1 Water Resources Engineer, State of Utah Division of Water Resources, 1594 W. North Temple, Suite 310, Salt Lake City,

UT, 84114, Email: aaronspencer@utah.gov 2 Associate Professor, Utah State University, 8200 Old Main Hill, Logan, UT 84322-8200, Email: blake.tullis@usu.edu

MILLSITE DAM ARCED LABYRINTH WEIR DESIGN: APPLYING RESEARCH AND MODELING FOR AN ATYPICAL APPROACH CONDITION

Aaron C. Spencer, P.E.1, Blake Tullis, PhD2

Abstract

Millsite Dam, located in Ferron, Utah is a 115 foot tall, 4150 foot long, zoned earthfill dam. The existing spillway is incapable of passing the inflow design flood (IDF) (31,520 cfs peak), as dictated by Utah State code and NRCS standards. As part of a larger dam safety upgrade project, the spillway control structure will be replaced with a new arced labyrinth spillway (the first in the US), which protrudes into the reservoir. The advantages of using an arced labyrinth spillway are examined in the report, particularly the increased capacity relative to an in-channel labyrinth design and other spillway types. The preliminary Millsite arced labyrinth weir layout was designed, in part, by referencing published hydraulic structure research data. Unique site conditions (e.g., a confined, shallow upstream approach), which varied from the laboratory test conditions, necessitated the use of a physical model (Utah Water Research Laboratory at Utah State University) to confirm the weir design and document the hydraulic performance. Some of the case-specific findings included the influence of varied wall thickness to weir height ratios, abutting the labyrinth into a sloping, overflowable abutment rather than vertical abutment walls, and documenting approach flow velocity profiles for bank protection design.

Introduction

Millsite Dam, which was designed and constructed by the Soil Conservation Service (NRCS today) in 1971, is located in Ferron, Utah. The dam is a 115-ft tall, 4150-ft long zoned earthfill dam (see Fig. 1); the 18,000 acre-ft, 435-acre reservoir serves the Ferron Reservoir and Canal Company, and is used primarily for irrigation. The reservoir also provides municipal water for the city of Ferron and industrial supply to the Hunter Power Plant (Pacificorp). The existing spillway consists of a 50-ft long, 60-ft wide duckbill that drains into a straight chute followed by a flip bucket and a 68-ft cliff with a dissipation basin below. The spillway is incapable of passing the flows required by the current design standards of both the State of Utah and the National Resource Conservation Service (NRCS). In a joint project between the Utah Division of Water Resources, NRCS, and the Owners, the spillway will be replaced as part of a larger dam safety upgrade project for the dam. Other upgrades include raising the dam 4 ft (to recuperate volume lost to sedimentation), construction of a downstream stability berm to address unstable liquefiable foundation soils, and extending the outlet works. Key existing and proposed elevation reference data are provided in Table 1.

Table 1. Millsite Dam Critical Elevations

Feature Dam Crest Spillway Existing Elevation (NAVD88) 6222.5 ft 6215 ft

Proposed Elevation (NAVD88) 6226.6 ft 6219 ft

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Figure 1. Millsite Dam site layout and spillway flip bucket. To increase the spillway capacity without incurring the need to increase the spillway chute width, an arced labyrinth weir was chosen as a replacement for the existing duckbill. Arced labyrinth weir research published by Crookston and Tullis (2012) was used to develop a preliminary design. Variations between the site (shallower, channelized) and laboratory (deeper, 180º converging flow) conditions necessitated the use of a physical model to finalize the design. This paper briefly discusses this process of utilizing current research findings for hydraulic structure design and the importance of understanding the limitations associated with research and design methodologies, and the use of physical modeling to minimize hydraulic performance uncertainties. Spillway Design Considerations The following were some of the key performance requirements and restrictions were the following: 1. The water level cannot exceed the dam crest elevation while routing the PMF through the

reservoir (Peak inflow of 31,520 cfs). Zero freeboard is permitted during the PMF. 2. No additional freeboard will be provided. 3. Avoid designs which require alterations to the relatively new city-run golf course which

surrounds the dam and reservoir, or designs that would interfere with or inconvenience patrons, or would negatively alter the aesthetics of the course.

