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Beyond Sa_GMRotI: Conversion to Sa_Arb, Sa_SN, and Sa_MaxRot

¹ Watson-Lamprey Consulting
1212 32nd Street
Oakland, California 94608
Jennie.WatsonLamprey{at}gmail.com
 (J.W.L.)
² U.S. Geological Survey, MS 977
345 Middlefield Road
Menlo Park, California 94025
boore{at}usgs.gov
 (D.M.B.)

In the seismic design of structures, estimates of design forces are usually provided to the engineer in the form of elastic response spectra. Predictive equations for elastic response spectra are derived from empirical recordings of ground motion. The geometric mean of the two orthogonal horizontal components of motion is often used as the response value in these predictive equations, although it is not necessarily the most relevant estimate of forces within the structure. For some applications it is desirable to estimate the response value on a randomly chosen single component of ground motion, and in other applications the maximum response in a single direction is required. We give adjustment factors that allow converting the predictions of geometric-mean ground-motion predictions into either of these other two measures of seismic ground-motion intensity. In addition, we investigate the relation of the strike-normal component of ground motion to the maximum response values. We show that the strike-normal component of ground motion seldom corresponds to the maximum horizontal-component response value (in particular, at distances greater than about 3 km from faults), and that focusing on this case in exclusion of others can result in the underestimation of the maximum component. This research provides estimates of the maximum response value of a single component for all cases, not just near-fault strike-normal components. We provide modification factors that can be used to convert predictions of ground motions in terms of the geometric mean to the maximum spectral acceleration (Sa_MaxRot) and the random component of spectral acceleration (Sa_Arb). Included are modification factors for both the mean and the aleatory standard deviation of the logarithm of the motions.