Advanced Numerical Modeling of Sediment Transport in Gravel-Bed Rivers
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water Article Advanced Numerical Modeling of Sediment Transport in Gravel-Bed Rivers Van Hieu Bui 1,2,* , Minh Duc Bui 1 and Peter Rutschmann 1 1 Institute of Hydraulic and Water Resources Engineering, Technische Universität München, Arcisstrasse 21, D-80333 München, Germany; [email protected] (M.D.B.); [email protected] (P.R.) 2 Faculty of Mechanical Engineering, Thuyloi University, 175 Tay Son, Dong Da, Hanoi 100000, Vietnam * Correspondence: [email protected]; Tel.: +49-152-134-15987 Received: 15 February 2019; Accepted: 13 March 2019; Published: 17 March 2019 Abstract: Understanding the alterations of gravel bed structures, sediment transport, and the effects on aquatic habitat play an essential role in eco-hydraulic and sediment transport management. In recent years, the evaluation of changes of void in bed materials has attracted more concern. However, analyzing the morphological changes and grain size distribution that are associated with the porosity variations in gravel-bed rivers are still challenging. This study develops a new model using a multi-layer’s concept to simulate morphological changes and grain size distribution, taking into account the porosity variabilities in a gravel-bed river based on the mass conservation for each size fraction and the exchange of fine sediments between the surface and subsurface layers. The Discrete Element Method (DEM) is applied to model infiltration processes and to confirm the effects of the relative size of fine sediment to gravel on the infiltration depth. Further, the exchange rate and the bed porosity are estimated while using empirical formulae. The new model was tested on three straight channels. Analyzing the calculated results and comparing with the observed data show that the new model can successfully simulate sediment transport, grain sorting processes, and bed change in gravel-bed rivers. Keywords: numerical modelling; bed porosity; grain sorting; gravel-bed rivers 1. Introduction Sediment transport processes that are due to flowing water in gravel-bed rivers can be formed from bed load, suspended load, and movement inside the bed layer. More importantly, in the same hydraulics condition, the transport rate of coarse size fraction may be different from the rate of fine size fraction. These reasons lead to the distinct forms of gravel-bed rivers. Due to high-flow velocity, all of the finer particles may be eroded, leaving a layer of coarse particles. When the flow is unable to carry the coarse particles, then no more erosion occurs, which is known as an armoring process [1,2]. Inversely, under low-flow conditions, sediment transport can cause the extensive infiltration of fine sediment into void spaces in coarse bed material [3,4], which is also known as clogging or colmation [5,6] (see Figure1). Water 2019, 11, 550; doi:10.3390/w11030550 www.mdpi.com/journal/water Water 2019, 11, 550 2 of 21 Water 2019, 10, x FOR PEER REVIEW 2 of 21 FigureFigure 1. 1. PorosityPorosity variatio variationn of of grain grain system system due due to to fine fine grain grain exchange exchange.. TheThe change change in in grain size distribution ofof coarsecoarse andand finefine sediment sediment not not only only leads leads to to the the variation variation in inbed bed profile, profile but, but it also it also mainly mainly results results in the in changethe change in bed in porosity bed porosity defined defined as a fraction as a fraction of the volume of the volumeof voids of over voids the over total the volume total volume of the gravel-bedof the gravel river.‐bed Accordingriver. According to [7,8 ],to the [7,8 porosity], the porosity of sand-gravel of sand‐ gravelmixtures mixtures can vary can from vary aboutfrom about 0.10 to 0.10 0.50. to For 0.50. example, For example, the measured the measured porosity porosity values values in the in Rhine the RhineRiver River range range from 0.06from to 0.06 0.48 to [9 0.4]. 8 [9]. TheThe study study of variationvariation inin porosity porosity is is vital vital for for fluvial fluvial geomorphology geomorphology assessment assessment as well as well as in as river in riverecosystem ecosystem management. management. From From a river a river management management point point of view, of view, the amount the amount of fine of sediment fine sediment stored storedin the voidin the space void of space gravel-bed of gravel up‐ tobed 22% up [ 10to] may22% be[10 neglected] may be duringneglected calculation during bycalculation considering by consideringconstant porosity. constant Furthermore, porosity. Furthermore the porosity, the may porosity exert may strong exert influence strong oninfluence the rate on of the bed rate level of bedchanges level [changes11,12]. The [11, impact12]. The of impact void space of void of gravel-bedspace of gravel on habitats‐bed on forhabitats fish and for aquaticfish and insects aquatic is insectsessential, is essential, and particularly and particularly the importance the importance of assessing of assessing the change the inchange the void in the structure