Expert Answer
1. To initiate movement in the channel with a loose gravel bed, the flow velocity must be greater than the critical velocity required to overcome the gravitational forces acting on the gravel particles. The critical velocity can be determined using the Shields criterion.
The Shields criterion relates the shear stress acting on the bed to the particle size and density, and it can be expressed as:
? / (?s - ?w)gD50 = ?
where ? is the shear stress, ?s is the density of the gravel, ?w is the density of water, g is the acceleration due to gravity, D50 is the median particle size, and ? is the Shields parameter.
For the initiation of particle movement, the Shields parameter (?) should reach a critical value, typically around 0.03 to 0.05.
2. Along the channel, if the median particle size (D50) reduces to 14 mm, the flow depth required for particle motion can be estimated by considering the modified Shields parameter. Assuming the sediment transport conditions are still governed by the Shields criterion, the new Shields parameter (?') can be calculated using the new particle size:
where D14 is the new median particle size.
The flow depth required for motion will depend on the value of the modified Shields parameter (?') and the flow conditions.
3. If the bed depth falls below the size of the gravel particles (9 mm in this case), it means that the flow depth is insufficient to entrain and transport the particles. In such a scenario, there will likely be minimal or no particle movement. However, it's important to note that other factors, such as local variations in flow velocity and turbulence, can still cause some particle displacement, albeit to a lesser extent compared to when the bed depth is above the particle size.