Expected annual loss (EAL), which can be expressed in dollars, is an effective way of communicating the seismic vulnerability of constructed facilities to owners and decision makers. A concise method for computing EAL without the inherent bias of requiring a specific analytical probability distribution is presented. The relationships between intensity measures and engineering demand parameters resulting from an Incremental Dynamic Analysis are sorted into fractal intervals by way of spectral reordering and modified to incorporate additional sources of uncertainty and randomness. Damage measures are defined to determine thresholds for damage states. Damage is quantified by loss ratios defined as repair cost divided by replacement cost. The results are numerically integrated to give EAL. An example illustrating the method is performed, comparing the seismic vulnerability of two highway bridge piers; one pier traditionally designed for ductility, and the other designed for damage avoidance. The damage avoidance pier has a clear advantage over the conventional pier, with an EAL some 85% less than its ductile counterpart. This is shown to be primarily due to its inherent damage-free behaviour for almost all ground motions, except for very rare events that could potentially lead to toppling.
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