Modelación numérica bidimensional de la socavación local en pilas de puente incluyendo efectos de flujo secundario

ilustraciones

Autores:: Durán Santana, Leandro

Tipo de recurso:

Fecha de publicación:: 2021

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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repository_id_str
dc.title.spa.fl_str_mv	Modelación numérica bidimensional de la socavación local en pilas de puente incluyendo efectos de flujo secundario
dc.title.translated.eng.fl_str_mv	Two-Dimensional Numerical Modeling of Local Scour in Bridge Piles including Secondary Flow Effects Two-dimensional numerical modeling of local scour in bridge piles including secondary flow effects
title	Modelación numérica bidimensional de la socavación local en pilas de puente incluyendo efectos de flujo secundario
spellingShingle	Modelación numérica bidimensional de la socavación local en pilas de puente incluyendo efectos de flujo secundario 620 - Ingeniería y operaciones afines::627 - Ingeniería hidráulica Socavación Local Flujos Secundarios Morfodinámica Sisyphe Local Scour Secondary Flows Morphodynamic Ingeniería hidráulica
title_short	Modelación numérica bidimensional de la socavación local en pilas de puente incluyendo efectos de flujo secundario
title_full	Modelación numérica bidimensional de la socavación local en pilas de puente incluyendo efectos de flujo secundario
title_fullStr	Modelación numérica bidimensional de la socavación local en pilas de puente incluyendo efectos de flujo secundario
title_full_unstemmed	Modelación numérica bidimensional de la socavación local en pilas de puente incluyendo efectos de flujo secundario
title_sort	Modelación numérica bidimensional de la socavación local en pilas de puente incluyendo efectos de flujo secundario
dc.creator.fl_str_mv	Durán Santana, Leandro
dc.contributor.advisor.none.fl_str_mv	Escobar Vargas, Jorge Alberto Ordoñez Ordoñez, Jaime Iván
dc.contributor.author.none.fl_str_mv	Durán Santana, Leandro
dc.contributor.researchgroup.spa.fl_str_mv	Grupo de Investigación en Ingeniería de Recursos Hidrícos - GIREH
dc.subject.ddc.spa.fl_str_mv	620 - Ingeniería y operaciones afines::627 - Ingeniería hidráulica
topic	620 - Ingeniería y operaciones afines::627 - Ingeniería hidráulica Socavación Local Flujos Secundarios Morfodinámica Sisyphe Local Scour Secondary Flows Morphodynamic Ingeniería hidráulica
dc.subject.proposal.spa.fl_str_mv	Socavación Local Flujos Secundarios Morfodinámica
dc.subject.proposal.none.fl_str_mv	Sisyphe
dc.subject.proposal.eng.fl_str_mv	Local Scour Secondary Flows Morphodynamic
dc.subject.unesco.none.fl_str_mv	Ingeniería hidráulica
description	ilustraciones
publishDate	2021
dc.date.accessioned.none.fl_str_mv	2021-07-01T16:31:38Z
dc.date.available.none.fl_str_mv	2021-07-01T16:31:38Z
dc.date.issued.none.fl_str_mv	2021
dc.type.spa.fl_str_mv	Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv	info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv	info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv	Text
dc.type.redcol.spa.fl_str_mv	http://purl.org/redcol/resource_type/TM
status_str	acceptedVersion
dc.identifier.uri.none.fl_str_mv	https://repositorio.unal.edu.co/handle/unal/79751
dc.identifier.instname.spa.fl_str_mv	Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv	Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv	https://repositorio.unal.edu.co/
url	https://repositorio.unal.edu.co/handle/unal/79751 https://repositorio.unal.edu.co/
identifier_str_mv	Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv	spa
language	spa
