Stiffness matrix of rigid footings embedded m elastic half space limited or not by a rigid layer

Abstract

ln the paper a formulation to calculate the consistent stiffness matrix of a rigid footings embedded in an elastic half space is presented.  The footing may have any shape and is represented by a set of nodes in its plane. Using Mindlin fundamental solution a flexibility matrix referred to those nodes is computed, associating to each node a surface element of constant stress. The need of some integration is discussed in order to remove the singularity when calculating the diagonal terms of the matrix.

To the nodes are then imposed the displacements induced by the unit rigid body displacements of the footing, and the stiffness matrix elements are obtained by summation of the corresponding nodal forces.

The formulation is extended to other cases, namely when the footing is perfectly rough or perfectly smooth, and when a rigid layer, parallel to the surface or not, exists at a certain depth.

The technique presented is fully integrated in the structural analysis formulation and leads to accurate results with a small volume of calculations.  It can be easily included in structural analysis as subroutine, in order to incorporate soil structure interaction.

The technique is compared with good agreement to the results published by other authors.