Influencia de la succión en la compresibilidad de suelos no saturados en trayectorias k0

ilustraciones, fotografías, gráficas, tablas

Autores:: Orjuela Garzón, Angélica Marcela

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	Influencia de la succión en la compresibilidad de suelos no saturados en trayectorias k0
dc.title.translated.eng.fl_str_mv	Influence of suction on the compressibility of unsaturated soils in k0 paths
title	Influencia de la succión en la compresibilidad de suelos no saturados en trayectorias k0
spellingShingle	Influencia de la succión en la compresibilidad de suelos no saturados en trayectorias k0 620 - Ingeniería y operaciones afines::624 - Ingeniería civil Estabilización de suelos Compactación de suelos Soil stabilization Comportamiento volumétrico Potencial de colapso Suelos compactados Suelos parcialmente saturados Consolidómetro de succión controlada Volumetric behaviour Collapse potential Compacted soils Partially saturated soils Suction-controlled oedometer
title_short	Influencia de la succión en la compresibilidad de suelos no saturados en trayectorias k0
title_full	Influencia de la succión en la compresibilidad de suelos no saturados en trayectorias k0
title_fullStr	Influencia de la succión en la compresibilidad de suelos no saturados en trayectorias k0
title_full_unstemmed	Influencia de la succión en la compresibilidad de suelos no saturados en trayectorias k0
title_sort	Influencia de la succión en la compresibilidad de suelos no saturados en trayectorias k0
dc.creator.fl_str_mv	Orjuela Garzón, Angélica Marcela
dc.contributor.advisor.none.fl_str_mv	Colmenares Montañez, Julio Esteban
dc.contributor.author.none.fl_str_mv	Orjuela Garzón, Angélica Marcela
dc.contributor.researchgroup.spa.fl_str_mv	Geotechnical Engineering Knowledge and Innovation Genki
dc.subject.ddc.spa.fl_str_mv	620 - Ingeniería y operaciones afines::624 - Ingeniería civil
topic	620 - Ingeniería y operaciones afines::624 - Ingeniería civil Estabilización de suelos Compactación de suelos Soil stabilization Comportamiento volumétrico Potencial de colapso Suelos compactados Suelos parcialmente saturados Consolidómetro de succión controlada Volumetric behaviour Collapse potential Compacted soils Partially saturated soils Suction-controlled oedometer
dc.subject.lemb.spa.fl_str_mv	Estabilización de suelos Compactación de suelos
dc.subject.lemb.eng.fl_str_mv	Soil stabilization
dc.subject.proposal.spa.fl_str_mv	Comportamiento volumétrico Potencial de colapso Suelos compactados Suelos parcialmente saturados Consolidómetro de succión controlada
dc.subject.proposal.eng.fl_str_mv	Volumetric behaviour Collapse potential Compacted soils Partially saturated soils Suction-controlled oedometer
description	ilustraciones, fotografías, gráficas, tablas
publishDate	2021
dc.date.issued.none.fl_str_mv	2021
dc.date.accessioned.none.fl_str_mv	2022-02-14T16:26:32Z
dc.date.available.none.fl_str_mv	2022-02-14T16:26:32Z
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/80974
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/80974 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	Ajdari, M., Monghassem, M., & Reza Lari, H. (2016). A modified osmotic diaphragmatic oedometer for investigating the hydro-mechanical response of unsaturated soils. Geotechnical Testing Journal, 39(6), 906–921. https://doi.org/10.1520/GTJ20150142 Alonso, Gens, A., & Hight, D. W. (1987). Special problems soils. General Report, proceedings of the 9th European Conference on Soil Mechanics. Dublin Vol 3: 1087–1146. Alonso, Gens, A., & Josa, A. (1990). A constitutive model for partially saturated soils. Géotechnique, 40(3), 405–430. https://doi.org/10.1680/geot.1990.40.3.405 Alshameri, B. (2020). Maximum dry density of sand – kaolin mixtures predicted by using fine content and specific gravity. SN Applied Sciences, 2(10), 1–7. https://doi.org/10.1007/s42452-020-03481-9 Bardanis, M., & Grifiza, S. (2016). Swelling and collapse of compacted soils to be used as earth dam cores. Proc. of the 3rd European Conference on Unsaturated Soils, 9. https://doi.org/10.1051/e3sconf/20160919003 Bhaskar, P., Boluk, B., Mosadegh, L., Banerjee, A., & Puppala, A. J. (2020). Effect of fines on hysteretic hydraulic conductivity of unsaturated soil. Geo-Congress, 60–69. Bishop, A.W. (1959). The principle of effective stress. Teknik Ukebland, 39: 859-863. Blatz, J. A., Cui, Y. J., & Oldecop, L. (2008). Vapour Equilibrium and Osmotic Technique for Suction Control. Geotechnical and Geological Engineering, 26(6), 661–673. https://doi.org/10.1007/s10706-008-9196-1 Burland, J. B., & Ridley, A. M. (1994). Discussion A new instrument for the measurement of soil moisture suction. Géotechnique, Vol. 44, pp. 551–556. https://doi.org/10.1680/geot.1994.44.3.551 Chiu, T.