Riding the Right Wavelet: Quantifying Scale Transitions in Fractured Rocks

• Published in: Geophysical research letters Vol. 44; no. 23; pp. 11,808 - 11,815
• Main Authors: Rizzo, Roberto E., Healy, David, Farrell, Natalie J., Heap, Michael J.
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 16.12.2017; American Geophysical Union
• Subjects: Catastrophic failure analysis; Change detection; Coalescing; Cracks; Deformation; Deformation mechanisms; Ductile-brittle transition; Earth Sciences; Earthquakes; failure; Faults; Foundry sands; Fracture mechanics; Fractures; Geophysics; Image analysis; Image processing; Laboratories; Laboratory experiments; Landslides; Landslides & mudslides; Localization; Mechanics; Microcracks; Micrometers; Morlet; Nondestructive testing; Orientation; Physics; Porous materials; Rock; Rocks; Sandstone; Sciences of the Universe; Sedimentary rocks; Seismic activity; Stress; Stresses; transition; Two dimensional analysis; Volcanic eruptions; wavelet; Wavelet analysis
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1002/2017GL075784

The mechanics of brittle failure is a well‐described multiscale process that involves a rapid transition from distributed microcracks to localization along a single macroscopic rupture plane. However, considerable uncertainty exists regarding both the length scale at which this transition occurs and the underlying causes that prompt this shift from a distributed to a localized assemblage of cracks or fractures. For the first time, we used an image analysis tool developed to investigate orientation changes at different scales in images of fracture patterns in faulted materials, based on a two‐dimensional continuous wavelet analysis. We detected the abrupt change in the fracture pattern from distributed tensile microcracks to localized shear failure in a fracture network produced by triaxial deformation of a sandstone core plug. The presented method will contribute to our ability of unraveling the physical processes at the base of catastrophic rock failure, including the nucleation of earthquakes, landslides, and volcanic eruptions. Plain Language Summary Rocks contain cracks; these cracks are important because when rocks are placed under load (whether natural or man made), these flaws concentrate stress. Stress concentrations lead cracks to link up to form throughgoing features, such as faults. This is how earthquakes, landslides, and volcanic eruptions start: processes occurring at a small scale (e.g., micrometers) have large‐scale consequences. Laboratory experiments have shown that there is a rapid transition in behavior of porous materials under stress: at a certain point, the cracks interact and coalesce in a narrow zone, rather than being distributed throughout the material. In this work we present a novel technique that is able to quantify the transition between distributed (“stable”) deformation and localized (“unstable”) deformation, in terms crack sizes and orientations at the point of failure. This will help us to understand the physics underlying the initiation of catastrophic events, such as earthquakes, landslides, and volcanic eruptions. Key Points We use fully anisotropic directional Morlet wavelet analysis on synthetic and real fracture patterns We detected the abrupt change in the fracture pattern from distributed tensile microcracks to localized shear failure Morlet wavelet allowed the identification, on laboratory scale, of the critical crack length to achieve coalescence