# Study on Dynamic Splitting Properties of S-PP Hybrid Fiber Concrete after High Temperatures
## 3 Experimental Results and Analysis
### Analysis of Damage Variables Based on Dissipative Energy  
The typical energy variation of a specimen with time in a dynamic splitting test is shown in Figure 8. The incident energy, reflected energy, and dissipated energy increase gradually with time until they become stable. The incident and reflected energy are enormous, the dissipated energy is small, and the transmitted energy is minimal, which is close to a parallel line. Due to the influence of the loading mode, the contact area between the specimen and the bar is small, resulting in most of the energy being reflected, and a small part of the energy being transferred to the transmission bar. While the stress wave passes through the concrete specimen, the energy of the stress wave is continuously consumed. The specimen gradually absorbs energy, causing internal damage and eventually destruction. Due to the small conversion of heat energy, the kinetic energy and other energy consumption can be ignored. The total dissipated energy is the energy consumed by the dynamic loading failure of the specimen [25]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Temperature** & **Fiber Content** & \(f_{st,d}\) & **Temperature** & **Fiber Content** & \(f_{st,d}\) \\ (\({}^{\circ}\)**C**) & **(\%)** & **(MPa)** & **(\({}^{\circ}\)**C)** & **(\%)** & **(MPa)** \\ \hline \multirow{6}{*}{25} & PC & 7.20 & & PC & 7.77 \\  & S0.5 PP0.2 & 12.13 & & S0.5 PP0.2 & 14.05 \\  & S1 PP0.2 & 14.89 & & S1 PP0.2 & 16.38 \\  & S1.5 PP0.2 & 13.52 & 100 & S1.5 PP0.2 & 14.55 \\  & S0.5 PP0.4 & 11.42 & & S0.5 PP0.4 & 12.53 \\  & S1 PP0.4 & 10.81 & & S1 PP0.4 & 11.37 \\  & S1.5 PP0.4 & 10.17 & & S1.5 PP0.4 & 10.41 \\ \hline \multirow{6}{*}{200} & PC & 8.16 & & PC & 6.05 \\  & S0.5 PP0.2 & 14.52 & & S0.5 PP0.2 & 11.81 \\  & S1 PP0.2 & 16.93 & & S1 PP0.2 & 12.95 \\  & S1.5 PP0.2 & 15.13 & 400 & S1.5 PP0.2 & 12.44 \\  & S0.5 PP0.4 & 13.32 & & S0.5 PP0.4 & 10.51 \\  & S1 PP0.4 & 8.52 & & S1 PP0.4 & 5.73 \\  & S1.5 PP0.4 & 8.20 & & S1.5 PP0.4 & 5.41 \\ \hline \multirow{6}{*}{600} & PC & 4.14 & & PC & 2.55 \\  & S0.5 PP0.2 & 7.73 & & S0.5 PP0.2 & 5.12 \\  & S1 PP0.2 & 8.39 & & S1 PP0.2 & 5.82 \\  & S1.5 PP0.2 & 8.06 & 800 & S1.5 PP0.2 & 5.51 \\  & S0.5 PP0.4 & 7.28 & & S0.5 PP0.4 & 4.60 \\  & S1 PP0.4 & 4.33 & & S1 PP0.4 & 2.20 \\  & S1.5 PP0.4 & 3.87 & & S1.5 PP0.4 & 1.84 \\ \hline \hline \end{tabular} Note. “PC” refers to plain concrete; “S” refers to steel fiber; “PP” refers to polypropylene fiber; and the number next refer to the percentage of volume content.  
\end{table} 
Table 4: Summary of experimental results. To avoid lengthy space, to achieve the research purpose, only S1 PP0.2 concrete and PC with the best splitting performance can be used for energy analysis. Figure 9 shows the time history curve of dynamic splitting dissipation energy of PC and S1 PP0.2 concrete in different temperature groups. It can be seen from the figure that the dynamic splitting dissipation energy of concrete materials increases first and then decreases with the increase of temperature. Compared with PC, the energy dissipation effect of S1 PP0.2 concrete at the same temperature is significantly improved, and the variation law of HFRC dissipation energy and splitting strength with temperature is consistent. Figure 8: Energy variation of a specimen with time in a dynamic splitting test. Figure 7: Relationship between the splitting tensile strength and the temperature of a specimen. Introducing damage variables into concrete materials can better study the deformation and failure characteristics of materials. In the constitutive relationship, the accompanying variable of damage variable, namely the damage propagation force, refers to the energy dissipation density, so it is more meaningful to define the damage variable from the perspective of energy dissipation. According to the energy point of view, concrete material deforms after being subjected to impact load, and the bearing capacity of the material gradually decreases in this process. That is, the constitutive energy of the material also decreases.