Polydispersity in granular flows: Exploring effects in dry and immersed environments

Granular flows are complex and evolving systems where grains interact with each other and, if immersed, interact with an ambient fluid. These flows occur at different velocities and state variables, and could behave like solids, liquids or even gases. Granular flows are involved in many circumstance...

Full description

Autores:
Polanía Meneses, Oscar Santiago
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2023
Institución:
Universidad de los Andes
Repositorio:
Séneca: repositorio Uniandes
Idioma:
eng
OAI Identifier:
oai:repositorio.uniandes.edu.co:1992/73261
Acceso en línea:
https://hdl.handle.net/1992/73261
Palabra clave:
Granular Flows
Polydispersity
Immersed
Ingeniería
Rights
openAccess
License
Attribution-NonCommercial-NoDerivatives 4.0 International
id UNIANDES2_be233823451745a77463721fb46c8fcc
oai_identifier_str oai:repositorio.uniandes.edu.co:1992/73261
network_acronym_str UNIANDES2
network_name_str Séneca: repositorio Uniandes
repository_id_str
dc.title.eng.fl_str_mv Polydispersity in granular flows: Exploring effects in dry and immersed environments
title Polydispersity in granular flows: Exploring effects in dry and immersed environments
spellingShingle Polydispersity in granular flows: Exploring effects in dry and immersed environments
Granular Flows
Polydispersity
Immersed
Ingeniería
title_short Polydispersity in granular flows: Exploring effects in dry and immersed environments
title_full Polydispersity in granular flows: Exploring effects in dry and immersed environments
title_fullStr Polydispersity in granular flows: Exploring effects in dry and immersed environments
title_full_unstemmed Polydispersity in granular flows: Exploring effects in dry and immersed environments
title_sort Polydispersity in granular flows: Exploring effects in dry and immersed environments
dc.creator.fl_str_mv Polanía Meneses, Oscar Santiago
dc.contributor.advisor.none.fl_str_mv Estrada Mejía, Nicolás
Cabrera Cabrera, Miguel Ángel
dc.contributor.author.none.fl_str_mv Polanía Meneses, Oscar Santiago
dc.contributor.jury.none.fl_str_mv Caicedo Hormaza, Bernardo
dc.contributor.researchgroup.none.fl_str_mv Facultad de Ingeniería::Geomateriales y Sistemas de Infraestructura
dc.subject.keyword.eng.fl_str_mv Granular Flows
topic Granular Flows
Polydispersity
Immersed
Ingeniería
dc.subject.keyword.none.fl_str_mv Polydispersity
Immersed
dc.subject.themes.spa.fl_str_mv Ingeniería
description Granular flows are complex and evolving systems where grains interact with each other and, if immersed, interact with an ambient fluid. These flows occur at different velocities and state variables, and could behave like solids, liquids or even gases. Granular flows are involved in many circumstances and scales, from geophysical mass flows such as landslides, debris flows, pyroclastic flows, and snow avalanches, to industrial processes like pharmaceuticals, food production, and construction. For simplicity, granular flows are commonly studied with a monodisperse distribution of grains (e.i., grains with nearly the same size); however, among these flows, the grains involved in these processes have different sizes, a property termed as polydispersity. This thesis focuses on the study of granular flows and, specifically, on the influence that polydispersity has on granular flows. We explore the effect that polydispersity has on steady flows with low inertia, where granular materials can be considered as solids, and high inertia, where granular materials can be considered as fluids. Additionally, we study dry and immersed granular flows in the granular column collapse configuration, that is a benchmark geometry for studying granular flows with phases of acceleration and deceleration. We study granular flows by means of experimental and numerical methods. The numerical simulations of granular flows are done with discrete element methods (DEM) and, for immersed cases, we use a coupled finite element method (FEM) with