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

Chapter 1: Energy Dissipator Design

Under many circumstances, discharges from culverts and channels may cause erosion problems. To mitigate this erosion, discharge energy can be dissipated prior to release downstream. The purpose of this circular is to provide design procedures for energy dissipator designs for highway applications. The first six chapters of this circular provide general information that is used to support the remaining design chapters. Chapter 1 (this chapter) discusses the overall analysis framework that is recommended and provides a matrix of available dissipators and their constraints. Chapter 2 provides an overview of erosion hazards that exist at both inlets and outlets. Chapter 3 provides a more precise approach for analyzing outlet velocity than is found in HDS 5. Chapter 4 provides procedures for calculating the depth and velocity through transitions. Chapter 5 provides design procedures for calculating the size of scour holes at culvert outlets. Chapter 6 provides an overview of hydraulic jumps, which are an integral part of many dissipators.

For some sites, appropriate energy dissipation may be achieved by design of a flow transition (Chapter 4), anticipating an acceptable scour hole (Chapter 5), and/or allowing for a hydraulic jump given sufficient tailwater (Chapter 6). However, at many other sites more involved dissipator designs may be required. These are grouped as follows:

• Internal Dissipators (Chapter 7)
• Stilling Basins (Chapter 8)
• Streambed Level Dissipators (Chapter 9)
• Riprap Basins and Aprons (Chapter 10)
• Drop Structures (Chapter 11)
• Stilling Wells (Chapter 12)

The designs included are listed in Table 1.1. Experienced designers can use Table 1.1 to determine the dissipator type to use and go directly to the appropriate chapter. First time designers should become familiar with the recommended energy dissipator design procedure that is discussed in this chapter.

Most of the information presented has been taken from the literature and adapted, where necessary, to fit highway needs. Recent research results have been incorporated, wherever possible, and a field survey was conducted to determine States' present practice and experience.

1.1 Energy Dissipator Design Procedure

The designer should treat the culvert, energy dissipator, and channel protection designs as an integrated system. Energy dissipators can change culvert performance and channel protection requirements. Some debris-control structures represent losses not normally considered in the culvert design procedure. Velocity can be increased or reduced by changes in the culvert design. Downstream channel conditions (velocity, depth, and channel stability) are important considerations in energy dissipator design. A combination of dissipator and channel protection might be used to solve specific problems.

• 1. Debris notes: N = none, L = low, M = moderate, H = heavy
• 2. Bed slope must be in the range 4% < S_o < 25%
• 3. Check headwater for outlet control
• 4. Discharge, Q < 11 m³/s (400 ft³/s)and Velocity, V < 15 m/s (50 ft/s)
• 5. Drop < 4.6 m (15 ft)
• 6. Drop < 3.7 m (12 ft)
• 7. At release point from culvert or channel
• 8. Culvert rise less than or equal to 1500 mm (60 in)
• na = not applicable.

The energy dissipator design procedure, illustrated in Figure 1.1, shows the recommended design steps. The designer should apply the following design procedure to one drainage channel/culvert and its associated structure at a time.

Step 1. Identify and Collect Design Data.

Energy dissipators should be considered part of a larger design system that includes a culvert or a chute, channel protection requirements (both upstream and downstream), and may include a debris control structure. Much of the input data will be available to the energy dissipator design phase from previous design efforts.

1. Culvert Data: The culvert design should provide: type (RCB, RCP, CMP, etc); height, D; width, B; length, L; roughness, n; slope, S_o; design discharge, Q; tailwater, TW; type of control (inlet or outlet); outlet depth, y_o; outlet velocity, V_o; and outlet Froude number, Fr_o. Culvert outlet velocity, V_o, is discussed in Chapter 3. HDS 5 (Normann, et al., 2001) provides design procedures for culverts.
2. Transition Data: Flow transitions are discussed in Chapter 4. For most culvert designs, the designer will have to determine the flow depth, y, and velocity, V, at the exit of standard wingwall/apron combinations.

