The Simulation of Grouting Behavior in the Pea Gravel Filling Layer Behind a Double-Shield TBM Based on the Level Set Method
Abstract
1. Introduction
2. Numerical Model for Grout Permeability in Backfilling Layers
2.1. Modeling Strategy and Computational Methods
2.2. Construction of the Numerical Model
- Both segmental lining and surrounding rock can be treated as impermeable layers.
- The circumferential diffusion speed of the grout is generally much greater than the axial diffusion speed in engineering applications [24].
- The circumferential perimeter of the backfilling layer is significantly larger than its thickness and axial length, making circumferential diffusion the dominant mode of grout flow.
- Pressure Boundary Condition: A fixed pressure is applied at the inlet.
- Flow Velocity Boundary Condition: A constant flow velocity is applied at the inlet.
3. Analysis of Results
3.1. Diffusion Behavior
3.2. Pressure Boundary Conditions
3.3. Velocity Boundary Conditions
4. Analytical Formula for Grouting Pressure
5. Conclusions
- (1)
- When grout diffuses downward, the diffusion speed is relatively fast, and the transition zone between the grout and air is longer. In contrast, when grout diffuses upward, the diffusion speed is slower, and the transition zone is shorter. Under the same time conditions, the grouting effect is better when the grouting port is at 90° compared to the cases at 30° and 150°.
- (2)
- Under the pressure boundar y condition, the grout flow rate increases rapidly during the initial stage and reaches its peak at approximately 0.2 s. The grouting position has a noticeable effect on the peak flow rate: when grouting is applied at the upper part of the segment, the peak flow rate is higher, reaching approximately 0.25 m2/s, whereas grouting at the middle and lower parts results in a lower peak, around 0.18 m2/s. Subsequently, the flow rate gradually decreases and stabilizes, entering a steady-state phase.
- (3)
- Under velocity boundary conditions, the grouting pressure remains approximately stable during the initial stage of the process. As grouting progresses, the pressure gradually increases. The position of the grouting port has a significant influence on the pressure variation: the lower the port is positioned, the faster the pressure increases. At 2 s into the grouting process, the grouting pressures at the upper, middle, and lower ports are 16.92 kPa, 25.40 kPa, and 31.54 kPa, respectively. The abnormally high grouting pressure may be attributed to locally dense regions, which increase flow resistance and consequently result in elevated grouting pressure.
- (4)
- The analytical formula developed in this study can predict the variation in grouting pressure to a certain extent. Compared to the predicted values, the simulated pressures are lower in the early stage of grouting and higher in the later stage. Porosity, grout viscosity, and injection velocity all have significant effects on grouting pressure. As porosity decreases or injection velocity increases, the discrepancy between the numerical simulation results and the theoretical predictions becomes more pronounced, indicating that the existing formula provides greater accuracy and applicability under low injection velocity conditions.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Density of Air | Viscosity of Air | Density of Grout | Viscosity of Grout |
---|---|---|---|
1.204 kg/m3 | 1.81 × 10−5 Pa·s | 1500 kg/m3 | 0.01 Pa·s |
Sum of Grain Perimeter | Length of Fluid Domain | Width of Fluid Domain | Equivalent Width |
---|---|---|---|
55.414 m | 3.456 m | 0.2 m | 0.00185 m |
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Li, X.; Zhang, Y.; Cao, D.; Liu, Y.; Chen, L. The Simulation of Grouting Behavior in the Pea Gravel Filling Layer Behind a Double-Shield TBM Based on the Level Set Method. Appl. Sci. 2025, 15, 7542. https://doi.org/10.3390/app15137542
Li X, Zhang Y, Cao D, Liu Y, Chen L. The Simulation of Grouting Behavior in the Pea Gravel Filling Layer Behind a Double-Shield TBM Based on the Level Set Method. Applied Sciences. 2025; 15(13):7542. https://doi.org/10.3390/app15137542
Chicago/Turabian StyleLi, Xinlong, Yulong Zhang, Dongjiao Cao, Yang Liu, and Lin Chen. 2025. "The Simulation of Grouting Behavior in the Pea Gravel Filling Layer Behind a Double-Shield TBM Based on the Level Set Method" Applied Sciences 15, no. 13: 7542. https://doi.org/10.3390/app15137542
APA StyleLi, X., Zhang, Y., Cao, D., Liu, Y., & Chen, L. (2025). The Simulation of Grouting Behavior in the Pea Gravel Filling Layer Behind a Double-Shield TBM Based on the Level Set Method. Applied Sciences, 15(13), 7542. https://doi.org/10.3390/app15137542