A 3D macroelement to model the seismic behavior of shallow foundations

The design of shallow foundations under seismic load requires to account for the non linearities in the soil and at the soil-foundation interface. For nuclear plants, in a context of a new seismic zoning, specific design methods are implemented in order to account for soil-structure interaction in an appropriate way. In this aim, a three-dimensional elastoplastic macroelement is proposed to model the seismic behaviour of shallow foundations. The foundation behaviour is described using generalized variables in terms of forces and displacements and is also located in particular points where the geometric and material non-linearities are concentrated. The non linear behaviour is represented by yield surfaces inspired from the Eurocode criteria. A hardening law is associated to each surface to depict its evolution in the general loading space. The multisurface plasticity theory is used to combine the different mechanisms (punching, overturning, and sliding). This macroelement is implemented in the framework of the finite element method (CESAR-LCPC). The calibration of the macroelement parameters is based on the analysis of the static response of a foundation. Then, it is extended to take into account dynamic aspects. The results easily allow to analyze the forces acting on the shallow foundation in the time domain. It is also possible to study the variations of the safety factor during the earthquake as well as the effect of the non linearities on the shallow foundation design.