The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

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VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

▪ Abstract In this paper, an overview is presented of coupled processes linking thermo-hydro-mechanical (THM) effects in fractured rocks. A formulation is first presented to show the linkage mathematically, which can be used as a basis for numerical solutions and for further developments. Two simple examples of hydromechanical (HM) and thermo-hydro-mechanical (THM) coupled processes are discussed to convey physical insight into such couplings. Finally, three large-scale, long-term experiments currently under way are described. These are being conducted specifically to study coupled processes in situ.

/pdf/linking-thermal-hydrological-and-mechanical-processes-in-5e7fwuy6jc.pdf

Linking Thermal, Hydrological and Mechanical Processes in Fractured Rocks

Accepted for publication by Water Resources Research OBSERVATIONS OF A POTENTIAL SIZE-EFFECT IN EXPERIMENTAL DETERMINATION OF THE HYDRAULIC PROPERTIES OF FRACTURES P. A. Witherspoon, C. H. Amick, C. E. G a l e , and K. I w a i Department of Materials Science and Mineral Engineering and Lawrence Berkeley Laboratory University of California Berkeley, California May 1979 NOTICE Ttili report wit prepared u an account of work iponiored by the United Stitei Government. Neither ihe United Slatei not the United State* Department of Energy, nor my of thetr employee!, nor any of their contractors, lUbcontncton, of their employee*, mite* •ny wirnnty, eKprcu 01 Implied, 01 uiumei any tegal tUbllliy of tetponiibillty Tor the accuracy, completeneu or UMiUlnett or iny Information, ipparatut, product or i proctH dUclcwed, or itpietenU that t u ox would not I infitajw privately owntd rlfhtt. Now with Liftech Consultants, I n c . , Oakland, C a l i f o r n i a . Now at the Department of Earth Sciences, University of Waterloo, Waterloo, Ontario, Canada. Now with Nakano-Corporation, Niigatashi, Japan. !Tio7RlBimOH OF THIS DOCUMENT lis VMAM££bXl\

/pdf/observations-of-a-potential-size-effect-in-experimental-2l9ahx5ls3.pdf

OBSERVATIONS OF A POTENTIAL SIZE-EFFECT IN EXPERIMENTAL DETERMINATION OF THE HYDRAULIC PROPERTIES OF FRACTURES - eScholarship

Numerical simulations of the effect of bolt inclination on the shear strength of rock joints

Constitutive models for rock joints are reviewed in this contribution. Emphasis is given to the different approaches for theoretical and empirical formulations of constitutive models, their validation against experimental results, new developments for roughness representations, dilation laws and coupled hydro-mechanical behaviour of rock joints.

Y. Ohnishi

Papers

Constitutive models for rock joints