1. Reference problem#
1.1. Geometry#
Here we are considering a cube of dimension \(\mathrm{1m}\mathrm{\times }\mathrm{1m}\mathrm{\times }\mathrm{1m}\).
Z
1 m
D
C
1 m
B
A
Y
1 m
X
Coordinates of the points (in \(m\)):
\(A\) |
|
|
|
||
\(x\) |
0 |
0 |
0 |
0.5 |
1 |
\(y\) |
0 |
1 |
1 |
0.5 |
1 |
\(z\) |
0 |
0 |
0 |
0.5 |
1 |
1.2. Material properties#
Parameters of the law of elastic behavior:
\(E\mathrm{=}4500\mathit{MPa}\) |
\(\nu \mathrm{=}0.3\) |
Parameters of the modified Hoek-Brown law:
\({\gamma }^{\mathit{rup}}\mathrm{=}0.005\) |
\({\gamma }^{\mathit{res}}\mathrm{=}0.017\) |
\({(S{\sigma }_{c}^{2})}^{\mathit{end}}\mathrm{=}225{\mathit{MPa}}^{2}\) |
\({(S{\sigma }_{c}^{2})}^{\mathit{rup}}\mathrm{=}482.5675{\mathit{MPa}}^{2}\) |
\({(m{\sigma }_{c}^{2})}^{\mathit{end}}\mathrm{=}13.5\mathit{MPa}\) |
\({(m{\sigma }_{c}^{2})}^{\mathit{rup}}\mathrm{=}83.75\mathit{MPa}\) |
\(\beta \mathrm{=}3\mathit{MPa}\) |
\({\phi }^{\mathit{rup}}\mathrm{=}15°\) |
\({\phi }^{\mathit{res}}\mathrm{=}30°\) |
\(\alpha \mathrm{=}3.3\) |
1.3. Initial conditions, limits and loading#
The test is divided into two phases:
First, the sample is brought to a homogeneous state
. For this, the corresponding confinement pressure is imposed on the front faces (
), right lateral (
) and higher (
), the water pressures are zero everywhere and the movements are taken zero on the back faces (
), left lateral (
) and lower (
).
Once the homogeneous state is obtained, the movements are kept blocked on the rear, left and lower lateral faces. Hydraulic flows are zero on all sides. A displacement is imposed on the upper side (
) so as to obtain a deformation
equal to — 25% from the start of the second phase, in constant deformation increments
. On the front and right lateral faces, limit conditions under total stress are imposed:
.