Scour Technology  Bridge Hydraulics  Culvert Hydraulics  Highway Drainage  Hydrology  Environmental Hydraulics 
FHWA > Engineering > Hydraulics > HEC 15 
Design of Roadside Channels with Flexible Linings

Retardance Class  Cover^{1}  Condition 

A  Weeping Love Grass  Excellent stand, tall, average 760 mm (30 in) 
Yellow Bluestem Ischaemum  Excellent stand, tall, average 910 mm (36 in)  
B  Kudzu  Very dense growth, uncut 
Bermuda Grass  Good stand, tall, average 300 mm (12 in)  
Native Grass Mixture (little bluestem, bluestem, blue gamma, and other long and short midwest grasses)  Good stand, unmowed  
Weeping lovegrass  Good stand, tall, average 610 mm (24 in)  
Lespedeza sericea  Good stand, not woody, tall, average 480 mm (19 in)  
Alfalfa  Good stand, uncut, average 280 mm (11 in)  
Weeping lovegrass  Good stand, unmowed, average 330 mm (13 in)  
Kudzu  Dense growth, uncut  
Blue Gamma  Good stand, uncut, average 280 mm (11 in)  
C  Crabgrass  Fair stand, uncut 250 to 1200 mm (10 to 48 in) 
Bermuda grass  Good stand, mowed, average 150 mm (6 in)  
Common Lespedeza  Good stand, uncut, average 280 mm (11 in)  
GrassLegume mixturesummer (orchard grass, redtop, Italian ryegrass, and common lespedeza)  Good stand, uncut, 150 to 200 mm (6 to 8 in)  
Centipede grass  Very dense cover, average 150 mm (6 in)  
Kentucky Bluegrass  Good stand, headed, 150 to 300 mm (6 to 12 in)  
D  Bermuda Grass  Good stand, cut to 60 mm (2.5 in) height 
Common Lespedeza  Excellent stand, uncut, average 110 mm (4.5 in)  
Buffalo Grass  Good stand, uncut, 80 to 150 mm (3 to 6 in)  
GrassLegume mixturefall, spring (orchard grass, redtop, Italian ryegrass, and common lespedeza)  Good stand, uncut, 100 to 130 mm (4 to 5 in)  
Lespedeza sericea  After cutting to 50 mm (2 in) height. Very good stand before cutting.  
E  Bermuda Grass  Good stand, cut to height, 40 mm (1.5 in) 
Bermuda Grass  Burned stubble 
^{1}Covers classified have been tested in experimental channels. Covers were green and generally uniform.
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 m^{2} (ft^{2}). A good grass lining will have about 2,000 to 4,000 stems/m^{2} (200 to 400 stems/ft^{2}). A poor cover will have about onethird of that density and an excellent cover about fivethirds (USDA, 1987, Table 3.1). While grass density can be determined by physically counting stems, an easier direct method of estimating the densitystiffness property is provided in Appendix E of this manual.
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 densitystiffness property of grass is defined by the C_{s} coefficient. C_{s} can be directly measured using the FallBoard 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.
Conditions  Excellent  Very Good  Good  Fair  Poor 

C_{s} (SI)  580  290  106  24  8.6 
C_{s} (CU)  49  25  9.0  2.0  0.73 
The combined effect of grass stem height and densitystiffness is defined by the grass roughness coefficient.
(4.1) 
where,
C_{n}  = grass roughness coefficient 
C_{s}  = densitystiffness coefficient 
h  = stem height, m (ft) 
α  = unit conversion constant, 0.35 (SI), 0.237 (CU) 
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.
Stem Height m (ft)  Excellent  Very Good  Good  Fair  Poor 

0.075 (0.25)  0.168  0.157  0.142  0.122  0.111 
0.150 (0.50)  0.243  0.227  0.205  0.177  0.159 
0.225 (0.75)  0.301  0.281  0.254  0.219  0.197 
SCS retardance values relate to a combination of grass stemheight and density. C_{n} 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.
