Hydraulic Loss Coefficients for Culverts (2012)

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31 5.1 Summary In general, multibarrel culvert design is based on the assump- tion that the head-discharge relationships for the individual cul- vert barrels in a multibarrel culvert assembly are independent of the other culvert barrels and that the multibarrel culvert head- discharge relationship may be developed by multiplying the single culvert discharge by the number of barrels (assuming all culvert barrels are the same size, geometry, and material type and are installed at the same elevation and slope). This study evaluated that assumption for a variety of multibarrel culvert configurations (i.e., two- and three-culvert assemblies with various culvert spacings) and approach flow conditions. Single-barrel culvert performance data were also collected for comparison. The results of the two-barrel multibarrel culvert tests showed that average individual-barrel flow rate for the multi- barrel culvert (total flow rate divided by the number of barrels) was essentially the same as the single-barrel culvert performance for the same headwater and approach flow condi- tions. The three-barrel test results were similar with respect to matching the single-barrel performance except for tests where the approach flow was non-uniform. The average individual- barrel flow rate for the non-uniform inlet invert configura- tion was still within 3% of the single-barrel performance. For the non-uniform approach modeled, the single-barrel model accurately predicts the average barrel flow rate over most of the unsubmerged inlet range. For the near- and full-submergence inlet conditions, the non-uniform-approach three-barrel (uni- form inlet invert elevation) condition produced an average bar- rel discharge 10% less than the single-barrel discharge. While the average individual-barrel flow rate in the multibarrel cul- vert assemblies correlated well with the single-barrel data, the measured individual-barrel flow rates varied by as much as ±7% of the flow predicted by the single-barrel model, a cir- cumstance that may warrant consideration when considering fish passage and/or scour protection at the outlet. 5.2 Introduction Culverts are the primary means for transporting water through road embankments, and the FHWA and others have published a significant amount of culvert design data. One of the most widely used culvert design documents is FHWA’s HDS-5 (Normann et al., 2001). This manual is based primar- ily on a number of tests conducted by John L. French (1955, 1956, 1957, 1961, 1966a, 1966b, 1967) for the National Bureau of Standards (now the National Institute of Standards and Technology, NIST) under the sponsorship of the Bureau of Public Roads (now FHWA). Several researchers before and after have both verified and expanded the dataset. In the many years since French’s work (French, 1955, 1956, 1957, 1961, 1966a, 1966b, 1967), most public agencies have designed culverts and multibarrel culverts according to HDS-5. While HDS-5 was primarily developed for single-barrel culverts, designers have used the same procedures to design multibarrel culverts, treating each barrel in the multibarrel culvert assembly as a single, independent culvert and summing the individual flow capacities (superposition). Multibarrel culverts are commonly used (instead of a single, larger culvert design) for wide, shallow channels or flood plains (relative to the road embankment height) and for channels where sediment transport and/or fish passage are a concern at low-flow conditions. Some common fish pas- sage designs (Bates et al., 2003) exclude multibarrel culverts due to the general undersizing of the culvert relative to fish and habitat needs. To improve fish passage and sediment transport conditions through multibarrel culverts at low discharge conditions, one of the culvert barrels (typically the barrel nearest the center of the stream) is sometimes installed at a lower elevation than the other barrels, restricting low discharges to a single culvert barrel. Concentrating low discharges in a single culvert barrel increases flow depth, which aids fish passage, and flow velocity, which aids sedi- ment transport. C h a p t e r 5 Inlet Control Hydraulics of Multiple Circular Culverts

