MODULE 3 OPEN CHANNEL DESIGN Introduction An open channel is defined as any conveyance system where a liquid is moved under the influence of gravity in the presence of an air-water interface. Open channel flow occurs in natural water courses, channels, diversions, and culverts. In all of these cases, the energy source causing the water to move is gravity; water flows down hill. This chapter will discuss the principles and equations needed to properly analyze and design open channels used to convey water. There are two accepted methods of designing open channels; (1) to limit the average water velocity, or () limit the tractive force (shear stress) on the channel lining. Depth of water and channel slope tend to increase both of these parameters thus causing the channel lining and the soil under the lining to erode. The continuity equation Q = AV (1) where Q is the discharge in ft 3 /sec (cfs), A is the channel s cross-sectional area of flow in ft, and V is the average flow velocity perpendicular to the cross-sectional area in ft/sec or fps. The cross-sectional area used in equation 1, is the area through which the water is flowing as it moves down a channel, see Figure 3-1. Figure 3-1. Typical Channel Cross Section. F Wetted parameter Cross-sectional area The velocity of water flowing in an open channel, has been described by Manning's equation (Chow, 1959) as:
V = 1.486 1 R 3 S n () where V is the average flow velocity in a channel in fps, n is the Manning s roughness coefficient with units of ft 1/6, R is the hydraulic radius in ft, and S is the channel s slope in direction of flow in ft/ft. The Manning s n is obtained from a descriptive statement of the channel roughness. Typical design Manning s n values are shown in Table 3-1 and Figure 3-3. In both of these presentations the accepted design roughness Manning n values are given. Other references such as Chow (1959) and Schwab et al. (1966) show ranges of Manning roughness coefficients for most of these conditions. There is no substitute for experience in interpreting and selecting values of n. The parameter called the hydraulic radius, R is defined as: A R = (3) where the cross-sectional area, A and the wetted perimeter, W p are defined in Figure 3-1. In a crude way the hydraulic radius can be thought of as the depth of flow. The basic geometric relationships of cross-sectional area, wetted perimeter, hydraulic radius, and top width are given in Figure 3- for several common channel shapes. Most channels can be approximated by one of the five geometric shapes shown in Figure 3-. The area, wetted perimeter, and hydraulic radius formulae are most often used in evaluation and design computations. The top width formulae are useful when designing a channel. Most of the parameters shown in the sketches and used in the formulae are self explanatory; d is the water flow depth in feet, D is the total depth of the channel in feet (D is equal to the flow depth, d plus freeboard) [D = d + F], b is the channel s bottom width in feet, t is the channel top width at the depth of water flow, T is the channel top width at the channel s total depth, D in feet, and z is the side slope expressed as a ratio as z(h):1(v). z is shown as being equal to the ratio e/d where e is the horizontal distance and d is the vertical distance of the sloping side of a channel. In general, Manning's equation can be used with the continuity equation to; (1) describe and evaluate the capacity and velocity of an existing channel, or () to determine the required channel dimensions so the desired amount of water can be safely transported. Channel Freeboard Freeboard is an unused portion of a structure created to hold or carry water. Freeboard is a way of adding or creating a factor of safety that is built into a water W p a. Trapezoidal Cross-Section Cross-Sectional Area, A Wetted Perimeter, W p Hydraulic Radius, R = A/W p Top Width
D d t b e bd + zd b+ d z + 1 or b+ dz approximate bd + zd b+ d z + 1 or bd + zd b+ dz t = b+ dz T = b+ Dz b. Triangular Cross-Section t D d d e Cross-Sectional Area, A Wetted Perimeter, W p zd d z + 1 or dz approximate Hydraulic Radius, R = A/W p zd d z + 1 or d Top Width t = dz T = Dz c. Parabolic Cross-Section t D d Cross-Sectional Area, A 3 td Wetted Perimeter, W p t d + 8 3t or t approximate Hydraulic Radius, R = A/W p t d 15. t + 4d or d 3 T t Top Width A = 067d. = t( D/ d) 05. d. Semi-Circular Cross-Section t Cross-Sectional Area, A π d Wetted Perimeter, W p πd Hydraulic Radius, R = A/W p d Top Width t = d d e. Rectangular Cross-Section t D d Cross-Sectional Area, A bd Wetted Perimeter, W p b + d Hydraulic Radius, R = A/W p bd b + d Top Width t = b T = b b Figure 3-. Channel cross-section notation and formulas for a. trapezoidal, b. triangular, c. parabolic, d. semi-circular, and e. rectangular channels. Freeboard = D - d. (Adapted from USDA-SCS 197c)
