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

Laboratory brittle deformation experiments have shown that a rapid transition exists in the behaviour of porous materials under stress: at a certain point, early formed and spatially distributed tensile cracks interact and coalesce forming a shear plane. In this work, we present and apply a novel image processing tool which is able to quantify this transition between distributed (‘stable’) damage accumulation and localised (‘unstable’) deformation, in terms of the size, density, and orientation of cracks at the point of strain localisation. Our technique, based on a two‐dimensional Morlet wavelet analysis, can recognise, extract and visually separate the multi‐scale changes occurring in the crack network during the deformation process. We first performed a series of triaxial experiments (σ1 > σ2 = σ3) on core plugs of Hopeman Sandstone (Scotland, UK) at different effective pressures (from 5 to 30 MPa). We then processed high‐resolution back‐scattered electron microscope images of thin sections of these core plugs and found differences in the strain localisation process as effective pressure was increased. The critical length of tensile cracks required before the onset of strain localisation was reduced from 0.24 to 0.15 mm as the effective pressure was increased to 30 MPa, resulting in a narrow fracture zone. Critically, by comparing patterns of fractures in these deformed sandstone samples, we can quantitatively explore the relationship between the observed geometry of the cracks and the inferred mechanical processes. This will eventually help us to better understand the physics underlying the initiation of catastrophic events, such as earthquakes, landslides and volcanic eruptions.