numerical simulation of armour layer development under ... - AIIA2011

Convegno di Medio Termine dell’Associazione Italiana di Ingegneria AgrariaBelgirate, 22-24 settembre 2011memoria n.NUMERICAL SIMULATION OF ARMOUR LAYER DEVELOPMENTUNDER CONDITIONS OF SEDIMENT STARVATIONG. Kaless 1(*) , L. Mao 2(1) Department of Land and Agro-forest Environment, University of Padova, (*) Cor. Author(2) Faculty of Science and Technologies, Free University of Bozen-BolzanoABSTRACTGravel‐bed rivers in perennial regimes are usually characterized by a coarser surfacelayer of sediment, commonly called armour layer, which influence bedload transport, aswell as hyporheic flows and fish habitats. If the armour is created by selective transportof finer sediment fraction from the bed, it is called static, and can be replicated inlaboratory if no sediment is fed from upstream. The paper presents a relatively simplenumerical modelling approach to simulate armouring processes, which has beenapplied to replicate bedload transport measured during static armouring flumeexperiments in order to assess the performance of few bedload formulas. Overall, themodel proved to be able to simulate well the vanishing sediment transport due toboth slope reduction and surface coarsening. All formulas tend to overpredict theactual sediment transport, especially at the lower rates, and to underestimate thegrain size of transported material.Keywords: armour layer, numerical modelling, bedload formulas.1 INTRODUCTIONGravel‐bed rivers typically exhibit an armoured surfaces covering a finer subsurfacemix of sediments. The coarser surface has implications for hyporheic flow exchange,fish habitats, and bedload transport estimation (e.g. Bathurst, 2007). The amour is calledstatic when is created by a flow that selectively entrains only the finer elements (Churchet al., 1998) from a non-uniform bed material. Static armour is typical in sedimentsupply-limitedsystems (e.g. reaches located downstream of lakes or dams). Armouringprocess has been observed both experimentally and in the field and its extent dependson the flow strength applied to the bed and the grain size distribution of the bed mixture(Church et al., 1998).In a flume, static armour is usually created exposing a non-uniform mixture to aconstant flow rate with no sediment input. After a first phase of bed degradation whichcauses an initial decrease in the slope of the bed, there is a gradual increase of thesurface grain size distribution. Under these conditions, sediment transport rate is at itsmaximum during the first short period, and then gradually decreases (Proffitt, 1980;Tait et al., 1992; Aberle & Nikora, 2006; Mao et al., 2011). Proffitt (1980) showed thatthe development of a static armour involves both the elective transport of the finer

G. Kaless, L. Maoparticles and a following re-arrangement of the coarser fractions. Using a laser scannerdevice, Mao et al. (2011) recently depicted the highly structured and imbricated natureof the static armour layers, which became topographically less complex at higherforming flow strengths, with significant implications for sediment mobility and bedroughness. Static armour development as observed in flume experiments has beensimulated numerically with success using different approaches (e.g. Ashida & Michiue,1971; Proffitt, 1980; Bettess & Frangipane, 2003). The aim of the present work is topresent a simple approach for reproducing numerically static armour development, todiscuss the simulation of the sediment transport rate reduction through time, and toassess the best performing bedload formula.2 MATERIALS AND METHODS2.1 Numerical modellingThe numerical model is intended to predict the evolution of the bed profile and thesurface grain size distribution given a certain flow strength and a sediment transportcapacity. The model is based on mass and energy conservation principles and fractionssediment transport process is described by means of the sediment conservation equationand a sediment transport model. Being developed for poorly‐sorted sediment grain‐sizemixtures, the model is based on the Parker & Sutherland (1990) extension to theExner’s conservation equation for the case of heterogeneous mixtures. Parker &Sutherland (1990) model considers a surface layer that directly interacts with sedimenttransport and a subsurface layer that interacts with the upper layer by means ofdegradation/aggradation:∂z∂t = − 1 ∂q bT1 − λ p ∂x(1)∂F si∂t = 1 ∂(z − L a )*fL Iia ∂t− F si∂L a∂t − ∂q bi∂x 4where q bT is the total volumetric sediment transport, λ P is the sediment porosity, F si ,and f Ii are the volume fraction of material in the i th grain size range corresponding to thesurface layer, and the exchanged material between layers, respectively; L a is thethickness of the active layer and q bi is the volumetric sediment transport of the i th grainsize range. In case of bed degradation, the surface grain size distribution equals thesubsurface mixture, whereas in the case of bed aggradation a linear mixing modelconsidering bedload grain size and the armour layer is applied (Hoey & Ferguson,1994). As to the active layer, its thickness is comparable to the surface D 90 (size such90% of material is finer).The sediment transport process can be described by many models based on thesurface material. For this study two models based on field data (Parker, 1990 andPowell et al., 2003) and three models derived from flume experiments (Wilcock &Crowe, 2003; Wu et al., 2000 and Hunziker & Jaeggi, 2002) have been selected. All themodels are suitable for computing fractional sediment transport (i.e. the transport ofeach grain size classes is calculated separately).The model has been applied to simulate static armour development in a closed(2)