structure. When a channel is properly designed, most of the channel depth is expected to fill with and carry water when the design discharge occurs. Schwab et al. (1966) states that all channels should have a minimum freeboard of 0. feet. A second, often used freeboard concept is to make freeboard a function of the flow velocity and the flow depth. PA-DER (1990) requires that channel freeboard be greater than or equal to F = 0. 075Vd (4) where V is the channel flow velocity in fps and d is the depth of water in feet. The best method of determining channel freeboard is to prescribe the larger of these two criteria. Channel Design Process Open channels, whose flow is governed by Manning s and the continuity equations can be evaluated or designed based on two different concepts. Failure of an open channel can occur as a result of either of two conditions; (1) the channel does not have the capacity to carry the water it was designed to carry and overbank flooding occurs, and () the channel lining does not have the ability to with stand the flow velocities or shear stresses on the channel lining and, therefore, erodes. One method is to determine the maximum permissible velocity of the channel lining and then select the channel s geometry so that the velocity does not exceed this value. The second method is based on the shear stress or tractive force acting on the channel lining. Again, based on the lining s ability to withstand a tractive force, the channel s geometry is selected so the tractive force does not exceed the maximum allowable tractive force. Both of these methods will be presented. But before these two design approaches are presented, let s take a look at channel linings and define the design parameters for each lining. Channel Linings Open channels are typically distinguished by either their shape (trapezoidal, triangular, parabolic, circular, or rectangular) of their lining. How various shapes affect the flow of water in the channel will be discussed at length during the design section of the module. Channel linings can be classified several ways: (1) by the effect the lining has on the friction or roughness of the channel, () by the effect the lining has on preventing channel erosion, (3) by how quickly the lining will biodegrade and disappear, (4) by how hard and permanent the lining is, and (5) by how much maintenance the lining will need.
Table 3-1. Manning s roughness coefficients. (Summarized and adapted from Schwab et al., 1966, USDA-SCS, 197b, and PA-DER, 1990). Type of Channel and Lining Design n Rigid Lined Channels Asphalt 0.015 Concrete 0.017 Concrete rubble 0.04 Gabions 0.07 Metal, smooth (flumes) 0.013 Metal, corrugated 0.07 Plastic lined 0.013 Reno Mattress 0.05 Shotcrete 0.016 Wood, (flumes) 0.013 Earth Lined Channels Firm loam, fine sand, sandy loam, silt loam 0.0 Stiff clay, alluvial silts, colloidal 0.05 Shales, hardpans, coarse gravels 0.05 Graded silt or loam 0.03 Alluvial silt 0.0 Earth, straight and uniform 0.03 Earth bottom, rubble sides 0.0 Coarse Gravel 0.0 Rock cuts, shale and hardpan 0.0 Durable rock cuts, jagged and irregular 0.0 Cobbles and shingles 0.035 Stony bed, weeds on bank 0.035 Straight, uniform 0.05 Winding, sluggish 0.05 Natural Stream Channels Clean, straight, full stage, deep pools 0.03 Clean, straight, full stage, weeds and stones 0.035 Winding, some pools and shoals 0.039 Sluggish river reaches, weedy, w/ deep pools 0.065 Very weedy reaches 0.11 Pipes Asbestos-Cement 0.009 Cast Iron 0.01 Clay, drainage tile 0.01 Concrete 0.015 Corrugated Plastic Drainage pipe 0.015 Metal, corrugated 0.05 Steel, riveted, spiral 0.016 Vitrified Sewer pipe 0.013
Manning s Roughness Coefficient, n For purposes of channel design and channel performance, channel linings are best divided into three categories, (1) linings with Manning s roughness coefficients that remain constant as the flow conditions in the channel change, () linings with Manning s roughness coefficients that change as the depth of flow increases, and (3) linings with Manning s roughness coefficients that change with a variety of flow conditions. Each of these three types of linings will be addressed separately. Linings with constant Manning s roughness coefficient. Channel linings that are generally considered to have constant roughness coefficients, meaning that Manning s n remains constant as the channel s flow depth and velocity change, are summarized in Table 3-1. Most of the linings listed in Table 3-1 are hard linings that have minimal or no biological components. The exceptions are the natural streams, which, in some cases are considered to change as the vegetation in the riparian buffer develops and matures. Linings with Manning s roughness coefficients that vary with flow depth. Rocks are valuable channel liners. In areas were velocities are too fast for bare soil or vegetated linings, rock placed by itself, as riprap, or placed in wire baskets, as gabions or Reno Mattresses, forms a channel lining that will yield very good protection against erosion. Riprap is a permanent, erosion-resistant ground cover of large, loose, angular stone. Riprap protects the soil surface from the erosive forces of concentrated flow. Riprap slows the velocity of concentrated runoff while enhancing the potential for infiltration and stabilizes slopes with seepage problems and/or non-cohesive soils. Riprap is classified as either graded or uniform depending on the range of rock sizes present in the rock mixture. Graded riprap should contain a mixture of stones that vary in size from about 0.5D to D. Uniform riprap contains stones that are all nearly the same size, D. Graded riprap is preferred to uniform riprap in erosion and sedimentation control. It is cheaper to install, requiring only that the stones be dumped so they remain a well-graded mass. Hand or mechanical placement of individual stones is limited to achieving the proper, uniform thickness. Stone for riprap should consist of fieldstone or rough unhewn quarry stone of approximately rectangular shape. The stone should be hard and angular and should not disintegrate on exposure to water or weathering. Riprap should be placed by end dumping (from a truck) to prevent segregation by sizes. It should never be pushed downhill by a dozer or dropped down a chute, because these operations cause segregation of particles.
