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

assumption of an elastic continuum, distinct element method modeling techniques will
become increasingly important (e.g. Antonellini and Pollard, 1995; Morgan, 1999;
Morgan and Boettcher, 1999).
Nonetheless, we believe that progress can be made toward understanding the outcrop-
scale implications of grain-scale effects within the framework of the current model by
implementing refined petrographic observations as more sophisticated schemes for
applying boundary conditions on the band elements and as more nuanced propagation
criteria. The key to these refined observations lies in detecting and describing the shape
and nature of the damage zone around the uniformly compacted inclusion of grains
currently recognized as a CB (Figure 4.23) or, alternatively, conclusively demonstrating
the absence of any such damage envelope. In either case, the mechanical implications at
both the grain and outcrop scales would be profound.
These various shortcomings aside, the current model simulation results do suggest
and support several interpretations and inferences.
1. The maximum normalized near-tip compressive stress concentration (σθθ at r
= 5 mm) that can be realized for a realistic distribution of Dn is no more than
about 2.5 (equivalent to 100 MPa). Even taking this value as a lower threshold
because the data is derived from field measurements of CBs that stopped
propagating, it appears that large stresses are not required to promote the
quasi-static progression of compaction as accommodated by relatively
coherent quartz grain plasticity in the Aztec sandstone.
2. Judged in comparison to our simulation results, the variety of CB interactions
observed in Aztec outcrop—ranging from gently anastomosing sub-parallel
arrays of bands spaced up to a meter apart to the near ubiquity of hooking tip
and eye structures to strongly meandering patterns of anastomosis—suggest
that the prevailing remote paleo stress state was close to isotropic (σ22 r ≈
0.9σ11 r , σ d ≈ 0.1).
3. Although the remote state of sub-horizontal paleo stress in the Aztec was
apparently nearly isotropic (σ d ≈ 0.1 in the x1-x2 plane), the state of stress in
the x1-x3 plane, where σ33 r was essentially due to overburden, was decidedly
anisotropic (σ d = 0.5 by definition in our model set up). Our simulation
121