## 2 Superimposed Static and Dynamic Loading Experiments  
### Experimental Apparatus and Loading Scheme  
Rock samples were taken from the roof layer above the #3 coal seam at the Zhaolou Coal Mine, Shandong Province, China. The roof rock is grayish white medium-fine sandstone, which is mainly composed of quartz and contains a large amount of mica fragments. The middle part is sandwiched with thin layers of medium sandstone, and the grain size becomes coarser from top to bottom. The lower part is sandwiched with thin layers of fine siltstones interbedded with each other, with nearly horizontal bedding. The rock hardness coefficient f is 6-7. The samples were sliced and polished into standard specimens in shape with a diameter of 25 mm and a height of 50 mm according to the International Society for Rock Mechanics (ISRM). The experimental apparatus mainly consists of an RMT-201 servo control testing system and a DIC observation system (Figure 1). As shown in Figure 1b, linear variable different transformers (LVDT) were used in the RMT-201 to measure the axial and lateral deformation. As shown in Figure 1c, the DIC observation system consists of industrial cameras, light sources, a data acquisition instrument and a DIC control software. Two high-speed cameras are used to continuously record the images of the specimen surface and the data acquisition instrument, and the highest shooting rate is more than 10,000 pictures per second. Two GT3400 cameras were used in this study (the resolution is 3384 \(\times\) 2074, lens focal length is 80 mm). In one direction, each speckle occupies about 3-5 pixels, subset size is 29 pixels and step size is 4 pixels. The overall score is 0.010 of the calibration result as shown in the bottom image. An optimum matching algorithm (e.g., Newton-Ralphson) matching the correlation function and sub-pixel algorithms (0.01 pixel) were used. We used the standard cross-correlation function, and the correlation coefficient was larger than 0.95, close to 1. Practice showed that the system has high accuracy, and the accuracy reached 0.01 pixels. The random trigger mode was used to take photos in the static loading stage; each time the trigger button is pressed, the left and right cameras take a picture. The start trigger mode was used to take photos in the dynamic loading stage. The DIC control software was Vic-3D, which can be used to calculate the full deformation field evolution and strain field evolution, and can be used for localized deformation analysis of specimens with various loading conditions. According to [PERSON] et al. [29], a loading process with a strain rate lower than \(10^{-5}\) s\({}^{-1}\) is considered a static loading condition, and that with a strain rate higher than \(10^{-3}\) s\({}^{-1}\) is considered dynamic loading condition. Therefore, we applied the dynamic and static loads in this study as follows: the uniaxial compressive strength (UCS) of rock specimens was obtained first under uniaxial static loading condition, the range of the UCS is 71.3-81.5 MPa by repeated experiments, and the result of the average UCS is 77.1 MPa. This result served as a parameter basis for applying static pre-stress in superimposed static and dynamic loads. Figure 2 shows the loading path for the combined dynamic and static loading experiments. We found that the stress concentration in coal and rock mass is large in the process of coal mining, when the working face is about 11 m away from the monitoring section, the maximum stress is close to 60 MPa [48]. Based on the data, four static pre-stresses (30.84, 38.55, 46.26 and 53.97 MPa) were considered, accounting for 40%, 50%, 60% and 70% of the UCS, respectively. The specimens were loaded in a displacement control mode, and the strain rate was controlled at 5 \(\times\) 10\({}^{-6}\) s\({}^{-1}\) for static pre-stress until the axial stress reached the target value.