# Influence of Crack Geometry on Dynamic Damage of Cracked Rock: Crack Number and Filling Material
## 2 SHPB Test
### Typical Strain Gauge Records  
The influence of the crack number and the filling material on the dynamic damage of cracked rock were investigated in this study. Incident, reflected and transmitted stress waves of the specimens with different numbers or different filling materials of cracks were obtained. A typical strain history recorded by the strain gauges is shown in Figures 5 and 6. Figure 5 shows the strain wave of the specimen with one crack and filled with sand. The waveforms of other specimens with different numbers of cracks were very similar. Figure 6 shows the strain wave of the specimen with two cracks filled with soil. The waveforms of other specimens with different filling materials had little difference. Since the impact velocity of the striker bar was controlled at almost the same value for each group, similar wave forms of incident waves were generated in the incident bar. The waveforms of the transmitted and reflected waves were very similar when the specimens were different. However, the amplitude of the strain wave was different, which was associated with the geometric characteristics of cracks.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Filling Materials** & **Normal Stress (kPa)** & **Strength (kPa)** & **Cohesive Strength (kPa)** \\ \hline \multirow{3}{*}{ISO sand} & 100 & 125 & \multirow{3}{*}{0.20} \\  & 200 & 242 & \\  & 300 & 382 & \\  & 400 & 489 & \\ \hline \multirow{3}{*}{Liaoning soil} & 100 & 109 & \multirow{3}{*}{37.60} \\  & 200 & 128 & \\ \cline{1-1}  & 300 & 153 & \\ \cline{1-1}  & 400 & 179 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: The values of cohesive strength and strength of ISO sand and Liaoning soil used as the filling materials.  
Figure 4: (**a**) Specimens with different numbers of cracks. (**b**) Specimens with different filling materials.  
Moreover, the dynamic force balance was critically assessed for the dynamic compressive tests in this study. According to the suggested method by the International Society for Rock Mechanics (ISRM), the pulse shaping technique placed at the free end of the incident bar (Figure 1) was applied to achieve the dynamic force balance. Based on the one-dimensional (1D) stress wave theory, the dynamic forces on the incident end (\(P_{1}\)) and the transmitted end (\(P_{2}\)) of the specimen are:  
\[P_{1}=AE(\varepsilon_{\mathrm{i}}+\varepsilon_{\mathrm{r}}),\ \ \ \ \ P_{2}=AE \varepsilon_{\mathrm{t}} \tag{1}\]  
Figure 7 shows the forces on both ends of the specimen in a typical dynamic compressive test. The forces (\(P_{1}\) and \(P_{2}\)) on both ends of the specimen were approximately equal during the whole dynamic loading period (Figure 7). Consequently, the dynamic force balance on both loading ends of the specimen was achieved, i.e., \(P_{1}\approx P_{2}\).  
Figure 5: Typical waveforms of incident, reflected and transmitted pulses of the specimen with one crack filled with sand.  
Figure 6: Typical waveforms of incident, reflected and transmitted pulses of the specimen with two cracks filled with soil.  
Figure 7: Dynamic force balance in typical dynamic compressive test. Note: In, force derived from the incident wave; Re, force derived from the reflected wave; Tr, force derived from the transmitted wave.