## 5 Conclusions  
Single and repeated impact tests of sandstone specimens were carried out using a large SHPB setup. The dynamic stress equilibrium guaranteed the effectiveness of the test. Based on the analysis of the test results, the failure patterns and damage evolution law of the sandstone specimens were analyzed. Moreover, a set of methods for systematically determining the parameters of the HJC model for sandstone specimens was proposed. The main conclusions of this paper are as follows. The typical dynamic constitutive curve of sandstone specimens is divided into four stages, namely the linear elastic stage, the new fracture formation stage, the plastic strengthening stage and the unloading stage. The failure mode of sandstone is mostly splitting tensile failure, and the impact damage threshold of sandstone is 45 J. The sandstone specimen under repeated impacts showed only one fracture surface compared with that subjected to a single impact. The sandstone damage under a single impact is exponentially related to the stress wave amplitude. A model to describe the relationship between the damage and stress wave amplitude is \(\mathrm{D}=0.0029\cdot\mathrm{exp}(5.4127\cdot\sigma/76.13)-0.0504\). Under repeated impacts, the cumulative damage presented the development form of 'rapid rise-steady development  
Figure 23: The numerical calculation results using the HJC model with the calibrated parameters. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Category**} & **Impact Velocity** & **Strain Rate** & \multicolumn{2}{c}{**Dynamic**} & \multirow{2}{*}{**Maximum**} \\  & **(m/s)** & **(s\({}^{-1}\))** & & **Compressive** & \\  & & & **Strength (MPa)** & \\ \hline \multirow{3}{*}{Simulation} & 7.50 & 55.53 & 48.08 & 1820 \\  & 9.50 & 64.06 & 63.18 & 2170 \\  & 11.50 & 81.36 & 88.94 & 3920 \\  & 13.50 & 85.25 & 97.14 & 6080 \\ \hline \multirow{3}{*}{Experiment} & 7.50 & 52.39 & 50.93 & 2000 \\  & 9.50 & 64.71 & 63.32 & 2260 \\ \cline{1-1}  & 11.50 & 78.23 & 95.87 & 3900 \\ \cline{1-1}  & 13.50 & 90.69 & 102.74 & 6017 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison between the simulation and experiment for the dynamic mechanical characteristics of sandstone. rapid rise', which can be expressed by the inverse transformation of the Goeppitz function, i.e., \(\mathrm{D}=0.265-0.328\cdot\ln(\ln 13.989/\mathrm{n})\). The amplitude of the reflected wave and the area enclosed by the reflected wave and the abscissa axis gradually increase with an increasing number of impacts, while the transmitted wave amplitude and the area enclosed by the transmitted wave and the abscissa axis gradually decrease. As the number of impacts increases, the dynamic compressive strength and elastic modulus gradually decrease, while the strain corresponding to the peak stress increases gradually. The dynamic compressive strength decreases convexly with an increasing number of impacts. The maximum strain is positively correlated with the number of impacts. The parameters of the HJC model are divided into five categories, namely the basic mechanical parameters, limit surface parameters, pressure parameters, damage parameters and rate effect parameters. A set of methods to determine the HJC model parameters for sandstone was proposed, which includes a single impact test, repeated impact test, uniaxial compression test and triaxial compression test. Then, the parameters for sandstone specimens were determined and used to simulate SHPB tests. The numerical simulation results showed that the strain rate, dynamic compressive strength and maximum strain of the sandstone specimen were highly similar to the experimental results. The method for determining the parameters of the HJC model for rock materials provided in this paper is effective. Conceptualization, S.L. and S.H. ; methodology, S.W. ; software, S.W. ; validation, S.L., S.H. and S.W. ; formal analysis, S.L. and S.H. ; investigation, S.H. ; resources, S.L. ; data curation, S.L. ; writing--original draft preparation, S.H. ; writing--review and editing, S.H.