# Numerical Investigation of Slurry Fracturing during Shield Tunneling under a Reservoir
## 5 Conclusions  
Relying on the large-diameter shield tunnel crossing large drinking water reservoir project, this paper uses the XFEM numerical simulation to study the occurrence and extension of slurry fracturing in shield tunnels in cohesive soil layers. 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. The XFEM method was verified by comparing the numerical simulation calculation of the blind-hole samples with the test data. Typical sections of the shield tunnel that cross the reservoir in this project were selected for simulation. The variation law of slurry fracturing pressure in the process of slurry fracturing and propagation is analyzed. The effects of shield slurry support pressure, overburden thickness, formation shear strength, and slurry viscosity on fracture propagation pressure and propagation path were studied. Based on numerical simulation and analysis, the upper limit of the shield slurry support pressure of the shield tunnel crossing the reservoir in this project is briefly given, and the following results are obtained:  
1. Both tensile and shear failures exist in the slurry fracturing process of the clay formation. The error of the fracture initiation pressure obtained by simulation under different confining pressures is basically within 5%, compared with the test results. After introducing the combined tensile-shear failure criterion, the calculation results of the XFEM method are in good agreement with the test data of slurry fracturing of clay samples. 2. The slurry fracturing pressure of cohesive soil increases with the increase of soil stress, unconfined compressive strength, and slurry viscosity. When the slurry viscosity reaches a certain level (about 25 s), the slurry fracturing pressure is no longer significantly affected by the slurry viscosity. The slurry fractures are deflected in the direction of the maximum principal stress. 3. The shield slurry fracturing pressure in the same stratum will rise with the increase of tunnel burial and overlying water depths. With the slurry continuously injected, the slurry pressure reaches the peak at the initiation of shield slurry fracturing in cohesive soil layers. The slurry pressure gradually decreases with the extension of the fracture, and the slurry pressure will be equal to the water pressure of the tunnel vault after the fracture penetrates to the surface. 4. Precisely controlling the shield slurry support pressure to be less than the upper limit of the support pressure is important to avoid slurry fracturing. Increasing the viscosity of slurry can slow down the expansion of fractures. In the process of shield construction, the proper increase in viscosity of the slurry can slow down the spreading speed of the slurry fracturing. The shield can drive quickly to seal the fracture opening to prevent further extension of the fracture. When the upper limit of the shield support pressure is too small, making it difficult to control during construction, it can be optimized from the perspective of shield tunnel site selection and buried depth design to avoid slurry fracturing. Conceptualization, B.H. and D.Y. ; methodology, B.H. and D.Y. ; software, B.H. and T.W. ; validation, B.H., T.W. and Z.W. ; formal analysis, B.H. ; investigation, B.H. ; resources, D.Y. ; data curation, B.H. and Z.W. ; writing--original draft preparation, B.H. ; writing--review and editing, B.H. and T.W. ; visualization, T.W. ; supervision, D.Y. ; project administration, D.Y. ; funding acquisition, D.Y. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the National Natural Science Foundation of China under Grant No. 52008021, and the Key Project of High-speed Rail Joint Fund of National Natural Science Foundation of China under Grant No. U1834208. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.