9. Existing case tests and studies#

9.1. Code_Aster test cases#

9.1.1. Time patterns#

Mean acceleration diagram (§ 2.2 )

  • SDND102B and SDND102C - Seismic response of a multi-supported nonlinear mass-spring system.

  • SDNL130 - Seismic response of a reinforced concrete beam (rectangular section) with non-linear behavior.

Scheme HHT * (§ 2.2 )

  • SDNL111C - Impact of two beams using DYNA_NON_LINE.

Schemes DIFF_CENT and TCHAMWA * (§ 2.2 )

  • SDND102 - Seismic response of a multi-supported nonlinear mass-spring system.

9.1.2. Modelizations and associated behavior models#

Massive 3D + ENDO_ISOT_BETON

  • SSNV149 - ENDO_ISOT_BETON test.

Massive 3D + ENDO_ORTH_BETON

  • SSNV176 - Identification of law ENDO_ORTH_BETON.

  • SSNV177 - William’s test.

Multi-layer shells + ENDO_ISOT_BETON

  • SSNS106 - Flat reinforced concrete plate under cyclic loading (multilayer shell modeling is used to identify the parameters of the GLRC_DM model).

  • SSNS108 — Simulation of an SAFE test.

Multi-layer shells + ENDO_ORTH_BETON

No tests available.

Multifiber beams + MAZARS_UNIL

Main test cases for validating modeling POU_D_EM and POU_D_TGM for static and dynamic reinforced concrete beams:

  • SSLL111 - Static response of a reinforced concrete beam (T-section) with linear behavior

  • SDLL130 - Seismic response of a reinforced concrete beam (rectangular section) with linear behavior.

  • SSNL119 - Static response of a reinforced concrete beam (rectangular section) with non-linear behavior.

  • SDNL130 - Seismic response of a reinforced concrete beam (rectangular section) with non-linear behavior.

Behavioral model validation test case MAZARS_UNIL:

  • SSNL120 - Cyclic response of concrete behavior laws in 1D.

Other simple modeling validation test cases POU_D_EM:

  • SSLL102J - Embedded beam subjected to unitary forces.

  • SSNL106G and SSNL106H - Elastoplastic beam in pure tension and flex.

Global plates and shells + GLRC_DM or DHRC

Main test cases for the validation of modeling DKTG and model GLRC_DM for statically reinforced concrete plates:

  • SSNS106A - Flat reinforced concrete plate under cyclic traction/compression loading.

  • SSNS106B - Flat reinforced concrete plate under cyclic flexural loading.

  • SSNS106C - Flat reinforced concrete plate under cyclic loading of traction/compression + flexure.

  • SSNS106D - Flat reinforced concrete plate under cyclic shear loading in the plane.

  • SSNS106E - Flat reinforced concrete plate under cyclic loading of flexure + shear in the plane.

  • SSNS106H - Flat reinforced concrete plate under cyclic loading of traction/compression + flexure: high level of loading.

  • SSNS106I - Flat reinforced concrete plate under cyclic flexural loading: high loading level.

  • SSNS106J - Flat reinforced concrete plate under cyclic loading of traction/compression + flexure: high level of loading.

  • SSNS106L - Flat reinforced concrete plate under cyclic shear loading in the plane: high loading level.

  • SSNS106M - Flat reinforced concrete plate under cyclic loading of flexure + shear in the plane: high level of loading.

  • SSNS106N - Flat reinforced concrete plate under cyclic loading of alternating anticlastic flexure: high level of loading.

  • SSNS106O - Flat reinforced concrete plate under thermomechanical loading.

Main test cases for the validation of modeling DKTG and model GLRC_DM + plasticity for statically reinforced concrete plates:

  • SSNS106F - Flat reinforced concrete plate under cyclic traction/compression loading in the plane. Model GLRC_DM + plasticity.

  • SSNS106G - Flat reinforced concrete plate under cyclic shear loading in the plane. Model GLRC_DM + plasticity.

9.1.3. Loading#

Mono-support with the use of CALC_CHAR_SEISME (§ 5.4.1 )

  • SDNL113A - Lyre-shaped pipe (ELSA) under seismic loading.

  • SDNL130 - Seismic response of a reinforced concrete beam (rectangular section) with non-linear behavior.

Multi-support with the use of DDL_IMPO (§ 5.4.2 )

  • SDNL131 - Calculation of an elastoplastic pipe line under earthquake.

9.1.4. Rayleigh damping#

For the use of Rayleigh damping (§ 5.5), reference may be made, among others, to:

  • SDLL113B - Transient dynamic substructuring: simple tension beam.

  • SDNL130 - Seismic response of a reinforced concrete beam (rectangular section) with non-linear behavior.

9.1.5. Post-treatment#

Calculating spectra (SPEC_OSCI, § 8.1.2 )

  • FORMA12C — TP for seismic analysis of a pipe line with DYNA_TRAN_MODAL and COMB_SISM_MODAL.

