This paper presents a stress-induced variable aperture model to characterise the effect of polyaxial stress conditions on the permeability of a three-dimensional (3D) fractured sedimentary layer. The 3D fracture network is created by extruding a 2D outcrop pattern of a limestone bed that exhibits a ladder structure consisting of a “through-going” joint set abutted by later short fractures. Geomechanical modelling of the fractured rock is achieved by the 3D finite-discrete element method (FEMDEM), which can capture the deformation of matrix blocks, the variation of stress fields, the reactivation of pre-existing fractures and the propagation of new cracks. A joint constitutive model (JCM) is implemented to simulate the rough wall interaction behaviour of individual fractures associated with roughness characteristics. The combined JCM-FEMDEM model gives realistic fracture behaviour with respect to opening, closing, shearing and dilatancy, and includes the recognition of the important size effect. A series of 3D geomechanical simulations is conducted for the fractured rock under various polyaxial in-situ stresses. Fluid flow is further modelled for the stressed but static solid skeletons based on the hybrid finite element-finite volume method (FEFVM). The magnitude of the equivalent permeability varies significantly with respect to the change of stress ratio.


Natural fractures are ubiquitous in crustal rocks in the form of faults, bedding planes, joints and veins over different length scales (Lei and Wang, 2016). These naturally occurring discontinuities often comprise complex networks and dominate the geomechanical and hydromechanical behaviour of subsurface media (Rutqvist and Stephansson, 2003). The understanding of the nontrivial effects of fractures on the overall behaviour of such highly disordered geological media has important implications for many engineering applications including geothermal energy, nuclear repository safety and petroleum recovery.

Discrete fracture networks (DFNs) are often used to mimic naturally faulted or jointed geological structures (Dershowitz and Einstein, 1988). Compared to the conventional dual porosity model (Warren and Root, 1963) and analytical solution for mathematically idealised discontinuity networks (Oda, 1985), the discrete fracture approach possesses the advantage of explicit representation of fracture geometries together with specific description of hydraulic transmissivity (Herbert, 1996). Flow properties, such as the block or equivalent permeability tensor, of a finite-sized fracture system can be studied from steady state fluid flow modelling (Lang et al., 2014; Renard and de Marsily, 1997).

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