Résumé: The goal of this study is to find out how nonlinear soil behavior affects the dynamic impedance of a rigid surface foundation under a harmonic dynamic load. Researchers can use a computational code that combines the boundary element method (BEM) and the thin layer method (TLM) to calculate the nonlinear dynamic impedances (stiffness and damping) of foundations in the frequency domain. This method integrates nonlinear soil behavior into a linear framework. The soil's nonlinear behavior is evident in the changes observed in its dynamic properties, specifically the decrease in the normalized shear modulus (G/Gmax), the increase in the normalized hysteretic damping coefficient (ξ/ξmax), and the variation in the equivalent shear wave velocity (Vs/Vsmax) as a result of the seismic excitation applied to the soil, which is dependent on the unit shear strain (γ/γr). The parameters are derived using the equivalent linear approach employed in the Caldynasoil computational code for various levels of seismic loading. We conducted a comprehensive analysis to assess how soil non-linearity affects the behavior of a soil-foundation system under various conditions. This included considering factors such as the soil's homogeneity or heterogeneity, the shape of the foundation, and whether the foundation was supported by a semi-infinite soil or constrained by bedrock. The study also considered different levels of seismic deformation, using five seismic accelerations ranging from 0.01g to 0.4g as reference points. The linear and nonlinear dynamic impedance coefficients of the massless foundation were determined for all vibration modes (translation, rocking, and torsion) as a function of the dimensionless excitation frequency a0

Résumé: In presence of a non-linear soil behavior induced by a strong earthquake, the stiffness and damping characteristics of the soil as well as the dynamic response of the structure can be affected. Therefore, this work aims to study the influence of the non-linear soil behavior on the seismic response of the soil-structure system with a new approach using the Caldynasoil computational code based on equivalent-linear method. Using the analytic method, the seismic response of the selected structure was obtained for a nonlinear soil behavior and for two forms of impedance functions. Two types of analyses were performed: first, through an analytical formulation based on the dynamic equilibrium of the soil-structure system modeled by an analog model with three degrees of freedom, and then through a numerical analysis performed with 2D finite element modeling using Abaqus software. The results of the latter type of analysis were compared with those of the analytical solution for validate the obtained results in the first analysis. Finally, we propose new analytical nonlinear relationships between the displacements of the structure, the seismic acceleration level, and the excitation frequencies, taking into account the equivalent linear soil behavior. The change in soil behavior due to the imposed seismic motion in this work shows a significant effect on the response and displacement of the structure. This effect is characterized by an overestimation of the displacement of the structure and a strong dependence on the type of impedance function and soil properties. Excellent agreement between finite element analysis and analytical results was obtained due to the reasonable representation of the model.

Résumé: For a given structural geometry, the stiffness and damping parameters of the soil and the dynamic response of the structure may change in the face of an equivalent linear soil behavior caused by a strong earthquake. Therefore, the influence of equivalent linear soil behavior on the impedance functions form and the seismic response of the soil-structure system has been investigated. Through the substructure method, the seismic response of the selected structure was obtained by an analytical formulation based on the dynamic equilibrium of the soil-structure system modeled by an analog model with three degrees of freedom. Also, the dynamic response of the soil-structure system for a nonlinear soil behavior and for the two types of impedance function forms was also analyzed by 2D finite element modeling using ABAQUS software. The numerical results were compared with those of the analytical solution. After the investigation, the effect of soil nonlinearity clearly showed the critical role of soil stiffness loss under strong shaking, which is more complex than the linear elastic soil behavior, where the energy dissipation depends on the seismic motion amplitude and its frequency, the impedance function types, the shear modulus reduction and the damping increase. Excellent agreement between finite element analysis and analytical results has been obtained due to the reasonable representation of the model.

