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Prediction of bed level variations in nonuniform sediment bed channel

  • B R Andharia
  • P L Patel
  • V L Manekar
  • P D Porey
Article
  • 60 Downloads

Abstract

In the present study, a numerical model, based on one-dimensional de Saint-Venant equations along with sediment continuity equation, is developed for prediction of bed levels in non-cohesive sediments in aggrading alluvial channels. One-dimensional, unsteady flow equations and sediment continuity equations are solved using ‘shock-capturing’, second order accurate, explicit MacCormack finite difference scheme while considering upstream and downstream boundary conditions in the channel. Series of experimental investigations have been undertaken for measurements of bed and water levels in an aggrading channel due to overloading of nonuniform sediments, extracted from the bed of Tapi River at Surat City, in a flume installed in Advanced Hydraulics Laboratory of SVNIT, Surat, India. A satisfactory coupling between the water flow and sediment flow has been achieved. The sediment continuity equation is used for the each size class to compute the volume of each size class after each time step at any computational node in the computational grid. The fractional bed and suspended load transport capacities for different size fractions have been computed using fractional transport laws for nonuniform sediments. The active bed layer concept has been implemented in finite difference scheme to consider the interaction and exchange of sediment and water flow near the mixing layer. The performance of developed numerical model has been satisfactorily verified with independent experimental data of nonuniform sediment bed. Also, consideration of sediment nonuniformity in computation of bed level variation has been demonstrated by comparing the results based on sediment transport functions of uniform and nonuniform sediments.

Keywords

Numerical model aggradation non-cohesive sediment mixture active bed layer fractional sediment transport 

Notation

B0

width of channel at initial time line, t = 0

Cn

Courant number

d

diameter of sediment particle

da

arithmetic mean diameter of sediment particle (mm)

dg

geometric mean size of sediment mixture

dj

particular size fraction of sediment mixture; geometric mean size of sieve sizes d 1 and d 2

d15.9

sizes such that 15.9% of particles are finer, by weight, than these sizes

d84.1

sizes such that 84.1% of particles are finer, by weight, than these sizes

d90

sediment size such that 90% of the material, by weight, is finer than this size,

fi

probability of occurrence of size d i Under consideration

F

flux vector

g

acceleration due to gravity

h

depth of flow

h0

initial flow depth

L

length of channel

M

Kramer’s uniformity coefficient

M1

represents sediment mixture 1 of the present study

M2

represents sediment mixture 2 of the present study

n

Manning’s roughness co-efficient or total number of observations

p

porosity of bed layer

pj

percentage of sediment size fraction, d j , in the ABL

Δpj

change in percentage weight corresponding to size d j

P1

percentage finer by weight for sieve size d 1

q

water discharge per unit width

q0

initial uniform flow discharge

qT0

rate of equilibrium sediment discharge per unit width of channel

ΔqT

increase in sediment discharge due to overloading

qB

rate of bed load transported per unit width, by weight, (N/s/m)

qT

rate of total sediment transport by weight per unit width of channel (N/s/m), (q T  = q B  + q S )

qTin

sediment overloading rate at upstream fictitious node (qT0 + Δq T )

qBj

fractional bed load transport rates of jth size fraction

qsj

fractional suspended load transport rates of jth size fraction

Q

flow discharge (m3/s)

r

total number of size fractions

S0

longitudinal slope of the channel at t = 0

S

source term vector

Sf

friction slope

t

time scale of computational grid

tlast

last computational step

Δt

temporal step in y direction

Tb

thickness of active bed layer

U

average flow velocity

U

dependent variable vector

U

variable representing the unknown (h, q and z) for finite difference discretization in present

Vi,jk

total volume of any particle size, d j , present in the active layer per unit length of the channel, at ith space node and kth time line

x

distance along the channel

Δx

space interval in computational grid (m)/distance increment

z0

initial bed level

z

bed elevation

Z0

hydraulic roughness parameter

zi+1k+1

bed level at computational node i + 1 for unknown time level k + 1 for each time step

Greek symbol

σg

geometric standard deviations of bed material

τ0

mean shear stress (N/m2)

τ0c

critical shear stress (N/m2)

є

residual error

Superscript and subscript

i

denotes the space node

j

denotes size fractions in sediment mixture

k

denotes the time node

o

stands for initial values

superscript values of the variables after the predictor steps at the unknown time k + 1 level

∗∗

superscript values of the variables after the corrector steps at the unknown time k + 1 level

Abbreviations

ABL

active bed layer

BL

bed level

FCM

fully coupled model

MASE

mean absolute standard error

RMSE

root mean square error

SD

standard deviation

WL

water level

Notes

Acknowledgements

The authors would like to thank the Department of Science and Technology (DST), New Delhi, Government of India, for the financial support for installing the flume facilities through the Research Project “Erosion of nonuniform unimodal and bimodal sediments” with project Grant No. SR/S3/MERC/015/2009.

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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  • B R Andharia
    • 1
  • P L Patel
    • 1
  • V L Manekar
    • 1
  • P D Porey
    • 1
  1. 1.Department of Civil EngineeringS.V. National Institute of TechnologySuratIndia

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