EFFECT OF COHESIVE WASH LOAD ON TRANSPORT OF NONUNIFORM SEDIMENTS

Abstract

The sediment transport by streams has been the subject of profuse research efforts since long time. The interest in sediment transport research has stemmed from the requirement to mitigate the soil erosion in catchment area and erosion of channel banks, design of stable channels, design and maintenance of hydraulic structures, reservoir sedimentation, transport of pollutants, and effects on aquatic communities etc. The total sediment load of alluvial streams can be distinguished into two major classes i.e. bed material load and wash load. The bed material load consists of grain sizes represented in the bed material and may be transported either as bed load or as suspended load. The wash load is generally transported in suspension. The wash load is composed of sediment particles finer than those present in the bed material and predominantly consists of silt, clay and fine sand. Einstein et al. (1940) established a boundary between the bed material load and wash load and termed the later as the grain size of which 10 per cent of the bed material is finer. The conventional assumptions for wash load are that it is independent of channel's hydraulic conditions. It is also generally considered that wash load does not interact with the material of stream bed and banks and it is dependent on catchment characteristics, and therefore, difficult to predict. It is however considered that presence of wash load affects the resistance to flow. The wash load carried by many rivers originating from Himalaya like Sutlej, Ganga etc. consists of clay material which is cohesive in nature. Cohesive sediments possess strong interparticle forces due to their surface ionic charges and therefore, these affect the fluid properties as well as the settling velocity of the larger sediment particles. The lack of relation between flow conditions in rivers and wash load has so far posed a major obstacle to the development of any method to predict the wash load transport rate and its effects on the bed material transport rates. Therefore, the present study was taken up to investigate in depth the effect of presence of cohesive wash load on resistance to flow and transport of bed material load. Vanoni (1946), Einstein and Chien (1955), Vanoni and Nomicos (1960), Parker and Coleman (1986), Wang et al. (1998), Cellino and Graf (1999) and Peng et al. (2001) found that the resistance to flow was smaller in sediment laden flows than in corresponding clear water flows. Taggart et al. (1972), Ippen (1973) and Lyn (1991) were among those found the resistance to flow for sediment laden flows was greater than that for clear water flow. Pullaiah (1978), Arora (1983) and Khullar et al. (2007) found that friction factor for sediment laden flows may increase or decrease with an increase in concentration of suspended load. Knowledge of limit deposition condition of suspended load is very important in the design of lined channels, sewers and other hydraulic structures. Rossinsky and Kuzumin (1964), Bagnold (1966), Novak and Nalluri (1975), Arora et al. (1984), Wiuff (1985), Westrich (1985) and Nalluri and Spaliviero (1998) and many others proposed relationships for determining the limiting concentration of suspended load transport. Following the work of Einstein (1968), there have been many laboratory and field studies on the subject of fine sediment infiltration (Beschta and Jackson, 1979; Frostick et a/., 1984; Carling, 1984; Diplas and Parker, 1985; Lisle, 1989). A common observation from these studies was that fine sediment infiltrated to a finite depth, usually to a depth within a few diameters of the largest bed material particles rather than settling to the bottom. Einstein (1950) proposed the first semi-theoretical model for fractionwise computation of bed load transport rates. Einstein and Chien (1953 a) introduced the phenomenonof sheltering of fine particles behind the coarse particles. Misri et al. (1984) and Samaga et al. (1986 a) pointed out the exposure effects of coarser particles. Kikkawa and Fukuoka (1969), Woo et al. (1987) and Khullar (2002) found that the rate of bed material transport increased with increase in wash load concentration. Wan (1985) and Diplas and Parker (1992) found reduction in bed load transport rates in presence of wash load in suspension. The critical review presented above on the subject indicates that the bed material transport is affected by the presence of wash load in suspension. However, the effect of presence of cohesive wash load on these processes in not well investigated as yet. Therefore, the present study was taken up to investigate in depth the effect of presence of cohesive wash load on resistance to flow and transport of bed material load. Extensive experimental program was conducted in two recirculating tilting flumes, one having mobile bed while the other having rigid bed. One nonuniform and two uniform sediments were used as bed material. The arithmetic mean size da and geometric standard deviation crg of the bed material used in the present study were varied from 1.03 mm to 2.33 mm and 1.15 to 2.25 respectively. The cohesive wash material used was 0.0039 mm of size. Nine series of experiments were performed in mobile bed channel. Six different series of experiments were performed in the rigid bed channel to study the depositional conditions of fine cohesive sediments in the suspension. The first run in each series was conducted as reference run without wash load in the flow to provide reference set of measurements. In each series subsequent runs with increasing concentration of cohesive wash load were conducted until the depositional condition was achieved. Flow parameters were selected such that the bed material was transported as bed load only. Experiments were conducted under subcritical steady uniform flow conditions. The corresponding data available in literature have also been compiled. Equilibrium condition was assumed to be attained as soon as rate of removal of fines became equal to the rate of deposition. After each run, the sediment bed was allowed to drain off excess water through it and samples of bed compositions at different sections along the flume were collected for different sediment laden runs. Observations for velocity, concentration of suspended load and bed material transport rates were also made for all flow conditions. Laboratory and field data collected in the past