Hydraulic Loss Coefficients for Culverts (2012)

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68 8.1 Summary Composite roughness in open channel flow describes a condition where different roughness materials line different parts of a channel cross-section. Some examples of com- posite roughness channels include concrete rectangular or trapezoidal channels where the channel invert has been cov- ered with sand and/or gravel as a result of sediment trans- port; vegetation can also be present in the channel invert. Fish passage culverts, such as those discussed in Chapter 2, are another example of composite roughness channels. Most open channel flow problems are solved using Manning’s Equation. Estimating the head-discharge relationship for com- posite roughness channels poses a unique challenge because Manning’s Equation is a one-dimensional head-discharge relationship that is being applied to what are very likely three- dimensional flow problems. Ideally, a representative Man- ning’s n hydraulic roughness coefficient would be defined that accounts for the three-dimensional nature of the com- posite roughness flow condition. A literature search produced a list of 16 different relation- ships that have been proposed for estimating representative composite roughness n values, referred to as ne, which are dependent upon the n values of the individual channel lin- ing materials, referred to as ni, that make up the composite roughness boundary geometry. The degree to which these relationships have been evaluated against experimental com- posite roughness data is limited. In this study, 12 different composite roughness channel configurations were tested in a rectangular laboratory flume, using combinations of the boundary roughness materials evaluated in Chapter 6 (acrylic sheeting, metal lath, blocks, and trapezoidal corrugations). The composite roughness configurations were categorized into three different channel types: Type I featured rougher walls and a smoother floor, Type II featured smoother walls and a rougher floor, and Type III featured rough walls and floor. The 16 different ne relationships, which use a weighted average of the ni values that is based on a corresponding flow subarea and/or wetted perimeter to each roughness material comprising the composite roughness boundary, were evalu- ated along with different methods for evaluating ni. It was determined that for hydraulically rougher boundary rough- ness materials where n varies with flow conditions (e.g., n varied with Rh/K for all of the materials tested except for the smooth acrylic sheeting) the variation in ni should be applied to the ne relationships. In general, some of the relationships performed worse than the others, but no relationship proved to be more accurate than the other predictive relationships for all composite roughness configurations. The predictive error, which was represented by root-mean-square (RMS) values, ranged from approximately 5 to 90%, with the major- ity of the methods producing RMS values in the range of 5 to 20%. Based on the fact that the more complicated ne predic- tive methods didn’t produce more accurate results than the simpler ne predictive methods, the simpler ne predictive methods are recommended, namely the Horton method, with the caveat that the level of uncertainty can still be sig- nificantly high. It should also be noted that even though the range of hydraulic roughness boundary materials (ni) was broader, the number of composite roughness geometries tested (12) was larger, and the number of ne relationships evaluated was significantly larger than in previous studies. The applicability of the test results to channels with cross- sections that are different than the one tested in this study, as well as applicability to composite roughness geometries that feature irregular roughness element patterns (the indi- vidual boundary roughness elements used in this study all feature uniform roughness element patterns) have not been determined. Until more accurate data are available, the results from this study are recommended as a first-order approximation for composite roughness problems in prac- tice. The inclusion of a reasonable factor of safety is also recommended. C h a p t e r 8 Open Channel Flow Resistance: Composite Roughness

69 8.2 Introduction It is not uncommon in open channel flow field applications for the wetted perimeter of a cross-section to be made up of more than one roughness material [e.g., concrete channels with the invert covered in sediment, gravel, and/or vegetation or buried-invert culverts (see Chapter 2)]. Yen (2002) refers to such channels as composite channels. The composite chan- nel flow resistance will be a function of the combined effects of the individual flow boundary roughness materials. The most commonly used open channel flow equations (Man- ning, Chezy, Darcy-Weisbach), however, are one-dimensional and are limited to a single, representative hydraulic rough- ness coefficient. Yen (2002) published 16 different compos- ite Manning’s n (ne) relationships (see Table 8-1) as possible candidates for use with Manning’s Equation (Equation 8-1) to predict flow resistance in composite channels. V K n R Sn e h e= 2 3 1 2 8( )-1 Name ne Secondary Assumptions Equation Mean velocity assumption methods Horton SI = So Eqn. (8-2) Colebatch Same as Horton but adjusted by a factor of C = Rwall/Rbase Eqn. (8-3) Total force assumption methods Pavlovskii Yen (2002): Vi/V = (Ri/R) 1/6 or Flintham & Carling (1992): Vi = V and R = R Eqn. (8-4) Total F2 Vi/V = (Rhi/Rh) 2/3 Eqn. (8-5) Total F3 Vi = V Eqn. (8-6) Total F4 Vi/V = (Rhi/Rh) 1/2 Eqn. (8-7) Total discharge assumption methods Lotter Si = So Eqn. (8-8) Lotter II )9-8(.nqE– Total Q1 Si/So = (Rhi/Rh) 4/3 Eqn. (8-10) Total Q2 Si/So = (Rhi/Rh) 10/3 Eqn. (8-11) Total Q3 Si/So = (Rhi/Rh) Eqn. (8-12) Total shear velocity assumption methods LAD Vi/V = (Rhi/Rh) 7/6 Eqn. (8-13) TexDOT Vi/V = (Rhi/Rh) 1/6 Eqn. (8-14) Total U*1 Vi = V Eqn. (8-15) Total U*2 Vi/V = (Rhi/Rh) 2/3 Eqn. (8-16) Total U*3 Vi/V = (Rhi/Rh) 1/2 Eqn. (8-17) – indicates no secondary assumptions i Table 8-1. Composite channel ne relationships.

