Empirical Correlations of Spectral Input Energy with Peak Amplitude, Cumulative, and Duration Intensity Measures

In earthquake engineering, it is acknowledged that a vector of intensity measures (IMs) can better predict seismic structural responses than a single measure. Hence, a vector of IMs is widely applied in a number of applications, such as probabilistic seismic hazard analysis, probabilistic seismic risk analysis, and ground-motion selections. Spectral input energy (E-I) has been demonstrated as a promising IM in earthquake engineering, especially in the energy-based seismic design of structures. However, this important measure has not been included in the vector of IMs. Therefore, it is worthwhile to incorporate E-I with other important IMs by examining correlations. This study analyzes the empirical correlations of spectral E-I with peak amplitude-based IMs, cumulative-based IMs, and duration-related IMs. It is found that spectral absolute E-I has strong correlations with peak ground velocity at all investigated periods. However, spectral E-I is negatively correlated with duration-based IMs. To demonstrate the applicability of the examined correlations, a simple example is finally presented by employing E-I for the ground-motion selections and seismic hazard assessment based on the generalized conditional intensity measure approach.