Introductory consideration supporting the idea of the release of unloading elastic waves in the steady state response of hysteretic soil

Resonance of a structure with soil elastic waves released in non-linear hysteretic soil upon unloading

“…Regarding the numerical results shown in this work, it is important to highlight that these are not dependent on the chosen constitutive model. The other works of the author (Kowalczyk, 2020;Kowalczyk & Gajo, 2022) showed that the same patterns of high-frequency motion computed in soil (and representative of soil elastic waves) can be obtained with different soil constitutive models.…”

“…The results are obtained with the chosen calibration of the hypoplastic sand model in a simple numerical study of a 0.8-m-high soil column (32 quadratic finite elements of the size of 0.025 m). Indeed, this numerical example shows the essence of the potential presence of soil elastic waves released upon unloading in the steady-state part of dynamic response (as per the patterns shown in more detail in a parallel work by Kowalczyk & Gajo, 2022). The soil elastic waves are particularly visible for loading cases when the driving frequency (5 Hz) of the input motion is smaller than the soil natural frequency (approximately 25 Hz), such as the case presented in Figure 4.…”

“…different non-linearity types) in the modelling of soil constitutive behaviour as sources of such high harmonics. Moreover, the most recent advanced numerical studies (Kowalczyk, 2020;Kowalczyk & Gajo, 2022) show a novel idea in the stress wave propagation and an introductory proof that high-frequency content observed in soil can be a result of the propagation of unloading waves. In detail, the latter work (Kowalczyk & Gajo, 2022) shows in numerical studies and by comparison with some shear stack experiments from the past (Dar, 1993;Durante, 2015) how unloading elastic waves can potentially be released upon unloading/reloading in the steady-state response in a non-linear material of hysteretic stress-strain behaviour, that is, such as soil.…”

“…Moreover, the most recent advanced numerical studies (Kowalczyk, 2020;Kowalczyk & Gajo, 2022) show a novel idea in the stress wave propagation and an introductory proof that high-frequency content observed in soil can be a result of the propagation of unloading waves. In detail, the latter work (Kowalczyk & Gajo, 2022) shows in numerical studies and by comparison with some shear stack experiments from the past (Dar, 1993;Durante, 2015) how unloading elastic waves can potentially be released upon unloading/reloading in the steady-state response in a non-linear material of hysteretic stress-strain behaviour, that is, such as soil. The suggested idea of the existence of elastic waves in the steady-state response is novel since the presence of elastic waves is recognised solely in the case of transient dynamic response (e.g.…”

“…Kramer, 1996). To sum up, there are some research studies showing the source of high-frequency content in non-linear soil; nevertheless, the studies on the impact of soil-generated high-frequency motion on the structural response received very little attention and were only very briefly shown, mainly in relation to the response of kinematic piles, in other works of the author (Kowalczyk, 2020(Kowalczyk, , 2021Kowalczyk & Gajo, 2022).…”