A generalized ground-motion model for consistent mainshock–aftershock intensity measures using successive recurrent neural networks

Several recent studies have investigated the risk posed to structures by earthquake sequences, proposing state-dependent fragility/vulnerability models for assets in damaged conditions. However, a critical component for such efforts, i.e., ground-motion record selection, has received relatively minor consideration. Specifically, utilization of “consistent” mainshock (MS)–aftershock (AS) ground motions is desirable in practical applications. Such consistency in selecting MS–AS sequences requires proper consideration of the correlations between and within the intensity measures of MS and AS ground motions. Most of the studies in this domain utilize spectral accelerations as the considered ground-motion intensity measures and rely on empirical linear correlation models between the intensity measures of MS and AS ground motions for developing, for instance, record selection approaches. This study proposes a generalized ground-motion model (GGMM) to estimate consistent 30 × 1 vectors of intensity measures for mainshocks (denoted as IM _MS) and aftershocks (denoted as IM _AS) using a framework of successive long-short-term-memory (LSTM) recurrent neural network (RNN). The vectors of IM _MS and IM _AS consist of geometric means of significant duration (D _{5 - 95 , g e o m}), Arias intensity (I _{a , g e o m}), cumulative absolute velocity (CAV _geom), peak ground velocity (PGV _geom), peak ground acceleration (PGA _geom) and RotD50 spectral acceleration (S _a(T)) at 25 periods for both MS and AS ground motions. The proposed RNN-based GGMM is trained on a carefully selected set of ~ 700 crustal and subduction recorded MS–AS sequences. The inputs to the framework include a 5 × 1 vector of source and site parameters for MS and AS recordings. The residuals of the trained LSTM-based RNN are further used to develop empirical covariance structures for IM _MS and IM _AS. The proposed framework is finally illustrated to select MS–AS ground motions based on IM _MS and IM _AS using a multi-criteria objective function. The selected MS–AS ground motion sequences are then used to perform non-linear time-history analyses of a case-study two-spanned symmetric bridge structure. The obtained engineering demand parameters are evaluated and critically discussed.