   Figure 1.1. Energy Dissipator Design Procedure

   

3. Channel Data: The following channel data is used to determine the TW for the culvert design: design discharge, Q; slope, S_o; cross section geometry; bank and bed roughness, n; normal depth, y_n = TW; and normal velocity, V_n. If the cross section is a trapezoid, it is defined by the bottom width, B, and side slope, Z, which is expressed as 1 unit vertical to Z units horizontal (1V:ZH). HDS 4 (Schall, et al., 2001) provides examples of how to compute normal depth in channels. The size and amount of debris should be estimated using HEC 9 (Bradley, J.B., et al., 2005). The size and amount of bedload should be estimated.
4. Allowable Scour Estimate: In the field, the designer should determine if the bed material at the planned exit of the culvert is erodible. If it is, the potential extent of scour should be estimated: depth, h_s; width, W_s; and length, L_s. These estimates should be based on the physical limits to scour at the site. For example, the length, L_s, can be limited by a rock ledge or vegetation. The following soils parameters in the vicinity of planned culvert outlets should be provided. For non-cohesive soil, a grain size distribution including D₁₆ and D₈₄ is needed. For cohesive soil, the values needed are saturated shear strength, S_v, and plasticity index, PI.
5. Stability Assessment: The channel, culvert, and related structures should be evaluated for stability considering potential erosion, as well as buoyancy, shear, and other forces on the structure (see Chapter 2). If the channel, culvert, and related structures are assessed as unstable, the depth of degradation or height of aggradation that will occur over the design life of the structure should be estimated.

Step 2. Evaluate Velocities.

Compute culvert or chute exit velocity, V_o, and compare with downstream channel velocity, V_n. (See Chapter 3.) If the exit velocity and flow depth approximates the natural flow condition in the downstream channel, the culvert design is acceptable. If the velocity is moderately higher, the designer can evaluate reducing velocity within the barrel or chute (see Chapter 3) or reducing the velocity with a scour hole (step 3). Another option is to modify the culvert or chute (channel) design such that the outlet conditions are mitigated. If the velocity is substantially higher and/or the scour hole from step 3 is unacceptable, the designer should evaluate energy dissipators (step 4). Definition of the terms "approximately equal," "moderately higher," and "substantially higher" is relative to site-specific concerns such as sensitivity of the site and the consequences of failure. However, as rough guidelines that should be re-evaluated on a site-specific basis, the ranges of less than 10 percent, between 10 and 30 percent, and greater than 30 percent, respectively, may be used.

Step 3. Evaluate Outlet Scour Hole.

Compute the outlet scour hole dimensions using the procedures in Chapter 5. If the size of the scour hole is acceptable, the designer should document the size of the expected scour hole for maintenance and note the monitoring requirements. If the size of the scour hole is excessive, the designer should evaluate energy dissipators (step 4).

Step 4. Design Alternative Energy Dissipators.

Compare the design data identified in step 1 to the attributes of the various energy dissipators in Table 1.1. Design one or more of the energy dissipators that substantially satisfy the design criteria. The dissipators fall into two general groups based on Fr:

1. Fr < 3, most designs are in this group
2. Fr > 3, tumbling flow, USBR Type III stilling basin, USBR Type IV stilling basin, SAF stilling basin, and USBR Type VI impact basin

Debris, tailwater channel conditions, site conditions, and cost must also be considered in selecting alternative designs.

Step 5. Select Energy Dissipator.

Compare the design alternatives and select the dissipator that has the best combination of cost and velocity reduction. Each situation is unique and the exercise of engineering judgment will always be necessary. The designer should document the alternatives considered.

1.2 Design Examples

The energy dissipator design procedure is best illustrated by applying it and the material presented in the energy dissipator design chapters to a series of design problems. These examples are intended to provide an overview of the design process. Pertinent chapters should be consulted for design details. The two design examples illustrate the process for cases where the Froude number is greater than 3 with a defined channel (tailwater) and less than 3 without a defined channel (no tailwater), respectively.

