Stress‐dependent permeability and wave dispersion in tight cracked rocks: Experimental validation of simple effective medium models

Abstract

We experimentally assess the impact of microstructure, pore fluid, and frequency on wave velocity, wave dispersion, and permeability in thermally cracked Carrara marble under effective pressure up to 50 MPa. The cracked rock is isotropic, and we observe that (1) P and S wave velocities at 500 kHz and the low‐strain (<10−5) mechanical moduli at 0.01 Hz are pressure‐dependent, (2) permeability decreases asymptotically toward a small value with increasing pressure, (3) wave dispersion between 0.01 Hz and 500 MHz in the water‐saturated rock reaches a maximum of ~26% for S waves and ~9% for P waves at 1 MPa, and (4) wave dispersion virtually vanishes above ~30 MPa. Assuming no interactions between the cracks, effective medium theory is used to model the rock's elastic response and its permeability. P and S wave velocity data are jointly inverted to recover the crack density and effective aspect ratio. The permeability data are inverted to recover the cracks' effective radius. These parameters lead to a good agreement between predicted and measured wave velocities, dispersion and permeability up to 50 MPa, and up to a crack density of ~0.5. The evolution of the crack parameters suggests that three deformation regimes exist: (1) contact between cracks' surface asperities up to ~10 MPa, (2) progressive crack closure between ~10 and 30 MPa, and (3) crack closure effectively complete above ~30 MPa. The derived crack parameters differ significantly from those obtained by analysis of 2‐D electron microscope images of thin sections or 3‐D X‐ray microtomographic images of millimeter‐size specimens.

Development and Recovery of Stress‐Induced Elastic Anisotropy During Cyclic Loading Experiment on Westerly Granite

“…Without differential stress, hydrostatic stress may be enough to close cracks, and hence, they are not observable from elastic properties. However, while a strong recovery is observed on wave velocity during subsequent unloading, damage produced during loading remains within the rock specimens and are expected to affect other physical properties, such as permeability or porosity (Sarout et al, ). Our results suggest that elastic measurement of natural rock samples should be made with both confining pressure and deviatoric stress to highlight the full amount of damage recorded from natural deformation under crustal pressure conditions.…”

Pressure‐Dependent Elastic and Transport Properties of Porous and Permeable Rocks: Microstructural Control

“…In practice, the permeability for a medium made exclusively of tube‐like pores is κ tube ~10 −13 m 2 (e.g., Sarout, ). For purely cracked media, one, however, expects a value of κ c ~10 −17 to 10 −18 m 2 at the lowest pressure (e.g., Benson, Schubnel, et al, ; Sarout et al, ). Hence, if κ t ( P c ) is additive (equation ), the contribution of the cracks to the total flow is negligible compared to that of the subnetwork of tubes and κ t ( P c ) ~ κ tube .…”

Experimental Observation of the Onset of Percolation in Freshwater Granular Ice

“…Elastic properties of the samples were determined from the measured density ρ and the ultrasonic velocities measured along the x 1 , x 2 , and x 3 directions using the noninteracting crack effective medium approach (Kachanov, 1994). While numerous effective elastic medium theory models of cracked materials have been developed over the last 30 years (e.g., Eshelby et al, 1951;Hudson, 1981;O'Connell & Budiansky, 1974;Walsh, 1965), the range of validity of one of the simplest effective elastic medium theories, Kachanov's (1994) noninteractive crack model, has been shown to extend to relatively high crack densities, including for symmetries up to orthorhombic (Sarout et al, 2017;Schubnel et al, 2006). For example, Snyder et al (2015) showed good agreement between the predictions of Kachanov's crack model and direct measurements of crack densities in columnar ice for single set crack densities (i.e., α ii , see below) up to~0.1.…”