## 1 Introduction  
\"Accelerating the construction of a country with strong transportation network and improving the comprehensive transport corridor\" is the core initiative of the 14 th Five-Year Plan of the China, and the tunnel project is an important support for the grand strategy of realizing a country with a strong transportation network [1]. At present, China has been the country with the largest scale, the largest number, the most difficult, and the fastest development of tunnels in the world, and a large number of road, railway, and water diversion tunnels have been constructed in areas with complex topographical and geological conditions and abundant groundwater. Fault fracture zones with loose, broken, and poorly self-stabilized rock masses are common adverse geological conditions faced in tunnel construction. There is a significant difference in physical and mechanical properties between the fault and the rock mass around the fault, and various geological hazards are often encountered when tunnelling approaches the fault. Among them, water inrush and mud outburst that possess extremely high risks are the most frequently encountered, which not only affects the regular construction of tunnels, resulting in delays, but also seriously threatens the safety of personnel and construction machinery in the field [2; 3; 4; 5]. During the construction of the Anshi tunnel on the Yunfeng Expressway, a hidden aquifer fracture zone was confirmed in the right-upper part of the right hole at mileage of K42 + 955. Two large-scale water inrush and mud outburst disasters occurred when the face was advanced to the mileage of YK42 + 951.6, which caused 12 deaths, 10 injuries, and a direct economic loss of 2,520,100 CNY. The Dafengyakou tunnel, a controlling project of Yuanjiang-Maohei Expressway, experienced a large-scale water inrush and mud outburst when the excavation of the tunnel passed through the fault-concentrated development zone, with a water inrush amount of 24,000 m\({}^{3}\) and a mud outburst amount of 11,000 m\({}^{3}\). When the Baiyun tunnel on the Nanning-Guangzhou Railway was excavated to the mileage of DK334 + 733, a large-scale water inrush and mud outburst occurred, with a mud outburst amount of about 2000 m\({}^{3}\) and a water inrush rate of about 300 m\({}^{3}\)/h, which resulted in 5 deaths. Therefore, it is very urgent to perform the research regarding the water inrush mechanism to provide theoretical guidance for the tunnel construction adjacent to the fault. In recent years, a large number of scholars have explored the water inrush mechanism of tunnels adjacent to faults, and the results are quite fruitful. In terms of theoretical analyses, many scholars worldwide have deeply examined the water inrush mechanism of faults according to theories such as the total potential energy principle, silo theory, and limit equilibrium method [6; 7; 8; 9]. However, the water inrush in the face of the tunnel adjacent to the fault is a systematic imbalance process that is affected by a triggering factor of excavation disturbance and a coupling of multiple factors and conditions in the water-resistant rock mass at the face, which is a highly non-linear mathematical problem. It is difficult to theoretically depict the whole process of the water inrush disaster in the water-resistant rock mass. The model test can simulate the destabilization of the water-resistant rock mass at the face and reproduce the whole process of the water inrush disaster. Many scholars have studied the change characteristics of displacement, water surge, and permeability pressure in the rock mass when a water inrush disaster occurs in a tunnel adjacent to the fault by conducting physical model tests [10; 11; 12; 13; 14]. Since physical model tests require a large amount of manpower, material resources, and time, it is difficult to carry out multiple large-scale tests.