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### Gabion Design

## Design of Roadside Channels with Flexible Linings

Hydraulic Engineering Circular Number 15, Third Edition### Chapter 7: Gabion Lining Design

Gabions (rock filled wire containers) represent an approach for using smaller rock size than would be required by riprap. The smaller rock is enclosed in larger wire units in the form of mattresses or baskets. Gabion baskets are individual rectangular wire mesh containers filled with rock and frequently applied for grade control structures and retaining walls. Gabion mattresses are also rock filled wire mesh containers. The mattresses are composed of a series of integrated cells that hold the rock allowing for a greater spatial extent in each unit. Potential roadside applications for the gabion mattress include steep channels and rundowns.

The thickness of the gabion mattress may be less than the thickness of an equivalently stable riprap lining. Therefore, gabion mattresses represent a trade-off between less and smaller rock versus the costs of providing and installing the wire enclosures. Gabion mattresses are rarely cost effective on mildly sloped channels.

#### 7.1 Manning's Roughness

Roughness characteristics of gabion mattresses are governed by the size of the rock in the baskets and the wire mesh enclosing the rock. For practical purposes, the effect of the mesh can be neglected. Therefore, Manning's roughness should be determined using the D

_{50}of the basket rock as applied to the relationships provided for riprap and gravel linings. (See Section 6.1.)#### 7.2 Permissible Shear Stress

Values for permissible shear stress for gabion mattresses are based on research conducted at laboratory facilities and in the field. However, reports from these studies are difficult to reconcile. Simons, et al. (1984) reported permissible shear stresses in the range of 140 to 190 N/m

^{2}(3 to 4 lb/ft^{2}) while Clopper and Chen (1988) reported values approaching 1700 N/m^{2}(35 lb/ft^{2}). Simons, et al. tested mattresses ranging in depth from 152 to 457 mm (6 to 18 in) and on slopes of up to 2 percent. Since the objective was to test embankment overtopping, Clopper and Chen tested 152 mm (6 in) mattresses on 25 and 33 percent slopes.The difference in reported permissible shear stresses may be partly due to the definition of failure. In the Clopper and Chen report, failure was noted after rocks within the basket had shifted to the downstream end of the baskets and an undulating surface was formed leaving part of the embankment exposed. Although this may be an appropriate definition for a rare embankment-overtopping event, such failure is not appropriate for the more frequently occurring roadside design event. For this reason as well as to provide for conservative guidance, the Simons et al. results are emphasized in this guidance.

Permissible shear stress for gabions may be estimated based on the size of the rock fill or based on gabion mattress thickness. Both estimates are determined and the largest value is taken as the permissible shear stress.

Equation 7.1 provides a relationship for permissible shear stress based on rock fill size (Simons, et al., 1984). This shear stress exceeds that of loose riprap because of the added stability provided by the wire mesh. The equation is valid for a range of D

_{50}from 0.076 to 0.457 m (0.25 to 1.5 ft)(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.

#### 7.3 Design Procedure

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/TStep 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.

##### Design Example: Gabion Design (SI)

Determine the flow depth and required thickness of a gabion mattress lining for a trapezoidal channel.

Given:

Q = 0.28 m

^{3}/sS = 0.09 m/m

B = 0.60 m

Z = 3

##### Solution

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 mStep 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 mStep 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}/sProceed 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.

##### Design Example: Gabion Design (CU)

Determine the flow depth and required thickness of a gabion mattress lining for a trapezoidal channel.

Given:

Q = 10 ft

^{3}/sS = 0.09 ft/ft

B = 2.0 ft

Z = 3

##### Solution

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 ftStep 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 ftStep 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}/sProceed 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.

#### 7.4 Additional Considerations

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.

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