0.10 0.09 Manning's n 0.08 0.07 0.06 0.05 0.04 1 in in in 4 in5 3 in 6 in 8 in 10 in 1 in 0.03 0.0 0.01 0.00 0.1 1 10 Flow Depth, d (ft) Figure 3-3. Manning's roughness coefficients for riprap lined channels. (Taken from PA-DER, 1990). In open channels, lined with rock, the Manning s roughness coefficient is greatest at shallow depths of water and decreases as the depth of water increases. Figure 3-3 shows that when the depth of water in a rock or riprap lined channel is of the same order of magnitude as the rock lining (d/d 1), the friction is very high, i.e. Manning s n = 0.06 to 0.07. As the depth of flow increases relative to the rock size (d/d > 10, the friction decreases and approaches a constant that is dependent on the rock size used in the lining, i.e. n = 0.05 for D = 1" rock; n = 0.08 for D = " rock and n = 0.0 for D = 3" rock. The curves plotted in Figure 3-3 are the solution to the following equation (USDA- NRCS, 1977) 1 6 d n = (5) 1.6 log ( d / D ) + 14.0] [ 10
where d is the depth of flow in the rock-lined channel in feet, D is the average rock diameter in feet and n is Manning's roughness coefficient. According the PADEP (000), some of the newer temporary erosion blankets also create a situation where Manning s n varies with flow depth, see Table 3-. Table 3-. Manning s roughness coefficients (n) for commonly used temporary channel linings. (PADEP, 000). Manning s n Water Depth Ranges Lining Type 0 0.5 ft 0.5.0 ft >.0 ft Jute Net 0.08 0.0 0.019 Curled Wood Mat 0.066 0.035 0.08 Synthetic Mat 0.036 0.05 0.01 Linings with Manning s roughness coefficients that vary with flow depth and velocity. Vegetation lined channels have roughness coefficients that vary greatly depending on the type of vegetation and the length of the vegetation. Table 3-3. Retardance Classifications of Various Grasses. (Adapted from USDA-SCS, 1947). Retardance Class Cover Condition A. Very High a = -0.5 Weeping love grass Yellow bluestem ischaemum Excellent stand, tall (avg in) Excellent stand, tall (avg 36 in) B. High a = C. Moderate a = 5 D. Low a = 7 E. Very Low a = 11 Kudzu Bermuda grass Native grass mixture (little blue-stem, blue gama, and other long and short Midwest grasses. Grass-legume mixture (Timothy, bromegrass) Weeping love grass Lespedeza series Alfalfa Blue Gama Crab grass Bernuda grass Common lespedeza Grass-legume mixture-summer (orchard grass, redtop, Italian rye grass, common lespedeza) Centipede grass Kentucky bluegrass Bermuda grass Common lespedeza Buffalo grass Grass-legume mixture-summer (orchard grass, redtop, Italian rye grass, common lespedeza) Lespedeza series Bermuda grass Bermuda grass Very dense growth, uncut Good stand, tall (avg 1 in) Good stand, unmowed Good stand, uncut (avg 0 in) Good stand, tall (avg 13 to 4 in) Good stand, not woody, tall (avg 19 in) Good stand, uncut (avg 11 in) Good stand, uncut (avg 13 in) Fair stand, uncut (avg 10-48 in) Good stand, Mowed (avg 6 in) Good stand, uncut (avg 11 in) Good stand, uncut (6 to 8 in) Very dense cover (avg 6 in) Good stand, headed (avg 6-1 in) Good stand, cutto.5 in height Excellent stand, uncut (avg 4.5 in) Good stand, uncut (avg 3-6 in) Good stand, uncut (avg 4-5 in) After cutting to -in height, very good stand before cutting Good stand, cut to 1.5-inch height Burned stubble
Table 3-3 shows additional information required to select the retardance classes for the vegetation. This table also shows the a coefficient needed to apply equation 6, which computes the Manning s roughness coefficient as a function of the flow velocity (fps) and the hydraulic radius (ft) (Schwab et al., 1993) 1 n = [.1+.3a + 6 ln(1.017vr)]. (6) In addition to the difficulties that come from having a roughness coefficient that varies with VR, it is also necessary to account for whether the grass will be maintained at or near a constant height or left to grow throughout the growing season. As can be seen in Table 3-3, most grasses change retardance classes when they are left to grow. For example Bermuda grass can be in classes B, C, D, or E depending on how high it is mowed. Table 3-4. Maximum permissible velocities for non-vegetated channel linings. (Adapted from USDA-SCS, 197b and PA-DER, 1990). 