Design of Grass-Lined Channels: Procedure and Software Update

Paper Number: 03xxxx An ASAE Meeting Presentation

Design of Grass-Lined Channels: Procedure and Software Update

Darrel M. Temple, PE USDA, Agricultural Research Service, Stillwater, OK Kevin R. Cook, PE USDA, Agricultural Research Service, Stillwater, OK Mitchell L. Neilsen Department of Computer and Information Sciences, KSU, Manhattan, KS Sathish K. R. Yenna Department of Computer and Information Sciences, KSU, Manhattan, KS

Written for presentation at the 2003 ASAE Annual International Meeting Sponsored by ASAE Riviera Hotel and Convention Center Las Vegas, Nevada, USA 27- 30 July 2003 Mention any other presentations of this paper here, or delete this line.

Abstract. The allowable erosionally effective stress design procedures of Agricultural Handbook #667 are widely used for design of grassed waterways and other grass-lined channels. However, the design aids, including computational software, provided in that publication have become outdated. It has also been observed that for trapezoidal channels with flat bank slopes, direct application of the traditional n-VR curves results in over-sensitivity of flow resistance to changes in bank slope at flow depths near vegetal overtopping. The nature of the transition from unsubmerged to submerged flow conditions in these channels is discussed and software using a computational procedure that appropriately accounts for this action is presented.

Keywords. Grass-Lined Channel, Waterway, Vegetated Channel, Open Channel Flow.

The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the official position of the American Society of Agricultural Engineers (ASAE), and its printing and distribution does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer review process by ASAE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is from an ASAE meeting paper. EXAMPLE: Author's Last Name, Initials. 2003. Title of Presentation. ASAE Meeting Paper No. 03xxxx. St. Joseph, Mich.: ASAE. For information about securing permission to reprint or reproduce a technical presentation, please contact ASAE at [email protected] or 69-429-0300 (2950 Niles Road, St. Joseph, MI 49085-9659 USA). Introduction Grass has long been used as a channel lining for waterways, spillways and floodways experiencing infrequent flows. Some of the earliest work on quantifying the protective capability of grass as a channel liner was that done at Spartanburg, SC by the Soil Conservation Service beginning in 1935 and by the Oklahoma Agricultural Experiment Station in Stillwater, OK beginning in 1939. This research led to the establishment of an outdoor laboratory at Stillwater, OK with the original mission of investigating hydraulic characteristics of vegetation used for waterway lining. Experiments similar to those conducted in South Carolina and Oklahoma were also conducted at McCredie, MO by the USDA and the Missouri Agricultural Experiment Station. The primary driving force behind this early research was the need for channels to drain agricultural fields that were being terraced to reduce erosion. Detailed descriptions of the grassed waterway tests were published by Cox and Palmer (1948), Ree and Palmer (1949), and Jamison et al. (1968). The results of the research were quantified in a 1954 update of 1947 Soil Conservation Service design criteria (SCS, 1954). This design document, SCS TP-61, served as the basis for most grass-lined channel design for a number of years and is still considered to represent acceptable practice. Using this approach, the basis for design was permissible velocity with the flow resistance determined from curves of Manning’s n versus the product of velocity and hydraulic radius. As was appropriate for the time it was developed, the approach emphasized graphical determination of the design parameters with soils, slopes, and covers categorized into discrete groups for determination of permissible velocity and retardance class. Much has been learned about the interaction of flow with a vegetated boundary since the permissible velocity approach was first developed as a basis for design, and additional data have been acquired. Research focus has ranged from detailed velocity measurements and analyses such as those of Corolo et al. (2002) to more general investigation of slope and/or type of vegetal cover (Eastgate, 1966; Ree and Crow, 1977; Temple, 1985). Investigation has also included flume studies with vegetation simulated with both flexible and rigid elements (Kouwen and Unny, 1973; Thornton et al., 2000). Although these efforts have extended our knowledge of the flow-vegetal interaction, the data from the work of the early researchers and their general approach of relating flow resistance to channel Reynolds number simplified to the form of the product of velocity and hydraulic radius, remain the basis for most grass-lined channel design. This is, at least in part, due to the extent of the carefully performed full-scale experiments and the fact that the original flow resistance (n-VR) curves captured the dominant elements of a complex interaction that is difficult to quantify in detail under field conditions. This is not to imply, however, that there have not been changes in design procedure or that further change is not to be expected. As the digital computer came into common usage, equations were developed to describe the relation of flow resistance to the velocity-hydraulic radius product. One of the early attempts was that of Gwinn and Ree (1979) where a separate equation was fit to each of the original retardance classes. In the development of an erosionally effective tractive stress approach to grass-lined channel design, Temple (1982) re-analyzed the available data and used a single equation form to represent all retardance classes and related retardance class to the length and density of the vegetal elements in the form of a retardance curve index. Details of utilizing this relation in conjunction with erosionally effective stress on the soil boundary were documented in USDA Agriculture Handbook #667 (Temple et al., 1987) along with example graphical, computer, and calculator applications. The erosionally effective stress approach was extended to prediction of time to failure of vegetated earth spillways experiencing flow and stress levels