Calculation of damaged natural frequencies (MODE_VIBR, § 8.1.3 )

  • SDNV106 — Eigenvalue analysis in DYNA_NON_LINE (stability and vibration modes).

Calculation of stresses in the thickness of a multilayer shell (SIGM_ELNO, § 8.2.3 )

  • SSLS115 - Composite square plate under uniform pressure.

  • SSLS118 - Square plate placed under sinusoidal pressure.

Calculation of the stresses in a fiber of a multifiber beam (TEST_RESU or RECU_FONCTION with SOUS_POINT, § 8.2.4 )

  • SSNL120 - Cyclical response of the law of concrete behavior (TEST_RESU).

  • SSNL127E - Tensile test with model CORR_ACIER (RECU_FONCTION).

9.2. Examples of studies carried out#

9.2.1. Type P4 floor#

Essay Description [2]

Tests were carried out at CEA/EMSI (Saclay) in order to characterize the non-linear behavior of the floors of the BAS -BL 1300 MWe building subjected to a vertical earthquake. The designed model was sized so as to be representative of a real floor. The tests were carried out on the Azalée vibrating table at CEA in Saclay. The experimental program consists of 9*runs* of increasing acceleration levels. The nonlinear flexural behavior of the main slab is studied.

Modeling made [25] , [26]

We adopt a multi-layer DKT plate modeling for concrete and a GRILLE model for reinforcement reinforcements. Model ENDO_ISOT_BETON is used in plane constraints using the De Borst approach. Starting from the static solution under its own weight, the seismic calculations are carried out one after the other. The final state of the previous calculation serves as the initial state for the next calculation. The damage suffered by the reinforced concrete slab is analyzed for the acceleration levels achieved.

Comparison with the experimental results shows that the modeling carried out makes it possible to correctly represent the non-linear behavior of the slab, in particular the state of cracking at the end of the stresses. The comparison of the temporal responses of vertical displacements at the center of the slab is very satisfactory. The residual deflection of the cracked slab under its own weight at the end of the highest loads studied is well determined by calculation.

9.2.2. Shear sails SAFE — T5#

Essay Description [27]

Program SAFE (Weakly Slender Reinforced Structures, CCR - ISPRA, 1998) concerns a series of 13 pseudo-dynamic tests on shear walls. Unlike a dynamic test on a vibrating table, the pseudo-dynamic method is a hybrid numeric/experimental method that combines the calculation of the displacement of the structure (here a degree of freedom of horizontal translation) and the measurement of the force used by a control system to impose this displacement. The differences between each series of tests are essentially related to the proportion of wall reinforcement, to the initial frequency of the test (from which the mass at the head of the veil to be applied is determined) and to the average vertical load that one seeks to maintain constant during the test. Each series generally comprises at least 3 tests, carried out by varying the intensity of the reference accelerogram.

Modelings made [11] , [23] , [24]

Two modeling approaches were carried out: 3D representation by volume finite elements (HEXA), and multilayer shells (DKT). 3 studies were carried out: monotonic statics (push-over), alternating statics and transient dynamics (DYNA_NON_LINE).

The study with local modeling (concrete represented using massive elements) shows that enormous numerical difficulties are rapidly encountered both in statics and in non-linear dynamics. The behavior models implemented are not very robust for this type of problem.

Global modeling makes it possible to represent in a satisfactory manner the behavior of the veil for the lowest level of stress (push-over statics, alternating statics, seismic dynamics). We do not encounter numerical difficulties. Model GLRC_DM makes it possible to provide the static envelope for the experimental cycles (push-over). In dynamics, the comparison of the temporal responses of movements at the head of the sail is very satisfactory. However, irreversible deformations are not modelled in this study. This is why we are currently continuing this study with model GLRC_DM coupled with membrane elastoplasticity.

9.2.3. Model CAMUS 2000#

Essay Description [4]

Model CAMUS 2000 is a 1/3 scale structure composed of two walls and five reinforced concrete floors. The base of the structure is very strongly reinforced in order to ensure anchoring to the vibrating table. The total height of the model is \(\mathrm{5,10}m\). Lateral reinforcement systems are added to the structure in order to increase its strength. Additional masses are placed on the floors in order to represent the stress state required at the foot of the structure. The total mass of the model is 36 tons. The test program is composed of 3 seismic runs of increasing levels of excitement. The loading is bi-directional horizontal.

Models made [4]

The calculations were carried out using multi-fiber beam modeling (POU_D_EM) and the LABORD_1Dpour concrete behavior model.

The results obtained by the calculation in terms of overall quantities (displacements, generalized efforts,…) are relatively close to those obtained experimentally. The comparison of the moments of bending in the plane for the first stage of the right wall and for the various load levels shows that there is a good agreement between the calculation and the test. The Code_Aster multifiber beam modeling implemented is adapted to simulate this type of simple structure under seismic loading.