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Grouting mechanism of quick-setting slurry in fracture with random fracture opening considering time–space characteristics of viscosity

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Abstract

The coupling effect between the spatial variability of slurry diffusion and the time-varying viscosity of quick-setting slurry is the time–space characteristics of slurry viscosity (TSCSV). The TSCSV is the governing factor for the complex and uncontrollable flow of slurry in fractures. In this regard, the flow pattern of quick-setting slurry is considered as a Bingham fluid with viscosity spatiotemporal characteristics. Using the fractal function with random parameters (W-M function), a single fracture with random fracture opening (RFO) is drawn, and a theoretical model on grouting diffusion in fractures is established considering the TSCSV. The RFO is corrected for head loss, and the spatiotemporal distribution equation of the RFO grouting pressure is derived. The relationship between grouting pressure, grouting time, and slurry diffusion distance is obtained. Additionally, the effects of the RFO, the fractal dimension of the fracture curve, the horizontal movement distance of the lower end face of the fracture, and the effects of viscosity and grouting rate on the viscosity and grouting pressure in the slurry diffusion space are discussed. Finally, by predefining the spatial distribution function of slurry viscosity for a single fracture in the numerical calculation model, a numerical simulation of random fracture distribution grouting considering viscosity spatiotemporal characteristics is achieved. The rationality of the model is validated through a comparison of theoretical analysis and numerical simulation, providing reference for the determination of grouting parameters in practical grouting projects.

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Data availability

Data will be made available on request.

Abbreviations

q :

Grouting rate

r :

Slurry diffusion distance

i :

Number of fracture segments

B i :

Fracture opening (when i takes different values, Bi has different values, and the following variables are similar)

b i :

Fracture opening after conversion

m :

Length of fracture segmented

r m :

Local diffusion distance of slurry (diffusion distance within segment length m)

D :

Crack thickness (fixed at 1 mm)

µ(t):

The apparent viscosity of the slurry

τ :

Shear stress of the slurry

τ 0 :

The yield shear force of the slurry

τ i :

Shear stress of grout in each fracture segment

h oi :

Height of nucleus retention area

h maxi :

Maximum height of nuclear retention area

p i :

Grouting pressure in fracture segment

P zn :

Grouting pressure at grouting point (total pressure)

P zni :

The increased pressure caused by slurry diffusion through a fracture section

muQR:

Slurry viscosity

t :

Grouting time

mut:

Slurry viscosity reaction time (equal to t)

\(\xi_{i}\) :

Head loss coefficients

h si :

Head loss

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Acknowledgements

This research was financially supported by National Natural Science Foundation of China (Nos. 42307192, 52308408). Supported by the CRSRI Open Research Program (Program SN: CKWV20231175/KY). We would also like to acknowledge the editor and reviewers for their valuable comments, which have greatly improved this paper.

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Authors and Affiliations

  1. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, 210098, China

    Shu Zhu, Jianfu Shao, Zhende Zhu & Junyu Wu

  2. Department of Civil Engineering, College of Environmental Science and Engineering, Donghua University, Shanghai, 201620, China

    Feiyang Wang

  3. LaMcube UMR9013 CNRS, University of Lille, 59000, Lille, France

    Jianfu Shao

  4. College of Civil and Architecture Engineering, Chuzhou University, Chuzhou, 239000, Anhui, China

    Hexuan Zhu

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Contributions

Shu Zhu was involved in conceptualization, methodology, validation, resources, writing—reviewing and editing, and funding acquisition. Hexuan Zhu and Feiyang Wang was responsible for software, validation, investigation, formal analysis, data curation, writing—original draft and visualization. Jianfu Shao and Zhende Zhu contributed to validation and writing—reviewing and editing. Junyu Wu participated in writing—reviewing and editing, and supervision.

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Correspondence to Shu Zhu.

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Zhu, S., Shao, J., Zhu, H. et al. Grouting mechanism of quick-setting slurry in fracture with random fracture opening considering time–space characteristics of viscosity. Acta Geotech. 19, 6517–6534 (2024). https://doi.org/10.1007/s11440-024-02378-w

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