This paper presents a methodology for post-earthquake probabilistic risk (of damage) assessment that we propose in order to develop a computational tool for automatic or semi-automatic assessment. The methodology utilizes the same so-called risk integral which can be used for pre-earthquake probabilistic assessment. The risk integral couples (i) ground motion hazard information for the location of a structure of interest with (ii) knowledge of the fragility of the structure with respect to potential ground motion intensities. In the proposed post-mainshock methodology, the ground motion hazard component of the risk integral is adapted to account for aftershocks which are deliberately excluded from typical pre-earthquake hazard assessments and which decrease in frequency with the time elapsed since the mainshock. Correspondingly, the structural fragility component is adapted to account for any damage caused by the mainshock, as well as any uncertainty in the extent of this damage. The result of the adapted risk integral is a fully-probabilistic quantification of post-mainshock seismic risk that can inform emergency response mobilization, inspection prioritization, and reoccupancy decisions.

We present a methodology for developing fragilities for mainshock-damaged structures, "aftershock fragility", by performing incremental dynamic analysis (IDA) with a sequence of mainshock-aftershock ground motions. The aftershock fragility herein is distinguished from a conventional fragility for an intact structure. We estimate seismic response of a mainshock-damaged building by performing nonlinear time history analysis with a sequence of mainshock and aftershock ground motions (so-called "back-to-back" dynamic analysis). We perform the back-to-back dynamic analyses for a number of levels of mainshock response/damage, and a number of sequences of mainshock and aftershock ground motions. With estimated seismic responses from the back-to-back dynamic analyses, we compute various damage state transition probabilities, the probability of exceeding a higher damage state from an aftershock given a damage state due to a mainshock. For an illustration of the methodology, we develop an aftershock fragility for a typical New Zealand 5-storey reinforced concrete moment frame building. The building is modeled using a single-degree-of-freedom (SDOF) damped nonlinear oscillator with force-deformation behavior represented by a multi-linear capacity/pushover curve with moderate pinching hysteresis and medium cyclic deterioration.

Seismic risk assessment involves the development of fragility functions to express the relationship between ground motion intensity and damage potential. In evaluating the risk associated with the building inventory in a region, it is essential to capture ‘actual’ characteristics of the buildings and group them so that ‘generic building types’ can be generated for further analysis of their damage potential. Variations in building characteristics across regions/countries largely influence the resulting fragility functions, such that building models are unsuitable to be adopted for risk assessment in any other region where a different set of building is present. In this paper, for a given building type (represented in terms of height and structural system), typical New Zealand and US building models are considered to illustrate the differences in structural model parameters and their effects on resulting fragility functions for a set of main-shocks and aftershocks. From this study, the general conclusion is that the methodology and assumptions used to derive basic capacity curve parameters have a considerable influence on fragility curves.