70 In Equation 8-1, V is the mean velocity, Kn = 1.49 (1.0 SI units), Rh is the hydraulic radius [the ratio of the flow area (A) to the wetted perimeter (P)], and Se is the friction slope, which at uniform depth is equal to the channel slope. The ne relationships published by Yen (2002) are based on vari- ous techniques for weighting the resistance of the individual boundary roughness materials in the channel cross-section. This is accomplished by partitioning A and/or P (resulting in component Ai and/or Pi values) between the boundary roughness materials and applying the individual n values of the boundary roughness materials, referred to as component n values (ni), to each partitioned section. The result is a single, representative ne value that then is applied to Equation 8-1. Previous studies compared relatively small subsets of the ne relationships listed in Table 8-1 (Pillai, 1962; Cox, 1973; Flintham and Carling, 1992); in total, the performances of 5 of the 16 ne relationships presented by Yen (2002) have been evaluated using experimental data. Yen (2002) states that the amount of published data available for composite channels is limited and therefore it is yet to be determined which of the 16 predictive ne relationships is best suited for use. The current study provides an expanded experimental data set for evaluating the performance of the 16 ne relationships using combinations of the four boundary roughness materials (acrylic sheeting, metal lath, trapezoidal corrugations, and blocks) discussed in Chapter 6. The ni values for the individual boundary roughness materials used in the current study ranged from ni = 0.0096 for the smooth acrylic sheeting to ni = 0.033 to 0.086 (Rh or Rh/k dependent) for the blocks. This range of ni values exceeded the range of hydraulic roughness values evaluated in the previous studies (Pillai, 1962; Cox, 1973; Flintham and Carling, 1992). The composite channel flow resistance testing of the current study includes 12 different composite channel lining combinations of the individual lining materials. According to Flintham and Carling (1992), the accuracy of ne relationships should be dependent upon two factors: (1) the method used to partition the channel cross-sectional flow area into the subareas directly influenced by each rough- ness material lining the boundary and (2) an accurate deter- mination of the ni values. The influence of the flow area partitioning technique on ne was found by Flintham and Carling (1992) to be relatively negligible when compared to the significance of the ni values selected. This study examines the behavior of ni (the dependence of ni on Rh in a uniformly lined channel) and the influence of ni on the ne relationships. 8.3 Background Component n values (ni) Chow (1959) states that the most difficult task in the use of Equation 8-1 is assigning a roughness coefficient (n) value and that the inexact methods for doing so range from guess- work to empirical relationships. Although the ne relationships in Table 8-1 are fundamentally based on channel geometry and the distribution of hydraulic roughness boundary materials over the wetted perimeter, there remains a certain level of uncertainty in ne due to the inherent uncertainty associated with specifying ni. The relationship between n (or ni) and Re, Rh/k, and other factors is discussed in Chapters 6 and 7. Manning’s objective in developing the one-dimensional, open channel flow equation (Equation 8-1) was to find a rela- tionship where the hydraulic roughness coefficient (n) would be constant (dependent only on k and independent of the flow conditions). After evaluating Equation 8-1 (using the con- stant n assumption for boundary roughness) using numer- ous experimental data sets, Manning (1889) concluded that the equation was “sufficiently accurate.” Chow (1959) states that, in general, n is not constant but decreases with increasing stage for most streams, a fact that was confirmed in Chapters 6 and 7. Other studies, meanwhile, have shown that n can vary with stage, discharge, and slope in certain uniformly lined channel applications (Limerinos, 1970; Bray, 1979; Bathurst et al., 1981); Yen (2002) recommends that n may be consid- ered nearly a constant and almost independent of flow condi- tions. These apparent contradictions suggest that some level of uncertainty still exists regarding the appropriateness of the constant n assumption and Manning’s Equation. The n (or ni) data for this study were determined in the rectangular test flume, uniformly lined with each boundary material separately. The ni data, the constant and/or variable nature of which depends in part upon the boundary rough- ness (k) and Rh, are presented in Figure 8-1 for the smooth acrylic sheeting, metal lath sheeting, blocks, and trapezoidal corrugations. The acrylic sheeting Manning’s n data in Figure 8-1, which represents the smoothest boundary roughness material tested, remain relatively constant over the full range of Rh tested. The metal lath and trapezoidal corrugation n values vary with Rh over the lower 20 to 30% of the data range and are relatively con- stant above that limit. The block data varies over the full range of Rh tested; however, the fact that the block n data appears to be approaching a constant value suggests that the absence of a constant n range in the experimental data set is likely due more to flow capacity limitations than boundary roughness char- acteristics. These same boundary roughness materials were used to create the composite channel linings in the current study; the data in Figure 8-1 were used to generate the ni values used in evaluating the ne relationships in Table 8-1. The bound- ary roughness materials are identified in this chapter as follows: A (acrylic sheeting), B (metal lath), D (blocks), and E (trapezoi- dal corrugations). For all composite roughness test configura- tions, a common roughness material was used on the walls and a different roughness material was used on the floor.

