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.

中文翻译：

---

使用KiK-net数据对垂直地面运动的非线性土壤特性进行原位表征

强烈的垂直地震动对工程结构的地震响应具有重大影响。然而，与水平地面运动相比，垂直地面运动的土壤非线性受到的关注较少。在这项研究中，使用KiK-net的地震观测资料来研究垂直地面运动的土壤非线性。提出了一个新的拟合公式，以考虑地下水的影响来估算整体约束模量退化曲线。与广泛使用的拟合公式相比，所提出的公式具有更高的拟合优度，并且与先前研究的理论解决方案一致。正应变线性阈值的大小顺序约为10 ^-6这与剪切应变相同。此外，与剪切模量不同，当法向应变在10 ^-5到10 ^-4之间时，所选工位的约束模量迅速减小，而在10 ^-4以上时，减小速度减慢。该结果与基于先前研究的实验室测试数据的理论结果一致。利用土壤应变与峰值地面加速度（PGA）之间的拟合关系，我们发现垂直非线性的PGA阈值可低至30 cm / s ²并且通常高于水平非线性。此外，研究了强震后剪切模量和约束模量减少的差异，这可能与泊松比的变化有关。