CHAPTER 4: VEGETATIVE LINING AND BARE SOIL DESIGN

Grass-lined channels have been widely used in roadway drainage systems for many years. They are easily constructed and maintained and work well in a variety of climates and soil conditions. Grass linings provide good erosion protection and can trap sediment and related contaminants in the channel section. Routine maintenance of grass-lined channels consists of mowing, control of weedy plants and woody vegetation, repair of damaged areas and removal of sediment deposits.

The behavior of grass in an open channel lining is complicated by the fact that grass stems bend as flow depth and shear stress increase. This reduces the roughness height and increases velocity and flow rate. For some lining materials (bare earth and rigid linings), the roughness height remains constant regardless of the velocity or depth of flow in the channel. As a result, a grass-lined channel cannot be described by a single roughness coefficient.

The Soil Conservation Service (SCS) (1954) developed a widely used classification of grass channel lining that depends on the degree of retardance. In this classification, retardance is a function of the height and density of the grass cover (USDA, 1987). Grasses are classified into five broad categories, as shown in Table 4.1. Retardance Class A presents the highest resistance to flow and Class E presents the lowest resistance to flow. In general, taller and denser grass species have a higher resistance to flow, while short flexible grasses have a low flow resistance.

Kouwen and Unny (1969) and Kouwen and Li (1981) developed a useful model of the biomechanics of vegetation in open-channel flow. This model provides a general approach for determining the roughness of vegetated channels compared to the retardance classification. The resulting resistance equation (see HEC-15 Appendix C.2) uses the same vegetation properties as the SCS retardance approach, but is more adaptable to the requirements of highway drainage channels. The design approach for grass-lined channels was developed from the Kouwen resistance equation.

Grass linings provide erosion control in two ways. First, the grass stems dissipate shear force within the canopy before it reaches the soil surface. Second, the grass plant (both the root and stem) stabilizes the soil surface against turbulent fluctuations. Temple (SCS, 1954) developed a relationship between the total shear on the lining and the shear at the soil surface based on both processes.

A simple field method is provided to directly measure the density-stiffness parameter of a grass cover. Grass linings for roadside ditches use a wide variety of seed mixes that meet the regional requirements of soil and climate. These seed mix designs are constantly being adapted to improve grass-lined channel performance. Maintenance practices can significantly influence density and uniformity of the grass cover. The sampling of established grasses in roadside ditch application can eliminate much of the uncertainty in lining performance and maintenance practices.

Expertise in vegetation ecology, soil classification, hydrology, and roadway maintenance is required in the design of grass-lined channels. Engineering judgment is essential in determining design parameters based on this expert input. This includes factoring in variations that are unique to a particular roadway design and its operation.

4.1 GRASS LINING PROPERTIES

The density, stiffness, and height of grass stems are the main biomechanical properties of grass that relate to flow resistance and erosion control. The stiffness property (product of elasticity and moment of inertia) of grass is similar for a wide range of species (Kouwen, 1988) and is a basic property of grass linings.

Density is the number of grass stems in a given area, i.e., stems per m² (ft²). A good grass lining will have about 2,000 to 4,000 stems/m² (200 to 400 stems/ft²). A poor cover will have about one-third of that density and an excellent cover about five-thirds (USDA, 1987, Table 3.1). While grass density can be determined by physically counting stems, an easier direct method of estimating the density-stiffness property is provided in Appendix E of HEC-15.

For agricultural ditches, grass heights can reach 0.3 m (1.0 ft) to over 1.0 m (3.3 ft). However, near a roadway grass heights are kept much lower for safety reasons and are typically in the range of 0.075 m (0.25 ft) to 0.225 m (0.75 ft).

The density-stiffness property of grass is defined by the C_s coefficient. C_s can be directly measured using the Fall-Board test (Appendix E) or estimated based on the conditions of the grass cover using Table 4.2. Good cover would be the typical reference condition.

