# Double-Borehole Superimposed Effect of a New Non-Explosive Directional Rock-Breaking Method
## 3 Results  
### Numerical Simulation Results of IESF  
#### 3.1.1 Stress Field Evolution Law for Double-Hole Fracture  
The stress evolution processes during fracturing by CB, SCB, and IESF are illustrated in Figures 12-14, respectively, with negative values denoting tensile stress and positive values indicating compressive stress. In CB, during the detonation wave phase (Steps 0-50), stress waves generated from both slotted boreholes interacted through superposition, initiating fractures under dynamic loading conditions. In the blast-induced gas phase (Steps 51-100), the blast-induced gas facilitated the crack propagation, with high compressive stress concentrated near the borehole wall that gradually diminished radially outward, and tensile stress concentration zones developed at the fracture tips. During the detonation wave phase (Steps 0-50) of SCB, both slotted boreholes exhibited directional fracture initiation along their predetermined splitting orientations. Tensile stress concentrations developed along the predetermined splitting orientations, while compressive stress dominated along the perpendicular orientations. The borehole wall experienced peak compressive stress magnitudes, which exhibited a gradient reduction from the wall outward into the surrounding rock mass. During the blast-induced gas phase, the fractures from both slotted boreholes propagated and ultimately coalesced. Prior to coalescence, the tensile stress concentrations at the fracture tips within the inter-borehole region interacted through superposition, intensifying stress concentration levels and creating larger tensile stress zones compared to those on the outer-borehole region. Following coalescence, the tensile stress concentrations diminished in both the inter-borehole region and the outer-borehole region. The stress evolution of IESF exhibited symmetric stress distribution aligned with the slotted orientation. During fracture initiation and extension, tensile stress superposition between boreholes progressively intensified, while compressive stress concentrations in non-slotted directions expanded radially. Following coalescence, stress concentration levels diminished significantly. This technique achieved directional rock fragmentation through tensile-dominated fracturing governed by high-pressure gas expansion, demonstrating superior directional fracture control capability compared to SCB. Figure 11: Charge structure of roof cutting (**a**) CB, (**b**) SCB, and (**c**) IESF. Figure 12: The stress evolution in CB. Figure 13: The stress evolution in SCB. At Step 80, a concentric circle with a 0.2 m radius was selected around the right slotted borehole. Stress values at 0\({}^{\circ}\), 30\({}^{\circ}\), 60\({}^{\circ}\), 90\({}^{\circ}\), 120\({}^{\circ}\), 150\({}^{\circ}\), 180\({}^{\circ}\), 210\({}^{\circ}\), 240\({}^{\circ}\), 270\({}^{\circ}\), 300\({}^{\circ}\), and 330\({}^{\circ}\) positions along this circle were recorded for CB, SCB, and IESF, as shown in Figures 15-17. In CB, the stress values at these 12 measurement points were recorded as follows: 13.45 MPa, \(-\)8.56 MPa, 26.81 MPa, \(-\)6.27 MPa, 11.36 MPa, \(-\)9.77 MPa, 32.52 MPa, 33.28 MPa, 21.75 MPa, 15.19 MPa, 8.37 MPa, and \(-\)3.62 MPa. Among these, tensile stresses were observed at 30\({}^{\circ}\), 90\({}^{\circ}\), 150\({}^{\circ}\), and 330\({}^{\circ}\), while compressive stresses dominated the remaining eight angular positions. Therefore, CB exhibited a random stress distribution pattern. In SCB, tensile stress concentrations were observed along the energy-focused directions (0\({}^{\circ}\) and 180\({}^{\circ}\)). Specifically, tensile stresses of \(-\)10.89 MPa and \(-\)8.33 MPa were recorded at 180\({}^{\circ}\) and 0\({}^{\circ}\), respectively. The tensile stress at 180\({}^{\circ}\) exceeded that at 0\({}^{\circ}\) by 2.56 MPa, which displayed that the tensile stresses between the two holes were superimposed on each other, indicating enhanced stress-superimposed effects within the inter-borehole region compared to the outer-borehole region.