVA can lead to an increase in compressive strength with the two matrix strengths. Under the quasi-static state, the maximum growth values for the FRC of C30 and C40 are 15.1% and 8.7%, respectively, relative to the two types of plain concrete. With the increase of strain rate, there is a significant difference in the increase of the compressive strength with different fiber volume contents. The two types of concrete with a fiber content of 0.2% show the maximum growth at different strain rates, which is related to the most uniform distribution of PVA fibers in concrete, similar to previous findings [6].  
From the experimental results, it can be seen that the matrix strength of concrete is another important factor that affects the compressive strength of FRC, in addition to fiber volume content and  
Figure 4: The uniaxial compressive strength of FRC (C40).  
Figure 3: Uniaxial compressive strength of FRC (C30).  
loading rate. The higher the matrix strength of the concrete, the smaller the effect of PVA on the increase in compressive strength, which is consistent with experimental results from literature [18; 26]. Taking the FRC with a volume content of 0.2% as an example, the growth values of uniaxial compressive strength for a matrix strength of C30 are 15.1, 20.9, 20.6, and 23.5%, respectively for each strain rate tested compared with plain concrete at the same strain rates. For C40, the values are 8.7, 12.3, 14.2, and 8.1% for each strain rate, respectively, which are significantly lower than those of C30. The reason for this phenomenon is related to the bond strength and the matrix strength between the fiber and the concrete [1]. Under the same conditions, the reinforcing effect of the fiber is constant. The higher the matrix strength, the lower the proportion of the fiber reinforcement in the high strength concrete. This, in turn, will weaken the fiber-reinforcing effect.  
In order to describe the dynamic strength characteristics of FRC under different loading rates, a series of empirical formulas are proposed, including a logarithmic function [27], exponential function [28], and Fib model code [29], which have many practical applications. In the uniaxial compression experiment, as the reinforcing effect of the concrete with 0.2% content is the best, the empirical formula of dynamic compressive strength with different matrix strengths is established by fitting the relevant experimental data for the FRC with 0.2% PVA content. The fitting dynamic impact factor formulas and the fitting curves are shown below, as in Figure 5. The fitting results clearly confirm the above conclusions that the higher the matrix strength, the weaker the fiber-reinforcing effect.  
\[DIF_{c}=\frac{f_{c}}{f_{cs}}=1.1591+0.0258\lg\left(\frac{\dot{\varepsilon}}{ \dot{\varepsilon}_{s}}\right)\ \text{for C30 PVA0.2} \tag{1}\]  
\[DIF_{c}=\frac{f_{c}}{f_{cs}}=1.0951+0.0193\lg\left(\frac{\dot{\varepsilon}}{ \dot{\varepsilon}_{s}}\right)\ \text{for C40 PVA0.2} \tag{2}\]  
where \(DIF_{c}\), \(f_{c}\), \(f_{cs}\), \(\dot{\varepsilon}\), and \(\dot{\varepsilon}_{s}\) are the dynamic impact factor of compression strength, dynamic compression strength, quasi-static compressive strength, dynamic strain rate, and quasi-static compression strength, respectively.