MODELAGEM DE CANAIS INCISIVOS - REVISÃO
DOI:
https://doi.org/10.5380/raega.v8i0.3384Palavras-chave:
Sulco, voçoroca, desagregação, estabilidade de agregados, erosão, Rill, gully, detachment, aggregate stability, erosion.Resumo
O objetivo deste artigo é documentar as mais importantes pesquisas e aspectos histórico-cronológicos sobre a modelagem da incisão de canais. São apresentados os aspectos qualitativos e quantitativos envolvidos, desde a dedução das equações de Saint-Venant e de Exner, até as mais recentes pesquisas sobre o alargamento e o deslizamento das margens dos canais, considerando a coesão das mesmas. Do ponto de vista quantitativo, ainda há muitos processos importantes a serem solucionados, com destaque para os mecanismos envolvidos na desagregação e transporte de partículas de solo coesivas. Pesquisas recentes mostram que a estimativa da desagregação pelos métodos tradicionais de determinação da resistência do solo pode não ser a mais recomendada para avaliar a resistência na interface solo-água. Isto aponta para a importância dos processos físico-químicos envolvidas na estabilidade das partículas do solo e, conseqüentemente, na sua suscetibilidade à erosão, assim como a importância da sua representação matemática e inclusão na modelagem do processo de incisão de canais.
Incised channel modeling - revision
Abstract
This paper aims at documenting some of the more important research and historical-chronological aspects concerning incised channels modelling. Qualitative and quantitative aspects are presented, beginning with the deduction of the Saint-Venant and Exner equations and going through the more recent equations explaining the enlargement and stability of cohesive riverbanks. From a quantitative point of view, there are still many important processes to be solved, specially those regarding detachment mechanisms and transport of cohesive soil aggregates. Recent research has shown that soil evaluation aggregates detachment by conventional methods (soil strength determination) cannot measure the properties at the soil-water interface with the necessary resolution. These results allow visualizing the importance of the physicochemical mechanisms involved on aggregate stability at the soilwater interface; and, consequently, its degradation suscetibility. These mechanisms should be mathematically described and included in incised channel modeling.
Referências
AL-SHAYEA, N. The combined effect of clay and moisturecontent on the behavior of remolded unsaturated soils.Engineering Geology, Amsterdam, v. 62, n. 4, p. 319-342, 2001.
ALVARENGA, R. C. et al. Índices de erosividade da chuva, per-das de solo e fator erodibilidade para dois solos da região deSete Lagoas. Disponível em: <http://www.cnpms.embrapa.br/pesq2498.html> Acesso em: 16 fev. 2003.
EMBRAPA. (nãopublicado).AZIZ, N. M.; PRASAD, S. N. Sediment transport in shallowflows.Journal of Hydraulic Engineering, New York, 1985. v.111, n. 10, p. 1327-1343.
BAGNOLD, R. A. An approach to the sediment transportproblem from general physics. Geological SurveyProfessional Paper, Washington, v. 422-I, p. 1-37, 1966.
BAHIA, V. G. et al. Fundamentos de erosão do solo: tipos,formas, mecanismos, fatores determinantes e controle. Infor-me Agropecuário, Belo Horizonte, v. 16, n. 176, p. 25-31, 1992.
BHALLAMUDI, B. M.; CHAUDHRY, M. H. Numerical modelingof aggradation and degradation in alluvial channels. Journalof Hydraulic Engineering, New York, 1991. v. 117, n. 9, p. 1145-1164.
BIGARELLA, J. J.; MOUSINHO, M. R.; SILVA, J. X. da.Considerações a respeito da evolução das vertentes. BoletimParanaense de Geografia, Curitiba, v. 16 e 17, p. 85-116, 1965.
BJORNEBERG, D. L. et al. Evaluating WEPP - predictedinfiltration, runoff, and soil erosion for furrow irrigation.Transactions of the American Society of Agricultural Engineers,St. Joseph, v. 42, n. 6, p. 1733-1741, 1999.