71 Composite Manning’s n (ne) Equations The 16 ne relationships listed in Table 8-1 are divided into four groups based on the main assumption used in their deri- vation. These assumptions are as follows: • The Mean Velocity Assumption: The mean velocity in the cross-sectional flow subarea associated with each boundary roughness material is equal to the mean velocity of the entire channel cross-section. • The Total Force Assumption: The sum of the forces resisting the flow in each subarea is equal to the total force resisting the flow in the channel. • The Total Discharge Assumption: The sum of the subarea discharges is equal to the total channel discharge. • The Total Shear Velocity (U*) Assumption: The weighted sum of the shear velocities of each subarea is equal to the total shear velocity of the channel. Secondary assumptions are also typically required for the derivation of these equations. The secondary assumptions for each relationship, where applicable, are also listed in Table 8-1. The ne relationships shown in Table 8-1 are dependent on the way in which subareas of the channel cross-sectional flow area are apportioned to each boundary roughness material comprising the composite wetted perimeter. In Equations 8-2 through 8-17, Rhi is equal to the ratio of Ai to Pi (Rhi = Ai/Pi) and the subscript i denotes the different subareas of the channel cross-section associated with each of the roughness material components comprising the wetted perimeter. Two different subarea partitioning techniques are illustrated in Figure 8-2 (the 90° velocity contour bisecting method and the angle bisect- ing method for a rectangular channel cross-section). Komora (1973) recommended that the cross-sectional flow area of a composite channel be subdivided by curves that intersect the cross-sectional velocity contours at right angles, as depicted in Figure 8-2. This requires detailed velocity data that are not likely to be available for most practical applica- tions. To avoid this complication, Colebatch (1941) recom- mended using a straight line to bisect the angle at the point of the boundary roughness change (e.g., In Figure 8-2, the 45°-angled lines from the corner separate the flow subareas in the rectangular channel featuring different boundary rough- ness materials on the floor and walls). Flintham and Carling (1992) compared both methods to their data set and con- cluded that there were no obvious advantages with either sub- area delineation method. For convenience, the angle bisection method was used throughout this study for the ne equations. Wherever the subarea dividing line is drawn, it is assumed that shear stress is equal to zero along that boundary (although not necessarily true). Consequently, only wetted perimeters cor- responding to physical channel boundaries (Pi) are included in flow resistance calculations, as shown in Figure 8-2. Flow boundaries between adjacent subareas are not included as part of the Pi dimension (Yen, 2002). Previous Studies Three published studies were reviewed that evaluated the effectiveness of various subsets of the ne relationships shown in Table 8-1. Each study featured a unique set of composite channel boundary roughness materials and configurations. Figure 8-1. Manning’s n data from channels with uniform roughness materials.

72 The experimental composite channel results were compared with the predictive ne relationships. Pillai (1962) studied composite roughness flow resistance in both rectangular and trapezoidal channels and evaluated the Horton (1933), Pavlovskii (1931), and Lotter (1933) ne rela- tionships using two different boundary roughness materials described as (1) smooth cement with fine sand and (2) cement plastered with gravel that passes a ½-in. sieve and was retained on a ¼-in. sieve. Pillai (1962) selected ni as the average experi- mental n value (naverage) for each boundary roughness material, which values were reported as 0.009836 (cement and fine sand mix) and 0.0178 (cement and gravel). Of the three relation- ships evaluated by Pillai (1962), the Lotter relationship was the only one requiring subarea delineation. Lotter’s relationship was only applied to the trapezoidal channel data where the subareas were divided using vertical lines originating at the corners of the channel cross-section. Pillai (1962) concluded that the Horton relationship performed the best and that the Lotter relationship gave inconsistent results. Cox (1973) conducted composite roughness testing in a rectangular channel using the bisecting angle method for subarea delineation. Two roughness materials were tested, a plastic-coated plywood (n = 0.0095) and crushed limestone particles that passed a No. 4 sieve and were retained on a No. 8 sieve (naverage = 0.0165). Cox (1973) compared the Horton (1933), Colebatch (1941), and Los Angeles District (LAD) relationships and recommended the LAD and Colebatch relationships over the Horton. Flintham and Carling (1992) studied composite roughness in a trapezoidal channel using the bisecting angle method for subarea delineation. Three roughness materials were tested: plywood, 0.24-in.-diameter gravel, and 0.55-in.-diameter gravel. The reported average Manning’s n values for the 0.24-in. and 0.55-in. gravels were 0.019 and 0.022, respec- tively (the plywood n was not published). Flintham and Car- ling (1992) were the only ones to use ni values that varied by boundary material in their analysis. They concluded that, with respect to the boundary roughness materials tested, using the varying ni values improved the accuracy of the predictive rela- tionships relative to using average n values. Their study was lim- ited, however, to channel roughness configurations where the floor roughness exceeded the sidewall roughness. Flintham and Carling (1992) evaluated the Horton, Colebatch, Pavlovskii, and Lotter methods. They concluded that the Pavlovskii relationship was the most accurate, the Horton and Colebatch relationships were satisfactory, and the Lotter relationship performed poorly. Four of the five relationships evaluated in the three differ- ent studies were identified at least once as a “best performer,” but consensus was not achieved regarding an overall best method. The Lotter relationship, on the other hand, was sin- gled out in each study as “not recommended for use.” In the current study, all 16 predictive ne relationships were evaluated against the experimental data set developed in the study. The number of boundary roughness materials tested in the cur- rent study (four), exceeded the number of roughness materi- als tested in any of the three previous studies. The diversity in composite roughness channel lining configurations and the hydraulic roughness characteristics of the boundary rough- ness materials used in the current study were also broader than those used in the previous studies. 8.4 Experimental Setup All composite roughness testing was conducted in a 4-ft- wide by 3-ft-deep by 48-ft-long rectangular flume. Flow was supplied to the flume through either 8-in. or 20-in. diameter supply piping. Each supply pipe contained a calibrated orifice flow meter. Figure 8-2. Cross-sectional area partitioning of subareas.

