Analysis of reinforced concrete shells with transverse shear forces

This research investigates the simultaneous effect of in-plane and transverse loads in reinforced concrete shells. The infinitesimal shell element is divided into layers (with triaxial behavior) that are analyzed according to the smeared rotating crack approach. The set of internals forces includes the derivatives of the in-plane components. The corresponding generalized strains are determined using an extension of the equivalent section method, valid for shells. The formulation yields through-the-thickness distributions of stresses and strains and the spatial orientation of the concrete struts. Although some simplifications are necessary to establish a practical first-order approximation, higher-order solutions could be developed. Despite the fact that constitutive matrices are not symmetric, because of the tension-softening formulation, the equilibrium and compatibility conditions are satisfied, the stiffness derivatives are explicitly calculated and the algorithms show good convergence. The formulation predicts results that agree with experimental data obtained by other researchers. Although comparative analysis with additional experimental data is still necessary, the proposed theory provides a promising solution for the design of reinforced concrete shells

Modelling strong seismic ground motion: three-dimensional loading path versus wavefield polarization

Seismic waves due to strong earthquakes propagating in surficial soil layers may both reduce soil stiffness and increase the energy dissipation into the soil. To investigate seismic wave amplification in such cases, past studies have been devoted to one-directional shear wave propagation in a soil column (1D-propagation) considering one motion component only (1C-polarization). Three independent purely 1C computations may be performed ('1D-1C' approach) and directly superimposed in the case of weak motions (linear behaviour). This research aims at studying local site effects by considering seismic wave propagation in a 1-D soil profile accounting for the influence of the 3-D loading path and non-linear hysteretic behaviour of the soil. In the proposed '1D-3C' approach, the three components (3C-polarization) of the incident wave are simultaneously propagated into a horizontal multilayered soil. A 3-D non-linear constitutive relation for the soil is implemented in the framework of the Finite Element Method in the time domain. The complex rheology of soils is modelled by mean of a multisurface cyclic plasticity model of the Masing-Prandtl-Ishlinskii-Iwan type. The great advantage of this choice is that the only data needed to describe the model is the modulus reduction curve. A parametric study is carried out to characterize the changes in the seismic motion of the surficial layers due to both incident wavefield properties and soil non-linearities. The numerical simulations show a seismic response depending on several parameters such as polarization of seismic waves, material elastic and dynamic properties, as well as on the impedance contrast between layers and frequency content and oscillatory character of the input motion. The 3-D loading path due to the 3C-polarization leads to multi-axial stress interaction that reduces soil strength and increases non-linear effects. The non-linear behaviour of the soil may have beneficial or detrimental effects on the seismic response at the free surface, depending on the energy dissipation rate. Free surface time histories, stress-strain hysteresis loops and in-depth profiles of octahedral stress and strain are estimated for each soil column. The combination of three separate 1D-1C non-linear analyses is compared to the proposed 1D-3C approach, evidencing the influence of the 3C-polarization and the 3-D loading path on strong seismic motions

Transverse shear and normal stresses in the nonlinear analysis of reinforced shells

This research investigates the simultaneous effect of in-plane and transverse loads in reinforced concrete shells. The infinitesimal shell element is divided into layers with triaxial behavior that are analyzed according to the smeared rotating crack approach. The transverse shear strength of shell elements is associated to an "equivalent" surface, which takes into account the nonlinear material behavior, using traditionally accepted hypotheses for shells. The set of internal forces includes the derivatives of the in-plane components. Although some simplifications are necessary to establish a practical first-order approximation, higher-order solutions could be developed. The whole set of equilibrium, compatibility and constitutive equations are satisfied, the stiffness derivatives are explicitly calculated and the algorithms show good convergence. The formulation yields through-the-thickness distributions of stresses and strains and the spatial orientation of the concrete struts. The formulation satisfactorily predicts the ultimate capacity under different load combinations, agreeing with experimental data obtained by other researchers. Although comparative analysis with additional experimental data is still necessary, the proposed theory provides a promising solution for the design of reinforced concrete shells

Analysis of Nonlinear Soil-Structure Interaction Effects on the response of Three-Dimensional Frame Structures using a One-Direction Three-ComponentWave Propagation Model

In this paper, a model of one-directional propagation of three-component seismic waves in a nonlinear multilayered soil profile is coupled with a multi-story multi-span frame model to consider, in a simple way, the soil-structure interaction modelled in a finite element scheme. Modeling the three-component wave propagation enables the effects of a soil multiaxial stress state to be taken into account. These reduce soil strength and increase nonlinear effects, compared with the axial stress state. The simultaneous propagation of three components allows the prediction of the incident direction of seismic loading at the ground surface and the analysis of the behavior of a frame structure shaken by a three-component earthquake. A parametric study is carried out to characterize the changes in the ground motion due to dynamic features of the structure, for different incident wavefield properties and soil nonlinear effects. A seismic response depending on parameters such as the frequency content of soil and structure and the polarization of seismic waves is observed

Strong Ground Motion in the 2011 Tohoku Earthquake: a 1Directional - 3Component Modeling

