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Experimental Study of the Nonlinear Flow Characteristics of Fluid in 3D Rough-Walled Fractures During Shear Process

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Abstract

To understand the influence of shear on the hydraulic properties of rock fractures, shear-flow tests were carried out on rock fractures with different surface roughnesses. Each rough-walled fracture was replicated in four specimens, which were sheared at different displacements under normal stresses that varied from 0.5 to 2.0 MPa. At each shear displacement, a series of hydraulic tests with different hydraulic gradients were performed, and the nonlinear flow regimes of the fluid within the fractures were investigated. The results show that Forchheimer’s law can well describe the nonlinear relationship between the flow rate and the hydraulic gradient in rough-walled fractures. Both the linear coefficient and nonlinear coefficient decrease during shearing but increase as the normal stress increases. The critical hydraulic gradient increases with an increase in the shear displacement and normal stress. With an increase in the joint roughness coefficient, the critical hydraulic gradient decreases. The normalized transmissivity exhibits a strong correlation with the Reynolds number. As the shear displacement increases, the fitted curves of the normalized transmissivity versus the Reynolds number shift upward but the curves shift downward with an increase in normal stress. Additionally, the Forchheimer coefficient decreases with an increase in the shear displacement but increases with an increase in the applied normal stress. Visualization tests show that the number of flow paths is large when the shear displacement is small due to various distributions of the contact areas and that the flow of dyed water over the entire fracture decreases. As the shear displacement increases, the flow resistance decreases due to the shear dilation-induced increase in the aperture, and the advantage channel flow is distinct in the fracture. The contact ratio rapidly decreases as the shear displacement increases from 1 to 3 mm and then slightly varies with a continuously increasing maximum shear displacement of 9 mm.

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Abbreviations

A:

Cross-sectional area of a fracture

a :

Linear coefficient in the Forchheimer’s law

b :

Nonlinear coefficient in the Forchheimer’s law

b h :

Hydraulic aperture

d :

Shear displacement

d contra :

Minimum normal displacement

d dilation :

Dilation of the fracture

d normal :

Ultimate normal displacement

d peak :

Peak shear displacement

E :

Nonlinear effect factor

J :

Hydraulic gradient

J c :

Critical hydraulic gradient

JRC:

Joint roughness coefficient

k :

Fracture permeability

K s :

Shear stiffness

L :

Fracture length

P :

Hydraulic pressure

Q :

Volumetric flow rate

Re:

Reynolds number

Rec :

Critical Reynolds number

T :

Transmissivity

T/T0 :

Normalized transmissivity

\(w\) :

Width of a fracture

z i :

Coordinates of the fracture surface profile

\({\text{Z}}_{{2}}\) :

Dimensionless roughness parameter

\({\rho }\) :

Fluid density

\(\mu\) :

Dynamic viscosity

σ n :

Normal stress

τ p eak :

Peak shear strength

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Acknowledgements

This study has been partially funded by National Natural Science Foundation of China (Grant Nos. 51979272 and 51709260), Natural Science Foundation of Jiangsu Province, China (Grant No. BK20170276), JSPS-NSFC Bilateral Joint Research Project (Grant No. 51611140122) and China Scholarship Council (CSC NO. 201608370099). These supports are gratefully acknowledged.

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Authors and Affiliations

  1. State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province, Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao, People’s Republic of China

    Changsheng Wang & Yujing Jiang

  2. School of Engineering, Nagasaki University, Nagasaki, 852-8521, Japan

    Changsheng Wang, Yujing Jiang, Richeng Liu, Chen Wang & Satoshi Sugimoto

  3. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221116, People’s Republic of China

    Richeng Liu

  4. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400044, People’s Republic of China

    Zhenyu Zhang

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  1. Changsheng Wang
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Correspondence to Yujing Jiang.

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Appendix A

Appendix A

See Fig. 17.

Fig. 17
figure 17figure 17

Relationships between hydraulic gradient (J) and volumetric flow rate (Q) for G2–G4 under different normal stresses

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Wang, C., Jiang, Y., Liu, R. et al. Experimental Study of the Nonlinear Flow Characteristics of Fluid in 3D Rough-Walled Fractures During Shear Process. Rock Mech Rock Eng 53, 2581–2604 (2020). https://doi.org/10.1007/s00603-020-02068-5

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