2 exceeding those that would be considered allowable for waterway design, and the resulting procedure is now used by NRCS for design and analysis of these spillways (NRCS, 1997). The relative success in predicting time of failure for grass spillway surfaces suggests that the erosionally effective stress approach incorporates the dominant processes associated with the interaction of the flow with a grassed boundary. However, the need remains for a simple computational procedure and/or desktop computer application to design grass-lined channels such as waterways based on peak discharge rather than the full hydrograph. The example computational routines originally provided in Agriculture Handbook #667 are outdated, and experience with computerized design has revealed an inconsistency related to application of the flow resistance relations to trapezoidal channels. This report reviews the fundamental characteristics of flow in grass-lined channels and their relation to the identified inconsistency. A slightly modified computational procedure and example software are introduced to address the problem.

Vegetal Flow Resistance

Flow-Vegetal Interaction In describing his observation of the characteristics of flow in grass-lined channels, Ree (1949) identified three regions of flow based on the relative depth and discharge. These were: 1. Low discharge flows in which the vegetal elements are upright and not submerged, 2. Intermediate discharge flows where at least a portion of the vegetal elements are fully submerged, and 3. High discharge flows where all of the elements are submerged and their deflected height is small compared with flow depth. Temple (1982) discusses this behavior in more detail, observing that the nature of the flow resistance offered by the vegetation is different for the low and intermediate flow regions. For the low flow region with the flow through the vegetal elements, the stem density, leaf structure, and amount of debris available to plug the flow paths between vegetal elements will tend to dominate the flow resistance exhibited by the vegetal cover. For the intermediate and high discharge flows, the flow resistance is governed by drag along the length of the individual stems. For most grasses, the leaves tend to collapse around the stem, and the relation of flow resistance to flow conditions is governed by the number and length of the vegetal elements with length dominating. Therefore, covers having a similar stem length and roughly the same number of stems, but different growth characteristics, may exhibit similar flow resistance characteristics in the intermediate flow range, but exhibit different behavior relative to flow resistance in the low flow range. Similarly, covers of different length but similar growth characteristics may exhibit similar interaction with low flows, but offer a different level of flow resistance after submergence. As might be expected, the depth and discharge associated with transition from low flow (unsubmerged) to intermediate flow (submerged) conditions is observed to be dependent on the parameters governing the flow resistance in both flow ranges plus the stiffness of the vegetal elements. Therefore, a comprehensive set of relations describing the flow resistance behavior of vegetation for the full range of flow conditions would necessarily include a relatively large number of vegetal parameters in addition to a description of flow energy and discharge. The problem is complicated by the fact that vegetal covers are never completely uniform over the entire channel boundary. This means that overtopping of the vegetation does not occur everywhere at once, even in a wide flat-bottomed channel. In typical channels of triangular,

3 parabolic, or trapezoidal cross-section, and the complex interaction of flow with the vegetal elements further distorts the velocity and stress distribution within the section. The difficulty in accurately predicting flow resistance for the low flow and transition regions suggested by the preceding discussion has not presented a major problem for waterway and spillway design because most of the flows governing the design of stable grass-lined channels fall into the intermediate flow region. It may also be noted that the typical design approach is to compute depth of flow from discharge, and the changes in flow resistance that take place during overtopping make depth less sensitive to discharge. Therefore, design procedures have generally utilized retardance relations applicable to the intermediate flow region. Temple et al. (1987) concluded that for practical application using information anticipated to be available for design, the flow resistance in the form of Manning’s n could be reasonably estimated by the relation:

2 n= EXP{CI[0.0133 ln (VR/a) – 0.0954 ln(VR/a) +0.297]-4.16} (1) Within the bounds:

2.5 0.0025 CI < VR/a < 36 (2) Where

1/3 1/6 CI = 2.5 h M (3) and n = Manning’s coefficient CI = the retardance curve index, V = the mean velocity of the flow, R = the hydraulic radius of the channel, h = the rms value of the stem length of the vegetal elements, M = the density in number of stems per unit area, a = 1.0 ft2/s = 0.093 m2/s, and EXP() indicates the inverse of the natural log. For values of VR/a outside of the bounds indicated by equation 2, the value of n is set to its value at the nearest bound. Although this allows reasonable estimation of flow resistance using only the vegetal information required for the intermediate flow range, it is noted that this approach can provide only an estimate. Attempts by the senior author to refine this estimate using his own data plus that of Cox and Palmer (1948), Ree and Palmer (1949), and Ree and Crow (1977) have suggested that more detailed information than is generally available would be required to meaningfully improve prediction.

