1. Introduction

In seismic calculations involving soil-structure interaction, the current practice is to consider a uniform free field movement at any point on the ground surface. However, recent observations of strong movements on seismographic networks have revealed spatial variations on fairly small scales. Taking into account the spatial variability of the incident field leads to a filtering of the translational movements for high frequencies. The introduction of spatial variability can thus lead to reduced floor spectra.

The response is calculated in three steps:

• Calculation of the generalized matrices of the embedded structure on the interface.

Determination of interface impedance matrices and seismic force by MISS3D: The MISS3D software is based on a substructuring method. The field of study is broken down into sub-domains - in our case soil and structure - coupled together by interfaces. A multi-domain resolution method is applied and only the interfaces between domains need to be meshed by finite border elements. This makes it possible to model the structure (building) as well as the loads that are applied to it entirely by*Code_Aster. Code MISS3D, for its part, makes it possible to determine the interface impedances between soil and structure as well as the seismic force exerted by the incident field at the interface level. The resolution of the dynamics problem and the post-processing are done again with*Code_Aster*.

• Resolution of the dynamics problem on a reduced basis (resulting from substructuring) in the frequency domain (DYNA_ISS_VARI) and post-processing.