## 6 Conclusions  
1. A coupled fluid-solid model that accurately reflects the L-CO\({}_{2}\) phase transition blasting fracturing process in coal seams was established. The state equation parameters for three typical L-CO\({}_{2}\) blasting tubes, with explosive loads of 150 MPa, 210 MPa, and 270 MPa, were calibrated with an error of no more than 4%. The RHT constitutive model, which accounts for the dynamic mechanical properties of the coal, was appropriately selected. A quasi-2D numerical model for L-CO\({}_{2}\) phase transition blasting fracturing of a 10 m \(\times\) 10 m coal seam was constructed.
2. In situ stress was applied to the model. The results show that as in situ stress increases, both radial and circumferential stresses rise. When the stresses in both directions are unequal, the radial compressive stress in the direction of maximum in situ stress exceeds that in the direction of minimum in situ stress, while the circumferential stress is less than that in the direction of minimum in situ stress. Increased in situ stress significantly inhibits the propagation of explosive fractures, while stress difference facilitates the extension of explosive fractures along the direction of maximum principal stress.
3. The time-varying process of L-CO\({}_{2}\) phase transition blasting fracturing was analyzed. The results indicate that between 500 \(\upmu\)s and 800 \(\upmu\)s after an explosion, the plastic deformation around the borehole and the smash zone are essentially formed. By 2000 \(\upmu\)s, the fissure zone due to L-CO\({}_{2}\) impact is largely established. With increasing explosive load, both the smash zone area and the fissure zone range significantly expand. The number of primary fractures generated by the explosion ranged from 0 to 12, the size of the pulverized zone varied from 1170 cm\({}^{2}\) to 2875 cm\({}^{2}\), and the total fracture length ranged from 44.4 cm to 1730.2 cm. As in situ stress rises, the range of the fissure zone will significantly decrease. As stress difference rises, the aspect ratio of the external ellipse of the explosion fracture zone will range between 1.00 and 1.72.
4. Using the total fracture length (\(F_{4}\)) as a response indicator, a response model was established to assess the effects of explosive load, in situ stress, and stress difference on explosive fracturing effectiveness. The results indicate interactions among the factors affecting explosive fracturing effectiveness. The suppressive effects of in situ stress and stress difference on fracturing effectiveness increase with their numerical values, while the enhancing effect of explosive load on fracturing effectiveness shows an increasing trend with a steeper slope as its value increases. This study provides data support for the optimization of L-CO\({}_{2}\) phase transition explosive fracturing processes.  
**Author Contributions:** Methodology, X.G. and C.C.; Software, X.C. and Y.W.; Formal analysis, X.G.; Investigation, X.G. and C.C.; Data curation, X.C.; Writing--original draft, X.G.; Writing--review & editing, X.C., Q.L. and J.X.; Visualization, C.C. and Y.W.; Supervision, Q.L. and J.X. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Conflicts of Interest:** Authors [PERSON], [PERSON] and [PERSON], were employed by the company China Coal Energy Research Institute Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.