In situ characterization of nonlinear soil behavior of vertical ground motion using KiK-net data

Strong vertical ground motion has significant influences on the seismic response of engineered structures. However, the soil nonlinearity of vertical ground motion has received less attention compared with that of horizontal ground motion. In this study, seismic observations from KiK-net were used to investigate the soil nonlinearity of vertical ground motion. A new fitting formula was proposed to estimate the global constrained modulus degradation curve considering the influence of groundwater. The proposed formula was verified by the higher goodness of fit compared with a widely used fitting formula and the consistency with the theoretical solution from a former study. The order of the magnitude of the normal strain linear threshold was approximately 10−6 which is the same as that of the shear strain. Furthermore, different from the shear modulus, the constrained modulus of the selected stations decreased quickly when normal strain was between 10−5 and 10−4, and the reduction speed slowed down when it was above 10−4. This result was consistent with the theoretical result based on the laboratory test data from a previous study. Using the fitted relationships between the soil strain and peak ground acceleration (PGA), we found the PGA threshold for vertical nonlinearity could be as low as 30 cm/s2 and was generally higher than that for horizontal nonlinearity. Moreover, the difference in reduction between the shear modulus and constrained modulus after a strong earthquake was investigated which could be related to the change in Poisson’s ratio.