Minimum magnitude boundaries in probabilistic seismic hazard analysis: an insight from structural engineering

In order to systematically advance our understanding of the minimum magnitude limit (M_min) in the probabilistic seismic hazard analysis (PSHA) calculations, a novel and useful approach utilising a broad range of Single-Degree-of-Freedom oscillators and hazard conditions is being developed and tested. We have determined the most reasonable M_min value for a variety of structures by examining the impact of M_min on the mean annual frequency (MAF) of various limit states (LSs) (including the collapse capacity). The originality of the suggested methodology in the current work, known as the MAF saturation strategy, is the recommended M_min, which is the cut-off value at which lesser magnitude events do add to the hazard but do not significantly change the MAF. The current work is the first to offer the MAF saturation strategy methodology, which searches for the cut-off magnitude at which the MAF value essentially remains constant even when smaller values of this cut-off are utilised as M_min for hazard assessments. Therefore, given a series of carefully chosen ground motions in each oscillator instance, an incremental dynamic analysis is carried out (by applying the Hunt and Fill algorithm), and the appropriate LS (including the collapse capacity defined as global instability) points are calculated. Thus, the relationship between the distribution of LSs and the Engineering Demand Parameter and intensity measure is found. A simple point source hazard curve is convoluted with this distribution, yielding the structure-specific MAF. In order to find the cut-off lower magnitude (M_min), this convolution is repeated for several M_min values. This cut-off is defined as the point at which, when lower values are utilised as M_min in the PSHA computation, the MAF’s values do not change considerably (with a five per cent threshold). The acquired data were thoroughly discussed in relation to various structural features and seismic input factors. The primary findings showed that each of the structures under consideration requires a M_min value in the range of 4–4.3. Put otherwise, the suggestions seen in technical literature, which range from 4.5 to 5, are not cautious, at least not when it comes to probabilistic structural limit state frequency. The derived M_min value is mostly controlled by the natural period of the structure and is largely unaffected by other structural characteristics like ductility, damping ratio and overstrength factor.