Contents preface (VII) introduction 1—37

7.2. INCIPIENT MOTION OF SEDIMENT
Consider the case of flow of clear water in an open channel of a given slope with a movable bed of non-cohesive material. At low discharges, the bed material remains stationary and, hence, the channel can be treated as rigid. With the increase in discharge, a stage will come when the shear force exerted by the flowing water on a particle will just exceed the force opposing the movement of the particle. At this stage, a few particles on the bed move intermittently. This condition is called the incipient motion condition or, simply, the critical condition.
A knowledge of flow at the incipient motion condition is useful in fixing slope or depth for clear water flow in an alluvial channel. Knowledge of the incipient motion condition is also

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required in some methods of calculation of sediment load. Hence, there is a need to understand the phenomenon which initiates motion of sediment particles.

The experimental data on incipient motion condition have been analysed by different investigators using one of the following three approaches (1):
(i) Competent velocity approach, (ii) Lift force approach, and

(iii) Critical tractive force approach.

Competent velocity is the mean velocity of flow which just causes a particle to move. A relationship among the size of the bed material, its relative density, and the competent velocity is generally developed and used.
Investigators using the lift force approach assume that the incipient motion condition is established when the lift force exerted by the flow on a particle just exceeds submerged weight of the particle.
The critical tractive force approach is based on the premise that it is the drag (and not lift) force exerted by the flowing water on the channel bed which is responsible for the motion of the bed particles.
Of these three approaches, the critical tractive force approach is considered most logical and is most often used by hydraulic engineers. Hence, only this approach has been discussed here.
The critical tractive (or shear) stress is the average shear stress acting on the bed of a channel at which the sediment particles just begin to move. Shields (2) was the first investigator to give a semi -theoretical analysis of the problem of incipient motion. According to him, a particle begins to move when the fluid drag F₁ on the particle overcomes the particle resistance F₂. The fluid drag F₁ is given as

	L	2	1		2 O
^F1	= k1 MC D d			ρ ud	P
	2
		N				Q

and the particle resistance F₂ is expressed as