Design Example: RCB (Fr > 3) with Defined Downstream Channel (SI)

Evaluate the outlet velocity from a 3048 mm x 1829 mm RCB and determine the need for an energy dissipator.

Solution

Step 1. Identify Design Data.

1. Culvert Data: Type, D, B, L, n, S_o, Q, TW, Control, y_o, V_o, Fr_o

   RCB, D = 1.829 m, B = 3.048 m, L = 91.44 m, n = 0.012

   S_o = 6.5%, Q = 11.8 m³/s, TW = 0.579 m, inlet control

   Elevation of outlet invert = 30.48 m

   y_o = 0.457 m, V_o = 8.473 m/s, Fr_o = 4

2. Transition Data: y and V at end of apron, Chapter 4

   The standard outlet with 45° wingwalls is an abrupt expansion. Since the culvert is in inlet control, the flow at the end of the apron will be supercritical: y = y_o = 0.457 m and V = V_o = 8.473 m/s

3. Channel Data: Q, S_o, geometry, n, z, b, y_n, V_n, debris, bedload

   Q = 11.8 m³/s, S_o = 6.5%, trapezoidal, 1:2 (V:H), b = 3.048 m, n = 0.03

   y_n = 0.579 m, V_n = 4.846 m/s

   Graded gravel bed with no boulders, little floating debris

4. Allowable Scour Estimate: h_s, W_s, L_s, D₁₆, D₈₄, σ, S_v, PI

   Scour hole should be contained within channel W_s = L_s = 3.048 m and should be no deeper than 1.524 m. This allowable estimate can be obtained by observing scour holes in the vicinity.

5. Stability Assessment:

   The channel, culvert, and related structures are evaluated for stability considering potential erosion, as well as buoyancy, shear, and other forces on the structure. If the channel, culvert, and related structures are assessed as unstable, the depth of degradation or height of aggradation that will occur over the design life of the structure should be estimated. In this case, the channel appears to be stable. No long-term degradation or head cutting was observed in the field.

Step 2. Evaluate Velocities.

Since V_o = 8.473 m/s is much larger than V_n = 4.846 m/s, increasing culvert n is not practical. Determine if a scour hole is acceptable (Step 3) or design an energy dissipator (Step 4).

Step 3. Evaluate Outlet Scour Hole.

h_s, W_s, L_s, V_s from Chapter 5. If these values exceed allowable values in step 1, protection is required. y_e = 0.835 m, h_s = 2.530 m, W_s = 15.850 m, L_s = 21.640 m, V_s = 737 m³ Scour appears to be a problem and consideration should be given to reducing the V_o = 8.473 m/s to the 4.846 m/s in the channel.

Step 4. Design Alternative Energy Dissipators.

The following dissipators were determined from Table 1.1 by comparing the limitations shown against the site conditions. Since Fr > 3, tumbling flow, increased resistance, as well as, USBR Type IV, SAF stilling basin, and USBR Type VI streambed level dissipators will be designed. The outlet weir and outlet drop/weir were also assessed, but were not feasible without increasing the size of the culvert. Furthermore, a broken-back culvert was not considered and the culvert is too large for a riprap apron.