DEM. We also conduct a controlled experimental campaign in the triaxial test apparatus where we systematically vary the polydispersity level, aiming to study the strength of polydisperse granular materials in quasi-static conditions. Furthermore, we do the physical modelling of immersed and dry gravity-driven flows in the granular column collapse configuration. Our goal is to explore the influence of polydispersity on granular flows and to identify the influence of the basal fluid pressure on the mobility of granular flows. For the experiments, we use spherical beads, exclusively focusing on the effect that size polydispersity has on granular flows. Our results allow us to conclude that the shear strength of granular materials is independent of the size polydispersity from a quasistatic condition to a condition of high inertia. For very large inertial conditions, the shear strength of polydisperse materials is smaller compared to that of monodisperse materials. We found that this difference arises from distinct variations in geometric and force parameters belonging to the contact and force network. Additionally, we provide evidence that immersed granular flows are strongly influenced by an increase in polydispersity levels. We show that the difference between monodisperse and polydisperse materials essentially arises from different evolutions of the basal fluid pressure. The initiation of polydisperse flows is delayed compared to monodisperse flows, due to a sustained negative fluid pressure change with large amplitude. Then, as the flow deposits, polydisperse systems reach longer runout distances due to the generation of exceeding pore pressure that lasts longer than the exceeding pore pressure provoked by monodisperse systems. Finally, we propose a model that links flow kinetic energy with the mobility of granular flows, which applies to different polydispersity levels, and has been successfully validated through simulations and experiments. The results of this thesis provide new insights into the role of polydispersity in both dry and immersed granular flows.
publishDate 2023
dc.date.issued.none.fl_str_mv 2023-12-05
dc.date.accessioned.none.fl_str_mv 2024-01-16T14:58:34Z
dc.date.available.none.fl_str_mv 2024-01-16T14:58:34Z
dc.type.none.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.none.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.coar.none.fl_str_mv http://purl.org/coar/resource_type/c_db06
dc.type.content.none.fl_str_mv Text
dc.type.redcol.none.fl_str_mv https://purl.org/redcol/resource_type/TD
format http://purl.org/coar/resource_type/c_db06
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/1992/73261
dc.identifier.instname.none.fl_str_mv instname:Universidad de los Andes
dc.identifier.reponame.none.fl_str_mv reponame:Repositorio Institucional Séneca
dc.identifier.repourl.none.fl_str_mv repourl:https://repositorio.uniandes.edu.co/
url https://hdl.handle.net/1992/73261
identifier_str_mv instname:Universidad de los Andes
reponame:Repositorio Institucional Séneca
repourl:https://repositorio.uniandes.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.rights.en.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
dc.rights.uri.none.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.accessrights.none.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.coar.none.fl_str_mv http://purl.org/coar/access_right/c_abf2
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.none.fl_str_mv 137 páginas
dc.format.mimetype.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidad de los Andes
dc.publisher.program.none.fl_str_mv Doctorado en Ingeniería
dc.publisher.faculty.none.fl_str_mv Facultad de Ingeniería
publisher.none.fl_str_mv Universidad de los Andes
institution Universidad de los Andes
bitstream.url.fl_str_mv https://repositorio.uniandes.edu.co/bitstreams/ef66b1c8-b8e3-4c42-a170-5d45516b2e87/download
https://repositorio.uniandes.edu.co/bitstreams/b65a0d88-4ce3-4fca-8b5d-e3c532b75f5d/download
https://repositorio.uniandes.edu.co/bitstreams/99bf2305-b0d0-4673-b813-651bf40f01e8/download
