Hydraulic Design of Energy Dissipators for Culverts and Channels
Hydraulic Engineering Circular Number 14, Third Edition

Chapter 5: Estimating Scour At Culvert Outlets

This chapter presents a method for predicting local scour at the outlet of culverts based on discharge, culvert shape, soil type, duration of flow, culvert slope, culvert height above the bed, and tailwater depth. In addition to this local scour, channel degradation (discussed in Chapter 2) should be evaluated. The procedures in this chapter provide a good method for estimating the extent of the local scour hole. The designer should also review maintenance history, site reconnaissance and data on soils, flows, and flow duration to determine the best estimate of the potential scour hazard at a culvert outlet.

The prediction equations presented in this chapter are intended to serve along with field reconnaissance as guidance for determining the need for energy dissipators at culvert outlets. The designer should remember that the equations do not include long-term channel degradation of the downstream channel. The equations are based on tests that were conducted to determine maximum scour for the given condition and therefore represent what might be termed worst-case scour geometries. The equations were derived from tests conducted by the Corps of Engineers (Bohan, 1970) and Colorado State University (Abt, et al., 1985; Abt, et al., 1987; Abt, 1996; Doehring, 1994; Donnell and Abt, 1983; Ruff, et al., 1982).

5.1 Cohesionless Soils

The general expression for determining scour geometry in a cohesionless soil at the culvert outlet is:

where,

h_s = depth of scour, m (ft)

W_s = width of scour, m (ft)

L_s = length of scour, m (ft)

V_s = volume of scour, m³ (ft³)

R_c = hydraulic radius at the end of the culvert (assuming full flow)

Q = discharge, m³/s (ft³/s)

g = acceleration of gravity, 9.81 m/s² (32.2 ft /s²)

t = time in minutes

σ = (D₈₄/D₁₆)^0.5, material standard deviation

α, β, θ are coefficients, see Table 5.1

C_s = slope correction coefficient, see Table 5.2

C_h = drop height adjustment coefficient, see Table 5.3

The bed-material grain-size distribution is determined by performing a sieve analysis (ASTM DA22-63). The values of D₈₄ and D₁₆ are extracted from the grain size distribution. If σ < 1.5, the material is considered to be uniform. If σ > 1.5, the material is classified as graded. Typical values for σ are 2.10 for gravel and 1.87 for sand.

5.1.1 Scour Hole Geometry

Investigators Bohan (1970) and Fletcher and Grace (1972) indicate that the scour hole geometry varies with tailwater conditions with the maximum scour geometry occurring at tailwater depths less than half the culvert height (Bohan, 1970); and that the maximum depth of scour, h_s, occurs at a location approximately 0.4 L_s downstream of the culvert outlet (Fletcher and Grace, 1972) where L_s is the length of scour. The α, β, θ coefficients to determine scour geometry are shown in Table 5.1.

5.1.2 Time of Scour

The time of scour is estimated based upon knowledge of peak flow duration. Lacking this knowledge, it is recommended that a time of 30 minutes be used in Equation 5.1. The tests indicate that approximately 2/3 to 3/4 of the maximum scour depth occurs in the first 30 minutes of the flow duration. The exponents for the time parameter in Table 5.1 reflect the relatively flat part of the scour-time relationship (t > 30 minutes) and are not applicable for the first 30 minutes of the scour process.

5.1.3 Headwalls

Installation of a perpendicular headwall at the culvert outlet moves the scour hole downstream (Ruff, et al., 1982). However, the magnitude of the scour geometry remains essentially the same as for the case without the headwall. If the culvert is installed with a headwall, the headwall should extend to a depth equal to the maximum depth of scour.

5.1.4 Drop Height

The scour hole dimensions will vary with the height of the culvert invert above the bed. The scour hole shape becomes deeper, wider, and shorter, as the culvert invert height is increased (Doehring, 1994). The coefficients, C_h, are derived from tests where the pipe invert is adjacent to the bed. In order to compensate for an elevated culvert invert, Equation 5.1 can be modified to where C_h, expressed in pipe diameters, is a coefficient for adjusting thecompound scour hole geometry. The values of C_h are presented in Table 5.2.

5.1.5 Slope

The scour hole dimensions will vary with culvert slope. The scour hole becomes deeper, wider, and longer as the slope is increased (Abt, 1985). The coefficients presented are derived from tests where the pipe invert is adjacent to the bed. In order to compensate for a sloped culvert, Equation 5.1 can be adjusted with a coefficient, C_s, adjusting for scour hole geometry. The values of C_s are shown in Table 5.3.

5.1.6 Design Procedure

Step 1. Determine the magnitude and duration of the peak discharge. Express the discharge in m³/s (ft³/s) and the duration in minutes.

Step 2. Compute the full flow hydraulic radius, R_c

Step 3. Compute the culvert invert height above the bed ratio, H_d, for slopes > 0%.