73 Four boundary roughness materials were used in this study: • Acrylic flume walls and floor used as a smooth surface (see Figure 6-2), • A commercially available metal lath sheeting material measuring ¹⁄8-in. in height (see Figure 6-3), • Wooden blocks that were 3.5 in. long (in the flow direction), 4.5 in. wide, and 1.5 in. tall, with a 1-in. radius rounded top edge (see Figures 6-4 and 6-5), and • Trapezoidal corrugations that were 1.5 in. tall, 4.5 in. wide at the base, and 1.5 in. wide at the top (see Figures 6-6 and 6-7). The blocks were attached to a plywood base in a staggered pattern with 1.83 in. between blocks, as shown in Figure 6-5. The trapezoidal strips were also attached to a plywood base and oriented perpendicular to the flow direction at a spac- ing of 1.5 in., as shown in Figure 6-7. The acrylic, metal lath, block, and trapezoidal corrugation roughness materials are hereafter identified as boundary roughness materials A, B, D, and E, respectively. Manning’s n data for each boundary roughness material were determined as described in Section 6-4. The n data for Material A were relatively constant (naverage =0.0096), as shown in Figure 8-1. The n data for materials B, D, and E varied with Rh (see Figure 8-1) and trend line functions were used to rep- resent ni in the ne calculations. Twelve different composite channel geometries were cre- ated through various combinations of the materials A, B, D, and E. In all cases, the channel sidewalls featured a com- mon boundary roughness material while the floor featured another. The three-letter notation for the composite rough- ness configurations represents the sidewall, floor, and sidewall boundary roughness materials. The following combinations were tested: ABA, BAB, ADA, DAD, BDB, DBD, AEA, EAE, BEB, EBE, EDE, and DED. An example of the BDB com- posite roughness configuration (metal lath on the sidewalls and wooden blocks on the floor) is shown in Figure 8-3. The same procedure discussed in Section 6-4 to determine ni for the uniform channel roughness lining tests was also used to determine the experimental composite ne. The composite roughness channel configurations were also categorized into three channel types. A Type I channel is one where the floor roughness exceeds the wall roughness (e.g., ABA, ADA, BDB, AEA, BEB); a Type II channel is one where the wall roughness exceeds the floor roughness (e.g., BAB, DAD, DBD, EAE, EBE); and a Type III channel is one where the walls and floor both feature “large roughness element” boundary materials of different types (e.g., EDE, DED). 8.5 Experimental Results Optimization of the ne Relationship The results of the comparison between the experimental ne data and the 16 ne relationships shown in Table 8-1 were quantified using the RMS (Equations 8-18 and 8-19). Dou- bling the RMS represents a 95% confidence interval. RMS PE samples = Σ 2 8( )-18 PE predicted measured measured = − 100 8( )-19 In Equations 8-18 and 8-19, PE is the percent predictive error and samples represents the total number of data points sampled. The bias is the mean value of PE. RMS values of each equation were calculated for both the individual com- posite channel configurations (EAE, BDB, etc.) and each of the composite channel types (Types I, II, and III). The bias of each equation was also determined. Flintham and Carling (1992) emphasized the sensitivity of the specific ni values assigned to represent the individual roughness boundaries in a composite roughness channel when calculating ne. Three different methods for determining ni were used in the current study in an effort to investigate the influence of the Rh dependence of ni on ne. Method 1 assumed Figure 8-3. Examples of composite roughness channel types: Type I (BDB) (A), Type II (DAD) (B), and Type III (EDE) (C).