32 not been adequately verified. Jones et al. (2006) suggest that multibarrel box culverts behave similarly to single-barrel box culverts. Charbeneau et al. (2002, 2006) also reported simi- larities between single-barrel and multibarrel box-culvert performance data but suggest that HDS-5 data (Normann et al., 2001) may over predict box-culvert spans by 17% for one design example. One limitation to the findings from these studies is that neither study reported directly measur- ing the individual-barrel flow rates. Based on their work with culverts on steep slopes, Korr and Clayton (1954) noted that the presence of intermittent vortices could cause the flow regime to fluctuate back and forth between open channel flow (inlet control) and full- pipe (outlet control), causing both the upstream head and discharge to fluctuate. French (1961) also noted these effects and artificially suppressed vortex activity for some labora- tory tests. Blaisdell (1966) reported vortex-based flow regime instability for 1 < Hw/D < 3. Similar flow regime fluctuations were noted in the current study. French (1961) studied the effect of pipe wall thickness and determined that, for pipe wall thickness values less than 0.04D, flow contraction was initiated at and controlled by the outer edge of the culvert at the inlet; for wall thickness values greater than 0.04D, the inside edge was the control. The pipe used in the current study had a pipe wall thickness of 0.02D (8-in. PVC pipe). 5.3 Research Objectives The objective of this study was to test the superposition- based multibarrel culvert design process by comparing single-barrel and multibarrel culvert hydraulic perfor- mance under various barrel layout and approach flow con- ditions. A culvert test facility was constructed at the Utah Water Research Laboratory (Utah State University), and inlet control culvert experimental data were collected for this purpose. The results of multibarrel culvert performance tests were compared with single-barrel experimental results as well as single-barrel data in HDS-5 (Normann et al., 2001). Empirical coefficients are presented for use in the traditional inlet control head-discharge relationships presented in HDS-5 (Equations 1-2 through 1-4). This research was limited to cir- cular culverts operating under inlet control. All tests were conducted using square-edged, thin-wall, projecting, 8-in. PVC pipe. In an effort to determine where multibarrel culverts are used in the United States, along with the extent to which designs featuring one culvert barrel installed lower than the other barrels are used, a survey of state departments of transportation (DOTs) was conducted with approximately half of the States responding. The survey results are shown in Table 5-1. Multibarrel culverts can be problematic in drainages that transport large debris elements (e.g., branches, trees, shop- ping carts, etc.) as the individual-barrel sizes may be too small to pass such debris during flood events. Some federal agen- cies, including the Federal Emergency Management Agency (FEMA), discourage the use of multibarrel culverts, perhaps in part because FEMA must deal with failed culverts that result primarily from extreme flow events that likely exceed the culvert design capacity. Mountainous states, such as Wash- ington, highly discourage the use of multiple culverts because of potential debris problems. An example of a multibarrel circular culvert is shown in Figure 5-1. The barrel spacings in Figure 5-1 are small enough that the amount of flow contraction experienced at the entrance of each barrel is likely influenced (reduced) by the presence of the adjacent barrels. As the amount of flow con- traction at the culvert barrel inlet decreases, the flow capacity of the culvert should increase. This suggests that the perfor- mance of individual barrels in a multibarrel culvert assembly may vary relative to the performance of summed singe-barrel culverts. A limited number of studies on circular, multibarrel culverts were found in the literature. Wargo and Weisman (2006) performed circular pipe tests comparing scour depths and culvert flow depths and their influence on fish passage. They speculated that backwater depths could potentially be less for multibarrel culverts than for single-barrel cul- verts, but their findings were not conclusive. Johnson and Brown (2000) tested multibarrel, circular culverts, but they focused mainly on stream impacts rather than head- discharge relationships. Applying the HDS-5 (Normann et al., 2001) single-barrel culvert data to multibarrel culvert design via superposition- ing is likely to be a common practice (primarily due to a lack of other alternatives), but the accuracy of this approach has Figure 5-1. Example of multibarrel culvert installation.

33 head equal to the total head. The head box pressure tap location is shown in Figure 5-2. Uniform approach flow into the reservoir and a relatively calm water surface were achieved by passing flow over a weir that spanned three sides of the reservoir. Culvert Barrels The test culverts were constructed of 8-in. diameter (I.D. = 7.8 in.) PVC pipe installed at a slope (So) of ~ 3% with square-edged, thin-wall, projecting end treatments. The parameters evaluated in this study that influence inlet 5.4 Experimental Method Test Facility The culvert testing was conducted using a 24-ft-long by 22-ft-wide by 5-ft-deep reservoir head box (shown in Fig ure 5-2). Water was supplied through 4-, 8-, and 20-in. parallel supply lines with calibrated orifice plates in each line facilitating accurate flow measurement over a wide range of flow rates. The orifice plate calibrations are trace- able to NIST by weight. The head box piezometer tap, used to determine Hw, was located in an area where the flow velocities were essentially zero, making the piezometric State Multibarrel Culvert Use Typical End Treatments One Barrel w/ Lowered Invert Alaska circular & box varies, headwall common sometimes Arkansas circular & box flared concrete section typically not California circular & box headwall/ flared end not usually Colorado circular & box headwall, no projecting sometimes Connecticut not specified headwall yes (1 to 2 ft lower typical) Georgia circular & box headwall w/ 45° wingwalls not usually Hawaii circular headwall w/ wingwalls not usually Idaho circular projecting no Indiana uncommon projecting if circular – Iowa box normally projecting common no Kentucky circular headwall no, training wall used for low flows Maine circular (mostly) & box projecting, mitered for D > 8 ft, few headwalls yes (0.5 to 1.0 ft lower typical) Maryland circular typically headwall, mitered, projecting buried-invert (embedded) culverts typically used Michigan precast (box?) – yes (>1 lower typical) Minnesota circular & box headwall sometimes (box: 2 ft lower typical) Missouri box sometimes – yes (box: 1 ft lower typical) Nebraska circular & box (>20 ft) headwalls for boxes sometimes (box: 0.5 to 1 ft lower typical) Nevada yes depends on situation depends New Mexico yes headwalls not usually North Dakota pipes and box headwall/flared maybe about 1 ft lower. Ohio rarely used – – South Carolina pipes and box Headwall yes (1 ft lower typical) Utah circular & box – yes Washington no multibarrel culverts – – Wyoming ? Headwall and flared end sections uncommon Table 5-1. State DOT multibarrel culvert use survey results (February 2007).

