Foundation impedance ordinates are identified from forced vibration tests conducted on a large-scale model test structure in Garner Valley, California. The structure is a steel moment frame with removable cross-bracing, a reinforced concrete roof, and a nonembedded square slab resting on Holocene silty sands. Low-amplitude vibration is applied across the frequency range of 5-15 Hz with a uniaxial shaker mounted on the roof slab. We describe procedures for calculating frequency-dependent foundation stiffness and damping for horizontal translational and rotational vibration modes. We apply the procedures to test data obtained with the structure in its braced and unbraced configurations. Experimental stiffness ordinates exhibit negligible frequency dependence in translation but significant reductions with frequency in rotation. Damping increases strongly with frequency, is stronger in translation than in rocking, and demonstrates contributions from both radiation and hysteretic sources. The impedance ordinates are generally consistent with numerical models for a surface foundation on a half-space, providing that soil moduli are modestly increased from free-field values to account for structural weight, and hysteretic soil damping is considered.

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Ground motion prediction equations and seismic hazard analyses are used to evaluate design-basis ground motions that apply to a free-fi eld and ground surface condition. In this paper, we address the manner by which those motions can be utilized for the analysis and design of buildings with subterranean levels. Procedures for specifying ground motions in buildings that are utilized in current practice fail to account for kinematic interaction effects, which cause reductions of ground motion translation and the introduction of rocking for embedded foundations. Simple models that describe those effects (reduction of translation, introduction of rocking) for embedded rigid cylinders are reviewed. Those models are well validated by recordings from two nuclear reactor structures that have very stiff embedded foundations. Most building structures will not have foundations as stiff as those from the nuclear reactor structures, and hence the degree to which foundation fl exibility might affect the motions of embedded foundations was investigated using data from appropriately instrumented buildings. Preliminary analysis of the data suggests that: (a) the foundations are not rigid and rigid body displacements and rotations of the foundation explain only 60-80% of the power of the motion at the ground level; (b) using available models for kinematic interaction of embedded foundations, translational motions at the ground level of the investigated sites are dominated by base translation, with relatively small contributions from base rocking; and (c) for the investigated buildings, base rocking from inertial interaction appears to be more signifi cant in the frequency range of principal interest than base rocking from kinematic interaction.