investigations by various researchers have also been collected for use in the present study. Khullar et al. (2007) criterion for predicting the variation in friction factor in the presence of cohesive wash load in suspension was found unsuitable for the data used in the present study. in Data collected from literature and present study through mobile bed as well as rigid bed channels regarding resistance to flow were analyzed collectively. After making number of trials using all relevant dimensionless parameters, the following criteria are proposed for describing the variation of friction factor in an open channel: <1 /. £_ fo >1 when D* C when 1/16 D* C 'f u* aasQ \0-5 V v J ( A \°-5 <8 and >8 K v J Here / and f0 are the friction factor values for sediment laden and clear water flows respectively, Dt is dimensionless particle size, C is the volumetric concentration in ppm, w» is shear velocity, d50 median sediment grain diameter and v is kinematic viscosity of fluid. The generalized predictors for friction factor are developed for each of the above cases as below: Cm6\^^ v J > f (i.e. while—>1) L fo"•^MflF^Hsj (ii) For data having D* C1/16 fo Cn2CD -0.09(*-l>j ^ ^ =o.94e ]us fo '( u* dAso \05 V <8 IV f (i.e. while^-<1) fo for (s - !)• Clco C> US for(5-l)j^U5xl0-6 >5xl0" p Hereco is the fall velocity for sediment, U is mean velocity of flow, S is slope of the channel, Cp is the volumetric concentration in per cent and s is relative density of sediment. The relationships proposed above are applicable for determination of / for sediment laden flows in both mobile bed and rigid bed channels. The relations given by Rossinsky and Kuzumin (1964), Bagnold (1966), Novak and Nalluri (1975), Wiuff (1985), Westrich and Juraschek (1985) and Nalluri and Spaliviero (1998) for determining the capacity of a channel to transport the suspended load were checked. As these relations do not produce satisfactory results for the present data, new relationship is therefore proposed. After making number of trials using all relevant dimensionless parameters, it was found that the limiting concentration of suspended load in rigid bed as well as mobile bed channels of different shapes is uniquely related to the parameter qSc I D ] I A ' of2 fmdso\™yh) ^3 \ v Here q is rate of flow per unit width, Sc is slope parameter and obtained as Sc = , Aps is difference in mass densities of sediment and water, pw is mass Aps/pw density of water, D is central depth of flow, h is flow depth, A is a parameter dependent on Froude number and given by | — -1 for subcritical flows and j4 = 1.1xFr —1 for critical and supercritical flows, i?= (l + C„*)and dimensionless cohesion C*u =—-—, Ay,di here Cu is cohesion, Ays is difference in specific weights of sediment and water and c/, is sediment size for the i size fraction. A graphical relation between limiting capacity of uniform sediment in ppm by volume (Cv) with the above mentioned parameter is proposed to determine the limiting concentration of suspended load transport in both rigid bed and mobile bed channels. The numerical modeling of the process of routing of wash material through a stream having coarse bed material is carried out. The partial differential equation governing this process has been derived and given as dp aa d qs —- + a\ —— + a2 —^ = 0 dt dt dx where Qs is volume of wash load entering the control volume per unit time, Pp is porosity y of the course bed, a\ = and a2 = , b is width of the channel and Az UbAz bAz thickness of active bed layer. The assumption made in the derivation of governing equation is that only the thickness of active bed layer takes part in the process of infiltration/deposition of fines within the pores of coarse bed material and also the bed material transport occurring simultaneously does not affect this process. The predictor-corrector based finite difference numerical scheme of MacCormack -* (1969) was used for the solution of governing equation for uniform and steady flow conditions for the routing of wash material through a coarse bed stream. The present model was validated using data collected in the present study. Good agreement was achieved between the observed and computed values. The methods proposed by Patel and Ranga Raju (1996), Karim (1998) and Khullar et al. (2007) were checked for computing the bed load transport rates in the presence of cohesive wash load in the flow. Khullar et al. (2007) method was found to be valid for present data as well. Methods proposed by Samaga et al. (1986 b), Wu et al. (2000) and Khullar (2002) for computing the suspended load transport rates were checked for their accuracy. The Khullar (2002) method for fractionwise computation of suspended load transport of nonuniform bed material is suitably modified for the transport of cohesive wash load in suspension. The effect of various parameters on £,,, (sheltering-exposure-interference coefficient for suspended load transport for sediment size dt) was studied and the following functional relationship is proposed: VI 6W t0 di U C* roc da a>i where ro is total shear stress, roc is critical shear stress for arithmetic mean size as per Shields', &>, is fall velocity of sediment size d, and C*,, is nondimensional cohesion parameter and obtained as C,*,, Aydi , i'm, is the proportion of wash material in the active bed layer and C„,, is cohesion for the size dt. The detailed analysis of flume and field data led to the development of the following equation: 0.62 = 4.14 \da J rv\™ -i 0.68 B, -o.i Km Here Bt is cohesion parameter for size dj and given as 5, = (1 +C*„j) The value of £,,, for a particular size fraction J, can be computed by using the above relationship and therefore suspended load transport of that size $sA can be determined by using the suspended transport law given as <j>St ,• = 28 y £ • ° '*'' A A It is worthwhile to mention that wash load transport can also be determined by using the above relationship if the sediment parameters of the active bed layer viz. d^, da and Af* etc. are used. The discrepancy ratio and standard deviation are used to indicate the goodness of fit between the computed and the observed results. A comparison between computed and observed dimensionless suspended load transport parameters in terms of discrepancy ratio R and standard deviation a was also carried out to validate the proposed method for the computation of suspended load transport of nonuniform bed material in presence of wash load in the flow. vu