34 The barrel inlet invert reference elevations were referenced on the piezometer as follows. A 4-in. diameter beaker, partially filled with water, was hydraulically connected to the piezom- eter tube via flexible tubing. The water surface in the beaker was placed at the same elevation as the barrel inlet and the piezometer reading noted. The 4-in. diameter beaker was used in an effort to minimize the surface tension effects in refer- encing the inlet invert elevation. Because all flow depth mea- surements determined using the piezometers were differential measurements (i.e., a reference piezometer reading was sub- tracted from the indicated piezometer reading), no correction for piezometer surface tension effects was required. Outlet Structures A primary objective of this study was to identify the varia- tion in discharge between barrels in a multibarrel culvert assembly for various culvert configurations and approach flow conditions. To facilitate this objective, individual tail boxes were constructed for each culvert barrel. An elbow installed control flow efficiency included the number of barrels (two or three), the barrel spacing (two or three barrel diameters), and the approach flow conditions. The barrel lengths were 10, 15, and 20 ft, as shown in Figure 5-2. The projection distance of the barrels was typically 1.5 ft (2.25 pipe diameters) past the reservoir headwall, except for the skewed headwall configuration where the projection dis- tance was about 0.5 ft (0.75 pipe diameters). Two pressure taps were installed in each culvert barrel invert approximately four pipe diameters downstream from the barrel inlet and upstream of the barrel outlet for determining culvert flow depth and veloc- ity information at those locations. Barrel Froude numbers (Fr) were calculated to confirm supercritical flow and inlet control (Fr > 1.0). The inlet end of each culvert barrel rested on a false floor in the reservoir with the same slope as the culvert barrels (So). A uniform invert elevation was maintained for all barrels to ensure that each culvert barrel had a common Hw measurement reference. The barrels were supported at mid-span to minimize slope variations associated with culvert deflection. Longitudi- nal restraints were also used to keep the barrels in place. Figure 5-2. Overview of culvert testing facility.

35 meter to determine the flow rate into the head box. Piezome- ters were used to determine Hw and culvert barrel flow depths (y). The culvert invert elevation and invert of the barrels at the pressure tap locations reference elevations were identified on the appropriate piezometers to facilitate flow depth measure- ment. All tubing connected to pressure taps was thoroughly bled to expel air bubbles prior to collecting data. In some cases, measuring the flow depth in the culvert is not entirely straightforward. Figure 5-4 shows the surface waves present inside the culvert for one test condition. When water surface fluctuations were present, a visual averaging of the piezometric reading on the piezometer was required. Water surface fluctuations were more prevalent for submerged inlet conditions. Test Matrix The various single-barrel and multibarrel culvert configu- rations tested are listed in Table 5-2. Culvert combinations on the downstream end of each culvert directed the flow into a drop structure, which was enclosed to contain splash and was vented to atmosphere. The water entered a tail box via a screen structure, which improved the flow uniformity. A calibrated- in-place V-notch weir was used to measure the discharge as it exited the tail box. Stilling wells hydraulically connected to the tail boxes were used to determine the water depth or head on each weir. An overview photo of the tail box/V-notch weir assemblies is shown in Figure 5-3. The standard V-notch weir equation (Equation 5-1) was used for determining the discharge through each barrel/tail box assembly: Q gC Hd=   8 15 2 2 5 12 5tan ( ). θ - where Q is the volumetric flow rate, Cd is the discharge coefficient, q is the angle of the V-notch (q = 90° in this study), and H is the upstream flow depth measured relative to the invert of the V-notch. The calibrated-in-place Cd values, which varied slightly with flow rate, correlated very well with published Cd values [e.g., 0.585 (Henderson, 1966)]. Data Collection For each test condition, the following data were collected: flow rate into the head box (i.e., total multibarrel culvert flow rate), headwater depth, flow depth in each barrel (two loca- tions), individual-barrel discharges, and any general observa- tions such as vortex formation and persistence. Differential manometers were used in conjunction with the orifice flow Figure 5-3. V-notch weir/tail box assemblies. Figure 5-4. Example of surface waves inside the culvert.

