Rocking-isolated frame structures: Margins of safety against toppling collapse and simplified design approach

This paper aims to explore the limitations associated with the design of "rocking-isolated" frame structures. According to this emerging seismic design concept, instead of over-designing the isolated footings of a frame (as entrenched in current capacity-design principles), the latter are under-designed with the intention to limit the seismic loads transmitted to the superstructure. An idealized 2-storey frame is utilized as an illustrative example, to investigate the key factors affecting foundation design. Nonlinear FE analysis is employed to study the seismic performance of the rocking-isolated frame. After investigating the margins of safety against toppling collapse, a simplified procedure is developed to estimate the minimum acceptable footing width B, without recourse to sophisticated (and time consuming) numerical analyses. It is shown that adequate margins of safety against toppling collapse may be achieved, if the toppling displacement capacity of the frame d (i.e. the maximum horizontal displacement that does not provoke toppling) is sufficiently larger than the seismic demand d. With respect to the capacity, the use of an appropriate "equivalent" rigid-body is suggested, and shown to yield a conservative estimate of d. The demand is estimated on the basis of the displacement spectrum, and the peak spectral displacement SD is proposed as a conservative measure of d. The validity and limitations of such approximation are investigated for a rigid-block on rigid-base, utilizing rigorous analytical solutions from the bibliography; and for the frame structure on nonlinear soil, by conducting comprehensive nonlinear dynamic time history analyses. In all cases examined, the simplified SD approach is shown to yield reasonably conservative estimates.