An Innovative Method to Evaluate Hydraulic Conductivity of a Single Rock Fracture Based on Geometric Characteristics
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ORIGINAL PAPER
An Innovative Method to Evaluate Hydraulic Conductivity of a Single Rock Fracture Based on Geometric Characteristics Jie Tan1,2 · Guan Rong1,2 · Hongbin Zhan3 · Renhui He1,2 · Song Sha1,2 · Bowen Li1,2 Received: 30 October 2019 / Accepted: 7 July 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
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. Keywords Rock fracture · Quantitative description · Hydraulic aperture · Fracture geometry List of Symbols ∆ Absolute height of surface asperity (mm) α Contact ratio τ Tortuosity σe Standard deviation of aperture distribution (mm) e* Threshold aperture (mm) A* Normalized area
* Guan Rong [email protected] * Hongbin Zhan [email protected] 1
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
2
Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering, Ministry of Education, Wuhan University, Wuhan 430072, China
3
Department of Geology and Geophysics, Texas A&M University, College Station, TX 77843‑3115, USA
At Horizontal projection area of fracture surface (mm2) e0 Mean mechanical aperture (mm) em Maximum aperture value (mm) C Dimensionless fitting parameter Ai The approximation coefficients at decomposition level i (i = 1–8) Di The detail coefficients at decomposition level i (i = 1–8) A0
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