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

thin, but finite thickness. It is the extreme elliptical eccentricity of the band trace that
justifies the anticrack approximation in a BEM treatment (Sternlof et al., 2005).
Nonetheless, nothing in the theory or implementation of linear elastic fracture mechanics
precludes the virtual interpenetration of anticrack walls, as represented in our treatment
by positive Dn. By the same token, the code works just as well for opening-mode cracks,
with the signs of the stresses and displacements reversed.
6. Propagation simulation
As a first step toward realistic simulation of CB propagation, interaction and pattern
development, we used the model code to investigate the propagation behavior of a few
simple configurations comprised of one or two anticrack bands. In order to generate
results comparable to the field observations, only values for the model parameters
corresponding to estimates for the Aztec sandstone during CB formation are used
(Sternlof et al., 2005). For the remote stress conditions, these are σ11 r = 40 Mpa, 20 Mpa
≤ σ22 r ≤ 40 Mpa, and σ12 r = 0. For the elastic properties of the pristine (CB-free) infinite
medium, these are Young’s modulus (Es) equals 20 GPa and Poisson’s ratio (νs) equals
0.2, such that the shear modulus (Gs) equals 8.3 GPa. Finally, we normalized by 40 MPa
to produce a problem dimensionless in stress, such that σ11 r = 1, 0.5 ≤ σ22 r ≤ 1, σ12 r = 0
and Es = 500.
6.1. Model calibration and stability testing
As described in Section 2, the anticrack model for CBs is based on detailed
observations, and thickness and porosity measurements of relatively isolated, straight
(planar) bands. These data established the physical reality of the anticrack-like elliptical
distribution of pure closing-mode displacement for such CBs (Sternlof et al., 2005).
However, in order to produce unconstrained and potentially predictive simulations of
propagation and interaction that are not perfectly symmetric to the remote stress field, we
must leave all boundary element displacements unspecified and let the model determine
their equilibrium values. Currently, this means specifying linear elastic modulii (Eb and
νb) for every element. Given the inelastic nature of compaction apparent inside CBs, this
approach to applying boundary conditions has limited appeal others are being developed,
as mentioned above. Nonetheless, if the rate of propagation was fast relative to the rate of
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