6. D modeling#
6.1. Characteristics of modeling#
The characteristics used and the mesh are those deduced from the data in paragraph 1. The mesh is the same as for modeling A.
As for modeling B, the temporal response was calculated at point \(N11\) and the corresponding response spectrum was determined. Since the transfer function is equal to 1 for the case without spatial variability, the temporal response is equal to the input signal.
If spatial variability is taken into account, then the response is modified.
This modeling is used to test the “QUELCONQUE” interface option of the MODE_INTERF keyword with any foundation modes different from rigid body modes. Its results will be compared to those of modeling B.
6.2. Characteristics of the mesh#
The characteristics are those of modeling A.
6.3. Boundary conditions for modeling#
For the representation of the foundation movement, instead of rigid body translation modes, a base of any 30 modes obtained as natural modes, without blocking conditions, on a spring mat established from static ground impedances for the ground defined in §1.2 is used.
We therefore take as values of global rigidities to be distributed under the foundation with option RIGI_PARASOL of AFFE_CARA_ELEM:
\(KX=KY=6.36E10\), \(KZ=8.02E10\), \(KRX=KRY=2.07E13\), \(KRZ=2.70E13\)
6.4. Tested sizes and results#
6.4.1. Mita&Luco consistency function#
We check that, for \(\alpha =0.0\), the acceleration response is equal to the accelerogram at the input of the calculation (we recall that the transfer function is equal to 1 and that the function is rigid for this case study). The answer \(q(t)\) is determined in “DX” at the point \(N11\) for an excitation \(a(t)\) in “DX”. We treat the case where the transfer function is calculated for all the points (discretization of the accelerogram) and the case where the user enters FREQ_PAS, FREQ_FIN. In the latter case, DYNA_ISS_VARI interpolates calculated values to determine the temporal response due to the excitation by the accelerogram.
As in 4,3.1, we check that the oscillator response spectrum (SRO) of the calculated acceleration response is equal to SRO of the accelerogram as input.
test type |
frequency (\(Hz\)) |
reference SRO (\(g\)) |
tolerance (%) |
reference () |
ANALYTIQUE |
10.0 |
0.6573 |
0.1 |
|
ANALYTIQUE |
30.0 |
0.2970 |
0.2 |
For the case with spatial variability, values \(\alpha =0.7,{V}_{s}=200m/s\) were chosen. We consider a temporal seismic excitation in the “DX” direction given by an accelerogram corresponding to spectrum EUR for a rocky site (cf., red curve in the figure in §4.3.1). There is no reference (analytical) solution for this case. Also, we do a NON_REGRESSION test for the SRO obtained with spatial variability.
We also do a AUTRE_ASTER test with respect to the results of B modeling.
We’re testing two cases.
FREQ_FIN is t equal to the cutoff frequency:
test type |
frequency (Hz) |
reference SRO (g) |
tolerance (%) |
tolerance (%) |
NON_REGRESSION |
10.0 |
0.5418 |
0.0001 |
|
NON_REGRESSION |
30.0 |
0.2348 |
0.0002 |
|
AUTRE_ASTER |
10.0 |
0.535 |
1.3E0 |
|
AUTRE_ASTER |
30.0 |
0.2386 |
1.6E0 |
FREQ_FINest less than the cutoff frequency (\(35Hz\) instead of \(50Hz\)) and we complete by zero:
test type |
frequency (Hz) |
reference SRO (g) |
tolerance (%) |
tolerance (%) |
NON_REGRESSION |
10.0 |
0.5418 |
0.0002 |
|
NON_REGRESSION |
30.0 |
0.2333 |
0.0001 |
|
AUTRE_ASTER |
10.0 |
0.535 |
1.2E0 |
|
AUTRE_ASTER |
30.0 |
0.2386 |
2.2E0 |
6.4.2. Abrahamson coherence function#
We consider a temporal seismic excitation in the “DX” direction given by an accelerogram corresponding to spectrum EUR for a rocky site (cf., red curve in the figure in §4.3.1). We do a NON_REGRESSION test for the SRO obtained with spatial variability. We also do a AUTRE_ASTER test with respect to the results of modeling B:
test type |
frequency (Hz) |
reference SRO (g) |
tolerance (%) |
||
NON_REGRESSION |
10.0 |
0.5747 |
0.5747 |
0.0001 |
|
NON_REGRESSION |
30.0 |
0.23877 |
0.0001 |
||
AUTRE_ASTER |
10.0 |
0.5723 |
0.4 |
||
AUTRE_ASTER |
30.0 |
0.23903 |
0.1 |