## 1 Introduction  
In recent years, as shallow coal resources are increasingly depleted, the depth of coal mining worldwide continues to increase. Studies show that the gas pressure and gas content in coal seams rise with increasing mining depth, accompanied by a continuous increase in the original stress of the coal seams. This significantly increases the likelihood of gas outbursts and coal and gas outbursts [1]. Consequently, coal mine gas has become one of the major safety hazards restricting deep coal mining [2]. Gas extraction at the White Haven coal mine in the UK began as early as the 18 th century. In the United States, research into gas control started in the early 20 th century. In 1969, the U.S. Mine Safety and Health Administration (MSHA) initiated gas control in mined-out areas, achieving positive results. After 1973, coal mine gas extraction technologies began to be widely adopted in the U.S. Since 2002, the \"Safety Regulations for Coal Mines\" issued by the National Mine Safety Administration of China have stipulated that for high-gas and outburst-prone mines, coal seam gas must be pre-drained before mining to ensure that gas pressure and gas content are reduced below the safety limits of 0.74 MPa and 8 m\({}^{3}\)/t, respectively. It is clear that gas extraction is a fundamental strategy for preventing and controlling coal mine gas disasters [3]. Since most high-gas and outburst-prone coal seams in China typically exhibit low porosity and low permeability, measures such as pressure relief and enhanced permeability or fracturing are necessary to induce a network of fractures in the coal seam that facilitates gas migration [4]. Among these, fracturing techniques primarily target single coal seams lacking protective layer mining conditions. These techniques have developed into water-based fracturing technologies represented by hydraulic fracturing and hydraulic punching, as well as non-water fracturing technologies represented by deep hole blasting and liquid nitrogen fracturing [5; 6; 7]. The liquid carbon dioxide (L-CO\({}_{2}\)) phase change blasting technology originated from the Cardox tube technology invented in the United States in 1914 and has been applied in coal seam mining, step blasting, tunnel excavation, and other fields [8]. The L-CO\({}_{2}\) phase change blasting tube typically consists of a detonator, a cracking device, and a liquid storage tank. The detonator generates an electric spark that activates the activator loaded in the cracking device, causing the L-CO\({}_{2}\) in the storage tank to suddenly heat and pressurize, rapidly vaporizing and expanding to generate a powerful dynamic impact and high-pressure gas wedge effect on the surrounding rock [9]. Investigations have shown that in the 1940s, 25% of underground coal mines in the United States utilized L-CO\({}_{2}\) phase change blasting technology, with an annual blasting volume exceeding 2.8 million times [10; 11; 12]. Compared to other fracturing technologies, L-CO\({}_{2}\) phase change blasting offers advantages such as high operational efficiency, absence of toxic and harmful gasses, low blasting vibration response, adjustable and controllable blasting energy, fewer application restrictions, and high social acceptance, thus attracting widespread attention in fields like coal seam fracturing and transformation. Reports indicate that this technology has been widely applied in the comprehensive management of mine gas in China, including roadway pressure relief excavation, coal seam pressure relief and permeability enhancement, and top-coal safety fracturing [13]. Several scholars have demonstrated through field experiments that L-CO\({}_{2}\) phase change blasting can effectively increase coal permeability and enhance gas extraction efficiency. For instance, [PERSON] et al.