A note on peak inelastic displacement as a proxy for structural damage in seismic sequences

Structural reliability assessment for a building that may experience damage accumulation during a seismic sequence can play an important role in decision making for post-earthquake repair operations or demolition and rebuilding. This typically requires the integration of the aftershock ground motion hazard at the site with the probabilistic description of the damaged building's capacity to withstand the shaking of the seismic sequence. This is usually quantified as the conditional probability that the structure, starting from a specific damage state and for given shaking intensity, will reach a more severe one. In sequence-based seismic risk studies, an analytically-derived estimate of the peak inelastic displacement is often used as a proxy for structural damage. This paper investigates the issues behind this choice and the ability of inelastic displacement demand to adequately describe structural damage due to a seismic sequence, when compared with more direct metrics of damage, such as stiffness and strength degradation. To reach this objective, a series of inelastic single-degree-of-freedom systems, having different natural period, backbones and post-elastic behavior, were subjected to sequential dynamic analysis, while considering a series of arbitrarily chosen damage states, conventionally defined by displacement demand thresholds. The investigation showed that maintaining the attractive simplicity of deformation-based damage proxies in sequence-based risk analysis, can lead to some counterintuitive representations of seismic vulnerability. Some results suggest that such problems could be alleviated if one were to consider some dependence of damage state transition thresholds on the current state of the structure.