Retardance Class  A  B  C  D  E 

Stem Height, mm  910  610  200  100  40 
C_{s}  390  81  47  33  44 
C_{n}  0.605  0.418  0.220  0.147  0.093 
Retardance Class  A  B  C  D  E 

Stem Height, in  36  24  8.0  4.0  1.6 
C_{s}  33  7.1  3.9  2.7  3.8 
C_{n}  0.605  0.418  0.220  0.147  0.093 
Manning's roughness coefficient for grass linings varies depending on grass properties as reflected in the C_{n} 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.
(4.2) 
where,
τ_{o}  = mean boundary shear stress, N/m^{2} (lb/ft^{2}) 
α  = unit conversion constant, 1.0 (SI), 0.213 (CU) 
See Appendix C.2 for the derivation of Equation 4.2.
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.
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.
(4.3) 
where,
τ_{e}  = effective shear stress on the soil surface, N/m^{2} (lb/ft^{2}) 
τ_{d }  = design shear stress, N/m^{2} (lb/ft^{2}) 
C_{f}  = grass cover factor 
n_{s}  = soil grain roughness 
n  = overall lining roughness 
Soil grain roughness is taken as 0.016 when D_{75} < 1.3 mm (0.05 in). For larger grain soils, the soil grain roughness is given by:
(4.4) 
where,
n_{s}  = soil grain roughness (D_{75} > 1.3 mm (0.05 in)) 
D_{75}  = soil size where 75% of the material is finer, mm (in) 
α  = unit conversion constant, 0.015 (SI), 0.026 (CU) 
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 sodforming grasses than bunch grasses. In all cases a uniform stand of grass is assumed. Nonuniform 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.
Growth Form  Cover Factor, C_{f}  

Excellent  Very Good  Good  Fair  Poor  
Sod  0.98  0.95  0.90  0.84  0.75 
Bunch  0.55  0.53  0.50  0.47  0.41 
Mixed  0.82  0.79  0.75  0.70  0.62 
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 noncohesive soils (defined as soils with a plasticity index of less than 10) is due mainly to particle size, while finegrained 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 finegrained cohesive soils. An approximate method is also provided for cohesive soils.
The permissible soil shear stress for finegrained, noncohesive soils (D_{75} < 1.3 mm (0.05 in)) is relatively constant and is conservatively estimated at 1.0 N/m^{2} (0.02 lb/ft^{2}). For coarse grained, noncohesive soils (1.3 mm (0.05 in) < D_{75} < 50 mm (2 in)) the following equation applies.
(4.5) 
where,
τ_{p,soil}  = permissible soil shear stress, N/m^{2} (lb/ft^{2}) 
D_{75}  = soil size where 75% of the material is finer, mm (in) 
α  = unit conversion constant, 0.75 (SI), 0.4 (CU) 
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.
(4.6) 
where,
τ_{p,soil}  = soil permissible shear stress, N/m^{2} (lb/ft^{2}) 
PI  = plasticity index 
e  = void ratio 
c_{1}, c_{2}, c_{3}, c_{4}, c_{5}, c_{6}  = coefficients (Table 4.6) 
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/m^{3} (100 lb/ft^{3}), for silts and lean clays (ML, CL) 1.4 ton/m^{3} (90 lb/ft^{3}) and fat clays (CH, MH) 1.3 ton/m^{3} (80 lb/ft^{3}).
