A closed form solution for seismic risk assessment incorporating intensity bounds

• A risk equation incorporating intensity bounds is derived in closed form.
• The lower intensity bound represents the minimum limit-state intensity.
• An approximate method for the estimation of the upper intensity bound is proposed.
• The impact of intensity bounds depends on the selected intensity measure.
• An insight into the parameters affecting the seismic risk of RC frames is given.

A closed-form solution of the risk equation incorporating intensity bounds is derived and analysed. The new equation, compared to the well-known risk equation developed in the 1990s, includes a correction factor, which has a value less than one if the effect of the intensity bounds is significant. The lower bound of ground-motion intensity represents a minimum ground-motion intensity, which causes a designated limit state, whereas the upper bound of ground-motion intensity is, in general, related to the physics of earthquakes, the tectonic regime, and the geology of the terrain in the region from the epicentre to the site of the building. In the paper typical values of the minimum collapse intensity and of the fragility parameters of code-conforming frames are discussed. An approximate procedure for assessing the upper bound of ground-motion intensity on the basis of ground-motion prediction models is also proposed. Finally, the procedure for seismic risk assessment is demonstrated by assessing the collapse risk for a 4-storey and a 15-storey building. It is shown that the collapse risk assessed on the basis of peak ground acceleration can be significantly affected by the lower bound of the collapse intensity, whereas the impact of the upper bound of the ground-motion intensity on the collapse risk can be more pronounced when the assessment of the collapse risk is based on the spectral acceleration at the first vibration period.