## 5 Conclusions  
In this paper, the dynamic mechanical properties of polypropylene fiber concrete were tested under different thermal grades and different impact rates using improved SHPB equipment. A dynamic damage constitutive model of polypropylene fiber concrete that considered thermal effects was constructed according to the dynamic mechanical properties of polypropylene concrete under real-time high-temperature conditions. The main conclusions are as follows:  
A dynamic damage constitutive model of polypropylene concrete considering thermal effects based on the Z-W-T nonlinear viscoelastic model was established. The model considered the damage to polypropylene concrete caused by thermal conditions and the coupling effect of the temperature and impact load.  
There was an obvious thermal effect in the dynamic mechanical properties of polypropylene concrete. The dynamic elastic modulus of the polypropylene concrete decreased as the temperature grade increased. The effect of thermal on dynamic compressive strength was different: there was a threshold temperature grade, when the temperature grade was lower than this threshold, then the dynamic strength of polypropylene fiber concrete in-creased as the temperature grade increased, and when the temperature grade was higher than this  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Average Impact**} & \multirow{2}{*}{**Temperature**} & \multicolumn{3}{c}{**Calculated Parameters**} & \multicolumn{3}{c}{**Fitting Parameters**} & \multirow{2}{*}{**R\({}^{2}\)**} \\ \cline{3-3} \cline{5-8}
**Air Pressure** & & **Grade** & **m** & **F0** & **Ea** & **E2** & \(\theta_{2}\) \\ \hline \multirow{8}{*}{0.4} & 25 & 1.36 & 43.23 & 1.27 & \(-\)1.39 & 1.79 & 0.925 \\  & 200 & 1.69 & 41.61 & 5.25 & \(-\)4.51 & 1.56 & 0.948 \\  & 400 & 2.11 & 33.65 & 3.19 & \(-\)3.35 & 2.45 & 0.964 \\  & 600 & 4.01 & 20.51 & 2.21 & \(-\)1.87 & 3.60 & 0.915 \\  & 800 & 3.92 & 9.56 & 1.48 & \(-\)2.65 & 2.67 & 0.939 \\ \hline \multirow{8}{*}{0.6} & 25 & 1.41 & 52.39 & 1.54 & \(-\)3.32 & 2.41 & 0.959 \\  & 200 & 1.97 & 51.16 & 4.87 & \(-\)1.65 & 2.86 & 0.926 \\  & 400 & 3.47 & 38.76 & 4.36 & \(-\)3.78 & 3.75 & 0.959 \\  & 600 & 4.48 & 25.35 & 4.23 & \(-\)5.23 & 3.55 & 0.927 \\  & 800 & 4.29 & 8.61 & 6.79 & \(-\)5.11 & 1.37 & 0.949 \\  & 25 & 1.94 & 64.42 & 1.76 & \(-\)2.45 & 1.27 & 0.913 \\ \hline \multirow{8}{*}{0.8} & 200 & 2.58 & 61.15 & 1.53 & \(-\)3.12 & 1.53 & 0.914 \\  & 400 & 3.66 & 45.36 & 1.04 & \(-\)2.12 & 3.69 & 0.981 \\ \cline{1-1}  & 600 & 4.12 & 37.61 & 1.86 & \(-\)3.13 & 5.49 & 0.971 \\ \cline{1-1}  & 800 & 4.24 & 21.23 & 1.29 & \(-\)2.76 & 1.42 & 0.915 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Parameter values under different experimental conditions.  
Figure 10: The fitting curves of polypropylene concrete in different conditions. (**a**) Impact air pressure = 0.4 MPa, average impact = 5.5 m/s; (**b**) impact air pressure = 0.6 MPa, average impact = 7.5 m/s; (**c**) impact air pressure = 0.8 MPa, average impact = 9.5 m/s.  
threshold, the opposite situation takes place. In this paper, the threshold temperature grade was between 200 \({}^{\circ}\)C and 400 \({}^{\circ}\)C.  
Compared with the experimental data, it was determined that the model can describe the stress-strain curves of polypropylene concrete under different conditions well. The temperature effect and strain rate effect shown by the fitting curves are consistent with the experimental data.  
[PERSON], [PERSON] and [PERSON] designed the experiments; [PERSON] and [PERSON] carried out the experiments; [PERSON] analyzed the experimental results. [PERSON] analyzed data and developed the analysis tools. [PERSON] wrote the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (grant nos.11862010 and 51964023).  
Not applicable.  
The data used to support the findings of this study are included within the article.  
The authors declare no conflict of interest.