Numerical modelling of fluid flow tests in a rock fracture with a special algorithm for contact areas
Introduction
Coupled stress-flow processes in rock fractures are increasingly important research topics for the development and utilizations of deep underground spaces such as radioactive waste repositories, geothermal energy extractions and petroleum reservoirs. The performance of these facilities depends on the knowledge of permeability of rock masses, which varies with in situ and disturbed stress conditions and the hydro-mechanical behaviors of rock fractures. Especially for high-level radioactive waste disposal facilities in crystalline rocks, their safety assessments are mainly based on the knowledge of paths and travel times of radioactive nuclide transport that is dominated by groundwater flow in rock fractures.
As far as laboratory tests for rough rock fractures are concerned, laboratory studies focusing on the effect of both normal and shear stresses on fluid flow through rock fractures, so-called coupled shear-flow tests, have been a particular attraction due to its importance to understand and quantify the coupled stress-flow processes in fractured rocks [1], [2], [3], [4], [5], [6], [7]. In laboratory direct shear tests, the constant normal loading/stress (CNL) condition corresponds to the cases such as non-reinforced rock slopes. For deep underground opening or rock anchor-reinforced slopes, more representative in situ condition of rock fractures would be the one under constant normal stiffness (CNS) condition [8], [9]. Many of the coupled shear-flow tests have been performed under CNL condition and some new tests under CNS condition have been reported recently [2], [6], [7].
Many efforts have also been made to test fluid flow and tracer transport processes in rock fractures, with or without flow visualization and normal stress [10], [11], [12], [13]. It was found that fluid flows in rock fractures through connected and tortuous channels that bypass the contacts areas. However, the effects of contacts and the channel distribution patterns on the fluid flow and tracer transport processes in a rock fracture and their change due to both normal and shear displacements/stresses have not been fully understood. This is mainly due to the difficulties of quantitative measurements of changing fracture surface roughness and aperture during laboratory coupled stress-flow tests, especially the contact areas, as well as a number of technical difficulties exist in laboratory shear-flow testing, most notably the sealing of fluid during shear.
Flow simulations in rough fractures are often performed considering effects of only normal stress [14], [15] or small shear displacements without normal stress or with only very small normal stresses [16], [17], [18], [19], under well controlled hydraulic gradients. The Reynolds equation is commonly applied to simulate such tests instead of the Navier–Stokes equation. How to measure or calculate the fracture aperture under different normal stresses and shear displacements during the coupled stress-flow tests and numerical simulations are the most essential points to understand the process, interpret the testing and simulation results and quantify the hydraulic properties. The important phenomenon of shear induced anisotropy and heterogeneity of aperture distribution and its effects on fluid flow in fractures, such as the more significant flow in the direction perpendicular to the shear, was reported in [16], [17], [18], [19]. These findings represent an important step for more physically meaningful understanding of the coupled shear-flow processes in rock fractures. However in these works, due to numerical difficulties, very small aperture values were assigned to contact areas to avoid solving ill-formed matrix equations [17], [20], [21]. Therefore, there still exist some flow inside the contact areas, even they are small in magnitudes. Such treatment of contact areas as non-zero aperture elements is not only physically nonrealistic, but may have more significant effects on the particle transport simulations since such fluid-conducting contact areas will change the particle transport paths, which may affect the estimations of travel time, dispersivity and tortuosity. The work presented in [14] is the only case to treat contact areas correctly but they did not consider the effects of shear displacement.
In the present study, laboratory tests of fluid flow in three fracture replicas under different normal stresses and stiffness conditions were simulated by using numerical simulations with FEM, considering simulated evolutions of aperture and transmissivity with large shear displacements. The distributions of fracture aperture and its evolution during shearing and the flow rate were calculated from the initial aperture and shear dilations and compared with results measured in the laboratory coupled shear-flow tests. The contact areas in the fractures were treated correctly with zero-aperture values with a special algorism so that more realistic flow velocity fields and potential particle paths were captured, which is important for continued works on more realistic simulations of particle transport to be reported separately later.
Section snippets
Sample preparations
A natural rock fracture surface, labeled J3, were taken from the construction site of Omaru power plant in Miyazaki prefecture in Japan and used as the parent fracture surface in this study as shown in Fig. 1. This natural fracture surface is quite rough (JRC = 16–18) without major structural non-stationarities. Three replicas of fracture specimens were manufactured with the J3 as the parent fracture surface. The specimens are 100 mm in width, 200 mm in length and 100 mm in height, respectively.
Governing equations
When flow velocity is low and the fracture surface geometry does not vary too abruptly the Reynolds equation can be used, instead of the full Navier–Stokes equations, to describe the flow in fractures [16], [22]. Assuming that the flow of an incompressible fluid through the fracture follows the cubic law, in a steady state, the governing equation can be written aswhere Q is the source/sink term (positive when fluid is flowing into the fracture), and Txx and Tyy are the
Aperture, transmissivity and contact area evolutions during shear
Fig. 4. show the evolution of transmissivity fields of sample J3 under different normal loading conditions: J3-1, J3-2 and J3-3. In the figure, the white ‘islands’ indicate the contact areas. The grey intensity of the background in the flow areas indicates the magnitude of local transmissivities (see the legend in the figures). The simulation results show that shear induced new contact areas decrease slowly with increasing shear displacement (from full contact as the initial condition), reach a
Discussions and concluding remarks
In the present study, the fluid flow in rock fracture replicas during shear under normal stress and normal stiffness controls was simulated using the COMSOL Multiphysics code of FEM with a special algorism for contact areas, considering evolutions of aperture and transmissivity fields during shear, obtained from real coupled shear-flow tests of fracture specimens of realistic surface roughness features. The numerical models captured complex behavior of fluid flow in fracture samples with
Acknowledgements
The authors thank the Swedish Nuclear Power Inspectorate (SKI) for the financial support for the first author’s Ph.D. studies at Royal Institute of Technology (KTH), Stockholm, Sweden.
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2022, Computers and GeotechnicsCitation Excerpt :High-resolution models of single fractures were established that simulate fluid flow solving Reynolds or Navier-Stokes (NS) equations based on experimentally measured or artificially generated fracture surfaces/void spaces (Koyama et al., 2006; Javadi et al., 2010; Vilarrasa et al., 2011; Wang et al., 2016; Kang et al., 2016; Kong and Chen, 2018; Marchand et al., 2019). These models enable in-depth investigations on flow behavior in complex void spaces such as channelization and formation of eddies, which is over-simplified by parallel plate models (Koyama et al., 2009). Upon these models, coupled hydro-mechanical processes such as the permeability alteration induced by shear were extensively studied (Rojstaczer and Wolf, 1992; Brodsky et al., 2003; Elkhoury et al., 2006; Fang et al., 2017).