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

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.