36 sional drawings of some of the test configurations are shown in Figures 5-6 (A–D). Removable end caps were used to seal the extra barrels during the one- and two-barrel test configu- rations. The influence of the non-flowing culverts on adjacent flowing culverts was assumed to be minimal. 5.5 Experimental Results This section presents the experimental results for the single- barrel and multibarrel (two- and three-barrel) culvert tests. The single-barrel culvert data are used both as a baseline and to compare the performance of the individual barrels in the multibarrel assemblies. Observations of hydraulic phenomena that appeared to influence the culvert head-discharge relation- ships are also briefly discussed. tested included one, two, and three circular barrel culverts with various horizontal and vertical spacing distances and dif- ferent approach conditions. A culvert barrel installed lower than the other barrels in a multibarrel culvert assembly is referred to in this study as a “depressed barrel” or “depressed culvert.” For each test configuration shown in Table 5-2, data were collected for a range of flow rates and headwater values (submerged and unsubmerged inlet conditions). Sufficient time, sometimes up to 1 h, was allowed for each flow condi- tion to reach steady state. Steady state conditions were con- firmed by repeatedly measuring the Hw until changes were no longer observed. Test conditions were typically limited to Hw/D < 3.5. Photographic overviews of the various barrel and ap proach flow configurations are shown in Figure 5-5 (A–H). Dimen- Configuration No. # of Culvert Barrels Barrel Spacing Center-to-Center Approach Flow Angle (degrees) Upstream Channel Configuration Depressed Culvert Invert Offset 1 1 – 0 Reservoir 0 2 2 1.5D 0 Reservoir 0 3 2 2D 0 Reservoir 0 4 2 3D 0 Reservoir 0 5 3 1.5D 0 Reservoir 0 6 3 2D 0 Reservoir 0 7 3 3D 0 Channeled 0 8 3 3D 40 Channeled 0 9 3 3D 0 Reservoir 0 10 3 3D 0 Non-uniform 0 11 1 2D 0 Trapezoid 2:1 0.5D 12 2 2D 0 Trapezoid 2:1 0.5D 13 3 2D 0 Trapezoid 2:1 0.5D 14 3 3D 0 Trapezoid 2:1 0.5D Table 5-2. Single-barrel and multibarrel culvert test configurations. Figure 5-5(A). Two-barrel, 1.5D spacing with reservoir approach. Figure 5-5(B). Three-barrel, 2D spacing with reservoir approach.

Figure 5-5(C). Three-barrel, 3D spacing with reservoir approach. Figure 5-5(D). Three-barrel, 3D spacing with rectangular channel approach. Figure 5-5(E). Three-barrel, skewed, 3D spacing with rectangular channel approach. Figure 5-5(F). Three-barrel, 3D spacing with a non-uniform approach flow. Figure 5-5(G). Three-barrel, 2D horizontal spacing, 0.5D depressed culvert with a trapezoidal channel approach. Figure 5-5(H). Three-barrel, 3D horizontal spacing, 0.5D depressed culvert with a trapezoidal channel approach.

38 Clayton, 1954; Schiller, 1956) have also reported that vortex activity played a role in the hydraulic efficiency of submerged inlet culvert hydraulics for ranges of Hw/D consistent with those evaluated in this study. In the present study, vortex activity was most noticeable for 1.0 < Hw/D < 3.0 and for horizontal barrel spacings of 1.5D. Inlet Flow Contraction Figure 5-8 shows inlet flow conditions for the 1.5D hori- zontal culvert spacing (uniform inlet invert elevation) for an unsubmerged inlet and a nearly submerged inlet condition. Note the relatively large flow separation regions on the lateral side of the inlet for the outside barrels in the unsubmerged inlet condition; the flow separation regions for the center bar- rel are much less evident. The sizes of the separation regions for the transitional submergence case are similar in size but Observed Influences on Culvert Hydraulics Vortex Activity Water level fluctuations during “steady state” submerged inlet conditions were observed in the reservoir and V-notch weir head boxes and were tied to vortex activity at the cul- vert inlets. When aerated surface vortices or vortices that formed between barrel inlets (observed only with the 1.5D horizontal spacing culvert assemblies) were present, as shown in Figure 5-7, the culvert efficiencies reduced and the headwater depth increased. Once the vortices dissipated, the headwater depth decreased. The unsteady nature of vortex- induced reservoir level fluctuations was observable in the res- ervoir piezometer readings. Reservoir water levels were very stable for unsubmerged flow conditions and for the barrel inlets free of vortex activity. Previous studies (Blaisdell, 1966; French, 1955, 1956, 1957, 1961, 1966a, 1966b, 1967; Korr and Figure 5-6(A). Multibarrel culvert configuration with 2D horizontal barrel spacing and a trapezoidal approach channel.

