The foundations are subjected to static or dynamic load or combination of both. The static loads are imposed on the foundations slowly and gradually in such a way as to avoid any vibration of the foundation soil system.

The dynamic loads are time variable load, e.g. Earthquake, impact, blast loads etc. Displacement and stresses are time dependent. The inertia forces are part of the loading system.

But all the time varying activities are not dynamic such as filling of reservoir or construction activities etc. the dynamic loads lead to vibration of the soil and foundation system.

In this, Work done = Potential energy + Kinetic energy,

Displacement is connected to the stiffness of the structure and acceleration is connected to the inertia of the structure.

D'Alambert's principle:

A system may be set in state of dynamic equilibrium by adding to the external forces a fictitious force which is commonly known Inertia force. The resulting displacements are associated with accelerations which produce inertial forces resisting the acceleration.