-F., & Shackelford, C. D. (1998). Unsaturated Hydraulic Conductivity of Compacted Sand-Kaolin Mixtures. Journal of Geotechnical and Geoenvironmental Engineering, 124(February), 160–170. Colmenares, J. E. (2002). Suction and volume change of compacted sand-bentonite mixtures. University of London. Delage, P., Howat, M. D., & Cui, Y. J. (1998). The relationship between suction and swelling properties in a heavily compacted unsaturated clay. 50, 31–48. Dineen, & Burland. (1995). A new approach to osmotically controlled oedometer testing. Proceedings of the First International Conference on Unsaturated Soils. Alonso E.E: And Delage P., 2, 459–465. Dineen, K. (1997). The influnce of soil suction on compressibility and swelling. Phd Thesis, (August). El-Ehwany, M., & Houston, S. (1989). Settlement and moisture movement in collapsible soils. 116(10), 1521–1535. Escario V, and Sáez J (1986). The shear strenght of partly saturated soils. Geotechnique, 36(3), 453–456. Fredlund, D. G. (2002). Use of the soil-water characteristic curve in the implementation of unsaturated soil mechanics. Procc. Third International Conference on Unsaturated Soils. Recife, Brazil. Fredlund, D. G., Rahadjo, H., & Fredlund, M. G. (2012). Unsaturated Soil Mechanics in Engineering Practice (I. John Wiley & Sons, Ed.). https://doi.org/10.1002/9781118280492 Fuentes, W. M., Hurtado, C., & Lascarro, C. (2018). On the influence of the spatial distribution of fine content in the hydraulic conductivity of sand-clay mixtures. Earth Sciences Research Journal, 22(4), 239–249. https://doi.org/10.15446/esrj.v22n4.69332 Gallipoli, D., Gens, A., Sharma, R., & Vaunat, J. (2003). An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Géotechnique, 53(1), 123–136. https://doi.org/10.1680/geot.53.1.123.37251 Galvis Castro, A. C. (2018). Estudio del comportamiento esfuerzo – deformación – tiempo de un suelo derivado de ceniza volcánica. Universidad Nacional de Colombia. Garcia, J. C. (2003). Efectos de los cambios de humedad en la resistencia de un suelo parcialmente saturado derivado de ceniza volcánica. Universidad Nacional de Colombia. Gareau, L. F., Molenkamp, F., & Sharma, J. (2006). An improved oedometer apparatus to measure lateral stress during testing. Geotechnical Testing Journal, 29(3), 200–206. https://doi.org/10.1520/GTJ12341 Gens, A. (2010). Soil-environment interactions in geotechnical engineering. Geotechnique, 60(1), 3–74. https://doi.org/10.1680/geot.9.P.109 Georgiadis, K. (2003). Development, Implementation and Application of Partially Saturated Soil Models in Finite Element Analysis. Georgiadis, K., Potts, D. M., & Zdravkovic, L. (2005). Three-dimensional constitutive model for partially and fully saturated soils. International Journal of Geomechanics, 5(3), 244–255. https://doi.org/10.1061/(ASCE)1532-3641(2005)5:3(244) González, N. A. (2005). Influencia de la succión en el comportamiento volumétrico de suelos compactados. Universidad Nacional de Colombia, Bogotá, Colombia. Head, K. H. (2006). Manual of Soil Laboratory Testing: Soil Classification and Compaction Tests (3rd ed.). Scotland: Whittles Publishing. Heibrock, G., König, D., Datcheva, M., Pourzargar, A., Alabdullah, J., & Schanz, T. (2018). Prediction of effective stress in partially saturated sand–kaolin mixtures. Geomechanics for Energy and the Environment, 15, 85–94. https://doi.org/10.1016/j.gete.2018.06.001 Josa, A. (1988). Un modelo elastoplastico para suelos no saturados. Universidad Politécnica de Cataliña. Josa, Balmaceda, A., Gens, A., & Alonso, E. E. (1992). An elastoplastic model for partially saturated soils exhibiting a maximum of collapse. Proc. 3rd Int. Computational