ASTM Soil Classification^{(1)}  Applicable Range  c_{1}  c_{2}  c_{3}  c_{4}  c_{5}  c_{6} (SI)  c_{6} (CU) 

GM  10≤PI≤20  1.07  14.3  47.7  1.42  0.61  4.8x10^{3}  10^{4} 
20≤PI      0.076  1.42  0.61  48.  1.0  
GC  10≤PI≤20  0.0477  2.86  42.9  1.42  0.61  4.8x10^{2}  10^{3} 
20≤PI      0.119  1.42  0.61  48.  1.0  
SM  10≤PI≤20  1.07  7.15  11.9  1.42  0.61  4.8x10^{3}  10^{4} 
20≤PI      0.058  1.42  0.61  48.  1.0  
SC  10≤PI≤20  1.07  14.3  47.7  1.42  0.61  4.8x10^{3}  10^{4} 
20≤PI      0.076  1.42  0.61  48.  1.0  
ML  10≤PI≤20  1.07  7.15  11.9  1.48  0.57  4.8x10^{3}  10^{4} 
20≤PI      0.058  1.48  0.57  48.  1.0  
CL  10≤PI≤20  1.07  14.3  47.7  1.48  0.57  4.8x10^{3}  10^{4} 
20≤PI      0.076  1.48  0.57  48.  1.0  
MH  10≤PI≤20  0.0477  1.43  10.7  1.38  0.373  4.8x10^{2}  10^{3} 
20≤PI      0.058  1.38  0.373  48.  1.0  
CH  20≤PI      0.097  1.38  0.373  48.  1.0 
(1) Note:  Typical names 
GM  Silty gravels, gravelsand silt mixtures 
GC  Clayey gravels, gravelsandclay mixtures 
SM  Silty sands, sandsilt mixtures 
SC  Clayey sands, sandclay mixtures 
ML  Inorganic silts, very fine sands, rock flour, silty or clayey fine sands 
CL  Inorganic clays of low to medium plasticity, gravelly clays, sandy clays, silty clays, lean clays 
MH  Inorganic silts, micaceous or diatomaceous fine sands or silts, elastic silts 
CH  Inorganic clays of high plasticity, fat clays 
Figure 4.1. Cohesive Soil Permissible 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:
(4.7) 
where,
τ_{p}  = permissible shear stress on the vegetative lining, N/m^{2} (lb/ft^{2}) 
τ_{p,soil}  = permissible soil shear stress, N/m^{2} (lb/ft^{2}) 
C_{f}  = grass cover factor 
n_{s}  = soil grain roughness 
n  = overall lining roughness 
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:
Shape: Trapezoidal, B = 0.9 m, Z = 3
Soil: Clayey sand (SC classification), PI = 16, e = 0.5
Grass: Sod, height = 0.075 m
Grade: 3.0 percent
Flow: 0.5 m^{3}/s
The solution is accomplished using procedure given in Section 3.1 for a straight channel.
Step 1. Channel slope, shape, and discharge have been given.
Step 2. A vegetative lining on a clayey sand soil will be evaluated.
Step 3. Initial depth is estimated at 0.30 m
From the geometric relationship of a trapezoid (see Appendix B):
R = A/P = (0.54)/(2.8) = 0.193 m
Step 4. To estimate n, the applied shear stress on the grass lining is given by Equation 2.3
Determine a Manning's n value from Equation 4.2. From Table 4.3, C_{n} = 0.142
The discharge is calculated using Manning's equation (Equation 2.1):
Step 5. Since this value is more than 5 percent different from the design flow, we need to go back to step 3 to estimate a new flow depth.
Step 3 (2^{nd} iteration). Estimate a new depth solving Equation 2.2 or other appropriate method iteratively to find the next estimate for depth:
d = 0.21 m
Revise the hydraulic radius.
R = A/P = (0.321)/(2.23) = 0.144 m
Step 4 (2^{nd} iteration). To estimate n, the applied shear stress on the grass lining is given by Equation 2.3
Determine a Manning's n value from Equation 4.2. From Table 4.3, C_{n} = 0.142
The discharge is calculated using Manning's equation (Equation 2.1):
Step 5 (2^{nd} iteration). Since this value is within 5 percent of the design flow, we can proceed to step 6.
Step 6. The maximum shear on the channel bottom is.
Determine the permissible soil shear stress from Equation 4.6.