1. Tumbling flow (Chapter 7): Five elements 0.59 m in height spaced 5.02 m apart are required to reduce the velocity to V_c = 3.36 m/s. In order to accomplish this reduction, the last 25.1 m of culvert is used for the elements (4 spacing lengths between elements plus one-half spacing length before the first element and after the last element). In addition, this portion of the culvert must be increased in height to 2.1 m to accommodate the elements.
2. Increased resistance (Chapter 7): For a roughness height, h = 0.12 m, the internal resistance, n_LOW= 0.039 for velocity check and n_HIGH= 0.052 for Q check. The velocity at the outlet is 4.4 m/s. The elements are 1.2 m apart for 28 rows. Therefore, the modified culvert length required to accommodate the roughness elements is 33.6 m (27 spacing lengths between elements plus one-half spacing length before the first element and after the last element).
3. USBR Type IV stilling basin (Chapter 8): The dissipator length, L_B = 21.6 m, is located below the streambed at elevation 25.0 m. The total length of the stilling basin including transitions is 38.6 m. The exit velocity, V₂, is 4.85 m/s, which matches the channel velocity, V_n, of 4.846 m/s.
4. SAF stilling basin (Chapter 8): The dissipator length, L_B = 3.353 m, is located below the streambed at elevation 27.889 m. The total length of the stilling basin including transitions is 12.192 m. The exit velocity, V₂, is 4.877 m/s, which is close to channel velocity, V_n, of 4.846 m/s.
5. USBR Type VI impact basin (Chapter 9): The dissipator width, W_B, is 3.5 m. The height, h₁, equals 2.68 m and length, L, equals 4.65 m. The exit velocity, V_B, equals 3.7 m/s, which is calculated knowing the energy loss is 61 percent.

Step 5. Select Energy Dissipator.

The dissipator selected should be governed by comparing the efficiency, cost, natural channel compatibility, and anticipated scour for all the alternatives.

In this example, all the structures highlighted fit the channel, meet the velocity criteria, and produce significant energy losses. However, the costs of the USBR Type VI are lower than the other dissipators, so becomes the dissipator of choice.

Design Example: RCB (Fr > 3) with Defined Downstream Channel (CU)

Evaluate the outlet velocity from a 10 ft x 6 ft reinforced concrete box (RCB) culvert and determine the need for an energy dissipator.

Solution

Step 1. Identify Design Data:

1. Culvert Data: Type, D, B, L, n, S_o, Q, TW, Control, y_o, V_o, Fr_o

   RCB, D = 6 ft, B = 10 ft, L = 300 ft, n = 0.012

   S_o = 6.5%, Q = 417 ft³/s, TW = 1.9 ft, inlet control

   Elevation of outlet invert = 100 ft

   y_o = 1.5 ft, V_o = 27.8 ft/s, Fr_o = 4

2. Transition Data: y and V at end of apron, Chapter 4.

   The standard outlet with 45° wingwalls is an abrupt expansion. Since the culvert is in inlet control, the flow at the end of the apron will be supercritical: y = y_o = 1.5 ft and V = V_o = 27.8 ft/s

3. Channel Data: Q, S_o, geometry, n, z, b, y_n, V_n, debris, bedload

   Q = 417 ft³/s., S_o = 6.5%, trapezoidal, 1:2 (V:H), b = 10 ft, n = 0.03

   y_n = 1.9 ft, V_n = 15.9 ft/s

   Graded gravel bed with no boulders, little floating debris

4. Allowable Scour Estimate: h_s, W_s, L_s, D₁₆, D₈₄, σ, S_v, PI

   Scour hole should be contained within channel W_s = L_s = 10 ft and should be no deeper than 5 ft. This allowable estimate can be obtained by observing scour holes in the vicinity.

5. Stability Assessment:

   The channel, culvert, and related structures are evaluated for stability considering potential erosion, as well as buoyancy, shear, and other forces on the structure. If the channel, culvert, and related structures are assessed as unstable, the depth of degradation or height of aggradation that will occur over the design life of the structure should be estimated. In this case, the channel appears to be stable. No long-term degradation or head cutting was observed in the field.

Step 2. Evaluate Velocities.

Since V_o = 27.8 ft/s is much larger than V_n = 15.9 ft/s, increasing culvert n is not practical. Determine if a scour hole is acceptable (step 3) or design an energy dissipator (step 4).