Trapezoidal Channel The erosionally effective stress approach using equations 1 through 3 for prediction of flow resistance has proven effective for design of grass-lined channels despite the simplifications described in the preceding section. The example procedure outlined in USDA Agriculture Handbook #667 for solving the resulting simultaneous equations has also proven effective, although the discontinuous first derivative of the relation of Manning’s n to the velocity-hydraulic radius product represented by the lower bound of equation 2 means that a relatively robust convergence scheme must be applied for some conditions. Reduction of design calculations to solution of a system of simultaneous non-linear equations easily solved by personal computers has greatly simplified determination of channel dimensions for a given set of conditions. The capability to easily look at the sensitivity of design to variation

4 in parameters has also revealed an inconsistency in the results of direct application of the n-VR retardance curves, including the approach represented by equations 1 through 3. This inconsistency is illustrated by the curve of computed channel discharge versus trapezoidal bank slope shown in figure 1. Figure 1 was constructed by applying equations 1 and 2 with a retardance curve index of 7.6, a flow depth (d) of 0.43 m (1.4 ft), a channel bed width (B) of 9.1 m (30 ft), and a bed slope (S) of 3 percent. With this combination of variables, the main portion of the channel is in the transition region from low to intermediate flow as discussed above. The results are seen to be physically inconsistent in that increasing the bank slope, defined as the ratio of horizontal to vertical distance, results in a computed decrease in channel capacity with other values held constant. As discussed below, this inconsistency is the result of database limitations and approximations related to the application of the hydraulic radius based flow and flow resistance relations. Mathematically, the computed decrease in discharge with increasing bank slope is the result of the sensitivity of flow resistance to changes in the velocity-hydraulic radius product in this region combined with the properties of the trapezoidal section. In the region of interest, increasing the bank slope decreases the hydraulic radius through increasing the wetted perimeter more rapidly than the area. Application of Manning’s equation then decreases the computed velocity, further decreasing VR/a, and therefore increasing the computed value of n. This results in an over- sensitivity of computed mean velocity to bank slope, and the indicated reduction in computed channel capacity with increasing bank slope.

9.0 ) s / 3 m (

8.5 , y t i c a p a C

l 8.0 e n n a h C

7.0 0 5 10 15 20 25 30 Bank Slope, Z

Figure 1. Illustration of the over-sensitivity of channel capacity to bank slope for specified conditions (CI=7.6, d=0.43 m, B=9.1 m, S=0.03)

The inconsistency is observed for only a limited number range of conditions in the vicinity of overtopping of the vegetal elements in central sections of the channel. One of the reasons that

5 it was not identified during previous data analyses is that testing channels with widths and bank slopes in the region where the problem arises requires a relatively large volume of flow that is seldom available in laboratory situations. Several potential computational schemes were considered to correct this inconsistency for the purpose of developing an algorithm for use in design. The criteria on which these alternatives were evaluated were:  The results must be consistent with the historical data,  The computational scheme for trapezoidal channels must be consistent with the approach used in design of triangular and parabolic channels, and  The approach used should reflect the observed physical behavior of the flow to the greatest extent possible. The approach that appeared to best satisfy these criteria was to partition the channel based on the bank slope for which the first derivative of discharge with respect to bank slope was equal for a trapezoidal section and a triangular section. Discharge could then be computed based on flow resistance equations 1 through 3, and the overall resistance back computed from the sum of the discharge for each of the sections. This approach satisfies the specified criteria, including consistency with the data from parabolic, triangular, and trapezoidal channels tested in the outdoor laboratories. This approach is also consistent with the fundamentals of momentum transfer within the flow field of both the triangular and trapezoidal channels.