The combined effect of grass stem height and density-stiffness is defined by the grass roughness coefficient.

where:

Table 4.3 provides C_n values for a range of cover and stem height conditions based on Equation 4.1. Denser cover and increased stem height result in increased channel roughness.

SCS retardance values relate to a combination of grass stem-height and density. Cn values for standard retardance classes are provided in Table 4.4. Comparing Table 4.3 and 4.4 shows that retardance classes A and B are not commonly found in roadway applications. These retardance classes represent conditions where grass can be allowed to grow much higher than would be permissible for a roadside channel, e.g., wetlands and agricultural ditches. Class E would not be typical of most roadside channel conditions unless they were in a very poor state.

The range of C_n for roadside channels is between 0.10 and 0.30 with a value of 0.20 being common to most conditions and stem heights. In an iterative design process, a good first estimate of the grass roughness coefficient would be C_n = 0.20.

4.2 MANNING’S ROUGHNESS

Manning’s roughness coefficient for grass linings varies depending on grass properties as reflected in the Cn parameter and the shear force exerted by the flow. This is because the applied shear on the grass stem causes the stem to bend, which reduces the stem height relative to the depth of flow and reducing the roughness.

where,

See Appendix C.2 for the derivation of Equation 4.2.

4.3 PERMISSIBLE SHEAR STRESS

The permissible shear stress of a vegetative lining is determined both by the underlying soil properties as well as those of the vegetation. Determination of permissible shear stress for the lining is based on the permissible shear stress of the soil combined with the protection afforded by the vegetation, if any.

4.3.1 Effective Shear Stress

Grass lining moves shear stress away from the soil surface. The remaining shear at the soil surface is termed the effective shear stress. When the effective shear stress is less than the allowable shear for the soil surface, then erosion of the soil surface will be controlled. Grass linings provide shear reduction in two ways. First, the grass stems dissipate shear force within the canopy before it reaches the soil surface. Second, the grass plant (both the root and stem) stabilizes the soil surface against turbulent fluctuations. This process model (USDA, 1987) for the effective shear at the soil surface is given by the following equation.

where,

Soil grain roughness is taken as 0.016 when D₇₅ < 1.3 mm (0.05 in). For larger grain soils, the soil grain roughness is given by:

where,

Note that soil grain roughness value, n_s, is less than the typical value reported in Table 2.1 for a bare soil channel. The total roughness value for bare soil channel includes form roughness (surface texture of the soil) in addition to the soil grain roughness. However, Equation 4.3 is based on soil grain roughness.

The grass cover factor, C_f, varies with cover density and grass growth form (sod or bunch). The selection of the cover factor is a matter of engineering judgment since limited data are available. Table 4.5 provides a reasonable approach to estimating a cover factor based on (USDA, 1987, Table 3.1). Cover factors are better for sod-forming grasses than bunch grasses. In all cases a uniform stand of grass is assumed. Non-uniform conditions include wheel ruts, animal trails and other disturbances that run parallel to the direction of the channel. Estimates of cover factor are best for good uniform stands of grass and there is more uncertainty in the estimates of fair and poor conditions.

4.3.2 Permissible Soil Shear Stress

Erosion of the soil boundary occurs when the effective shear stress exceeds the permissible soil shear stress. Permissible soil shear stress is a function of particle size, cohesive strength, and soil density. The erodibility of coarse non-cohesive soils (defined as soils with a plasticity index of less than 10) is due mainly to particle size, while fine-grained cohesive soils are controlled mainly by cohesive strength and soil density.

New ditch construction includes the placement of topsoil on the perimeter of the channel. Topsoil is typically gathered from locations on the project and stockpiled for revegetation work. Therefore, the important physical properties of the soil can be determined during the design by sampling surface soils from the project area. Since these soils are likely to be mixed together, average physical properties are acceptable for design.

The following sections offer detailed methods for determination of soil permissible shear. However, the normal variation of permissible shear stress for different soils is moderate, particularly for fine-grained cohesive soils. An approximate method is also provided for cohesive soils.