G. Kaless, L. MaoTable 2 exposes bed load mean diameter averaged along the simulation span. As acommon rule, predictions for all the cases are below the actual measurements. Wilcock& Crowe’s model and Hunziker & Jaeggi’s models have the lowest differences, whileWu et al.’s predictions are half the observed magnitudes.4 DISCUSSIONDuring the first phase of the experiments that bed degrades, are flume conditionssimilar to those founded in ephemeral streams? In absence of an armour layer flowconditions are intense (dimensionless shear stress between 0.06 and 0.09) as well assediment transport (upto 207 gr m -1 s -1 ). Powell et al. (2003) studied the sedimenttransport of two streams located in a semiarid context. Sediment transport was very high(in the range of 10 1 to 10 5 gr m -1 s -1 ) as well as dimensionless shear stress (above 0.04upto 0.4); furthermore, both streams lacked for an armour layer. Laboratory initialconditions are within the range of validity of the empirical relation. Therefore the modelhas been able to predict very well the sediment transportAlthough flow strength can be high in the experiments it is even within the range ofvalidity of relations derived from laboratory experiments (such as Wilcock and Crowe,2003; Hunziker & Jaeggi, 2002; and Wu et al., 2000) or direct measure in streams but inhumid climates (like Oak Creek analyzed by Parker, 1990). After the first phase, thereis increase in surface grain size. Simulating the development of a static armour layerwith mobile-armour-based relations can induce a systematic error. Laboratoryexperiments show that static armour layers are coarser than mobile layers under thesame flow strength (Mao et al, 2011). Furthermore, interlocked grains or clustersincrease the dimensionless critic shear stress, so that grains have more resistance tomove in the presence of static armours. These experimental findings are furthersupported with field evidence (Church et al, 1998). It follows that, if we interpret thesimulations in a mobile armour context, then it is expected that sediment transportprediction should be higher than observed, and grain size distribution for predicted bedload should be finer than actually measured. This reasoning may explain the systematicdiscrepancies between observations and predictions from Wilcock and Crowe’s,Parker’s and Wu et al.’s models.The findings aforementioned seem to be in contradiction with Hunkizer & Jaeggi’smodels results. The simulations show a good agreement for solid discharges above 3 grm -1 s -1 , and underpredictions for discharges below this value. These authors proposed atransport relation with a dimensionless threshold for shear stress. That is, if shear stressis below this threshold then there is no sediment transport. A close inspection ofsimulation results reveals that during the first stage (above the 3 gr m -1 s -1 ) thetransported material is mainly coarse and similar to the filling material. Progressively, ittends to get finer, indicating the formation of the armour layer by selective transport offine sizes and erosion. As the surface coarsers and slope decreases, the shear stressdecreases approaching the threshold value, and due to the structure of the transportrelation, sediment transport falls quickly.5 CONCLUSIONSA one-dimensional hydraulic model able to solve the steady state gradually varied