Linear equivalent seismic response of a surface foundation excited by an SH harmonic wave

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/G(max) and the curve of increase of the normalised hysteretic damping coefficient xi/xi(max) as a function of the unit shear deformation gamma/gamma(r). 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 behaviour of the soil on the vibration modes of a rigid foundation subjected to a shear wave SH as a function of the dimensionless frequency a(0), and the angles of incidence theta(V) and theta(H). The conclusions that may predict from this research have shown the importance of the influence of the nonlinear behaviour 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.