#### Methods for Estimation of Bed Load:

The following methods are generally used for estimation of bed load.

1. Analytical Method:

For computation of bed-load movement using analytical method includes several relationships; they may be the empirical or analytical.

In general, the theoretical relationship are based on the following two basic concepts:

i. There a minimum fluid force is exerted on the soil particles before starting them to move.

ii. The force, which is subject to the soil particles on the channel bed is not constant, but varies about some mean value. This concept is based on the theory of turbulent flow.

The forces acting on the soil particles of non-cohesive materials are basically the gravity and fluid forces. The analytical method for computing the bed load transport involves several relationships.

Few of them are described as under:

a. Du Boys Formula:

This formula is based on the theory of tractive force, which was derived on the assumptions that the coarser particles are moved in the form of layers and subject to uniform tractive force and vertical velocity gradient of the moving coarser particles is linear. The formula for bed load estimation is written as under –

qs = Cs . τoo – τc) …(23.2)

Where,

qs = rate of bed load transport (volume per second per unit stream width).

Cs = coefficient, depends on the shape and size of the sediment particle = 0.173/d3/4, where d is the grain diameter (mm).

τo = average shear stress exerted on the channel boundary.

τc = critical shear stress.

This formula does not take care the theory of turbulent flow on sediment movement.

b. Shield’s Formula:

Shield’s formula is used for estimating the bed load movement consisting uniform size sediments. The equation was derived by considering the effect of specific gravity of the sediment. The Shield’s formula is given as under –

Where,

Ss = specific gravity of sediments, such as stones grains.

S = stream bed slope

qs = discharge rate (m3/s per unit width of stream)

q = discharge per unit channel width

γ = specific gravity of the fluid

d = diameter of sediment

c. Mayer Peter’s Formula:

This formula was developed by a Swiss-Engineer, by considering the effect of grain diameter, slope of channel bed and discharge characteristics of the flow on bed load movement. It is given as under –

Where,

Gs = rate of bed load transport per unit width of channel (kg/h.m).

N’ = Manning’s roughness coefficient for plain bed

= [(1/24) d1/6], in which, d is the effective grain diameter

N = actual value of Manning’s roughness coefficient for rippled bed. Generally, the value of N is taken as 0.020 for the discharge more than 11 cumec; and 0.0225 for a lower discharge value.

τo = unit tractive force, exerted by the flowing water

= 0.97 . γ . R.S.

τc = critical shear stress required to displace the sediments

= 0.07 d, kg/m2

R = hydraulic mean depth

S = stream bed slope

d. Chang Formula:

Chang reported following formula for estimating the bed load –

Where,

Gi = rate of bed-load transport (pounds/second/unit width)

k = constant

n = Manning’s roughness coefficient

τo = unit tractive force due to stream water flow

τc = critical shear stress required to displace the sediment

= 0.0175 (1.65 d)x when specific gravity of the sediment is 2.65, in which, d is the sediment diameter (mm) and x is the exponent which is either equal to unit or half, depending on whether the value of 1.65 d is greater or less than unit, respectively.

e. Schoklitsch Formula:

This formula was developed on the basis of experimental data, measured by installation of Hume in the stream. The Schoklitsh formula assumes that the bed-load contains the materials of uniform size. The formula is outlined as under –

Where,

Gi = rate of bed-load transport (F.P.S)

d = particle’s diameter

S = slope of stream bed

q = observed discharge

qc = critical discharge; it is given by

= 0.00021 d/S4/3 … (23.7)

#### Estimation of Bed Load Using Sampler:

The estimation of rate of bed load movement through stream flow is carried out by placing the sampler over the bed and measuring the amount of sediment materials collected for a given time. The samplers used for collecting the bed load samples, are known as bed load samplers.

The sampler is kept in position by a rod, when the depth of stream flow is less or by a cable from the boat, trolley or pulley running on a cable spanned across the river or from a bridge, if there. The lowering and raising of the sampler into the stream is done with the help of winch. The bed-load samplers are found in different types, based on their construction and principles of operation.

In general, the followings are the common type of bed load samplers:

This sampler consists of a box or basket, made of meshed material. The sampler is lowered into the stream over the bed, keeping its open end towards upstream side of the flow, to collect the sample of moving materials. This sampler has demerit that when it is introduced into the stream flow, then there develop an inward resistance to flow.

As result, the entrance velocity of flow into the sampler gets decrease as compared to the undisturbed stream flow velocity. Because of this reason, some of the materials from flow are dropped out before entering the sampler. In this way, the catching efficiency, i.e. the percentage of the materials caught by the sampler gets reduce than the actual value.

2. Tray or Pan Type Sampler:

The tray or pan type sampler consists of a flat pan or a tray shaped device. The baffles or slots are also provided in this sampler to check the materials, moving out from the sampler. This sampler has the same disadvantage as in the basket type sampler.

3. Pressure Difference Type Sampler:

This sampler is designed to overcome all the demerits found in above two samplers (i.e. decrease in the velocity at the entrance of the sampler). In this type of sampler a pressure drop is developed at the exit point to eliminate the energy loss due to inward resistance, causing the same entrance velocity as in undisturbed stream, there. This is incorporated by constructing a diverging section towards upstream side of the sampler. Sometimes, this sampler also has a screen in place of baffle to check the materials moving out from the sampler.

The bed-load samplers described above, require calibration before putting into operation. The calibration is carried out by measuring the actual sediments in a sump and comparing them with the sediments obtained by sampler.

For estimating the bed load, the samples collected through the samplers are dried and weighted. The dry weight is then divided by the time taken -for measurement and width of the stream bed to get the bed load movement per unit time and stream width. A curve between the rate of sediment movement and the stream flow is derived, from which the rate of bed load movement w.r.t. flow velocity through the stream can be determined.