dc.relation.references.spa.fl_str_mv	Alamgir, K. (2005). M.Sc. Thesis. Modelling local scour around bridge piers using TELEMAC. Cape Town: University of Cape Town. Alcrudo, F. (2007). Aerodinamica. Area de Mecanica de Fluidos. Zaragoza: PS-Universidad de Zaragoza. Anderson, J. (2005). Ludwig Prantls Boundary layer. Physics Today, (ef). Armitage, N., & McGahey, C. (2003). A unit stream power model for the prediction of local scour in rivers. South Africa: Water Research Commission. Ata, R. (2018). Telemac2d User Manual. Paris: Telemac-Mascaret, version v8p0. Badia, M. B. (2011). Tesina. Estudio Experimental de la erosion local en pilas de puente cuadradas. Influencia de la anchura de la pila. Barcelona, España: Escuela tecnica de Barcelona. Baker, R. (1986). M.Sc. Thesis. Local Scour at Bridge piers in non-uniform sediment. . Auckland: University of Auckland, New Zeland. Bresch, D. N. (2010). Matehmatical drivation of viscous shallow-water equations with zero surface tension. Hal <Hal-00456181. Breusers, H. N. (1965). Scouring around drilling platforms. Journal Hydraulic Research, 276. Breusers, H. N. (1977). Local Scour Around Cylindrical Piers. Journal of Hydraulic Research, 15, 211-250. Brownlie, W. (1983). Flow depth in sand-bed channels. Journal of Hydarulic Engineering, 959-990. Chauchat, J., Cheng, Z., Nagel, T., Bonamy, C., & Hsu, T. (2017). SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport. Geoscientific Model Development, 4367-4392. Chiew, Y., & Melville, B. W. (1987). Local Scour around birdge piers. Journal of Hydraulic Research, 15-25. Dargahi, B. (1989). The turbulent flow field around a circular cylinder. Experiment in fluids, 1-12. Dargahi, B. (1990). Controlling Mechanism of Local Scouring. Journal of Hydraulic Engineering, Pag. 1197-1214. Debnath, K., & Chaudhuri, S. (2012). Local scour around non-circular piers in clay-sand mixed cohesive sediment beds. Engineering Geology, 1-14. Escauriaza, C., & Sotiropoulos, F. (2011b). Lagrangian model of bed-load transport in turbulent junction flow. Jorunal Fluid Mechanics, 36-76. Ettema, R. (1976). M.Sc. Thesis. Influence of material gradation on local scour. Auckland: University of Auckland, New Zealand. Excauriaza, C., & Sotiropoulos, F. (2011a). Initial stages of erosion and bed form development in a turbulent flow around a cylindrical pier. Journal of Geophysical Research, 1-24. Ezzeldin, M., Moharram, S., Sarhan, T., & Elhamrawy, A. (2006). Scour around pile group of small bridge. Tenth Internacional Water Technology Conference. (págs. 985-1002). Alexandria: IWTC10. Garcia, M. (2008). Sedimentation Engineering. Iilinois: Manual 110, American Society of Civil Engineers. Ge, L., & Sotiropoulos, F. (2005). Unsteady RANS modeling of complex hydraulic engineering flows. Journal Hydraulic Engineering, 131(9), 800-808. Heidarpour, M., Afzalimehr, H., & Izadinia, E. (2010). Reduction of local scour around bridge pier groups using collars. Internacional Journal of Sediment Research, 411-422. Hervouet, J. (2007). Hydrodynamics of Free Surface Flows. Paris, Francia: Jhon Wiley & Sons. Jain, S. C., & Fisher, E. E. (1979). Scour around circular bridge piers at high Froude numbers. Springfield, Virginia: Report. Federal Highway Administration NTIS. Kalim, .. M., & K., O. (2002). Simulation of flow around piers. Jorunal of Hydraulic Research, 161-174. Khosronejad, A., Kang, S., & Sotiropoulos, F. (2012). Experimental and Computacional investigation of local scour around bridge piers. Advances in Water Resources, 37, 73-85. Kirkil, G., Constantinescu, G., & Ettema, R. (2008). Coherent Structures in the Flow Field around a Circular Cylinder with Scour Hole. Journal of Hydraulic Engineering, 572-587. Kirkil, G., Constantinescu, G., & Ettema, R. (2009). Detached Eddy Simulation Investigation of Turbulence at a Circular Pier with Scour Hole. Journal of Hydraulic Engineering, 888-901. Kothayari, U., Garde, R., & Raju, K. (1992). Temporal variation of scour around circular bridge piers. Journal of Hydraulic Engineering, 1091-1106. Kothyari, U., & Kumar, A. (2010). Temporal variation of scour around circular bridge piers. Journal of Hydraulic Engineering, 35-48. Kundu, P., & Cohen, I. (2002). Fluid Mechanics. San Diego: Academic Press. Laursen, E. M. (1960). Scour at bridge crossings. Proceedings