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

Piotr Kowalczyk
Piotr Kowalczyk
   | 22. Sept. 2022
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Article Category: Original Study
Online veröffentlicht: 22. Sept. 2022
Seitenbereich: 253 - 266
Eingereicht: 20. Okt. 2021
Akzeptiert: 22. Apr. 2022
DOI: https://doi.org/10.2478/sgem-2022-0015
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© 2022 Piotr Kowalczyk, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Geometry of numerically modelled experimental setup with a single degree of freedom (SDOF) structure: a) long side view, b) plan (dimensions in mm).
Geometry of numerically modelled experimental setup with a single degree of freedom (SDOF) structure: a) long side view, b) plan (dimensions in mm).

Figure 2

Mesh discretisation used in the 3D finite element model.
Mesh discretisation used in the 3D finite element model.

Figure 3

Calibration of the hypoplastic sand constitutive model in terms of shear stiffness degradation G/G0 against shear strain.
Calibration of the hypoplastic sand constitutive model in terms of shear stiffness degradation G/G0 against shear strain.

Figure 4

Free field response computed for the soil column with the chosen calibration of the hypoplastic sand model (Table 1): a) horizontal accelerations, b) shear strains, c) spectral response for horizontal accelerations at the soil base, d) spectral response for horizontal accelerations at the soil top, e) stress–strain behaviour.
Free field response computed for the soil column with the chosen calibration of the hypoplastic sand model (Table 1): a) horizontal accelerations, b) shear strains, c) spectral response for horizontal accelerations at the soil base, d) spectral response for horizontal accelerations at the soil top, e) stress–strain behaviour.

Figure 5

Comparison of the computations and the experimental measurements (Durante, 2015) in free field in the steady-state response: a) horizontal accelerations, b) evaluation of the spectral response of the computed horizontal accelerations, c) evaluation of the spectral response of the horizontal accelerations in the experiment.
Comparison of the computations and the experimental measurements (Durante, 2015) in free field in the steady-state response: a) horizontal accelerations, b) evaluation of the spectral response of the computed horizontal accelerations, c) evaluation of the spectral response of the horizontal accelerations in the experiment.

Figure 6

Comparison of relative horizontal displacements between the computations and the experimental measurements (Durante, 2015) obtained in free field in the steady-state response.
Comparison of relative horizontal displacements between the computations and the experimental measurements (Durante, 2015) obtained in free field in the steady-state response.

Figure 7

Comparison of the computations and the experimental measurements (Durante, 2015) obtained at the top of the structure in the steady-state response: a) horizontal accelerations, b) evaluation of the spectral response of the computed and measured horizontal accelerations.
Comparison of the computations and the experimental measurements (Durante, 2015) obtained at the top of the structure in the steady-state response: a) horizontal accelerations, b) evaluation of the spectral response of the computed and measured horizontal accelerations.

Figure A1

Comparison of a cyclic simple shear test simulated by the hypoplastic sand model and compared with experimental data from literature (Shahnazari & Towhata, 2002): a) stress–strain behaviour (simulation), b) stress–strain behaviour (experiment), c) volumetric response (simulation), d) volumetric response (experiment).
Comparison of a cyclic simple shear test simulated by the hypoplastic sand model and compared with experimental data from literature (Shahnazari & Towhata, 2002): a) stress–strain behaviour (simulation), b) stress–strain behaviour (experiment), c) volumetric response (simulation), d) volumetric response (experiment).

Calibration of the model parameters for the hypoplastic sand model.

Parameter Description Value
Basic hypoplastictiy φc Critical friction angle 33.0
hs Granular hardness (kPa) 2.5 × 106
n Stiffness exponent ruling pressure-sensitivity 0.42
ed0 Limiting minimum void ratio at p = 0 kPa 0.613
ec0 Limiting void ratio at p = 0 kPa 1.01
ei0 Limiting maximum void ratio at p = 0 kPa 1.21
α Exponent linking peak stress with critical stress 0.13
β Stiffness exponent scaling barotropy factor 0.8
Intergranular strain concept R Elastic range 0.00004
mR Stiffness multiplier 4.0
mT Stiffness multiplier after 90° change in strain path 2.0
βR Control of rate of evolution of intergranular strain 0.8
χ Control on interpolation between elastic and hypoplastic response 0.5
ϑ Control on strain accumulation 5.0
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