Computationally, this approach requires numerical determination of the bank slope (Zc) for which the change in discharge associated with a change in bank slope is equal for a trapezoidal channel having the bed width of the actual channel and a triangular channel. Both the triangular and trapezoidal sections are assumed to have the flow depth, bed slope, and retardance curve index of the actual trapezoidal channel. If the actual bank slope, Z, is less (steeper) than Zc, then no partitioning is required. If the actual bank slope is greater than Zc, the discharge through the trapezoidal section with a bank slope of Zc is added to the discharge through a triangular section having the actual bank slope, Z, less the discharge through a triangular section having a bank slope of Zc. The resulting discharge is then used to compute n from Manning’s equation for the entire section. Although this requires iterative computations with n for a trapezoidal channel being a function of flow depth, bank slope, bed slope, bed width, and retardance curve index rather than a simple function of VR/a, the required computations do not represent a significant challenge for today’s desktop computers. The results of applying this approach to the conditions represented by figure 1 are shown in figure 2. To evaluate the effect of this change on the computed value of depth, the approach was applied to 426,888 combinations of the variables in grid fashion over the range of: 0.03  d  1.5 m (0.1  d  5 ft) 0  B  30 m (0  B  100 ft) 2.8  CI  10, and 0.001  S  0.100.

6 The results showed that for 95% of the variable combinations examined, the difference between the discharge computed by direct application of the retardance relations and that computed using the modified computations was less than 10%.

9.0 ) s / 3 m (

, y t i c a p a C

l 8.0 e n n a h C

7.0 0 5 10 15 20 25 30 Bank Slope, Z Evaluating the same points for changes in flow depth for the specified discharge resulted in only 3.3% ofFigure the differences 2. Relation being of channel greater capacity than 5%. to bankIn all slopecases, for the specified difference conditions between using the the approachesmodified is considered computation to ofbe flow within resistance. the margin (C ofI=7.6, error d=0.43 for the m, computed B=9.1 m, values. S=0.03) Although the modified procedure is considered to better represent the physics of the flow-vegetal interaction, the primary benefit is the correction of the inconsistency associated with the effects of changing bank slope on channels flowing at near the point of vegetal submergence.

Application A simple desktop computer application was developed for use in performing the required design computations for grass-lined channels. Like the routines presented in USDA Agriculture Handbook #667, the application assumes normal depth conditions in a straight channel of constant slope. The routine was written in Visual Basic, includes help for the individual input fields, and is available in test form at http://www.pswcrl.ars.usda.gov. Because it is in test form, users are advised to carefully examine output and identify potential computational errors. In addition to the design computations illustrated in figure 3, the routine will compute flow depth or discharge for specified conditions, and will compute the slope corresponding to an allowable erosionally effective stress with geometric and cover conditions specified. With the exception of the flow resistance modification for trapezoidal channels described in the preceding section, the channel design routine uses the allowable erosionally effective stress procedure described in USDA Agriculture Handbook #667. Figure 3 illustrates the input and output screens used for typical design of a grass-lined channel section. The input is partitioned into three sections with a tab for each. The first tab, figure 3a, provides for input of channel geometry including bed slope and design discharge. The second tab, figure 3b, provides for input of the description of the erodible boundary material. The third tab, figure 3c, provides for

7 input describing the vegetal cover. The application was developed for the use of the English unit system. The required parameters describing the erodible boundary are the allowable effective stress and the grain roughness associated with the particles capable of being detached when the hydraulic stress exceeds the allowable. As shown in figure 3b, these values may be entered directly, or computed by the application from a description of the soil boundary. If the latter is selected, the relations used to compute the allowable stress and soil grain roughness are those documented in USDA Agriculture Handbook #667. The relation used to compute the applied effective stress for comparison to the entered allowable value is given by:

2 e=dS(1-CF)(ns/n) (4) where

e= the computed value of the applied erosionally effective stress, = the unit weight of water, S= the slope of the energy grade line (channel bed slope as applied), CF= the vegetal cover factor describing the type and condition of the grass cover, ns= the soil grain roughness expressed in terms of Manning’s coefficient, and n = the overall roughness of the channel. For stability design, two vegetal cover conditions are identified as indicated in figure 3c. The poorest anticipated cover conditions should be used for stability computations. These conditions will be used to determine the width of the channel required for the value of applied stress on the soil to be equal to the allowable. The vegetal cover factor for use in equation 4 is required for this condition as well as the retardance curve index used in computing Manning’s n. For computation of the maximum flow depth associated with the design discharge (capacity calculations), the cover anticipated to have the maximum density and stem length should be represented. The cover factor associated with this cover is not required. Multiple options for specifying the retardance curve index, CI, for use in equation 1 are provided for both the stability and capacity entries. The retardance curve index may be entered directly, implied by the retardance class corresponding to those described in SCS (1954), or computed by the application from stem length and density using equation 3. Direct entry of a constant value of Manning’s n is also accepted, but should be used only for non-vegetated conditions. Figure 4d shows the output associated with the design section at maximum flow depth (capacity cover conditions). Figure 4e is a sketch of the corresponding section for easy reference. Figure 4f provides details of the computations used for determination of channel width (stability cover conditions). The capability to print all output is provided. Input and output for triangular and parabolic channels are similar to the trapezoidal section illustrated. Limited checks on the consistency and completeness of the inputs are made at the time of computation. However, these checks do not guarantee that the input values represent valid combinations of the variables. Verification of the quality of the inputs and the applicability of the computations to the design condition remains the responsibility of the user.

