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Forward engineering applications often use modulus reduction and damping ratio curves (MRD) to represent the non-linear response of the soil as a strain dependent equivalent-linear response. While a multitude of such models are available for the shear-modulus, G, only a handful of studies have attempted to constrain MRD models for the compressional-related constrained modulus, M. In this study, nonlinearity associated with the constrained modulus was studied using an extensive analysis of records from 27 KiK-net seismic stations. To represent the response of dry soil, stations with at least 10 m ground water depth (GWD) were analysed. Using frequency shifts, the modulus degradation of the horizontal (H), the vertical (V) and the vertical P-wave window (P V ) components were characterized. Degradation models for the constrained modulus, for a coupled and uncoupled analysis with the shear component are suggested. We find that for PGA&gt;0.1 g, the H component has 91% probability of developing non-linear response, while for the V and P V  components it is only 55% and 43%, respectively. We further find that within those records in which nonlinearity was observed, the PGA threshold for H, V, and P V , is 0.1 g, 0.08 g, and 0.03 g, respectively. Finally, the differences we observe between the full vertical component and the extracted P-wave window suggest that the V component includes a combination of P and SV waves, implying that vertical site-response analysis should include both shear and compression-related soil properties.

Characterizing Nonlinear Effects in Vertical Site Response of Dry Soils Using KiK-Net Data