[cig-commits] commit: More work on spontaneous rupture section.

[Mercurial]

changeset:   56:0c8f25441ab1
tag:         tip
user:        Brad Aagaard <baagaard at usgs.gov>
date:        Tue Aug 30 16:13:05 2011 -0700
files:       faultRup.tex
description:
More work on spontaneous rupture section.


diff -r d7a986bedd87 -r 0c8f25441ab1 faultRup.tex
--- a/faultRup.tex	Tue Aug 30 15:56:41 2011 -0700
+++ b/faultRup.tex	Tue Aug 30 16:13:05 2011 -0700
@@ -554,10 +554,26 @@ corresponding to a perturbation in the L
   \tensor{K}_{m^-m^-} \vec{u}_{m^-} = - \tensor{L}_p \partial \vec{l}_p, \\
   \partial \vec{d} = \tensor{R} \left( \vec{u}_{m^+} - \vec{u}_{m^-} \right).
 \end{gather}
+This estimate is exact if all other degrees of freedom are constrained
+(which is generally only the case for simple toy problems), quite good
+if the deformation associated with the fault slip is confined close to
+the fault (which occurs in most simulations because the fault slip is
+limited to the middle of the domain), and poor if the deformation
+associated with fault slip extends to the boundaries (which occurs in
+races cases in which the domain has a through-going fault).
 
-\brad{Mention fault constitutive models currently implemented in PyLith
-(static friction, slip weakening, time weakening, Dieterich-Ruina
-rate- and state friction with aging law).}
+PyLith includes several commonly used fault constitutive models, all
+of which specify the shear traction on the fault $T_f$ as a function
+of the cohesive stress $T_c$, coefficient of friction, $\mu_f$, and
+normal traction $T_n$,
+\begin{equation}
+  T_f = T_c - \mu_f T_n.
+\end{equation}
+We use the sign convention that a compressive normal tractions are
+negative. The fault constitutive models include static friction,
+linear slip-weakening, linear time-weakening, and Dieterich-Ruina
+rate-state friction with an aging law (see \citeN{PyLith:manual:1.6.2}
+for details).
 
 % ------------------------------------------------------------------
 \section{Finite-Element Mesh Processing}\matt{Rough draft}