Step 4. Determine scour coefficients from Table 5.1 and coefficients for culvert drop height, C_h, from Table 5.2 and slope, C_s, from Table 5.3.

Step 5. Determine the material standard deviation, σ = (D₈₄/D₁₆)^0.5 from a sieve analysis of a soil sample at the proposed culvert location.

Step 6. Compute the scour hole dimensions using Equation 5.1.

Step 7. Compute the location of maximum scour, L_m = 0.4 L_s.

Design Example: Estimating Scour Hole Geometry in a Cohesionless Soil (SI)

Determine the scour geometry-maximum depth, width, length and volume of scour. Given:

• D = 457 mm CMP Culvert
• S = 2%
• Drop height = 0.914 m from channel degradation
• Q = 0.764 m³/s
• σ = 1.87 for downstream channel which is graded sand

Solution

Step 1. Determine the magnitude and duration of the peak discharge: Q = 0.764 m³/s and the peak flow duration is estimated to be 30 minutes.

Step 2. Compute the full flow hydraulic radius, R_c:

Step 3. Compute the height above bed ratio, H_d, for slopes > 0%:

Step 4. The Coefficients of scour obtained from Table 5.1, Table 5.2, and Table 5.3 are:

Step 5. Determine the material standard deviation. σ = 1.87

Step 6. Compute the scour hole dimensions using Equation 5.1:

Similarly,

Step 7. Compute the location of maximum scour. L_m = 0.4 L_s = 0.4 (7.06) = 2.82 m downstream of the culvert outlet.

Design Example: Estimating Scour Hole Geometry in a Cohesionless Soil (CU)

Determine the scour geometry-maximum depth, width, length and volume of scour. Given:

• D = 18 in CMP Culvert
• S = 2%
• Drop height = 3 ft from channel degradation
• Q = 27 ft³/s
• σ = 1.87 for downstream channel which is graded sand

Solution

Step 1. Determine the magnitude and duration of the peak discharge: Q = 27 ft³/s and the peak flow duration is estimated to be 30 minutes.

Step 2. Compute the full flow hydraulic radius, Rc:

Step 3. Compute the height above bed ratio, H_d, for slopes > 0%

Step 4. The coefficients of scour obtained from Table 5.1, Table 5.2, and Table 5.3 are:

Step 5. Determine the material standard deviation. σ = 1.87

Step 6. Compute the scour hole dimensions using Equation 5.1:

Similarly,

Step 7. Compute the location of maximum scour. L_m = 0.4 L_s = 0.4 (23.2) = 9.2 ft downstream of the culvert outlet.

5.2 Cohesive Soils

If the soil is cohesive in nature, Equation 5.2 should be used to determine the scour hole dimensions. Shear number expressions, which relate scour to the critical shear stress of the soil, were derived to have a wider range of applicability for cohesive soils besides the one specific sandy clay that was tested. The sandy clay tested had 58 percent sand, 27 percent clay, 15 percent silt, and 1 percent organic matter; had a mean grain size of 0.15 mm (0.0059 in); and had a plasticity index, PI, of 15. The shear number expressions for circular culverts are:

and for other shaped culverts:

where,

D = culvert diameter, m (ft)

y_e = equivalent depth (A/2)^1/2, m (ft)

A = cross-sectional area of flow, m² (ft²)

V = mean outlet velocity, m/s (ft/s)

τ_c = critical tractive shear stress, N/m² (lb/ft²)

ρ = fluid density of water, 1000 kg/m³ (1.94 slugs/ft³)

(ρV²)/τ_c is the modified shear number

α_e = α_e = α/0.63 for h_s, W_s, and L_s and α_e = α/(0.63)³ for V_s

α, β, θ, and α_e are coefficients found in Table 5.4

Use 30 minutes for t in Equation 5.2 and Equation 5.3 if it is not known.

The critical tractive shear stress is defined in Equation 5.4 (Dunn, 1959; Abt et al., 1996). Equations 5.2 and 5.3 should be limited to sandy clay soils with a plasticity index of 5 to 16.

τ_c = 0.001 (S_ν+ α_u) tan (30 + 1.73 PI)

where,

τ_c = critical tractive shear stress, N/m² (lb/ft²)

S_ν = the saturated shear strength, N/m² (lb/ft²)

α_u = unit conversion constant, 8630 N/m² (SI), 180 lb/ft² (CU)

PI = Plasticity Index from the Atterberg limits

The design procedure for estimating scour in cohesive materials with PI from 5 to 16 may be summarized as follows.

Step 1. Determine the magnitude and duration of the peak discharge, Q. Express the discharge in m³/s (ft³/s) and the duration in minutes.

Step 2. Compute the culvert average outlet velocity, V.

Step 3. Obtain a soil sample at the proposed culvert location.

1. Perform Atterberg limits tests and determine the plasticity index (PI) using ASTM D423-36.
2. Saturate a sample and perform an unconfined compressive test (ASTM D211-66-76) to determine the saturated shear stress, S _ν.

