§ 10.4.3.2. Stilling Basin

The stilling basin is used as an energy dissipator to trigger a hydraulic jump within the basin. The basin requires a tail water condition. These stilling basins normally operate within Froude numbers from 1.7 to 17. The Saint Anthony Falls (SAF) stilling basin is shown in Figure 10.4.3.2.A on the following page.

Figure 10.4.3.2.A - SAF Stilling Basin
(Source FHWA, Hydraulic Design of Energy Dissipators for Culverts and Channels, 2006)

The following is for the design of a SAF stilling basin. For the design of other stilling basins, refer to FHWA HEC14.

The following are seven (7) design steps used for a SAF basin.

Step 1.  Determine the velocity and depth at the culvert outlet. For the culvert outlet, calculate culvert brink depth (y _o ) velocity (V _o ) and (Fr _o .) For subcritical flow, use Figure 10.4.3.2.B or Figure 10.4.3.2.C found on the following pages. For supercritical flow, use normal depth in the culvert for y _o . (See FHWA HDS 5 (Normann, et al., 2001) for additional information on culvert brink depths.)

Figure 10.4.3.2.B - Dimensionless Rating Curves for the Outlets of rectangular Culverts
on Horizontal and Mild Slopes
(Simnos, 1970, Source FHWA, Hydraulic Design of Energy Dissipators for Culverts and Channels, 2006)

Figure 10.4.3.2.C - Dimensionless Rating Curves for the Outlets of Circular Culverts
on Horizontal and Mild Slopes
(Simnos, 1970, Source FHWA, Hydraulic Design of Energy Dissipators for Culverts and Channels, 2006)

Step 2.  Determine the velocity and TW depth in the receiving channel downstream of the basin.

Step 3.  Estimate the conjugate depth for the culvert outlet conditions using Equation 10.4.3.2.a to determine if a basin is needed. Substitute y _o and Fr _o for y ₁ and Fr ₁ , respectively. The value of C is dependent, in part, on the type of stilling basin to be designed. However, in this step the occurrence of a free hydraulic jump without a basin is considered so a value of one (1) is used. Compare y2 and TW. If y2 < TW, there is sufficient tail water and a jump will form without a basin. The remaining steps are unnecessary.

(Equation 10.4.3.2.a)

y ₂ = conjugate depth (ft.)
y ₁ = depth approaching the jump (ft.)
C _TW = ratio of tail water to conjugate depth (TW/y ₂ )
Fr ₁ = approach Froude number

Step 4.  The design engineer should select a basin width (W _B ). For box culverts, W _B must equal the culvert width (W _o ). For circular culverts, the basin width is taken as the larger of the culvert diameter and the value calculated according to the following Equation:

(Equation 10.4.3.2.b)

W _B = basin width (ft.)
Q = design discharge (fps)
D _o = culvert diameter (ft.)

The basin can be flared to fit an existing channel as indicated on Figure 10.4.3.2. The sidewall flare dimension z should not be greater than 0.5, i.e., 0.5:1, 0.33:1, or flatter.

Step 5.  Compute conjugate depth (C) is a function of Froude number as given by the following set of equations. Depending on the Froude number, C ranges from 0.64 to 1.08 implying that the SAF basin may operate with less tail water than the USBR basins, though tail water is still required.

(Equation 10.4.3.2.c - When 1.7 < FR ₁ < 5.5)

(Equation 10.4.3.2.d - When 5.5 < FR ₁ < 11)

C = 0.85

(Equation 10.4.3.2.e - When 11 < FR ₁ < 17)

The determination of the basin length, L _B , using Equation 10.4.3.2.f below.

(Equation 10.4.3.2.f)

Step 6.  Determine the needed radius of curvature for the slope changes entering the basin using Equation 10.4.3.2.g found below. The design engineer should determine if this step is required for the transition between the channel or culvert at the top of the drop to the transition slope and from the transitions slope to the bottom of the stilling basin floor. The curved slope change would provide improved flow conditions at the top and bottom of the drop.

