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Semi-two-dimensional numerical model for river morphological change prediction: theory and concepts

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Abstract

This paper presents a new numerical model for river morphological predictions. This tool predicts vertical and lateral cross-section variations for alluvial rivers, which is an important task in predicting the associated hazard zone after a flood event. The Model for the HYdraulics of SEdiments in Rivers, version 1.0 (MHYSER 1.0) is a semi-two-dimensional model using the stream tubes concept to achieve lateral variations of velocity, flow stresses, and sediment transport rates. Each stream tube has the same conveyance as the other ones. In MHYSER 1.0, the uncoupled approach is used to solve the set of conservation equations. After the backwater calculation, the river is divided into a finite number of stream tubes of equal conveyances. The sediment routing and bed adjustments calculations are accomplished separately along each stream tube taking into account lateral mass exchanges. The determination of depth and width adjustments is based on the minimum stream power theory. Moreover, MHYSER 1.0 offers two options to treat riverbank stability. The first one is based on the angle of repose. The bank slope should not be allowed to increase beyond a certain critical value supplied to MHYSER 1.0. The second one is based on the modified Bishop’s method to determine a safety factor evaluating the potential risk of a landslide along the river bank.

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Abbreviations

A d :

Volume of bed sediment per unit length (m2)

A s :

Volume of sediment in suspension at the cross-section per unit length (m2)

C L :

Energy loss coefficient (−)

C t :

Total sediment carrying capacity (m³/s)

D h :

Hydraulic depth (m)

F 0 :

Objective function value corresponding to a given base simulation parameter,

F f :

Total external friction force acting along the reach 1–2 boundary (N)

F :

αV/(gDh)1/2 = Froude number (−)

g :

Gravitational acceleration (m/s2)

h t :

Friction loss (−)

H :

Elevation of the energy line above the datum (m)

n :

Manning’s coefficient (m−1/3 s)

N :

Number of size fractions (−)

N :

Number of independent parameters,

M :

Number of stations along the reach (−)

p :

Pressure acting on a given cross-section (Pa)

P :

Wetted perimeter (m)

q slat :

Lateral sediment discharge per unit channel length (m2/s)

Q :

Flow rate (m³/s)

Q s :

Volumetric sediment discharge (m³/s)

R :

Hydraulic radius (m)

t :

Time (s)

V :

Flow velocity (m/s)

W g :

Weight of water enclosed between sections 1 and 2 (N)

x :

Longitudinal distance (m)

x1, x2,…, x k ,…, x N :

Independent parameters,

Y :

Water depth (m)

Y 0 :

Initial guess for water depth (m)

z :

Bed elevation (m)

Z :

Water surface elevation (m)

α :

Velocity distribution coefficient (−)

α k :

Sensitivity coefficient corresponding to the kth independent parameter, x k,

β :

Momentum coefficient (−)

β k :

Normalized sensitivity coefficient corresponding to the kth independent parameter, x k,

γ :

Specific weight of water (N/m³),

η :

Bulk volume of sediment (−)

θ :

Angle of inclination of the reach 1–2 (rd)

φ :

Weighting parameter (φ ≥ 0,5) for numerical discretization (−)

ΔZ i :

Bed changes at station i (m)

ΔZ ik :

Bed change for each particle size k at station i (m)

ΦT :

Total stream power (W)

γQS :

Stream power per unit river length (W/m)

S :

Energy slope (−)

N :

Number of stations along the reach (−)

Δx i :

Reach length, or distance between stations i and i + 1 (m)

Q i :

Discharge at station i (m³/s)

S i :

Energy slope at station i (m)

References

  • Abramson LW, Lee TS, Sharma S, Boyce GM (2002) Slope stability and stabilization methods. Wiley, New York, USA

    Google Scholar 

  • Ackers P, White W (1973) Sediment transport: new approach and analysis. J Hydraul Div ASCE 99(HY11):2041–2060

    Google Scholar 

  • Ariathurai R, Krone R (1976) Finite element model for cohesive sediment transport. J Hydraul Div ASCE 102(HY3):323–338

