LITMIR.BIZ

       1) The pseudo-static case: where the loadings are nearly time independent (a small number of cycles are accepted).

       2) The cyclic case: involving a large number of slow cycles (slow versus the time scales of any physical phenomena involved).

       3) The dynamic (mostly seismic) case: where inertia forces are taken into account.

       – The classical and well-known finite element method (FEM) using interface or contact elements available for coupled hydro-mechanical problems and in which the local plastic energy dissipation contributes to the classical global damping.

       – The distinct element method (DEM) in which the contact zones between soil and structure are described by local adapted interaction laws.

       – The finite difference method (FDM) using explicit algorithm in which interface or contact elements are available and straightforward for coupled hydro-mechanical, highly nonlinear with high deformation and dynamic problems.

       – The more recent approaches based on the macro-element concept and generalized variables in an incremental form available in static and dynamic situations, where a large volume of soil underlying and surrounding the-structure is represented by a small number of degrees of freedom. This method could be considered as an improved extension of the stiffness coefficient methods known for the piles as the t-z and p-y curves.

       – The seismology approach with inertia and viscous equivalent damping forces, in which the SSI is developed between several structures (like buildings in a town) using the notion of meta-materials. This point of view is especially useful when analyzing the movement of the buildings induced by a seismic event at the scale of a town.