Coupled response for rigid foundations

A matrix formulation to determine the coupled response of rigid foundations where soil properties are modeled by springs and dashpots is presented. Location and orientation of springs and dashpots can be arbitrary, thus a general solution is determined. The response is given in terms of translational and rotational displacements considering coupled effects. Physics of the problem presented here has been extensively studied and a broad range of useful formulae to determine springs and dashpots properties for soil-structure interaction is available. These published formulae for springs and dashpots properties are an input to the approach presented. Thus, the novelty of this approach is a matrix manipulation that leads to a simple expression allowing coupling all degrees of freedom even when springs and dashpots are not orthogonally oriented. For validation purposes, finite element solutions are compared with the approach presented.