39 suggests that the geometry created by the presence of the capped barrels did not inhibit the single-barrel culvert flow perfor- mance. The “trend line” data represents the unsubmerged inlet control Form 2 (Equation 1-3) head-discharge relationship for Hw/D < 1 and the submerged inlet control head-discharge relationship (Equation 1-4) for Hw/D >1 fit to the experimen- tal data. Experimental and trend line data for a single-barrel PVC circular culvert with a trapezoidal approach channel are also presented in Figure 5-9. The single-barrel culvert with the channelized approach is slightly more efficient than the reservoir approach condition, likely due to a decrease in the inlet flow contraction. The corresponding K, M, c, and Y co efficients for the data in Figure 5-9 are presented in Table 5-3. The single-barrel data presented in Figure 5-9 were used as the baseline data for evaluating the individual-barrel per- formance of the multibarrel culvert test assemblies. Multibarrel culvert configurations with reservoir approach conditions were vary in location. Flow separation at multibarrel culvert inlets appears to be a contributing factor to the performance varia- tions observed between single-barrel culvert and multibarrel culvert performance. Single-Barrel Test Results Figure 5-9 shows the experimental, quasi-dimensionless head-discharge data for a single-barrel PVC circular cul- vert with a thin-wall projecting end treatment and a reservoir approach. The single-barrel, thin-wall projecting, circular cul- vert data were collected for each barrel in the three-barrel 1.5D and 3D horizontal barrel spacing assemblies by placing sealed end caps on the inlets of the unused barrels. Figure 5-5(A) shows an example of a capped barrel inlet. The data for the six single-barrel test configurations are plotted as a single data set in Figure 5-9. The close agreement in the data in Figure 5-9 Figure 5-6(B). Multibarrel culvert configuration with 3D horizontal barrel spacing and a trapezoidal approach channel.

40 Figure 5-6(C). Multibarrel culvert configuration with 3D horizontal barrel spacing and a 40°, skewed, rectangular approach channel. Figure 5-6(D). Multibarrel culvert configuration with 3D horizontal barrel spacing and a non-uniform approach flow channel. (A) (B) Figure 5-7. Examples of an aerated surface vortex (A) and a submerged barrel-to-barrel vortex (B).

41 (A) (B) Figure 5-8. Variations in flow contraction patterns between the middle and outside barrels for unsubmerged (A) and nearly submerged or transitional submergence inlet conditions (B). Figure 5-9. Single-barrel, inlet control, head-discharge data and trend lines based on testing all three barrels individually with 1.5D and 3D horizontal barrel spacing and a reservoir approach or a trapezoidal channel approach flow condition. compared with the single-barrel, reservoir approach data. Multi- barrel culvert configurations with channelized approaches (i.e., trapezoidal or rectangular) were compared with the single-barrel, trapezoidal channel approach data. The inlet control, thin-wall projecting, corrugated metal pipe (CMP) head-discharge data with a reservoir approach condi- tion, calculated using the coefficients published in HDS-5, are plotted in Figure 5-9. The thin-wall projecting CMP culvert data, which represents the most similar culvert/end treatment configuration in HDS-5 to the single-barrel culverts tested in the current study, were included as a relative comparison and a quality-control check for the single-barrel data from this study. For 1 < Hw/D < 3.0, the agreement is very good. Outside that range, the performance varies. At Hw/D > 2.5–3.0, the slightly thicker pipe wall of the non-corrugated PVC pipe inlet becomes slightly more efficient. The general agreement between the two data sets is a good indication that it is likely that there were no systemic biases associated with the experimental method of the

42 2D and 3D horizontal barrel spacings, reservoir and trapezoi- dal channel approach flow conditions, and a 0.5D depressed middle barrel culvert. The experimental, two-barrel, quasi-dimensionless data for the different test conditions are plotted in Figures 5-10 through 5-13. As with the single-barrel data, the trend lines represent the average individual-barrel head-discharge relationship for the multibarrel culvert configurations using the Form 1 and Form 2 relationships (Equations 1-2 and 1-3) for unsubmerged inlet conditions (Hw/D < 1.0) and the submerged relationship current study and that the use of the single-barrel experimental data set for comparison with the multibarrel culvert assemblies is representative of published single-barrel performance data. Two-Barrel Test Results The two-barrel culvert tests were conducted using the three- barrel installation with one of the outside barrels capped off, as shown in Figure 5-5(A). The two-barrel test configuration variations included the middle barrel with each outside barrel, Test No. No. of barrels Culvert Barrel center- to- center Headwall- to- approach flow Upstream Approach Condition Depressed middle- barrel vertical offset Unsubmerged Form 1 Unsubmerged Form 2 Submerged (D) (deg) K M K M c Y 1 1 – 0 Reservoir 0 0.0885 0.5370 0.5870 0.5490 0.0506 0.6500 2 2 1.5 0 Reservoir 0 0.0900 0.6123 0.5874 0.5621 0.0482 0.7257 3 2 2.0 0 Reservoir 0 0.0846 0.6117 0.5825 0.5609 0.0508 0.6483 4 2 3.0 0 Reservoir 0 0.0936 0.5412 0.5924 0.5498 0.0499 0.6767 5 3 1.5 0 Reservoir 0 0.0844 0.5341 0.5859 0.5224 0.0503 0.6609 6 3 2.0 0 Reservoir 0 0.0858 0.5570 0.5840 0.5545 0.0494 0.6603 7 3 3.0 0 Channeled 0 0.0631 0.5986 0.5587 0.5615 0.0417 0.6952 8 3 3.0 40 Channeled 0 0.0941 0.2396 0.5925 0.5072 0.0501 0.5677 9 3 3.0 0 Reservoir 0 0.0914 0.5497 0.5885 0.5525 0.0502 0.6532 10 3 3.0 0 Non- uniform 0 0.0899 0.6812 0.5874 0.5777 0.0443 0.7659 11 1 2.0 0 Trapezoidal 2:1 0.5 0.0744 0.7984 0.5715 0.5462 0.0486 0.6202 12 2 2.0 0 Trapezoidal 2:1 0.5 0.0944 0.2737 0.5937 0.5068 0.0472 0.6635 13 3 2.0 0 Trapezoidal 2:1 0.5 0.0992 0.2716 0.6002 0.5076 0.0418 0.7512 14 3 3.0 0 Trapezoidal 2:1 0.5 0.0998 0.3753 0.6004 0.5265 0.0423 0.7196 Table 5-3. Inlet control empirical coefficients for Equations 1-3 and 1-4. Figure 5-10. Experimental data for two-barrel, 1.5D horizontal spacing tests with common invert elevations and a reservoir approach flow condition.