4.3.2.1 Non-cohesive Soils

The permissible soil shear stress for fine-grained, non-cohesive soils (D₇₅ < 1.3 mm (0.05 in)) is relatively constant and is conservatively estimated at 1.0 N/m² (0.02 lb/ft²). For coarse grained, non-cohesive soils (1.3 mm (0.05 in) < D₇₅ < 50 mm (2 in)) the following equation applies.

where,

4.3.2.2 Cohesive Soils

Cohesive soils are largely fine grained and their permissible shear stress depends on cohesive strength and soil density. Cohesive strength is associated with the plasticity index (PI), which is the difference between the liquid and plastic limits of the soil. The soil density is a function of the void ratio (e). The basic formula for permissible shear on cohesive soils is the following.

where,

A simplified approach for estimating permissible soil shear stress based on Equation 4.6 is illustrated in Figure 4.1. Fine grained soils are grouped together (GM, CL, SC, ML, SM, and MH) and coarse grained soil (GC). Clays (CH) fall between the two groups.

Higher soil unit weight increases the permissible shear stress and lower soil unit weight decreases permissible shear stress. Figure 4.1 is applicable for soils that are within 5 percent of a typical unit weight for a soil class. For sands and gravels (SM, SC, GM, GC) typical soil unit weight is approximately 1.6 ton/m³ (100 lb/ft³), for silts and lean clays (ML, CL) 1.4 ton/m³ (90 lb/ft³) and fat clays (CH, MH) 1.3 ton/m³ (80 lb/ft³).

Figure 4.1. Cohesive Soil Permissible Shear Stress

4.3.3 Permissible Vegetation/Soil Shear Stress

The combined effects of the soil permissible shear stress and the effective shear stress transferred through the vegetative lining results in a permissible shear stress for the vegetative lining. Taking Equation 4.3 and substituting the permissible shear stress for the soil for the effective shear stress on the soil, τ_e, gives the following equation for permissible shear stress for the vegetative lining:

where,

Design Example: Grass Lining Design (SI)

Evaluate a grass lining for a roadside channel given the following channel shape, soil conditions, grade, and design flow. It is expected that the grass lining will be maintained in good conditions in the spring and summer months, which are the main storm seasons.

Given:

Solution

The solution is accomplished using procedure given in Section 3.1 for a straight channel.

Design Example: Grass Lining Design (CU)

Evaluate a grass lining for a roadside channel given the following channel shape, soil conditions, grade, and design flow. It is expected that the grass lining will be maintained in good conditions in the spring and summer months, which are the main storm seasons.

Solution

The solution is accomplished using procedure given in Section 3.1 for a straight channel.

4.4 MAXIMUM DISCHARGE APPROACH

The maximum discharge for a vegetative lining is estimated following the basic steps outlined in Section 3.6. To accomplish this, it is necessary to develop a means of estimating the applied bottom shear stress that will yield the permissible effective shear stress on the soil. Substituting Equation 4.2 into Equation 4.3 and assuming the τ_o = 0.75•τ_d and solving for τ_d yields:

where,

The assumed relationship between τ_o and τ_d is not constant. Therefore, once the depth associated with maximum discharge has been found, a check should be conducted to verify the assumption.

Design Example: Maximum Discharge for a Grass Lining (SI)

Determine the maximum discharge for a grass-lined channel given the following shape, soil conditions, and grade.

Given:

Solution

The solution is accomplished using procedure given in Section 3.6 for a maximum discharge approach.

Design Example: Maximum Discharge for a Grass Lining (CU)

Determine the maximum discharge for a grass-lined channel given the following shape, soil conditions, and grade.

Given:

Solution

The solution is accomplished using procedure given in Section 3.6 for a maximum discharge approach.

