5. C modeling#
5.1. Characteristics of modeling#
C modeling is*bidimensional* and*quasistatic*. We use modeling with classical integration (MODELISATION = “HM”). The first difference with A modeling is linked to the transition from 3D_HM modeling to DPLAN_HM modeling. The second difference is due to the use of a secant stiffness matrix to resolve the overall balance of the structure between the internal forces and the external forces applied.
5.2. Characteristics of the mesh#
Each layer is represented by a QUAD8 element. The complete mesh is therefore made up of 11 QUAD8 elements.
5.3. Tested sizes and results#
The settlement is calculated at the top of each layer and compared to given solutions GEFDYN:
Settlement (in millimeters) of layer no. 1
Step number |
GEFDYN |
Tolerance (%) |
2 |
-4.648 |
4.00 |
3 |
-8.391 |
3.00 |
4 |
-11.940 |
2.00 |
5 |
-15.440 |
2.00 |
6 |
-18.980 |
2.00 |
7 |
-22.650 |
2.00 |
8 |
-26.470 |
2.00 |
9 |
-30.490 |
2.00 |
10 |
-34.730 |
2.00 |
Settlement (in millimeters) of layer no. 2
Step number |
GEFDYN |
Tolerance (%) |
3 |
-8.409 |
3.00 |
4 |
-15.720 |
2.00 |
5 |
-22.780 |
2.00 |
6 |
-29.830 |
2.00 |
7 |
-37.030 |
2.00 |
8 |
-44.510 |
2.00 |
9 |
-52.360 |
2.00 |
10 |
-60.610 |
2.00 |
Settlement (in millimeters) of layer no. 3
Step number |
GEFDYN |
Tolerance (%) |
4 |
-11.980 |
2.00 |
5 |
-22.800 |
2.00 |
6 |
-33.410 |
2.00 |
7 |
-44.120 |
2.00 |
8 |
-55.150 |
2.00 |
9 |
-66.650 |
2.00 |
10 |
-78.730 |
2.00 |
Settlement (in millimeters) of layer no. 4
Step number |
GEFDYN |
Tolerance (%) |
5 |
-15.470 |
2.00 |
6 |
-29.840 |
2.00 |
7 |
-44.110 |
2.00 |
8 |
-58.650 |
2.00 |
9 |
-73.690 |
2.00 |
10 |
-89.430 |
2.00 |
Settlement (in millimeters) of layer no. 5
Step number |
GEFDYN |
Tolerance (%) |
6 |
-19.020 |
2.00 |
7 |
-37.050 |
2.00 |
8 |
-55.150 |
2.00 |
9 |
-73.700 |
2.00 |
10 |
-92.980 |
2.00 |
Settlement (in millimeters) of layer No. 6
Step number |
GEFDYN |
Tolerance (%) |
7 |
-22.680 |
2.00 |
8 |
-44.540 |
2.00 |
9 |
-66.650 |
2.00 |
10 |
-89.440 |
2.00 |
Settlement (in millimeters) of layer No. 7
Step number |
GEFDYN |
Tolerance (%) |
8 |
-26.500 |
2.00 |
9 |
-52.380 |
2.00 |
10 |
-78.720 |
2.00 |
Settlement (in millimeters) of layer No. 8
Step number |
GEFDYN |
Tolerance (%) |
9 |
-30.520 |
2.00 |
10 |
-60.630 |
2.00 |
Settlement (in millimeters) of layer No. 9
Step number |
GEFDYN |
Tolerance (%) |
10 |
-34.750 |
2.00 |
The elementary calculation option INDL_ELGA is also tested in non-regression to validate its development in modeling DPLAN_HM. All components are tested on mesh \(\mathrm{M2}\), located at the base of the column, just above the elastic rock.
Step number |
Component INDL_ELGA |
Reference type |
Reference |
Tolerance (absolute) |
10 |
|
|
0.0 |
0.001 |
10 |
|
|
0.0 |
0.001 |
10 |
|
|
0.0 |
0.001 |
10 |
|
|
0.0 |
0.001 |
10 |
|
|
0.0 |
0.001 |
The elementary calculation option PDIL_ELGA is tested in non-regression to validate its development in modeling DPLAN_HM. The A1_ LC2 component is tested on mesh \(\mathrm{M2}\), located at the base of the column, just above the elastic rock.
Step number |
Component INDL_ELGA |
Reference type |
Reference |
Tolerance (absolute) |
|
10 |
A1_ LC2 |
|
0.0 |
0.001 |
5.4. Comments#
The relative error is at most \(\text{4\%}\), which is relatively satisfactory. The results are generally closer to the results from the reference, compared to the A and B models. It can be added that the algorithm used in this modeling to solve the balance of the structure is identical to that of the reference, which may explain these results.