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ORIGINAL PAPER

Permeability Evolution of Two‑Dimensional Fracture Networks During Shear Under Constant Normal Stiffness Boundary Conditions Bo Li1 · Ruyi Bao1 · Ye Wang1 · Richeng Liu2   · Cheng Zhao3 Received: 10 February 2020 / Accepted: 6 October 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020

Abstract The permeability evolution of fractal-based two-dimensional discrete fracture networks (DFNs) during shearing under constant normal stiffness (CNS) boundary conditions is numerically modeled and analyzed based on a fully coupled hydromechanical (HM) model. The effects of fractal dimension, boundary normal stiffness and hydraulic pressure on the evolutions of mechanical behaviors, aperture distributions and permeability are quantitatively investigated. The results show that with increasing confining pressure from 0 to 30 MPa, the permeability decreases from the magnitude of 1­ 0−13 ­m2 to 1­ 0−16 ­m2, which is generally consistent with previous models reported in the literature. With the increment of shear displacement from 0 to 500 mm, the variations in shear stress, normal stress and normal displacement exhibit the same patterns with the conceptual model. As shear advances, the permeability evolution exhibits a three-stage behavior. In the first stage, the permeability decreases due to the compaction of fractures induced by the increasing shear stress from 0 to the peak value. In the second stage, the permeability holds almost constant values under constant normal load (CNL) boundary conditions, whereas that under CNS boundary conditions decreases by approximately one order of magnitude. Under CNS boundary conditions, although the aperture of shearing fracture increases enhancing its own permeability, the apertures of surrounding fractures are compacted due to the simultaneous increases in the normal and shear stresses, which result in the decrease in the total permeability of DFNs. When the fractal dimension increases from 1.4 to 1.5, the permeability increases following exponential functions in the early stage of shear, which fail to characterize the permeability in the residual stage due to the complex flow path distributions. At the start of shear, the ratio of permeability perpendicular to the shear direction to that parallel to shear decreases approximately from 1.0 to 0.5 and then gradually decreases from 0.5 to 0.3 in the residual stage. The hydraulic pressure tends to open up the fractures and enhances the permeability. The magnitude in permeability enhancement is of approximately the same order with the increase in the hydraulic pressure. Keywords  Fracture network · Shear · Flow · Permeability · Constant normal stiffness

1 Introduction

* Richeng Liu [email protected] 1



Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province, Shaoxing University, Shaoxing 312000, People’s Republic of China

2



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

3

Depar