# TRACTIVE FORCE THEORY

• In the study of mechanics of sediment transport, the soil particles are always considered as incoherent.
• Most of the river beds are made up of sand and gravel and as such assumption in regard to soil being incoherent is correct.
• The basic mechanism that controls the sediment transport, is the drag force exerted by water in the direction of flow on the channel bed.
• This drag force is also known as tractive force or shear force.
• This force is nothing but a pull of water on the wetted area of the channel.
• Consider a channel of length L and cross-sectional area A.
• The volume of water in this length of channel would be A × L.
• If w is the unit weight of water, then weight of water stored in this length (L) of the channel will be wAL. Weight of water acting in vertical direction = wAL.
• The horizontal component of this weight = wAL sin θ.
• But θ is slope of the channel which is represented by S. Horizontal component of weight = wALS.
• This horizontal force exerted by water is nothing but tractive force.
• If average tractive force per unit of wetted area is τ, then
• Hence average unit tractive force also know shear stress is given by τ = wSR.

#### where

w = Unit of weight of water

S = Longitudinal slope of the channel

R = Hydraulic mean depth H.M.D.

• In the case of wide open channels, the value of hydraulic mean depth (H.M.D.) is almost equal to depth of the channel.
• Hence tractive force can be written as follows also

τ = wSD

• If tractive force becomes greater than the frictional resistance between particles, the particles are set in motion.
• The resistance of sediment to motion in proportional to the diameter d of the particle and the submerged weight of sediment in water.