Analytical Model for Longitudinal Soil Vibration

Abstract

An analytical model is derived to provide solutions for longitudinal vibration of soil columns. The model uses a Kelvin‐Voigt element in which the dynamic stresses are the sum of viscous and elastic components. Damping is represented by a viscous damping coefficient that is independent of frequency. This process produces a frequency‐dependent viscous component of stress. A two‐element solution is derived to allow modeling of nonhomogeneous columns. The soil column has a rigid cap at the top, and vertical accelerations at varying frequencies can be applied to the column base. Dynamic response is measured in terms of acceleration of the top cap, and stresses and strains within the column. Element properties can be varied to approximate nonlinear soil behavior. The tendency for failure to occur increases as the constant‐acceleration frequency approaches zero. Dynamic strain and elastic stress reach a maximum near zero frequency, not at the resonant frequency where maximum dynamic stress and particle acceleration occur.