BRADFORD, J. M.; BLANCHAR, R. W. Mineralogy and waterquality parameters in rill erosion of clay-sand mixtures. SoilScience Society of America Journal, Madison, 1999. v. 63, n.5, p. 1300-1307.
BRENN, G. et al. Experimental and numeral investigation ofliquid channel flows with dispersed gas and solid particles.International Journal of Multiphase Flow, Elmosford, 2003. v.29, n. 2, p. 219-247.
BRUNTON, D. A.; BRYAN, R. B. Rill network developmentand sediment budgets. Earth Surface Processes andLandforms, Chichester, v. 25, n. 7, p. 783-800, 2000.
BRUSH, L. M.; WOLMAN, M. G. Knickpoint behavior innoncohesive material: a laboratory study. Bulletin of the GeologicalSociety of America, Boulder, v. 71, n. 1, p. 59-74, 1960.
BRYAN, R. B. Soil erodibility and processes of water erosionon hillslopes. Geomorphology, Amsterdam, v. 32, n. 3 e 4, p.385-415, 2000.
CASALÍ, J.; BENNETT, S. J.; ROBINSON, K. M. Processes ofephemeral gully erosion. International Journal of SedimentResearch, Beijing, 2000. v. 15, n. 1, p. 31-41.
CASALÍ, J.; LÓPEZ, J. J.; GIRÁLDEZ, J. C. Ephemeral gullyerosion in southern Navarra. Catena, Giessen, v. 36, p. 65-84, 1999.
CAVAGUTI, N. et al. Boçoroca da pousada da esperança 2.In: SIMPÓSIO NACIONAL DE CONTROLE DE EROSÃO, 5.,1995, Bauru. Anais... Bauru: IBGE; Unesp, 1995. p. 501-503.
CHANG, F. M.; SIMONS, D. B.; RICHARDSON, E. V. Totalbed-material discharge in alluvial channels. U. S. GeologicalSurvey Water-Suppy Papper, Washington, n. 1498-I, p. 1-23,1965.
CHANG, H. H. River channel changes: adjustmens ofequilibrium.Journal of Hydraulic Engineering, New York, 1986.v. 112, n. 1, p. 43-55.
CHOW, V. T.; MAIDMENT, D. R.; MAYS, L. W. Appliedhydrology. New York: McGraw-Hill, 1988.
COELHO NETO, A. L. Mudanças ambientais recentes,mecanismos e variáveis-controle do voçorocamento atual nabacia do rio bananal, SP-RJ: bases metodológicas paraprevisão e controle de erosão. In: SIMPÓSIO NACIONALDE CONTROLE DE EROSÃO, 5., 1995, Bauru. Anais... Bauru:IBGE, UNESP, 1995. p. 377-379.
CUNGE, J. A.; HOLLY, F. M.; VERWEY, A. Practical aspectsof computational river hydraulics. Boston: Pitman AdvancedPublishing Program, 1980.
DANIELS, R. B.; HAMMER, R. D. Soil geomorphology. NewYork: John Wiley, 1992. 236 p.
DARBY, S. E.; THORNE, C. R. Numeric simulation of wideningand bed deformation of straight sand-bed rivers. I: Modeldevelopment.Journal of Hydraulic Engineering, New York,1996a, v. 122, n. 4, p. 184-193.
_____. Numeric simulation of widening and bed deformationos straight sand-bed rivers. II: Model evaluation. Journal ofHydraulic Engineering, New York, 1996b, v. 122, n. 4, p. 194-202.
DeBANO, L. F. Review: Water repellency in soils: a historicaloverview. Journal of Hydrology, Amsterdam, 2000, v. 231-232,n. 29, p. 4-32.
EINSTEIN, H. A. Formulas for the transportation of bed load.Transactions/American Society of Civil Engineers, n. 107, p.561-597, 1942.
_____. The bed load function for sediment transportation inopen channel flows. Technical Bulletin, n. 1026, p. 1-71, 1950.
ELLIOTT, J. G.; GELLIS, A. C.; ABY, S. B. Evolution of arroyos:incised channels of the Southwestern United States. In:DARBY, S. E.; SIMON, A. Incised river channels: processes,forms, engineering and management. New York: John Wiley,1999. p. 153-185.
