## Materials and Methods
### Experimental Scheme  
In this experiment, the C-CAST experimental system was used to study the mechanical property and failure behavior of coal samples under different loading rates and inclination angles. However, C-CAST system also has a limitation. When the inclination angle of the sample is greater than 30\({}^{\circ}\), it is difficult to exclude the large experimental error caused by the slip and dislocation of the adapter in the horizontal direction under the C-CAST system. Therefore, 6 groups of inclination angles were set in this experiment, namely 0\({}^{\circ}\), 5\({}^{\circ}\), 10\({}^{\circ}\), 15\({}^{\circ}\), 20\({}^{\circ}\) and 25\({}^{\circ}\); 8 groups of loading rates were set, namely 0.05, 0.50, 1.00, 2.00, 3.50, 5.00, 7.50 and 10.00 mm/min. Each group of experiments was repeated 5 times; the maximum and minimum values were removed, respectively, and the middle three groups of experimental results were taken as the research data.  
The specific experimental steps are as follows:  
Firstly, according to the installation steps of C-CAST system, the installation of test sample and equipment under specific inclination angle is completed. The top adapter of C-CAST system installed with sample is fixed on the loading end of electro-hydraulic servo universal testing machine through a rigidly fixed ring, and the top adapter of the system is located in the middle of the loading end.  
Secondly, petroleum jelly is applied on the end face of the sample to reduce the friction between the end of the sample in the circular groove and the surface of the circular groove in the scale disk to avoid the stress concentration. The universal testing machine is fine-tuned, the exposed end of the sample is slowly inserted into the circular groove of the lower scale disk of the C-CAST system, then the support block is installed and the test sample is fixed.  
Thirdly, the acoustic emission probe is pasted on the coal sample surface, and the installation position is arranged symmetrically and 30 mm away from the end face of the sample. There are four acoustic emission probes in total, and then the lead breaking experiment is carried out to ensure the sound coupling between the acoustic emission probe and the sample, as shown in Figure 3. The prestress of the testing machine is set to be 0.1 kN, that is, when the loading load of the sample reaches 0.1 kN, the experimental data will be recorded.  
Fourthly, the program-controlled system of the universal testing machine is used, and the initial loading rate is set at 3 mm/min. when the prestress reaches 0.1 kN, the loading process is terminated automatically. At this time, it is necessary to check whether the sample is completely fixed in the C-CAST system. If the sample is not fixed, the location of the bottom adapter is adjusted, then the experimental program and the preloading is started again. If the sample is well fixed, the next step is performed  
Lastly, after debugging all the equipment, the loading rate of the testing machine is set to the specified value according to the experimental scheme. At the same time, the testing machine and the acoustic emission acquisition system are started to ensure the synchronization of the collected data. When the sample is damaged, the above experimental system is terminated, and then the data are saved.  
Slowly raise the testing machine, remove the sample, repeat steps 1-5., and carry out the next set of experiments.