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An Innovative Method to Evaluate Hydraulic Conductivity of a Single Rock Fracture Based on Geometric Characteristics

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Abstract

Geometry of a single fracture has significant influence on the fluid flow in fractured rocks. However, quantification of geometry–flow relationship in a rock fracture is still far from being completed. The primary goal of this study was to identify a few key geometric parameters for quantifying its impact on fluid flow in a single rock fracture and then to evaluate its hydraulic conductivity. The concept of a threshold aperture is first introduced to estimate the effective area involved in the flow process in a single rock fracture. It is assumed that only those zones with greater apertures than a threshold value are involved in the flow process. The effect of variable aperture distributions on flow in a single rock fracture is quantified based on the cumulative distribution of individual apertures of sampling points. The surface roughness is decomposed into primary roughness (i.e. the large-scale waviness of the fracture morphology) and secondary roughness (i.e. the small-scale unevenness) with a wavelet analysis. The influence of surface roughness on the fluid flow in a single rock fracture is quantified with the normalized area of primary roughness and the standard deviation of secondary roughness. By combining the variable aperture distributions and the surface roughness on flow, an empirical equation to estimate the intrinsic hydraulic aperture and hydraulic conductivity of a single rock fracture is proposed. In addition, a series of high-precision hydraulic tests are conducted on 60 artificial tensile fractures to verify the proposed equation. The results show that the proposed equation predicts the intrinsic hydraulic aperture and hydraulic conductivity of a single rock fracture very well.

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Abbreviations

∆:

Absolute height of surface asperity (mm)

α :

Contact ratio

τ :

Tortuosity

σ e :

Standard deviation of aperture distribution (mm)

e*:

Threshold aperture (mm)

A*:

Normalized area

A t :

Horizontal projection area of fracture surface (mm2)

e 0 :

Mean mechanical aperture (mm)

e m :

Maximum aperture value (mm)

C :

Dimensionless fitting parameter

A i :

The approximation coefficients at decomposition level i (i = 1–8)

D i :

The detail coefficients at decomposition level i (i = 1–8)

A 0 :

Horizontal projection area of primary waviness surface (mm2)

A :

Average area of the upper and lower primary waviness surfaces (mm2)

σ II :

Standard deviation of secondary roughness (mm)

Q :

Volumetric flow rate (mL/min)

w :

Width of the fracture (mm)

µ :

Dynamic viscosity coefficient (Pa·s)

P :

Pressure (Pa)

\(e_{\text{h}}\) :

Hydraulic aperture (mm)

a :

Dimensionless regression coefficient

b :

Dimensionless regression coefficient

Re:

Reynolds number

\(e_{{{\text{h}}0}}\) :

Intrinsic hydraulic aperture (mm)

JRC:

Joint roughness coefficient

Z 2 :

Root mean square of the slope of fracture profile

n :

The number of data points along the length of each profile

z i :

Asperity height at point i (mm)

∆y :

Interval of data points (mm)

\(e_{\text{h0}}^{{{\text{mea}},j}}\) :

Measured intrinsic hydraulic aperture (mm)

\(e_{\text{h0}}^{{{\text{cal}},j}}\) :

Calculated intrinsic hydraulic aperture (mm)

j :

The jth fracture sample

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant nos. 41772305 and 51579189) and the China Scholarship Council (CSC) (Grant number 201906270116). These supports are gratefully acknowledged. The authors thank the Editor and two anonymous reviewers for their constructive comments which help us greatly improve the quality of the manuscript.

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Authors and Affiliations

  1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, 430072, China

    Jie Tan, Guan Rong, Renhui He, Song Sha & Bowen Li

  2. Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering, Ministry of Education, Wuhan University, Wuhan, 430072, China

    Jie Tan, Guan Rong, Renhui He, Song Sha & Bowen Li

  3. Department of Geology and Geophysics, Texas A&M University, College Station, TX, 77843-3115, USA

    Hongbin Zhan

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  1. Jie Tan
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Tan, J., Rong, G., Zhan, H. et al. An Innovative Method to Evaluate Hydraulic Conductivity of a Single Rock Fracture Based on Geometric Characteristics. Rock Mech Rock Eng 53, 4767–4786 (2020). https://doi.org/10.1007/s00603-020-02196-y

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