    Google Scholar 

  • Bahadori F, Ardeshir A, Tahershamsi A (2006) Prediction of alluvial river bed variation by SDAR model. J Hydraul Res 44(5):614–623

    Article  Google Scholar 

  • Bennett J, Nordin C (1977) Simulation of sediment transport and armoring. Bull Hydrol Sci 22:555–569

    Article  Google Scholar 

  • Bishop AW (1955) The use of the slip circle in the stability analysis of slopes. Géotechnique V5:7–17

    Article  Google Scholar 

  • Brooks GR, Lawrence DE (1999) The drainage of the Lake Ha! Ha! Reservoir and downstream geomorphic impacts along Ha! Ha! River, Saguenay Area, Quebec, Canada. Geomorphology 28:141–168

    Article  Google Scholar 

  • Brooks GR, Lawrence DE (2000) Geomorphic effects of flooding along reaches of selected rivers in the Saguenay Region, Quebec, July 1996. Géogr Phys Quat 54:281–299

    Google Scholar 

  • Chang HH (1979) Minimum stream power and river channel patterns. J Hydrol 41:303–327

    Article  Google Scholar 

  • Chang HH (1980a) Stable alluvial canal design. J Hydraul Div ASCE 106(HY5):873–891

    Google Scholar 

  • Chang HH (1980b) Geometry of gravel streams. J Hydraul Div ASCE 106(HY9):1443–1456

    Google Scholar 

  • Chang HH (1982a) Mathematical model for erodible channels. J Hydraul Div ASCE 108(HY5):678–689

    Google Scholar 

  • Chang HH (1982b) Fluvial hydraulics of deltas and alluvial fans. J Hydraul Div ASCE 108(HY11):1282–1295

    Google Scholar 

  • Chang HH (1983) Energy expenditure in curved open channels. J Hydraul Div ASCE 109(HY7):1012–1022

    Article  Google Scholar 

  • Chang HH, Hill JC (1976) Computer modeling of erodible flood channels and deltas. J Hydraul Div ASCE 102(HY10):1461–1477

    Google Scholar 

  • Chang HH, Hill JC (1977) Minimum stream power for rivers and deltas. J Hydraul Div ASCE 103(HY12):1375–1389

    Google Scholar 

  • Chang HH, Hill JC (1982) Modelling river-channel changes using energy approach. In: Smith PE (ed) Proceedings of the ASCE hydraulics division conference on applying research to hydraulic practice, Jackson, Miss., August 17–20, pp 454–465

  • Chow VT (1959) Open-channel hydraulics. McGraw-Hill, New York, NY

    Google Scholar 

  • Cunge JA, Holly FM, Verwey A (1980) Practical aspects of computational river hydraulics. Pitman, London

    Google Scholar 

  • De Vries M (1969) Solving river problems by hydraulic and mathematical models. Delft Hydraulics Laboratory Publication 76-II

  • Du Boys MP (1879) Le Rhône et les rivières à lit affouillable. Annales des Ponts et Chaussées 18(5):141–195

    Google Scholar 

  • Engelund F, Hansen E (1972) A monograph on sediment transport in alluvial streams. Teknish Forlag, Technical Press, Copenhagen, Denmark

    Google Scholar 

  • Henderson FM (1966) Open channel flow. MacMillan Book Company, New York

    Google Scholar 

  • Hirsh C (1990) Numerical computation of internal and external flows: fundamentals of numerical discretization. Wiley, New York

    Google Scholar 

  • INRS-Eau (1997) Simulation hydrodynamique et bilan sédimentaire des rivières Chicoutimi et Ha! Ha! lors des crues exceptionnelles de juillet 1996. Rapport INRS-Eau R487, Canada

  • Jain SC (2001) Open-channel flow. Wiley, New York

    Google Scholar 

  • Krone RB (1962) Flume studies of the transport of sediment in estuarine shoaling processes. Final Report. Hydraulic Engineering Laboratory, University of California, Berkeley