Step 3. Evaluate Outlet Scour Hole.

h_s, W_s, L_s, V_s from Chapter 5. If these values exceed allowable values in step 1, protection is required.

y_e = 2.74 ft, h_s = 8.3 ft, W_s = 52 ft, L_s = 71 ft, V_s = 963 ft³

Scour appears to be a problem and consideration should be given to reducing the V_o = 27.8 ft/s to the 15.9 ft/s in the channel.

Step 4. Design Alternative Energy Dissipators.

The following dissipators were determined from Table 1.1 by comparing the limitations shown against the site conditions. Since Fr > 3, tumbling flow, increased resistance, as well as the USBR Type IV, SAF stilling basin, and USBR Type VI streambed level dissipators will be designed. The outlet weir and outlet drop/weir were also assessed, but were not feasible without increasing the size of the culvert. Furthermore, a broken-back culvert was not considered and the culvert is too large for a riprap apron.

1. Tumbling flow (Chapter 7): Five elements 1.92 ft in height spaced 16.3 ft apart are required to reduce the velocity to V_c = 11.0 ft/s. In order to accomplish this reduction, the last 81.5 ft of culvert is used for the elements (4 spacing lengths between elements plus one-half spacing length before the first element and after the last element). In addition, this portion of the culvert must be increased in height to 6.7 ft to accommodate the elements.
2. Increased resistance (Chapter 7): For a roughness height, h = 0.4 ft, the internal resistance, n_Low,equals 0.039 for velocity check and n_HIGHequals 0.052 for Q check. The velocity at the outlet is 14.5 ft/s. The elements are 4.0 ft apart for 28 rows. Therefore, the modified culvert length required to accommodate the roughness elements is 112 ft (27 spacing lengths between elements plus one-half spacing length before the first element and after the last element).
3. USBR Type IV stilling basin (Chapter 8): The dissipator length, L_B = 70.9 ft, is located below the streambed at elevation 82.0 ft. The total length of the stilling basin including transitions is 126.5 ft. The exit velocity, V₂, is 16 ft/s, which is close to channel velocity, V_n, of 15.9 ft/s.
4. SAF stilling basin (Chapter 8): The dissipator length, L_B = 11 ft is located below the streambed at elevation 91.5 ft. The total length of the stilling basin including transitions is 40 ft. The exit velocity, V₂, is 16 ft/s, which is close to channel velocity, V_n, of 15.9 ft/s.
5. USBR Type VI impact basin (Chapter 9): The dissipator width, W_B, is 12 ft. The height, h₁ = 9.17 ft and length, L = 16 ft. The exit velocity, V_B, equals 12.9 ft/s, which is calculated knowing the energy loss is 61 percent.

Step 5. Select Energy Dissipator.

The dissipator selected should be governed by comparing the efficiency, cost, natural channel compatibility, and anticipated scour for all the alternatives.

In this example, all the structures highlighted fit the channel, meet the velocity criteria, and produce significant energy losses. However, the costs of the USBR Type VI are lower than the other dissipators, so becomes the dissipator of choice.

Design Example: RCB (Fr < 3) with Undefined Downstream Channel (SI)

Evaluate the outlet velocity from a 3048 mm x 1829 mm reinforced concrete box (RCB) and determine the need for an energy dissipator.

Solution

Step 1. Identify Design Data.

1. Culvert Data: Type, D, B, L, n, S_o, Q, TW, Control, y_o, V_o, Fr_o

   RCB, D = 1.524 m, B = 1.524 m, L = 64.922 m, n = 0.012

   S_o = 3.0%, Q = 5.66 m³/s, TW = 0.0 m, inlet control

   Elevation of outlet invert = 30.480 m

   y_o = 0.655 m, V_o = 5.791 m/s, Fr_o = 2.3

2. Transition Data: y and V at end of apron, Chapter 4

   The standard Outlet with 90° headwall is an abrupt expansion. Since the culvert is in inlet control, the flow at the end of the apron will be supercritical: y = y_o = 0.655 m and V = V_o = 5.791 m/s

3. Channel Data: Q, S_o, geometry, n, z, b, y_n, V_n, debris, bedload

   The downstream channel is undefined. The water will spread and decrease in depth as it leaves the culvert making tailwater essentially zero. The channel is graded sand with no boulders and has moderate to high amounts of floating debris.

