A Viscoelastic Model for the Dynamic Behavior of Saturated Poroelastic Soils

Bardet, Jean-Pierre

doi:10.1115/1.2899417

Cited by 64 publications

(43 citation statements)

References 14 publications

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“…Figure 7(b) shows some discrepancies between results obtained with a two-phase poroelastic material and the approximate viscoelastic model for a sediment with extremely high permeability (k = 10 m=s). A similar conclusion was reached by Bardet [19]. Results presented in the following correspond to a permeability value of k = 10 −3 m=s.…”

Section: Simpliÿed Sediment Modelssupporting

confidence: 78%

“…Thus the model accurately represents the e ects of the P1-and S-waves and ignores the P2-waves. Bardet [19] presented a Kelvin-Voigt viscoelastic model with linear frequency dependency of dissipation. Instead of the frequency dependency, the present model is based on the actual values of real and imaginary (damping) parts of the wave velocities, computed at each frequency for the porous material.…”

Section: Simpliÿed Sediment Modelsmentioning

confidence: 99%

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Three‐dimensional models of reservoir sediment and effects on the seismic response of arch dams

Maeso

Aznárez

Domínguez

2004

Earthq Engng Struct Dyn

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SUMMARYThe important e ects of bottom sediments on the seismic response of arch dams are studied in this paper. To do so, a three-dimensional boundary element model is used. It includes the water reservoir as a compressible uid, the dam and unbounded foundation rock as viscoelastic solids, and the bottom sediment as a two-phase poroelastic domain with dynamic behaviour described by Biot's equations. Dynamic interaction among all those regions, local topography and travelling wave e ects are taken into account. The results obtained show the important in uence of sediment compressibility and permeability on the seismic response. The former is associated with a general change of the system response whereas the permeability has a signiÿcant in uence on damping at resonance peaks. The analysis is carried out in the frequency domain considering time harmonic excitation due to P and S plane waves. The timedomain results obtained by using the Fourier transform for a given earthquake accelerogram are also shown. The possibility of using simpliÿed models to represent the bottom sediment e ects is discussed in the paper. Two alternative models for porous sediment are tested. Simpliÿed models are shown to be able to reproduce the e ects of porous sediments except for very high permeability values.

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Section: Simpliÿed Sediment Modelssupporting

confidence: 78%

Section: Simpliÿed Sediment Modelsmentioning

confidence: 99%

Three‐dimensional models of reservoir sediment and effects on the seismic response of arch dams

Maeso

Aznárez

Domínguez

2004

Earthq Engng Struct Dyn

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“…22,23,32 Additionally, Bardet demonstrated that an equivalent viscoelastic model can be derived by equating expressions for VE energy storage and attenuation with the analogous PE expressions. 33 The VE equivalent model closely matched PE behavior except in certain conditions, including when the actuation period is on the same order as the fluid equilibration time, 34 approximated by…”

Section: C Choice Of Model For Brain Tissuementioning

confidence: 99%

Suitability of poroelastic and viscoelastic mechanical models for high and low frequency MR elastography

et al. 2015

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Purpose: Descriptions of the structure of brain tissue as a porous cellular matrix support application of a poroelastic (PE) mechanical model which includes both solid and fluid phases. However, the majority of brain magnetic resonance elastography (MRE) studies use a single phase viscoelastic (VE) model to describe brain tissue behavior, in part due to availability of relatively simple direct inversion strategies for mechanical property estimation. A notable exception is low frequency intrinsic actuation MRE, where PE mechanical properties are imaged with a nonlinear inversion algorithm. Methods: This paper investigates the effect of model choice at each end of the spectrum of in vivo human brain actuation frequencies. Repeat MRE examinations of the brains of healthy volunteers were used to compare image quality and repeatability for each inversion model for both 50 Hz externally produced motion and ≈1 Hz intrinsic motions. Additionally, realistic simulated MRE data were generated with both VE and PE finite element solvers to investigate the effect of inappropriate model choice for ideal VE and PE materials. Results: In vivo, MRE data revealed that VE inversions appear more representative of anatomical structure and quantitatively repeatable for 50 Hz induced motions, whereas PE inversion produces better results at 1 Hz. Reasonable VE approximations of PE materials can be derived by equating the equivalent wave velocities for the two models, provided that the timescale of fluid equilibration is not similar to the period of actuation. An approximation of the equilibration time for human brain reveals that this condition is violated at 1 Hz but not at 50 Hz. Additionally, simulation experiments when using the "wrong" model for the inversion demonstrated reasonable shear modulus reconstructions at 50 Hz, whereas cross-model inversions at 1 Hz were poor quality. Attenuation parameters were sensitive to changes in the forward model at both frequencies, however, no spatial information was recovered because the mechanisms of VE and PE attenuation are different. Conclusions: VE inversions are simpler with fewer unknown properties and may be sufficient to capture the mechanical behavior of PE brain tissue at higher actuation frequencies. However, accurate modeling of the fluid phase is required to produce useful mechanical property images at the lower

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“…The interested reader can refer to [40,41,47] as well as the references therein for more information of the model's historical backgrounds and examples of its application in soil dynamics. It is interesting to note that the author in [13] showed that the Kelvin-Voigt model can be used to describe the dynamic response of the saturated poroelastic materials https://www.cambridge.org/core/terms. https://doi.org/10.4208/aamm.…”

Section: The Kelvin-voigt Modelmentioning

confidence: 99%

A Brief Review of Elasticity and Viscoelasticity for Solids

2011

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Abstract. There are a number of interesting applications where modeling elastic and/or viscoelastic materials is fundamental, including uses in civil engineering, the food industry, land mine detection and ultrasonic imaging. Here we provide an overview of the subject for both elastic and viscoelastic materials in order to understand the behavior of these materials. We begin with a brief introduction of some basic terminology and relationships in continuum mechanics, and a review of equations of motion in a continuum in both Lagrangian and Eulerian forms. To complete the set of equations, we then proceed to present and discuss a number of specific forms for the constitutive relationships between stress and strain proposed in the literature for both elastic and viscoelastic materials. In addition, we discuss some applications for these constitutive equations. Finally, we give a computational example describing the motion of soil experiencing dynamic loading by incorporating a specific form of constitutive equation into the equation of motion.

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A Viscoelastic Model for the Dynamic Behavior of Saturated Poroelastic Soils

Cited by 64 publications

References 14 publications

Three‐dimensional models of reservoir sediment and effects on the seismic response of arch dams

Three‐dimensional models of reservoir sediment and effects on the seismic response of arch dams

Suitability of poroelastic and viscoelastic mechanical models for high and low frequency MR elastography

A Brief Review of Elasticity and Viscoelasticity for Solids

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