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

form perpendicular to σ11 r , increasing σ22 r acts to reduce the effective differential stress
and inhibits, rather than enhances path stability.
In the second case, when the stress perturbations generated by adjacent anticracks
impinge, the effect can be understood by holding one stationary and considering how its
near-tip shear stress field (σ12) resolves onto the other tip propagating along a parallel
path. For example, if tip B approaches tip A from the upper right (Figure 4.14a), it first
enters an area where the sense of shear imposed on it by tip A is mildly positive (left
lateral). This rotates the direction of σθθ max in front of B slightly clockwise, causing it to
curve gently away from A. As B continues on its now sub-parallel path to the left, it
enters the area where the sense of shear induced by A becomes distinctly negative (right
lateral), rotating the direction of σθθ max abruptly counterclockwise and causing B to curve
strongly toward A. Conversely, if tip B overtakes tip A from the upper left (Figure 4.14b),
the sense and magnitude of shear imposed at first cause it to curve strongly away from
the plane of A (counterclockwise), and then gently toward it (clockwise). The net result is
that, if B approaches A, it steps closer to it along a curving path, while if B overtakes A,
it steps away. In both cases, the senses of curving and stepping are the same (mirror
images) if B propagates along a parallel path on the other side of A. If both A and B
propagate, then both paths also curve as described.
The path altering effects of the local and remote stress fields superimpose, generally
in opposition: local effects acting to curve propagation paths out of symmetry with the
remote principal stress state; and the remote differential stress acting to maintain
symmetry. Three additional contributors to path stability for a given CB anticrack would
be the geometry of the path it has already traveled, the distribution of inelastic
(unrecoverable) relative boundary displacements realized along that path, and the
physical properties (elastic or otherwise) of the compacted material inside it. All three of
these would tend to enhance propagation path stability, insofar as shear tractions imposed
on a curving tip would be transmitted into the existing band and resisted by its fixed
physical attributes. The nature of these effects can be thought of as the inertia of a CB to
changes in its path. Furthermore, the nonzero shear tractions imposed by the compacted
material inside a CB on its boundaries with the surrounding pristine sandstone preclude
the local principal state of stress from being symmetric to those boundaries. This fact
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