Résumé: The main objective of this study is to analyse the effect of the non-linear behaviour of the soil on the seismic response of a foundation by taking into account the soil-structure interaction. The foundation is square-shaped, and rigid, resting on the surface of a homogeneous semi-infinite soil, and solicited only by the incident harmonic wave SH. However, for higher deformations (during strong earthquakes), the behaviour of the soil will be characterised by a nonlinear behaviour law. The phenomenon of soil nonlinearity due to the seismic excitation imposed on the soil is reflected in the curve of reduction of the normalised shear modulus G/Gmax and the curve of increase of the normalised hysteretic damping coefficient ξ/ξmax as a function of the unit shear deformation γ/γr. This behaviour is obtained by the equivalent linear method with the Masing model implemented in the one-dimensional (1D) computational code Caldynasoil. In this study, first, determine the nonlinear behaviour of a soil profile stressed by different levels of seismic accelerations applied at the bedrock level. The Caldynasoil computational code was used to find the variations of the nonlinear dynamic properties of the soil profile for different levels of seismic loading. Secondly, integrating the nonlinear dimensionless properties of the soil in a three-dimensional computational code Fonvib_Wave based on the boundary elements method combined with the theory of thin layers (BEM-TLM) in the frequency domain allows calculating the nonlinear displacements of a surface foundation. The obtained results represent the influence of the nonlinear behavior of the soil on the vibration modes of a rigid foundation subjected to a shear wave SH as a function of the dimensionless frequency a0, and the angles of incidence θV and θH. The conclusions that may predict from this research have shown the importance of the influence of the nonlinear behavior of the soil and the angles of incidence of the SH wave on the response of the soil-foundation system compared to the linear case.

Résumé: This paper considers dynamic impedance functions and presents a detailed analysis of the soil plasticity influence on the pile-group foundation dynamic response. A three-dimensional finite element model is proposed, and a calculation method considering the time domain is detailed for the nonlinear dynamic impedance functions. The soil mass is modeled as a continuum elastoplastic solid using the Mohr-Coulomb shear failure criterion. The piles are modeled as continuum solids and the slab as a structural plate-type element. Quiet boundaries are implemented to avoid wave reflection on the boundaries. The model and method of analysis are validated by comparison with those published in the literature. Numerical results are presented in terms of horizontal and vertical nonlinear dynamic impedances as a function of the shear soil parameters (cohesion and internal friction angle), pile spacing ratio, and frequencies of the dynamic signal.

Résumé: The Youd etal liquefaction resistance curves developed in 2001 to characterize the cyclic resistance of soil based on SPT test are the most used in the context of the Seed and Idriss simplified procedure as a deterministic model. These curves were developed from a modified database of Seed et al. in 1985 with the assumption that the actual peak shear stress (τ d ) induced at depth h is always less than that predicted by the simplified procedure (τ r ) of Seed and Idriss (rd= τ d /τ r <1). By using a suite of equivalent linear site response analyses to adjust the dynamic and the simplified shear stress at depth h, Filali and Sbartai showed in 2017 that the dynamic peak shear stress for some earthquakes is greater than the simplified peak shear stress (rd>1). As in this case, the assumption of the simplified procedure is not verified, Filali and Sbartai have proposed a corrector factor (RC) in the range where r d >1 to adjust the deformable and rigid body. In this paper, we will present a probabilistic study for the evaluation of the liquefaction potential using a database based on SPT measurement compiled after the Chi-Chi Taiwan earthquake, in which the cyclic stress ratio is evaluated using the proposed corrector factor. The objective of this study is to present a probabilistic shape of the cyclic resistance ratio (CRR) curves based on the original simplified method of Seed and Idriss and the corrected version and a new formulation for computing the probability of liquefaction.

Résumé: Over the past thirty years, there has been significant progress in protecting structures from earthquakes through structural control, which effectively dissipates energy from dynamic loads. Numerous studies have shown the potential of active control methods in reducing structural responses, leading to improved human safety and seismic structure protection. However, existing control approaches often overlook uncertainties present in real-world scenarios, such as variations in structural coefficients and dynamics. To address this, we aim to employ μ-synthesis, a robust control technique widely used in various fields, which explicitly accounts for these uncertainties during controller design. This paper presents simulations of a three-story building subjected to seismic excitation, with an active bracing system attached to the first floor. We design a robust controller considering both parametric and dynamic uncertainties, demonstrating its effectiveness in significantly reducing structural response amid varying uncertainties. The robustness of the controller is evaluated by testing it under worst-case uncertainty variations.