## 1 Introduction  
Major water conservancy projects are the backbone and key components of the water conservancy infrastructure system, and the construction of hydraulic tunnels is an important part of water conservancy engineering. Currently, the TBM (Tunnel Boring Machine) method is commonly used for construction. Compared to traditional drilling and blasting methods, TBM construction has significant advantages regarding excavation speed, surrounding rock stability, and working environment [1, 2, 3]. However, complex geological conditions often lead to frequent machine jamming, greatly affecting construction efficiency and project progress [4; 5; 6]. The geological conditions of fault zones with fractured zones are complex, with poor formation stability, loose rock mass structure, and limited self-bearing capacity. When the TBM passes through the fault-fractured zone, multiple risks, such as collapse, water inflow, and machine jamming, may occur. These potential threats not only seriously jeopardize the safety of construction personnel but may also lead to delays in construction progress [7; 8; 9]. To address the adverse geology of fault-fractured zones, grouting reinforcement methods are commonly used to improve the physical and mechanical properties of the rock mass. By injecting grout into the rock mass to fill fractures, the integrity and stability of the rock mass are enhanced, significantly increasing its strength and resistance to deformation, thereby providing reliable protection for the safe and efficient passage of TBMs through poor geological sections [10; 11; 12]. Research on grouting reinforcement for tunnels in fault-fractured zones is divided into two categories based on the grouting area: grouting inside the tunnel and grouting outside the tunnel. For grouting inside the tunnel, the effect of pre-grouting reinforcement on tunnel passage through the fault-fractured zone can be studied using three-dimensional finite element numerical simulation methods with an optimal grouting range. At the same time, it is necessary to analyze the mechanisms of flow velocity and pressure evolution in the cross-section during the grouting sealing process of the fault-fractured zone [13; 14]. In the case of a TBM with an open face encountering machine jamming while passing through a fault-fractured zone, grouting plans should be developed based on the actual situation to ensure the TBM is successfully freed. Additionally, for water-rich fractured zones, research on full-face grouting technology should be conducted. By setting different grouting parameters for the curtain grouting, the patterns of tunnel crack initiation and propagation can be analyzed, with the results ultimately applied to the field [15; 16]. In the case of grouting outside the tunnel, the porosity and permeability of the grouting area can be calculated through theoretical analysis and numerical simulation, thereby determining the appropriate grouting scheme. Additionally, based on hydraulic fracturing theory, the minimum grouting pressure for surface pre-grouting at a specific depth can be determined. It is important to note that for fault-fractured zones, surface pre-grouting reinforcement should still be combined with on-site monitoring techniques to analyze the diffusion patterns of the grouting area and assess the grouting effect. For extremely fractured regions, a key technical system for directional borehole protection of tunnels through faults can be adopted, which is based on drilling construction techniques and high-pressure pre-grouting technology [17; 18; 19]. The computational modeling of mechanized tunneling, particularly in long and deep tunnels through challenging ground conditions, has been the subject of numerous studies. Notably, [PERSON] et al. [20] conducted extensive numerical investigations into TBM tunneling using various computational methods. In addition, [PERSON] and [PERSON] [21] developed dimensionless design nomograms, which were derived from computational analysis results.