74 a constant ni value for each material that corresponds to the large-Rh constant ni values shown in Figure 8-1 instead of the average ni value as used by Flintham and Carling (1992). The constant ni value for material D was estimated by extrapo lating the experimental data trend to larger Rh values (ni = 0.0335). Method 2 assumed that the ni = F(Rhi) relation- ships for the composite roughness channel subareas are equal to the n = F(Rh) relationships for the uniformly lined channel data (i.e., ni for each subarea was calculated based on Rhi for that subarea). Method 3 is similar to Method 2 except that ni for each subarea was calculated using Rh (the total channel hydraulic radius) rather than Rhi [i.e., ni = F(Rh)]. The RMS values for the trend line functions used to predict ni (using the n versus Rh data presented in Figure 8-1) for boundary roughness materials A, B, D, and E were 4.5%, 2.43%, 3.04%, and 4.29%, respectively. The resulting total RMS values—based on a combined data set from all composite channel configurations (e.g., ADA, BEB, etc.) in each channel type (Types I, II, or III) of the individual relationships in Table 8-1—are presented in Table 8-2 accord- ing to channel type and method, or combination of methods, applied to determine ni. Similar to the findings of previous studies, the Lotter (1933) relationship performed inconsis- tently with respect to its ability to match the experimental data from this study. The inconsistent results are shared by all the relationships within the total discharge assumption ne group and, as a result, the outcome for the total discharge assumption relationships will be discussed separately from the other relationships. It is clear that the predictive abilities of the ne relationships are significantly improved by applying variable ni (Method 2 or Method 3) where appropriate (see Table 8-2 and Figure 8-4 [A, B, and C]). This was a somewhat obvious or foregone con- clusion, given the results of the analysis presented in Chapters 6 and 7. Not so obvious, however, were the results of the Type II channel, where the accuracy of the relationships decreased when accounting for ni variability via Method 2 or Method 3 for the channel walls and the floor. Figure 8-4 (C) shows that at lower Rh values, too much emphasis is given to the channel wall roughness when calculating ne. The reasons for this are likely related to the way the channel is divided into subsections (the values of Pi, Ai, and/or Rhi) and the net effect of the assigned subsection parameters, along with ni, on pre- dicting the contribution of the sidewall hydraulic roughness on the overall composite flow resistance of the channel. It is also possible that the hydraulic roughness characteristics of boundary roughness elements are location dependent. Even for a uniformly lined channel, the flow resistance associated with the walls may very well differ from the flow resistance produced by the channel floor. It is important to note that, regardless of the technique used to estimate ne based on ni, an empirically based, one- dimensional equation [Manning’s Equation (Equation 8-1)] is still being used in an attempt to solve a three-dimensional flow problem. As shown in Figure 8-4 (B), applying Method 1 to the floor and the walls of the channel under-predicted ne values; applying either Method 2 or Method 3 to both the floor and the walls of the channel produced ne values that over-predicted the measured values. As a result, the analy- sis was repeated with Method 1 applied to the channel walls and either Method 2 or 3 to the floor of the channel. Figure 8-4 (B) shows that, by applying Method 3 to the floor and Method 1 to the walls, the predicted ne values more closely follow the trend of the experimental data over the range of Rh tested. They do not, however, provide a relatively good estimate of the measured ne data. For some of the equa- tions, the RMS values increased when using a combination- of-methods approach. For cases where the combination of methods resulted in an improvement (i.e., reduction in RMS values), the improvements were only modest [e.g., Type I and III channels as shown in Table 8-2 and Figure 8-4 (A and C)]. With respect to the Type II channel, the combination of methods provided an improvement only for the lowest Rh values tested, relative to Method 1. In general, it can be con- cluded that where data are available, a variable Manning’s n should be applied to the ni of the floor of the channel. A con- stant ni may be applied to the walls of the channel with little change in predictive error; in fact, in most cases it improved ne predictions. Comparison of ne Relationships A comparison of the predictive accuracies of the various composite roughness ne relationships listed in Table 8-2 shows that no single composite roughness ne relationship performs appreciably better than the rest. Table 8-3 also shows that there is moderate scatter in the accuracy of each of the pre- dictive ne relationships over the range of composite rough- ness boundary configurations tested. For example, Colebatch (RMS = 3.3%) performs better than Horton (RMS = 6.0%) in the ADA composite channel; the opposite is true in the AEA composite channel where Horton (RMS = 5.9%) per- forms better than Colebatch (RMS = 8.80%). The RMS values based on the collective data of all the channel configurations (“Total RMS” reported in Table 8-3) show that, from a broad perspective, neither relationship (Horton nor Colebatch) is notably better than the other for any of the channel types (I, II, or III). The mean velocity assumption group has a slight advantage over the other groups based on consistency of predictive accuracy for the three different channel types. The total discharge assumption group gives inconsistent results. The results for the individual relationships fluctuate, to a certain extent, with both the channel configuration and channel type, as shown in Table 8-3.