43 Figure 5-11. Experimental data for two-barrel, 2D horizontal spacing tests with common invert elevations and a reservoir approach flow condition. Figure 5-12. Experimental data for two-barrel, 3D horizontal spacing tests with common invert elevations and a reservoir approach flow condition. (Equation 1-4) for Hw/D > 1.0. The single-barrel culvert data for the same approach flow condition [i.e., reservoir or chan- nelized (trapezoidal channel)] are also plotted. The data points in Figures 5-10 through 5-13 were not seg- regated with respect to the individual barrels or pairings due to poor readability (congested data points). In general, the trend lines for each of the two-barrel test configurations [i.e., 1.5D (Figure 5-10), 2D (Figure 5-11), and 3D (Figure 5-12) horizon- tal spacing with a reservoir approach and the 2D horizontal, 0.5D depressed barrel with trapezoidal channel approach (Fig- ure 5-13)] correlate well with the single-barrel culvert trend lines. Note that the test data for the two-barrel 0.5D depressed barrel configuration shown in Figure 5-13 follow the same trend line, despite the offset in culvert inlet elevations. This correlation suggests that the practice of designing multibarrel culverts as multiples of single-barrel culverts (superposition) may be appropriate for determining multibarrel head-discharge relationships. The individual two-barrel data points in Figure 5-10, how- ever, show some variation from the trend line (±5%), suggest- ing that, while superposition may be a good predictor of the average performance, the variations in barrel flow rates and increases in velocities as the barrel spacing decreases may war- rant additional consideration with respect to culvert outlet

44 barrel culvert assemblies tested with the reservoir approach flow condition performed very similarly. The empirical co- efficients, corresponding to Equations 1-3 and 1-4 (i.e., K, M, c, and Y), for all inlet control two-barrel multibarrel culvert configurations tested are presented in Table 5-3. Three-Barrel Test Results The two-barrel culvert test configurations were repeated for the three-barrel culvert tests (i.e., 1.5D, 2D, and 3D hori- zontal spacing with a reservoir approach and the 2D horizon- tal, 0.5D depressed middle barrel with a trapezoidal channel approach). Several additional 3D horizontal spacing (uni- riprap protection and fish passage velocity requirements. The flow rate variations between individual barrels, correspond- ing to submerged inlet conditions, were usually attributable to sporadic surface or barrel-to-barrel vortex activity. All of the data for the two-barrel culvert configurations tested and the single-barrel experimental reference data are plotted in Figure 5-14. The quasi-dimensionless head- discharge relationships appear to be influenced more by the approach flow condition than the specific two-barrel, multi- barrel culvert configuration. Figure 5-14 shows that the single- barrel and multibarrel configurations tested with a trapezoidal approach channel were more efficient than those tested with a reservoir approach flow. All of the single-barrel and multi- Figure 5-13. Experimental data for two-barrel, 2D horizontal spacing, 0.5D depressed-barrel tests and single-barrel with trapezoidal channel approach flow condition. Figure 5-14. Trend line summary for all two-barrel culvert and single-barrel culvert configurations tested.