4. The effect on the discharge from smaller storms with shorter return periods must be accounted for.

5. Cost-effectiveness, including minimizing operation and maintenance costs. 6. Match the 4 foot raise in the dam crest being done to regain volume lost in the reservoir

due to sedimentation, 7. Minimize impacts to the aesthetics of the waterfall feature created by the current spillway

and work within existing topographic restrictions by minimizing the widening and deepening of the downstream end of the spillway chute,

8. Address the effect of narrow approach conditions on the capacity of the design.

Millsite Dam

Spillway

3

Current regulations and standard engineering practice require that spillway designs be capable of passing the Probable Maximum Flood (PMF) resulting from the Probable Maximum Precipitation (PMP) as determined by the National Oceanic and Atmospheric Administration’s (NOAA) publication “Hydrometeorological Report No. 49” (HMR49). Under the direction of the State Engineer, the Utah Climate Center (Donald T. Jensen) has modified HMR49 to better match conditions in Utah. The resulting studies, “USUL” (2003) and “USUS” (1995), provide modified rainfall depths to better match the elevations, mountainous topography, and meteorological characteristics of Utah. According to Utah Code, the runoff determined for the PMF must also be compared to a 100-year event with a saturated watershed, but in this case, the PMF governed. The findings of the hydrology study provided by the NRCS (Nathaniel Todea) are summarized in a separate report. The design storm was a 24-hour PMF with the following characteristics:

Table 2. Design Storm Characteristics

Feature Value Watershed Area (sq. mi.) 153

Rainfall Total (inches) 6.75

Discharge Volume (ac-ft) 29,164

Peak Inflow (cfs) 31,520

The storage volume in the reservoir above the proposed spillway elevation is 18,930 ac-ft. Because the volume of inflow is significantly higher than the storage capacity available, the discharge attenuation was minimal. The spillway must therefore pass a flow nearly equal to the maximum reservoir inflow (~ 30,000 cfs). Due to the relatively large design flows that must pass through the somewhat narrow spillway approach channel (and the spillway chute width is restricted by the narrow width of the cliff and gorge downstream), multiple spillway concepts that could discharge large volumes within a smaller footprint were investigated. Investigated concepts included radial gates, standard and folding Fuse gates (Hydroplus, Inc.), an enlarged duckbill, and finally a labyrinth weir spillway. Maintaining the existing spillway and constructing an emergency fuse plug spillway that drained through a portion of the golf course was also considered. Though each of these concepts held significant promise in the right application, it was determined that the duckbill and the labyrinth are the most favorable options due to their passive operation, cost, no capacity would be lost in the reservoir, and the PMF could be passed without requiring repairs to the control structure. The Folding Fusegate is also a recently developed product and was not yet available in the size required, and it was uncertain whether debris could interfere with the folding support mechanism. Since the duckbill and the labyrinth spillway are functionally similar, cost-effectiveness becomes the primary deciding factor, so a preliminary design and cost estimate was prepared for each option. For channelized approach conditions, the National Engineering Handbook (NEH), Section 14, Chute Spillways, Chapter 2c (Box Inlets) suggests that a reduction in duckbill or “box inlet” discharge capacity is required when located in a channel. According to the provisions of the NEH, a duckbill capable of passing the required flow exceeds the range of the

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published design graphs, would require a length of roughly 400 to 500 ft, and the channel width would have to be excavated an additional 100 to 150 ft. This eliminates the duckbill as a feasible option, leaving the labyrinth weir as the selection of choice, due to its higher discharge efficiency.

Hydraulic Analysis of Labyrinth Spillway

Labyrinth Design Research Falvey (2003) discusses labyrinth weir design methodologies presented by Lux and Hinchliff (1985), and Tullis et al. (1995); the Tullis et al (1995) method uses a common version of the general weir equation (Eq. 1) to calculate the flow. In Eq. 1, Q is the weir discharge, L is the weir crest length, g is acceleration due to gravity, and HT is the total upstream head in the reservoir; the weir discharge coefficient (Cd) is calculated using empirical relationships. The Tullis et al. (1995) design method was limited to quarter-round crest shapes. Falvey developed a slightly modified spreadsheet-based design method utilizing the Tullis et al (1995) data. The variables and nomenclature associated with labyrinth spillways are as illustrated in Figure 2. Willmore (2004) determined that some of the polynomial coefficients used to calculate the weir

coefficient in the Tullis et al (1995) method were incorrect (specifically = 6 and 8˚) labyrinth weir design method and the design database was expanded to include half-round crest shapes.

