## 4 The Fragmentation and Energy Analysis  
Dynamic deformation is the change in the shape of an object that occurs when the object is subjected to an external force. The fragments of the sample after the impact test were photographed. Figure 12 illustrates the fracture morphology of the samples under five types of impact pressures. It can be observed that as the impact pressure and incident energy increase, the degree of sandstone fragmentation gradually increases, the scale of the broken pieces reduces, and the amounts of the broken pieces rises. Figure 11: The evolution in dynamic elastic modulus of prefabricated fractured sandstone samples as average strain rate. In aiming to intuitively and quantitatively describe the degree of fragmentation of rock samples, fragments of the impact test samples of sandstone samples with prefabricated cracks are screened and the mean particle size of the fragments is calculated. The results of the screening tests are illustrated in Table 2.  
We have used the data collected from the incident, reflected, and transmitted waves to analyze the changes in the energy in the sample, and the energy equation is shown in Equation (5). \[\left\{ \begin{array}{l}W_{I}(t)=E_{0}C_{0}A_{0}\int_{0}^{t}\epsilon_{\tau}^{2 }(t)dt\\ W_{R}(t)=E_{0}C_{0}A_{0}\int_{0}^{t}\epsilon_{\tau}^{2}(t)dt\\ W_{T}(t)=E_{0}C_{0}A_{0}\int_{0}^{t}\epsilon_{T}^{2}(t)dt\\ W_{D}(t)=W_{I}(t)-W_{R}(t)-W_{T}(t)\end{array} \right. \tag{5}\]  
where \(W_{I}(t)\), \(W_{R}(t)\), \(W_{T}(t)\), and \(W_{D}(t)\) represent incident, reflected, transmitted, and sample absorbed energies, respectively; \(\epsilon_{I}\), \(\epsilon_{R}\), and \(\epsilon_{T}\) represent incident, reflected, and transmitted strains, respectively; \(E_{0}\) represents the modulus of elasticity of the compression bar; while \(C_{0}\) represents its longitudinal wave velocity, and \(A_{0}\) represents its cross-sectional area. \(W_{D}(t)\) is the absorbed energy by the specimen, which mainly includes crushing dissipation, ejection kinetic energy, and other dissipation. Crushing accounts for about 95 percent of absorbed energy, and absorbed energy can be an approximate substitute for crushed energy. Under axial compression, the variation of incident energy with the loading velocity of the prefabricated fractured sandstone samples is illustrated in Figure 13.  
As the impact loading rate grows, the incident energy grows, and the incident energy of the prefabricated fractured sandstone samples has a power function relationship with the loading velocity, and the fitting relationship is shown in Equation (6):  
\[W_{I}=0.23v^{2.12}\quad(R^{2}=0.9983) \tag{6}\]  
Under the action of axial compression, Figure 14 illustrates the relationships between the reflection, transmission, and absorption energies of the samples and the incident energy. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Impact Pressure (MPa)** & \multicolumn{6}{c}{**Size of Screen Mesh (mm)**} & \multicolumn{6}{c}{**Total**} & **Average** \\
**(MPa)** & **0** & **0.15** & **0.3** & **0.6** & **1.18** & **2.36** & **4.75** & **9.5** & **13.2** & **(g)** & **(mm)** \\ \hline
0.300 & 0.49 & 0.27 & 0.87 & 1.01 & 1.83 & 4.39 & 13.46 & 10.02  
After impact crushing under different impact pressures, the relationship between the mean particle size of the sample fragments vs. the absorbed energy is illustrated in Figure 15.  
Figure 14: The change in energy of samples with incident energy. Figure 13: The change in incident energy of prefabricated fractured sandstone samples with loading velocity. Figure 15: The change in mean particle size of prefabricated fractured rock samples vs. absorption energy. Figures 14 and 15 show a decrease in the average particle size of the fractured rock samples after impact as the absorbed energy increases. The reflective, transmitted, and absorbed energies of the samples increase vs. the growth in incident energy. The increase in transmission energy is close to that of absorption energy, and the growth in reflected energy is larger.