45 single-barrel trend line for either the reservoir or trapezoi- dal channel approach flow condition for comparison. The barrels are identified as viewed from the upstream direc- tion (i.e., left, middle, and right). Figures 5-15 through 5-22 indicate that, in general, the middle barrel is more efficient, likely due in part to the decrease in middle-barrel inlet flow contraction compared to the outside barrels. Despite the variation in the individual-barrel performances, the best- fit three-barrel trend lines generally correlate well with the single-barrel performance data. form inlet invert elevation) configurations were also tested, including a rectangular channel approach; a skewed headwall with a rectangular channel approach; a 3D horizontal spac- ing, 0.5D depressed middle-barrel configuration; and a non- uniform approach flow condition. The three-barrel experimental results are presented in Figures 5-15 through 5-22. In each plot, the individual- barrel data are presented along with a best-fit trend line [based on the Form 2 relationship (Equation 1-3) for unsubmerged and Equation 1-4 for submerged inlet conditions] and the Figure 5-15. Experimental data for three-barrel, 1.5D horizontal spacing tests with common invert elevations and a reservoir approach flow condition. Figure 5-16. Experimental data for three-barrel, 2D horizontal spacing tests with common invert elevations and a reservoir approach flow condition.

46 Figure 5-17. Experimental data for three-barrel, 3D horizontal spacing tests with common invert elevations and a reservoir approach flow condition. Figure 5-18. Experimental data for three-barrel, 3D horizontal spacing tests with common invert elevations and a rectangular channel approach flow condition. In Figure 5-15, the data points for the 1.5D spacing show more scatter than the other test configurations. A repeat of the test, including setup and data collection, produced simi- lar results. Closer inspection revealed an increase in surface and sub-surface (barrel-to-barrel) vortex activity for the 1.5D barrel spacing relative to the larger culvert spacing con- figurations. Barrel-to-barrel, sub-surface vortices were not observed for the 2D and 3D barrel spacing configurations. Intermittent surface vortices were observed for all barrel spacings, but in general, the duration of the individual sur- face vortices increased as the barrel spacing decreased. The trend lines for the 3D three-barrel with a rectangular channel approach (Figure 5-18) and the skewed headwall with a rectangular channel approach (Figure 5-19) match the single- barrel trapezoid approach trend line reasonably well. Only part of the 3D three-barrel with a trapezoidal channel approach data are plotted in Figure 5-18. During data collection, it was noted that at the higher discharge/headwater conditions, the drop structures at the outlet ends of the culvert barrels were not sufficiently vented, which allowed sub-atmospheric pressure to develop and increase the discharge capacity of the multibarrel culvert assembly. This caused the experimental data and the

47 5-6(D)] was of arbitrary design and is not necessarily rep- resentative of other non-uniform approach flow conditions. This non-uniform approach flow configuration successfully created a notable disparity in discharge capacity between the more efficient middle barrel and the outside barrels. The non-uniform approach produced a larger deviation between the three-barrel and the single-barrel trend lines than any other configurations tested. The single-barrel trend line had a max- imum under-prediction of the average three-barrel trend line (near Hw/D = 1.0) of approximately 10%. Figures 5-21 and 5-22 present the three-barrel test results with a 0.5D depressed middle barrel and a trapezoidal trend line to deviate from the single-barrel with a trapezoi- dal channel approach trend line. Following that test and prior to installing and testing the 3D, three-barrel skewed headwall with a rectangular channel approach, vent holes were added to the drop structures. Based on the good agreement between the three-barrel and single-barrel trend lines in Figure 5-19, it was assumed that the trend lines in Figure 5-18 would likely maintain their agreement at the higher Hw/D values with the vent holes and that the test did not warrant repeating. Figure 5-20 shows the 3D three-barrel performance with a non-uniform approach condition. Admittedly, the specific non- uniform approach flow condition [shown in Figures 5-5(F) and Figure 5-19. Experimental data for three-barrel, 3D horizontal spacing tests with common invert elevations, a skewed headwall, and a rectangular channel approach flow condition. Figure 5-20. Experimental data for three-barrel, 3D horizontal spacing tests with common invert elevations and a non-uniform approach flow condition.

48 to the outside barrels and the single-barrel trend line. The single-barrel trend line in Figure 5-21 underestimates the average individual-barrel trend line for the three-barrel con- figuration by approximately 4% at higher Hw/D values. Due to the limited Hw/D data range in Figure 5-22, a similar com- parison cannot be made; however, the data appear to have a similar trend to the data in Figure 5-21. These results suggest that single-barrel head-discharge relationships and super- channel approach. Note that for the individual test condi- tions, the middle-barrel data do not match up with the left- and right-barrel data (at common Hw/D values) because of the offset in barrel inlet inverts. The trend line for the unsub- merged and low submergence inlet flow regions matches the single-barrel flow curve fairly well. As the inlet submergence increased (Hw/D = 1.5 to 2.0 range), the discharge efficiency of the depressed middle barrel began to increase compared Figure 5-21. Experimental data for three-barrel, 2D horizontal spacing tests with a 0.5D depressed middle barrel and a trapezoidal channel approach flow condition. Figure 5-22. Experimental data for three-barrel, 3D horizontal spacing tests with a 0.5D depressed middle barrel and a trapezoidal channel approach flow condition.

