## 1 Introduction  
At the present time, the excavations of rock masses under general conditions are still mainly dependent on explosive blasting methods; however, due to the high safety risks and severe environmental impacts of explosive blasting, the management, and control of such explosives have become much stricter [1]. This has resulted in the reduced application feasibility of explosive blasting methods. Particularly, in many special environments, such as the implementation of excavations in densely populated areas or buildings, vibration-sensitive areas, and so on, conventional blasting methods cannot be safely applied [2]. As a result, safe and reliable non-blasting excavation methods have attracted increasing attention and have begun to be applied in rock excavation projects. Since the 1970s, researchers have carried out many relevant studies regarding non-blasting excavation methods [3, 4]. These methods can be mainly divided into three categories: Mechanical excavations, physical and chemical rock-breaking processes, and rock-breaking processesusing electrical equipment [4]. The most commonly used mechanical excavation methods involve hydraulic breakers and road-headers, which have the advantages of high safety performance results, strong environmental protection, and simple operations; therefore, mechanical excavation methods are considered to be suitable for the excavations of some types of soft rock masses; however, mechanical wear and tear are unavoidable [5; 6]. Further, it has been found that the above equipment cannot be applied in a large-scale project due to low work efficiency and slow construction progress. When electrical equipment excavation methods are used, it has been observed that there is less rock breakage; however, the effects of electrical equipment methods are only significant for hard rock masses, and the economic costs are high [5; 6; 7]. Physical and chemical work methods often utilize static cracking agents or metal burning agents [8; 9]. The use of such agents involves both physical and chemical reactions and presents certain potential environmental and safety hazards. Liquid CO\({}_{2}\) phase-transition fracturing technology is a new type of \"physical and chemical\" technology for rock mass excavations which falls into the category of physical blasting technology. This newly introduced technology has been found to have the ability to overcome the shortcomings of non-blasting excavation methods and traditional explosive blasting methods, and it has been observed that the energy utilization rates tend to be noticeably improved [10]. Moreover, the method's applications require no open fires, and are characterized by high safety, small vibrations, and low dust [11]; therefore, the potential of damages occurring to surrounding buildings, rock masses, and environments is greatly reduced. Due to these positive features of liquid CO\({}_{2}\) phase-transition fracturing technology, it can be widely used in rock mass excavations. Liquid CO\({}_{2}\) phase-transition fracturing technology was first proposed by Cardox Co. (United Kingdom) [12; 13]. It was first mainly used in the fracturing, permeability enhancement, and mining of low-permeability and high-gas coal seams, in order to reduce the risks of coal dust and gas explosions [1; 14]. With the development of liquid CO\({}_{2}\) fracturing technology and its proven enhancements of energy release processes, the applications of the technology were extended to ore mining and concrete cracking projects [15]. At the present time, researchers generally believe that CO\({}_{2}\) fracturing is a process of physical change. The energy that is released by the expansion of gases during physical explosions is mainly related to the gas pressure levels, container volumes, and the physical properties of the medium within the containers [16]. [PERSON], [PERSON] et al. [17; 18] conducted studies of the fracturing mechanism of CO\({}_{2}\) fracturing in coal seams.