latoT SMR rof seulav ne snoitauqe ni *dohtem yticoleV naeM ecroF latoT egrahcsiD latoT yticoleV raehS latoT sllaW roolF notroH hctabeloC iiksvolvaP latoT 2F latoT 3F latoT 4F rettoL rettoL II latoT Q latoT 2Q latoT 3Q DAL MDH latoT *U latoT 2*U latoT 3*U I EPYT LENNAHC 1 1 %6.52 %5.42 %8.42 %3.62 %2.52 %4.42 %5.52 %6.42 %9.72 %1.72 %1.92 %3.33 %7.82 %5.62 %6.52 %8.52 2 2 %8.7 %9.6 %3.7 %2.7 %6.7 %0.7 %6.31 %5.21 %3.61 %3.32 %5.51 %9.6 %2.9 %5.9 %9.7 %3.8 1 2 %9.7 %9.6 %3.7 %2.7 %6.7 %0.7 %7.31 %6.21 %5.61 %7.32 %7.51 %9.6 %2.9 %6.9 %9.7 %3.8 3 3 %5.6 %5.6 %3.6 %1.7 %4.6 %6.6 %4.21 %4.11 %3.51 %7.22 %4.41 %1.6 %5.7 %9.7 %5.6 %8.6 1 3 %5.6 %5.6 %3.6 %1.7 %4.6 %6.6 %5.21 %4.11 %4.51 %8.22 %5.41 %1.6 %5.7 %9.7 %5.6 %8.6 II EPYT LENNAHC 1 1 %0.31 %9.21 %4.41 %3.21 %9.51 %4.21 %7.81 %9.21 %3.22 %4.12 %3.02 %1.81 %8.02 %3.21 %2.31 %8.21 2 2 %0.25 %1.92 %0.88 %4.55 %201 %8.46 %7.02 %9.91 %6.81 %1.61 %1.91 %5.51 %1.72 %5.03 %6.91 %7.12 1 2 %9.11 %4.11 %1.51 %0.11 %2.81 %6.11 %2.12 %4.02 %2.91 %0.71 %7.91 %0.31 %0.11 %1.11 %8.11 %4.11 3 3 %3.23 %9.81 %6.35 %7.23 %9.26 %6.83 %9.02 %1.02 %9.81 %5.61 %4.91 %6.31 %6.81 %6.02 %9.41 %8.51 1 3 %9.11 %4.11 %1.51 %0.11 %2.81 %6.11 %1.12 %3.02 %2.91 %9.61 %6.91 %0.31 %0.11 %1.11 %8.11 %4.11 III EPYT LENNAHC 1 1 %3.42 %2.42 %2.42 %3.42 %3.42 %2.42 %1.42 %3.42 %1.52 %2.42 %2.42 %3.42 %4.42 %0.42 %5.42 %5.42 2 2 %5.7 %5.5 %3.8 %9.5 %8.9 %4.6 %3.6 %5.5 %4.5 %7.5 %5.5 %4.5 %8.6 %3.7 %8.5 %1.6 1 2 %9.6 %6.6 %8.6 %6.6 %7.6 %8.6 %7.7 %5.6 %7.6 %4.7 %9.6 %6.6 %9.6 %8.6 %0.7 %1.7 3 3 %3.5 %0.5 %4.5 %1.5 %9.5 %1.5 %5.5 %1.5 %9.4 %80.5 %0.5 %99.4 %91.5 %4.5 %99.4 %0.5 1 3 %5.5 %5.5 %5.5 %5.5 %3.5 %5.5 %1.6 %3.5 %3.5 %47.5 %4.5 %34.5 %54.5 %3.5 %85.5 %6.5 :1 dohteM * ni :2 dohteM ,tnatsnoc = ni = f(Ri :3 dohteM dna ,) ni = f(R) Table 8-2. Summary of RMS values based on combined data sets for all 12 composite roughness test configurations.

Figure 8-4. Examples of experimental and Horton relationship ne versus Rh data for Type I, II, and III composite roughness channels along with the corresponding experimental ni versus Rh data: (A) Type I (DBD), (B) Type II (DBD), (C) Type III (DED).

