The effectiveness of structural fuse mechanisms used to improve the performance of buildings during seismic loading depends on their capacity, ductility, energy dissipation, isolation, and self-centering characteristics. Although rocking shallow footings could also be designed to possess many of these desirable characteristics, current civil engineering practice often avoids nonlinear behavior of soil in design, due to the lack of confidence and knowledge about cyclic rocking. Several centrifuge experiments were conducted to study the rocking behavior of shallow footings, supported by sand and clay soil stratums, during slow lateral cyclic loading and dynamic shaking. The ratio of the footing area to the footing contact area required to support the applied vertical loads ͑A / A c ͒, related to the factor of safety with respect to vertical loading, is correlated with moment capacity, energy dissipation, and permanent settlement measured in centrifuge and 1 g model tests. Results show that a footing with large A / A c ratio ͑about 10͒ possesses a moment capacity that is insensitive to soil properties, does not suffer large permanent settlements, has a self-centering characteristic associated with uplift and gap closure, and dissipates seismic energy that corresponds to about 20% damping ratio. Thus, there is promise to use rocking footings in place of, or in combination with, structural base isolation and energy dissipation devices to improve the performance of the structure during seismic loading.

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Practical guidelines for characterization of soil-structure interaction (SSI) effects for shallow foundations are typically based on representing foundation-soil interaction in terms of viscoelastic impedance functions that describe stiffness and damping characteristics. Relatively advanced tools can describe nonlinear soil-foundation behavior, including temporary gap formation, foundation settlement and sliding, and hysteretic energy dissipation. We review two tools that describe such effects for shallow foundations and that are implemented in the computational platform OpenSees: a beam-on-nonlinear-Winkler foundation (BNWF) model and a contact interface model (CIM). We review input parameters and recommend parameter selection protocols. Model performance with the recommended protocols is evaluated through model-to-model comparisons for a hypothetical shear wall building resting on clay and model-data comparisons for several centrifuge test specimens on sand. The models describe generally consistent moment-rotation behavior, although shear-sliding and settlement behaviors deviate depending on the degree of foundation uplift. Pronounced uplift couples the moment and shear responses, often resulting in significant shear sliding and settlements. Such effects can be mitigated through the lateral connection of foundation elements with tie beams.

It has been recognized that the ductility demands on a superstructure might be reduced by allowing rocking behavior and mobilization of the ultimate capacity of shallow foundations during seismic loading. However, the absence of practical reliable foundation modeling techniques to accurately design foundations with the desired capacity and energy dissipation characteristics and concerns about permanent deformations have hindered the use of nonlinear soil-foundation-structure interaction as a designed mechanism for improving performance of structural systems. This paper presents a new "contact interface model" that has been developed to provide nonlinear relations between cyclic loads and displacements of the footing-soil system during combined cyclic loading ͑vertical, shear, and moment͒. The rigid footing and the soil beneath the footing in the zone of influence, considered as a macroelement, are modeled by keeping track of the geometry of the soil surface beneath the footing, along with the kinematics of the footing-soil system, interaction diagrams in vertical, shear, and moment space, and the introduction of a parameter, critical contact area ratio ͑A / A c ͒; the ratio of footing area ͑A͒ to the footing contact area required to support vertical and shear loads ͑A c ͒. Several contact interface model simulations were carried out and the model simulations are compared with centrifuge model test results. Using only six user-defined model input parameters, the contact interface model is capable of capturing the essential features ͑load capacities, stiffness degradation, energy dissipation, and deformations͒ of shallow foundations subjected to combined cyclic loading.