Seismic reliability implied by behavior-factor-based design

Force-based seismic design involves the reduction of elastic spectra by introducing a behavior factor, q. This approach is widespread in engineering practice; however, recent studies have shown that structures consistently designed at different sites will not share the same level of seismic risk, which can be defined as the annual rate of the structure failing to meet a seismic performance objective, despite seismic actions having the same exceedance return period at all sites. This paper investigates whether the definition of site-specific q factors can lead to uniform risk across sites characterized by varying levels of seismic hazard, based on the pushover curves of bare frame reinforced concrete buildings. These pushover curves are used to establish the backbones of equivalent single degree of freedom systems with varying lateral resistance. These systems are fictitiously placed at several Italian sites and their seismic failure risk is computed by integrating their fragility, assessed by means of incremental dynamic analysis, with each site's hazard curve. By assuming an arbitrary risk threshold, the same for all sites, the corresponding lateral strength leading to said threshold is determined and the corresponding behavior factor is back calculated. As expected, risk-targeted q factors tend to increase with decreasing seismic hazard and are highly sensitive to the shape of the hazard curve beyond the design return period. Coupled with the fact that at low hazard sites lateral strength is determined by detailing for gravity-load design and minimum code requirements, rather than seismic design actions, the results suggest that q factor-based design is unsuitable for warranting territorially uniform seismic safety, yet it may be suitable for setting an upper-bound to the annual failure probability