ELLIOT, W. J.; LAFLEN, J. M. A process-based rill erosionmodel.Transactions of the American Society of AgriculturalEngineers, St Joseph, v. 36, n. 1, p. 65-72, 1993.
ELLIOT, W. J. et al. Compendium of soil erodibility data fromWEPP Cropland Soil Field Erodibility Experiments 1987 and1988. USDA Agricultural Research Service, West Lafayette:The Ohrio State University. NSERL Report, n. 3. Disponívelem: <http://soils.ecn.purdue.edu/wepphtml/wepp/wepptut/comp/comp.html> Acesso em: 23 ago. 2002.
EMMETT, W. W. Overland flow. In: KIRKBY, M. J. Hillslopehydrology. New York: John Wiley, 1978. p. 145-176.
ERSKINE, W. D. Oscillatory response versus progressivedegradation of incised channels in Southeastern Austrália.In: DARBY, S. E.; SIMON, A. Incised river channels: processes,forms, engineering and management. New York: John Wiley,1999. p. 67-95.
FARIA, A. P.; MARQUES, J. S. O desaparecimento depequenos rios brasileiros. Ciência Hoje, São Paulo, v. 25, n.146, p. 56-61, 1999.
FOSTER, G. R. Modeling the erosion process. In: HAAN, C.T.; JOHNSON, H. P.; BRAKENSIEK, D. L. Hydrologic modelingof small watersheds. St. Joseph: American Society ofAgricultural Engineers (ASAE), 1982. p. 297-380.
FOSTER, G. R.; HUGGINS, L. F.; MEYER, L. D. A laboratorystudy of rill hydraulics: II. Shear stress relationships.Transactions of the American Society of Agricultural Engineers,St Joseph, v. 27, n. 3, p. 797-804, 1984b.
_____. A laboratory study of rill hydraulics: I. Velocity relation-ships. Transactions of the American Society of AgriculturalEngineers, St Joseph, v. 27, n. 3, p. 790-796, 1984a.
FOSTER, G. R. et al. Estimating erosion and sediment yieldon field-sized areas. Transactions of the American Society ofAgricultural Engineers, St Joseph, v. 24, n. 5, p. 1253-1262,1981.
FOSTER, G. R.; MEYER, L. D. A closed-form soil erosionequation for upland areas. In: SHEN, H. W. (Ed.).Sedimentation. Fort Collins: Colorado State University, 1972.p. 12.1-12.9.
FOSTER, G. R.; MEYER, L. D.; ONSTAD, C. A. An erosionequation derived from basic erosion principles. Transactionsof the American Society of Agricultural Engineers, St Joseph,v. 19, n. 4, p. 678-682, 1976.
FRANCE, R. L. Potential for soil erosion from decreasedlitterfall due to riparian clearcutting: Implications for borealforestry and warm-and cool-water fisheries. Journal of Soiland Water Conservation, Amsterdam, v. 52, n. 6, p. 452-455,1997.
FRANTI, T. G.; FOSTER, G. R.; MONKE, E. J. Modeling theeffects of incorporated residue on rill erosion. Part I: Modeldevelopment and sensitivity analysis. Transactions of theAmerican Society of Agricultural Engineers, St. Joseph, v. 39,n. 2, p. 535-542, 1996a.
_____. Modeling the effects of incorporated residue on rillerosion. Part II: Experimental results and model validation.Transactions of the American Society of Agricultural Engineers,St Joseph, v. 39, n. 2, p. 543-550, 1996b.
GALAY, V. J. Causes of river bed degradation. WaterResources Research, Washington, v. 19, n. 5, p. 1057-1090,1983.
GARDE, R. J.; RANGA RAJU, K. G. Mechanics of sedimenttransportation and alluvial stream problems. 2. ed. New Delhi:Wiley Eastern Limited, 1985.
GOVERS, G. Spatial and temporal variability in rilldevelopment processes at the Hundenberg Experimental Site.In: BRYAN, R. B. (Ed.). Rill erosion: process and significancep. 17-34, 1987. (Catena Suppl. n. 8). Catena Verlag,Cremlingen-Destedt.
