Elastic formulae for lateral displacement and rotation of arbitrarily-shaped embedded foundations

INTRODUCTION Foundations are frequently designed to transmit horizontal forces and/or moments. Such loading arises, for example, from wind, water and earth pressure, as well as from dynamic loads due to earthquakes, man-induced vibrations, and impacts. The list of special structures that impose significant lateral forces and moments includes transmission towers, radar antenna structures, large-span frames, and structures with heavy eccentric loads. Predicting and limiting the resulting horizontal displacement and rotation is a key geotechnical consideration, especially with many modern deformation-sensitive structures. Assessing the effects of soil-structure interaction on the behaviour of a superstructure involves estimating the ground compliance to such imposed lateral and moment loading. A review of the literature reveals that only a very small number of solutions to this problem are presently available; several of them are summarized in tabular and graphical form in Pol;los & Davis (1974). Most of these solutions refer either to uniformly distributed shear tractions or to linearly varying normal pressures applied directly to the surface of a homogeneous halfspace, and approximately simulating the action of a foundation carrying a horizontal force or a bending moment (Giroud 1968, 1969, 1970; Gerrard & Harrison 1970a and b). A few results are available for the more realistic case of loading applied through a rigid mat (Borowicka, 1943; Bycroft, 1956; Muskelishvili, 1963; Barkan, 1962; Gerrard & Harrison, 1970a and b). Solutions for embedded foundations are mainly available in the soil dynamics literature; they are recovered from the respective harmonic compliances when the frequency of oscillation approaches zero (Gazetas, 1983, 1987). Some static solutions have also been published for laterally loaded embedded foundations (e.g. Haritos & Keer, 1980; Johnson, Chris-