Sediment Transport

Not all channels are formed in sediment and not all rivers transport sediment. Some have been carved into bedrock, usually in headwater reaches of streams located high in the mountains. These streams have channel forms that often are dominated by the nature of the rock (of varying hardness and resistance to mechanical breakdown and of varying joint definition, spacing and pattern) in which the channel has been cut.

Competence : Competence refers to the largest size (diameter) of

sediment particle or grain that the flow is capable of moving; it is a hydraulic limitation. If a river is sluggish and moving very slowly it simply may not have the power to mobilize and transport sediment of a given size even though such sediment is available to transport. So a river may be competent or incompetent with respect to a given grain size. If it is incompetent it will not transport sediment of the given size. If it is competent it may transport sediment of that size if such sediment is available

Some Useful Definitions

Capacity refers to the maximum amount of sediment of a given size that a stream can transport in traction as bedload. Given a supply of sediment, capacity depends on channel gradient and discharge. Capacity transport is the competence-limited sediment transport (mass per unit time) predicted by all sediment-transport equations. Capacity transport only occurs when sediment supply is abundant (non-limiting).

Capacity:

Sediment supply refers to the amount and size of sediment available for sediment transport. Capacity transport for a given grain size is only achieved if the supply of that calibre of sediment is not limiting (that is, the maximum amount of sediment a stream is capable of transporting is actually available). Because of these two different potential constraints (hydraulics and sediment supply) distinction is often made between supply-limited and capacity-limited transport. Most rivers probably function in a sediment-supply limited condition although we often assume that this is not the case.

Sediment supply:

The sediment load of a river is transported in various ways although these distinctions are to some extent arbitrary and not always very practical in the sense that not all of the components can be separated in practice:

1. Dissolved load2. Suspended load3. Wash load4. Bed load

Modes of Sediment Transport

Dissolved load is material that has gone into solution and is part of the fluid moving through the channel. The amount of material in solution depends on supply of a solute and the saturation point for the fluid. For example, in limestone areas, calcium carbonate may be at saturation level in river water and the dissolved load may be close to the total sediment load of the river. In contrast, rivers draining insoluble rocks, such as in granitic terrains, may be well below saturation levels for most elements and dissolved load may be relatively small.

Dissolved Load

Total dissolved-material transport, Qs(d)(kg/s), depends on the dissolved load concentration Co (kg/m3), and the stream discharge, Q (m3/s): Qs(d) = CoQ

Suspended-sediment load is the clastic (particulate) material that moves through the channel in the water column. These materials, mainly silt and sand, are kept in suspension by the upward flux of turbulence generated at the bed of the channel. The upward currents must equal or exceed the particle fall-velocity (Figure ) for suspended-sediment load to be sustained.

Suspended-sediment load

Fall velocity vs grain size

Suspended-sediment concentration in rivers is measured with an instrument like the DH48 suspended-sediment sampler shown in Figure. The sampler consists of a cast housing with a nozzle at the front that allows water to enter and fill a sample bottle. Air evacuated from the sample bottle is bled off through a small valve on the side of the housing. The sampler can be lowered through the water column on a cable. the sampler is lowered from the water-surface to the bed and up to the surface again at a constant rate so that a depth-integrated suspended sediment sample is collected.

The instrument must be lowered at a constant rate such that the sample bottle will almost but not quite fill by the time it returns to the surface. The sample bottle is then removed and capped and returned to the laboratory where the fluid volume and sediment mass is determined for the calculation of suspended-sediment concentration.

Although wash load is part of the suspended-sediment load it is useful here to make a distinction. Unlike most suspended-sediment load, wash load does not rely on the force of mechanical turbulence generated by flowing water to keep it in suspension. It is so fine (in the clay range) that it is kept in suspension by thermal molecular agitation (sometimes known as Brownian motion, named for the early 19th-century botanist who described the random motion of microscopic pollen spores and dust). Because these clays are always in suspension, wash load is that component of the particulate or clastic load that is “washed” through the river system.