GOVINDARAJU, R. S.; KAVVAS, M. L. Characterization ofthe rill geometry over straight hillslopes through spatial scales.Journal of Hydrology, Amsderma, 1992. v. 130, n. 1-4, p. 339-365.
GOVINDARAJU, R. S.; KAVVAS, M. L.; JONES, S. E.Approximate analytical solutions to overland flows. WaterResources Research, v. 26, n. 12, p. 2903-2912, 1990.
GRAF, W. H. Hydraulics of sediment transport. Littleton: WaterResources Publications, 1984.
GUERRA, A. T; GUERRA, G. A. J. T. Novo dicionário geológi-co-geomorfológico.Rio de Janeiro: Bertrand Brasil, 1997.
HAGERTY, D. J. Piping/sapping erosion. I: Basicconsiderations.Journal of Hydraulic Engineering, New York,v. 117, p. 991-1008, 1991.
HEY, R. D.; THORNE, C. R. Stable channels with mobile gravelbeds.Journal of Hydraulic Engineering, New York, 1986. v.112, n. 8, p. 671-689.
HIRSCHI, M. C.; BARFIELD, B. J. KYERMO - a physicallybased research erosion model. Part 1. Model development.Transactions of the American Society of Agricultural Engineers,St Joseph, v. 31, n. 3, p. 804-813, 1988.
HUANG, C. H.; BRADFORD, J. M. Analyses of slope and runofffactors based on the WEPP erosion model. Soil ScienceSociety of America Journal, Madison, 1993. v. 57, n. 5, p.1176-1183.
HUSSEIN, M. H. Water erosion assessment and control inNorthern Iraq. Soil and Tillage Research, Amsterdam, v. 45,p. 161-173, 1998.
INTERNATIONAL COMMISSION ON LARGE DAMS.Technical dictionary on dams. Paris: ICOLD, 1978.
JACKSON, J. A. (Ed.). Glossary of geology. 4. ed. Alexandria,Virginia: American Geological Institute.
JAIN, S. C.; PARK, I. Guide fro estimating riverbeddegradation.Journal of Hydraulic Engineering, New York,1989. v. 115, n. 3, p. 356-366.
KALINSKE, A. A. Movement of sediment as bed-load in rivers.Transactions of the American Society of Agricultural Engineers,St Joseph, v. 28, n. 4, 1947.
KEMPER, W. D.; ROSENAU, R. C. Soil cohesion as affectedby time and water content.Soil Science Society of AmericaJournal, 1984. v. 48, n. 5, p.1001-1006.
KUNISCHIK, G. Aplicação da equação universal de perdasde solo na microbacia do Ribeirão das Araras, através detécnicas de sensoriamento remoto e geoprocessamento. SãoJosé dos Campos, 1996. Dissertação (Mestrado) – INPE.
KUZNETSOV, M. S.; GENDUGOV, V. M.; KHALILOV, M. S.;IVANUTA, A. A. An equation of soil detachment by flow. Soiland Tillage Research, Amsderdam, v. 46, n. 1-2, p. 97-102,1998.
LAGUNA, A.; GIRÁLDEZ, J. V. The description of soil erosionthrough a kinematic wave model. Journal of Hydrology,Amsterdam, 1993. v. 145, n. ½, p. 65-82.
LEE, H. Y.; HWANG, S. T. Migration of backward-facing step.Journal of Hydraulic Engineering, New York, 1994. v. 120, n.6, p. 693-705.
LEI, T. et al. Rill erosion and morphological evolution: asimulation model. Water Resources Research, Washington,v. 34, n. 11, p. 3157-3168, 1998.
LEWIS, S. M. et al. PRORIL - an erosion model usingprobability distributions for rill flow and density. I. Modeldevelopment.Transactions of the American Society ofAgricultural Engineers, St Joseph, v. 37, n. 1, p. 115-123, 1994.
