The occurrence of settlements induced by soil liquefaction will exert a substantial influence on buildings situated in earthquake-prone regions. Previous studies integrated the viscous-damping force into the governing equation to characterize building settlements and considered the apparent viscosity as an important parameter. The existing equation can be utilized to predict the settlement magnitude in the final stage as well as its evolution. However, due to the insufficient description of apparent viscosity, it is commonly regarded as a constant during the process of evaluating settlement. When adopting this mechanism, the evolution of building settlement often proves inadequate in fully capturing actual conditions. The aim of this study is to propose a prediction model for estimating liquefaction-induced settlement of shallow-founded buildings, which is formulated by an analytically differential equation. The proposed model incorporates the time-dependent viscosity of liquefied soil and introduces the concept of a soil column submerged in liquefied soil during seismic shaking. The evolution of settlement and the final settlement magnitude induced by soil liquefaction is evaluated through the analytical estimation, and these findings are subsequently compared with the results obtained from centrifuge experiments and numerical simulations. Furthermore, the proposed model is employed to investigate the correlation between building settlement and the geometric characteristics of shallow foundations. The proposed methodology shows considerable promise as an intermediate tool for assessing building settlement, offering practical simplicity in real scenarios.
