Average spectral acceleration: Ground motion duration evaluation

The quantitative assessment of the seismic collapse risk of a structure requires the usage of an optimal intensity measure (IM) which can adequately characterise the severity of the ground motion. Research suggests that the average spectral acceleration ($Sa_{avg}$) may be an efficient and sufficient alternate IM as compared to the more traditional first mode spectral acceleration, $Sa(T_1)$, particularly during seismic collapse risk estimation. This study primarily presents a comparative evaluation of the sufficiency of the average spectral acceleration with respect to ground motion duration, and secondarily assesses the impact of ground motion duration on collapse risk estimation. By assembling a suite of 100 historical ground motions, incremental dynamic analysis of 60 different inelastic single-degree-of-freedom (SDF) oscillators with varying periods and ductility capacities were analysed, and collapse risk estimates obtained. Linear regression models are used to comparatively quantify the sufficiency of $Sa_{avg}$ and $Sa(T_1)$ using four significant duration metrics. Results suggests that an improved sufficiency may exist for $Sa_{avg}$ when the period of the SDF system increases, particularly beyond 0.5, as compare to $Sa(T_1)$. In reference to the ground motion duration measures, results indicated that the sufficiency of $Sa_{avg}$ is more sensitive to significant duration definitions that consider almost the full wave train of an accelerogram ($SD_{a5-95}$ and $SD_{v5-95}$). In order to obtain a reduced variability of the collapse risk estimate, the 5-95% significant duration metric defined using the Arias integral ($SD_{a5-95}$) should be used for seismic collapse risk estimation in conjunction with $Sa_{avg}$.