4.5 TURF REINFORCEMENT WITH GRAVEL/SOIL MIXTURE

The rock products industry provides a variety of uniformly graded gravels for use as mulch and soil stabilization. A gravel/soil mixture provides a non-degradable lining that is created as part of the soil preparation and is followed by seeding. The integration of gravel and soil is accomplished by mixing (by raking or disking the gravel into the soil). The gravel provides a matrix of sufficient thickness and void space to permit establishment of vegetation roots within the matrix. It provides enhanced erosion resistance during the vegetative establishment period and it provides a more resistant underlying layer than soil once vegetation is established.

The density, size and gradation of the gravel are the main properties that relate to flow resistance and erosion control performance. Stone specific gravity should be approximately 2.6 (typical of most stone). The stone should be hard and durable to ensure transport without breakage. Placed density of uniformly graded gravel is 1.76 metric ton/m³ (1.5 ton/yd³). A uniform gradation is necessary to permit germination and growth of grass plants through the gravel layer. Table 4.7 provides two typical gravel gradations for use in erosion control.

The application rate of gravel mixed into the soil should result in 25 percent of the mixture in the gravel size. Generally, soil preparation for a channel lining will be to a depth of 75 to 100 mm (3 to 4 inches). The application rate of gravel to the prepared soil layer that results in a 25 percent gravel mix is calculated as follows.

where,

The gravel application rates for fine-grained soils (i_gravel = 0) are summarized in Table 4.8. If the soil already contains some coarse gravel, then the application rate can be reduced by 1- i_gravel.

The effect of roadside maintenance activities, particularly mowing, on longevity of gravel/soil mixtures needs to be considered. Gravel/soil linings are unlikely to be displaced by mowing since they are heavy. They are also a particle-type lining, so loss of a few stones will not affect overall lining integrity. Therefore, a gravel/soil mix is a good turf reinforcement alternative.

Design Example: Turf Reinforcement with a Gravel/Soil Mixture (SI)

Evaluate the following proposed lining design for a vegetated channel reinforced with a coarse gravel soil amendment. The gravel will be mixed into the soil to result in 25 percent gravel. Since there is no existing gravel in the soil, an application rate of 0.058 ton/m² is recommended (100 mm soil preparation depth). See Table 4.8.

Given:

Solution

The solution is accomplished using procedure given in Section 3.1 of HEC-15 for a straight channel.

Design Example: Turf Reinforcement with a Gravel/Soil Mixture (CU)

Evaluate the following proposed lining design for a vegetated channel reinforced with a coarse gravel soil amendment. The gravel will be mixed into the soil to result in 25 percent gravel. Since there is no gravel in the soil, an application rate of 0.056 ton/yd2 is recommended (4 inch soil preparation depth). See Table 4.8.

Given:

Solution

The solution is accomplished using procedure given in Section 3.1 of HEC-15 for a straight channel.

HEC-15 Section 6.2 – PERMISSIBLE SHEAR STRESS

Values for permissible shear stress for riprap and gravel linings are based on research conducted at laboratory facilities and in the field. The values presented here are judged to be conservative and appropriate for design use. Permissible shear stress is given by the following equation:

where,

• τ_p = permissible shear stress, N/m² (lb/ft²)
• F* = Shield’s parameter, dimensionless
• γ_s = specific weight of the stone, N/m³ (lb/ft³)
• γ = specific weight of the water, 9810 N/m³ (62.4 lb/ft³)
• D₅₀ = mean riprap size, m (ft)

Typically, a specific weight of stone of 25,900 N/m³ (165 lb/ft³) is used, but if the available stone is different from this value, the site-specific value should be used.

Recalling Equation 3.2,

τ_p ≥ SF.τ_d

and Equation 3.1,

τ_d = γ.d.S_o

Equation 6.7 can be written in the form of a sizing equation for D₅₀ as shown below:

where,

• d = maximum channel depth, m (ft)
• SG = specific gravity of rock (γ_s/γ), dimensionless

Changing the inequality sign to an equality gives the minimum stable riprap size for the channel bottom. Additional evaluation for the channel side slope is given in Section 6.3.2.