Equation 4.7 gives the permissible shear stress on the vegetation. The value of C_{f} is found in Table 4.5.
The safety factor for this channel is taken as 1.0.
Step 7. The grass lining is acceptable since the maximum shear on the vegetation is less than the permissible shear of 131 N/m^{2}.
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:
Shape: Trapezoidal, B = 3.0 ft, Z = 3
Soil: Clayey sand (SC classification), PI = 16, e = 0.5
Grass: Sod, height = 0.25 ft
Grade: 3.0 percent
Flow: 17.5 ft^{3}/s
The solution is accomplished using procedure given in Section 3.1 for a straight channel.
Step 1. Channel slope, shape, and discharge have been given.
Step 2. A vegetative lining on a clayey sand soil will be evaluated.
Step 3. Initial depth is estimated at 1.0 ft.
From the geometric relationship of a trapezoid (see Appendix B):
R = A/P = (6.00)/(9.32) = 0.643 ft
Step 4. To estimate n, the applied shear stress on the grass lining is given by Equation 2.3
Determine a Manning's n value from Equation 4.2. From Table 4.3, C_{n} = 0.142
The discharge is calculated using Manning's equation (Equation 2.1):
Step 5. Since this value is more than 5 percent different from the design flow, we need to go back to step 3 to estimate a new flow depth.
Step 3 (2^{nd} iteration). Estimate a new depth solving Equation 2.2 or other appropriate method iteratively to find the next estimate for depth:
d = 0.70 ft
Revise the hydraulic radius.
R = A/P = (3.57)/(7.43) = 0.481 ft
Step 4 (2^{nd} iteration). To estimate n, the applied shear stress on the grass lining is given by Equation 2.3
Determine a Manning's n value from Equation 4.2. From Table 4.3, C_{n} = 0.142
The discharge is calculated using Manning's equation (Equation 2.1):
Step 5 (2^{nd} iteration). Since this value is within 5 percent of the design flow, we can proceed to step 6.
Step 6. The maximum shear on the channel bottom is.
Determine the permissible soil shear stress from Equation 4.6.
Equation 4.7 gives the permissible shear stress on the vegetation. The value of C_{f} is found in Table 4.5.
The safety factor for this channel is taken as 1.0.
Step 7. The grass lining is acceptable since the maximum shear on the vegetation is less than the permissible shear of 2.7 lb/ft^{2}.
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:
(4.8) 
where,
α  = unit conversion constant, 1.26 (SI), 0.057 (CU) 
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.
Determine the maximum discharge for a grasslined channel given the following shape, soil conditions, and grade.
Given:
Shape: Trapezoidal, B = 0.9 m, z = 3
Soil: Silty sand (SC classification), PI = 5, D_{75} = 2 mm
Grade: 5.0 percent
The solution is accomplished using procedure given in Section 3.6 for a maximum discharge approach.
Step 1. The candidate lining is a sod forming grass in good condition with a stem height of 0.150 m.
Step 2. Determine the maximum depth. For a grass lining this requires several steps. First, determine the permissible soil shear stress. From Equation 4.5:
To estimate the shear, we will first need to use Equation 4.1 to estimate C_{n }with C_{s} taken from Table 4.2
Next, estimate the maximum applied shear using Equation 4.8.
Maximum depth from Equation 3.10 with a safety factor of 1.0 is:
Step 3. Determine the area and hydraulic radius corresponding to the allowable depth based on the channel geometry
R = A/P = (0.259)/(2.04) = 0.127 m
Step 4. Estimate the Manning's n value appropriate for the lining type from Equation 4.2, but first calculate the mean boundary shear.
Step 5. Solve Manning's equation to determine the maximum discharge for the channel.
Since Equation 4.8 used in Step 2 is an approximate equation, check the effective shear stress using Equation 4.3.
Since this value is less than, but close to τ_{p} for the soil 1.5 N/m^{2}, the maximum discharge is 0.38 m^{3}/s.
