## 3 Directional Hydraulic Fracturing Experiments in Gelatin Samples
### Results and Discussions  
Figures 3-5 provide the experimental results of Test Scenario 1 (Table 2), in which the gelatin concentration (\(w\)) increases from 6% to 10% and the differential stress (\(\sigma_{\text{d}}\)) is constant at 1000 Pa. The steel cutting tool effectively creates a radial initial notch around the open borehole wall as an artificial weakness for HF initiation (Figure 3a,b). Then the HF undergoes re-orientation and tends to propagate perpendicularly to the minimum in situ stress direction until it reaches the boundary of the experimental container (Figure 3c-e). Figure 3f shows the hydraulically fractured gelatin sample taken out from the container after the experiment. The sample surface looks uneven, and the guidance of the initial notch on HF propagation under this experimental condition (\(w\) = 6% and \(\sigma_{\text{d}}\) = 1000 Pa) is within a distance of about 5 to 6 times the borehole diameter. This indicates that HF re-orientation in DHF is not necessarily a near-borehole effect (i.e., within a distance twice the borehole diameter) [13], and the HF can propagate along the notch direction for a longer distance, depending on the experimental condition. Note that the differential stress in Test Case 1-1 is only 1000 Pa (which is much smaller than those in Table 1), and the HF still re-orientates after its directional initiation. Therefore, it could be the magnitude of the differential stress relative to the magnitude of another factor that determines the HF re-orientation distance. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Gelatin Concentration (\%)** & **Elastic Modulus of** & **Fracture Toughness of** \\  & **Gelatin/\(E\) (Pa)** & **Gelatin/\(K_{\text{c}}\) (Pa \(\cdot\sqrt{\text{m}}\))** \\ \hline
7.4 & 38,000 & 400 \\
12.3 & 90,000 & 1330 \\
13.8 & 110,000 & 1530 \\
16.7 & 283,000 & 3190 \\ \hline Linear regression result & \(K_{\text{c}}\) = 0.0108\(E\) + 205.68 (\(R^{2}\) = 0.9768) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Elastic moduli and fracture toughness of gelatin at different concentration measured by [PERSON] and [PERSON] [31]. Figure 2: Indentation test of gelatin specimen. Figure 3: Results of Test Case 1-1 (\(w=6\%\) and \(\sigma_{\text{d}}=1000\) Pa): (**a**) HF initiates from initial notch (plan view); (**b**) HF initiates from initial notch (section view); (**c**) HF propagates along notch direction for certain distance before re-orientation; (**d**) HF re-orientation observed from another angle; (**e**) irregular HF geometry; (**f**) fractured gelatin sample taken out from container. The gelatin concentration in Test Case 1-2 increases from 6% to 8% to examine the influence of the gelatin elastic modulus on DHF. Figure 4a,b show the HF trajectory that maintains a longer propagation distance along the notch direction until it re-orientates horizontally near the container boundary. The fracture surface of the sample in Test Case 1-2 (Figure 4c) becomes smoother compared with the S-shaped curved sample surface in Test Case 1-1 (Figure 3f). This demonstrates that the sample elastic modulus is another important factor affecting DHF, and the HF re-orientates more slowly towards its favorite propagation plane in a stiffer gelatin sample. The gelatin concentration further increases to 10% in Test Case 1-3, and the experimental results are provided in Figure 5. Figure 5a,b show the HF trajectories recorded from different angles during the DHF experiment, while Figure 5c,d give closer observation of the fractured sample that is taken out from the container after the experiment. The experimental device in this study is effective in presenting the complete HF initiation and propagation process through clear gelatin samples and the transparent container (Figure 5a,b), and the use of the thin POF shrink film allows convenient extraction of the fractured sample for detailed recoding of the final HF trajectory after the experiment (Figure 5c,d).