4. Allowable Scour Estimate: h_s, W_s, L_s, D₁₆, D₈₄, σ, S_v, PI

   A scour basin not more than 0.914 meters deep is allowable at this site. Allowable outlet velocity should be about 3 m/s.

5. Stability Assessment:

   The channel, culvert, and related structures are evaluated for stability considering potential erosion, as well as buoyancy, shear, and other forces on the structure. If the channel, culvert, and related structures are assessed as unstable, the depth of degradation or height of aggradation that will occur over the design life of the structure should be estimated. In this case, the channel appears to be stable. No long-term degradation or head cutting was observed in the field.

Step 2. Evaluate Velocities.

Since V_o = 5.791 m/s is much larger than V_allow = 3.0 m/s, increasing culvert n is not practical. Determine if a scour hole is acceptable (step 3) or design an energy dissipator (step 4).

Step 3. Evaluate Outlet Scour Hole.

h_s, W_s, L_s, V_s from Chapter 5. If these values exceed allowable values in step 1, protection is required.

y_e = 0.707 m, h_s = 1.707 m, W_S = 9.449 m, L_S = 14.935 m, V_S = 62 m³

Since 1.707 m is greater than the 0.914 m allowable, an energy dissipator will be necessary.

Step 4. Design Alternative Energy Dissipators.

The following dissipators were determined from Table 1.1 by comparing the limitations shown against the site conditions. For comparison purposes all the Fr < 3 dissipators will be designed (even those that cannot handle a moderate amount of debris). Dissipators meeting the Froude number requirement, but not designed are as follows (reason for exclusion in parentheses): SAF stilling basin (requires tailwater), Contra Costa basin (no defined channel); Broken-back culvert (mild site slope); outlet weir (infeasible without increasing culvert size); and riprap apron (culvert too large).

1. Tumbling flow (Chapter 7): The S_o = 3% is less than the 4% required, but the design is included for comparison. Five elements 0.55 m in height spaced 4.68 m apart are required to reduce the velocity to V_c = 3.32 m/s. In order to accomplish this reduction, the last 23.4 m of the culvert is used for the elements (4 spacing lengths between elements plus one-half spacing length before the first element and after the last element). In addition, this portion of the culvert must be increased in height to 2.0 m to accommodate the elements.
2. Increased resistance (Chapter 7): For a roughness height, h = 0.09 m, the internal resistance, n_LOW = 0.032 for velocity check and n_HIGH = 0.043 for Q check. The discharge check indicates that the culvert height has to be increased to 1.7 m. The velocity at the outlet is 3.2 m/s. The elements are 0.9 m apart for 34 rows. Therefore, the modified culvert length required to accommodate the roughness elements is 30.6 m (33 spacing lengths between elements plus one-half spacing length before the first element and after the last element).
3. CSU rigid boundary basin (Chapter 9): Width of basin, W_B = 9.144 m, length of basin, L_B = 8.534 m, number of roughness rows, N_r = 4, number of elements, N = 17, divergence, U_e = 1.9:1, width of elements, W₁ = 0.914 m, height of elements, h = 0.229 m, velocity at basin outlet, V_B = 2.896 m/s, depth at basin outlet, y_B = 0.213 m.
4. USBR Type VI impact basin (Chapter 9): The dissipator width, W_B, is 4.0 m. The height, h₁ = 3.12 m, and length, L = 5.33 m. The exit velocity, V_B, equals 4.2 m/s, which is calculated knowing the energy loss is 47 percent.
5. Hook basin (Chapter 9): Assuming the downstream velocity, V_n, equals the allowable, 3.0 m/s, V_o/V_n = 5.791/3.0 = 1.93. The dimensions for a straight trapezoidal basin are: length, L_B = 4.572 m, width, W₆ = 2W_o = 3.048 m, side slope = 2:1, length to first hook, L₁ = 1.905 m, length to second hooks, L₂ = 3.179 m, height of hook, h₃ = 0.716 m, target exit velocity, V_B = V_n = 3.0 m/s. From Figure 9.12, V_o/V_B = 2.0; actual V_B = 5.8/2.0 = 2.896 m/s, which is less than the target.
6. Riprap basin (Chapter 10): Assuming a diameter of rock, D₅₀ = 0.38 m, the depth of pool, h_s = 0.78 m, length of pool = 7.8 m, length of apron = 3.9 m, length of basin = 11.7 m, thickness of riprap on approach, 3D₅₀ = 1.14 m, and thickness of riprap for the remainder of basin, 2D₅₀ = 0.76 m.

