Numerical investigation on a grouting mechanism with slurry-rock coupling and shear displacement in a single rough fracture

  • Wenqiang Mu
  • Lianchong LiEmail author
  • Tianhong Yang
  • Guofeng Yu
  • Yunchun Han
Original Paper


A slurry diffusion model of a single random-roughness fissure is established to consider the slurry and geological fracture coupling based on the Navier-Stokes equation. The slurry flow characteristics and coupling response in a rough fracture are investigated. The influencing mechanism of roughness on the slurry flow was revealed. The calculation model of effective aperture is determined in a rough fracture. The shear displacement effects on the slurry flow are studied. The results show that this slurry diffusion model can more accurately reflect the grouting. A rougher fracture has a great effect on the flow because of the larger low-speed domains. The pressure gradient and maximum diffusion velocity increase parabolically with changes in the relative roughness. The conventional flat-panel model can cause an increasing deviation rate for determination of grouting parameters. The coupling degree distribution is temporal with spatial variations, and increases with the time-dependent viscosity, roughness (decreasing effective aperture), and a shortening path. The viscosity is the key controlling factor in grouting pressure. The roughness response after shear displacement is more significant, further revealing that on-site grout splitting often occurs at the narrow undulating tip with high viscosity and shear on a rough flow surface. The rough fracture model considering fluid-solid coupling is more consistent with the grouting phenomenon in engineering. And the roughness and shear are the key geological factors of grout splitting.


Grouting flow Rough fracture Coupling response Shear displacement Damage and splitting 


List of symbols


Grouting intensity number.


Coordinate of unit point i.


Elevation in coordinate system.

bj, i

Aperture of number i in fracture j.


Number of segmented units.

\( {\overline{b}}_j \)

Average aperture of fracture j.


Consistency coefficient.


Flow behavior index.


Young’s modulus.


Grouting pressure.


Grouting length.


Degree of freedom.


Rock deformation velocity.


Slurry velocity.


Unit normal vector.


Fracture aperture.


Slurry flow rate.


No shear deformation.


Shear deformation.




Pressure gradient.


Error rate.


Cement-sodium silicate.


Stress intensity factor.


Flexibility of fracture.

Greek symbols


Absolute roughness of fracture j.


Relative roughness of fracture j.


Shear stress.


Critical shear stress.


Slurry viscosity.


Initial viscosity.


Poisson’s ratio.


Rock density.


Slurry density.

\( \overset{\cdot }{\gamma } \)

Rate of shear strain.


Rock strain.


Slurry strain.


Rock stress.


Slurry stress.


Normalized pressure gradient.


Normalized aperture increment.


Normalized flow velocity.


Stress of tip i.



This work was conducted with support from the National Key R&D Program of China (grant no. 2017YFC1503100), National Natural Science Foundation of China (grant no. 51879041, U1710253), the Fundamental Research Funds for the Central Universities (grant no. N180105029), and Anhui Province Science and Technology Project of China (grant no. 17030901023).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Wenqiang Mu
    • 1
    • 2
  • Lianchong Li
    • 1
    • 2
    Email author
  • Tianhong Yang
    • 1
    • 2
  • Guofeng Yu
    • 3
    • 4
  • Yunchun Han
    • 4
  1. 1.Key Laboratory of Ministry Education on Safe Mining of Deep Metal MinesNortheastern UniversityShenyangChina
  2. 2.Center of Rock Instability and Seismicity Research, School of Resources and Civil EngineeringNortheastern UniversityShenyangChina
  3. 3.State Key Laboratory of Deep Coal Mining & Environment ProtectionHuainanChina
  4. 4.Ping An Coal Mining Engineering Technology Research Institute Co., Ltd.HuainanChina

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