Nonlinear site-response of vertical ground motions

The importance of vertical ground motions for design continues to gain recognition, as more evidence shows that vertical ground motions can significantly exceed their horizontal counterparts on very soft soils, at short source-site distances, and at short spectral periods. Assuming that the vertical component is largely comprised of compressional P-waves, new approaches and models are required to constrain the expected linear and nonlinear site response of the vertical component.

In this study, we combine empirical analysis with laboratory experiments, to study and define the nonlinear behavior of the vertical component. We use 27 Kik-net stations to analyze nonlinearity of dry sandy deposits, comparing the full vertical component with the P-wave window, to help define the partial contribution of P-waves to the entire vertical component. We develop modulus degradation and damping (MRD) curves for the case of uncoupled and coupled shear-compression response. In addition, we compare the empirical MRD curves with experimental MRD curves, describing the response of sandy soil to cyclic compressional loading under Ko conditions. We show that vertical ground motions are less nonlinear than their horizontal counterpart, for the same incoming ground motion. We also show that pure P-waves are less nonlinear than the full vertical motion, suggesting that the vertical component is comprised of a combination of P and SV waves, thus implying that vertical site-response analysis should include both shear and compression-related properties and procedures.