Step 5. Select Energy Dissipator.

The dissipator selected should be governed by comparing the efficiency, cost, natural channel compatibility, and anticipated scour for all the alternatives.

Right-of-way (ROW), debris, and dissipator cost are all constraints at this site. ROW is expensive making the longer dissipators more costly. Debris will affect the operation of the impact basin and may be a problem with the CSU roughness elements and tumbling flow designs. In the final analysis, the riprap basin was selected based on cost and anticipated maintenance.

Design Example: RCB (Fr < 3) with undefined Downstream Channel (CU)

Evaluate the outlet velocity from a 5 ft by 5 ft reinforced concrete box (RCB) and determine the need for an energy dissipator.

Solution

Step 1. Identify Design Data.

1. Culvert Data: Type, D, B, L, n, S_o, Q, TW, Control, y_o, V_o, Fr_o

   RCB, D = 5 ft, B = 5 ft, L = 213 ft, n = 0.012

   S_o = 3.0%, Q = 200 ft³/s, TW = 0.0 ft, inlet control

   Elevation of outlet invert = 100 ft

   y_o = 2.15 ft, V_o = 19 ft/s, Fr_o = 2.3

2. Transition Data: y and V at end of apron, Chapter 4

   The standard Outlet with 90° headwall is an abrupt expansion. Since the culvert is in inlet control, the flow at the end of the apron will be supercritical: y = y_o = 2.15 ft and V = V_o = 19 ft/s

3. Channel Data: Q, S_o, geometry, n, z, b, y_n, V_n, debris, bedload

   The downstream channel is undefined. The water will spread and decrease in depth as it leaves the culvert making tailwater essentially zero. The channel is graded sand with no boulders and has moderate to high amounts of floating debris.

4. Allowable Scour Estimate: h_s, W_s, L_s, D₁₆, D₈₄, σ, S_v, PI

   A scour basin not more than 0.914 meters deep is allowable at this site. Allowable outlet velocity should be about 10 ft/s.

5. Stability Assessment:

   The channel, culvert, and related structures are evaluated for stability considering potential erosion, as well as buoyancy, shear, and other forces on the structure. If the channel, culvert, and related structures are assessed as unstable, the depth of degradation or height of aggradation that will occur over the design life of the structure should be estimated. In this case, the channel appears to be stable. No long-term degradation or head cutting was observed in the field.

Step 2. Evaluate Velocities.

Since V_o = 19 ft/s is much larger than V_allow = 10 ft/s, increasing culvert n is not practical. Determine if a scour hole is acceptable (step 3) or design an energy dissipator (step 4).

Step 3. Evaluate Outlet Scour Hole.

h_s, W_s, L_s, V_s from Chapter 5. If these values exceed allowable values in step 1, protection is required.

y_e = 2.32 ft, h_s = 5.6 ft, W_S = 32 ft, L_S = 49 ft, V_S = 81 yd³

Since 5.6 ft is greater than the 3.0 ft allowable, an energy dissipator will be necessary.