American Society Civil Engineers, 86, 39-54. Laursen, E. M., & Toch, A. (1956). Scour around bridge piers and abutments. Ames: Bulletin N°4, Iowa Highway Research Board. Lee, S., & Sturm, T. W. (2009). Effect of Sediment Size Scaling on Physical Modeling of Bridge Pier Scour. Journal of Hydraulic Engineering, 793-802. Melville, B. W. (1975). Local scour at bridge sites. Univ. of Auckland, Rep 117. Melville, B. W. (1984). Live-Bed Scour at Bridge Piers. Journal of Hydraulic Engineering, 1234-1247. Melville, B. W. (1997). Pier and abutment scour: Integrated approach. Journal of the Hydraulic Division, ASCE., 123(2), 125-136. Melville, B. W., & Sutherland, A. J. (1988). Design method for local scour at bridge piers. Journal of the Hydraulic Division, ASCE, 118(9), 1306-1310. Melville, B., & Chiew, Y. (1999). Time-Scale for local scour at bridge piers. Journal of Hydraulic Engineering, 59-65. Mia, F., & Nago, H. (2003). Design method of time-dependent local scour at circular brige pier. Journal of Hydraulic Engineering, 420-427. Mohammed, Y. S. (2015). Experimental invertigaticon of local scour around multi-vents bridge piers. Alexandria Engineering Journal, 54, 197-203. Morales, D. S. (2011). Tesis. Estudio de las causas y soluciones estructurales del colapso total o parcial de los puentes vehiculares de Colombia desde 1986 al 2011, y la evaluacion de las consecuencias del derrumbamiento de uno de ellos. Bogota, Colombia: Pontificia Universidad Javeriana. Mostafa, A., & Moussa, A. (2017). Evaluation of local scour around bridge piers for various geometrical shapes using mathematical models. Journal Ain Shams Engineering, 1-10. Nadaoka, K., & Yagi, H. (1990). Single-phase fluid modeling of sheet-flow toward the development of numerical movile bed. Proceedings of the 22th internacional conference coastal engineering. ASCE., 2346-2359. Nagata, N., Hosoda, T., Nakato, T., & Muramoto, Y. (2005). Three-dimensional numerical model for flow and bed deformation around river hydraulic structures. Journal Hydraulic Engineering, 131(12), 1074-87. Nagel, T., Chauchat, J., Bonamy, C., Liu, X., Cheng, Z., & Hsu, T.-J. (2020). Three-dimensional scour simulations with a two-phase flow model. Advances in Water Resources, 1-20. Neill, C. R. (1964a). Local scour around bridge piers. Alberta, Canada: Research Council of Alberta. Nurtjahyo, P. Y. (2002). Ph.D. Thesis. Numerical simulation of pier scour and contraction scour. Texas: Department of Civil Engineering. Texas A&M University. Olsen, N. R., & Melaaen, M. C. (1993). Three-dimensional calculation of scour around cylinders. Journal Hydraulic Engineers, 119(9), 1048-1054. Olsen, N., & Kjellesvig, H. (1998). Three-dimensional numerical flow modeling for estimation of maximum local scour depth. Journal of Hydraulic Research, 579-590. Perez, C. P. (2012). Msc. Thesis. Modelacion Numerica de la Hidrodinamica de la erosion en pilas de puentes con esviaje empleando la dinamica de fluidos computacional CFD. Mexico. D.F: Facultad de Ingenieria. Universidad Nacional Autonoma de Mexico. Petryk, S. (1969). Drag on cylinders in open chanels flows. Colorado: Colorado State University Ft. Collins. Pope, S. (2000). Turbulent Flows. Ithaca: Cambrige University Press. Posey, C. J. (1949). Why bridges fail in floods. Civil Engineering, 42-90. Randle, T. J., Yang, C. T., & Daraio, J. (2006). Erosion and Reservoir Sedimentation. En U. D. Reclamantion, Erosion and Sedimentation Manual (págs. 2.1-2.86). Denver, United State: U.S. Department of the Interior Bureau of Reclamantion. Raudkivi, A. (1986a). Functional Trends of Scour at Bridge Piers. Jorunal of Hydraulic Engineering, pag. 1-13. Raudkivi, A., & Ettema, R. (1986b). Clear water scour at cylindrical piers. Journal of Hydraulics Engineering, 109(3), 338-350. Rhodes, J., & Trent, R. (1993). Economics of floods, scour, and bridge failures. Hydraulic Engineering, 928-933. Richardson, E., Simons, D., & Lagasse, P. (2001). River