Wash Load:

Unlike coarser suspended-sediment, wash load tends to be uniformly distributed throughout the water column. That is, unlike the coarser load, it does not vary with height above the bed.

Bed load is the clastic (particulate) material that moves through the channel fully supported by the channel bed itself. These materials, mainly sand and gravel, are kept in motion (rolling and sliding) by the shear stress acting at the boundary. Unlike the suspended load, the bed-load component is almost always capacity limited (that is, a function of hydraulics rather than supply). A distinction is often made between the bed-material load and the bed load.

Bed Load (Traction Load)

Bed-material load is that part of the sediment load found in appreciable quantities in the bed (generally > 0.062 mm in diameter) and is collected in a bed-load sampler. That is, the bed material is the source of this load component and it includes particles that slide and roll along the bed (in bed-load transport) but also those near the bed transported in saltation or suspension.

Empirical formulae developed for bedload, suspended load and total sediment transport rate using laboratory and field data. They are based on hydraulic and sediment conditions – Water depth, velocity, slope and average sand diameter etc. There can be significant differences between predicted and measured sediment transport rates, WHY?

Development of Sediment Transport Formulae

19

These differences are due to change in:- Water temperature,- Effect of fine sediment,- Bed roughness,- Armouring, and - Inherent difficulties in

measuring total sediment discharge. Use of most appropriate formula based on the availability of conditions, experience and knowledge of the engineer.

Development of Sediment Transport Formulae con’t

21

1. Bedload Formula – Meyer-Peter & Müller (1948)

2/3*cS

*b )FF(8q

Critical Shields Parameter = 0.047

)1( sgDo

1sgDD

qsbWhere D is average sand diameter

2/3)047.0(81 ssb FsgDDq

Valid for D > 3.0mm

Sediment Flow Ratem3/s/m

22

The Shields diagram empirically shows how the dimensionless critical shear stress required for the initiation of motion is a function of a particular form of the particle Reynolds number, Rep or Reynolds number related to the particle.

2. Total Sediment Transport Load – Ackers & White’s Formula (1973)

Dimensionless Grain Diameter

3/1

2

1)(

sgr

gDD

Mobility Number

n

ms

n

grDD

V

gD

uF

1

*

10log321)(

Flow velocity

Hydraulic mean depth

n

m

m

gr

grs u

V

D

qD

A

FCq

*

1Sediment Flow Ratem3/s/m

Flow discharge 23

3. Total Sediment Transport Load – Engelund/Hansen’s (1967) Formula

2/5/ 1.0 f

2/ 2

V

gSyf Friction

factor2/1

3

gDq s

s

t

Ds )(

Shields Parameter

350/

2/5

)1(1.0

Dsgf

q st Sediment transport load

N/s/m

24

Van Rijin’s Formula:

Where “Ca is the suspended sediment concentration,

“ X1”and “X2” are the parameters, D50 is the sediment particle diameter, ρS is the density of sediments (2650 kg/m3), ρW is the density of water(1000kg/m3),υ is the kinematic viscosity of water (10-6 m2/s) and g is the gravitational acceleration (9.81 N/m2), τ is the shear stress and τc is the critical bed shear stress determined by the following equation (2)

𝐶𝑎 = 𝑋1 𝐷50𝑋2[𝜏−𝜏𝑐𝜏𝑐 ]1.5

{𝐷50[(𝜌𝑠−𝜌𝑤)𝑔𝜌𝑤𝜐2 ]1 3ൗ�}0.3 − − − (1)

Where ρw is the density of water, “y” is the depth of flow“g” is the gravitational acceleration and “If” is the frictional slope If is calculated as follows (equation (3))

Where “M” is the Stickler’s coefficient “I” is the longitudnal slope of the canal and “U” is the velocity which is calculated by equation (4)

