## 2 Lab-Scale Hydraulic Fracturing Tests
### Analysis of the Results  
In this experiment, two parameters will be used to assess the propagation of hydraulic fracturing cracks: crack deflection angle (the angle by which the crack deviates from the preforming hole axis during propagation, which is used to describe the degree of deflection in the crack propagation direction) and deflection distance (the perpendicular distance from the preforming hole axis to the point where the crack changes from axial propagation to radial propagation). These two parameters serve as the evaluation criteria for the status of hydraulic crack propagation. Figure 3 shows the results of scheme 1-1 (gelatin concentration: 8%, confining pressure: 5800 Pa, preforming hole inclination angle: 90\({}^{\circ}\)). The morphology of the hydraulic fracturing cracks is not completely symmetrical (Figure 3a). After a post-dissection observation of the fractured gelatin sample, the main plane of the hydraulic fracture is relatively regular, where only one \"fold\" can be observed, indicating shear failure (Figure 3b, left wing fracture). The initiation of the hydraulic fracturing cracks occurs along the water discharge area in the middle of the fracturing rod. In this experiment, no single-wing crack was observed; instead, two cracks appeared. Both cracks show deflection and spiral deflection. Although \begin{table}
\begin{tabular}{c c c c} \hline
**Gelatin Sample** & **Elastic Modulus** & **Uniaxial Compressive** & **Apply Confining** \\
**Concentration (\%)** & **of Gelatin (Pa)** & **Strength of Rock (MPa)** & **Pressure (Pa)** \\ \hline
8 & 38,605 & 45.58 & 4960 \\
8 & 38,605 & 50.02 & 5800 \\
6 & 22,491 & 45.58 & 3400 \\
6 & 22,491 & 50.02 & 2800 \\ \hline \end{tabular}
\end{table} 
Table 1: The confining press applied to gelatin samples corresponding to each key strata for different gelatin concentrations. \begin{table}
\begin{tabular}{c c c c c} \hline
**Case** & **Confining** & **Concentration (\%)** & **Dip Angle of** & **Simulated Key Strata** \\  & **Pressure (Pa)** & **Concentration (\%)** & **Borehole (\({}^{\circ}\))** & **Serial Number** \\ \hline
1-1 & 5800 & 8 & 90 & first key strata \\
1-2 & 5800 & 8 & 45 & first key strata \\
1-3 & 4960 & 8 & 90 & second key strata \\
1-4 & 4960 & 8 & 45 & second key strata \\
2-1 & 3400 & 6 & 90 & first key strata \\
2-2 & 3400 & 6 & 45 & first key strata \\
2-3 & 2800 & 6 & 90 & second key strata \\
2-4 & 2800 & 6 & 4 these two cracks have similar shapes, they differ in size: the left wing crack is larger, and its spiral deflection is more pronounced than the right wing crack. The deflection angles of the left wing crack are 78\({}^{\circ}\) at the top and 63\({}^{\circ}\) at the bottom. The deflection angles of the right wing crack are 73\({}^{\circ}\) at the top and 47\({}^{\circ}\) at the bottom. The deflection distance of the left wing crack is 13 mm, while the deflection distance of the right wing crack is 14 mm. Figure 4 shows the results of scheme 1-1 (gelatin concentration: 8%, confining pressure: 5800 Pa, preforming hole inclination angle: 45\({}^{\circ}\)). In this set, two cracks appear on the left wing (left wing #1 crack and left wing #2 crack) and one crack on the right wing (right wing #1 crack). The left wing #2 crack and right wing crack form a crack pair. From the images of the sample after dissection in Figure 4c,d, it can be observed that the propagation trajectories of the three cracks are similar. They all initially propagate along the axis of the fracturing hole and then deflect under the effect of confining pressure. Each crack shows a tendency to deflect towards the horizontal, with all cracks showing spiral deflection. From Figure 4c, it can be seen that left wing #1 crack has extended to the horizontal direction, with obviously spiral propagation. Left wing #1 crack initially propagates along the axis of the fracturing hole and then deflects under confining pressure, extending radially and axially at both the upper and lower ends of the fracturing hole.