engineering for highway encroachments—Highways in the river environment. Hydraulic Design Series 6 Pub, No FHWA NHI 01-004, na. Richardson, J. E., & Panchang, V. G. (1998). Three-dimensional simulation of scour inducing flow at bridge piers. Journal Hydraulics Engineering, 124(5), 530-540. Richardson, J. R., & Richardson, E. V. (2008). Bridge Scour Evaluation. En M. R. Garcia, Sedimentation Engineering (págs. 505-542). Reston, United States: American Society of Civil Engineers. Rocha, A. (1998). Introduccion a la Hidraulica Fluvial. Lima, Peru: Universidad Nacional de Ingenieria. Roper, A. (1965). M.Sc. Thesis wake region of a circular in a turbulent boundary layer. Colorado: Colorado State University Ft. Collins. Roper, A., Schneider, V., & Shen, H. (1967). Analytical approach to local scour. Proc. 12th IAHR Congress, pag. 151-161. Roulund, A., Sumer, B., & Fredsoe, J. (2005). Numercial and experimental investigation of flow and scour around a circular pile. Journal Fluid Mechanics, 534, 351-401. Salaheldin, T., Imran, J., & Chaudhry, M. (2004). Numerical Modeling of Three-Dimensional Flow Field Around Circular Piers. Journal of Hydraulic Engineering, 91-100. Sandoval, A. A. (2012). Tesis. Estimacion de la socavacion en puentes para su uso en el calculo del riesgo fisico. Ciudad de Mexixo, Mexico: Universidad Nacional Autonoma de Mexico. Shen, H., & Schneider, V. (1970). Efect of Bridge Pier Shape on Local Scour. Prepr. No. 1238, ASCE Nat. Meeting on Transport Eng. Sheppard, D., Melville, B., & Demir, H. (2014). Evaluation of Existing Ecuacion for Local Scour at Bridge Piers. Journal of Hydraulic Engineering, 14-23. Shields, A. (1936). Application of similarity principles and turbulence research to bed load movement. California Intitute of Technology, (Translated from German). Shirole, A. M., & Holt, R. C. (1991). Planning for a Comprehensive Bridge Safety Assurance Program. Transportation Research Record 1290. Sumer, B. (2007). Mathematical modelling of scour: A review. Journal of Hydraulic Research, 723-735. Sumer, B., & Mutlu, E. (2006). Hydrodynamics Around Cylindrical structures. Singapore World Scientific, et. Talmon, A., Struiksma, N., & M., v. M. (1995). Laboratory measurements of the direction of sediment transport on transverse alluvial-bed slopes. Journal of Hydraulic Research, 495-517. Tassi, P. (2018). Sisyphe User Manual. Paris, Francia: Telemac-Mascaret, version v8p0. Tison, L. J. (1940). Erosion autour de piles de pont en riviere. Ann. des Travaux. Publics de Belgique, 813-871. Tseng, M., Yen, C. L., & Song, C. C. (2000). Computation of three-dimensional flow around square and circular piers. Internacional Journal for Numerical Methods in Fluids, 207-227. Unger, J., & Hager, W. H. (2007). Down-flow and horseshoe vortex characteristics of sediment embedded bridge piers. Exp Fluids, 1-19. Vanoni, V. (1975). Sedimentation Engineering. New York: Manual 54, American Society of Civil Engineers. Versteeg, H., & Malalasekera, W. (1995). An Introduction to Computational Fluid Dynamics. Essex, UK: Addison Wesley Longman Limited. Vittal, N. K. (1994). Clear-Water Scour around bridge pier Group. Journal of Hydraulic Engineering, 120, 1309-18. Wang, S. S., & Jia, Y. (1999). Computational simulations of local scour at bridge crossings-capabilities and limitations. Proceedings of the 1999 international water resources engineering conference., (ef). Xiong, W., Cai, C., Kong, B., & Kong, X. (2016). CFD Simulations and Analyses for Bridge-Scour Development Using a Dynamic-Mesh Updating Technique. Journal of Computing in Civil Engineering, 1-11. Yanmaz, M., & Alanbilek, D. (1991). Study of Time-Dependent local socur around bridge piers. Journal of Hydraulic Engineering, 1247-1268. Zhao, M., Cheng, L., & Zang, Z. (2010). Experimental and numerical investigation of local scour around a submerged vertical circular cylinder in steady currents. Coastal Engineering, 709-721.
