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

segments will self-correct to provide a reasonable, zig-zag approximation to the ideal
path, certainly for |β| less than ~10° so long as σ d ≠ 0.
In all the simulations presented below, we therefore adopted fixed values of Eb = 15
and r = 5 mm, and use 10 cm propagation elements so long as β < 10°. Insofar as
necessary to maintain numerical stability, and capture details of strong curvature and the
close approach of adjacent bands, we reduced the added element length to 2 cm. We also
verified that at no point in any simulation did Dn on any element become positive (i.e.
opening-mode). Finally, given the current lack of data on a critical σθθ threshold for
propagation to occur, we used a model threshold of σθθ max > σ11 r = 1. In practice, the
normalized magnitude of σθθ max never dropped below about 1.25.
6.2. Symmetric propagation
In order to examine the tendency for CBs to form symmetric (orthogonal) to σ11 r , we
simulated the propagation of a short, incipient band (three elements, 6 cm) over a range
of misalignment angles α (relative to the global coordinate system) for each of the remote
stress states σ d = 0.05, 0.25 and 0.5 (Figure 4.20). Not surprisingly, the results indicate
that the tendency of a misaligned incipient CB to propagate into symmetry with the
remote stress field decreases as σ d → 0. For a perfectly isotropic state of remote stress,
all band trends are preferred equally. For the maximum probable remote differential
stress (σ d = 0.5), the band trend orthogonal to σ11 r is strongly preferred. Even at σ d =
0.25 (σ22 r = 0.75σ11 r ), the symmetric orientation is clearly preferred, particularly if one
allows for the fact that 6 cm greatly exaggerates the length a misaligned incipient CB
would attain without starting to curve.
Another factor to consider in assessing the tendency toward symmetric propagation is
how σθθ max at the tips of the incipient model CB varies with α (Figure 4.20d). Even for
σ d = 0.05, a slight but appreciable increase of 5.4% in σθθ max is realized as α goes from
90° to 0°. For σ d = 0.25 and 0.5, the increase is 33.3% and 100%, respectively. These
results demonstrate that, even as σ d → 0, the propagation of incipient bands oriented
more nearly orthogonal to σ11 r is preferred, likely stranding those oriented at higher α.
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