Plasticity. Barcelona, España. Jotisankasa, A. (2005). Collapse Behaviour of a Compacted Silty Clay. Kikumoto, M., Kyokawa, H., Nakai, T., & Shahin, H. (2010). A simple elasto-plastic model for unsaturated soils and interpretations of collapse and compaction behaviours. In E. Alonso & A. Gens (Eds.), Proc. of the 5th International Conference on Unsaturated Soils (pp. 849–855). Barcelona, España. Lawton, E., Fragaszy, J., & Hardcastle, J. (1989). Collapse of compacted clayey sands. Journal of Geotechnical Engineering, 115(9), 1252–1267. Lawton, E., Fragaszy, J., & Hetherington, M. (1992). Review of the wetting-induced collapse in compacted soils. Journal of Geotechnical Engineering, 118(9), 1376–1394. Li, P., Vanapalli, S., & Li, T. (2016). Review of collapse triggering mechanism of collapsible soils due to wetting. Journal of Rock Mechanics and Geotechnical Engineering, 8(2), 256–274. https://doi.org/10.1016/j.jrmge.2015.12.002 Lu, N., & Likos, W. . (2004). Unsaturated soil mechanics (Wiley, Ed.). New York. Melgarejo Corredor, M. L. (2004). Laboratory and numerical investigations of soil retention curves. University of London. Mendes, J., & Buzzi, O. (2014). Performance of the University of Newcastle high capacity tensiometer. Proceedings of the Sixth International Conference on Unsaturated Soils, 2, 1611–1616. Mitchell, J. K. (1976). Fundamentals of Soil Behavior. New York: John Wiley & Sons. Monroy, R., Ridley, a., Dineen, K., & Zdravkovic, L. (2007). The suitability of the osmotic technique for the long-term testing of partly saturated soils. Geotechnical Testing Journal, 30(3), 220–226. https://doi.org/10.1520/GTJ100731 Peck, A., & Rabbidge, R. (1969). Design and Performance of an Osmotic Tensiometer for Measuring Capillary Potential. Proc Soil Science Society of America, 33, 196–202. Pedrotti, M., Tarantino, A., & Boeck, F. (2014). Experience gained from the conditioning of high-capacity tensiometers. Proceedings of the Sixth International Conference on Unsaturated Soils, 2, 1651–1657. Pirjalili, A., Akbari Garakani, A., Golshani, A., & Mirzaii, A. (2020). A Suction-Controlled Ring Device to Measure the Coefficient of Lateral Soil Pressure in Unsaturated Soils. Geotechnical Testing Journal, 43. https://doi.org/10.1520/GTJ20190099 Pourzargar, A., König, D., Heibrock, G., Datcheva, M., & Schanz, T. (2014). Comparison of Measured and Predicted Suction Stress in Partially Saturated Compacted Mixtures of Sand and Clay Partially Saturated Soils. Vadose Zone J, 13(5). https://doi.org/10.2136/vzj2013.06.0114 Prasad, L., & Kuwano, R. (2018). Triaxial apparatus equipped with elastic waves and matric suction measurement techniques. Soils and Foundations, 58(6), 1553–1562. https://doi.org/10.1016/j.sandf.2018.08.010 Puppala, A. J., Pradhan, A., Yu, X., & Zhang, N. (2016). Thermal conductivity of sand–kaolin clay mixtures. Environmental Geotechnics, 3(4), 190–202. https://doi.org/10.1680/jenge.15.00022 Ridley. (2015). Soil suction — what it is and how to successfully measure it. In Australian Centre for Geomechanics (Ed.), Proceedings of the 9th Symposium on Field Measurements in Geomechanics (pp. 27–46). https://doi.org/10.36487/acg_rep/1508_0.2_ridley Ridley, A. M. (1993). The measurement of soil moisture suction. University of London. Ridley, A. M., & Burland, J. B. (1993). A new instrument for the measurement of soil moisture suction. Geotechnique, 43, 321–324. Retrieved from http://www.scopus.com/inward/record.url?eid=2-s2.0-0027458157&partnerID=40&md5=e5dd992242bd13c538377f25b8da34b0 Ridley, A. M., & Burland, J. B. (1995). Measurement of suction in materials which swell. Applied Mechanics Reviews, 48(10), 727–732. Ridley, A. M., Dineen, K., Burland, J. B., & Vaughan, P. R. (2003). Soil matrix suction: Some examples of its measurement and application in geotechnical engineering. Geotechnique, 53(2), 241–253. https://doi.org/10.1680/geot.2003.53.2.241 Rogers, C. D. F. (1995). Types and distribution of collapsible soils. Genesis and Properties of Collapsible Soils. Proc. Workshop, Loughborough, 1994, 1–17. https://doi.org/10.1007/978-94-011-0097-7_1 Rojas, E., Arroyo, H., & Pérez-Rea, M. I. (2014a). Elastoplastic framework for the volumetric behavior of unsaturated soils. In