Some analytical results on lateral dynamic stiffness for footings supported on hysteretic soil medium

The nonlinearity of the soil affects soil–structure interaction to a considerable extent. For a reliable and safe analysis of soil interaction effects on the dynamic response of structures, a more realistic and relatively straightforward method incorporating the nonlinear hysteretic nature of the underlying soil–foundation system needs to be developed. The present paper models the soil–foundation system as a single degree of freedom spring–dashpot system with nonlinear hysteresis in form of elasto-perfectly plastic behavior. Analytical results for the lateral dynamic stiffness on footing have been presented. An example study has been carried out in case of circular footings. It is shown how the analytical results can be used to get a preliminary idea of the lateral dynamic stiffness of footings on a soil medium prior to a detailed computational geo-mechanics analysis provided the static nonlinear load–deformation characteristic of the soil medium is known and can be modeled by a hysteretic elasto-plastic behavior. The corresponding results are presented in a graphical form. The results have been computed showing parametric variations with the change in the amplitude and dimensionless frequency of the non-dimensional excitation force. Analytical results are also presented for the asymptotic cases at low and very high values of dimensionless frequency parameter.