## 3 Directional Hydraulic Fracturing Experiments in Gelatin Samples
### Results and Discussions
In the former case, HF propagation is mainly dictated by the minimum in situ stress direction, and borehole arrangement should adjust to the in situ stress condition. DHF in this situation decreases breakdown pressure and favors transverse initiation of HFs ([PERSON] et al., 2018). On the contrary, the initial notch in small-scale hydraulic fracturing is necessary for creating orientation-controllable HFs in order to cut the beam-like hard roof at the face end or near the gob-side entry. The HF trajectory can be directionally controlled by the initial notch under a low differential stress condition (relative to the rock elastic modulus), as supported by the experimental results in Test Cases 1-1 to 1-3 (Figures 3-5) and Test Cases 2-2 and 2-3 (Figures 7 and 8). Note that hard roofs in coal mining that have low caveability and need to be hydraulically fractured are normally strong and massive. This favors the directional propagation of HFs along the notch direction. Therefore, directional roof cutting by DHF is possible if the minimum principal stress direction in the fracturing area (the abutment stress must be considered in coal mining) is horizontal and perpendicular to the entry axis or the ratio of the differential stress to the rock elastic modulus is sufficiently low. Otherwise, the hydraulic fracturing strategy needs to be adjusted to improve the caveability of the roof mass in order for its immediate caving with the advance of the working face (e.g., fracturing an area 20 to 30 m around the mining entry) instead of creating a continuous cutting line to eliminate the beam-like structure. Recently, DHF extended its application to assist mechanical excavation in strong, massive rock masses (by road-headers) at Guojiawan Coal Mine, China. Normally, pre-conditioning is performed 10 m ahead of the excavation working face, which has a cross-section of about 6.4 m (in width) \(\times\) 4.2 m (in height). Effective notch cutting favors formation of a set of orientation-controllable radial HFs along the horizontal hydraulic fracturing borehole in order to reduce the block size of the rock mass and hence facilitate hard rock excavation [54]. Figure 9: Results of Test Case 3-1 (\(w=6\%\) and \(\sigma_{\text{d}}=2000\) Pa): (**a**) HF initiates from initial notch (plan view); (**b**) irregular and asymmetrical HF trajectory; (**c**) irregular and asymmetrical HF trajectory observed from another angle; (**d**) step-like fracture surface; (**e**) smooth notch surface and uneven fracture surface (due to HF re-orientation). Figure 2:0 Results of Test Case 3-2 (\(w=8\%\) and \(\sigma_{\text{d}}=2000\) Pa): (**a**) HF initiates from initial notch (plan view); (**b**) HF trajectory (section view); (**c**) fracture surface (plan view); (**d**) fractured gelatin sample taken out from container. Figure 2:1 Results of Test Case 3-3 (\(w=10\%\) and \(\sigma_{\rm d}=2000\) Pa): (**a**) HF trajectory; (**b**) HF trajectory observed from another angle; (**c**) fractured gelatin sample taken out from container; (**d**) fracture surface (section view); (**e**) fracture surface (plan view); (**f**) fracture surface (top view). In summary, the effects of the differential stress and the material elastic modulus on DHF are qualitatively examined and discussed in this study. The correlation between the differential stress and the material elastic modulus will be further quantitatively investigated in future studies in order for successful application of DHF with various purposes in the mining industry.