A nonparametric characterization of vertical ground motion effects

Design guidelines have traditionally oversimplified the vertical ground motion effects by defining a constant vertical-to-horizontal response spectral ratio (V/H). With the recognition that such practice is not always conservative, recent studies have proposed improvements to the representation of vertical seismic effects in design codes, based on empirical ground motion relations. Conventional empirical modeling requires selecting the functional form of the predictive model. Because of the complicated nature of ground motions, identification of the underlying function is a challenge. A related drawback to this approach is its high susceptibility to overfitting, especially with today's highly complex models. To address these issues, this paper proposes a nonparametric approach to characterize the vertical seismic effects. Using support vector machines, the V/H ratio is determined without an assumed functional form. The accuracy of the model is measured by adopting an epsilon-insensitive residual function with a regularization term added to prevent overfitting. An example application using ground motion records from strike-slip and normal faulting earthquakes is presented, and the results are compared with a current empirical model, for different magnitude, distance, and local soil conditions. The median V/H estimates from the two models are shown to be in good general agreement. The standard deviation estimates from the proposed model are consistently larger than the estimates from the empirical model. The results from this study show that the proposed method is a viable alternative and offers the opportunity to characterize vertical seismic effects without an assumed functional form.