dc.rights.spa.fl_str_mv	Derechos reservados del autor
dc.rights.coar.fl_str_mv	http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv	Atribución-NoComercial-SinDerivadas 4.0 Internacional
dc.rights.uri.spa.fl_str_mv	http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.accessrights.spa.fl_str_mv	info:eu-repo/semantics/openAccess
rights_invalid_str_mv	Atribución-NoComercial-SinDerivadas 4.0 Internacional Derechos reservados del autor http://creativecommons.org/licenses/by-nc-nd/4.0/ http://purl.org/coar/access_right/c_abf2
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dc.format.extent.spa.fl_str_mv	175 páginas
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dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv	Bogotá - Ingeniería - Maestría en Ingeniería - Recursos Hidráulicos
dc.publisher.department.spa.fl_str_mv	Departamento de Ingeniería Civil y Agrícola
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ingeniería
dc.publisher.place.spa.fl_str_mv	Bogotá, Colombia
dc.publisher.branch.spa.fl_str_mv	Universidad Nacional de Colombia - Sede Bogotá
institution	Universidad Nacional de Colombia
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spelling	Atribución-NoComercial-SinDerivadas 4.0 InternacionalDerechos reservados del autorhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Escobar Vargas, Jorge Albertofc79016e18c015017918698387e8c6e3Ordoñez Ordoñez, Jaime Iván575a8f9e83d5eb31d0d8156ccf635677Durán Santana, Leandro401f8ed7ced8695d5409af9fb1acf01cGrupo de Investigación en Ingeniería de Recursos Hidrícos - GIREH2021-07-01T16:31:38Z2021-07-01T16:31:38Z2021https://repositorio.unal.edu.co/handle/unal/79751Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustracionesLa socavación local en pilas de puentes es un proceso físico complejo debido a que el comportamiento del campo de flujo alrededor de la pila es tridimensional con procesos turbulentos, acción de flujos secundarios y estructuras vorticosas difíciles de predecir, todo esto actuando en un lecho que puede ser variable en el tiempo y en el espacio. Esta complejidad dificulta el desarrollo de modelos matemáticos y numéricos que tengan un grado aceptable de precisión, ahora bien, los modelos que permiten representar el proceso de la socavación local con esta precisión son costosos computacionalmente, lo que los vuelve imprácticos en los ejercicios habituales de ingeniería. Por lo tanto, el objetivo de esta investigación es construir un modelo numérico que permita representar la socavación local en pilas de puentes con un costo computacional moderado y sin comprometer su precisión. Para ello el modelo se basó en las ecuaciones bidimensionales de aguas someras y se le incluyó el efecto asociado a los flujos secundarios que se presentan alrededor de la pila. A partir de los resultados de un modelo tridimensional hidrodinámico se propone una parametrización de estos flujos secundarios que está en función del número de Froude, la profundidad del flujo y el diámetro de la pila. Adicionalmente, se propone un esfuerzo de corte modificado que tiene en cuenta tanto los flujos horizontales como los flujos secundarios o verticales. El modelo numérico que se propone en esta investigación se implementó en el solver morfodinámico Sisyphe y fue acoplado con el solver hidrodinámico Telemac2D. Finalmente, el modelo se validó con resultados reportados en la literatura de un canal de laboratorio de sección transversal rectangular, esta validación reveló que el modelo está en la capacidad de reproducir la profundidad de socavación en equilibrio al frente de la pila, al igual que este reprodujo relativamente bien el hueco de socavación, a excepción de la zona aguas abajo donde se presentó subestimación de las profundidades de socavación.Local scour in bridge piers is a complex physical process because flow field behavior around the pile is three-dimensional with turbulent processes, secondary flow action and vortex structures that are difficult to predict, all this acting on a bed that can be variable in time and space. This complexity makes it difficult to develop mathematical and numerical models that have an acceptable degree of precision, however, the models that allow representing the local scour process with this precision are computationally expensive, which makes them impractical in normal engineering exercises. Therefore, the objective of this research is to construct a numerical model that allows to represent the local scour in bridge piers with a moderate computational cost and without compromising its precision. For this, the model was based on the two-dimensional equations of shallow waters and the effect associated with the secondary flows that occur around the pile was included. Based on the results of a