Determine the maximum discharge for a grasslined channel given the following shape, soil conditions, and grade.
Given:
Shape: Trapezoidal, B = 3.0 ft, z = 3
Soil: Silty sand (SC classification), PI = 5, D_{75} = 0.08 in
Grade: 5.0 percent
The solution is accomplished using procedure given in Section 3.6 for a maximum discharge approach.
Step 1. The candidate lining is a sod forming grass in good condition with a stem height of 0.5 ft.
Step 2. Determine the maximum depth. For a grass lining this requires several steps. First, determine the permissible soil shear stress. From Equation 4.5:
To estimate the shear, we will first need to use Equation 4.1 to estimate C_{n }with C_{s} taken from Table 4.2
Next, estimate the maximum applied shear using Equation 4.8.
Maximum depth from Equation 3.10 with a safety factor of 1.0 is:
Step 3. Determine the area and hydraulic radius corresponding to the allowable depth based on the channel geometry
R = A/P = (2.81)/(6.73) = 0.42 ft
Step 4. Estimate the Manning's n value appropriate for the lining type from Equation 4.2, but first calculate the mean boundary shear.
Step 5. Solve Manning's equation to determine the maximum discharge for the channel.
Since Equation 4.8 used in Step 2 is an approximate equation, check the effective shear stress using Equation 4.3.
Since this value is less than, but close to τ_{p} for the soil 0.032 lb/ft^{2}, the maximum discharge is 13.5 ft^{3}/s.
The rock products industry provides a variety of uniformly graded gravels for use as mulch and soil stabilization. A gravel/soil mixture provides a nondegradable 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/m^{3} (1.5 ton/yd^{3}). 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.
Size  Very Coarse (D_{75}= 45 mm (1.75 in))  Coarse (D_{75}= 30 mm (1.2 in)) 

50.0 mm (2 in)  90  100   
37.5 mm (1.5 in)  35  70  90  100 
25.0 mm (1 in)  0  15  35  70 
19.0 mm (0.75 in)    0  15 
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.
(4.9) 
where,
I_{gravel}  = gravel application rate, metric ton/m^{2} (ton/yd^{2}) 
i_{gravel}  = fraction of gravel (equal to or larger than gravel layer size) already in the soil 
T_{s}  = thickness of the soil surface, m (ft) 
γ_{gravel}  = unit weight of gravel, metric ton/m^{3} (ton/yd^{3}) 
α  = unit conversion constant, 1.0 (SI), 0.333 (CU) 
The gravel application rates for finegrained 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}.
Soil Preparation Depth  Application Rate, I_{gravel} 

75.0 mm (3 in)  0.044 ton/m^{2} 0.041 ton/yd^{2} 
100.0 mm (4 in)  0.058 ton/m^{2} 0.056 ton/yd^{2} 
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 particletype lining, so loss of a few stones will not affect overall lining integrity. Therefore, a gravel/soil mix is a good turf reinforcement alternative.
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/m^{2} is recommended (100 mm soil preparation depth). See Table 4.8.
Given:
Shape: Trapezoidal, B = 0.9 m, Z = 3
Soil: Silty sand (SC classification), PI = 5, D_{75} = 2 mm
Grass: Sod, good condition, h = 0.150 m
Gravel: D_{75} = 25 mm
Grade: 5.0 percent
Flow: 1.7 m^{3}/s
The solution is accomplished using procedure given in Section 3.1 for a straight channel.
Step 1. Channel slope, shape, and discharge have been given.
Step 2. Proposed lining is a vegetated channel with a gravel soil amendment.
