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FHWA > Engineering > Hydraulics > HEC 15 
Design of Roadside Channels with Flexible Linings

(7.1) 
where,
τ_{p}  = permissible shear stress, N/m^{2} (lb/ft^{2}) 
F_{*}  = Shields' parameter, dimensionless 
D_{50}  = median stone size, m (ft) 
In the tests reported by Simons, et al. (1984), the Shields' parameter for use in Equation 7.1 was found to be equal to 0.10.
A second equation provides for permissible shear stress based on mattress thickness (Simons, et al., 1984). It is applicable for a range of mattress thickness from 0.152 to 0.457 m (0.5 to 1.5 ft).
(7.2) 
where,
MT  = gabion mattress thickness, m (ft) 
MT_{C}  = thickness constant, 1.24 m (4.07 ft) 
The limits on Equations 7.1 and 7.2 are based on the range of laboratory data from which they are derived. Rock sizes within mattresses typically range from 0.076 to 0.152 m (0.25 to 0.5 ft) rock in the 0.152 m (0.5 ft) thick mattresses to 0.116 to 0.305 m (0.33 to 1 ft) rock in the 0.457 m (1.5 ft) thick mattresses.
When comparing, the permissible shear for gabions with the calculated shear on the channel, a safety factor, SF is required for Equation 3.2. The guidance found in Table 6.1 is applicable to gabions. Since, the Shields parameter in Equation 7.1 is 0.10, the appropriate corresponding safety factor is 1.25. Alternatively, the designer may compute the particle Reynolds number and, using Table 6.1, determine both a Shields' parameter and SF corresponding to the Reynolds number.
The design procedure for gabions is as follows. It uses the same roughness relationships developed for riprap.
Step 1. Determine channel slope, channel shape, and design discharge.
Step 2. Select a trial (initial) mattress thickness and fill rock D_{50}, perhaps based on available sizes for the project. (Also, determine specific weight of proposed stone.)
Step 3. Estimate the depth. For the first iteration, select a channel depth, d_{i}. For subsequent iterations, a new depth can be estimated from the following equation or any other appropriate method.
Determine the average flow depth, d_{a} in the channel. d_{a} = A/T
Step 4. Calculate the relative depth ratio, d_{a}/D_{50}. If d_{a}/D_{50} is greater than or equal to 1.5, use Equation 6.1 to calculate Manning's n. If d_{a}/D_{50} is less than 1.5 use Equation 6.2 to calculate Manning's n. Calculate the discharge using Manning's equation.
Step 5. If the calculated discharge is within 5 percent of the design discharge, then proceed to step 6. If not, go back to step 3.
Step 6. Calculate the permissible shear stress from Equations 7.1 and 7.2 and take the largest as the permissible shear stress.
Use Equation 3.1 to determine the actual shear stress on the bottom of the channel.
Select a safety factor.
Apply Equation 3.2 to compare the actual to permissible shear stress.
Step 7. If permissible shear is greater than computed shear, the lining is stable. If not, repeat the design process beginning at step 2.
Determine the flow depth and required thickness of a gabion mattress lining for a trapezoidal channel.
Given:
Q = 0.28 m^{3}/s
S = 0.09 m/m
B = 0.60 m
Z = 3
Step 1. Channel characteristics and design discharge are given above.
Step 2. Try a 0.23 m thick gabion basket with a D_{50} = 0.15 m; γ_{s}= 25.9 kN/m^{3}
Step 3. Assume an initial trial depth of 0.3 m
Using the geometric properties of a trapezoid:
A = Bd+Zd^{2} = 0.6(0.3)+3(0.3)^{2} = 0.450 m^{2}
R = A/P =0.45/2.50 = 0.180 m
T = B+2dZ = 0.6+2(0.3)(3) = 2.40 m
d_{a} = A/T = 0.45/2.40 = 0.188 m
Step 4. The relative depth ratio, d_{a}/D_{50} = 0.188/0.150 = 1.3. Therefore, use Equation 6.2 to calculate Manning's n.
Calculate Q using Manning's equation:
Step 5. Since this estimate is more than 5 percent from the design discharge, estimate a new depth in step 3.
Step 3 (2^{nd} iteration). Estimate a new depth estimate:
Using the geometric properties of a trapezoid, the maximum and average flow depths are found:
A = Bd+Zd^{2} = 0.6(0.21)+3(0.21)^{2} = 0.258 m^{2}
R = A/P =0.258/1.93 = 0.134 m
T = B+2dZ = 0.6+2(0.21)(3) = 1.86 m
d_{a} = A/T = 0.258/1.86 = 0.139 m
Step 4. (2^{nd} iteration). The relative depth ratio, d_{a}/D_{50} = 0.139/0.150 = 0.9. Therefore, use Equation 6.2 to calculate Manning's n.
