For live-bed scour, an equilibrium will be re-established when the amount of the bed material transported from upstream equals the bed material removed by the vortex action. The strength of the horseshoe vortex is reduced as the depth of the scour increases.

This system of vortices removes bed material from around the base of the pier, producing a local scour hole. The boundary layer separation combined with downflow produces the horseshoe vortex wrapped around the base of the pier. We also recall from fluid dynamics that flow past a body separates from the body, and wake vortices form in the separation zone. Therefore, a downward hydraulic gradient develops in front of the pier that causes downflow directed towards the bed, as shown in Figure 7.16. The dynamic pressure is proportional to the square of the local velocity, and is lower near the bed. As we recall from basic fluid dynamics, the stagnation pressure is larger than the hydrostatic pressure by an amount equal to the dynamic pressure. Obstruction of flow by a pier results in a stagnation line on the front of the pier. Local scour at piers is caused by horseshoe vortices forming at the base of the pier. Richardson and Davis (2001) describe various procedures to estimate L′, which are beyond the scope of this text. In cases where the flow is distributed nonuniformly over the floodplain with most of the overbank flow occurring near the main channel, the difference between L′ and L is significant. It is suggested that L be replaced by L′ in the equation where L′ is defined as the length of the embankment (and abutment) blocking live flow. (7.56) if L is set equal to the total length of embankment (and abutment) projected normal to the flow. Richardson and Davis (2001) suggest that scour depth is overestimated by Eq. If the Froehlich equation is to be used for analysis or scour depth prediction purposes, the term (+y 4) should be left out. The term (+ y 4) was added to the equation in order to envelope 98% of the data. The terms y 4 and F r are evaluated for the main channel or an overbank area depending on whether the abutment is in the main channel or the overbank area.Įq. 7.1), and F r = Froude number at the approach section, and L = length of embankment projected normal to the flow. 7.19 and note θ 90 o if embankment points upstream), y 4 = average flow depth at the approach section (section 4 in Fig. Where y s = scour depth, K a 1 = abutment shape coefficient (see Table 7.12), K a 2 =(θ/90) 0.13 = correction factor for angle of attack, θ = angle of attack (see Fig.

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