Mass effect and ground radiative damping

Consider the case of a foundation, either shallow or deep, subjected to the application of a harmonic load F(t) = F ₀ .sin(ωt) in a given direction.

Analysis of the foundation's dynamic response under steady-state conditions reveals a much more complex behavior than that observed under "static" loading, with, on the one hand, a "mass" effect that induces a change in apparent stiffness as a function of load frequency, and, on the other, a phase shift between load and resulting displacement synonymous with the existence of a non-zero damping term. This results from the combination of two phenomena:

• material" dissipation of energy (damping specific to the material...