void structure of the bed of thematerial bed material has been has pointed been pointed out strongly out strongly [13]. [13]. ToTo model model sediment sediment transport transport processes processes as as well well as as bed bed deformation deformation,, multi multi-layer‐layer models models were were appliedapplied for for graded graded sediment sediment transport. transport. Despite Despite the the considerable considerable variations variations of of porosity, porosity, most most of of the the conventionalconventional models models assumed assumed that that the the porosity porosity of of bed material is constant. Therefore, Therefore, sediment sediment transporttransport in in the the form form of infiltration of infiltration into intothe void the spaces void spaces of the co ofarse the bed, coarse or fine bed, particles or fine in particles sublayers in andsublayers the entrainment and the entrainment of fine sediment of fine sedimentinto flow into from flow the from substrates the substrates,, is not taken is not into taken account. into account. This assumptionThis assumption can be can inappropriate be inappropriate for simulating for simulating the sediment the sediment transport transport and bed and variation bed variation in gravel in‐ bedgravel-bed rivers. Toro rivers.‐Escobar Toro-Escobar et al. [14] et al. accounted [14] accounted for this for process this process in terms in terms of an of appropriate an appropriate transfer transfer or exchangeor exchange function function at the at theinterface interface between between the the surface surface layer layer and and substrate. substrate. Based Based on onthe the data data from from a largea large-scale‐scale experiment experiment on onthe the aggradation aggradation and and the theselective selective depositio depositionn of gravel of gravel,, they they proposed proposed an empiricalan empirical form form for the for thetransfer transfer function, function, where where material material that thatis transferred is transferred to the to thesubstrate substrate can canbe representedbe represented as a as weighted a weighted average average of ofbedload bedload and and surface surface material, material, with with a abias bias toward toward bedload. bedload. ApplyingApplying this this function function with with th thee assumption assumption of of a a constant constant porosity, porosity, Cui Cui [ [1515]] developed developed a a numerical numerical modelmodel for for sand sand entrainment/infiltration entrainment/infiltration from/into from/into the the subsurface. subsurface. The The model model was was applied applied to to study study thethe dynamics dynamics of of grain grain size size distributions, distributions, including including the the fractions fractions of sand of sand in sediment in sediment depos depositsits and and on theon channel the channel bed surface. bed surface. Further, Further, Sulaiman Sulaiman et al. [ et16 al.] proposed [16] proposed an approximated an approximated bed variation bed variation model whilemodel considering while considering the change the change in bed inporosity, bed porosity, where where the thickness the thickness of each of eachlayer layer is assumed is assumed to be to constantbe constant and and equal. equal. Furthermore, Furthermore, the the exchange exchange be betweentween bed bed material material and and the the transported transported sediment sediment onlyonly takes takes place place on on the surface layer, andand sedimentsediment transporttransport fromfrom an an upper upper layer layer to to the the lower lower layer layer is isneglected. neglected These. These assumptions assumptions are are improper improper ingravel-bed in gravel‐bed rivers, rivers where, where finer finer sediment sediment possibly possibly drops dropsinto the into subsurface the subsurface layer. layer. To bridge above knowledge gap, in this paper we develop a numerical hydromorphological model that considers the bed porosity change and the exchange flux of fine sediment between two Water 2019, 11, 550 3 of 21 To bridge above knowledge gap, in this paper we develop a numerical hydromorphological model that considers the bed porosity change and the exchange flux of fine sediment between two different bed layers. Further, the Discrete Element Method (DEM) is employed for modeling the infiltration processes. We test the new numerical model for three straight gravel-bed open channels. The calculated results are then compared with the observed data to verify the improved model. 2. Methodology As usual, the structure of our proposed model consists of two modules: (1)—hydrodynamic module; and, (2)—sediment transport and bed variation module. In the hydrodynamic module, the backwater equation is employed for low Froude number conditions and the quasi normal flow assumption is applied for the high Froude number flow conditions. The friction slope is calculated with the Keulegan formulation, which is used for calculating the transport rate in the sediment transport and bed variation module. More details regarding the water flow equations can be found in the studies that were conducted by Cui and Parker [15,17–20].