# Numerical Investigation of Slurry Fracturing during Shield Tunneling under a Reservoir
## 1 Introduction  
The slurry shield method is widely used in the excavation of tunnels in soft soil and composite strata, especially for large-diameter underwater tunnel projects in soft soil [1]. Under complex engineering conditions such as weak stratum, shallow tunnel depth, and rich groundwater, the slurry shield balances the water and soil pressure on the tunnel excavation face by providing slurry support pressure, so as to maintain a safe and efficient tunnel excavation environment. Therefore, the core problem of shield excavation construction is to ensure the stability of the excavation face [2]. Reasonable setting of the shield slurry support pressure is key to realize stable control of the excavation face. However, in the face of the increasing number of large-diameter shallow-coveredunderwater shield tunnel projects, it is difficult to reasonably set the support pressure. Improper control of the support pressure will lead to instability of the excavation face, resulting in the destruction of the soil above and in front of the shield, thereby causing engineering accidents. When the slurry support pressure of the shield tunneling is too small, the tunnel excavation face will collapse, causing the soil in the front to pour into the shield, resulting in active instability and failure of the excavation face of the shield tunnel [3, 4]. When the shield slurry support pressure is too large, the shield slurry will fracture the stratum above the excavation face front, and the resulting slurry fracturing cracks extend to the surface. When the fracturing develops into a crack channel from the excavation face to the surface, shield slurry will push out from the surface, known as shield slurry blow-out. Shield slurry blow-out will cause dangerous situations, such as the escape of slurry support pressure and the backflow of overlying water, resulting in passive instability and damage to the excavation face of the shield tunnel [5, 6]. The active and passive instability of the excavation face can easily cause accidents such as shield machine downtime, damage, and tunnel collapse. Especially when the shield tunnel passes through water such as rivers, lakes, and seas, construction of the shield tunnel is faced with the situation of shallow covering soil and high water pressure. Slurry blow-out may cause water inrush accidents in the shield tunnel. When the shield tunnel passes through a large drinking water reservoir, shield slurry blow-out will inevitably pollute the drinking water source and endanger public water safety. Therefore, the requirements for preventing the occurrence of shield slurry blow-out are higher when the shield tunnel passes through a domestic water reservoir. The key contradiction in setting the support pressure of shield tunnels is that it is necessary to provide enough support pressure to resist the water and soil pressure on the excavation face of the tunnel; at the same time, it is necessary to avoid excessive support pressure, which will cause slurry fracturing on the excavation face of the slurry blow-out [7]. Especially for large-diameter shallow-buried tunnels, the relatively low thickness of overburden and the larger shield diameter aggravate this contradiction, making it more difficult to determine the reasonable range of shield excavation face support pressure. In order to predict the active instability failure of the shield tunnel excavation face, many theoretical models and results have been produced in existing research [8, 9, 10, 11]. However, there are few theoretical studies on the passive instability of slurry fracturing on the excavation face of shield tunnels. The research on the slurry fracturing phenomenon of shield tunnels originated from the Tokyo Bay Subsea Tunnel Project in Japan. The phenomenon of shield slurry fracturing mainly includes two basic processes: fracture initiation and crack extension [12]. [PERSON] and [PERSON] et al.