Equation 6.8 is based on assumptions related to the relative importance of skin friction, form drag, and channel slope. However, skin friction and form drag have been documented to vary resulting in reports of variations in Shield’s parameter by different investigators, for example Gessler (1965), Wang and Shen (1985), and Kilgore and Young (1993). This variation is usually linked to particle Reynolds number as defined below:

where,

• R_e = particle Reynolds number, dimensionless
• V* = shear velocity, m/s (ft/s)
• ν = kinematic viscosity, 1.131×10^-6 m²/s at 15.5 deg C (1.217×10^-5 ft²/s at 60 deg F)

Shear velocity is defined as:

where,

• g = gravitational acceleration, 9.81 m/s² (32.2 ft/s²)
• d = maximum channel depth, m (ft)
• S = channel slope, m/m (ft/ft)

Higher Reynolds number correlates with a higher Shields parameter as is shown in Table 6.1. For many roadside channel applications, Reynolds number is less than 4×104 and a Shields parameter of 0.047 should be used in Equations 6.7 and 6.8. In cases for a Reynolds number greater than 2×105, for example, with channels on steeper slopes, a Shields parameter of 0.15 should be used. Intermediate values of Shields parameter should be interpolated based on the Reynolds number.

Higher Reynolds numbers are associated with more turbulent flow and a greater likelihood of lining failure with variations of installation quality. Because of these conditions, it is recommended that the Safety Factor be also increased with Reynolds number as shown in Table 6.1. Depending on site-specific conditions, safety factor may be further increased by the designer, but should not be decreased to values less than those in Table 6.1.

As channel slope increases, the balance of resisting, sliding, and overturning forces is altered slightly. Simons and Senturk (1977) derived a relationship that may be expressed as follows:

where,

• Δ = function of channel geometry and riprap size.

The parameter Δ can be defined as follows (see HEC-15 Appendix D for the derivation):

where,

• α = angle of the channel bottom slope
• β = angle between the weight vector and the weight/drag resultant vector in the plane of the side slope
• θ = angle of the channel side slope
• Φ = angle of repose of the riprap.

Finally, β is defined by:

where,

• η = stability number.

The stability number is calculated using:

Riprap stability on a steep slope depends on forces acting on an individual stone making up the riprap. The primary forces include the average weight of the stones and the lift and drag forces induced by the flow on the stones. On a steep slope, the weight of a stone has a significant component in the direction of flow. Because of this force, a stone within the riprap will tend to move in the flow direction more easily than the same size stone on a milder gradient. As a result, for a given discharge, steep slope channels require larger stones to compensate for larger forces in the flow direction and higher shear stress.

The size of riprap linings increases quickly as discharge and channel gradient increase. Equation 6.11 (not shown) is recommended when channel slope is greater than 10 percent and provides the riprap size for the channel bottom and sides. Equation 6.8 is recommended for slopes less than 5 percent. For slopes between 5 percent and 10 percent, it is recommended that both methods be applied and the larger size used for design. Values for safety factor and Shields parameter are taken from Table 6.1 for both equations.

HY-8: POLYNOMIAL COEFFICIENTS

Table 1. Polynomial Coefficients – Circular

EQ #’s: REFERENCE

• 1-9: Calculator Design Series (CDS) 3 for TI-59, FHWA, 1980, page 60
• 1-10: Hydraulic Computer Program (HY) 1, FHWA, 1969, page 18

Table 2. Polynomial Coefficients – Embedded Circular

EQ #’s: REFERENCE

• 1-12: NCHRP 15-24 report

Table 3. Polynomial Coefficients – Box

EQ #’s: REFERENCE

• 1-6: Hydraulic Computer Program (HY) 6, FHWA, 1969, subroutine BEQUA
• 1,4,5: Hydraulic Computer Program (HY) 3, FHWA, 1969, page 16
• 1,3,4,6: Calculator Design Series (CDS) 3 for TI-59, FHWA, 1980, page 16

