Contents preface (VII) introduction 1—37

8.4. ALLUVIAL CHANNELS CARRYING CLEAR WATER
Compared to the design methods used for rigid boundary channels, the design of stable alluvial channels is more complex. Alluvial channels carrying clear water should be designed such that the erodible material of the channel boundary is not scoured. The design of such channels is, therefore, based on the concept of tractive force.

286 IRRIGATION AND WATER RESOURCES ENGINEERING
Scour on a channel bed occurs when the tractive force on the bed exerted by the flow is adequate to cause the movement of the bed particles. A sediment particle resting on the sloping side of a channel will move due to the resultant of the tractive force in the flow direction and the component of gravitational force which makes the particle roll or slide down the side slope. If the tractive force acting on the bed or the resultant of the tractive force and the component of the gravitational force both acting on the side slopes is larger than the force resisting the movement of the particle, erosion starts. The following method of design of stable alluvial channels based on this principle was proposed by Lane (1) and is also known as the USBR method.

In uniform flow, the average tractive stress, τ0 is given as
τo = ρgRS	(8.5)

The shear stress is not uniformly distributed over the channel perimeter. Figure 8.4 shows the variation of the maximum shear stresses acting on the side, τ_sm and the bed, τ_bm of a channel. It should be noted that for the trapezoidal channels, the maximum tractive shear on the sides is approximately 0.76 times the tractive shear on the channel bed.
For a particle resisting on a level or mildly sloping bed, on can write the following expression for the incipient motion condition :

τbl a = Ws tan θ

(8.6)

where, W_s is the submerged weight of the particle and a, the effective area of the particle over which the tractive stress τ_bl is acting, and θ is the angle of repose for the particle. τ_bl is, obviously, the critical shear stress τ_c for the bed particles. Since the aim is to avoid the movement of the movement of the particles (5), τ_bl may be kept less than τ_c , say 0.9 τ_c.
For a particle resting on the sloping side of a channel (Fig. 8.5), the condition for the incipient motion is

(W_s sin α)² + (τ_sl

∴ W_s² sin² α + (τ_sl
or
a)² = (W_s cos α tan θ)² a)² = W_s² cos² α tan² θ

τ

=