1 Channel Linings Maximum Permissible Velocity (ft/sec) Earth Lined Channels Fine Sand 1. Sandy Loam 1.75 Silt Loam (non-colloidal).00 Ordinary Firm Loam, Fine gravel. Stiff Clay (very colloidal) 3.75 Graded, Loam 3.75 Alluvial Silts (colloidal) 3.75 Graded, Silt 4.0 Coarse Gravel (non-colloidal) 4.0 Cobbles and Shingles 5.0 Shales and Hardpans 6.0 Durable Bedrock 8.0 Rolled Erosion Control Products (RECP) Am. Excelsior Co.; Curlex Net Free 3.0 Am. Excelsior Co.; Straw; 1 net 3.5 Am. Excelsior Co.; Straw; nets 4.5 N. Am. Green; Straw; single net 5.0 Am. Excelsior Co.; Curlex I.73; 1 net 5.0 Geocoir/Dekowe; Straw; RS-1 6.0 N. Am. Green; Straw; double net 6.0 Am. Excelsior Co.; Curlex I.98; 1 net 6.0 Am. Excelsior Co.; Curlex II.73; nets 7.0 N. Am. Green; 70% straw: % Coconut; double net 8.0 Geocoir/Dekowe; 8.0 Geocoir/Dekowe; Straw; RS- 8.0 Am. Excelsior Co.; Curlex II.98; nets 8.5 N. Am. Green; Polypropylene; double net; Bare soil 9.0 Geocoir/Dekowe; 70% Straw % Coconut; RSS/C-3 10.0 1 Company names are used for clarity and do not imply endorsement by NCSU or NC DOT.
N. Am. Green; Coconut; double net 10.0 Am. Excelsior Co.; Curlex III; nets 10.0 Am. Excelsior Co.; Curlex Enforcer; nets; Bare soil 10.0 Am. Excelsior Co.; Curlex High Velocity; nets 10.0 Geocoir/Dekowe; 700 10.0 Geocoir/Dekowe; Poly/Fiber; RSP-5 1.0 Geocoir/Dekowe; Coconut, RSC-4 1.0 Geocoir/Dekowe; 900 15.0 N. Am. Green; Polypropylene; double net; Vegetated 16.0 Turf Reinforced Mats (TRM) North American Green SC; Bare soil 9.5 North American Green C3; Bare soil 10.5 Profile/Enkamat; 7003, seed w/ bonded fiber matrix (BFM) 1.0 North American Green P5; Bare soil 1.5 Profile/Enkamat II; seed and BFM; Bare 13.0 Profile/Enkamat; 7010, 7018, 700, seed and hydromulch 14.0 Profile/Enkamat; 7010 70, seed and BFM; Vege. 14.0 North American Green SC; Vegetated 15.0 Am. Excelsior Co.; Recyclex 17.0 Profile/Enkamat II; seed and BFM; Vege. 19.0 Profile/Enkamat; 790, seed and BFM; Vege. 19.0 North American Green C3; Vegetated 0.0 Profile/Enkamat; 7010-70, seed and BFM; Bare 0.0 North American Green P5; Vegetated 5.0 Rock Lined Channels a Graded Rock, D (inches) 0.75 [Min = No. 8; Max = 1.5 ]. 1. [Min = 1 ; Max = 3 ] 4. 3.00 [Min = ; Max = 6 ] 6. 6.00 [Min = 3 ; Max = 1 ] 9.00 9.00 [Min = 5 ; Max = 18 ] 11. 1.00 [Min = 7 ; Max = 4 ] 13.00 15.00 [Min = 1 ; Max = ] 14. Reno Mattress, 3 to 6-inch rock, 6 inches thick 13. Reno Mattress, 3 to 6-inch rock, 9 inches thick 16.00 Reno Mattress, 4 to 6-inch rock, 1 inches thick 18.00 Gabions.00 Rigid Lined Channels Asphalt 7.00 Wood 9.00 a D refers to the median rock size in graded rock. Maximum Permissible Velocities, V max When designing a channel using the maximum permissible velocity procedure, it is necessary to have reliable values of V max available for use in Manning s equation (V = V max ). Maximum permissible velocities non-vegetated linings are presented in Table 3-4. Table 3-5 contains the maximum permissible velocities for vegetative linings. Because these linings are living plants that are rooted in the soil from which the channel was cut, it is necessary to not only consider the type of vegetation, but also the