8 (a) (b)

(b) (d)

(e) (f)

Figure 3. Example input and output screens from grass-lined channel design application: a) channel properties input, b) soil parameters input, c) vegetal parameters input, d) capacity design output, e) cross section sketch output, and f) stability design output. Program uses English unit system.

9 Summary and Conclusions Grass has proven to be an effective lining for water conveyance channels such as waterways and spillways that experience only infrequent flows. Progress in the area of desktop computing has outdated the previously published routines for erosionally effective stress design of these channels and shown an inconsistency in the results of application of the traditional curves of flow resistance versus velocity-hydraulic radius product. The physical and mathematical implications of this inconsistency were found to be related to the limitations of the historical data-base and subsequent computational simplification of the complex interaction of the flow with the vegetal elements. Review of these considerations also reveals that substantially more information on the nature of the vegetal cover would be required to refine estimates of flow resistance for unsubmerged or partially submerged vegetation. However, present flow resistance relations are adequate for most engineering design applications and the identified inconsistency can be overcome computationally for desktop computer applications. An example application for use in grass-lined channel design is currently available in test format. The application uses the allowable effective stress approach of USDA Agriculture Handbook #667 to design a stable cross-section flowing at normal depth. For stability design, the channel width is determined using a minimum cover condition and flow depth is determined using a maximum cover condition. The application is capable of solving for flow depth, discharge, or stable slope in addition to the typical design computations.

References Corolo, F. G., V. Ferro, and D. Termini. 2002. Flow velocity measurements in vegetated channels. J. Hydraulic Engineering 128(7): 664-673. Cox, M. B., and V. J. Palmer. 1948. Results of tests on vegetated waterways and method of field application. Misc. Pub. No. MP-12, Stillwater, Okla.: Oklahoma Agricultural Experiment Station, Oklahoma A. and M College. Eastgate, W. I. 1966. Vegetated stabilization of grassed waterways and dam bywashes. MS thesis. St. Lucia, Queensland, Australia: Univ. of Queensland. Gwinn, W. R., and W. O. Ree. Maintenance effects on the hydraulic properties of a vegetation- lined channel. ASAE Paper No. 79-2063. St. Joseph, Mich.: ASAE. Jamison, V. C., D. D. Smith, and J. F. Thornton. 1968. Soil and water research on a claypan soil. Tech. Bul. No. 1379, USDA, Agricultural Research Service, Washington, DC. Kouwen, N., and T. Unney. 1973. Flexible roughness in open channels. J. Hydr. Div. ASCE 99(HY5): 713-728. Ree, W. O., and V. J. Palmer. 1949. Flow of water in channels protected by vegetative linings. Tech. Bul. No. 967, Washington, D.C.: USDA, Soil Conservation Service. Ree, W. O., and F. R. Crow. 1977. Friction factors for vegetated waterways of small slope. Pub. ARS-S-151. Washington, D. C.: USDA Agricultural Research Service. Temple, D. M. 1982. Flow retardance of submerged grass channel linings. Trans. ASAE 25(5): 1300-1303. Temple, D. M. 1985. Stability of grass-lined channels following mowing. Trans. ASAE 28(3): 750-754. Temple, D. M., K. M. Robinson, R. M. Ahring, and A. G. Davis. 1987. Stability design of grass- lined open channels. Ag. Handbook No. 667. Washington, D.C.: USDA Agricultural Research Service.

10 Thornton, C. I., S. R. Abt, C. E. Morris, and J. C. Fischenich. 2000. Calculating shear stress at channel-overbank interfaces in straight channels with vegetated floodplains. J. Hydraulic Engineering 126(5): 929-936 USDA, Soil Conservation Service. 1954. Handbook of channel design for soil and water conservation. SCS-TP-61, Washington, D.C. USDA, Natural Resources Conservation Service. 1997. Earth spillway erosion model. Chapt. 51, National Engineering Handbook Part 628 Dams. Washington, D. C.