https://repositorio.uniandes.edu.co/bitstreams/77a1bad3-f893-48be-b5f5-64c94efa4313/download
https://repositorio.uniandes.edu.co/bitstreams/b086f329-abbd-414c-a595-4c7c4748aae7/download
https://repositorio.uniandes.edu.co/bitstreams/41ea81e6-46de-478b-9cba-761b65958eae/download
https://repositorio.uniandes.edu.co/bitstreams/83fe6b35-fcf2-47ea-b235-76dd54bd75cf/download
https://repositorio.uniandes.edu.co/bitstreams/0b3c32b7-8898-4f41-8b0f-32916280a25e/download
bitstream.checksum.fl_str_mv ffd27a8b6ed032daa71a5752d30732f3
f7d51d991b760b5d152475e92a2130bf
ae9e573a68e7f92501b6913cc846c39f
4460e5956bc1d1639be9ae6146a50347
1e364559cf5ba61614c1f76991fe4fe0
70ec3d5690309e72a7f5070ec301cdfe
5f9f6afefa1715a80f2442c21b7c7bcb
2fe5908a7951cf30294ec10b1e34a07e
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio institucional Séneca
repository.mail.fl_str_mv adminrepositorio@uniandes.edu.co
_version_ 1808390500842995712
spelling Estrada Mejía, Nicolásvirtual::56-1Cabrera Cabrera, Miguel Ángelvirtual::57-1Polanía Meneses, Oscar SantiagoCaicedo Hormaza, Bernardovirtual::58-1Facultad de Ingeniería::Geomateriales y Sistemas de Infraestructura2024-01-16T14:58:34Z2024-01-16T14:58:34Z2023-12-05https://hdl.handle.net/1992/73261instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/Granular flows are complex and evolving systems where grains interact with each other and, if immersed, interact with an ambient fluid. These flows occur at different velocities and state variables, and could behave like solids, liquids or even gases. Granular flows are involved in many circumstances and scales, from geophysical mass flows such as landslides, debris flows, pyroclastic flows, and snow avalanches, to industrial processes like pharmaceuticals, food production, and construction. For simplicity, granular flows are commonly studied with a monodisperse distribution of grains (e.i., grains with nearly the same size); however, among these flows, the grains involved in these processes have different sizes, a property termed as polydispersity. This thesis focuses on the study of granular flows and, specifically, on the influence that polydispersity has on granular flows. We explore the effect that polydispersity has on steady flows with low inertia, where granular materials can be considered as solids, and high inertia, where granular materials can be considered as fluids. Additionally, we study dry and immersed granular flows in the granular column collapse configuration, that is a benchmark geometry for studying granular flows with phases of acceleration and deceleration. We study granular flows by means of experimental and numerical methods. The numerical simulations of granular flows are done with discrete element methods (DEM) and, for immersed cases, we use a coupled finite element method (FEM) with DEM. We also conduct a controlled experimental campaign in the triaxial test apparatus where we systematically vary the polydispersity level, aiming to study the strength of polydisperse granular materials in quasi-static conditions. Furthermore, we do the physical modelling of immersed and dry gravity-driven flows in the granular column collapse configuration. Our goal is to explore the influence of polydispersity on granular flows and to identify the influence of the basal fluid pressure on the mobility of granular flows. For the experiments, we use spherical beads, exclusively focusing on the effect that size polydispersity has on granular flows. Our results allow us to conclude that the shear strength of granular materials is independent of the size polydispersity from a quasistatic condition to a condition of high inertia. For very large inertial conditions, the shear strength of polydisperse materials is smaller compared to that of monodisperse materials. We found that this difference arises from distinct variations in geometric and force parameters belonging to the contact and force network. Additionally, we provide evidence that immersed granular flows are