1. Reference problem#
1.1. Geometry#
Here we are considering a cube of dimension \(\mathrm{1m}\times \mathrm{1m}\times \mathrm{1m}\).
Coordinates of the points (in \(m\)):
\(A\) |
|
|
|
||
\(x\) |
0 |
1 |
1 |
0.5 |
1 |
\(y\) |
0 |
0 |
0 |
0.5 |
1 |
\(z\) |
0 |
0 |
0 |
0.5 |
1 |
1.2. Material properties#
Parameters of the law of elastic behavior:
\(E=4500\mathrm{MPa}\) |
\(\nu =0.3\) |
Parameters of the modified Hoek-Brown law:
\({\gamma }^{\mathrm{rup}}=0.005\) |
\({\gamma }^{\mathrm{res}}=0.017\) |
\({(S{\sigma }_{c}^{2})}^{\mathrm{end}}=225{\mathrm{MPa}}^{2}\) |
\({(S{\sigma }_{c}^{2})}^{\mathrm{rup}}=482.5675{\mathrm{MPa}}^{2}\) |
\({(m{\sigma }_{c})}^{\mathrm{end}}=13.5\mathrm{MPa}\) |
\({(m{\sigma }_{c})}^{\mathrm{rup}}=83.75\mathrm{MPa}\) |
\(\beta =3\mathrm{MPa}\) |
\({\phi }^{\mathrm{end}}=15°\) |
\({\phi }^{\mathrm{rup}}=15°\) |
\({\phi }^{\mathrm{res}}=15°\) |
\(\alpha \mathrm{=}3.3\) |
1.3. Initial conditions, limits and loading#
The test is divided into two phases:
++————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————–+ ||First, the sample is brought to a homogeneous state | ++ + || | ++ .. image:: images/Object_17.svg + || :width: 98 | ++ :height: 26 + || | ++ + || | ++ + || | ++. To do this, the corresponding confinement pressure is imposed on the front (\(z\mathrm{=}1\)), right lateral (\(x\mathrm{=}1\)) and upper (\(y\mathrm{=}1\)) faces, while the movements are taken to zero on the rear ( + || | ++ + || .. image:: images/Object_21.svg | ++ :width: 98 + || :height: 26 | ++ + || | ++ + || | ++ + ||) and left lateral faces ( | ++ + || | ++ .. image:: images/Object_22.svg + || :width: 98 | ++ :height: 26 + || | ++ + || | ++ + || | ++) and lower ( + || | ++ + || .. image:: images/Object_23.svg | ++ :width: 98 + || :height: 26 | ++ + || | ++ + || | ++ + ||). | ++————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————–+ ||Once the homogeneous state is obtained, the movements are kept blocked on the rear, left and lower lateral faces and the confinement pressure is always imposed on the front and right lateral faces. A displacement is imposed on the upper face ( | ++ + || | ++ .. image:: images/Object_24.svg + || :width: 98 | ++ :height: 26 + || | ++ + || | ++ + || | ++) in order to obtain a deformation \({\varepsilon }_{\mathit{yy}}\) equal to — 25% from the start of the second phase, by constant deformation increments \(\Delta {\varepsilon }_{\mathit{yy}}\mathrm{=}\mathrm{-}2.5E\mathrm{-}4\). + || | ++————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————–+