erosiveness of the soil in which the vegetation is growing and the slope of the channel. In this table the channel s soil is divided into two categories defined by the RUSLE s K-value found in Module, erosion resistant (K < 0.37) and easily eroded (K > 0.37). The values given in Table 3-5 are for good vegetative stands. If the stand of vegetation used provides less than full coverage, the values in Table 3-5 should be decreased accordingly. Table 3-5. Maximum permissible velocities for vegetation lined channels. (Modified from Ree, 1949 and PA-DER, 1990). Maximum Permissible Velocities Erosion Resistant Soils Easily Eroded Soils K < 0.37 K > 0.37 (percent slope) (percent slope) 0-5 5-10 Over 10 0-5 5-10 Over 10 Cover fps fps fps fps fps fps Bermuda Grass 8 7 6 6 5 4 Buffalo Grass Kentucky Bluegrass Smooth Bromegrass 7 6 5 5 4 3 Blue Grama Tall Fescue Grass Mixture 5 4 NR a 4 3 NR Reed Canarygrass 5 4 NR 4 3 NR Lespedeza Weeping Lovegrass Red Top Kudzu 3.5 NR NR.5 NR NR Alfalfa Red Fescue Crabgrass Annuals for Temporary Protection 3.5 NR NR.5 NR NR Sudangrass 3.5 NR NR.5 NR NR a Not Recommeded. Maximum Allowable Shear Stress or Tractive Force, τ all Maximum allowable tractive force is a measure of the shear stress exerted by the flowing water on the channel lining. If the actual shear stress, in lbs/ft, exceeds the maximum allowable shear stress or tractive force, the flowing water will erode the channel, usually at its deepest depth. Maximum allowable tractive forces for non-cohesive soils smaller than 6.35 mm (sands and gravels) are given in Figure 3-4. Allowable tractive forces for a wide variety of channel linings are shown in Table 3-6. The dimensions for the North Carolina rock classification are given in Table 3-7. Suggested products for use in controlling erosion on side slopes are given in Table 3-8.
Allowable Tractive Force; D 75 < 6.35 mm Allowabe Tractive Force (lbs/ft ) 1.00 0.10 Clear Water Low Content High Content 0.01 0.1 1.0 10.0 Median Particle Size (D ) mm Figure 3-4. Allowable tractive forces for non-cohesive soils; D 75 < 6.35 mm or 0.5 inches (Adapted from USDA-SCS, 1964). Finally, it is important to note that the tractive force, or shear stress in a channel does not remain constant across the entire channel. Figure 3-6 shows how the shear stress changes across a trapezoidal channel. The important thing to keep in mind is that shear stress is almost always maximum at the point in the channel where the depth of flow is the greatest. Table 3-6. Allowable Tractive Forces and Manning s n Values for Various Channel Linings (PADEP, 000). 1 Allowable Tractive Force, τ (lbs/ft ) Channel Lining Category Lining Type Unlined Erodible Soils (K > 0.37) Silts, Fine Medium Sands 0.03 Coarse Sands 0.04 Very Coarse Sands 0.05 Fine Gravel 0.10 Erosion Resistant Soils (K < 0.37) Sandy loam 0.0 Gravely, Stony, Channery loam 0.05 Stony or Channery silt loam 0.07 Loam 0.07 Sandy clay loam 0.10 Silt loam 0.1 Silty clay loam 0.18 Clay loam 0.5 Shale & Hardpan 1.00 Durable Bedrock.00 RECP Jute Netting 0.45 Geocoir/Dekowe; Straw; RS-1 0.83 Profile; Futerra 1.00 Am. Excelsior Co.; Curlex Net Free 1.00 Am. Excelsior Co.; Straw; 1 net 1.5 Geocoir/Dekowe; Straw; RS- 1.5
E. Coast Ero. Blank.; Straw/Coir, Jute 1.35 nets Am. Excelsior Co.; Straw; nets 1. N. Am. Green; Straw; single net 1.55 Am. Excelsior Co.; Curlex I.73; 1 net 1.55 E. Coast Ero. Blank.; Straw, 1 net 1.55 E. Coast Ero. Blank.; Coir, Jute nets 1.63 Am. Excelsior Co.; Curlex I.98; 1 net 1.65 Am. Excelsior Co.; Curlex II.73; nets 1.75 N. Am. Green; Straw; double net 1.75 E. Coast Ero. Blank.; Excelsior, 1 net 1.80 Geocoir/Dekowe; 70% Straw % Coconut; 1.85 RSS/C-3 N. Am. Green; 70% straw: % Coconut;.00 double net N. Am. Green; Polypropylene; double net;.00 Bare soil Am. Excelsior Co.; Curlex II.98; nets.00 Geocoir/Dekowe; Poly/Fiber; RSP-5.00 Geocoir/Dekowe; Coconut, RSC-4.00 E. Coast Ero. Blank.; Excelsior, nets.00 E. Coast Ero. Blank.; Straw, Jute net.10 E. Coast Ero. Blank.; Straw, nets.10 N. Am. Green; Coconut; double net.5 Am. Excelsior Co.; Curlex III; nets. Am. Excelsior Co.; Curlex Enforcer; nets;. Bare soil E. Coast Ero. Blank.; Straw/Coir, nets.60 Am. Excelsior Co.; Curlex High Velocity; 3.00 nets Geocoir/Dekowe; 3.10 E. Coast Ero. Blank.; Coir, nets 3.0 E. Coast Ero. Blank.; Polypropylene, nets 3.1 Geocoir/Dekowe; 700 4.46 Geocoir/Dekowe; 900 4.63 N. Am. Green; Polypropylene; double net; 8.00 Vegetated Turf Reinforced Mats (TRM) North Am. Green SC; Bare soil. North Am. Green C3; Bare soil 3.00 North Am. Green P5; Bare soil 3.5 E. Coast Ero. Blank.; Coir, 3 nets 3. Profile/Enkamat; 7003, seed w/ bonded 5.00 fiber matrix (BFM) Profile/Enkamat; 7010, seed and 6.00 hydromulch Profile/Enkamat; 7010 70, seed and 6.0-8.0 BFM; Vege. Profile/Enkamat; 7010-70, seed and 6.7-11. BFM; Bare Profile/Enkamat; 7018, seed and 7.00 hydromulch North Am. Green SC; Vegetated 8.00 Profile/Enkamat; 700, seed and hydromulch 8.00
