Micromechanics and Strain Localization in Sand in the Ductile Regime

Abstract

Critical processes including seismic faulting, reservoir compartmentalization, and borehole failure involve high‐pressure mechanical behavior and strain localization of sedimentary rocks such as sandstone. Sand is often used as a model material to study the mechanical behavior of poorly lithified sandstone. Recent studies exploring the multi‐scale mechanics of sand have characterized the brittle, low‐pressure regime of behavior; however, limited work has provided insights into the ductile, high‐pressure regime of behavior via in‐situ measurements. Critical features of the ductile regime, including grain breakage, grain micromechanics, and volumetric strain behavior therefore remain under‐explored. Here, we use a new high‐pressure triaxial apparatus with in‐situ x‐ray tomography to provide new insights into deformation banding, grain breakage, and grain micromechanics in Ottawa sand subjected to triaxial compression under confining pressures between 10 and 45 MPa. We observed strain‐hardening at pressures above 15 MPa and strain‐neutral responses at pressures below 15 MPa. Compacting shear bands and grain breakage were observed at all pressures with no significant variation due to grain size, except for minor increases in breakage in less‐rounded sands. Grain breakage emerged at stress levels lower than the assumed yield threshold and more intense breakage was associated with thinner deformation bands. Contact sliding at inter‐grain contacts demonstrated a bifurcation into a bimodal distribution, with intense sliding within deformation bands and reduced but non‐negligible sliding outside of deformation bands, suggesting that off‐band zones remain mechanically active during strain hardening.

Assessing continuum plasticity postulates with grain stress and local strain measurements in triaxially compressed sand

“…The use of this approach, the only known approach through which grain stresses can be measured experimentally, necessitates using of higher confining pressures and smaller samples than are typically used in experimental studies of dilatant shear bands performed in the soil mechanics communities. Our triaxial tests therefore feature compactive, rather than dilative, shear bands, which emerge naturally in many geomaterials deformed under relatively high confining pressures ( 2 , 12 , 13 ). Experimental constraints also required the use of less than 2,000 particles per sample, suggesting the possibility of finite size and boundary effects.…”

“…These tests have also revealed the ubiquitous emergence of shear bands, or regions of localized shear strain which become fully developed when a material approaches a macroscopic critical state. The emergence of shear bands may be accompanied by dilation at low pressures, compaction at high pressures, or may feature a more complex volumetric evolution depending on a soil’s initial density, breakage susceptibility, and the confining pressure applied to the sample ( 2 , 12 – 15 ).…”

“…The mechanical behavior of these materials, and specifically their propensity to develop shear and deformation bands, is of significant importance because of their application as reservoirs for hydrocarbon extraction and CO 2 storage ( 20 ). These materials have therefore been tested under conditions similar to those found in their reservoir applications (5 to 50 MPa) ( 13 , 19 – 22 ), and their mechanical behaviors have been interpreted using critical state plasticity theories ( 16 – 18 ).…”

“…To examine strain localization and the preceding assumptions experimentally, prior research has employed photoelasticity in biaxial compression experiments ( 27 , 34 , 35 ), X-ray radiography ( 29 ), acoustic emissions measurements ( 20 ), and high-resolution X-ray computed tomography (XRCT) in triaxial tests ( 13 , 36 – 38 ). These studies have offered evidence supporting the assumptions of coaxiality in 2D granular packings ( 27 , 34 , 35 ) and zero extension and vanishing dilation at critical state in shear bands in sands ( 29 , 39 ).…”

“…These studies have offered evidence supporting the assumptions of coaxiality in 2D granular packings ( 27 , 34 , 35 ) and zero extension and vanishing dilation at critical state in shear bands in sands ( 29 , 39 ). Recent experiments using XRCT have revealed rich particle scale kinematics in shear bands, including rotations, breakage, and force chain structures ( 12 , 13 , 36 – 38 , 40 – 44 ), which are not considered in conventional plasticity theories but are incorporated into some modern constitutive frameworks such as continuum breakage mechanics ( 45 , 46 ). Detailed discrete element method (DEM) simulations, recently applied to “digital twins” or direct replicas of physical specimens, have also quantified force chains and principal stress rotations in shear bands ( 47 – 49 ).…”