MARTINÉZ-MENA, M.; CASTILHO, V.; ALBADEJO, J.Relations between interril erosion processes and sedimentparticle size distribution in a semiarid Mediterranean area ofSE of Spain. Geomorphology, Amsterdam, v. 45, n. 3-4, p.261-275, 2002.
MELTON, M. A. The geomorphic and palaeoclimaticsignificance of alluvial deposits in southern Arizona. Journalof Geology, Chicago, v. 73, n. 1, p 1-38, 1965.
MEYER, L. D.; FOSTER, G. R.; NIKOLOV, S. Effect of flowrate and canopy on rill erosion. Transactions of the AmericanSociety of Agricultural Engineers, St Joseph, v. 18, n. 5, p.905-911, 1975.
MEYER, L. D.; WISCHMEIER, W. H. Mathematical simulationof the process of soil erosion by water. Transactions of theAmerican Society of Agricultural Engineers, St Joseph, v. 12,n. 6, p. 754-758, 1969.
MOSLEY, M. P. Experimental study of rill erosion. Transactionsof the American Society of Agricultural Engineers, St Joseph,v. 17, n. 5, p. 909-913; 916, 1974.
NEARING, M. A. Probabilistic model of soil detachment byshallow turbulent flow. Transactions of the American Societyof Agricultural Engineers, St Joseph, v. 34, n. 1, p. 81-85, 1991.
NEARING, M. A. et al. A process-based soil erosion modelfor USDA-Water Erosion Prediction Project technology.Transactions of the American Society of Agricultural Engineers,St Joseph, v. 32, n. 4, p. 1587-1593, 1989.
NEARING, M. A. et al. Hydraulics and erosion in eroding rills.Water Resources Research, Washington, v. 33, n. 4, p. 865-876, 1997.
NÈGRE, M. et al. Effects of the chemical composition of soilhumic acids on their viscosity, surface pressure, andmorphology. Soil Science, Baltimore, 2002. v. 167, n. 10, p.636-651.
NOVOTNY, E. H. et al. Soil management system effects onsize fractionated humic substances. Geoderma, Amsterdam,v. 92, n. 1-2, p. 87-109, 1999.
O’BRIEN, M. P.; RINDLAUB, B. D. The transportation of bed-load by streams. Transactions of the American geophysicalUnion, v. 15, p. 593-603, 1934.
OLDEMAN, L. R. The global extent of soil degradation. In:GREENLAND, D. J.; SZABOLCS, I. (Eds.). Soil erosionresearch methods. Ankeny, Iowa: Conservation Society(SWCS), 1994. p. 235-263.
OOSTWOUD WIJDENES, D. J. et al. Gully-head morphologyand implications for gully development on abandoned fieldsin a semi-arid environment, Sierra de Gata, southeast Spain.Earth-Surface-Processes-and-Landforms, Chichester, v. 24,n. 7, p. 585-603, 1999.
OSMAN, A. M.; THORNE, C. R. Riverbank stability analysis.I: Theory. Journal of Hydraulic Engineering, New York, v. 114,n. 2, p. 135-150, 1988.
PALIS, R. G.; ROSE, C. W.; SAFFIGNA, P.G. Soil erosionprocesses and nutrient loss. IV. Effect of slope length on runoff,sediment yield, and total nitrogen loss from steep slopes inpeneapple cultivation. Australian Journal of Soil Research,Washington, v. 35, n. 4, p. 907-923, 1997.
PAOLA, C.; SEAL, R. Grain size patchiness as a cause ofselective deposition and downstream fining. Water ResourcesResearch, Washington, v. 31, n. 5, p. 1395-1407, 1995.
PATTON, P. C.; SCHUMM, S. A. Gully erosion, northwesternColorado: a threshold phenomenon. Geology, Boulder, v. 3,n. 2, p. 88-90, 1975.
PICCOLO, A. Humus substances in terrestrial ecosystems.In:
_____. Humus and soil conservation. Amsterdam: ElsevierScience, 1996. p. 225-264.
PICCOLO, A.; MBAGWU, J. S. C. Effects of different organicwastes amendments on soil micro aggregates stability andmolecular sizes of humic substances. Plant and Soil, TheHague, v. 123, n. 1, p. 27-37, 1990.
