Micro and macroscopic processes on the collapse and growth of cavity regions in a granular material due to viscous flow

Sano, Osamu; Nagata, Yusaku

doi:10.1201/9781315106656-68

Cited by 3 publications

(5 citation statements)

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“…Duran 1997). We have chosen the front-end boundary of respective cavities to be such positions, which is supported in our 2D experiment (Kaneko and Sano 2005, Sano and Nagata 2006, 2006b, Sano 2020. Generally speaking, however, granular material is more often inhomogeneous in practice, so that a catastrophic configuration change can be triggered at any positions.…”

Section: Discussionmentioning

confidence: 99%

“…Enhancement of the flow at the center of a cavity as much as three times of the undisturbed flow is noteworthy for the accurate prediction of the groundwater flow by a single boring method in the field work measurement. They also pointed out the possibility of the collapse of the cavities and global fluidization, which are caused by the local enhancement of the stress on the cavity boundaries due to the concentration of incident flow (Kaneko and Sano 2005, Sano and Nagata 2006, 2006b, Koizumi et al 2009, Sano 2011, Sano et al 2013.…”

Section: Introductionmentioning

confidence: 99%

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Viscous flow through macroscopic spherical cavities in an arbitrary configuration in a granular material

Sano

2023

Fluid Dyn. Res.

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Viscous flow through macroscopic spherical cavities in a granular material is theoretically investigated. Number, size and configuration of the cavities are arbitrary, except that cavities are sufficiently distant to allow asymptotic analysis on their interaction, which is taken into account up to $O(a/l)^3$, where $a$ and $l$ are the characteristic radius and inter-cavity distance, respectively. Dependence of the flow field, flux into respective cavities and stress field {¥it etc} on the cavity size, separation distance and orientation are analyzed. As further examples, 1D-, 2D-, and 3D-array of equal size cavities are examined, by which onset of the collapse of cavity and development of the collapsed region are elucidated. The latter may predict landslides and other flow-induced catastrophic changes in the material with quasi-equilibrium solid structure, as well as microscale waterway formation in human tissue known as angiogenesis.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Viscous flow through macroscopic spherical cavities in an arbitrary configuration in a granular material

Sano

2023

Fluid Dyn. Res.

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“…If, however, a number of cavities are distributed within a well-interacting distance, the fluidized region will merge to form a long waterway. The details on the flow through a noncircular cavity are given in [7,8], while evolution of the cavity shape, migration and merging of cavities are given in [10][11][12][13][14]. Furthermore, if many such waterways spread sheet-like and slanted, as is often observed on the boundary of impermeable layer of stratum, one side of the granular layer is disconnected to the other side, which can be a cause of landslide at a heavy rainfall.…”

Section: Discussionmentioning

confidence: 99%

“…Flow concentration enhances the local stress on the upstream-side boundary of the cavity, so that the grains of that part will be eroded and carried to the downstream-side boundary if it exceeds certain criteria. This process effectively causes the migration of the cavity towards the upstream direction, or a narrow waterway formation in the medium as was previously shown [10][11][12][13][14][15]. In this paper, we reformulate the analysis on the fundamental flow through a single cavity, and apply it to the interaction of two cavities.…”

Section: Introductionmentioning

confidence: 87%

“…In the present granular material, however, the grains are multiply and randomly in contact with each other, so that theoretical prediction of the maximum static force for the breakdown of structure will be improbable. In our apparatus, we determined U c (= 0.62 [cm s −1 ]) experimentally (see the details in refs [9][10][11][12][13]), by which U ∞ is normalized, i.e. U * = U ∞ /U c .…”

Section: Collapse Of Cavities (A) Characteristic Process Of the Collapse Of Cavities Due To Viscous Flowmentioning

confidence: 99%

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Viscous flow and collapse of macroscopic cavities in a granular material in terms of a Darcylet

Sano

2020

Phil. Trans. R. Soc. A.

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Viscous flow through a granular material that has a macroscopic cavity is obtained on the basis of the Stokes and the generalized Darcy’s equation. A new singularity termed ‘Darcylet’, a fundamental flow in the granular material that acts like a point force with negative direction, is proposed, which is applied to elucidate the interaction of two cavities. Depending on the configuration of the latter, the volume flux into the cavity increases, which enhances the local stresses on the boundary, causes the collapse of cavities and triggers landslides. This article is part of the theme issue ‘Stokes at 200 (Part 1)’.

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Viscous flow around three-dimensional macroscopic cavities in a granular material: asymptotic theory for two sufficiently distant spherical cavities of arbitrary configuration

2023

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Viscous flow around two spherical macroscopic cavities (or void spaces) in a granular material, which is exposed to an otherwise uniform flow at infinity, is investigated. The flow field is obtained analytically by solving the Stokes equation inside and the Darcy–Brinkman equation outside of the cavities, where continuity of the velocity and that of the stress are assumed on the boundary. In our previous complementary paper (Sano, Karmakar & Sekhar, J. Fluid Mech., vol. 931, 2022, A20), we obtain that two cavities of equal size in a tandem position are more prone to collapse for a shorter centre-to-centre distance with low permeability. In the present study, the asymptotic analysis of the interaction of two spherical cavities of different sizes with arbitrary configuration is presented. Particular attention is paid to the configuration dependence of two cavities of equal radius. The velocity field and the volume flux into respective cavities are calculated, which reveal that two cavities with orientation less than a certain critical angle are given a larger volume flux and are more prone to collapse. The present results are applicable to predicting the behaviour in a fixed-bed regime of a solid–gas transport system, microscale waterway formation in a granular material, onset of landslides, collapse of cliffs and river banks, etc.

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Micro and macroscopic processes on the collapse and growth of cavity regions in a granular material due to viscous flow

Cited by 3 publications

References 1 publication

Viscous flow through macroscopic spherical cavities in an arbitrary configuration in a granular material

Viscous flow through macroscopic spherical cavities in an arbitrary configuration in a granular material

Viscous flow and collapse of macroscopic cavities in a granular material in terms of a Darcylet

Viscous flow around three-dimensional macroscopic cavities in a granular material: asymptotic theory for two sufficiently distant spherical cavities of arbitrary configuration

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