1. Reference problem#

1.1. Geometry#

_images/Object_1.svg

Point coordinates (in meters):

\(A\)

\(B\)

\(C\)

\(x\)

0.5

\(y\)

0.5

\(z\)

0.5

1.2. Property of materials#

\(E\mathrm{=}\mathrm{22,4}{10}^{3}\mathit{kPa}\)

\(\nu \mathrm{=}\mathrm{0,3}\)

Biot coefficient \(b\mathrm{=}1\)

Water is supposed to be incompressible: \(\text{UN\_SUR\_K}\mathrm{=}0\)

Settings CJS1: \(\beta \mathrm{=}\mathrm{-}\mathrm{0,03}\)

\(\gamma \mathrm{=}\mathrm{0,82}\)

\({R}_{m}\mathrm{=}\mathrm{0,289}\)

\({P}_{a}\mathrm{=}\mathrm{-}100\mathit{kPa}\)

1.3. Initial conditions, boundary conditions, and loading#

1.3.1. Pure mechanical modeling#

Phase 1:

The sample is brought to a homogeneous state:

_images/Object_2.svg

, by imposing the corresponding confinement pressure on the front, right lateral and upper faces. The movements are blocked on the back sides (

_images/Object_3.svg

), left lateral (

_images/Object_4.svg

) and lower (

_images/Object_5.svg

).

Phase 2:

We keep the movements blocked on the rear faces (

_images/Object_6.svg

), left lateral (

_images/Object_7.svg

) and lower (

_images/Object_8.svg

). An imposed displacement is applied on the upper face:

_images/Object_9.svg

, so as to obtain a deformation

_images/Object_10.svg

(counted from the start of phase 2). On the front and right lateral faces, the displacements are respectively imposed.

_images/Object_11.svg

and

_images/Object_12.svg

, so as to have zero volume deformation for the sample, that is to say finally that we impose

_images/Object_13.svg

. This is the way to reproduce the behavior of the solid phase during an undrained triaxial test.

1.3.2. Modeling coupled with hydraulics#

Phase 1:

The sample is brought to a homogeneous state of effective constraints:

_images/Object_14.svg

, by imposing the corresponding total pressure on the front, right lateral and upper faces and by imposing zero water pressures everywhere. The movements are blocked on the back sides (

_images/Object_15.svg

), left lateral (

_images/Object_16.svg

) and lower (

_images/Object_17.svg

).

Phase 2:

We keep the movements blocked on the rear faces (

_images/Object_18.svg

), left lateral (

_images/Object_19.svg

) and lower (

_images/Object_20.svg

).

On all sides, hydraulic flows are zero.

An imposed displacement is applied to the upper face in order to obtain a deformation.

_images/Object_21.svg

(counted from the start of phase 2). On the front and right lateral faces, limit conditions under total stress are imposed:

_images/Object_22.svg