Dynamic Impedance Functions of a Square Foundation Estimated with an Equivalent Linear Approach Badreddine Sbartai 1,2(&) 1 Université Badji Mokhtar, Annaba, Algeria bsbartai@hotmail.fr 2 LMGHU, Université 20 Août 1955, Skikda, Algeria Abstract. This paper presents the role of the intensity of an earthquake on the estimation of dynamic impedance functions. For various seismic shaking we will have different nonlinear behavior of the soil, which may have significant effects on the amplitude and shape of the dynamic stiffness and damping coef ficient. However, under the assumption of linear elastic behavior of the soil, loss of soil stiffness under strong shaking is not taken into account in the dynamic impedance functions. The dynamic impedance functions are estimated using an equivalent linear process and compared relative to the linear elastic case. The vibrations originate from the rigid foundation embedded in the soil layer, which are subjected to harmonic loads of translation, rocking, and torsion. The dynamic responses of the rigid surface foundation are solved from the wave equations by taking into account their interaction. The solution is formulated using the frequency domain boundary element method (BEM), in conjunction with Kausel-Peek Green’s function for a layered stratum and the thin layer method (TLM) to account for the interaction between the soil-foundation. A parametric analysis is performed for surface foundation in a semi-infinite soil limited by bedrock and subjected to three earthquake records. 1 Introduction The analysis of the behavior of foundations under dynamic loads has grown consid- erably over the past four decades. The stringent security requirements imposed on design of certain types of structures have played a particularly important role in the development of analytical and numerical methods. The key step in studying the dynamic response of foundations is the determination of the relationship between forces and displacements. This relationship is expressed using impedance functions (dynamic stiffness) or the compliance functions (dynamic flexibility). The considera- tion of the soil-structure interaction in the analysis of the dynamic behavior of foun- dations allows taking realistically into account the influence of soil on its vibration. Several methods have been proposed in the literature to solve the soil-structure inter- action problem. To simplify the problem, linear-analysis techniques have been developed. One of the most commonly used approaches is the substructures method that allows the problem to be analyzed in two parts Kausel et al., Aubrey et al. and Pecker. In this approach, the dynamic responses of superstructure and of the © Springer International Publishing AG 2018 H. Rodrigues et al. (eds.), Facing the Challenges in Structural Engineering, Sustainable Civil Infrastructures, DOI 10.1007/978-3-319-61914-9_35