[cig-commits] r15786 - doc/geodynamics.org/benchmarks/trunk/long
luis at geodynamics.org
luis at geodynamics.org
Wed Oct 7 12:15:57 PDT 2009
Author: luis
Date: 2009-10-07 12:15:55 -0700 (Wed, 07 Oct 2009)
New Revision: 15786
Modified:
doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html
doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst
Log:
Fixed figures in long/drucker-prager.rst
Modified: doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html 2009-10-07 19:15:48 UTC (rev 15785)
+++ doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.html 2009-10-07 19:15:55 UTC (rev 15786)
@@ -5,7 +5,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="Docutils 0.5: http://docutils.sourceforge.net/" />
<title>Drucker-Prager</title>
-<link rel="stylesheet" href="../css/default.css" type="text/css" />
+<link rel="stylesheet" href="../css/voidspace.css" type="text/css" />
</head>
<body>
<div class="document" id="drucker-prager">
@@ -13,8 +13,8 @@
<div class="section" id="analytic-treatment">
<h1>Analytic Treatment</h1>
-<p>For the Drucker-Prager rehology in 2D, we can write the yielding relation
-as</p>
+<p>For the Drucker-Prager rehology in 2D, we can write the
+yielding relation as</p>
<blockquote>
[;\sigma_{ns}=\sigma_{nn}\tan\varphi+C,;]</blockquote>
<p>where [;\sigma_{ns};] is the shear stress perpendicular to the fault plane,
@@ -24,9 +24,10 @@
gives</p>
<blockquote>
[;\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>
+<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>
<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
@@ -34,45 +35,46 @@
</div>
<div class="section" id="model-setup">
<h1>Model Setup</h1>
-<p>We performed a shortening experiment as shown in Figure
-[fig:Mohr-Coulomb-setup]. We only solve the Stokes equation and look at
-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.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,
-and the low viscosity region has a radius of 0.01 (its size is
-exaggerated).</div>
+<p>We performed a shortening experiment as shown in <a class="reference internal" href="#figure-1">Figure 1</a>.
+We only solve the Stokes equation and look at the strain rate invariant
+to find incipient faults. We do not take any time steps, removing
+any confounding effects they may cause.</p>
+<!-- fig:Mohr-Coulomb-setup -->
+<div align="center" class="figure">
+<img alt="images/Mohr_Coulomb_setup.png" src="images/Mohr_Coulomb_setup.png" style="width: 40%;" />
+<p class="caption"><span class="target" id="figure-1">Figure 1</span>:
+The setup for the shortening experiment.
+The box is 1 unit on a side, and the low viscosity region
+has a radius of 0.01 (its size is exaggerated).</p>
</div>
</div>
<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^{\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
-confidence that, at least in compression(sp?) in 2D, our Drucker-Prager
-implementation gives the correct results.</p>
-<div class="figure">
-<img alt="images/Mohr_coulomb_resolutions.png" src="images/Mohr_coulomb_resolutions.png" />
-<p class="caption">Figure [fig:Mohr-Coulomb-sri]</p>
-<div class="legend">
+<p><a class="reference internal" href="#figure-2">Figure 2</a> shows the results for three different 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.
+<a class="reference internal" href="#figure-3">Figure 3</a> shows a plot of the numerical vs. analytic
+results for several different angles for medium resolution.
+This gives us confidence that, at least in compression in 2D,
+our Drucker-Prager implementation gives the correct results.</p>
+<!-- fig:Mohr-Coulomb-sri -->
+<div align="center" class="figure">
+<img alt="images/Mohr_coulomb_resolutions.png" src="images/Mohr_coulomb_resolutions.png" style="width: 80%;" />
+<p class="caption"><span class="target" id="figure-2">Figure 2</span>:
Strain rate invariant for the shortening experiment where
[;\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>
+Any differences between the medium and high resolution runs
+are swamped by uncertainties in determining the overall
+angle of faulting.</p>
</div>
-<div class="figure">
+<!-- fig:Mohr-Coulomb-comparison -->
+<div align="center" class="figure">
<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">
+<p class="caption"><span class="target" id="figure-3">Figure 3</span>:
Numerical vs. analytic results for fault angles as a function of
-internal angle of friction.</div>
+internal angle of friction.</p>
</div>
</div>
</div>
Modified: doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst 2009-10-07 19:15:48 UTC (rev 15785)
+++ doc/geodynamics.org/benchmarks/trunk/long/drucker-prager.rst 2009-10-07 19:15:55 UTC (rev 15786)
@@ -5,8 +5,8 @@
Analytic Treatment
------------------
-For the Drucker-Prager rehology in 2D, we can write the yielding relation
-as
+For the Drucker-Prager rehology in 2D, we can write the
+yielding relation as
[;\\sigma_{ns}=\\sigma_{nn}\\tan\\varphi+C,;]
@@ -18,9 +18,10 @@
[;\\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
-shear stress. Assuming that the fault forms where the shear stress
-[;\\sigma_{I}-\\sigma_{III};] is a minimum, a little algebra gives us
+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
[;\\Theta=\\pm\\left(\\frac{\\pi}{4} + \\frac{\\varphi}{2}\\right).;]
@@ -31,45 +32,54 @@
Model Setup
-----------
-We performed a shortening experiment as shown in Figure
-[fig:Mohr-Coulomb-setup]. We only solve the Stokes equation and look at
-the strain rate invariant to find incipient faults. We do not take any
-time steps, removing any confounding effects they may cause.
+We performed a shortening experiment as shown in `Figure 1`_.
+We only solve the Stokes equation and look at the strain rate invariant
+to find incipient faults. We do not take any time steps, removing
+any confounding effects they may cause.
+.. fig:Mohr-Coulomb-setup
.. figure:: images/Mohr_Coulomb_setup.png
+ :align: center
+ :width: 40%
- Figure [fig:Mohr-Coulomb-setup]
+ _`Figure 1`:
+ The setup for the shortening experiment.
+ The box is 1 unit on a side, and the low viscosity region
+ has a radius of 0.01 (its size is exaggerated).
- The setup for the shortening experiment. The box is 1 unit on a side,
- and the low viscosity region has a radius of 0.01 (its size is
- exaggerated).
Numerical Results
-----------------
-Figure [fig:Mohr-Coulomb-sri] shows the results for three different
-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
-confidence that, at least in compression(sp?) in 2D, our Drucker-Prager
-implementation gives the correct results.
+`Figure 2`_ shows the results for three different 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 3`_ shows a plot of the numerical vs. analytic
+results for several different angles for medium resolution.
+This gives us confidence that, at least in compression in 2D,
+our Drucker-Prager implementation gives the correct results.
+
+.. fig:Mohr-Coulomb-sri
.. figure:: images/Mohr_coulomb_resolutions.png
+ :align: center
+ :width: 80%
- Figure [fig:Mohr-Coulomb-sri]
-
+ _`Figure 2`:
Strain rate invariant for the shortening experiment where
[;\\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.
+ Any differences between the medium and high resolution runs
+ are swamped by uncertainties in determining the overall
+ angle of faulting.
+
+.. fig:Mohr-Coulomb-comparison
.. figure:: images/mohr_coulomb_angles.png
+ :align: center
- Figure [fig:Mohr-Coulomb-comparison]
-
+ _`Figure 3`:
Numerical vs. analytic results for fault angles as a function of
internal angle of friction.
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