# Energy Dissipation and Stress Equilibrium Behavior of Granite under Dynamic Impact
## 2 Methods
### Test Preparation  
To check whether the incident wave and the transmission wave of the initial waveform diagram are semi- sinusoidal waves, we preform Hopkinson impact with no specimen before the formal test. The amplitude attenuation of the transmission wave is much smaller than that of the incident wave, indicating that the incident rod and the transmission rod of the device are well connected. The transmission rate of the wave energy at the two-bar connection is large. The incident wave rises slowly and has enough time to allow the rock to reach the stress balance. Option of length-diameter ratio  
In order to obtain test data closer to the intrinsic relationship of the rock, it is necessary to ensure that the granite specimen is in a uniform state of stress during the loading process. Different length-diameter ratios change the time of single propagation of stress waves within the rock and the number of transverse reflections within the rock. The length-diameter ratio has an effect on the rock stress equilibrium process, which leads to differences in rock fragmentation patterns. The diameter of the granite specimen used in the test is 50 mm. In order to better reflect the stress wave response characteristics in the range of mechanical properties of granite rocks, the selected length-diameter ratios are 0.6, 0.8, 1.0, 1.2, and 1.4, respectively. Option of strain rate  
The strain rate is the essence of reflecting the dynamic load response characteristics of the rock, and the strain rate is controlled by the impact air pressure and impact loading during the test. We chose impact velocity of 8 m/s, 10 m/s, 12 m/s, and 14 m/s. The corresponding strain rates are 63.8 s\({}^{-1}\), 109.8 s\({}^{-1}\), 156.8 s\({}^{-1}\), and 253.2 s\({}^{-1}\). Determining a reasonable range of strain rate can provide a longer constant strain rate loading time before specimen fracture. The reason for the low uniformity of rock crushing under the action of high strain rate may be that the high-speed impact cannot reach the stress equilibrium state, and the study of strain rate can be helpful to the uniformity of rock crushing to improve the stress equilibrium time. Option of data range  
In order to determine the appropriate loading range, impact tests were conducted on 1.0 length-diameter ratio specimens. When the impact strength is lower than 0.1 MPa, the specimen has no obvious fracture deformation and the rock longitudinal wave velocity has no obvious change. The impact test data at this point are invalid and are not included within the experimental study. When the impact strength exceeds 0.23 MPa (the strain rate is about 253.2 s\({}^{-1}\)), the rock is violently deformed under the action of a single impact. The degree of rock fragmentation is higher and it is more difficult to obtain effective data during the propagation of stress waves. The loading data are shown in Table 1.  
In order to research the stress equilibrium time before the rock broken, we performed pre-experiments to choose the loading test data, such as loading strain rate, length-diameter ratio, and impact velocity. The feasibility of the experiment is ensured by the above theory and pre-experiments. Analysis methods  
The most common processing methods for the electrical signals obtained from strain gauges on the incident and transmission rods are the two-wave and three-wave methods. \begin{table}
\begin{tabular}{c c} \hline \hline
**Loading Condition** & **Range** \\ \hline Loading strain rate & 50 s\({}^{-1}\)\(\sim\)300 s\({}^{-1}\) \\ Impact strength & 0.12 MPa\({}^{-0.25}\) MPa \\ Impact velocity & 8 m/s\({}^{-14}\) m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Loading range. We use the three-wave method to process the strain signal because the three-wave method can reduce the perceived measurement error and is more reliable for brittle materials [14]. When the compression bar is in an elastic state, the waveform of the one-dimensional elastic stress wave is the same at any position when propagates in the bar.