[cig-commits] r15770 - doc/geodynamics.org/benchmarks/trunk/long
luis at geodynamics.org
luis at geodynamics.org
Mon Oct 5 15:49:16 PDT 2009
Author: luis
Date: 2009-10-05 15:49:15 -0700 (Mon, 05 Oct 2009)
New Revision: 15770
Modified:
doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html
doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst
Log:
Fixes to long/drucker-prager.rst
Modified: doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html 2009-10-05 22:49:11 UTC (rev 15769)
+++ doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html 2009-10-05 22:49:15 UTC (rev 15770)
@@ -16,19 +16,19 @@
<p>For the Drucker-Prager rehology in 2D, we can write the yielding relation
as</p>
<blockquote>
-[;sigma_{ns}=sigma_{nn}tanvarphi+C,;]</blockquote>
-<p>where [;sigma_{ns};] is the shear stress perpendicular to the fault plane,
-[;sigma_{nn};] is the shear stress parallel to the fault plane, [;varphi;]
+[;\sigma_{ns}=\sigma_{nn}\tan\varphi+C,;]</blockquote>
+<p>where [;\sigma_{ns};] is the shear stress perpendicular to the fault plane,
+[;\sigma_{nn};] is the shear stress parallel to the fault plane, [;\varphi;]
is the internal angle of friction, and [;C;] is the cohesion. Decomposing this
-into principal stresses [;sigma_{I};], [;sigma_{II};], and [;sigma_{III};]
+into principal stresses [;\sigma_{I};], [;\sigma_{II};], and [;\sigma_{III};]
gives</p>
<blockquote>
-[;sin(2Theta)(sigma_{I}-sigma_{III})/2=tanvarphileft((sigma_{I}+sigma_{III})/2+cos(2Theta)(sigma_{I}-sigma_{III})/2right)+C,;]</blockquote>
-<p>where [;Theta;] is the angle that the fault makes relative to the maximum
+[;\sin(2\Theta)(\sigma_{I}-\sigma_{III})/2=\tan\varphi\left((\sigma_{I}+\sigma_{III})/2+\cos(2\Theta)(\sigma_{I}-\sigma_{III})/2\right)+C,;]</blockquote>
+<p>where [;\Theta;] is the angle that the fault makes relative to the maximum
shear stress. Assuming that the fault forms where the shear stress
-[;sigma_{I}-sigma_{III};] is a minimum, a little algebra gives us</p>
+[;\sigma_{I}-\sigma_{III};] is a minimum, a little algebra gives us</p>
<blockquote>
-[;Theta=pmleft(frac{pi}{4} + frac{varphi}{2}right).;]</blockquote>
+[;\Theta=\pm\left(\frac{\pi}{4} + \frac{\varphi}{2}\right).;]</blockquote>
<p>Using this, we can construct a simple plasticity experiment and make sure
that Gale gives the correct faulting angle.</p>
</div>
@@ -39,7 +39,7 @@
the strain rate invariant to find incipient faults. We do not take any
time steps, removing any confounding effects they may cause.</p>
<div class="figure">
-<img alt="images/Mohr_Coulomb_setup.eps" src="images/Mohr_Coulomb_setup.eps" />
+<img alt="images/Mohr_Coulomb_setup.png" src="images/Mohr_Coulomb_setup.png" />
<p class="caption">Figure [fig:Mohr-Coulomb-setup]</p>
<div class="legend">
The setup for the shortening experiment. The box is 1 unit on a side,
@@ -50,8 +50,8 @@
<div class="section" id="numerical-results">
<h1>Numerical Results</h1>
<p>Figure [fig:Mohr-Coulomb-sri] shows the results for three different
-resolutions for [;varphi=45^{deg};]. There is not much difference between
-the medium ([;256 times 256;]) and high ([;512 times 512;]) results,
+resolutions for [;\varphi=45^{\circ};]. There is not much difference between
+the medium ([;256 \times 256;]) and high ([;512 \times 512;]) results,
suggesting that we have sufficient resolution. Figure
[fig:Mohr-Coulomb-comparison] shows a plot of the numerical vs. analytic
results for several different angles for medium resolution. This gives us
@@ -62,13 +62,13 @@
<p class="caption">Figure [fig:Mohr-Coulomb-sri]</p>
<div class="legend">
Strain rate invariant for the shortening experiment where
-$varphi=45^{deg}$ with three different resolutions:
-$128 times 128$, $256 times 256$, $512 times 512$.
+[;\varphi=45^{\circ}$ with three different resolutions:
+[;128 \times 128;], [;256 \times 256;], [;512 \times 512;].
