Time–Frequency Filter for Computation of Surface Acceleration for Liquefiable Sites: Equivalent Linear Stockwell Analysis Method

Abstract

This paper presents a novel method for performing equivalent linear analysis that allows for a variation of the stiffness and equivalent viscous damping properties throughout the duration of shaking. The ability to change the dynamic properties throughout the analysis comes from the conversion of the input ground motion into the time-frequency domain using the Stockwell transform whereby different transfer functions can be applied at different times before converting back to the time domain. The equivalent linear Stockwell analysis (ELSA) method provides a fully decoupled approach to modeling the dynamic site response of liquefiable soil deposits that can account for changes in properties due to strain effects and the build-up of excess pore pressure. The simplicity of the method means that only a limited number of dynamic soil properties are required, the same as those used in an equivalent linear analysis, as well as an estimation of the build-up of excess pore pressure and the relative density of the soil. While there are drawbacks of decoupling the estimation of the build-up of excess pore pressure from the dynamic response, this approach means that the effects of liquefaction on ground shaking can be independently assessed using different models for estimating pore pressure. Furthermore, the influence of liquefaction mitigation interventions, or the presence of a building, can present significant modeling challenges for fully-coupled or loosely coupled approaches, whereas they can easily be assessed using simple decoupled tools. Changing the dynamic properties throughout time using the ELSA method provides a rational way to correct equivalent linear analyses for the known drawback of using the same properties throughout the whole duration. Validation studies are presented of the ELSA method against field downhole recordings from the Wildlife Array and fully-coupled nonlinear effective stress analyses.