Step 4. Design Alternative Energy Dissipators.

The following dissipators were determined from Table 1.1 by comparing the limitations shown against the site conditions. For comparison purposes all the Fr < 3 dissipators will be designed (even those that cannot handle a moderate amount of debris). Dissipators meeting the Froude number requirement, but not designed are as follows (reason for exclusion in parentheses): SAF stilling basin (requires tailwater), Contra Costa basin (no defined channel); Broken-back culvert (mild site slope); outlet weir (infeasible without increasing culvert size); and riprap apron (culvert too large).

1. Tumbling Flow (Chapter 7): The S_o = 3% is less the 4% required, but the design is included for comparison. Five elements 1.8 ft in height spaced 15.4 ft apart are required to reduce the velocity to V_c = 10.9 ft/s. In order to accomplish this reduction, the last 77.0 ft of the culvert is used for the elements (4 spacing lengths between elements plus one-half spacing length before the first element and after the last element). In addition, this portion of the culvert must be increased in height to 6.5 ft to accommodate the elements.
2. Increased resistance (Chapter 7): For a roughness height, h = 0.3 ft, the internal resistance, n_LOW = 0.032 for velocity check and n_HIGH = 0.043 for Q check. The discharge check indicates that the culvert height has to be increased to 5.6 ft. The velocity at the outlet is 10.6 ft/s. The elements are 3.0 ft apart for 34 rows. Therefore, the modified culvert length required to accommodate the roughness elements is 102 ft (33 spacing lengths between elements plus one-half spacing length before the first element and after the last element)
3. CSU Rigid Boundary basin (Chapter 9): Width of basin, W_B = 30 ft, length of basin, L_B = 28 ft, number of roughness rows, N_r = 4, number of elements, N = 17, divergence, U_e = 1.9:1, width of elements, W₁ = 3.0 ft, height of elements, h = 0.75 ft, velocity at basin outlet, V_B = 9.5 ft/s, depth at basin outlet, y_B = 0.70 ft.
4. USBR Type VI (Chapter 9): The dissipator width, W_B, is 13 ft. The height, h₁ = 10.17 ft, and length, L = 17.33 ft. The exit velocity, V_B, equals 13.9 ft/s, which is calculated knowing the energy loss is 47 percent.
5. Hook (Chapter 9): Assuming the downstream velocity, V_n, equals the allowable, 10 ft/s, V_o/V_n = 19/10 = 1.9. The dimensions for a straight trapezoidal basin are: length, L_B = 15 ft, width, W₆ = 2W_o = 10 ft, side slope = 2:1, length to first hook, L₁ = 6.25 ft, length to second hooks, L₂ = 10.43 ft, height of hook, h₃ = 2.35 ft, target exit velocity, V_B = V_n = 10 ft/s. From Figure 9.12, V_o/V_B = 2.0; actual V_B = 19/2.0 = 9.5 ft/s which is less than the target.
6. Riprap basin (Chapter 10): Assuming a diameter of rock, D₅₀ = 1.2 ft, the depth of pool, h_s = 2.7 ft, length of pool = 27 ft, length of apron = 13.5 ft, length of basin = 40.5 ft, thickness of riprap on approach, 3D₅₀ = 3.6 ft, and thickness of riprap for the remainder of basin, 2D₅₀ = 2.4 ft.

Step 5. Select Energy Dissipator.

The dissipator selected should be governed by comparing the efficiency, cost, natural channel compatibility, and anticipated scour for all the alternatives.

Right-of-way (ROW), debris, and dissipator cost are all constraints at this site. ROW is expensive making the longer dissipators more costly. Debris will affect the operation of the impact basin and may be a problem with the CSU roughness elements and tumbling flow designs. In the final analysis, the riprap basin was selected based on cost and anticipated maintenance.