    Google Scholar 

  • Lapointe MF, Secretan Y, Driscoll SN, Bergeron N, Leclerc M (1998) Response of the Ha! Ha! River to the Flood of July 1996 in the Saguenay Region of Quebec: large-scale avulsion in a glaciated valley. Water Res 34(9):2383–2392

    Article  Google Scholar 

  • Laursen E (1958) The total sediment load of streams. J Hydraul Div ASCE 84(HY1):1–36

    Google Scholar 

  • MacDonald I, Baines MJ, Nichols NK, Samuels PG (1997) Analytic benchmark solutions for open-channel flow. J Hydrol Eng ASCE 123(11):1041–1045

    Article  Google Scholar 

  • Madden E (1993) Modified Laursen method for estimating bed-material sediment load. USACE-WES. Contract Report HL-93-3

  • Mahdi T (2003) Prévision par modélisation de la zone de risque bordant un tronçon de rivière. PhD thesis, Department of Civil Geological and Mining, Ecole Polytechnique de Montreal

  • Mahdi T (2007) Pairing geotechnics and fluvial hydraulics for the prediction of the hazard zones of an exceptional flooding. J Nat Hazards 42(1):225–236

    Article  Google Scholar 

  • Mahdi T, Marche C (2003) Prévision par modélisation numérique de la zone de risque bordant un tronçon de rivière subissant une crue exceptionnelle. Can J Civil Eng 30(3):568–579

    Article  Google Scholar 

  • Meyer-Peter E, Müller R (1948) Formula for bed-load transport. 2nd IAHR Congress Stockholm, pp 39–64

  • Orvis C, Randle T (1987) STARS: sediment transport and river simulation model. U.S. Bureau of Reclamation, Technical Service Center, Denver, Colorado

    Google Scholar 

  • Parker G (1990) Surface based bedload transport relationship for gravel rivers. J Hydraul Res 28(4):417–436

    Google Scholar 

  • Partheniades E (1965) Erosion and deposition of cohesive soils. J Hydrol Div ASCE 91(HY1):105–139

    Google Scholar 

  • Song CCS, Zheng Y, Yang CT (1995) Modeling of river morphologic changes. Int J Sediment Res 10(2):1–20

    Google Scholar 

  • Toffaleti F (1968) Definitive computations of sand discharge in rivers. J Hydraul Div ASCE 95(HY1):225–246

    Google Scholar 

  • Wallingford HR (1990) Sediment transport, the Ackers and White theory revised. Report SR237 HR Wallingford, England

  • Yang CT (1973) Incipient motion and sediment transport. J Hydraul Div ASCE 99(HY10):1679–1704

    Google Scholar 

  • Yang CT (1979) Unit stream power equations for total load. J Hydrol 40:123–138

    Article  Google Scholar 

  • Yang CT (1984) Unit stream power equation for gravel. J Hydraul Div ASCE 110(HY12):1783–1797

    Article  Google Scholar 

  • Yang CT, Simões FJM (2002) User’s manual for GSTARS 3.0 (Generalized Stream Tube model for Alluvial River Simulation version 3.0). U.S. Bureau of Reclamation, Technical Service Center, Denver, Colorado

    Google Scholar 

  • Yang CT, Molinas A, Wu B (1996) Sediment transport in the Yellow River. J Hydraul Eng 122(5):237–244

    Article  Google Scholar 

  • Yang CT, Treviño MA, Simões FJM (1998) User’s manual for GSTARS 2.0 (Generalized Stream Tube model for Alluvial River Simulation version 2.0). U.S. Bureau of Reclamation, Technical Service Center, Denver, Colorado

    Google Scholar 

Download references

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  1. Département des génies civil, géologique et des mines (CGM), École Polytechnique de Montréal, C.P. 6079, Succ. Centre-ville, Montréal, QC, H3C 3A7, Canada

    Tew-Fik Mahdi

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Mahdi, TF. Semi-two-dimensional numerical model for river morphological change prediction: theory and concepts. Nat Hazards 49, 565–603 (2009). https://doi.org/10.1007/s11069-008-9304-9

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