Step 4. Compute the critical tractive shear strength, τ_c, from Equation 5.4.

Step 5. Compute the modified shear number, S_nm, at the peak discharge and height above bed ratio, H_d, for slopes > 0%.

and

Step 6. Determine scour coefficients from Table 5.4 and, if appropriate, coefficients for culvert drop height, C_h, from Table 5.2 and slope, C_s, from Table 5.3.

Step 7. Compute the scour hole dimensions using Equation 5.2 for circular culverts and Equation 5.3 for other shapes.

Step 8. Compute the location of maximum scour. L_m = 0.4 L_s.

Design Example: Estimating Scour Hole Geometry in a Cohesive Soil (SI)

Determine the scour geometry: maximum depth, width, length and volume of scour. Given:

• D = 610 mm CMP Culvert
• S = 0%
• Drop height = 0 m
• Q = 1.133 m³/s
• PI = 12 and S_v = 23,970 N/m² for downstream channel

Solution

Step 1. Determine the magnitude and duration of the peak discharge: Q = 1.133 m³/s and the peak flow duration is estimated to be 30 minutes.

Step 2. Compute the culvert average outlet velocity, V:

Step 3. Obtain a soil sample at the proposed culvert location: The sandy-clay soil was tested and found to have:

1. Plasticity index (PI) = 12
2. Saturated shear stress, S_ν = 23,970 N/m².

Step 4. Compute the critical tractive shear strength, τ_c, from Equation 5.4.

τ_c = 0.001 (S_ν+ α_u) tan (30 + 1.73 PI)

τ_c = 0.001 (23970 + 8630) tan [30 + 1.73(12)]

τ_c = 0.001 (32600) tan (50.76) = 39.9 N/m²

Step 5. Compute the modified shear number, S_nm, at the peak discharge and height above bed ratio, H_d, for slopes > 0%.

Step 6. Determine scour coefficients from Table 5.4 and coefficients for culvert drop height, C_h, from Table 5.2 and slope from Table 5.3: C_h = 1 and C_s = 1

Step 7. Compute the scour hole dimensions using Equation 5.2 for circular culverts:

h_s = (1.0)(1.0)(0.86)(377.3)^0.18(0.09)^0.10(0.61) = 1.2 m

Similarly,

W_s = (1.0)(1.0)(3.55)(377.3)^0.17(0.09)^0.07(0.61) = 5.02 m

L_s = (1.0)(1.0)(2.82)(377.3)^0.33(0.09)^0.09(0.61) = 9.81 m

V_s = (1.0)(1.0)(0.62)(377.3)^0.93(0.09)^0.23(0.61)³ = 20.15 m³

Step 8. Compute the location of maximum scour. L_m = 0.4 L_s = 0.4(9.81) = 3.92 m downstream of culvert outlet.

Design Example: Estimating Scour Hole Geometry in a Cohesive Soil (CU)

Determine the scour geometry: maximum depth, width, length and volume of scour. Given:

• D = 24 in CMP Culvert
• S = 0%
• Drop height = 0 ft
• Q = 40 ft³/s
• PI = 12 and S_v = 500 lb/ft² for downstream channel

Solution

Step 1. Determine the magnitude and duration of the peak discharge: Q = 40 ft³/s and the peak flow duration is estimated to be 30 minutes.

Step 2. Compute the culvert average outlet velocity, V:

Step 3. Obtain a soil sample at the proposed culvert location: The sandy-clay soil was tested and found to have:

1. Plasticity index, PI = 12
2. Saturated shear stress, S_ν = 500 lb/ft².

Step 4. Compute the critical tractive shear strength, τ_c, from Equation 5.4.

τ_c = 0.001 (S_ν+ α_u) tan (30 + 1.73 PI)

τ_c = 0.001 (500 + 180) tan [30 + 1.73(12)]

τ_c = 0.001 (680) tan (50.76) = 0.83 lb/ft²

Step 5. Compute the modified shear number, S_nm, at the peak discharge and height above bed ratio, H_d, for slopes > 0%.

Step 6. Determine scour coefficients from Table 5.4 and coefficients for culvert drop height, C_h, from Table 5.2 and slope from Table 5.3: C_h = 1 and C_s = 1

Step 7. Compute the scour hole dimensions using Equation 5.2 for circular culverts:

h_s = (1.0)(1.0)(0.86)(379.4)^0.18(0.09)^0.10(2) = 3.9 ft

Similarly,

W_s = (1.0)(1.0)(3.55)(379.4)^0.17(0.09)^0.07(2) = 16.5 ft

L_s = (1.0)(1.0)(2.82)(379.4)^0.33(0.09)^0.09(2) = 32.2 ft

V_s = (1.0)(1.0)(0.62)(379.4)^0.93(0.09)^0.23(2)³ = 713.7 ft³

Step 8. Compute the location of maximum scour. L_m = 0.4 L_s = 0.4(32.2) = 12.9 ft downstream of culvert outlet.