Nonlinear seismic response of a soil deposit using the Volterra series

The equivalent linear method introduced in the sixties is still the most used technique to calculate the seismic response of soil deposits with nonlinear behavior. This paper presents an alternative approach based on the higher-order frequency response functions (HOFRF) that results from the application of the Volterra series in the frequency domain. To obtain the seismic response of soils requires a method capable of solving nonlinear problems in the frequency domain. This is because the best model to describe the energy dissipation in soils is the hysteretic or complex modulus damping, which is only defined in the frequency domain. Moreover, even under moderate earthquakes soils behave in a nonlinear fashion. So far, the approximate equivalent linear method and the proposed technique are the only methods capable of dealing with this problem. Numerical examples of the application of the HOFRF method are presented and the results are compared with the equivalent linear method.