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

_images/Object_1.svg

D

C

1 m

_images/Object_2.svg _images/Object_3.svg _images/Object_4.svg

B

A

Y

1 m

X

_images/1000010A0000271000002710863D401C4058C571.svg

Coordinates of the points (in \(m\)):

\(A\)

\(B\)

\(C\)

\(D\)

\(x\)

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:

  1. First, the sample is brought to a homogeneous state

    _images/Object_17.svg

. For this, the corresponding confinement pressure is imposed on the front faces (

_images/Object_18.svg

), right lateral (

) and higher (

), the water pressures are zero everywhere and the movements are taken zero on the back faces (

), left lateral (

) and lower (

).

  1. 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:

.