Table 4. Polynomial Coefficients – Ellipse

EQ #’s: REFERENCE

• 27-30: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 20
• 31-33: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 22

Table 5. Polynomial Coefficients – Pipe Arch

EQ #’s: REFERENCE

• 12-23: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 17
• 24-26: Calculator Design Series (CDS) 4 for TI-59, FHWA, 1982, page 24
• 12,16,20: Hydraulic Computer Program (HY) 2, FHWA, 1969, page 17

Table 6. Polynomial Coefficients – Concrete Open-Bottom Arch

Span:Rise Ratio	Wingwall Angle (Inlet Configuration)	KE	SR	A	BS	C	DIP	EE	F	Diagram/Notes
2:1	0 Degrees (Mitered to Conform to Slope)	0.7	0.0	0.0389106557	0.6044131889	-0.1966160961	0.0425827445	-0.0035136880	0.0001097816	2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.
2:1	45 Degrees (45-degree Wingwall)	0.5	0.0	0.0580199163	0.5826504262	-0.1654982156	0.0337114383	-0.0026437555	0.0000796275	2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.
2:1	90 Degrees (Square Edge with Headwall)	0.5	0.0	0.0747688320	0.5517030198	-0.1403253664	0.0281511418	-0.0021405250	0.0000632552	2:1 Coefficients are used if the span:rise ratio is less than or equal to 3:1.
4:1	0 Degrees (Mitered to Conform to Slope)	0.7	0.0	0.0557401882	0.4998819105	-0.1249164198	0.0219465031	-0.0015177347	0.0000404218	4:1 coefficients are used if the span:rise ratio is greater than 3:1
4:1	45 Degrees (45-degree Wingwall)	0.5	0.0	0.0465032346	0.5446293346	-0.1571341119	0.0312822438	-0.0024007467	0.0000704011	4:1 coefficients are used if the span:rise ratio is greater than 3:1
4:1	90 Degrees (Square Edge with Headwall)	0.5	0.0	0.0401619369	0.5774418238	-0.1693724912	0.0328323405	-0.0024131276	0.0000668323	4:1 coefficients are used if the span:rise ratio is greater than 3:1

References for Concrete Open-bottom Arch polynomial coefficients:

• Thiele, Elizabeth A. Culvert Hydraulics: Comparison of Current Computer Models. (pp. 121-126), Brigham Young University Master’s Thesis (2007).
• Chase, Don. Hydraulic Characteristics of CON/SPAN Bridge Systems. Submitted Study and Report (1999)

