Critical Evolution of Damage Toward System‐Size Failure in Crystalline Rock

Abstract

Rock failure under shear loading conditions controls earthquake and faulting phenomena. We study the dynamics of microscale damage precursory to shear faulting in a quartz‐monzonite rock representative of crystalline rocks of the continental crust. Using a triaxial rig that is transparent to X‐rays, we image the mechanical evolution of centimeter‐size core samples by in situ synchrotron microtomography with a resolution of 6.5 μm. Time‐lapse three‐dimensional images of the samples inside the rig provide a unique data set of microstructural evolution toward faulting. Above a yield point there is a gradual weakening during which microfractures nucleate and grow until this damage span the whole sample. This leads to shear faults oriented about 30° to the main compressive stress in agreement with Anderson's theory and macroscopic failure. The microfractures can be extracted from the three‐dimensional images, and their dynamics and morphology (i.e., number, volume, orientation, shape, and largest cluster) are quantified as a function of increasing stress toward failure. The experimental data show for the first time that the total volume of microfractures, the rate of damage growth, and the size of the largest microfracture all increase and diverge when approaching faulting. The average flatness of the microfractures (i.e., the ratio between the second and third eigenvalues of their covariance matrix) shows a significant decrease near failure. The precursors to faulting developing in the future faulting zone are controlled by the evolving microfracture population. Their divergent dynamics toward failure is reminiscent of a dynamical critical transition.

Detecting the Onset of Strain Localization Using Two‐Dimensional Wavelet Analysis on Sandstone Deformed at Different Effective Pressures

“…Morlet wavelet analysis has detected that the inclination of the final shear plane, in all three samples, is in a range between 26 ∘ and 30 ∘ with respect to the maximum compression axis (Figures 5d, 8d, and 9d). Similar angular values were found both via experimental procedures (20-30 ∘ , Engelder, 1974;Reches & Lockner, 1994;Renard et al, 2018) and numerical models (26 ∘ , Healy et al, 2006a). We emphasize that our results are based on the assumption that all the mapped cracks were produced solely during the compression tests.…”

Dynamics of Microscale Precursors During Brittle Compressive Failure in Carrara Marble

“…• Microfracture dynamics explains complex physical processes guiding the macroscopic failure in Carrara marble • Statistical parameters measuring microfracture volume, growth, and spatial organization showed power law scaling with applied stress • Evolution of several microstructural parameters is in agreement with models that establish compressive failure as a critical phase transition deformation (e.g., Renard et al, 2017;Renard, Mcbeck, et al, 2019;Renard, Weiss, et al, 2018;Iglauer & Lebedev, 2017). This technique provides three-dimensional microstructural information on damage distribution as failure is approached and is complementary to other imaging techniques such as acoustic emissions (e.g., Renard, McBeck, et al, 2019).…”

“…In the range 0.02 < ∆ D < 0.2, this acceleration followed a power law D φ ∼ ∆ D −( β − 1) with an exponent ( β − 1) = 1.5 (inset of Figures and S3). Here the exponent ( β − 1) comes from the fact that the exponent β is defined for the incremental damage, dD φ / d∆ D , for which we expect a power law acceleration d D φ /d ∆ D ~ ∆ D −β (see Renard, McBeck, et al, ; Renard, Weiss, et al, , and below), while the total damage, D φ , is the integral of this quantity (Figure ). For this sample, D φ tapered at small values of the control parameter and showed an exponential evolution for ∆ D < 0.02.…”

“…These scaling laws argue for an interpretation of compressive failure as a critical phase transition from an intact to a failed state (Alava et al, ; Girard et al, ; Vu et al, ). Different theoretical models can be proposed to interpret such critical transition, yielding specific scaling laws and critical exponents (Renard, Weiss, et al, ). A comparison of these predictions with our results is detailed below.…”

“…Optical microscopy (Moore & Lockner, ; Tapponnier & Brace, ), scanning electron microscopy (Brace et al, ), laser scanning confocal microscopy (Fredrich et al, ), and acoustic emissions (Lockner et al, ) have revealed some of the microstructural origins of precursors prior to macroscopic failure. Complementary to these techniques, dynamic X‐ray microtomography coupled with triaxial load cell is a unique tool for imaging the microstructure of crustal rocks that are subjected to deformation (e.g., Renard et al, ; Renard, Mcbeck, et al, ; Renard, Weiss, et al, ; Iglauer & Lebedev, ). This technique provides three‐dimensional microstructural information on damage distribution as failure is approached and is complementary to other imaging techniques such as acoustic emissions (e.g., Renard, McBeck, et al, ).…”