SUMMARYA method to obtain the dynamic response of an extended rigid foundation supported on an elastic half-space when subjected to a spatially varying ground motion including both random and deterministic effects is presented. The method relies on an integral representation of the response of the foundation in terms of the free-field ground motion. Numerical results for a rigid square foundation and for a ground motion characterized by a particular spatial coherence function are described. The results obtained indicate that the spatial randomness of the ground motion produces effects similar to the deterministic effects of wave passage including reduction of the translational components of the response at high frequencies and creation of rocking and torsional response components. The possibility of defining an effective apparent horizontal velocity which produces effects equivalent to those from a given spatial randomness is explored.

SUMMARYForced vibration tests designed to isolate the effects of soil-structure interaction are described and the results obtained for the nine-storey reinforced concrete Millikan Library Building are analysed. It is shown that it is possible to determine experimentally the fixed-base natural frequencies and modal damping ratios of the superstructure. These values may be significantly different from the resonant frequencies and damping ratios of the complete structure-foundation-soil system. It is also shown that forced vibration tests can be used to obtain estimates of the foundation impedance functions.In the case of the Millikan Library it is found that during forced vibration tests the rigid-body motion associated with translation and rocking of the base accounts for more than 30 per cent of the total response on the roof and that the deformation of the superstructure at the fundamental frequencies of the system is almost entirely due to the inertial forces generated by translation and rocking of the base.

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SUMMARYAn integral equation technique to calculate the dynamic response of foundations embedded in a layered viscoelastic halfspace when subjected to external forces and moments is presented. The technique is based on representing the radiated field as resulting from a set of sources distributed over a surface internal to the actual boundary of the foundation and by imposing the boundary conditions in an integral sense. The resulting non-singular integral equation with symmetric kernel is solved by discretization and reduction to a system of linear algebraic equations. The technique is validated by comparison with previous results for cylindrical foundations with different embedment ratios.

The problem of determining the response of a rigid strip footing bonded to an elastic half plane is considered. The footing is subjected to vertical, shear, and moment forces with harmonic time-dependence; the bond to the half plane is complete. Using the theory of singular integral equations the problem is reduced to the numerical solution of two Fredholm integral equations. The results presented permit the evaluation of approximate footing models where assumptions are made about the interface conditions.