PIEST, R. F.; BRADFORD, J. M.; WYATT, G. M. Soil erosionand sediment transport from gullies. Journal of the HydraulicsDivision, Ann Arbor, 1975. v. 101, n. 1, p. 65-80.
PROSSER, I. P.; CHAPPELL, J.; GILLESPIE, R. Holocenevalley aggradations and sediment transport in headwatercatchments, south-eastern highland of Australia. Earth SurfaceProcesses and Landforms, Chic Hester, v. 19, n. 5, p. 465-480, 1994.
RIGHETTO, A. M.; AKABASSI, L. Erosão distribuída em áreasde encosta. Revista Brasileira de Recursos Hídricos, PortoAlegre, v. 5, n. 2, p. 43-57, 2000.
ROBINSON, K. M. Predicting stress and pressure at an overfall.Transactions of the American geophysical Union, v. 35, n.2, p. 561-569, 1992.
ROBINSON, K. M. et al. Processes of head cut growth andmigration in rills and gullies. International Journal of SedimentResearch, Beijing, v. 15, n. 1, p. 69-82, 2000.
ROBINSON, K. M.; HANSON, G. J. A deterministic head cutadvance model. Transactions of the American Society ofAgricultural Engineers, St. Joseph, v. 37, n. 5, p. 1437-1443,1994.
_____. Gully head cut advance. Transactions of the AmericanSociety of Agricultural Engineers, St. Joseph, v. 39, n. 1, p.33-38, 1996._
____. Large-scale headcut erosion testing. Transactions ofthe American Society of Agricultural Engineers, St. Joseph, v.38, n. 2, p. 429-434, 1995.
ROLOFF, G. Gully development as influenced by regolithstratigraphy in the thick loessial region of central Missouri.Columbia, 1978. Dissertação, (Mestrado) - University ofMissouri.
RÖMKENS, M. J. M.; PRASAD, S. N.; GERITS, J. J. P. Soilerosion models of sealing soils: a phenomenological study.Soil Technology, Amsterdam, v. 11, p. 31-41, 1997.
RÖMKENS, M. J. M.; PRASAD, S. N.; HELMING, K. Sedimentconcentration in relation to surface and subsurface hydrologicsoil conditions. In: FEDERAL INTERAGENCYSEDIMENTATION CONF. VI.: Las Vegas: 1996.Proceedings.... Las Vegas, v. 2, p. 9-16, 1996.
SCHUMM, S. A. Causes and controls of channel incision. In:DARBY, S. E.; SIMON, A. Incised river channels: processes, forms, engineering and management. New York: John Wiley,1999. p. 19-33.
SCHUMM, S. A.; HARVEY, M. D.; WATSON, C. C. Incisedchannels: morphology, dynamics and control. 3. ed. Littleton,Colorado: Water Resources Publications, 2001.
SHAINBERG, J. et al. Hydraulic flow and water qualitycharacteristics in rill erosion. Soil Science society of AmericaJournal, Madison, 1994. v. 58, n. 4, p. 1007-1012.
SHAMES, I. H. Mecânica dos fluidos: análise de escoamen-tos. São Paulo: Edgard Blücher, v. 2. 1976.
SIDORCHUK, A. Dynamic and static models of gully erosion.Catena, Giessen, v. 37, n. 3-4, p. 401-414, 1999.
SILVA, M.; CRUZ, R. Erosão urbana no jardim paulista. In:SIMPÓSIO NACIONAL DE CONTROLE DE EROSÃO, 5.,1995, Bauru. Anais... Bauru: IBGE; UNESP, 1995. p. 505-507.
SIMON, A. A model of channel response in disturbed alluvialchannels.Earth Surface Processes and Landforms, ChicHester, v. 14, n. 1, p. 11-26, 1989.
_____. Energy, time, and channel evolution in catastrophicallydisturbed fluvial system. Geomorphology, Amsterdam, v. 5, n.3/5, p. 345-372, 1992.
