# Numerical Investigation of Slurry Fracturing during Shield Tunneling under a Reservoir
## 1 Introduction
Simulation of the hydraulic fracturing process usually involves four processes: (i) mechanical deformation, induced by fluid pressure on fracture surfaces, (ii) fluid flow within the fracture, (iii) fracture propagation, and (iv) coupling of seepage and stress in the computational domain around the fracture [23]. At present, algorithms related to hydraulic fracturing or fracture propagation can be mainly divided into the following categories: the finite element method (FEM) [24], the extended finite element method (XFEM) [25], the discrete element method (DEM) [26], the displacement discontinuity method (DDM) [27], the boundary element method (BEM) [28], etc. Each method has its own advantages and disadvantages. It is necessary to choose the appropriate method according to the application scenario. Among these methods, XFEM has the advantage of high solution accuracy and allows cracks to expand arbitrarily within the element. XFEM overcomes a major challenge in modeling fractures with conventional FEM, by allowing the presence of discontinuities in an element and enriching displacement degrees of freedom. In addition, XFEM can be extended to model hydraulic fracture growth in porous materials by introducing additional pore pressure degrees of freedom to the elements [29]. The XFEM method can be applied to the theory of fracture mechanics well, and is often used to analyze the hydraulic fracturing of rocks [30; 31]. When focusing on the propagation path of hydraulic fracturing in rock and soil under a complex stress state, XFEM has good applicability and application potential. At present, XFEM has not been applied to the analysis of shield slurry fracturing. According to current research, the phenomenon of slurry fracturing in shield tunneling occurs in soft soil layers and is difficult to observe. Simplified theoretical models and model tests have difficulty describing the occurrence process of slurry fracturing, due to the complex stress on the stratum above the shield excavation front. The history of using numerical simulation methods in the field of rock hydraulic fracturing is relatively short. Slurry fracturing of shield tunnels in soft soil is different from rock hydraulic fracturing in terms of failure mechanism and scale. The XFEM numerical simulation method should be a powerful tool to study the slurry fracturing of shield tunneling, but there is no relevant research at present. A better description of shield slurry fracturing in soft soil is very important, to prevent slurry blow-out and to ensure construction safety. This paper takes the Jinan Jiluo Road Crossing the Yellow River Tunnel North Extension Project, to be built in China and intersecting the Queshan reservoir, as the research object. The purpose is to analyze the risk and prevention methods of slurry blow-out caused by slurry fracturing during shield tunnel construction under the reservoir. Based on the extended finite element method (XFEM), the secondary development of the ABAQUS extended finite element was carried out, and the embedded tension-shear combined failure criterion was realized. Through the establishment of the slurry fracturing extension model, the slurry fracturing process of shield tunneling in sticky soil layer is simulated, the variation law of fracture slurry pressure in the process of fracture extension is studied, and the influence of shield slurry support pressure, overburden thickness, formation shear strength, and slurry viscosity on fracture extension pressure and extension path are analyzed. According to the numerical analysis results, suggestions for preventing slurry blow-out in the construction of shield tunnel crossing reservoirs are put forward.