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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which point the inelastic strain has attained a critical value (<br />
p<br />
ε )crit . This process is<br />
illustrated schematically in Figure 3.4, where the reduction <strong>of</strong> stress occurs over an<br />
endzone distance R . Further analysis <strong>of</strong> the spatial <strong>and</strong> temporal distribution <strong>of</strong> energy<br />
dissipation suggested by the more than 5 meters <strong>of</strong> elliptical taper near the ends <strong>of</strong> the<br />
b<strong>and</strong>s reported by Sternl<strong>of</strong> et al. (2005) is warranted <strong>and</strong> should contribute to a better<br />
underst<strong>and</strong>ing <strong>of</strong> the conditions needed for <strong>propagation</strong>.<br />
σ −<br />
σ<br />
σp<br />
σ −<br />
σ + = M∆/h<br />
R x<br />
σp<br />
σ −<br />
σ<br />
(ε ) crit<br />
p<br />
Figure 3.4. Schematic illustration <strong>of</strong> the hypothetical spatial distribution <strong>of</strong> stress near<br />
the edge (tip) <strong>of</strong> a CB. (a) As the tip is approached from the right (σ+ side), the stress<br />
increases to a maximum value σp , then drops below the remote background value <strong>of</strong> σ+<br />
to approach the relaxed value <strong>of</strong> σ— as the total inelastic compactive strain (ε p ) reaches<br />
its critical value (ε p )crit at a distance R behind the tip.<br />
6. Acknowledgements<br />
The authors thank Jim Rice for a suggestion concerning the model <strong>and</strong> Teng-fong<br />
Wong for discussion <strong>of</strong> his laboratory results. Principal financial support for this work<br />
was provided by the U. S. Department <strong>of</strong> Energy, Office <strong>of</strong> Basic Energy Science,<br />
Geosciences Research Program through grants to Northwestern University (John<br />
Rudnicki) <strong>and</strong> <strong>Stanford</strong> University (David Pollard <strong>and</strong> Atilla Aydin). Partial support<br />
during preparation <strong>of</strong> the initial manuscript while Rudnicki was a visitor at the Kavli<br />
Institute for Theoretical Physics was provided by the National Science Foundation under<br />
Grant No. PHY99-07949 (Preprint No. NSF-KITP-05-26). Additional support was<br />
provided by the <strong>Stanford</strong> Rock Fracture Project.<br />
84<br />
ε p