Profile/Enkamat II; seed and BFM; Vege. 8.00 Profile/Enkamat; 790, seed and BFM; 8.00 Vege. North Am. Green C3; Vegetated 10.0 Profile/Enkamat II; seed and BFM; Bare 10.0 Am. Excelsior Co.; Recyclex 10.0+ North Am. Green P5; Vegetated 1.5 Grass Liners Class D; a = 7 0.60 Class C; a = 5 1.00 Class B; a =.10 Aggregate & Riprap #57 0.5 (See Table 3-7) #5 0. Class A 1.00 Class B.00 Class 1 3.00 Class 4.00 Reno Mattress & Gabion 8.35 Concrete. Table 3-7. Aggregate and Riprap gradation. Graded Rock Size (in) Class or # Maximum D Minimum #57 1 ½ No. 8 #5 1 3/4 3/8 A 6 4 B 1 8 5 1 17 10 5 3 14 9
Figure 3-5. Channel lining selection guide. Table 3-8. Permissible Shear Stress of Various RECP s. (Adapted from Table 6.17a NCDENR (006)) 1 Category Product Type Max. Permissible Shear Stress (lbs/ft ) Slopes Up to RECP N. Am. Green; Straw; 1 net 1.55 3:1 Am. Excelsior Co.; Curlex Net Free 1.00 3:1 Am. Excelsior Co.; Straw; 1 net 1.5 3:1 Geocoir/Dekowe; Straw; RS-1 0.83 3:1 N. Am. Green; Straw; nets 1.75 :1 Am. Excelsior Co.; Curlex I.73; 1 net 1.55 :1 Am. Excelsior Co.; Curlex I.98; 1 net 1.65 :1 Am. Excelsior Co.; Straw; nets 1. :1 Geocoir/Dekowe; Straw; RS- 1.5 :1 Geocoir/Dekowe; 70% Straw % 1.85 :1 Coconut; RSS/C-3 Geocoir/Dekowe; Poly/Fiber; RSP-5.00 :1 Geocoir/Dekowe; Coconut, RSC-4.00 :1 Am. Excelsior Co.; Curlex II.73; nets 1.75 1.5:1 Am. Excelsior Co.; Curlex II.98; nets.0 1.5:1 Am. Excelsior Co.; Straw/Coconut; 1.5:1 nets N. Am. Green; 70% straw: % Coir;.00 1:1 nets N. Am. Green; Coconut; nets.5 1:1 Am. Excelsior Co.; Curlex III; nets.3 1:1 N. Am. Green; Polypropylene; nets;.0 1:1 Bare soil N. Am. Green; Polypropylene; nets; 8.0 1:1 Vegetated Am. Excelsior Co.; Coconut; nets 1:1 Am. Excelsior Co.; Curlex Enforcer; 0.75:1 nets Am. Excelsior Co.; Curlex High Velocity; 3.0 0.75:1 nets TRM Profile/Enka; 7003, Vege. 5.0 3.5:1 Profile/Enka; 7010, 710, 7910, Vege. 6.0 :1 Profile/Enka; 70, 700, Vege. 8.0 1.5:1 Profile/Enkamat II 8.0 1:1 Profile/Enka; 7, Vege. 8.0 0.5:1 Am. Excelsior Co.; Recyclex 10.0+ 0.5:1 NCDENR Specs Degradable RECP s Nets and Mulch 0.1 0. 0:1 (Unvegetated) Coir Mesh 0.4 3.0 3:1 Blanket Single Net 1.55.0 :1 Blanket Double net 1.65 3.0 1:1 Nondegradable Unvegetated 4 1:1 Turf Reinforced Mats Partially Vegetated 4 6 >1:1 Fully Vegetated 5-10 >1:1
Figure 3-6. How tractive force varies in a trapezoidal channel. Selecting Channel Linings Applying the maximum permissible velocity, Vmax criteria to channel lining selection is difficult, requiring that the lining be chosen before the channel is designed. The maximum allowable tractive force, can however be applied quite easily to channel lining selection. Tractive force, τ is a measure of the frictional resistance to flow in a channel and is the weight of the water in the channel on the channel bottom times the channel slope or τ = γrs. (7) In this equation τ is the average shear stress acting on the channel lining across the width of the channel. In a wide channel with a rectangular cross-section, the depth can be assumed to equal the hydraulic radius, d = R. If we substitute the depth into equation 7, we get an expression of shear stress that is a function of flow depth and slope as τ = γds. (8) In a channel with a rectangular cross-section, the tractive force is nearly constant, see Figure 3-5. In channels having cross-sections where the depth is not constant, the maximum tractive force occurs where the depth of flow is greatest. Thus, if τ is set equal to the maximum allowable shear stress (from one of the above tables or figures), equation 8 can be solved for, what is the maximum allowable flow depth, d max as d τ all = γs max (9)