Step 3. Initial depth is estimated at 0.30 m
From the geometric relationship of a trapezoid (see Appendix B):
R = A/P = (0.540 m^{2})/(2.80 m) = 0.193 m
Step 4. To estimate n, the applied shear stress on the grass lining is given by Equation 2.3
Determine a Manning's n value from Equation 4.2. From Table 4.3, C_{n} = 0.205
The discharge is calculated using Manning's equation (Equation 2.1):
Step 5. Since this value is more than 5 percent different from the design flow, we need to go back to step 3 to estimate a new flow depth.
Step 3 (2^{nd} iteration). Estimate a new depth solving Equation 2.2 or other appropriate method iteratively to find the next estimate for depth:
d = 0.35 m
Revise hydraulic radius.
R = A/P = (0.682)/(3.11) = 0.219 m
Step 4 (2^{nd} iteration). To estimate n, the applied shear stress on the grass lining is given by Equation 2.3
Determine a Manning's n value for the vegetation from Equation 4.2. From Table 4.3, C_{n} = 0.142
The discharge is calculated using Manning's equation (Equation 2.1):
Step 5 (2^{nd} iteration). Since this value is within 5 percent of the design flow, we can proceed to step 6.
Step 6. The maximum shear on the channel bottom is.
Determine the permissible shear stress from Equation 4.4. For turf reinforcement with gravel/soil the D_{75} for the gravel is used instead of the D_{75} for the soil.
A Manning's n for the soil/gravel mixture is derived from Equation 4.4:
Equation 4.7 gives the permissible shear stress on the vegetation. The value of C_{f} is found in Table 4.5.
The safety factor for this channel is taken as 1.0.
Step 7. The grass lining reinforced with the gravel/soil mixture is acceptable since the permissible shear is greater than the maximum shear.
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/yd^{2} is recommended (4 inch soil preparation depth). See Table 4.8.
Given:
Shape: Trapezoidal, B = 3 ft, Z = 3
Soil: Silty sand (SC classification), PI = 5, D_{75} = 0.08 in
Grass: sod, good condition, h = 0.5 in
Gravel: D_{75} = 1.0 in
Grade: 5.0 percent
Flow: 60 ft^{3}/s
The solution is accomplished using procedure given in Section 3.1 for a straight channel.
Step 1. Channel slope, shape, and discharge have been given.
Step 2. Proposed lining is a vegetated channel with a gravel soil amendment.
Step 3. Initial depth is estimated at 1.0 ft
From the geometric relationship of a trapezoid (see Appendix B):
R = A/P = (6.00)/(9.32) = 0.644 ft
Step 4. To estimate n, the applied shear stress on the grass lining is given by Equation 2.3
Determine a Manning's n value from Equation 4.2. From Table 4.3, C_{n} = 0.205
The discharge is calculated using Manning's equation (Equation 2.1):
Step 5. Since this value is more than 5 percent different from the design flow, we need to go back to step 3 to estimate a new flow depth.
Step 3 (2^{nd} iteration). Estimate a new depth solving Equation 2.2 or other appropriate method iteratively to find the next estimate for depth:
d = 1.13 ft
Revise hydraulic radius.
R = A/P = (7.22)/(10.1) = 0.715 ft
Step 4 (2^{nd} iteration). To estimate n, the applied shear stress on the grass lining is given by Equation 2.3
Determine a Manning's n value from Equation 4.2. From Table 4.3, C_{n} = 0.205
The discharge is calculated using Manning's equation (Equation 2.1):
Step 5 (2^{nd} iteration). Since this value is within 5 percent of the design flow, we can proceed to step 6.
Step 6. The maximum shear on the channel bottom is.
Determine the permissible shear stress from Equation 4.4. For turf reinforcement with gravel/soil the D_{75} for the gravel is used instead of the D_{75} for the soil.
A Manning's n for the soil/gravel mixture is derived from Equation 4.4:
Equation 4.7 gives the permissible shear stress on the vegetation. The value of C_{f} is found in Table 4.5.
The safety factor for this channel is taken as 1.0.
Step 7. The grass lining reinforced with the gravel/soil mixture is acceptable since the permissible shear is greater than the maximum shear.