Analytical solutions for changes in predominant frequency of a site based on characteristic parameters of liquefiable interlayer

Although the effect of soil liquefaction on seismic ground motion and the recognition of site liquefaction based on seismic records respectively represent forward and inverse derivation problems, the change in the self-vibration characteristics in the horizontal direction caused by soil liquefaction is the physical characteristic that is shared commonly by these two issues. Thus, the natural vibration characteristics of a site should be the basis for studying these two issues. From this perspective, the present work proposes an analytical approach for predicting the proportional decrease in the predominant frequency of a site after the occurrence of soil liquefaction (δ). The soil is treated as a layered and parallel structure, and a three-particle system including a liquefiable interlayer is employed to represent the sites susceptible to liquefaction. The approach is based on the characteristic parameters of the liquefiable interlayer. The effect of these parameters on δ is also discussed. The results show that the presence of a liquefied interlayer reduces the predominant frequency of the site. The value of δ is mainly related to the ratio of the overburden layer thickness to the thickness of the liquefiable layer , the ratio of the liquefiable layer thickness to the thickness of the substratum layer , and the degree of softening of the liquefiable layer. The ratio plays the dominant role in controlling δ according to three modes: an exponentially decreasing mode, an exponentially increasing mode, and a mode where δ first increases and then decreases, with the latter being the main representation. The ratio plays a secondary role in affecting δ, where δ initially increases rapidly with the increasing up to a transition point, after which δ increases slowly. The results show that the value of the transition point is related to . Although δ increases with an increasing degree of softening of the liquefied layer, the maximum absolute increment is only 0.15, which provides a negligible effect.