2. Modeling A#
2.1. Characteristics of modeling#
The modeling is \(\mathrm{3D}\) with a hydro-mechanical coupling in quasistatic non-linear mode.
In loading phase \(1\), the sample is brought to consolidation pressure \({\sigma }_{\mathit{xx}}^{0}={\sigma }_{\mathit{yy}}^{0}={\sigma }_{\mathit{zz}}^{0}={\sigma }_{0}=-50\mathit{kPa}\). This state of confinement makes it possible to consider the sample as dense sand.
We use Hujeux’s law cyclic.
2.2. Characteristics of the mesh#
Number of knots: \(20\)
Number of meshes and type: 1 \(\mathit{HEXA20}\) and 6 \(\mathit{QUAD8}\).
2.3. Tested sizes and results#
The solutions are calculated at point \(C\) and compared to references GEFDYN. They are given in terms of isotropic pressure, plastic volume deformation \({\epsilon }_{v}^{p}\) and mobilization factors, and summarized in the following tables:
\(Q=\sqrt{\frac{1}{2}{\sigma }_{\text{ij}}^{d}\mathrm{:}{\sigma }_{\text{ij}}^{d}}\left(\mathit{kPa}\right)\)
\({\epsilon }_{\text{zz}}\) |
Reference type |
GEFDYN (\(\mathit{kPa}\)) |
tolerance (%) |
-1.E-3 |
|
3.154E+1 |
3.0 |
-2.E-3 |
|
4.013E+1 |
2.0 |
-5.E-3 |
|
5.194E+1 |
1.0 |
-1.E-2 |
|
6.829E+1 |
1.0 |
-2.E-2 |
|
1.032E+2 |
1.0 |
\(3\text{.}P\text{'}={\sigma }_{\text{ij}}\cdot {\delta }_{\text{ij}}\left(\mathit{kPa}\right)\)
\({\epsilon }_{\text{zz}}\) |
Reference type |
GEFDYN (\(\mathit{kPa}\)) |
tolerance (%) |
-1.E-3 |
|
-1.389E+2 |
1.0 |
-2.E-3 |
|
-1.338E+2 |
1.0 |
-5.E-3 |
|
-1.250E+2 |
1.0 |
-1.E-2 |
|
-1.368E+2 |
1.0 |
-2.E-2 |
|
-1.860E+2 |
1.0 |
\({\epsilon }_{v}^{p}=\text{trace}\left({\epsilon }^{p}\right)\)
\({\epsilon }_{\text{zz}}\) |
Reference type |
GEFDYN |
tolerance (%) |
-1.E-3 |
|
-2.42E-5 |
6.0 |
-2.E-3 |
|
-3.55E-5 |
4.0 |
-5.E-3 |
|
-5.56E-5 |
3.0 |
-1.E-2 |
|
-2.88E-5 |
5.0 |
-2.E-2 |
|
7.437E-5 |
5.0 |
\(\left({r}_{\text{iso}}^{m}+{r}_{\text{ela}}^{s,m}\right)\)
\({\epsilon }_{\text{zz}}\) |
Reference type |
GEFDYN |
tolerance (%) |
-1.E-3 |
|
0.02 |
1.0 |
-2.E-2 |
|
0.0248 |
1.0 |
\(\left({r}_{\text{iso}}^{c}+{r}_{\text{ela}}^{s,c}\right)\)
\({\epsilon }_{\text{zz}}\) |
Reference type |
GEFDYN |
tolerance (%) |
-1.E-3 |
|
1.49E-3 |
2.0 |
-2.E-3 |
|
2.18E-3 |
2.0 |
-5.E-3 |
|
3.36E-3 |
2.0 |
-1.E-2 |
|
1.68E-3 |
3.0 |
\(\left({r}_{\text{dev}}^{m}+{r}_{\text{ela}}^{d,m}\right)\)
\({\epsilon }_{\text{zz}}\) |
Reference type |
GEFDYN |
tolerance (%) |
-1.E-3 |
|
0.353 |
3.0 |
-2.E-3 |
|
0.451 |
2.0 |
-5.E-3 |
|
0.593 |
1.0 |
-1.E-2 |
|
0.699 |
1.0 |
-2.E-2 |
|
0.794 |
1.0 |
2.4. notes#
The comparison between Code_Aster and GEFDYN solutions is relatively good, with generally fewer \(1\text{\%}\) errors. Relative errors greater than \(1\text{\%}\) appear for levels of test values that are relatively low and close to the numerical precision applied during the calculation.