Elastic Properties of Fractured Rock Masses With Frictional Properties and Power Law Fracture Size Distributions

Abstract

We derive the relationships that link the general elastic properties of rock masses to the geometrical properties of fracture networks, with a special emphasis to the case of frictional crack surfaces. We extend the well‐known elastic solutions for free‐slipping cracks to fractures whose plane resistance is defined by an elastic fracture (shear) stiffness ks and a stick‐slip Coulomb threshold. A complete set of analytical solutions have been derived for (i) the shear displacement in the fracture plane for stresses below the slip threshold and above, (ii) the partitioning between the resistances of the fracture plane on the one hand and of the elastic matrix on the other hand, and (iii) the stress conditions to trigger slip. All the expressions have been checked with numerical simulations. The Young's modulus and Poisson's ratio were also derived for a population of fractures. They are controlled both by the total fracture surface for fractures larger than the stiffness length lS (defined by ks and the intact matrix elastic properties) and by the percolation parameter of smaller fractures. These results were applied to power law fracture size distributions, which are likely relevant to geological cases. We show that if the fracture size exponent is in the range −3 to −4, which corresponds to a wide range of geological fracture networks, the elastic properties of the bulk rock are almost exclusively controlled by ks and the stiffness length, meaning that the fractures of size lS play a major role in the definition of the elastic properties.

How Does In Situ Stress Rotate Within a Fault Zone? Insights From Explicit Modeling of the Frictional, Fractured Rock Mass

“…It should be noted that the normal stiffness kn for natural fractures is generally much larger than the shear stiffness ks. Therefore, we can neglect the compressive normal displacement for sake of computational efficiency without much loss of accuracy, which has been numerically verified by Davy et al (2018).…”

“…(4). Generally, there are two theoretical methods to calculate the effective properties, depending on whether the fracture interaction is considered or not (Kachanov, 1992;Davy et al, 2018). One method is the Non-Interaction Approximation (NIA), which states that each fracture can be regarded as isolated and that its surrounding medium is maintained intact as the initial elastic matrix.…”

“…The negligible pore pressure effect in this series of simulations can be accounted for by the fracture constitutive behavior. As pointed out by Davy et al (2018), the mechanical behavior of the fracture network is mainly controlled by the stiffness length ls, which is defined as the fracture length for which the fracture shear stiffness equals to the average shear stiffness of matrix (k s = k ̅ m ):…”

Automatic Fault Mapping in Remote Optical Images and Topographic Data With Deep Learning

“…However, refined vectorization approaches are needed to recover the individual fault lengths accurately. With these additional refinements, the M Ref predictions will provide among the key information necessary to quantify the mechanical properties of the faulted rocks (e.g., Bonnet et al., 2001; Davy et al., 2018), an issue of critical importance in tectonic damage zones embedding master faults. The quantification of the elastic properties of the faulted/fractured rocks embedding a master fault is indeed critical to assess the behavior of an earthquake rupture on that fault (initiation, propagation, slip and acceleration amount and distribution, e.g., Cappa et al., 2014; Huang & Ampuero, 2011; Thakur et al., 2020).…”

On the Density Variability of Poissonian Discrete Fracture Networks, with application to power-law fracture size distributions

“…Characterizing fracture networks in geosciences is a key challenge for many industrial projects such as deep waste disposal, hydrogeology or petroleum resources, because it may change the mechanical (Davy et al, 2018;Grechka and Kachanov, 2006) and hydrological (Bogdanov et al, 2007;De Dreuzy et al, 2001a, b) behaviour of the rock mass. Fractures being ubiquitous and at all scales, the description of these physical properties is often far beyond the reach of a continuum approach (Jing, 2003).…”