Shields formula

In fact, the Shields method determines whether or not the soil material will move.

This dimensionless ratio (the Shields parameter) was first described by Albert Shields and reads: where: The shear stress that works on the bottom (with a normal uniform flow along a slope) is: where: It is important to realise that

This parameter is also called the granular reynolds number: Shields has performed tests with grains of different densities, and the found value of

[1] Van Rijn found that instead of the granular reynolds number a dimensionless grain size could be used:[3] Because usually the values of

are quite constant, the true grain size can also be set on the horizontal axis (see right figure b).

From this follows that for grains greater than 5 mm the Shields parameter gets a constant value of 0,055.

Shields has defined as "movement" that almost all grains move on the bottom.

This is a useful definition for defining the beginning of sand transport by flow.

However, if one wants to protect a bed from erosion, the requirement is that grains should hardly move.

In practice, this means that for bed protections (where the grain is always larger than 5mm), a design value of Ψ=0.03 must be used.

Question: At what speed of flow does sand of 0.2cm move at a water depth of 1m?

Question: What stone size is needed to defend this soil against a current of 2 m/s?