The mixology of precursory strain partitioning approaching brittle failure in rocks

Abstract

We examine the strain accumulation and localization process throughout twelve triaxial compression experiments on six rock types deformed in an X-ray transparent apparatus. In each experiment, we acquire 50-100 tomograms of rock samples at differential stress steps during loading, revealing the evolving 3D distribution of X-ray absorption contrasts, indicative of density. Using digital volume correlation (DVC) of pairs of tomograms, we build time series of 3D incremental strain tensor fields as the rocks are deformed toward failure. The Pearson correlation coefficients between components of the local incremental strain tensor at each stress step indicate that the correlation strength between pairs of local strain components, including dilation, contraction and shear strain, are moderate-strong in eleven of twelve experiments. In addition, changes in the local strain components from one DVC calculation to the next show differences in the correlations between pairs of strain components. In particular, the correlation of the local changes in dilation and shear strain tends to be stronger than the correlation of changes in dilation-contraction and contraction-shear strain. In eleven of twelve experiments, the most volumetrically frequent mode of strain accommodation includes a synchronized increase in multiple strain components. Early in loading, under lower differential stress, the most frequent strain accumulation mode involves the paired increase in dilation and contraction at neighboring locations. Under higher differential stress, the most frequent mode is the paired increase in dilation and shear strain. This mode is also the first or second most frequent throughout each complete experiment. Tracking the mean values of the strain components in the sample and the volume of rock that each component occupies reveals fundamental differences in the nature of strain accumulation and localization between the volumetric and shear strain modes. As the dilative strain increases in magnitude throughout loading, it tends to occupy larger volumes within the rock sample and thus delocalizes. In contrast, the increasing shear strain components (left- or right-lateral) do not necessarily occupy larger volume and so involve localization. Consistent with these evolutions, the correlation length of the dilatational strains tends to increase by the largest amounts of the strain components from lower to higher differential stress. In contrast, the correlation length of the shear strains does not consistently increase or decrease with increasing differential stress.

Rate and State Friction as a Spatially Regularized Transient Viscous Flow Law

“…The temporal patterns of localization and delocalization that occur in our model yield testable predictions that tie in to a recent surge in interest in similar patterns observed in the lab and in nature (e.g., Ben‐Zion & Zaliapin, 2020; McBeck, Aiken, et al., 2020; McBeck, Ben‐Zion, & Renard, 2020; McBeck et al., 2018, 2021). It could be the scope of future research to reinterpret anelastic strain rate in our model as a measure of the activity of a statistical distribution of cracks of various properties and compare to aforementioned lab and field observations.…”

Imaging strain localisation in porous andesite using digital volume correlation

“…However, imaging failure in complex rocks such as shales or compaction localisation in sandstone typically requires image analysis (e.g., Louis et al 2006;Lenoir et al, 2007). For example, digital image correlation techniques were used to investigate strain localisation in sedimentary rocks (e.g., Louis et al, 2007;Charalampidou et al, 2010;Dautriat et al, 2011;Ji et al, 2015;Tudisco et al, 2015;McBeck et al, 2018;Renard et al, 2017Renard et al, , 2019McBeck et al, 2020). Recently, digital volume correlation (DVC) was used to study failure in lowporosity basalt from Mt Etna using in situ X-ray synchrotron microtomography .…”

Predicting the Timing of Catastrophic Failure During Triaxial Compression: Insights from Discrete Element Method Simulations

“…The orientation of individual fractures, however, within such system-spanning fault networks may remain oriented parallel to the direction of r 1 , rather than along the apparent macroscopic orientation (McBeck et al, 2021a). Despite this difference between the true orientation of individual fractures and the overall fracture network, such fracture networks can accommodate shear strain (McBeck et al, 2019(McBeck et al, , 2020bRenard et al, 2019).…”

“…In addition, the numerical simulations accumulate less dilative strain than the intact rocks deformed in the experiments. Indeed, comparing the proportion of the volume of the experiments and simulations that host dilation, where I 1 [0, out of the total volume throughout each experiment and simulation indicate that the laboratory rocks host 40-60% dilation (McBeck et al, 2020b), whereas the simulations host about 30% (Fig. 13).…”

“…The simulations may experience less dilation than the experiments due to the initial porosity caused by the packing of the spherical particles. Whereas these experimental rocks generally have \ 10% porosity (McBeck et al, 2020b), the initial porosity of these simulations is about 20%, although we use the maximum feasible range of particle radii to achieve the lowest initial porosity under the computational constraints. The higher initial porosity of the simulations promotes more contraction, and enables shear deformation to occur without significant dilation.…”