Where S is the channel slope in feet/foot and γ is the unit weight of water (6.4 lbs/ft 3 ). In most cases, where channel linings are to be chosen, it is better to solve equation 9 for the maximum shear stress, which occurs at the point of maximum flow depth as τ max = γd max S. (10) By comparing the maximum shear stress from equation 10 with the maximum allowable shear stresses from the tables and figures above a channel lining can be selected. The following example will show the procedure. Table 3-9. North Carolina DOT guidelines for selecting channel linings. Channel Slope (%) Recommended Channel Lining 0.0 to 1.5 Seed and mulch >1.5 to 5.0 Temporary liners >5.0 Turf Reinforced Mats or Hard In North Carolina, DOT has a rule of thumb to assist in selecting road ditch linings. These guidelines are shown in Table 3-9. The following example will show that the NC DOT guidelines are consistent with meeting the allowable shear stress limitations. Example 1. A proposed triangular road ditch channel has :1 side slopes, a slope of 3%, and the road will be serviced by an 18-inch culvert; the design depth of flow in the proposed road ditch is generally about the same depth as the diameter of the culvert. Select a suitable channel lining for this channel. Solution: Since the road is serviced by an 18-inch culvert, it is safe to assume that the maximum flow depth in the ditch will be about 18 inches or 1.5 feet. From equation 10 compute the maximum shear stress in this channel as τ max = 6.4)(1.5)(0.0) = 1.9lbs / ( ft Now look on the tables and figures above and select a channel lining that has a maximum allowable shear stress that is >1.9 lbs/ft. Table 3-8 shows that a double-sided non-degradable RECP without vegetation maybe okay (actually this channel pushes the upper limits of when such a liner is expected to do the job of controlling erosion. This is consistent with the guidelines in Table 3-9. It should be noted that for slopes greater than the % used in this example, temporary liners are going to be subjected to excessive shear stresses and will be expected to fail. If this example is re-worked using a ditch slope of 1%, the maximum shear stress in the channel will be just less than 1.0 lbs/ft, which is probably okay for seed and mulch. If, with the flatter slope, we also assume a
smaller culvert, say 1-inch, then the shear stresses are more reasonable for the seed and mulch application. It is hard to understand how channel slope relates or controls depth of flow. North American Green Software A procedure, not greatly different from the one developed above for trapezoidal channels has been developed and published by North American Green, Inc (Lancaster and Nelsen, 00). This software package is available from North American Green, Inc and you are encouraged to go to http://www.nagreen.com/software/ and download the software package named ECMDS version 4. onto your own computer. Sizing Pipes for Open Channel Flow Though circular channels obey the continuity and Manning s equations, the geometry of circular channels is much more complex. Therefore, it is suggested that you use Figure 3-7 for sizing pipes that have relatively smooth linings such as clay or concrete pipe or corrugated plastic pipe with the smooth inner lining. For corrugated plastic pipe, Figure 3-8 is appropriate. In both of these figures the pipe slope, in %, is located on the x-axis and the pipe discharge, in gpm, is located on the y-axis. The solid sloping lines (low on the left and rising toward the right) represent each pipe (diameter shown below the line) flowing full.
