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Evaluation of simplified methods to estimate
displacement demands of structures on
rocking shallow foundations
Krishnan Athipotta Variam, Andreas Gerasimos Gavras & Bruce Lloyd Kutter
University of California – Davis, Davis, California, U.S.A.
ABSTRACT
Experimental efforts over the last decade have shown that rocking foundations have beneficial seismic performance
features: re-centering and energy dissipation with little damage. As a result, the concept of a controlled share of ductility
demand between the superstructure and the foundation as a key ingredient for a rational and integrated approach to the
seismic design of foundations and structures has been gaining acceptance within the research and practicing earthquake
engineering communities.
In this paper, two simplified methods to estimate the maximum displacement demand of single-degree-of-freedom-like
structures supported on rocking shallow foundations are evaluated. The first method is a Displacement-Based Design
approach proposed by Deng et al. (2014) -- an iterative equivalent linearization approach, in which, the maximum
displacement is estimated as the maximum spectral displacement accounting for nonlinearity by elongating the system
period and increasing the damping. In the second method, nonlinear dynamic time history analyses are performed to
predict the drift of a lumped mass at the top of a column for which the soil-foundation interaction is represented by a
nonlinear rotational spring and dashpot. Two moment-rotation relations of the rotational spring were considered: a bilinear
elastic hysteretic model and a bilinear elastic-perfectly plastic model. The accuracy (correlation, scatter and bias) of each
method is assessed against data from a new database of dynamic rocking foundation experiments (FoRDy) that is briefly
introduced. The database currently contains 159 event case histories compiled from five centrifuge and three 1g shaketable test series, spanning a variety of rocking system properties, soil types and input ground motions. For all three
methods, the 68% of the predictions were within a factor of 1.5 to 1.6 of the experimental measurements.