N. Khalili, A. R. Rusell, & A. Khoshghalb (Eds.), Unsaturated soils: Research & Aplications (pp. 323–328). Sydney, Australia. Rojas, E., Arroyo, H., & Pérez-Rea, M. I. (2014b). Elastoplastic framework to simulate the collapse of soils. In N. Khalili, A. R. Rusell, & A. Khoshghalb (Eds.), Unsaturated Soils: Research & Applications (pp. 329–334). Sydney, Australia. Rojas, E., & Chávez, O. (2013). Volumetric behavior of unsaturated soils. Canadian Geotechnical Journal, 50(2), 209–222. https://doi.org/10.1139/cgj-2012-0341 Satyanaga, A., Rahardjo, H., & Zhai, Q. (2017). Estimation of unimodal water characteristic curve for gap-graded soil. Soils and Foundations, 57(5), 789–801. https://doi.org/10.1016/j.sandf.2017.08.009 Sheng. 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Universidad Nacional de Colombia, Bogotá, Colombia. Venkatarama, B. V., Reddy, & Jagadish, K. S. (1993). Technical note: The static compaction. Geotechnique, 43(2), 337–341. Wheeler, S. J., & Sivakumar, V. (1995). An elasto-plastic critical state framework for unsaturated soil. Géotechnique, 45(1), 35–53. https://doi.org/10.1680/geot.1995.45.1.35 Williams, J., & Shaykewich, C. F. (1969). An Evaluation of Polyethylene Glycol P.E.G. 6000 and P.E.G. 20000 in the Osmotic Control of Soil Water Matric Potential. Canadian Journal of Soil Science, 49, 397–401. Zhang, N., Yu, X., & Pradhan, A. (2017). Application of a thermo-time domain reflectometry probe in sand-kaolin clay mixtures. Engineering Geology, 216, 98–107. https://doi.org/10.1016/j.enggeo.2016.11.016 Zhou, A. N., Sheng, D., Sloan, S. W., & Gens, A. (2012a). Interpretation of unsaturated soil behaviour in the stress-saturation space. II: Constitutive relationships and validations. Computers and Geotechnics, 43, 111–123. https://doi.org/10.1016/j.compgeo.2012.02.009 Zhou, A. N., Sheng, D., Sloan, S. W., & Gens, A. (2012b). Interpretation of unsaturated soil behaviour in the stress - Saturation space, I: Volume change and water retention behaviour. Computers and Geotechnics, 43, 178–187. https://doi.org/10.1016/j.compgeo.2012.04.010
dc.rights.spa.fl_str_mv	Derechos reservados al autor, 2021
dc.rights.coar.fl_str_mv	http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv	Reconocimiento 4.0 Internacional
dc.rights.uri.spa.fl_str_mv	http://creativecommons.org/licenses/by/4.0/
dc.rights.accessrights.spa.fl_str_mv	info:eu-repo/semantics/openAccess
rights_invalid_str_mv	Reconocimiento 4.0 Internacional Derechos reservados al autor, 2021 http://creativecommons.org/licenses/by/4.0/ http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv	openAccess
dc.format.extent.spa.fl_str_mv	197 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 - Geotecnia
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	Reconocimiento 4.0 InternacionalDerechos reservados al autor, 2021http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Colmenares Montañez, Julio Estebancc92ffe792a53c34a8258076fac18bbbOrjuela Garzón, Angélica Marcela13a5df0fc25af7e30e97c51b572df34dGeotechnical Engineering Knowledge and Innovation Genki2022-02-14T16:26:32Z2022-02-14T16:26:32Z2021https://repositorio.unal.edu.co/handle/unal/80974Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, fotografías, gráficas, tablasEl control del potencial de colapso, inducido por humedecimiento, en suelos compactados, es primordial para evitar la formación de grietas y fallas dentro los rellenos que podrían derivar en el daño de las estructuras. Se realizó una investigación de tipo experimental que evaluó el potencial de cambio volumétrico por inundación de mezclas compactadas de arena y caolín bajo dos niveles de esfuerzo vertical constante. Se encontró que las mezclas compactadas a pesos unitarios secos cercanos al máximo de la compactación normal y esfuerzos verticales de 47 kPa y 86 kPa presentaron un comportamiento volumétricamente estable, mientras que mezclas compactadas a pesos unitarios secos por debajo de 16 kN/m3 y contenidos de agua menores al óptimo, desarrollaron porcentajes de colapso hasta de 12%. Durante la investigación, se desarrolló y construyó un equipo de consolidación con control de succión que permite la medición de esfuerzos radiales y el control de la succión. Lo anterior