Analyzing the Sufficiency of Alternative Scalar and Vector Intensity Measures of Ground Shaking Based on Information Theory

The seismic risk assessment of a structure in performance-based design (PBD) may be significantly affected by the representation of ground motion uncertainty. In PBD, the uncertainty in the ground motion is often represented by a probabilistic description of a scalar parameter, or low-dimensional vector of parameters, known as the intensity measure (IM), rather than a full probabilistic description of the ground motion time history in terms of a stochastic model. In this work, a new procedure employing relative sufficiency measure is introduced on the basis of information theory concepts to quantify the suitability of one IM relative to another in the representation of ground motion uncertainty. On the basis of this relative sufficiency measure, several alternative scalar- and vector-valued IMs are compared in terms of the expected difference in information they provide about a predicted structural response parameter, namely, the seismically induced drift in an existing reinforced-concrete frame structure. It is concluded that the most informative of the eight considered IMs for predicting the nonlinear drift response are two scalar IMs and a vector IM that depend only on the spectral ordinates at the periods of the first two (small-amplitude) modes of vibration.