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