Table 7. Polynomial Coefficients – South Dakota Concrete Box

Description	KE	SR	A	BS	C	DIP	EE	F	Diagram/Notes
Sketch 1: 30 degree-flared wingwalls; top edge beveled at 45 degrees	0.5	0.5	0.0176998563	0.5354484847	-0.1197176702	0.0175902318	-0.0005722076	-0.0000080574
Sketch 2: 30 degree-flared wingwalls; top edge beveled at 45 degrees; 2, 3, and 4 multiple barrels	0.5	0.5	0.0506647261	0.5535393634	-0.1599374238	0.0339859269	-0.0027470036	0.0000851484
Sketch 3: 30 degree-flared wingwalls; top edge beveled at 45 degrees; 2:1 to 4:1 span-to-rise ratio	0.5	0.5	0.0518005829	0.5892384653	-0.1901266252	0.0412149379	-0.0034312198	0.0001083949
Sketch 4: 30 degree-flared wingwalls; top edge beveled at 45 degrees; 15 degrees skewed headwall with multiple barrels	0.5	0.5	0.2212801152	0.6022032341	-0.1672369732	0.0313391792	-0.0024440549	0.0000743575
Sketch 5: 30 degree-flared wingwalls; top edge beveled at 45 degrees; 30 degrees to 45 degrees skewed headwall with multiple barrels	0.5	0.5	0.2431604850	0.5407556631	-0.1267568901	0.0223638322	-0.0016523399	0.0000490932
Sketches 6 & 7: 0 degree-flared wingwalls (extended sides); square-edged at crown and 0 degree-flared wingwalls (extended sides); top edge beveled at 45 degrees; 0- and 6-inch corner fillets	0.5	0.5	0.0493946080	0.7138391179	-0.2354755894	0.0473247331	-0.0036154348	0.0001033337
Sketches 8 & 9: 0 degree-flared wingwalls (extended sides); top edge beveled at 45 degrees; 2, 3, and 4 multiple barrels and 0 degree-flared wingwalls (extended sides); top edge beveled at 45 degrees; 2:1 to 4:1 span-to-rise ratio	0.5	0.5	0.1013668008	0.6600937637	-0.2133066786	0.0437022641	-0.0035224589	0.0001078198
Sketches 10 & 11: 0 degree-flared wingwalls (extended sides); crown rounded at 8-inch radius; 0- and 6-inch corner fillets and 0 degree-flared wingwalls (extended sides); crown rounded at 8-inch radius; 12-inch corner fillets	0.5	0.5	0.0745605288	0.6533033536	-0.1899798824	0.0350021004	-0.0024571627	0.0000642284
Sketch 12: 0 degree-flared wingwalls (extended sides); crown rounded at 8-inch radius; 12-inch corner fillets; 2, 3, and 4 multiple barrels	0.5	0.5	0.1321993533	0.5024365440	-0.1073286526	0.0183092064	-0.0013702887	0.0000423592
Sketch 13: 0 degree-flared wingwalls (extended sides); crown rounded at 8-inch radius; 12-inch corner fillets; 2:1 to 4:1 span-to-rise ratio.	0.5	0.5	0.1212726739	0.6497418331	-0.1859782730	0.0336300433	-0.0024121680	0.0000655665

References for South Dakota Concrete Box polynomial coefficients:

• Thiele, Elizabeth A. Culvert Hydraulics: Comparison of Current Computer Models. (pp. 121-126), Brigham Young University Master’s Thesis (2007).
• Effects of Inlet Geometry on Hydraulic Performance of Box Culverts (FHWA Publication No. FHWA-HRT-06-138, October 2006)

Table 8. User Defined, Open Bottom Arch, Low-Profile Arch, High-Profile Arch, and Metal Box HW/D Values.

Reference for User-defined interpolation coefficients: FHWA HDS-5, Appendix D, Chart 52B

HEC-15 Section 6.1 – MANNING’S ROUGHNESS

Manning’s roughness is a key parameter needed for determining the relationships between depth, velocity, and slope in a channel. However, for gravel and riprap linings, roughness has been shown to be a function of a variety of factors including flow depth, D₅₀, D₈₄, and friction slope, S_f. A partial list of roughness relationships includes Blodgett (1986a), Limerinos (1970), Anderson, et al. (1970), USACE (1994), Bathurst (1985), and Jarrett (1984). For the conditions encountered in roadside and other small channels, the relationships of Blodgett and Bathurst are adopted for this manual.

Blodgett (1986a) proposed a relationship for Manning’s roughness coefficient, n, that is a function of the flow depth and the relative flow depth (d_a/D₅₀) as follows (Equation 6.1):

where,

• n = Manning’s roughness coefficient, dimensionless
• d_a = average flow depth in the channel, m (ft)
• D₅₀ = median riprap/gravel size, m (ft)
• α = unit conversion constant, 0.319 (SI) and 0.262 (CU)

Equation 6.1 is applicable for the range of conditions where 1.5 ≤ d_a/D₅₀ ≤ 185. For small channel applications, relative flow depth should not exceed the upper end of this range.