three-dimensional hydrodynamic model, a parameterization of these secondary flows is proposed, which is a function of Froude number, depth flow and diameter of the pile. Additionally, a modified shear stress is proposed that considers both horizontal flows and secondary or vertical flows. Numerical model proposed in this research was implemented in the Sisyphe morphodynamic solver and was coupled with the Telemac2D hydrodynamic solver. Finally, the model was validated with results reported in the literature of a rectangular cross-sectional laboratory channel, this validation revealed that the model can reproduce the equilibrium depth of scour in at the front of the pile, just like this reproduced the scour hole relatively well, except for the downstream area where scour depths were underestimated.MaestríaMagíster en Ingeniería - Recursos HidráulicosHidráulica Fluvial175 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ingeniería - Maestría en Ingeniería - Recursos HidráulicosDepartamento de Ingeniería Civil y AgrícolaFacultad de IngenieríaBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá620 - Ingeniería y operaciones afines::627 - Ingeniería hidráulicaSocavación LocalFlujos SecundariosMorfodinámicaSisypheLocal ScourSecondary FlowsMorphodynamicIngeniería hidráulicaModelación numérica bidimensional de la socavación local en pilas de puente incluyendo efectos de flujo secundarioTwo-Dimensional Numerical Modeling of Local Scour in Bridge Piles including Secondary Flow EffectsTwo-dimensional numerical modeling of local scour in bridge piles including secondary flow effectsTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAlamgir, K. (2005). M.Sc. Thesis. Modelling local scour around bridge piers using TELEMAC. Cape Town: University of Cape Town.Alcrudo, F. (2007). Aerodinamica. Area de Mecanica de Fluidos. Zaragoza: PS-Universidad de Zaragoza.Anderson, J. (2005). Ludwig Prantls Boundary layer. Physics Today, (ef).Armitage, N., & McGahey, C. (2003). A unit stream power model for the prediction of local scour in rivers. South Africa: Water Research Commission.Ata, R. (2018). Telemac2d User Manual. Paris: Telemac-Mascaret, version v8p0.Badia, M. B. (2011). Tesina. Estudio Experimental de la erosion local en pilas de puente cuadradas. Influencia de la anchura de la pila. Barcelona, España: Escuela tecnica de Barcelona.Baker, R. (1986). M.Sc. Thesis. Local Scour at Bridge piers in non-uniform sediment. . Auckland: University of Auckland, New Zeland.Bresch, D. N. (2010). Matehmatical drivation of viscous shallow-water equations with zero surface tension. Hal <Hal-00456181.Breusers, H. N. (1965). Scouring around drilling platforms. Journal Hydraulic Research, 276.Breusers, H. N. (1977). Local Scour Around Cylindrical Piers. Journal of Hydraulic Research, 15, 211-250.Brownlie, W. (1983). Flow depth in sand-bed channels. Journal of Hydarulic Engineering, 959-990.Chauchat, J., Cheng, Z., Nagel, T., Bonamy, C., & Hsu, T. (2017). SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport. Geoscientific Model Development, 4367-4392.Chiew, Y., & Melville, B. W. (1987). Local Scour around birdge piers. Journal of Hydraulic Research, 15-25.Dargahi, B. (1989). The turbulent flow field around a circular cylinder. Experiment in fluids, 1-12.Dargahi, B. (1990). Controlling Mechanism of Local Scouring. Journal of Hydraulic Engineering, Pag. 1197-1214.Debnath, K., & Chaudhuri, S. (2012). Local scour around non-circular piers in clay-sand mixed cohesive sediment beds. Engineering Geology, 1-14.Escauriaza, C., & Sotiropoulos, F. (2011b). Lagrangian model of bed-load transport in turbulent junction flow. Jorunal Fluid Mechanics, 36-76.Ettema, R. (1976). M.Sc. Thesis. Influence of material gradation on local scour. Auckland: University of Auckland, New Zealand.Excauriaza, C., & Sotiropoulos, F. (2011a). Initial stages of erosion and bed form development in a turbulent flow around a cylindrical pier. Journal of Geophysical Research, 1-24.Ezzeldin, M., Moharram, S., Sarhan, T., & Elhamrawy, A. (2006). Scour around pile group of small bridge. Tenth Internacional Water Technology Conference. (págs. 985-1002). Alexandria: IWTC10.Garcia, M. (2008). Sedimentation Engineering. Iilinois: Manual 110, American Society of Civil Engineers.Ge, L., & Sotiropoulos, F. (2005). Unsteady RANS modeling of complex hydraulic engineering flows. Journal Hydraulic Engineering, 131(9), 800-808.Heidarpour, M., Afzalimehr, H., & Izadinia, E. (2010). Reduction of local scour around bridge pier groups using collars. 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Modelación numérica bidimensional de la socavación local en pilas de puente incluyendo efectos de flujo secundario

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