If the transition slope is 1H:0.5V or steeper, use a circular curve at the transition with a radius defined by Equation 10.4.3.2.g (Meshgin and Moore, 1970). It is also advisable to use the same curved transition going from the transition slope to the stilling basin floor.

(Equation 10.4.3.2.g)

r = radius of the curved transition (ft.)
Fr = Froude number
y = depth approaching the curvature (ft.)

For the curvature between the culvert outlet and the transition, the Froude number and depth are taken at the culvert outlet. For the curvature between the transition and the stilling basin floor, the Froude number and depth are taken as Fr ₁ and y ₁ .

Step 7.  Sizing the basin elements (chute blocks, baffle blocks, and an end sill), the following guidance is recommended. The height of the chute blocks (h ₁ ) is set equal to y ₁ . The number of chute blocks is determined by Equation 10.4.3.2.h, below, rounded to the nearest integer.

(Equation 10.4.3.2.h)

N _c = number of chute blocks

Block width and block spacing are determined by the equation on the following page:

(Equation 10.4.3.2.i)

W ₁ = block width (ft.)
W ₂ = block spacing (ft.)

Equations 10.4.3.2.h and 10.4.3.2.i will provide N _c blocks and N _c spaces between those blocks. A one-half block (.05) is placed at the basin wall so there is no space at the wall. The height, width, and spacing of the baffle blocks are shown in Figure 10.4.3.2.A. The height of the baffles (h ₃ ) is set equal to the entering flow depth (y ₁ ). The width and spacing of the baffle blocks must account for any basin flare. If the basin is flared as shown in Figure 10.4.3.2.A, the width of the basin at the baffle row is calculated according to the following equation:

(Equation 10.4.3.2.j)

W _B2 = basin width at the baffle row (ft.)
L _B = basin length (ft.)
z = basin flare, z:1 as defined in Figure 10.4.3.2.A (z=0.0 for no flare)

The top thickness of the baffle blocks should be set at 0.2h ₃ with the back slope of the block on a 1:1 slope. The number of baffles blocks is calculated using the following equation :

(Equation 10.4.3.2.k)

N _B = number of baffle blocks (rounded to an integer)

Baffle width and spacing are determined using the following equation:

(Equation 10.4.3.2.l)

W ₃ = baffle width (ft.)
W ₄ = baffle spacing (ft.)

Equations 10.4.3.2.k and 10.4.3.2.l will provide N _B baffles and N _B -1 spaces between those baffles. The remaining basin width is divided equally for spaces between the outside baffles and the basin sidewalls. No baffle block should be placed closer to the sidewall than 3y ₁ /8. Verify that the percentage of W _B2 obstructed by baffles is between forty and fifty-five percent (40-55%). The distance from the downstream face of the chute blocks to the upstream face of the baffle block should be LB/3.

The height of the final basin element is calculated using the following equation:

(Equation 10.4.3.2.m)

h ₄ = height of the end sill (ft.)

The end sill will extend across the basin.

Wingwalls should be equal in height and length to the stilling basin sidewalls. The top of the wingwall should have a 1H:1V slope. Flaring wingwalls are preferred to perpendicular or parallel wingwalls. The best overall conditions are obtained if the triangular wingwalls are located at an angle of forty-five degrees (45°) to the outlet centerline.

The stilling basin sidewalls may be parallel (rectangular stilling basin) or diverge as an extension of the transition sidewalls (flared stilling basin). The height of the sidewall above the floor of the basin is given by the equation below :

(Equation 10.4.3.2.n)

h ₅ = height of the sidewall (ft.)

A cutoff wall should be used at the end of the stilling basin to prevent undermining. The depth of the cutoff wall must be greater than the maximum depth of anticipated erosion at the end of the stilling basin. The cutoff wall, toe down, to be a minimum depth of twenty-four (24) inches.