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A Hydromechanical Model for a Single Rock Fracture Subjected to Shearing

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Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

Accurately predicting the hydromechanical behaviour of rock fractures is challenging due to the significant influence of shear-induced fracture geometries. This work proposes an improved shear-flow model that accurately estimates nonlinear fluid flow behaviour as well as shear mechanical behaviour. To predict shear mechanical behaviour, the model employs a modified multi-scale roughness shear constitutive model that accounts for water moisture effects. In addition, the evolution of the fracture void structure subjected to shearing is computed by a fracture void space model. A Forchheimer equation-based model incorporating fracture surface roughness and fluid flow tortuosity is introduced to model fluid flow nonlinearity. Laboratory shear-flow tests are conducted under constant normal stresses of 1, 1.5, and 2 MPa, utilising a newly developed shear-flow testing apparatus. The predicted shear mechanical and hydraulic behaviours of the fracture agree well with the experimental results, with \({\tilde{\sigma }}_{ave}\) of 11.6% for shear strength, NOF of 0.25 for shear dilation, and NOF of 0.14 for fluid flow rate. The proposed model improves the understanding and prediction accuracy of hydromechanical behaviours of fractures in engineering and geological applications.

Highlights

  • A multi-scale shear model using adhesion and abrasion theories is introduced.

  • The effect of water moisture on shear behaviours is considered.

  • The surface roughness and flow tortuosity are considered in the flow model.

  • The evolution of fracture geometry is computed by the fracture void space model.

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Data availability

The datasets used and analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

2D,3D:

Two-dimensional, three-dimensional

3DEC:

Three-dimensional distinct element code

A, B :

The linear and nonlinear coefficients of the Forchheimer equation

\({a}_{D}\), \({b}_{D}\) :

Dimensionless linear and nonlinear coefficients of the Forchheimer equation

\({a}_{o}\) :

Laboratory-scale unevenness asperity inclination angle

BB model:

Barton–Bandis shear constitutive model

CCD:

Charge-coupled device

CNL:

Under constant normal loading conditions

\({d}_{n}\), \({d}_{s}\) :

Normal displacements due to the normal and shear effects

\({e}_{o}\) :

Initial mechanical aperture

\({e}_{h}\) :

Hydraulic aperture

\({e}_{m}\) :

Mechanical aperture

\(\langle {e}_{m}\rangle\) :

Mean value of fracture aperture

\({e}_{m({x}_{i},{y}_{j})}\) :

Local mechanical aperture at (\({x}_{i}\), \({y}_{j}\))

i :

Laboratory-scale waviness asperity inclination angle

JRC:

Joint roughness coefficient

JRCmob:

Mobilised JRC

\({K}_{ad}\) :

A dimensionless wear coefficient

\({K}_{s}\) :

Shear stiffness

\({k}_{1}\) :

Geometry factor

K :

Softening coefficient for a given shear test

L :

Fracture length

M :

Damage coefficient

NOF:

Normalized Objective Function

\({N}_{x},\) \({N}_{y}\) :

The number of points along the x and y directions

∇P:

Hydraulic pressure gradient

Q :

Flow rate

RMSE:

Root mean square error

\({R}_{s}\) :

Surface roughness coefficient

Re:

The Reynolds number

\({T}_{s}\) :

Joint interface roughness

UCS :

Uniaxial compressive strengths

\({u}_{peak}\) :

Peak shear displacement

\({u}_{s}\) :

Shear displacement

\({u}_{s}^{e}\) :

The shear displacement for the onset of the total dilation

w :

Fracture width

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

The root-mean-square of the 2D surface profile

\(\gamma\) :

The slope of linear regression between the

\(\Delta {u}_{s}\) :

Incremental shear displacement

\(\Delta {d}_{s}\) :

The corresponding incremental normal displacement

\(\vartheta\) :

Fluid tortuosity

\({\theta }^{*}\) :

Surface roughness parameter based on local apparent dip angle of asperities

\({\lambda }_{p},{\lambda }_{s}\) :

Laboratory-scale waviness and unevenness asperity wavelengths

\(\mu\) :

Dynamic viscosity of fluid

\({\mu }_{{p}_{mob}}\) :

Mobilised shear-off component

\({\mu }_{pp},{\mu }_{ps}\) :

Shear-off components corresponding to laboratory-scale waviness and unevenness

\(\xi\) :

Peak asperity height

\(\xi /{e}_{h}\) :

Relative roughness

\({\xi }_{{x}_{i},{y}_{j}}\), \({\xi }_{{x}_{i+1},{y}_{j}},{\xi }_{{x}_{i},{y}_{j+1}}\) :

Asperity height at point (\({x}_{i},{y}_{j}\)), (\({x}_{i+1},{y}_{j}\)) and (\({x}_{i},{y}_{j+1}\))

\(\rho\) :

Fluid density

\({\sigma }_{n}\) :

Normal stress (MPa)

\({\sigma }_{T}\) :

Transitional normal stress

\({\sigma }_{ape}\) :

Standard deviations of mechanical aperture

\({\tilde{\sigma }}_{ave}\) :

Average error

\(\tau\) :

Shear stress (MPa)

\(\tau \left(k\right)\), \(\tau (k-1):\) :

Shear stress at the current and previous time-step

\({\chi }_{measure}\), \({\chi }_{predict}:\) :

Experimental and predicted values

\({\overline{\chi }}_{measure}\) :

The mean value of the experimental data

\({\psi }_{mob}\) :

Mobilised dilation angle

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Authors and Affiliations

  1. School of Minerals and Energy Resources Engineering, University of New South Wales, Sydney, NSW, 2052, Australia

    Min Gao, Xu Zhu, Chengguo Zhang & Joung Oh

Authors
  1. Min Gao
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  2. Xu Zhu
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  3. Chengguo Zhang
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  4. Joung Oh
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Corresponding author

Correspondence to Chengguo Zhang.

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Gao, M., Zhu, X., Zhang, C. et al. A Hydromechanical Model for a Single Rock Fracture Subjected to Shearing. Rock Mech Rock Eng (2024). https://doi.org/10.1007/s00603-023-03588-6

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  • DOI: https://doi.org/10.1007/s00603-023-03588-6

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