iiksvolvaP hctabeloC notroH .gifnoC latoT 2F latoT 3F latoT 4F rettoL rettoL II Q latoT latoT 2Q latoT 3Q MDH DAL latoT 1*U latoT 2*U latoT 3*U I EPYT LENNAHC ABA saiB %7.7- %3.7- %7.8- %4.8- %7.5- %7.8- %0.31- %0.9- %0.7- %4.8- %4.5- %5.7- %6.4- %9.6- %1.5- %6.7- SMR %7.7 %0.9 %3.6 %1.8 %6.5 %5.7 %0.6 %2.8 %3.8 %9.7 %3.9 %0.9 %5.6 %3.9 %5.31 %6.9 ADA saiB %7.6- %8.5- %3.9- %5.8- %7.2- %5.42- %0.73- %0.62- %3.91- %7.02- %2.0 %6.3- %6.1 %3.2- %2.0- %9.4- SMR %7.7 %9.6 %2.01 %4.9 %5.4 %0.52 %1.73 %4.62 %0.02 %3.12 %1.3 %7.4 %6.3 %9.3 %3.3 %0.6 BDB saiB %1.4- %4.3- %9.5- %3.5- %9.0- %6.9- %8.71- %4.01- %3.6- %9.7- %3.0 %9.2- %5.1 %9.1- %4.0 %4.3- SMR %9.6 %4.8 %0.3 %2.4 %4.3 %6.3 %0.3 %6.4 %1.5 %5.4 %7.6 %2.6 %1.3 %0.01 %1.81 %8.01 AEA saiB %8.0- %1.0 %2.3- %4.2- %1.3 %2.31- %4.42- %5.41- %8.8- %2.01- %5.5 %8.1 %9.6 %0.3 %2.5 %6.0 SMR %3.5 %5.5 %8.5 %5.5 %9.6 %9.31 %6.42 %1.51 %9.9 %2.11 %3.9 %6.6 %5.01 %4.7 %8.8 %9.5 BEB saiB %3.0 %8.0 %1.1- %7.0- %9.2 %0.2- %0.8- %5.2- %4.0 %2.1- %5.3 %8.0 %6.4 %6.1 %8.3 %6.0 SMR %9.6 %7.6 %6.8 %2.7 %3.9 %6.7 %7.8 %1.7 %0.7 %1.7 %8.6 %8.6 %0.8 %9.6 %1.01 %0.7 saiB latoT %8.3- %1.3- %6.5- %1.5- %7.0- %6.11- %0.02- %5.21- %2.8- %7.9- %8.0 %3.2- %0.2 %3.1- %8.0 %0.3- SMR %8.6 %5.6 %9.7 %5.7 %1.6 %5.41 %8.22 %4.51 %4.11 %5.21 %6.6 %4.6 %1.7 %3.6 %5.6 %5.6 II EPYT LENNAHC BAB saiB %7.1 %0.1 %6.4 %5.3 %3.0- %5.3- %6.0- %0.3- %0.4- %3.5- %9.2 %6.8 %7.1 %3.6 %7.0 %8.4 SMR %3.8 %3.9 %5.5 %6.9 %2.5 %6.7 %2.5 %5.6 %2.5 %2.5 %4.6 %8.5 %5.5 %8.7 %9.5 %4.7 DAD saiB %4.7- %8.8- %3.2- %2.4- %0.21- %2.22- %8.81- %7.12- %9.22- %8.32- %8.1 %1.51 %5.1- %0.01 %3.7- %4.2 SMR %2.02 %9.02 %4.81 %9.81 %0.32 %7.23 %8.92 %3.23 %5.33 %2.43 %4.71 %0.42 %5.71 %5.02 %7.91 %9.71 DBD saiB %8.7- %5.8- %0.5- %0.6- %9.9- %0.41- %9.01- %4.31- %6.41- %8.51- %1.6- %6.0- %3.7- %8.2- %7.8- %5.4- SMR %8.11 %5.21 %7.9 %4.01 %8.31 %2.81 %2.51 %7.71 %9.81 %9.91 %1.01 %2.7 %2.11 %9.7 %5.21 %1.9 EAE saiB %0.3 %4.1 %0.9 %7.6 %4.2- %3.41- %2.01- %7.31- %2.51- %2.61- %2.31 %3.82 %5.9 %6.22 %0.3 %1.41 SMR %7.7 %5.7 %1.11 %5.9 %6.8 %9.91 %0.61 %3.91 %9.02 %8.12 %6.41 %4.92 %3.11 %6.32 %5.7 %4.51 EBE saiB %4.0- %1.1- %7.2 %5.1 %6.2- %9.6- %5.3- %2.6- %5.7- %9.8- %2.1 %1.7 %1.0- %8.4 %4.1- %1.3 SMR %9.8 %3.01 %6.4 %7.8 %3.4 %7.6 %3.4 %2.5 %9.3 %0.4 %7.4 %1.4 %7.4 %2.8 %1.5 %6.7 saiB latoT %2.2- %2.3- %8.1 %3.0 %4.5- %2.21- %8.8- %6.11- %9.21- %0.41- %6.2 %7.11 %5.0 %2.8 %8.2- %0.4 SMR %4.11 %8.11 %1.11 %0.11 %0.31 %6.91 %9.61 %2.91 %3.02 %1.12 %6.11 %2.81 %0.11 %1.51 %4.11 %9.11 III EPYT LENNAHC EDE saiB %3.1- %0.1- %6.1- %6.1- %2.0 %1.1- %6.3- %1.1- %70.0 %5.1- %20.0 %1.1- %6.0 %9.0- %4.0 %2.1- SMR %0.5 %2.5 %4.5 %2.5 %6.5 %3.5 %5.5 %2.5 %2.5 %2.5 %1.5 %1.5 %4.5 %9.4 %3.5 %8.4 DED saiB %0.5- %0.5- %5.4- %8.4- %5.4- %9.4- %1.5- %7.4- %5.4- %0.6- %7.4- %4.4- %5.4- %7.4- %5.4- %7.4- SMR %6.5 %8.6 %6.5 %5.5 %5.5 %7.5 %5.5 %7.5 %9.5 %9.5 %6.5 %8.5 %5.5 %9.5 %1.6 %7.5 saiB latoT %2.3- %0.3- %1.3- %2.3- %2.2- %0.3- %3.4- %9.2- %2.2- %8.3- %3.2- %8.2- %9.1- %8.2- %0.2- %0.3- SMR %3.5 %1.6 %5.5 %3.5 %5.5 %5.5 %5.5 %5.5 %6.5 %6.5 %3.5 %5.5 %4.5 %4.5 %7.5 %3.5 Table 8-3. Total RMS and bias for ne relationships using Method 3 on the walls and Method 1 on the floor.