Some channels may experience conditions below the lower end of this range where protrusion of individual riprap elements into the flow field significantly changes the roughness relationship. This condition may be experienced on steep channels, but also occurs on moderate slopes. The relationship described by Bathurst (1991) addresses these conditions and can be written as follows (See Appendix D for the original form of the equation):

where,

• d_a = average flow depth in the channel, m (ft)
• g = acceleration due to gravity, 9.81 m/s² (32.2 ft/s²)
• Fr = Froude number
• REG = roughness element geometry
• CG = channel geometry
• α = unit conversion constant, 1.0 (SI) and 1.49 (CU)

Equation 6.2 is a semi-empirical relationship applicable for the range of conditions where 0.3<d_a/D₅₀<8.0. The three terms in the denominator represent functions of Froude number, roughness element geometry, and channel geometry given by the following equations:

where,

• T = channel top width, m (ft)
• b = parameter describing the effective roughness concentration.

The parameter b describes the relationship between effective roughness concentration and relative submergence of the roughness bed. This relationship is given by:

Equations 6.1 and 6.2 both apply in the overlapping range of 1.5 ≤ d_a/D₅₀ ≤ 8. For consistency and ease of application over the widest range of potential design situations, use of the Blodgett equation (6.1) is recommended when 1.5 ≤ d_a/D₅₀. The Bathurst equation (6.2) is recommended for 0.3<d_a/D₅₀<1.5.

As a practical problem, both Equations 6.1 and 6.2 require depth to estimate n while n is needed to determine depth setting up an iterative process.

Computed pipe diameters should be increased to a larger nominal dimension to avoid pressure flow. Standard English and metric nominal sizes used for storm drains are given in the table below.

HEC-15 Section 3.1 & HDM Index 864.2

Shear Stress Equation

The maximum shear stress is given by:

τ = γ⋅H_n⋅S

where:

• τ = shear stress in channel at maximum depth (N/m² or psf)
• γ = unit weight of water
• H_n = depth of flow in channel (ft or m)
• S = channel bottom slope

Per the Caltrans Highway Design Manual Index 309.1(2), the roadside environment can and should be made as safe as practical. A clear recovery zone is an unobstructed, relatively flat (4:1 or flatter) or gently sloping area beyond the edge of the traveled way which affords the drivers of errant vehicles the opportunity to regain control.

The AASHTO Roadside Design Guide provides detailed design guidance for creating a forgiving roadside environment. Channels should be safe for vehicles accidentally leaving the traveled way. The figure below illustrates the preferred geometric cross section for ditches with gradual slope changes in which the front and back slopes are traversable (AASHTO 2002).

This figure (from HDS-4 Section 5.1) is applicable for rounded ditches with bottom widths of 8 ft (2.4 m) or more, and trapezoidal ditches with bottom widths equal to or greater than 4 ft (1.2 m).

HEC-15

Section 2.1.3 Resistance to Flow

For rigid channel lining types, Manning’s roughness coefficient, n, is approximately constant. However, for very shallow flows the roughness coefficient will increase slightly. (Very shallow is defined where the height of the roughness is about one-tenth of the flow depth or more.)

For a riprap lining, the flow depth in small channels may be only a few times greater than the diameter of the mean riprap size. In this case, use of a constant n value is not acceptable and consideration of the shallow flow depth should be made by using a higher n value.

Tables 2.1 and 2.2 provide typical examples of n values of various lining materials. Table 2.1 summarizes linings for which the n value is dependent on flow depth as well as the specific properties of the material. Values for rolled erosion control products (RECPs) are presented to give a rough estimate of roughness for the three different classes of products. Although there is a wide range of RECPs available, jute net, curled wood mat, and synthetic mat are examples of open-weave textiles, erosion control blankets, and turf reinforcement mats, respectively. Chapter 5 contains more detail on roughness for RECPs.

Table 2.2 presents typical values for the stone linings: riprap, cobbles, and gravels. These are highly depth-dependent for roadside channel applications. More in-depth lining-specific information on roughness is provided in Chapter 6. Roughness guidance for vegetative and gabion mattress linings is in Chapters 4 and 7, respectively.