Effect of damping on response spectral ordinates of ground motions recorded on soft soils in the San Francisco Bay Area

The seismic hazard intensity at a site is typically characterized by 5%-damped pseudo-acceleration spectral ordinates. However, structures can have damping ratios lower or higher than 5% damping, and therefore, seismic demands can be higher or lower than those corresponding to this generic value typically used in ground motion models and probabilistic seismic hazard analyses. Adjustment of spectral ordinates is typically done using modification factors. This study examines damping modification factors corresponding to damping ratios ranging from 1% to 20% computed using ground motions recorded on soft soils in the San Francisco Bay Area. A statistical study is conducted based on 313,200 ratios computed using a database of 348 ground motions recorded in the soft soil regions of the San Francisco Bay Area. As part of the statistical study, a new simplified method is proposed to obtain the predominant period of vibration of the soil deposit for a given site based on the 2%-damped pseudo-velocity response spectrum. It is shown that damping modification factors are very sensitive to changes in the period of vibration relative to modal periods of the soil deposit. Simplified equations are proposed to estimate the mean and logarithmic standard deviation damping modification factors as well as the correlation coefficient between the logarithms of the 5%-damped pseudo-acceleration response spectrum and damping modification factors as a function of the level of damping and of the period of vibration normalized by the predominant period of the soil deposit. Comparisons of empirical and proposed damping modification factors are made between those for soft soils in the San Francisco Bay Area and those in Mexico City from prior work conducted by the authors. Additionally, comparisons are presented between the damping modification factors proposed in this work to those proposed from ground motions recorded on rock or firm soil.