Local wave amplification due to strong seismic motions in surficial multilayered soil is influenced by several parameters such as the wavefield polarization and the dynamic properties and impedance contrast between soil layers. The present research aims at investigating seismic motion amplification in the 2011 Tohoku earthquake through a one-directional three-component (1D-3C) wave propagation model. A 3D nonlinear constitutive relation for dry soils under cyclic loading is implemented in a quadratic line finite element model. The soil rheology is modeled by mean of a multi-surface cyclic plasticity model of the Masing-Prandtl-Ishlinskii-Iwan (MPII) type. Its major advantage is that the rheology is characterized by few commonly measured parameters. Ground motions are computed at the surface of soil profiles in the Tohoku area (Japan) by propagating 3C signals recorded at rock outcrops, during the 2011 Tohoku earthquake. Computed surface ground motions are compared to the Tohoku earthquake records at alluvial sites and the reliability of the 1D-3C model is corroborated. The 1D-3C approach is compared with the combination of three separate one-directional analyses of one motion component propagated independently (1D-1C approach). The 3D loading path due to the 3C-polarization leads to multiaxial stress interaction that reduces soil strength and increases nonlinear effects. Time histories and spectral amplitudes, for the Tohoku earthquake, are numerically reproduced. The 1D-3C approach allows the evaluation of various parameters of the 3C motion and 3D stress and strain evolution all over the soil profile.Comment: Bulletin of the Seismological Society of America 103, 2B (2013) 1394-1410. arXiv admin note: substantial text overlap with arXiv:1308.194

Étude de la réponse structurelle d’un bâtiment de grande hauteur à partir d’enregistrements accéléromètriques et de la modélisation par éléments finis

International audienceThe Nice prefecture is equipped by 24 accelerometric sensors, located at different levels, which continuously record the building response. A finite element model of the building is created based in design plans and information about materials provided during the conception project. Such model is used to obtain the natural frequencies of the structure, the modal shapes and the seismic response acceleration time histories. Modal frequencies of the building obtained from the data analysis are used to calibrate the numerical model. The response of the building to earthquakes, in the form of acceleration time histories at different storeys, is evaluated using the finite element model. Signals recorded during the recent Barcelonnette earthquake (April 2014, Mw = 4.9) are used as excitation at the base of the building. The imposition of a single or multiple signals at the base of the structure shows the importance of taking into account the rocking effects in the building response modelling. The numerical results are in agreement, in amplitude and phase, with accelerometric records filtered at different frequency bands.La préfecture de Nice est équipée d’un ensemble de 24 capteurs accélérométriques, répartis sur différents étages, qui enregistrent en continu les vibrations du bâtiment. Un modèle par éléments finis du bâtiment est créé à partir des plans de construction et des données sur les matériaux, issues du projet de dimensionnement d’origine. Ce modèle est utilisé pour obtenir les fréquences propres de vibration de la structure, les déformées modales et la réponse sismique dans le temps. Les fréquences modales du bâtiment obtenues par l’analyse des enregistrements sont utilisées pour calibrer le modèle numérique. La réponse du bâtiment aux séismes, en terme de séries temporelles d’accélération aux étages, est évaluée par le modèle d’éléments finis. Les signaux enregistrés lors du récent séisme de Barcelonnette (avril 2014, Mw = 4.9) sont utilisés comme sollicitations appliquées à la base du bâtiment. L’imposition d’une seule ou plusieurs excitations à la base de la structure mon- tre l’importance de la prise en compte des effets de «rocking» du bâtiment pour mieux comprendre sa réponse aux séismes. Les signaux numériques sont en accord dans différentes bandes de fréquence, en amplitude et en phase, avec les enregistrements

Effet de la pression interstitielle sur la réponse sismique des sols : modélisation numérique 1D-3 Composantes

International audienceDuring strong quakes, the propagation of seismic waves in soil layers involves nonlinearities changing with the excitation level. A nonlinear hysteretic law is necessary to describe the variations of the stiffness and the energy dissipation during the seismic shaking. Furthermore, the influence of the pore pressure (cyclic mobility and liquefaction) cannot be neglected for saturated soils under strong quakes. Starting from a FEM formulation describing 1D propagation and three-dimensional loading ("1D-3 components approach"), the influence of the water is accounted for through a relation between the pore pressure and the work of the shear stress initially proposed by Iai. This model describes the variations of the pore pressure from the three-dimensional stress state of the soil. It has been validated through comparisons to laboratory tests (cyclic triaxial tests on saturated sands) and an analysis under three-dimensional excitations (seismic loading polarized along the 3 directions of space). The results involving 3 simultaneous excitation components and a single component in 3 separated analyses show the influence of the loading path on the seismic response and the pore pressure build-up

STRONG SEISMIC MOTIONS ESTIMATED FROM A ONE DIRECTION-THREE COMPONENTS ("1D-3C") APPROACH, APPLICATION TO THE CITY OF ROME, ITALY

International audienceStrong seismic motions in soils generally lead to both a stiffness reduction and an increase of the energy dissipation in the surficial layers. In order to study such phenomena, several nonlinear constitutive models were proposed and were generally implemented for 1D soil columns. However, one of the main difficulties of complex rheologies is the large number of parameters needed to describe the model. In this sense, the multi-surface cyclic plasticity approach, developed by Iwan in 1967 but linked to Prandtl or Preisach theoretical work, is an interesting choice: the only data needed is the modulus reduction curve. Past studies have generally implemented such models for one-directional shear wave propagation in a "1D" soil column considering one motion component only ("1C"). Conversely, this work aims at studying strong motion amplification by considering seismic wave propagation in a "1D" soil column accounting for the influence of the 3D loading path on the nonlinear behavior of each soil layer. In the "1D-3C" approach, the three components (3C) of the outcrop motion are simultaneously propagated into a horizontally layered soil for which a three-dimensional constitutive relation is used (Finite Element Method). The alluvial site considered in this study corresponds to the Tiber River Valley, close to the historical centre of Rome (Italy). The computations are performed considering the waveforms referred as the 14th October 1997 Umbria-Marche earthquake, recorded on outcropping bedrock. Time histories and stress-strain hysteretic loops are computed all along the soil column. The octahedral stress, the strain-depth profiles and the transfer functions in acceleration (surface/outcrop spectral ratios) are estimated for the 1D-1C and the 1D-3C approaches, evidencing the influence of the three-dimensional loading path