Supercritical CO₂ phase transition rock-breaking is a dynamic destruction process under the combined action of shock waves and high-pressure gas. To deeply investigate the rock-breaking mechanisms of supercritical CO₂ phase transition under multi-hole synchronous initiation and in-situ stress coupling conditions, targeting the actual working conditions of CO₂ field rock-breaking, the initial rock-breaking pressure of a single hole was analyzed based on the thin-walled cylinder theory. A predictive model for the joint rock-breaking radius of multi-hole shock waves and high-pressure gas under in-situ stress was developed by integrating the one-dimensional detonation gas expansion theory. Field experiments on multi-hole CO₂ phase transition rock-breaking were subsequently conducted for comparative validation. The results show that when the fracturing pipe is buried shallowly, the influence of in-situ stress on the stress distribution of the rock mass is relatively weak. When the pressure of a single hole is consistent, the more fracturing holes there are, the greater the superposed peak stress of each hole. In the direction perpendicular to the layout of the test hole, the peak stress of each hole shows a U-shaped parabolic distribution. The superposed stress of the fracturing holes at both ends is the largest. In the direction parallel to the layout of the test hole, the peak stress of each hole shows an inverted U-shaped parabolic distribution, and the superposed stress of the middle fracturing hole is the largest. In addition, the rock mass damage and fracture range under multi-pore impact obtained by acoustic wave testing in the field is in the shape of a three-dimensional funnel. The vertical damage and fracture range is between 5.05 and 5.73 m, and the planar damage and fracture range is between 4.3 and 5.6 m. The error between the measured value of the planar damage and fracture range and the theoretically calculated value is between 5.0% and 18.7%. The calculation error mainly comes from the uneven superposition stress of each fracturing hole. Further analysis shows that the radius of supercritical CO₂ phase transition rock-breaking increases semi-parabolically with the superposed stress of the fracturing hole and increases logarithmically with the depth of the fracturing hole. As the compressive strength of the rock mass increases, the rock fracture toughness increases nearly linearly, and the corresponding rock-breaking radius decreases nearly linearly. The research results can provide a quantitative design basis for optimizing engineering parameters in the multi-pore supercritical CO₂ phase transition for rock-breaking.

The traditional algorithm is unable to accurately calculate the ultimate bearing capacity of heavy soil foundation, whereas numerical limit analysis methods can do so precisely. It can be seen that numerical limit analysis can solve geotechnical engineering problems more complex than traditional analytical methods. The incremental load method is used, which applies the principle of failure of engineering materials from quantitative to qualitative changes in stress. As the foundation load gradually increases, the stress on the soil foundation transitions from elastic to plastic, and finally reaches the ultimate failure state, obtaining the corresponding ultimate load value. The ultimate bearing capacity of the foundation under strip foundation load was obtained by combining engineering examples, and compared with the traditional empirical results of Terzaghi, Vesic, and Chen. The results show that the numerical limit analysis method can save 40%, 20%, and similar foundation engineering quantities compared to Terzaghi, Vesic, and Chen empirical methods, respectively. At present, both Terzaghi formula and Vesic formula are applied in practical projects, while Chen formula has not been applied yet.