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Physical Modelling of Stress-dependent Permeability in Fractured Rocks

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Abstract

This paper presents the results of laboratory experiments conducted to study the impact of stress on fracture deformation and permeability of fractured rocks. The physical models (laboratory specimens) consisted of steel cubes simulating a rock mass containing three sets of orthogonal fractures. The laboratory specimens were subjected to two or three cycles of hydrostatic loading/unloading followed by the measurement of displacement and permeability. The results show a considerable difference in both deformation and permeability trends between the first loading and the subsequent loading/unloading cycles. However, the micrographs of the contact surfaces taken before and after the tests show that the standard deviation of asperity heights of measured surfaces are affected very little by the loadings. This implies that both deformation and permeability are rather controlled by the highest surface asperities which cannot be picked up by the conventional roughness characterization technique. We found that the dependence of flow rate on mechanical aperture follows a power law with the exponent n smaller or larger than three depending upon the loading stage. Initially, when the maximum height of the asperities is high, the exponent is slightly smaller than 3. The first loading, however, flattens these asperities. After that, the third loading and unloading yielded the exponent of around 4. Due to the roughness of contact surfaces, the flow route is no longer straight but tortuous resulting in flow length increase.

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Abbreviations

Q :

Flow rate

Q res :

The residual flow rate

h :

Hydraulic head

Δh :

Hydraulic head difference

C :

Constant and \( C = \frac{W}{L}\frac{\rho g}{12\mu } \)

W :

Plate width

L :

Plate length

ρ :

Fluid density

g :

Gravity

μ :

Dynamic viscosity of fluid

b :

Fracture aperture

b h :

Hydraulic aperture

b 0 :

Maximum aperture at zero normal stress

b m :

Mechanical aperture

f :

Roughness modification coefficient

α :

Contact area ratio

δ :

Normal displacement

δ max :

Maximum fracture displacement

N c :

Total number of asperities in contact as a function of fracture closure

b a :

Apparent aperture

n :

Exponent

P :

Applied pressure

k :

Permeability

k 0 :

Initial permeability

γ w :

Specific gravity of water

P c :

Confining pressure

s :

Constant

ΔV j :

Joint closure

V m :

Maximum closure

σ i :

Initial normal stress

σ n :

Normal stress

\( \sigma_{\text{n}}^{\prime } \) :

Effective normal stress

K n0 :

Initial normal stiffness when normal stress is zero

K n :

Normal stiffness which changes with normal stress

m :

Constant

b j :

Average aperture thickness

JRC:

Joint roughness coefficient

JCS:

Joint compression strength

A, B, E, D :

Constants

a, d, c :

Constants

b true :

True aperture of a fracture

b a :

Apparent aperture

b res :

Residual aperture

R 2 :

Coefficient of determination

renorm:

Value of the squared 2-norm of the residual at certain solution

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Acknowledgments

The study is funded by the CSIRO Earth Science & Resource Engineering of Australia grants 2009, 2010. Support from the Western Australian Geothermal Centre of Excellence, China Scholarship Council and China National 973 Program (grant No. 2011CB013504) is acknowledged.

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Authors and Affiliations

  1. Research Institute of Geotechnical Engineering, Hohai University, 1 Xikang Road, Nanjing, 210098, China

    Lifang Zou & Weiya Xu

  2. School of Civil and Resource Engineering, University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia

    Lifang Zou, Boris G. Tarasov & Arcady V. Dyskin

  3. CSIRO Earth Science and Resource Engineering, 1 Technology Court, Pullenvale, QLD, 4069, Australia

    Deepak P. Adhikary

  4. School of Mechanical and Chemical Engineering, University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia

    Elena Pasternak

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  1. Lifang Zou
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  2. Boris G. Tarasov
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Correspondence to Lifang Zou.

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Zou, L., Tarasov, B.G., Dyskin, A.V. et al. Physical Modelling of Stress-dependent Permeability in Fractured Rocks. Rock Mech Rock Eng 46, 67–81 (2013). https://doi.org/10.1007/s00603-012-0254-x

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