Static stiffness of rigid foundation resting on elastic half-space using a Galerkin boundary element method

In this work, a simple and effective numerical model is proposed for studying flexible and rigid foundations in bilateral and frictionless contact with a three-dimensional elastic half-space. For this purpose, a Galerkin Boundary Element Method for the substrate is introduced, and both surface vertical displacements and half-space tractions are discretized by means of a piecewise constant function. The work focuses on a transversely isotropic substrate having the plane of isotropy parallel to the half-space boundary, hence the relationship between vertical displacements and half-space reactions is given by Michell solution, reducing to Boussinesq solution for an isotropic half-space. Several numerical tests are performed for showing the effectiveness of the model, on one hand by determining vertical displacements of flexible rectangular foundations subjected to vertical pressures, on the other hand by accurately determining the translational and rotational stiffness of rigid rectangular and L-shaped foundations. Particular attention is given to the determination of the center of stiffness in case of unsymmetrical foundations, since it turns out to be not coincident with foundation area centroid.