Abstract
Grouting is a complex process involving interactions of slurry and water phase. The viscosity of slurry is of spatiotemporal variation and significant loss of slurry was observed in grouting processes. These phenomena are difficult to address in numerical models. Therefore, a numerical method of grouting considering the loss of slurry is developed in this work. Firstly, by solving the transport time of slurry, the spatiotemporal evolution of slurry viscosity is implemented. Secondly, by assuming that the water phase and slurry phase is miscible, a diffusion term is added to the transport equation of the slurry volume fraction and the dispersed phase interface of slurry and water is realized. In addition, the simulation result of the new method is compared with our precious experiment data. We show that better agreement is obtained in the variation of grouting pressure, flow rate and slurry loss rate. The effectiveness of the method is verified. Finally, the applicability of our method in engineering scale is verified at engineering scales. The results show that this method could address the interphase miscibility of slurry and water in grouting processes, and it can provide a certain theoretical reference for grouting practice in engineering.
Highlights
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A new numerical model considering interphase miscibility is developed to address the slurry-water interaction in grouting processes.
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The proposed algorithm is experimentally verified, showing good agreement in the computation of grouting parameters.
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By applying the proposed algorithm, the grouting process of karst conduits is studied.
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All data, models, and code generated or used during the study appear in the submitted article.
Abbreviations
- g:
-
Gravity acceleration (m/s2)
- M:
-
Momentum (kg/m2 s2)
- p :
-
Pressure (Pa)
- T:
-
Transport time (s)
- t :
-
Time (s)
- U:
-
Velocity (m/s)
- Udj :
-
Drift velocity of phase d (m/s)
- U r :
-
Relative velocity (m/s)
- α :
-
Volume fraction
- Γ:
-
Diffusion coefficient (m2/s)
- μeff :
-
Effective viscosity (Pa s)
- ν t :
-
Turbulent viscosity (m2/s)
- ρ :
-
Density (kg/m3)
- τ :
-
Viscous stress tensor (kg/m s2)
- c :
-
Continuous phase
- d :
-
Dispersed phase
- i :
-
Phase i
- m :
-
Mixture phase
- s :
-
Slurry phase
- w :
-
Water phase
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Acknowledgements
We would like to acknowledge the support from the National Science Fund for Excellent Young Scholars (Grant No.: 52022053), the National Natural Science Foundation of China (Grant No.: 52109129), the Science Fund for Distinguished Young Scholars of Shandong Province (Grant No.: ZR201910270116), and the Natural Science Foundation of Shandong Province (Grant No.: ZR2021QE163).
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Xu, Z., Zhang, Y., Pan, D. et al. A Novel Grouting Simulation Method Considering Diffusion and Loss of Slurry in Flowing Water: Interphase Miscible-Transport Time-Tracking (IM-3T) Method. Rock Mech Rock Eng 56, 5815–5832 (2023). https://doi.org/10.1007/s00603-023-03347-7
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DOI: https://doi.org/10.1007/s00603-023-03347-7