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Commit f2ff281a authored by wenqing's avatar wenqing
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[web] Added the documentation of the new test of BGRa creep model

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date = "2018-08-10T11:46:45+01:00"
title = "Creep in a rectangle domain with hole under pressure on its top surface"
weight = 171
project = "ThermoMechanics/CreepBGRa/CreepAfterExcavation/CreepAfterExcavation.prj"
author = "Wenqing Wang"
[menu]
[menu.benchmarks]
parent = "thermo-mechanics"
+++
{{< data-link >}}
-------------------------------------------------------------------------
Following up the benchmark about the BGRa creep model described on the
[this page](https://www.opengeosys.org/docs/benchmarks/creepbgra/creepbrga/),
this example represents the creep in the near field of
drift in the deep rock salt after excavation. The domain and the
geometry are shown in the following figure:
<figure>
<img src="../mesh.png" alt="Mesh and Geometry" id="fig_6"
style="height:400px;width:490px;">
<figcaption>Mesh and Geometry.</figcaption>
</figure>
The domain has two material groups, which are highlighted by different
colors. The material group that is in the
top part of the domain represents a cap rock type, while the other
material group is for rock salt. The material properties of the rocks are given in the following table:
---------------------- ---------- ----------- ------------
| |Cap rock | Rock salt| Unit|
| --- |:---------:| -----:|----:|
|Density | 2000 | 2170 | kg/m$^{3}$|
|Young’s Modulus | 7.0 | 7.65 | GPa |
|Poisson ratio | 0.3 | 2.7 | - |
|Thermal conductivity | 5 | 5 | W/(mK) |
---------------------- ---------- ----------- ------------
The parameters of the BGRa creep model are $A=0.18\, \mbox{d}^{-1}$,
$m=5$, $Q=54 \mbox{ kJ/mol}$.
The width
and the height of of the domain are 300 m and 340 m, respectively. The
height of the cap rock portion is 40 m. The drift to be excavated has a
radius of 50 m.
Here we consider the creep of the rock after excavation. Therefore, we
assume a steady state of stress and temperature of excavation at the
beginning of the current simulation. For this assumption, the boundary
conditions are given as:
- top boundary: $\tau_x = \sigma_x=0$, $\tau_y=\sigma_y=70$ MPa,
$T=310$ K.
- two lateral boundaries: normal displacement is fixed, and no heat
flux.
- bottom boundary: normal displacement is fixed, and $T=320$ K.
- circle of drift surface: traction free
(${ \mathbf\sigma}\cdot \mathbf n = 0$), and $T=300$ K as excavation
conditions.
The boundary conditions of the mechanical process lead to a distinct
stress field after excavation. Besides, heat capacity is neglected in
order to pose a steady state temperature field after excavation. The
initial stresses are zero and the initial temperature is linearly
distributed from top to bottom with the boundary values of temperature.
The time step sizes of the simulation are: One step of 0.001 day, 10 steps of 0.1 day, and the
remaining steps of 1 day.
The following three figures are plotted by using the results of the simulation of 1000 days creep.
The three figures display the distribution of horizontal and vertical stresses at times of
108 days, 409 days and 1000 days, respectively.
In theses three figures,
the left sub-figure show the time variations of horizontal and vertical stresses
at a position just close to the top of the drift, and the
green vertical line in it marks the time of the displayed stress field.
<figure>
<img src="../stress_xx_yy_20.png" alt="Stress distribution at the time of 109 days." id="fig_2">
<figcaption>Stress distribution at the time of 109 days.</figcaption>
</figure>
<figure>
<img src="../stress_xx_yy_50.png" alt="Stress distribution at the time of 409 days." id="fig_3">
<figcaption>Stress distribution at the time of 409 days.</figcaption>
</figure>
<figure>
<img src="../stress_xx_yy_110.png" alt="Stress distribution at the time of 1000 days." id="fig_4">
<figcaption>Stress distribution at the time of 1000 days.</figcaption>
</figure>
The above three figures show that the absolute value of the horizontal stress increase
signification in the areas above and beneath the drift due to the creep,
and the change of the vertical stress is slow compared to that of the
horizontal stress.
The following figure shows the strain distribution at the
end of the simulation time at 1000 days.
<figure>
<img src="../strain.png" alt="Strain distribution at the time of 1000 days." id="fig_5">
<figcaption>Strain distribution at the time of 1000 days.</figcaption>
</figure>
The steady-state temperature distribution is displayed in the following figure
<figure>
<img src="../T.png" alt="Temperature distribution at the time of 1000 days." id="fig_6">
<figcaption>Temperature distribution at the time of 1000 days.</figcaption>
</figure>
## Note:
For the automatic benchmarking, the time duration of creep is reduced to 50 days in order to reduce the run time.
If one wants to test this benchmark for 1000 days' creep, please change the end time in the tag of `<t_end> `
in the project file as
```
<t_end>1000</t_end>
```
\ No newline at end of file
web/content/docs/benchmarks/creep-after-excavation-bgra/T.png

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web/content/docs/benchmarks/creep-after-excavation-bgra/mesh.png

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web/content/docs/benchmarks/creep-after-excavation-bgra/strain.png

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web/content/docs/benchmarks/creep-after-excavation-bgra/stress_xx_yy_110.png

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web/content/docs/benchmarks/creep-after-excavation-bgra/stress_xx_yy_20.png

131 B

web/content/docs/benchmarks/creep-after-excavation-bgra/stress_xx_yy_50.png

131 B

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