, 43:55 | Cite as

Prediction of bed level variations in nonuniform sediment bed channel

  • B R Andharia
  • P L Patel
  • V L Manekar
  • P D Porey


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.


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



width of channel at initial time line, t = 0


Courant number


diameter of sediment particle


arithmetic mean diameter of sediment particle (mm)


geometric mean size of sediment mixture


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


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


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


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


probability of occurrence of size d i Under consideration


flux vector


acceleration due to gravity


depth of flow


initial flow depth


length of channel


Kramer’s uniformity coefficient


represents sediment mixture 1 of the present study


represents sediment mixture 2 of the present study


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


porosity of bed layer


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


change in percentage weight corresponding to size d j


percentage finer by weight for sieve size d 1


water discharge per unit width


initial uniform flow discharge


rate of equilibrium sediment discharge per unit width of channel


increase in sediment discharge due to overloading


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


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


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


fractional bed load transport rates of jth size fraction


fractional suspended load transport rates of jth size fraction


flow discharge (m3/s)


total number of size fractions


longitudinal slope of the channel at t = 0


source term vector


friction slope


time scale of computational grid


last computational step


temporal step in y direction


thickness of active bed layer


average flow velocity


dependent variable vector


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


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


distance along the channel


space interval in computational grid (m)/distance increment


initial bed level


bed elevation


hydraulic roughness parameter


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

Greek symbol


geometric standard deviations of bed material


mean shear stress (N/m2)


critical shear stress (N/m2)


residual error

Superscript and subscript


denotes the space node


denotes size fractions in sediment mixture


denotes the time node


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



active bed layer


bed level


fully coupled model


mean absolute standard error


root mean square error


standard deviation


water level



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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