0.43
L′
ys
Fr 0.61 + 1
= 2.27 K 1 K 2
(7.16)
ya
ya
where:
K1
=
Coefficient for abutment shape (Table 7.4)
K2
=
Coefficient for angle of embankment to flow
(θ/90)0.13 (Figure 7.10 for definition of θ)
K2
=
θ<90 if embankment points downstream
θ>90 if embankment points upstream
L
=
Length of abutment projected normal to flow, m, ft
Ae
=
Flow area of the approach cross section obstructed by the
embankment, m2, ft2
Froude Number of approach flow upstream of the abutment = Ve/(gya)1/2
Fr
=
Ve
=
Qe/Ae, m/s, ft/s
Qe
=
Flow obstructed by the abutment and approach embankment,
m3/s, ft3/s
ya
=
Average depth of flow on the floodplain, m, ft
ys
=
Scour depth, m, ft
Note: That as L tends to 0, ys also tends to 0. In a regression equation, 50 percent of the
data are above or below the regression line. The 1 was added to the equation so as to
encompass 98 percent of the data.
7.8.6 1975 and 1990 HIRE Equation
An equation in HIRE was developed from Corps of Engineers field data of scour at the end of
spurs in the Mississippi River (Richardson et al. 1975, 1990). This field situation closely
resembles the laboratory experiments for abutment scour in that the discharge intercepted by
the spurs was a function of the spur length. The HIRE equation is applicable when the ratio
of projected abutment length (a) to the flow depth (y1) is greater than 25. This equation can
be used to estimate scour depth (y1) at an abutment where conditions are similar to the field
conditions from which the equation was derived: the equation is:
yS
k
= 4 Fr 0.33 1
(7.17)
y1
0.55
where:
ys
=
Scour depth, m, ft
y1
=
Depth of flow at the abutment on the overbank or in the main channel, m, ft
Fr
=
Froude Number based on the velocity and depth adjacent to and upstream
of the abutment
K1
=
Coefficient for abutment shape (Table 7.4)
7.26
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