ACRES DRAINED,000,000 8000 0 0 000 00 0 000 0,000 10,000 48 4 36 V=10 V=1 V=15 V=0 00 0 0 000 000 0 0 0 0 000 0 0 0 5,000 4,000 3,000,000 4 18 16 14 V=9 V=8 V=7 V=6 0 0 0 00 00 0 00 DISCHARGE (GPM) 1,000 0 V=3 V=4 1 V=5 10 8 6 00 0 00 0 00 5 0 10 V= 4 0 10 0 10 5 4 10 5 V=1 10 5 4 3 3 1 5 4 4 3.1..3.4.5 1.0.0 3.0 4.0 5.0 10 1/4 1/ 1 3/8 3/4 SLOPE IN FEET PER FEET (%) DRAINAGE COEFF. Based on Manning s n=0.0108 Figure 3-7. Pipe sizing chart for clay, concrete and corrugated plastic pipe with a smooth inner liner (Jarrett, 000).
10,000 V=10 V=1 ACRES DRAINED 900 10 0 600 0 5,000 4,000 3,000 V=4 V=5 V=6 V=7 V=8 0 0 00 0 00,000 V=3 0 00 1,000 18 V= 00 00 15 DISCHARGE (GPM) 0 00 1 10 8 0 0 10 0 6 0 10 V=1 5 0 10 5 4 10 5 4 3 10 5 4 3 3 5 4 4 3 0 5 4 1 3 3 1 10 1.5 V=.5.4 1.5 5.1..3.4.5 1.0.0 3.0 4.0 5.0 10 1/4 1/ 1 3/8 3/4 SLOPE IN FEET PER FEET (%) DRAINAGE COEFF. Based on Manning s n=0.015 Figure 3-8. Pipe sizing chart for corrugated plastic pipe. (Jarrett, 000)..6.3.4
Flow Regimes Water flowing in an open channel will exist in either the subcritical or supercritical regime. Briefly, most natural streams are subcritical meaning that the energy due to the depth of flow (potential energy) is greater than the kinetic energy of motion (velocity). Occasionally, in steep channel reaches the flow may become supercritical. This means that the kinetic energy of flow is greater than the depth energy. Why is it important that you be aware of whether the flow in your channels is sub or super critical? Because if your channel has supercritical flow, the water MUST go through a hydraulic jump before it can return to subcritical flow. A hydraulic jump is a big energy dissipater, which has the potential to erode large quantities of soil into the stream. A channel can easily be checked to determine if the design flow will be sub or super critical by computing the Froude Number as Q t F r = (11) 3 ga Where Q is the flow rate in the channel (in cfs), t is the top width of flow in the channel (in feet), g is the acceleration of gravity (as 3. ft/sec ), and A is the cross-sectional area of flow (in ft ). When the Froude Number is less than 1.0, the flow is subcritical; just the way you want it. When the Froude Number is greater than 1.0, the flow is supercritical, and you will need to design an energy dissipater to protect the channel where the slope decreases and the flow will change to subcritical. If the Froude Number equals 1.0 the flow is critical. This is so rare we need not worry about it. Table 3-10 shows how key channel flow parameters are affected by flow regimes. Table 3-10. Relationship between key channel flow parameters and flow regime. Flow Regimes Parameters Subcritical Critical Supercritical Velocity < V c = V c >V c Depth > d c = d c < d c Slope < S c = S c > S c Regime Changes As discussed earlier, when subcritical flow passes through a transition the flow depth will decrease. Conversely, when supercritical flow passes through a transition the flow depth will increase. In many cases, the transition is so great that the flow after the transition has not just changed in depth, but has also been transformed into a different flow regime. For instance, when water flowing in a diversion, having a 1% slope, passes through a slope change (transition) into a channel of conveyance, having an 8% slope, the flow depth will not only decrease, but may also change from subcritical to supercritical
flow. The only correct way to determine whether a regime change has (or will) occur is to check the Froude Number before and after the transition. Subcritical to Supercritical Flow. The transition from subcritical (F r < 1.0) to supercritical (F r > 1.0) flow is a smooth, seldom noticed transition. The flow depth simply drops from a subcritical depth to a supercritical depth as the flow velocity increases. As long as the channel lining(s) are able to withstand the flow velocities, there is nothing to worry about. No special lining or channel protection is generally needed. Supercritical to Subcritical Flow. The transition from supercritical (F r > 1.0) to subcritical (F r < 1.0) flow is, however, a very different situation. This regime change occurs by passing the water through what is called a 'hydraulic jump' where the depth of flow suddenly changes, often with white water, from the supercritical depth to what appears to be the subcritical depth. The purpose of white-water rafting is to ride these hydraulic jumps and experience the thrill of the sudden depth change. In addition to a sudden depth change and white water (if the change in Froude Number is great) there is also a large amount of energy lost or dissipated onto the channel bottom at the point of the hydraulic jump. Therefore, any portion of a channel that experiences a hydraulic jump must be carefully protected with a channel lining that can withstand the elevated turbulence and velocities associated with a hydraulic jump. Channel linings such as riprap, gabions or other durable material must be used to line these channel portions.