structural geology, propagation mechanics and - Stanford School of ...

undamaged host rock. That CBs cannot exactly be represented as traction-free surfaces of
displacement discontinuity suggests that not all their interactions should be crack-like, as
indeed some are not, notably their tendency to approach at low angle to within
millimeters and then continue along parallel trends for meters. One can infer, for example,
that the middle of a cm-thick CB, within which up to 50% of the available porosity has
already been lost, represents a substantial physical barrier to the cross propagation of an
adjacent, porosity-consuming band. Certainly, the complex material evolution occurring
inside a propagating and curving band will affect the magnitude and distribution of
displacement discontinuity (shear and compaction) realized across it. Nonetheless, the
linear elastic anticrack approach to modeling CB mechanical interactions at the outcrop
scale is substantially justified in that the physical inclusions which define them only
accumulate as a direct consequence of the predominant closing-mode sense of
displacement they accommodate.
4. Mechanical theory
Sternlof et al. (2005) provide a thorough development and justification for the 2-D
(plane strain) mechanical model of an isolated, static CB as an anticrack within an
infinite, homogeneous, linear elastic, isotropic material subjected to uniform principal
remote compressive stress loading (σ11 r ≥ σ22 r , σ12 r = 0). So long as the scale of
observation exceeds a few millimeters, this constitutes a reasonable approximation of
CBs in the porous, granular Aztec sandstone as visible in the sub-horizontal plane of
outcrop exposure (Sternlof et al., 2005). In this section, we expand the anticrack model to
consider the theoretical implications for propagation and interaction between multiple
bands, with reference by analogy to classical elastic fracture mechanics (Irwin, 1960;
Lawn and Wilshaw, 1975) as successfully applied to natural opening-mode fractures in
rock and summarized by Olson and Pollard (1989) and Thomas and Pollard (1993).
Throughout the rest of the paper, compression, compaction, and left-lateral senses of
shear stress and displacement are taken as positive, as illustrated in Figure 4.10.
For an isolated, perfectly linear (planar) anticrack oriented symmetric to σ11 r , the
local state of stress induced in the near-tip region and expressed in the global (remote
principal) coordinate system resembles the example distributions shown in Figure 4.11.
High concentrations of compressive normal stress (σ11 and σ22) are readily apparent
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