Critical Velocity

transported into the contracted section is essentially zero and maximum scour occurs when

the shear stress or velocity reaches the critical shear stress or critical velocity of the bed

material in the section. Chapter 3 and HEC-18 give equations and methods for calculating

critical shear stress or critical velocity.

Live-bed contraction scour occurs at a bridge when there is transport of bed material in the

upstream reach into the bridge cross section. With live-bed contraction scour, the area of the

contracted section increases until, in the limit, the transport of bed material out of the

contracted section equals the bed material transported in. Normally, the width of the

contracted section is constrained and depth increases until the limiting conditions are

reached.

Clear-water contraction scour occurs in a long contraction when (1) there is no bed material

transport from the upstream reach into the downstream reach or (2) the material being

transported in the upstream reach is transported through the downstream reach mostly in

suspension and at less than capacity of the flow. With clear-water contraction scour, the

area of the contracted section increases until, in the limit, the velocity (V) of the flow or the

shear stress (τo) on the bed is equal to the critical velocity (Vc) or the critical shear stress (τc)

of a certain particle size (D) in the bed material. Normally, the width (W) of the contracted

section is constrained and the depth (y) increases until the limiting conditions are reached.

Live-bed scour depths may be limited if there are appreciable amounts of large-sized

particles in the bed material. It is appropriate, then, to use the clear-water scour

equation in addition to the live-bed scour equation and use the smaller of the two

depths. Also, it is appropriate to use the clear-water scour equation if the transport of

bed material from upstream of the contraction is small in quantity or composed of fine

material that washes through the contraction in suspension.

There are four conditions (cases) of contraction scour at bridge sites depending on the type

of contraction, and whether there is overbank flow or relief bridges. Regardless of the case,

contraction scour can be evaluated using two basic equations: (1) live-bed scour, and (2)

clear-water scour. For any case or condition, it is only necessary to determine if the flow in

the main channel or overbank area upstream of the bridge, or approaching a relief bridge, is

transporting bed material (live-bed) or is not (clear-water), and then apply the appropriate

equation with the variables defined according to the location of contraction scour (channel or

overbank).

Critical Velocity. To determine if the flow upstream of the bridge is transporting bed material,

calculate the critical velocity for beginning of motion Vc of the D50 size of the bed material and

compare it with the mean velocity V of the flow in the main channel or overbank area

upstream of the bridge opening. If the critical velocity of the bed material is larger than the

mean velocity (Vc > V), then clear-water contraction scour will exist. If the critical velocity is

less than the mean velocity (Vc < V), then live-bed contraction scour will exist. To calculate

the critical velocity use the equation derived in Chapter 3. This equation is:

Vc = K u y1/ 6 D1/ 3

(7.1)

where:

Critical velocity above which bed material of size D and smaller will be

transported, m/s (ft/s)

Depth of flow, m (ft)

7.9