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.

When multiple earthquakes occur within a short period of time, damage may accumulate in a building, affecting its ability to withstand future ground shaking. This study aims to quantify the post-earthquake capacity of a nonductile 4-story concrete building in New Zealand through incremental dynamic analysis of a nonlinear multipledegree-of-freedom simulation model. Analysis results are used to compute fragility curves for the intact and damaged buildings, showing that extensive damage reduces the structure’s capacity to resist seismic collapse by almost 30% percent. The damage experienced by the building in mainshock, can be compared with the ATC-20 building tagging criteria for post-earthquake inspections, the purpose of which is to ensure public safety. Extensively damaged buildings, which are likely be red tagged, pose a significant safety hazard due to decreased strength in future earthquakes. The effect of mainshock damage is also compared for multiple and simplified single-degree-of-freedom models of the same building.

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.