A bed pressure correction of the friction term for depth-averaged granular flow models

Depth-averaged models, such as the Savage-Hutter model with Coulomb or Pouliquen fric tion laws, do not in some cases preserve the physical threshold of motion. In particular, the simulated granular mass can start to flow (or stay at rest) even if the slope angle of its free surface is lower (or hig...

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Autores: Bouchut, François, Delgado Sánchez, Juan Manuel, Fernández Nieto, Enrique Domingo, Mangeney, Anne, Narbona Reina, Gladys
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/131084
Acceso en línea:https://hdl.handle.net/11441/131084
https://doi.org/10.1016/j.apm.2022.01.034
Access Level:acceso abierto
Palabra clave:Depth averaged
Landslides
Bed pressure
Debris flows
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spelling A bed pressure correction of the friction term for depth-averaged granular flow modelsBouchut, FrançoisDelgado Sánchez, Juan ManuelFernández Nieto, Enrique DomingoMangeney, AnneNarbona Reina, GladysDepth averagedLandslidesBed pressureDebris flowsDepth-averaged models, such as the Savage-Hutter model with Coulomb or Pouliquen fric tion laws, do not in some cases preserve the physical threshold of motion. In particular, the simulated granular mass can start to flow (or stay at rest) even if the slope angle of its free surface is lower (or higher) than the repose angle of the granular material involved. The problem is related to the hydrostatic pressure assumption, associated with the direction of integration, which is orthogonal to a reference plane or a reference bottom. We propose here an initial method to correct this misleading behavior. Firstly, we define a correction of the friction term that accounts for the Jacobian of a change of coordinates, making it possible to reproduce the physical threshold of motion and thus the solutions at rest. Sec ondly, we observe that the 3D model presented in [F. Bouchut, I. Ionescu, and A. Mangeney. An analytic approach for the evolution of the static-flowing interface in viscoplastic granular flows. Commun, Math. Sci., 14(8):2101–2126, 2016] verifies the physical thresholds of mo tion because it is based on a second order correction of the pressure valid for slow granu lar flows. The correction proposed here ensures that the model preserves, up to the second order, the physical threshold of motion defined by the repose angle of the material. Sev eral numerical tests are presented to illustrate certain problems related to classical depth averaged models and the remedial effect of the proposed correction, in particular through comparisons with experimental data. We finally show that this correction is not exact far from the starting and stopping phases of the granular avalanche and should be improved by adding other second order terms in the pressure approximationMinisterio de Ciencia, Innovación y Universidades RTI2018- 096064-B-C22European Research Council ERC-CG-2013-PE10-617472 SLIDEQUAKESElsevierMatemática Aplicada IMinisterio de Ciencia, Innovación y Universidades (MICINN). EspañaEuropean Research Council (ERC)2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/131084https://doi.org/10.1016/j.apm.2022.01.034reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésApplied Mathematical Modelling, 106 (June 2022), 627-658.RTI2018- 096064-B-C22ERC-CG-2013-PE10-617472 SLIDEQUAKEShttps://www.sciencedirect.com/science/article/pii/S0307904X22000531info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1310842026-06-17T12:51:07Z
dc.title.none.fl_str_mv A bed pressure correction of the friction term for depth-averaged granular flow models
title A bed pressure correction of the friction term for depth-averaged granular flow models
spellingShingle A bed pressure correction of the friction term for depth-averaged granular flow models
Bouchut, François
Depth averaged
Landslides
Bed pressure
Debris flows
title_short A bed pressure correction of the friction term for depth-averaged granular flow models
title_full A bed pressure correction of the friction term for depth-averaged granular flow models
title_fullStr A bed pressure correction of the friction term for depth-averaged granular flow models
title_full_unstemmed A bed pressure correction of the friction term for depth-averaged granular flow models
title_sort A bed pressure correction of the friction term for depth-averaged granular flow models
dc.creator.none.fl_str_mv Bouchut, François
Delgado Sánchez, Juan Manuel
Fernández Nieto, Enrique Domingo
Mangeney, Anne
Narbona Reina, Gladys
author Bouchut, François
author_facet Bouchut, François
Delgado Sánchez, Juan Manuel
Fernández Nieto, Enrique Domingo
Mangeney, Anne
Narbona Reina, Gladys
author_role author
author2 Delgado Sánchez, Juan Manuel
Fernández Nieto, Enrique Domingo
Mangeney, Anne
Narbona Reina, Gladys
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Ministerio de Ciencia, Innovación y Universidades (MICINN). España
European Research Council (ERC)
dc.subject.none.fl_str_mv Depth averaged
Landslides
Bed pressure
Debris flows
topic Depth averaged
Landslides
Bed pressure
Debris flows
description Depth-averaged models, such as the Savage-Hutter model with Coulomb or Pouliquen fric tion laws, do not in some cases preserve the physical threshold of motion. In particular, the simulated granular mass can start to flow (or stay at rest) even if the slope angle of its free surface is lower (or higher) than the repose angle of the granular material involved. The problem is related to the hydrostatic pressure assumption, associated with the direction of integration, which is orthogonal to a reference plane or a reference bottom. We propose here an initial method to correct this misleading behavior. Firstly, we define a correction of the friction term that accounts for the Jacobian of a change of coordinates, making it possible to reproduce the physical threshold of motion and thus the solutions at rest. Sec ondly, we observe that the 3D model presented in [F. Bouchut, I. Ionescu, and A. Mangeney. An analytic approach for the evolution of the static-flowing interface in viscoplastic granular flows. Commun, Math. Sci., 14(8):2101–2126, 2016] verifies the physical thresholds of mo tion because it is based on a second order correction of the pressure valid for slow granu lar flows. The correction proposed here ensures that the model preserves, up to the second order, the physical threshold of motion defined by the repose angle of the material. Sev eral numerical tests are presented to illustrate certain problems related to classical depth averaged models and the remedial effect of the proposed correction, in particular through comparisons with experimental data. We finally show that this correction is not exact far from the starting and stopping phases of the granular avalanche and should be improved by adding other second order terms in the pressure approximation
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/131084
https://doi.org/10.1016/j.apm.2022.01.034
url https://hdl.handle.net/11441/131084
https://doi.org/10.1016/j.apm.2022.01.034
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Applied Mathematical Modelling, 106 (June 2022), 627-658.
RTI2018- 096064-B-C22
ERC-CG-2013-PE10-617472 SLIDEQUAKES
https://www.sciencedirect.com/science/article/pii/S0307904X22000531
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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