Anticrack inclusion model for compaction bands in sandstone

Abstract

[1] Detailed observations of compaction bands exposed in the Aztec Sandstone of southeastern Nevada indicate that these thin, tabular, bounded features of localized porosity loss initiated at pervasive grain-scale flaws, which collapsed in response to compressive tectonic loading. From many of these Griffith-type flaws, an apparently self-sustaining progression of collapse propagated outward to form bands of compacted grains a few centimeters thick and tens of meters in planar extent. These compaction bands can be idealized as highly eccentric ellipsoidal bodies that have accommodated uniform uniaxial plastic strain parallel to their short dimension within a surrounding elastic material. They thus can be represented mechanically as contractile Eshelby inclusions, which generate near-tip compressive stress concentrations consistent with self-sustaining, in-plane propagation. The combination of extreme aspect ratio ($10 À4 ) and significant uniaxial plastic strain ($10%) also justifies an approximation of the bands as anticracks: sharp boundaries across which a continuous distribution of closing mode displacement discontinuity has been accommodated. This anticrack interpretation of compaction bands is analogous to that of pressure solution surfaces, except that porosity loss takes the place of material dissolution. We find that displacement discontinuity boundary element modeling of compaction bands as anticracks within a two-dimensional linear elastic continuum can accurately represent the perturbed external stress fields they induce.

Mechanics of pressure solution seam growth and evolution

“…[35] In the previous studies of the mechanics of LVRSs, such as Katsman et al [2006] and Sternlof et al [2005], it was found that the significant compressive stress concentration occurs at the tip areas of the LVRSs, which rationalizes the in-plane lateral growth of the LVRSs. Our results are consistent with these results.…”

“…[38] Fletcher and Pollard [1981] and Sternlof et al [2005] proposed an anticrack-inclusion model for mechanical analyses of pressure solution surfaces and compaction bands, respectively, as LVRSs using the displacement discontinuity boundary element method. Sternlof [2006] expanded this method to simulate the propagation and interaction of two elliptical anticrack bands approaching each other along parallel paths.…”

“…Here x/a = 1 denotes the tip locations of the LVRSs. As noted by Sternlof et al [2005], the stresses are difficult to determine precisely close to the structures' tips. Nevertheless, it can still be observed that the tip stress amplifications for the elliptical LVRSs are relatively higher than that for the rectangular LVRSs.…”

“…They found that the normal stresses at the tips of LVRSs are compressive and significantly amplified with respect to the remote stresses, whereas on the flanks compressive normal stresses are slightly reduced. Sternlof et al [2005] idealized compaction bands as anticracks and analyzed the stress field around them using a boundary element method. Their numerical results showed a high compressive normal stress concentration at the tip areas of the anticracks.…”

Dynamical effects during compaction band formation affecting their spatial periodicity

“…Since the occurrence of CBs typically involves localized large strains, the formulation by Gajo and Denzer [2011] was adopted, which builds upon Biot's theory providing the theoretical framework and the finite element implementation for dynamic analyses within a hyperelastic framework [Gajo, 2010] for saturated porous media with compressible constituents subjected to finite strains. The adoption of an elastic framework to model a problem involving inelastic deformation is a simplification, already adopted by other authors in similar contexts [e.g., see Sternlof et al, 2005], justified by the fact that after the onset of a CB, typically plastic deformation occurs solely within the band while the rest of the domain undergoes elastic unloading Rudnicki, 1980, Chemenda, 2009]. Further explanation of this assumption is provided by the main analysis results, discussed in section 3.…”