SIMON, A.; DARBY. S. E. The nature and significance ofincised river channels. In: DARBY, S. E.; SIMON, A. Incisedriver channels: processes, forms, engineering andmanagement. New York: John Wiley, 1999. p. 3-18.
SIMONS, D. B.; SENTÜRK, F. Sediment transport technology:water and sediment dynamics. Colorado: Water ResourcesPublications, 1992. 897 p.
SLATTERY, M. C.; BURT, T. P. Particle size characteristics ofsuspended sediment in hill slope runoff and stream flow. EarthSurface Processes and Landforms, Chic Hester, v. 22, n. 8, p.705-719, 1997.
STEIN, O. R.; JULIEN, P. Y. Criterion delineating the mode ofheadcut migration. Journal of Hydraulic Engineering, NewYork, 1993. v. 119, n. 1, p. 37-50.
STEIN, O. R.; JULIEN, P. Y.; AALONSO, C. V. Mechanics ofjet scour downstream of a headcut. Journal of HydraulicResearch, Delft, 1992. v. 31, n. 6, p. 723-738.
TAKKEN, I. et al.Spatial evaluation of a physically-baseddistributed erosion model (LISEM). Catena, Giessen, v. 37, n.3-4, p. 431-447, 1999.
TEMPLE, D. M. Estimating flood damage to vegetated deepsoil spillways. Applied Engineering in Agriculture, St. Joseph,v. 8, n. 2, p. 237-242, 1992.
THORNE, C. R.; OSMAN, A. M. Riverbank stability analysis.II. Applications. Journal of Hydraulic Engineering, New York,1988. v. 114, n. 2, p. 151-172.
TISDALL, J. M. OADES, J. M. Organic matter and water-stableaggregate in soils. The Journal of Soil Science, Oxford, 1982.v. 33, n. 2, p. 141-163, 1982.
TRUMAN, C.; BRADFORD, J. M.; FERRIS, J. E. Antecedentwater content and rain fall energy influence on soil aggregatebreakdown.Soil Science Society of America Journal, Madison,1990. v. 54, n. 5, p. 1385-1392.
TYNNEY, E. R. The process of channel degradation. Journalof Geophysical Research, Washington, 1962. v. 67, n. 4, p.1475-1480.
ZHANG, B.; ZHAO, Q. G.; BRAUMGARTL, T. Shear strengthof surface soil as affected by soil bulk density and soil watercontent.Soil and Tillage Research, Amsterdam, v. 59, n. 3-4,p. 97-106, 2001.
ZHANG, J.; HAAN, C. T. Evaluation of uncertainty in estimatedflow and phosphorus loads by FHANTM. Applied EngineeringAgriculture, St. Joseph, v. 12, n. 6, p. 663-669, 1996.
ZHENG, F.; TANG, K. Rill erosion process on steep slope landof the loess plateau. International Journal of SedimentResearch, Beijing, 1997, v. 12, n. 1, p. 52- 59.
ZHU, J. C. et al. Comparison of concentrated-flow detachmentequations for low shear stress. Soil and Tillage Research,Amsterdam, v. 61, n. 3-4, p. 203-212, 2001.
Downloads
Como Citar
Edição
Seção
Licença
Declaro que o ARTIGO submetido é INÉDITO, ORIGINAL e de MINHA RESPONSABILIDADE. Declaro que o artigo não foi submetido ou está em avaliação em outra revista/periódico.
Estou ciente dos itens presentes na LEI Nº 9.610/98 (DIREITOS AUTORAIS) e me responsabilizo por quaisquer problemas relacionados a PLÁGIO.
Estou ciente de que o artigo submetido poderá ser removido da Revista, caso se observe A QUALQUER TEMPO que ele se encontra publicado integralmente ou em parte em outro PERIÓDICO científico.
Declaro, COMO PRIMEIRO AUTOR, que os demais autores do trabalho estão cientes desta submissão e de que NÃO receberão qualquer tipo de remuneração pela divulgação do trabalho.
Como primeiro autor, autorizo, de antemão, a RA’E GA - O Espaço Geográfico em Análise(ISSN 2177-2738), a publicar o artigo, caso aceito.