𝜏= 𝜌𝑤𝑔𝑦𝐼𝑓 − − − − − − − − − − − − − − −ሺ2ሻ

𝐼𝑓 = 𝑈2𝑀2𝑦4/3 − − − − − − − − − − − − − − (3)

“rh” is the hydraulic depth which is assumed to be equal to the depth of flow because the width of the cross-section of the canal is very large. Critial shear stress is calculated by equation (5)

Where τc is the critical shear stress, “C” is the Shield’s parameter determined by Shield’s curve in which Reynolds number is along abscissa and “C” is in ordinate. Reynolds number is calculated by equation (6)

𝑈= 𝑀𝑟ℎ23𝐼12 − − − − − − − − − − − − − − − (4)

𝜏𝑐 = 𝐶𝑔ሺ𝜌𝑠 − 𝜌𝑤ሻ𝐷50 − − − − − − − − − − − (5)

Where u* is the shear velocity, “d” is the particle’s diameter and “υ” is the viscosity of water. Velocity “U” for logarithmic profile is calculated by equation (7)

Where “u*” is the shear velocity, “k” is constant=0.4, “y” is the flow depth and “ks” is the bed roughness height calculated by equation (8)

𝑅= 𝑢∗𝑑𝜐 − − − − − − − − − − − − − − − − (6)

𝑈𝑢∗= 1𝑘ln൬30𝑦𝑘𝑠 ൰− − − − − − − − − − − − − (7)

𝑘𝑠 = (26∗𝑛)6 − − − − − − − − − − − − − −(8)

“u*” in equation 7 is calculated by equation (9)

Hunter Rouse concentration “Cy”is calculated as

Where “y” is the water depth, “h” is the depth of each layer from the bottom and the suspension parameter “z” is calculated by equation (11)

𝑢∗= ඨ𝜏𝜌𝑤 − − − − − − − − − − − − − − − − (9)

𝐶𝑦𝐶𝑎 = (𝑦− ℎℎ 𝑎𝑦− 𝑎)𝑧 − − − − − − − − − − − − − (10)

𝑧= 𝑤𝑘𝑢∗− − − − − − − − − − − − − − − (11)

Root mean square error is calculated by

𝐸= ඨ1𝑛 [𝐶𝑠ሺ𝑖ሻ− 𝐶𝑜ሺ𝑖ሻ𝐶𝑠ሺ𝑖ሻ ]2 − − − − − − − − − (12)𝑛

𝑖=1

Cell no(1)

Distance from

bed(m)(2)

Velocity(m/s)(3)

Hunter Rouse Conc.

(m3/m3)(4)

Cell height(m)

(5)

Cell flux (m3/m3)

(6)=(3)*(4)*(5)

8 3.716 2.365 3.22669E-10 0.3912 2.98448E-107 3.325 2.334 2.03269E-08 0.3912 1.8559E-086 2.934 2.300 1.79447E-07 0.3912 1.61434E-075 2.543 2.261 9.272E-07 0.3912 8.19922E-074 2.151 2.215 3.88495E-06 0.3912 3.36596E-063 1.760 2.160 1.53559E-05 0.3912 1.29745E-052 1.369 2.091 6.43409E-05 0.3912 5.26315E-051 0.587 1.859 0.002934879 0.5867 0.003201703

The values of Manning’s “n” used in optimization were 0.0143, 0.017, 0.02 and 0.025 where the optimized value of “n” becomes 0.02 having minimum error in sediment concentration, bed levels and the water levels. So the optimized bed roughness is 0.0197, calculated from equation 8. Different parameters in Van Rijin’s equation were optimized by using MATLAB. The values of empirical parameter “X1” were 0.015, 0.3 and 1.5 while for “X2” 5%, 10% 15% and 20% of depth of flow were used for optimization process as explained by Olsen (2011)

The optimized value of “X1” was obtained as 0.015 and “X2” was 15% of depth of flow. Optimization was done for each month (from May 2011 to October 2011). Results of sensitivity analysis are shown in the graphs in the next slide