Modelling the steady-state motion of a soil column including nonlinear hysteretic damping under periodic excitations

Abstract

Soil exhibits hysteretic damping. A commonly used implementation of this type of damping are the Masing rules. They consist of a loading and an unloading branch, dened as a piecewise function and having a nonsmooth character. This paper presents a framework how steady-state solutions of the motion of a soil column, with nonlinear hysteretic damping, can be obtained by using a variant of the Harmonic Balance Method (HBM), the Alternating Frequency/Time Harmonic Balance Method (AFTHBM), applied on a discretised soil column (a lattice system). The theoretical background of the method is presented, as well as its application to a soil column with both shear strain-dependent stiness and damping. Results show that the AFTHBM is an efficient method for obtaining steady-state results for nonsmooth nonlinear behaviour, which is in this paper presented by simulations for nonlinear media. The results of the AFTHBM are sensitive to time sampling and convergence tolerances; nonetheless, if these parameters are properly chosen, the application of AFTHBM leads to good results.