The post here introduces using HEC-18 equation to calculate horizontal contraction scour under non-pressure flow condition and this post is to explain vertical contraction scour (pressure flow scour). When a bridge is under pressure flow, no matter it is overtopped or not, the pressurized high speed flow under the bridge deck, which behaves like an orifice flow or a sluice gate flow, will erode the river bed and create a pressure flow scour (Figure 1).
The separation zone thickness t is calculated by HEC-18 Eq 6.16 (Figure 2). The weir flow height hw is zero if the bridge is not overtopped.
y2 is to be calculated by either clear-water or live-bed contraction equations (refer to Figure 4 and this post) and the final pressure flow scour depth is expressed as ys=y2+t-hb as indicated in Figure 1. When applying clear-water or live-bed equations to calculate y2, the Q2 flow value should exclude the overtopping weir flow if the bridge is overtopped.
When the bridge is overtopped under the live-bed condition, Q1 should be adjusted to Que as indicated in Figure 4.
Unless there is a setback between top bank of the main channel and the abutments, the pressure flow scour calculation only needs to be performed for the bridge opening area. In this case, the Q1 is the flow in the main channel of the bridge upstream approach section, not including overbank flows; and Q2 is the total flow going through the bridge opening (see HEC-18 Page 6.10). If an abutment setback exists, the pressure flow scour can be calculated separately for the main channel and the left and/or right overbank areas using the corresponding HEC-RAS model detailed results.
FHWA Hydraulic Toolbox is easy to use for bridge scour analysis under pressure flow condition (Figure 5). The required parameters can be retrieved from a successful steady state HEC-RAS model run and bridge survey or as-builts (vertical bridge opening height hb or blockage height T). The Hydraulic Toolbox parameter window is dynamic, which means optional items or parameters previously selected/entered would determine what items or contents will be displayed next.
Two example problems of HEC-18, Example Problem 3 on Page 6.28 and Example Problem 4 on Page 6.29 are solved in Hydraulic Toolbox for demonstration (Figure 6 and Figure 7). The results from Hydraulic Toolbox match those calculated on HEC-18 well.
Note: it appears the live-bed equation for pressure flow scour in Hydraulic Toolbox has a bug: it uses Y1 and Q1 to calculate Y2, not Hue or Que.