3. Modeling A#
3.1. Characteristics of modeling#
AXIS_HH2MS modeling on a single QUAD8 mesh.
Coordinates of mesh nodes (unit):
Knots |
\(X\) |
|
\(\mathit{N1}\) |
0 |
0 |
\(\mathit{N2}\) |
1 |
0 |
\(\mathit{N3}\) |
1 |
1 |
\(\mathit{N4}\) |
0 |
1 |
\(\mathit{N5}\) |
0.5 |
0 |
\(\mathit{N6}\) |
1 |
0.5 |
\(\mathit{N7}\) |
0.5 |
1 |
\(\mathit{N8}\) |
0 |
0.5 |
One second is simulated by 500 steps of time.
3.2. Results#
The Figure 3.2-a shows the evolution of the total stress as a function of the capillary pressure (homogeneous at all points, the post-treatment is here done at node \(\mathit{N3}\)). In the saturated part (\({P}_{c}\mathrm{\le }0\)), the decrease in capillary pressure corresponds to an increase in water pressure and the total stress increases linearly. It can be seen that the slope of the curve is continuous.
The parameters \(A\) and \({\beta }_{m}\) were calculated in such a way as to find an inflation pressure of \(7\mathit{MPa}\). When saturation reaches 1 (or capillary pressure 0), the swelling pressure is given by the following formula:
\(\frac{{P}_{\mathit{gf}}}{A}\mathrm{=}\frac{\sqrt{\pi }}{2\sqrt{{\beta }_{m}}}+\frac{1}{2{\beta }_{m}}\)
We therefore find the classic appearance of the swelling constraint and we check that the curve intersects the y-axis (\({P}_{c}\mathrm{=}0\)) with a value of \(7\mathit{Mpa}\).
Figure 3.2-a swelling test
The figure shows the evolution of capillary pressure as a function of time corresponding to the loading of the problem:
Figure 3.2-b : capillary pressure ( \(\mathit{N3}\) )
3.3. Tested sizes and results#
This test case has no reference value, so we make it a non-regression case.
Tests are carried out on two values:
\(N\) |
Time ( \(s\) ) |
\(\mathit{SIXX}\) Aster |
\(\mathit{N3}\) |
|
|
\(\mathit{N3}\) |
|
|