3. Modeling A#
3.1. Characteristics of modeling#
The characteristics used and the mesh are those deduced from the data in [§1]. We use 2 calculation frequencies corresponding respectively to a frequency in the low range and a frequency in the high range for respective values of the adimensional frequency parameter \(a0=\mathrm{\omega }R/\mathit{Vs}\) of \(0.4\) and \(1.2\), i.e. \(8.5\) and \(25.5\mathit{Hz}\) if we take a value of \(6m\) for \(R\) equal to the half-width of the foundation.
In CALC_MISS we use the automated calculation mode of the parameters of MISS3D.
3.2. Characteristics of the mesh#
The mesh provided to*Code_Aster* contains QUAD4 meshes to model the rectangular foundation modeled by DST elements. It is important to have oriented the surface elements of the foundation with normal entering the ground. A total of 108 surface meshes are obtained for the foundation with a mesh size of about \(2m\) horizontally and \(4m\) vertically (we have unrefined vertically to reduce the calculation time but the recommended value is \(2m\)).
The mesh also contains 23040 HEXA8 cells to model the volume of homogeneous soil surrounding the foundation with massive 3D elements. The outer surface of this soil volume is discretized by 3888 QUAD4 cells affected by 3D_ ABSO elements to represent the absorbent border condition.
3.3. Tested sizes and results#
The inverse transfer functions of the impedances obtained by the chaining between Code_Aster and MISS3D are compared to those obtained by another calculation method, using an exclusive modeling by Code_Aster, where the condition of an infinite medium is represented by absorbent elements assigned to the boundaries of the homogeneous soil volume surrounding the foundation.
The values of the transfer functions below are tested for each of the 6 components with 2 frequency values corresponding respectively to a high range and a low range and to values of \(\mathit{a0}\) close to \(0.4\) and \(1.2\) respectively.
Reference calculation (Code_Aster only) :
Identification |
Reference Value |
Reference Type |
Tolerance |
\(\mathit{U11}\) (\(8.5\mathit{Hz}\)) |
“NON_REGRESSION” |
||
\(\mathit{U11}\) (\(25.5\mathit{Hz}\)) |
“NON_REGRESSION” |
||
\(\mathit{U22}\) (\(8.5\mathit{Hz}\)) |
“NON_REGRESSION” |
||
\(\mathit{U22}\) (\(25.5\mathit{Hz}\)) |
“NON_REGRESSION” |
||
\(\mathit{U33}\) (\(8.5\mathit{Hz}\)) |
“NON_REGRESSION” |
||
\(\mathit{U33}\) (\(25.5\mathit{Hz}\)) |
“NON_REGRESSION” |
||
\(\mathit{U44}\) (\(8.5\mathit{Hz}\)) |
“NON_REGRESSION” |
||
\(\mathit{U44}\) (\(25.5\mathit{Hz}\)) |
“NON_REGRESSION” |
||
\(\mathit{U55}\) (\(8.5\mathit{Hz}\)) |
“NON_REGRESSION” |
||
\(\mathit{U55}\) (\(25.5\mathit{Hz}\)) |
“NON_REGRESSION” |
||
\(\mathit{U66}\) (\(8.5\mathit{Hz}\)) |
“NON_REGRESSION” |
||
\(\mathit{U66}\) (\(25.5\mathit{Hz}\)) |
“NON_REGRESSION” |
Calculation***Code_Aster* **- MISS3D :
Comparison with Code_Aster calculation only
Identification |
Reference Value |
Reference Type |
Tolerance |
\(U11b\) (\(8.5\mathit{Hz}\)) |
4.405562E-06-3.103320E-06J |
“AUTRE_ASTER” |
7% |
\(U11b\) (\(25.5\mathit{Hz}\)) |
9.786317E-07-2.972870E-06J |
“AUTRE_ASTER” |
11% |
\(U22b\) (\(8.5\mathit{Hz}\)) |
4.174931E-06-2.920876E-06J |
“AUTRE_ASTER” |
9% |
\(U22b\) (\(25.5\mathit{Hz}\)) |
1.042063E-06-2.641335E-06J |
“AUTRE_ASTER” |
18% |
\(U33b\) (\(8.5\mathit{Hz}\)) |
3.670733E-06-3.539087E-06J |
“AUTRE_ASTER” |
21% |
\(U33b\) (\(25.5\mathit{Hz}\)) |
5.687622E-07-2.420604E-06J |
“AUTRE_ASTER” |
18% |
\(U44b\) (\(8.5\mathit{Hz}\)) |
6.997733E-08-1.411643E-08J |
“AUTRE_ASTER” |
35% |
\(U44b\) (\(25.5\mathit{Hz}\)) |
4.736895E-08-4.387128E-08J |
“AUTRE_ASTER” |
35% |
\(U55b\) (\(8.5\mathit{Hz}\)) |
3.938570E-08-1.105361E-08J |
“AUTRE_ASTER” |
26% |
\(U55b\) (\(25.5\mathit{Hz}\)) |
1.757004E-08-2.782686E-08J |
“AUTRE_ASTER” |
21% |
\(U66b\) (\(8.5\mathit{Hz}\)) |
3.058106E-08-6.790613E-09J |
“AUTRE_ASTER” |
7% |
\(U66b\) (\(25.5\mathit{Hz}\)) |
1.627885E-08-2.253177E-08J |
“AUTRE_ASTER” |
11% |
Comparison with the bibliographic reference
Identification |
Reference Value |
Reference Type |
Tolerance |
\(U11b\) (\(25.5\mathit{Hz}\)) |
1.2679e-06-3.03637e-06j |
“SOURCE_EXTERNE” |
0.7% |
\(U22b\) (\(8.5\mathit{Hz}\)) |
4.37312e-06-3.25212e-06j |
“SOURCE_EXTERNE” |
2% |
\(U22b\) (\(25.5\mathit{Hz}\)) |
1.42056e-06-2.83346e-06j |
“SOURCE_EXTERNE” |
2% |
\(U33b\) (\(8.5\mathit{Hz}\)) |
4.3762e-06-4.24318e-06j |
“SOURCE_EXTERNE” |
2% |
\(U33b\) (\(25.5\mathit{Hz}\)) |
6.76519e-07-2.78195e-06j |
“SOURCE_EXTERNE” |
2% |
\(U44b\) (\(8.5\mathit{Hz}\)) |
8.69847e-08-2.13947e-08j |
“SOURCE_EXTERNE” |
7% |
\(U44b\) (\(25.5\mathit{Hz}\)) |
6.02497e-08-5.34563e-08j |
“SOURCE_EXTERNE” |
7% |
\(U55b\) (\(8.5\mathit{Hz}\)) |
4.75128e-08-1.46293e-08j |
“SOURCE_EXTERNE” |
4% |
\(U55b\) (\(25.5\mathit{Hz}\)) |
2.08904e-08-3.20829e-08j |
“SOURCE_EXTERNE” |
4% |
\(U66b\) (\(8.5\mathit{Hz}\)) |
3.23981e-08-7.32988e-09j |
“SOURCE_EXTERNE” |
0.8% |
\(U66b\) (\(25.5\mathit{Hz}\)) |
1.91983e-08-2.22916e-08j |
“SOURCE_EXTERNE” |
0.8% |