49 dition. The channelized approach flow associated with the upstream trapezoidal channel was more efficient than the reservoir approach flow condition, primarily due to a reduction in flow contraction entering the cul- vert barrel with the channelized approach flow. 3. The single-barrel head-discharge relationships (reservoir and trapezoidal channel approaches) correlated very well with the average-barrel head-discharge relationships for all two- and three-barrel multibarrel culvert configurations listed in Table 5-2. The three-barrel depressed culvert tests with 2D and 3D horizontal spacing and a 0.5D vertical offset of the middle barrel with a trapezoidal channel approach (Tests No. 13 and 14 in Table 5-3) and the three-barrel, non- uniform approach flow condition (Test No. 10 in Table 5-3) deviated the most from the single-barrel culvert perfor- mance. For Hw/D > 3.0, the single-barrel culvert relationship underestimated the average individual-barrel depressed cul- vert relationships by up to approximately 4% (for the range of experimental data). The single-barrel culvert relationship underestimated the average individual-barrel relationship for the 3D, three-barrel configuration with a non-uniform approach flow by as much as 10%. 4. Determining the total multibarrel culvert discharge using single-barrel design data and superposition is likely to be appropriate for most multibarrel culvert applications, with the exception of some non-uniform approach flow conditions, provided that representative single-barrel culvert design data are available (i.e., similar culvert type and approach flow condition). 5. For some test configurations, particularly the 1.5D and 2D horizontal spacing three-barrel culverts, the middle barrel had a higher discharge than the outside barrels by as much as 7% at common Hw/D values. Intermittent surface and sub-surface vortex activity, which was more prevalent for the 1.5D, two-, and three-barrel test configurations with a res- ervoir upstream approach, and flow contraction variations between the middle and outside barrels were contributing factors to the disparity between individual-barrel discharges. Individual-barrel discharge variations for the two-barrel tests were as high as ±5%. 6. The variation in the individual-barrel discharges for the two- and three-barrel multibarrel test configurations sug- gest that while superposition may be a good predictor of the overall culvert discharge, additional considerations may be warranted for applications such as energy dissipation and riprap protection at the individual-barrel outlets and fish passage velocity requirements. 7. Inclusion of the inlet control empirical coefficients pre- sented in Table 5-3 for the single-barrel and multibarrel culvert configurations in culvert design manuals, such as HDS-5, would be beneficial to culvert designers. position can be used to predict with reasonable accuracy total culvert discharge in the design of multibarrel culverts with a depressed middle barrel and a trapezoidal channel approach. In summary, good correlation was observed between the single-barrel and the average individual-barrel head- discharge relationships for all three-barrel culvert test con- ditions, with the exception of the non-uniform approach flow condition, suggesting that superposition is a reasonable design method for estimating the total culvert discharge. The variation in individual culvert barrel discharges increased as the barrel spacing decreased (7% for 1.5D), or as the non- uniformity of the approach flow increased (10%). As was discussed for the two-barrel test results, when designing barrel-discharge-specific applications such as outlet energy dissipation, outlet riprap, or fish passage, the single-barrel superposition design method may produce non-conservative discharge predictions for the middle barrel. The empirical coefficients, corresponding to Equations 1-3 and 1-4 (i.e., K, M, c, and Y), for all inlet control three-barrel multibarrel culvert configurations tested are presented in Table 5-3. Tabular support data for the Chapter 5 experimental results are included in Appendix E. 5.6 Conclusions The objective of this study was to evaluate the inlet con- trol head-discharge relationships (quasi-dimensionless) for a variety of multibarrel culvert configurations and compare the individual-barrel, the average-barrel, and the single-barrel head-discharge performances using experimental data collected using laboratory-scale (8-in.) culverts and a culvert testing facil- ity. The comparisons were made in an effort to determine the appropriateness of the superposition approach to designing multibarrel culverts using single-barrel culvert design data, such as is presented in HDS-5. The empirical coefficients (i.e., K, M, c, and Y) corresponding to Equations 1-2 (unsubmerged inlet, Form 1 relationship), 1-3 (unsubmerged inlet, Form 2 relationship), and 1-4 (submerged inlet relationship) for all inlet control, multibarrel culvert configurations tested were also calculated and presented in Table 5-2. The results of this study are the basis of the following conclusions: 1. The single-barrel, thin-wall projecting PVC culvert head- discharge data developed in this study compared favorably with the thin-wall projecting CMP culvert performance calculated using HDS-5 data, indicating that no signifi- cant systemic biases or quality-control issues were present in the current study. 2. The single-barrel, thin-wall projecting culvert head- discharge relationships varied with approach flow con-