A computationally efficient framework for rotation dependent and rotation independent intensity measures

Orientation of a structure in a site is generally known but not the direction of maximum shaking during a future seismic event. Two different types of intensity measures (IMs) are usually used to approximately account for this directionality effect, namely, the rotation dependent such as RotDxx and GMRotDxx and the rotation independent such as RotIxx and GMRotIxx. Rotation dependent IMs are presently constructed by performing time history analysis for all possible orientation (usually @ 1 degree) of the input ground motion set followed by picking the xx-percentile spectral ordinate. In other words, the construction of RotDxx spectrum requires a set of 180 time history analysis of an oscillator per spectral ordinate. Similarly, the construction of GMRotDxx requires time history analysis of an oscillator against 90 pairs of orthogonal components per spectral ordinate. This paper presents a framework that enables the construction of rotation dependent IMs by performing time history analysis against a pair of as-recorded components with some nominal supplemental processing. This reduces the computational cost more than 90% when compared with the state of the art. Rotation independent IMs are defined through finding out the rotation that minimizes the error (often termed as the penalty function) with respect to the target spectra of associated rotation dependent IM as the benchmark. Resulting rotation independent IMs show somewhat sensitivity on the maximum time period used in spectral representation. This paper presents an alternate definition (involving scaling and rotation) for rotation independent IMs that nearly eliminates such sensitivity.