Calculate Q using Manning's equation:
Since this estimate is also not within 5 percent of the design discharge, further iterations are required. Subsequent iterations will produce the following values:
d = 0.185 m
n = 0.055
Q = 0.29 m^{3}/s
Proceed to step 6 with these values.
Step 6. Calculate the permissible shear stress from Equations 7.1 and 7.2 and take the largest as the permissible shear stress.
Permissible shear stress for this gabion configuration is, therefore 241 N/m^{2}.
Use Equation 3.1 to determine the actual shear stress on the bottom of the channel and apply Equation 3.2 to compare the actual to permissible shear stress.
SF=1.25:
Step 7. From Equation 3.2: 241>1.25(163), therefore, the selected gabion mattress is acceptable.
Determine the flow depth and required thickness of a gabion mattress lining for a trapezoidal channel.
Given:
Q = 10 ft^{3}/s
S = 0.09 ft/ft
B = 2.0 ft
Z = 3
Step 1. Channel characteristics and design discharge are given above.
Step 2. Try a 0.75 ft thick gabion basket with a D_{50} = 0.5 ft; γ_{s}= 165 lb/ft^{3}
Step 3. Assume an initial trial depth of 1 ft.
Using the geometric properties of a trapezoid:
A = Bd+Zd^{2} = 2.0(1.0)+3(1.0)^{2} = 5.0 ft^{2}
R = A/P =5.0/8.3 = 0.601 ft
T = B+2dZ = 2.0+2(1.0)(3) = 8.0 ft
d_{a} = A/T = 5.0/8.0 = 0.625 ft
Step 4. The relative depth ratio, d_{a}/D_{50} = 0.625/0.50 = 1.3. Therefore, use Equation 6.2 to calculate Manning's n.
Calculate Q using Manning's equation:
Step 5. Since this estimate is more than 5 percent from the design discharge, estimate a new depth in step 3.
Step 3 (2^{nd} iteration). Estimate a new depth estimate:
Using the geometric properties of a trapezoid, the maximum and average flow depths are found:
A = Bd+Zd^{2} = 2.0(0.70)+3(0.70)^{2} = 2.87 ft^{2}
R = A/P =2.87/6.43 = 0.446 ft
T = B+2dZ = 2.0+2(0.70)(3) = 6.20 ft
d_{a} = A/T = 2.87/6.20 = 0.463 ft
Step 4. (2^{nd} iteration). The relative depth ratio, d_{a}/D_{50} = 0.496/0.50 = 1.0. Therefore, use Equation 6.2 to calculate Manning's n.
Calculate Q using Manning's equation:
Step 5 (2^{nd} iteration). Since this estimate is also not within 5 percent of the design discharge, further iterations are required. Subsequent iterations will produce the following values:
d = 0.609 ft
n = 0.055
Q = 10.2 ft^{3}/s
Proceed to step 6 with these values.
Step 6. Calculate the permissible shear stress from Equations 7.1 and 7.2 and take the largest as the permissible shear stress.
Permissible shear stress for this gabion configuration is, therefore 5.1 lb/ft^{2}.
Use Equation 3.1 to determine the actual shear stress on the bottom of the channel and apply Equation 3.2 to compare the actual to permissible shear stress.
SF=1.25:
Step 7. From Equation 3.2: 5.1>1.25(3.4), therefore, the selected gabion mattress is acceptable.
As with riprap linings, the ability to deliver the expected channel protection depends on the proper installation of the lining. Additional design considerations for gabion linings include consideration of the wire mesh; freeboard; proper specification of gradation and thickness; and use of a filter material under the gabions.
The stability of gabions depends on the integrity of the wire mesh. In streams with high sediment concentrations or with rocks moving along the bed of the channel, the wire mesh may be abraded and eventually fail. Under these conditions the gabion will no longer behave as a single unit but rather as individual stones. Applications of gabion mattresses and baskets under these conditions should be avoided. Such conditions are unlikely for roadside channel design.
Extent of gabions on a steep gradient (the most common roadside application for gabions) must be sufficient to protect transition regions of the channel both above and below the steep gradient section. The transition from a steep gradient to a culvert should allow for slumping of a gabion mattress.
Gabions should be placed flush with the invert of a culvert. The break between the steep slope and culvert entrance should equal three to five times the mattress thickness. The transition from a steep gradient channel to a mild gradient channel may require an energy dissipation structure such as a plunge pool. The transition from a mild gradient to a steep gradient should be protected against local scour upstream of the transition for a distance of approximately five times the uniform depth of flow in the downstream channel (Chow, 1959).
Freeboard should equal the mean depth of flow, since wave height will reach approximately twice the mean depth. This freeboard height should be used for both transitional and permanent channel installations.
The rock gradation used in gabions mattress must be such that larger stones do not protrude outside the mattress and the wire mesh retains smaller stones.
When gabions are used, the need for an underlying filter material must be evaluated. The filter material may be either a granular filter blanket or geotextile fabric. See section 6.4.3 for description of the filter requirements.