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

About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test

The initiation and propagation of failure in intact rock are a matter of fundamental importance in rock engineering. At low confining pressures, tensile fracturing initiates in samples at 40%–60% of the uniaxial compressive strength and as loading continues, and these tensile fractures increase in density, ultimately coalescing and leading to strain localization and macro-scale shear failure of the samples. The Griffith theory of brittle failure provides a simplified model and a useful basis for discussion of this process. The Hoek–Brown failure criterion provides an acceptable estimate of the peak strength for shear failure but a cutoff has been added for tensile conditions. However, neither of these criteria adequately explains the progressive coalition of tensile cracks and the final shearing of the specimens at higher confining stresses. Grain-based numerical models, in which the grain size distributions as well as the physical properties of the component grains of the rock are incorporated, have proved to be very useful in studying these more complex fracture processes.

Fracture initiation and propagation in intact rock – A review

Review: Calibration of the discrete element method

Numerical simulation of drained triaxial test using 3D discrete element modeling

https://yade-dem.org/w/images/3/30/CMAME_YADE_2008.pdf

A new open-source software developed for numerical simulations using discrete modeling methods

Modeling fractures in rock blasting

The Discrete Element Method (DEM) is increasingly used to simulate the behavior of rock. Despite their intrinsic capability to model fracture initiation and propagation starting from simple interaction laws, classical DEM formulations using spherical discrete elements suffer from an intrinsic limitation to properly simulate brittle rock behavior characterized by high values of UCS/TS ratio associated with non-linear failure envelopes, as observed for hard rock like granite. The present paper shows that the increase of the interaction range between the spherical discrete elements, which increases locally the density of interaction forces (or interparticle bonds), can overcome this limitation. It is argued that this solution represents a way to implicitly take into account the degree of interlocking associated to the microstructural complexity of rock. It is thus shown that increasing the degree of interlocking between the discrete elements which represent the rock medium, in addition to enhancing the UCS/TS ratio, results in a non-linear failure envelop characteristic of low porous rocks. This approach improves significantly the potential and predictive capabilities of the DEM for rock modeling purpose. A special emphasis is put on the model ability to capture the fundamental characteristics of brittle rocks in terms of fracture initiation and propagation. The model can reproduce an essential component of brittle rock failure, that is, cohesion weakening and frictional strengthening as a function of rock damage or plastic strain. Based on model predictions, it is finally discussed that frictional strengthening may be at the origin of the brittle ductile transition occurring at high confining pressures.

Frédéric-Victor Donzé

Papers

Numerical simulation of drained triaxial test using 3D discrete element modeling

A new open-source software developed for numerical simulations using discrete modeling methods

Modeling fractures in rock blasting

A DEM model for soft and hard rocks: Role of grain interlocking on strength

Modelling progressive failure in fractured rock masses using a 3D discrete element method