## 3 Directional Hydraulic Fracturing Experiments in Gelatin Samples
### Results and Discussions
The HF geometry in Test Case 3-1 (\(w\) = 6% and \(\sigma\)d = 2000 Pa) shows a very irregular, asymmetric pattern (Figure 9b-d) even if the HF directionally  
Figure 8: Results of Test Case 2-3 (\(w\) = 10% and \(\sigma\)d = 1500 Pa): (**a**) HF initiates from initial notch (plan view); (**b**) HF initiates from initial notch (section view); (**c**) HF propagates obliquely; (**d**) smooth fracture surface; (**e**) fractured gelatin sample taken out from container. initiates from the initial notch (Figure 9a,e). A step-like HF geometry is noticed in Figure 9d, which is consistent with Daneshy and Services's ([PERSON] and Services, 2018) and [PERSON] et al. 's ([PERSON], 2018) findings of HF re-orientation from oriented perforations. This implies that both shear failure and tensile failure occur during HF re-orientation, and hence shear strength of a material must be considered in the numerical simulation of DHF ([PERSON], 2018). Otherwise, the HF re-orientation distance could be overestimated, as in [PERSON] et al. 's ([PERSON] et al., 2018) study, which only includes the tensile fracture toughness of the material. Nevertheless, it should be noted that formation of step-like HFs is not a necessity in DHF (e.g., Figure 6). The HF shape depends on the differential stress state and also the material elastic modulus (or material strength). In all the test cases, steps are only found in Test Case 3-1, which has the lowest gelatin concentration (\(w=6\%\)) and the highest differential stress (\(\sigma_{\rm d}=2000\) Pa). In the other two test cases (\(w=8\%\) and \(w=10\%\)) in Test Scenario 3 (\(\sigma_{\rm d}=2000\) Pa), HFs maintain planar shapes and re-orientate very quickly to the horizontal direction (Figures 10 and 11). Thus, the occurrence of irregular step-like HF geometries is dependent on the combined effect of the differential stress and the gelatin elastic modulus. Additionally, guidance of initial notches on HF propagation becomes extremely limited in a much higher differential stress state (\(\sigma_{\rm d}=2000\) Pa), and HF orientations in this situation are dictated by the minimum in situ stress direction. From the above experimental results, it is concluded that the efficiency of DHF in field application depends on both the differential stress and the rock elastic modulus. More specifically, it is the relative magnitude of the differential stress and the rock elastic modulus that determines HF propagation rather than the absolute magnitudes of these two factors. The initial notch is able to ensure the formation of radial HFs (rather than axial HFs), as evidenced by the experimental results of all the test cases. Hence, the application of DHF in field-scale hydraulic fracturing is important to prevent near-borehole tortuosity of HFs (due to their axial initiation) and can contribute to more regular HF geometries and longer HF radii. This is recognized by [PERSON] et al. 's ([PERSON] et al., 2018) and [PERSON] et al. 's ([PERSON] et al., 2018) field observations at Cadia East Mine (a hard rock mine in Australia) and Narrabri Mine (a coal mine in Australia), respectively. Nevertheless, HFs could propagate asymmetrically if hydraulic fracturing is carried out in relatively weak rock masses under high differential stresses (Figures 6 and 9). In this situation, a closer borehole distance is required to ensure that the rock mass is fully hydraulically fractured. In the mining industry, hydraulic fracturing is performed on either a relatively large scale (e.g., orebody pre-conditioning in hard rock mining ([PERSON] and [PERSON], 2018; [PERSON], 2018) and hard roof pre-conditioning before the initial mining stage in coal mining ([PERSON], 2018; [PERSON], 2018) in which the HF radius is about 20 to 30 m) or a relatively small scale (e.g., caveability control of hanging roofs at the face end in coal mining ([PERSON], 2018) and hard roof cutting near gob-side entries ([PERSON], 2018) in which the HF radius is about 3 to 5 m).