78 Based on the total RMS values for Channel Type I, on aver- age the LAD, Horton, Colebatch, Pavlovskii, Total F3, Total F4, Total U*2, and Total U*3 predictive relationships performed the best (all within 1% of one another), with the LAD relation- ship producing a slightly smaller RMS value than the others. For the Type II channel, the Total F2, Horton, Colebatch, Total F4, HDM, Total U*1, Total U*2 and Total U*3 predictive rela- tionships performed the best (all within 1.0% of one another), with Total F2 being slightly better than the others. For the Type III channel, all of the predictive ne relationships performed essentially the same, with the total discharge relationships pro- ducing a slightly smaller RMS than the other relationships. The results of the data presented in Table 8-3 show that no obvious advantage exists in using the more complicated subarea-dividing-based ne relationships over the simpler-to- use relationships that only use Pi as the weighting parameter for the ni in the channel. There is no need to divide the cross- section of the channel into subareas because (1) Pi is the sole weighting parameter in these relationships and (2) Method 3, which uses the total hydraulic radius (Rh) of the channel instead of Rhi, has been shown to work as well as or better than the other methods. There is one such equation per assump- tion group: the Horton relationship (mean velocity assump- tion group), Pavlovskii’s relationship (total force assumption group), total Q2 (total discharge assumption group), and the HDM relationship (total shear velocity assumption group). Of those relationships, Horton is the most consistent when considering all three channel types (I, II, and III). It is important to remember that the data in this study were collected in a channel with a simple and uniform cross-section (rectangular). In addition, although the range or boundary roughness materials varied appreciably in this study, it should be noted that a high level of roughness element uniformity existed for each composite roughness boundary material (no random roughness elements within a given boundary rough- ness material) in relation to itself. The extent to which these results can be applied to other types of composite roughness channels that feature different channel cross-sections and variation in the degree of component boundary roughness element uniformity (e.g., a buried-invert fish passage cul- vert, as shown in Figure 2-1) has yet to be determined. In the absence of better information, however, the data from this study can be used as a first-order approximation for other composite roughness channel applications. It is also impor- tant to note that, based on the variability in the RMS values in Table 8-3 for the individual composite roughness geom- etries (e.g., ADA, etc.), the predictive ne values associated with any of the relationships listed in Table 8-2 should be consid- ered approximate. This is especially true when looking at the “Total RMS” (presented in Tables 8-2 and 8-3), which is based on a compilation of all of the data from composite channel configurations in a single channel type (I, II, or III). 8.6 Conclusions The conclusions associated with composite roughness open channel flow resistance in a rectangular flume that result from this study include the following: 1. It is important to note that, regardless of the technique used to estimate ne based on ni, in general, composite roughness open channel flow conditions are three-dimensional flow problems that researchers have attempted to solve with the empirically based one-dimensional, Manning’s Equation (Equation 8-1). The likelihood of finding a robust ne predic- tion method that will work with Equation 8-1 for solving a wide range of composite roughness channel configurations is low due to the complex nature of the problem. 2. Where data are available, a variable Manning’s n (the appropriate n value for a given flow condition) should be used on the channel floor. A constant ni may be applied to the walls of the channel with little negative impact to the predictive error; in fact, in most cases in this study, it improved ne predictions. 3. The mean velocity assumption relationships, as a group, performed more consistently than the other groups as a whole; however, there are only two equations in the mean velocity group compared to the four or five equations of the others. The total discharge assumption relationships, as a group, performed inconsistently relative to the other relationships. 4. Based on the data obtained for this study, there is no evi- dence that a single ne equation has a clear advantage over the rest. Taking into consideration the results from all three channel types, the most consistent equations (those which were within 1% of the lowest RMS of each channel type) were Horton, Colebatch, Total F4, Total U*2, and Total U*3. 5. Of these equations, there is no conclusive evidence that the more complex ne equations will produce better results than the simplest equation (Horton’s Equation, Horton 1933). 6. Due to the inconsistent results of the ability of the ne equa- tions to predict ne for channels where the wall is relatively rough in comparison to the floor of the channel (Type II channels), it is recommended that further study be con- ducted to examine the difference between the resistance provided by a specific roughness material, whether it be on the wall of the channel or on the floor of the channel. For example, Christensen (1992) proposed an alternate definition of Rh, relative to the traditional A/P, rather than adjusting the hydraulic resistance coefficient to account for the variation in shear stress values along the wet- ted perimeter of the channel walls. Future works should include channels with cross-sectional shapes different than the rectangular shape tested in this study.