permitió estudiar la influencia de trayectorias de humedecimiento y secado en el potencial de colapso de una mezcla de arena y caolín. Para dicha mezcla se halló que el cambio volumétrico es estable una vez se desarrolló la trayectoria de humedecimiento. (Texto tomado de la fuente)The control of wetting-induced collapse potential in compacted soils is essential to prevent the formation of cracks and faults within the fills that may later result in damage to the engineering structures. An experimental research was conducted to study the volumetric change potential of compacted mixtures of sand and kaolin by flooding the samples under two levels of constant vertical stress. Mixtures compacted at dry unit weights close to the maximum of normal compaction and vertical forces of 47 kPa and 86 kPa were found to have volumetrically stable behaviour, while mixtures compacted at dry unit weights below 16 kN/m3 and water contents below optimal, developed collapse percentages up to 12%. During the research, a suction-controlled equipment was developed and built that allows the measurement of radial stress and the control of suction, which allowed us to study the influence of wetting and drying paths on the collapse potential of a mixture of sand and kaolin. For this mixture, it was found that the volumetric change is stable once the wetting path was developed.MaestríaMagíster en Ingeniería - GeotecniaRelaciones constitutivas de suelos, rocas y materiales afines197 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ingeniería - Maestría en Ingeniería - GeotecniaDepartamento de Ingeniería Civil y AgrícolaFacultad de IngenieríaBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá620 - Ingeniería y operaciones afines::624 - Ingeniería civilEstabilización de suelosCompactación de suelosSoil stabilizationComportamiento volumétricoPotencial de colapsoSuelos compactadosSuelos parcialmente saturadosConsolidómetro de succión controladaVolumetric behaviourCollapse potentialCompacted soilsPartially saturated soilsSuction-controlled oedometerInfluencia de la succión en la compresibilidad de suelos no saturados en trayectorias k0Influence of suction on the compressibility of unsaturated soils in k0 pathsTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAjdari, M., Monghassem, M., & Reza Lari, H. (2016). A modified osmotic diaphragmatic oedometer for investigating the hydro-mechanical response of unsaturated soils. Geotechnical Testing Journal, 39(6), 906–921. https://doi.org/10.1520/GTJ20150142Alonso, Gens, A., & Hight, D. W. (1987). Special problems soils. General Report, proceedings of the 9th European Conference on Soil Mechanics. Dublin Vol 3: 1087–1146.Alonso, Gens, A., & Josa, A. (1990). A constitutive model for partially saturated soils. Géotechnique, 40(3), 405–430. https://doi.org/10.1680/geot.1990.40.3.405Alshameri, B. (2020). Maximum dry density of sand – kaolin mixtures predicted by using fine content and specific gravity. SN Applied Sciences, 2(10), 1–7. https://doi.org/10.1007/s42452-020-03481-9Bardanis, M., & Grifiza, S. (2016). Swelling and collapse of compacted soils to be used as earth dam cores. 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Computers and Geotechnics, 43, 178–187. https://doi.org/10.1016/j.compgeo.2012.04.010EstudiantesInvestigadoresPúblico generalORIGINAL1077146390.2021.pdf1077146390.2021.pdfTesis de Maestría en Ingeniería - Geotecniaapplication/pdf10324396https://repositorio.unal.edu.co/bitstream/unal/80974/3/1077146390.2021.pdf6a197ee188215a43822f27fe0b6df7a1MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-84074https://repositorio.unal.edu.co/bitstream/unal/80974/2/license.txt8153f7789df02f0a4c9e079953658ab2MD52THUMBNAIL1077146390.2021.pdf.jpg1077146390.2021.pdf.jpgGenerated Thumbnailimage/jpeg4899https://repositorio.unal.edu.co/bitstream/unal/80974/4/1077146390.2021.pdf.jpgf949dd6ed8673ee1097645eef5b8a0c2MD54unal/80974oai:repositorio.unal.edu.co:unal/809742024-08-03 23:09:54.127Repositorio Institucional Universidad Nacional de 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Influencia de la succión en la compresibilidad de suelos no saturados en trayectorias k0

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