Any differences between the medium and high resolution runs are swamped
by uncertainties in determining the overall angle of faulting.</div>
</div>
<div class="figure">
-<img alt="images/mohr_coulomb_angles.eps" src="images/mohr_coulomb_angles.eps" />
+<img alt="images/mohr_coulomb_angles.png" src="images/mohr_coulomb_angles.png" />
<p class="caption">Figure [fig:Mohr-Coulomb-comparison]</p>
<div class="legend">
Numerical vs. analytic results for fault angles as a function of
Modified: doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst 2009-10-05 22:49:11 UTC (rev 15769)
+++ doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst 2009-10-05 22:49:15 UTC (rev 15770)
@@ -8,21 +8,21 @@
For the Drucker-Prager rehology in 2D, we can write the yielding relation
as
- [;\sigma_{ns}=\sigma_{nn}\tan\varphi+C,;]
+ [;\\sigma_{ns}=\\sigma_{nn}\\tan\\varphi+C,;]
-where [;\sigma_{ns};] is the shear stress perpendicular to the fault plane,
-[;\sigma_{nn};] is the shear stress parallel to the fault plane, [;\varphi;]
+where [;\\sigma_{ns};] is the shear stress perpendicular to the fault plane,
+[;\\sigma_{nn};] is the shear stress parallel to the fault plane, [;\\varphi;]
is the internal angle of friction, and [;C;] is the cohesion. Decomposing this
-into principal stresses [;\sigma_{I};], [;\sigma_{II};], and [;\sigma_{III};]
+into principal stresses [;\\sigma_{I};], [;\\sigma_{II};], and [;\\sigma_{III};]
gives
- [;\sin(2\Theta)(\sigma_{I}-\sigma_{III})/2=\tan\varphi\left((\sigma_{I}+\sigma_{III})/2+\cos(2\Theta)(\sigma_{I}-\sigma_{III})/2\right)+C,;]
+ [;\\sin(2\\Theta)(\\sigma_{I}-\\sigma_{III})/2=\\tan\\varphi\\left((\\sigma_{I}+\\sigma_{III})/2+\\cos(2\\Theta)(\\sigma_{I}-\\sigma_{III})/2\\right)+C,;]
-where [;\Theta;] is the angle that the fault makes relative to the maximum
+where [;\\Theta;] is the angle that the fault makes relative to the maximum
shear stress. Assuming that the fault forms where the shear stress
-[;\sigma_{I}-\sigma_{III};] is a minimum, a little algebra gives us
+[;\\sigma_{I}-\\sigma_{III};] is a minimum, a little algebra gives us
- [;\Theta=\pm\left(\frac{\pi}{4} + \frac{\varphi}{2}\right).;]
+ [;\\Theta=\\pm\\left(\\frac{\\pi}{4} + \\frac{\\varphi}{2}\\right).;]
Using this, we can construct a simple plasticity experiment and make sure
that Gale gives the correct faulting angle.
@@ -36,7 +36,7 @@
the strain rate invariant to find incipient faults. We do not take any
time steps, removing any confounding effects they may cause.
-.. figure:: images/Mohr_Coulomb_setup.eps
+.. figure:: images/Mohr_Coulomb_setup.png
Figure [fig:Mohr-Coulomb-setup]
@@ -48,8 +48,8 @@
-----------------
Figure [fig:Mohr-Coulomb-sri] shows the results for three different
-resolutions for [;\varphi=45^{\deg};]. There is not much difference between
-the medium ([;256 \times 256;]) and high ([;512 \times 512;]) results,
+resolutions for [;\\varphi=45^{\\circ};]. There is not much difference between
+the medium ([;256 \\times 256;]) and high ([;512 \\times 512;]) results,
suggesting that we have sufficient resolution. Figure
[fig:Mohr-Coulomb-comparison] shows a plot of the numerical vs. analytic
results for several different angles for medium resolution. This gives us
@@ -61,12 +61,12 @@
Figure [fig:Mohr-Coulomb-sri]
Strain rate invariant for the shortening experiment where
- $\varphi=45^{\deg}$ with three different resolutions:
- $128 \times 128$, $256 \times 256$, $512 \times 512$.
+ [;\\varphi=45^{\\circ}$ with three different resolutions:
+ [;128 \\times 128;], [;256 \\times 256;], [;512 \\times 512;].
Any differences between the medium and high resolution runs are swamped
by uncertainties in determining the overall angle of faulting.
-.. figure:: images/mohr_coulomb_angles.eps
+.. figure:: images/mohr_coulomb_angles.png
Figure [fig:Mohr-Coulomb-comparison]
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