Material damping for lumped-parameter models of foundations

In foundation dynamics two mechanisms of energy dissipation exist, wave radiation and material damping. Elastic continuum models of the soil capture only the radiation effect. To incorporate material damping, use is made of the fact that the dynamic-stiffness relationships of all elastic foundations may be simulated by discrete assemblages of springs, dashpots and masses. (Such lumped-parameter models are exact for simple cone models of the soil and approximate for more involved cases.) By application of the correspondence principle directly to the discrete elements of the lumped-parameter model, it is possible to introduce Voigt viscoelasticity. Each original spring is augmented by a dashpot, and each original dashpot is augmented by a mass, attached in a special way. Going a step further, more realistic non-linear-hysteretic damping is represented by replacing the augmenting dashpots and masses by frictional elements. The analysis, which is effected solely in the time domain, is illustrated by an example from earthquake engineering.