High frequency content in nonlinear soil response: A numerical artifact or a reality?

This article probes the reasons for the presence of high frequency components, which are not a part of the input, in the output of nonlinear site response analysis. The nonlinear site response analysis of a single soil element, under a single frequency sinusoidal displacement, is conducted to demonstrate the presence of frequencies higher than the input frequency in the soil element's shear stress and the free surface acceleration. The parameters of this one element problem are chosen carefully to minimize numerical errors. The shape of the stress-strain hysteresis loop is found to be the main cause for the presence of these higher frequencies. A quasi-static problem similar to the direct shear test is then considered to analyze the effect of different hysteresis shapes. Through this analysis, it is numerically and analytically shown that any deviation of the stress-strain hysteresis shape from a perfect ellipse results in output frequencies higher than the input frequency and the number of higher frequencies produced depends on whether the hysteresis shape is smooth or pointed.