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High-frequency motion is often observed in small-scale experimental works carried out in flexible containers under simplified seismic loading conditions when single harmonic sine input motions are introduced at the base of a soil specimen. The source of the high-frequency motion has often been sought in experimental inaccuracies. On the other hand, the most recent numerical studies suggested that high-frequency motion in the steady-state dynamic response of soil subjected to harmonic excitation can also be generated as a result of soil elastic waves released in non-linear hysteretic soil upon unloading. This work presents an example of a finite element numerical study on seismic soil–structure interaction representative of an experimental setup from the past. The results show how high-frequency motion generated in soil in the steady-state response, apparently representative of soil elastic waves, affects the steady-state response of a structure, that is, it is presented how the structure in the analysed case resonates with the soil elastic waves. The numerical findings are verified against the benchmark experimental example to indicate similar patterns in the dynamic response of the structure.

High frequency motion is typically observed in experimental works on seismic soil behaviour in centrifuge and in 1-g laboratory tests even if single harmonic sinusoidal input motions are imposed at base. Often these high frequencies are associated with the imperfections of the experimental setups, such as imprecise actuating systems or interaction between specimen and soil containers. On the other hand, the most up-to-date advanced numerical studies suggested that such higher frequencies can also be generated by soil due to its nonlinear behaviour. This work presents results of a numerical study on seismic soil-structure interaction representative of a typical experimental setup. Two advanced soil constitutive models are used. In detail, the results show that soil generates higher harmonics of motion in free field for a single harmonic sinusoidal input motion applied at base. Further, the presence of higher harmonics of motion on a kinematic pile embedded in soil is amplified and can be thought as a potential example of a superharmonic resonance, i.e. a resonance of a structure with one of the soil-generated higher harmonics. The results of the numerical study are compared with the results of a relevant experimental work from the past in order to validate the findings of this paper. The explanation of the higher harmonics of motion generated by soil is also briefly drafted. Finally, the importance of soil generated high frequency motion is briefly discussed, especially in the context of masonry old buildings, often of heritage significance, which are commonly damaged due to high frequency content of recent earthquakes recorded in Europe.

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This short communication identifies some inconsistencies in the numerical predictions of three advanced soil constitutive models. The chosen constitutive models are subject to simple numerical tests in the small strain range relevant to the cyclic response of soil in seismic, offshore and urban applications. The numerical tests comprise: a cyclic simple shear test in the small strain range, a simple shear test with very small strain unloading-reloading loops, and a test on the dependence of the rate of the shear stiffness degradation with increasing shear strain on changing mean confining stress.The results are briefly discussed and, in some cases, the reasons for the observed inconsistencies and potential improvements in the formulations of the investigated constitutive models are initially drafted.