3. B modeling#
3.1. Characteristics of modeling#
The modeling is 3D with a hydro-mechanical coupling in a semi-static non-linear fashion.
In loading phase \(1\), the sample is brought to consolidation pressure \({\sigma }_{\mathrm{xx}}^{0}={\sigma }_{\mathrm{yy}}^{0}={\sigma }_{\mathrm{zz}}^{0}={\sigma }_{0}=-200\mathrm{kPa}\). This state of confinement makes it possible to consider the sample as moderately dense sand.
We use Hujeux’s law cyclic.
3.2. Characteristics of the mesh#
Number of knots: \(20\)
Number of meshes and type: 1 HEXA20 and 6 QUAD8.
3.3. 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 \({\varepsilon }_{v}^{p}\) and mobilization factors, and summarized in the following tables:
\(Q\mathrm{=}\sqrt{\frac{1}{2}{\sigma }_{\text{ij}}^{d}\mathrm{:}{\sigma }_{\text{ij}}^{d}}(\mathit{kPa})\)
\({\varepsilon }_{\text{zz}}\) |
Reference type |
GEFDYN (\(\mathit{kPa}\)) |
tolerance (%) |
-1.E-3 |
|
1.015E+2 |
3.0 |
-2.E-3 |
|
1.343E+2 |
2.0 |
-5.E-3 |
|
1.808E+2 |
1.0 |
-1.E-2 |
|
2.139E+2 |
1.0 |
-2.E-2 |
|
2.495E+2 |
1.0 |
\(3\text{.}P\text{'}\mathrm{=}{\sigma }_{\text{ij}}\mathrm{\cdot }{\delta }_{\text{ij}}(\mathit{kPa})\)
\({\varepsilon }_{\text{zz}}\) |
Reference type |
GEFDYN (\(\mathit{kPa}\)) |
tolerance (%) |
-1.E-3 |
|
-5.889E+2 |
1.0 |
-2.E-3 |
|
-5.823E+2 |
1.0 |
-5.E-3 |
|
-5.638E+2 |
1.0 |
-1.E-2 |
|
-5.439E+2 |
1.0 |
-2.E-2 |
|
-5.442E+2 |
1.0 |
\({\varepsilon }_{v}^{p}\mathrm{=}\text{trace}({\varepsilon }^{p})\)
\({\varepsilon }_{\text{zz}}\) |
Reference Type |
GEFDYN |
Tolerance (%) |
-1.E-3 |
|
-1.37E-5 |
8.0 |
-2.E-3 |
|
-2.19E-5 |
6.0 |
-5.E-3 |
|
-4.51E-5 |
3.0 |
-1.E-2 |
|
-7.03E-5 |
2.0 |
-2.E-2 |
|
-7.00E-5 |
2.0 |
\(({r}_{\text{iso}}^{c}+{r}_{\text{ela}}^{s,c})\)
\({\varepsilon }_{\text{zz}}\) |
Reference Type |
GEFDYN |
Tolerance (%) |
-1.E-3 |
|
1.51E-3 |
1.0 |
-2.E-3 |
|
2.40E-3 |
1.0 |
-5.E-3 |
|
4.91E-3 |
1.0 |
-1.E-2 |
|
7.60E-3 |
1.0 |
-2.E-2 |
|
1.16E-3 |
2.0 |
\(({r}_{\text{dev}}^{m}+{r}_{\text{ela}}^{d,m})\)
\({\varepsilon }_{\text{zz}}\) |
Reference Type |
GEFDYN |
Tolerance (%) |
-1.E-3 |
|
0.334 |
3.0 |
-2.E-3 |
|
0.436 |
2.0 |
-5.E-3 |
|
0.583 |
1.0 |
-1.E-2 |
|
0.693 |
1.0 |
-2.E-2 |
|
0.790 |
1.0 |
3.4. notes#
The comparison between Code_Aster and GEFDYN solutions is relatively good, with generally less than \(1\text{\%}\) 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.