Rigid circular footing on the surface of a transversely isotropic linear elastic half-space

It is sometimes convenient to treat a relatively rigid footing as a single element subjected to up to six force-resultants: vertical load, horizontal load in two directions, overturning moment about two axes, and torsion. Applications include calculations of initial, elastic settlement; foundation responses under seismic loading or for machine vibrations; and fixity of an offshore jackup foundation under cyclic wave loading. Present codes of practice provide formulae that assume fully isotropic and linear elastic soil, and in some case assume no friction between footing and soil. This paper uses recent theoretical advances to develop solutions for stiffnesses of rigid circular footings on transversely isotropic linear elastic soil, including with interface friction. Closed form solutions are developed for vertical load and overturning moment on a frictionless interface, and for vertical load and torsion on a frictional interface. A boundary element analysis is presented for the cases of lateral load and overturning moment on a frictional interface. By fitting expected forms to the results, new formulae are proposed for stiffnesses for these cases. Effects of interface friction on limiting loads are calculated. Practical applications are outlined, and some limitations are briefly discussed.