strongly influenced by an increase in polydispersity levels. We show that the difference between monodisperse and polydisperse materials essentially arises from different evolutions of the basal fluid pressure. The initiation of polydisperse flows is delayed compared to monodisperse flows, due to a sustained negative fluid pressure change with large amplitude. Then, as the flow deposits, polydisperse systems reach longer runout distances due to the generation of exceeding pore pressure that lasts longer than the exceeding pore pressure provoked by monodisperse systems. Finally, we propose a model that links flow kinetic energy with the mobility of granular flows, which applies to different polydispersity levels, and has been successfully validated through simulations and experiments. The results of this thesis provide new insights into the role of polydispersity in both dry and immersed granular flows.Doctor en IngenieríaDoctorado137 páginasapplication/pdfengUniversidad de los AndesDoctorado en IngenieríaFacultad de IngenieríaAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Polydispersity in granular flows: Exploring effects in dry and immersed environmentsTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttps://purl.org/redcol/resource_type/TDGranular FlowsPolydispersityImmersedIngeniería201810393Publicationhttps://scholar.google.es/citations?user=9Mm7xv4AAAAJvirtual::58-1https://scholar.google.es/citations?user=XvhZCvwAAAAJvirtual::57-10000-0002-9236-8130virtual::57-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000002929virtual::56-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000246379virtual::58-197f760aa-7d5b-4f4e-9b7c-2079d17ab699virtual::56-1f2957fb4-17e4-47e9-86c8-74d835ff1b4evirtual::57-197f760aa-7d5b-4f4e-9b7c-2079d17ab699virtual::56-1f2957fb4-17e4-47e9-86c8-74d835ff1b4evirtual::57-176fcc284-15ff-46ea-8bd7-c7f7cf3cb821virtual::58-176fcc284-15ff-46ea-8bd7-c7f7cf3cb821virtual::58-1ORIGINALPolydispersity in granular flows.pdfPolydispersity in granular flows.pdfapplication/pdf89378123https://repositorio.uniandes.edu.co/bitstreams/ef66b1c8-b8e3-4c42-a170-5d45516b2e87/downloadffd27a8b6ed032daa71a5752d30732f3MD51OSPM_Autorizacion_Tesis_Biblioteca.pdfOSPM_Autorizacion_Tesis_Biblioteca.pdfHIDEapplication/pdf270359https://repositorio.uniandes.edu.co/bitstreams/b65a0d88-4ce3-4fca-8b5d-e3c532b75f5d/downloadf7d51d991b760b5d152475e92a2130bfMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-82535https://repositorio.uniandes.edu.co/bitstreams/99bf2305-b0d0-4673-b813-651bf40f01e8/downloadae9e573a68e7f92501b6913cc846c39fMD52CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repositorio.uniandes.edu.co/bitstreams/77a1bad3-f893-48be-b5f5-64c94efa4313/download4460e5956bc1d1639be9ae6146a50347MD53TEXTPolydispersity in granular flows.pdf.txtPolydispersity in granular flows.pdf.txtExtracted texttext/plain101672https://repositorio.uniandes.edu.co/bitstreams/b086f329-abbd-414c-a595-4c7c4748aae7/download1e364559cf5ba61614c1f76991fe4fe0MD55OSPM_Autorizacion_Tesis_Biblioteca.pdf.txtOSPM_Autorizacion_Tesis_Biblioteca.pdf.txtExtracted texttext/plain2032https://repositorio.uniandes.edu.co/bitstreams/41ea81e6-46de-478b-9cba-761b65958eae/download70ec3d5690309e72a7f5070ec301cdfeMD57THUMBNAILPolydispersity in granular flows.pdf.jpgPolydispersity in granular flows.pdf.jpgGenerated Thumbnailimage/jpeg12264https://repositorio.uniandes.edu.co/bitstreams/83fe6b35-fcf2-47ea-b235-76dd54bd75cf/download5f9f6afefa1715a80f2442c21b7c7bcbMD56OSPM_Autorizacion_Tesis_Biblioteca.pdf.jpgOSPM_Autorizacion_Tesis_Biblioteca.pdf.jpgGenerated Thumbnailimage/jpeg11408https://repositorio.uniandes.edu.co/bitstreams/0b3c32b7-8898-4f41-8b0f-32916280a25e/download2fe5908a7951cf30294ec10b1e34a07eMD581992/73261oai:repositorio.uniandes.edu.co:1992/732612024-01-17 03:13:11.335http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internationalopen.accesshttps://repositorio.uniandes.edu.coRepositorio institucional Sénecaadminrepositorio@uniandes.edu.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