Standard Weir Equation

√

⁄ (1)

Figure 2. In-channel labyrinth weir geometric variables.

CYCLE APEX

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Falvey cited a study by Houston (1983) suggesting the flow can be increased up to 20% by projecting the labyrinth weir into the reservoir, rather than locating it entirely within the spillway channel, but did not provide a method for calculating the increase in flow in the design manual. The prominent design methods already referenced do not account for reservoir-projecting weirs, as they were developed using models placed within flumes. Therefore, in order to complete such a design, alternate methodologies were researched. Crookston and Tullis (2012) evaluated the hydraulic performance of various labyrinth weirs configurations, including projecting and arced projecting labyrinth weirs specific to reservoir applications. Crookston and Tullis (2012a) provided empirical 3rd-order polynomial Cd relationships for various specific projecting labyrinth weir geometries along with standardized nomenclature for arced labyrinth weirs (see Fig. 3 and nomenclature section). The “in-channel” labyrinth weir spreadsheet design program was adjusted using the arced labyrinth weir Cd data published by Crookston and Tullis (2012a) for the Millsite design.

Figure 3. Typical Layout of Arced, Projecting Labyrinth Weir.

The equations are of the forms shown below. The coefficients for each equation (A through D) and guidance on their proper use can be found in Crookston and Tullis (2012a). Crookston and Tullis Coefficient of Discharge for

Projecting Labyrinth Weirs

(2)

DCBA P

H

P

H

P

HC T

2

T

3

Td

6

Crookston and Tullis Coefficient of Discharge for Labyrinth Weirs Located in Flumes

(3)

The only w/P ratio tested for projecting weirs was 2.0. The in-channel w/P labyrinth weir design data ranges from 2 to 4, and for the purposes of this design it was assumed that the

same ratios would be acceptable for projecting weirs. HT/P ratios from 0.05 to 0.7 and = 6 and 12º were tested for projecting labyrinth weirs by Crookston and Tullis (2012a). The design was optimized by calculating an approximate cost for the walls and floor of the labyrinth within the spreadsheet, and then using the Solver add-in to find the design that resulted in the least cost while still passing the required flows. The ratio and angle limits defined in the design method were set as constraints on the solution, as well as the required flow, with the objective set to minimize cost. Solver was run with various starting values and different solver engines to ensure the true optimum had been obtained, rather than a localized minimum. The resulting calculations showed that the discharge capacity of a linear, projecting labyrinth weir decreased relative to the in-channel application; the arced projecting labyrinth

weir, however, showed a significant increase in capacity. An arc angle (Ɵ) of 10º and =12º was determined to be the optimal spillway design for meeting the required discharge capacity while minimizing the required footprint. Trends observed in the optimization of the spillway

suggested that > 12º might produce a more cost-effective design, but the sidewall angle was limited to 12º due to topographical and footprint constraints, and to remain within the tested limits of the design method. The final design used a half-round crest on the weir. A total width of 120 feet was used since this allowed for an effective labyrinth design, but prevented a sharp change in the angle of the walls in the discharge channel. This width was also chosen because it would likely not exacerbate the effects of the narrow approach conditions that would introduce uncertainty into the design calculation. Figures 4 thru 6 show the preliminary design layout and dimensions for the spillway. The apexes were sized to allow for the required thickness of the walls and to accommodate formwork.

DP

HAC

P

HB

Td

CT

7

Figure 4. Dimensions of Preliminary Labyrinth Spillway Design.

Figure 5. Profile of Preliminary Labyrinth Spillway Design.

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Figure 6. Plan View of Preliminary Labyrinth Spillway Design.

The 3:1 sloping retaining walls separating the embankment from the spillway chute also function as abutment walls for the projecting labyrinth weir; the abutment walls overtop adding to the effective length of the weir. This makes it necessary to reinforce the embankment slopes near the spillway, but it also contributes to the total discharge. The contribution to total discharge associated with the abutment walls was estimated using a segmental linear weir approach using a weir discharge coefficient (Cw) of 3.1 (Cd=0.58) [National Engineering Handbook, Section 14 (NEH)] and the average weir crest elevation of each segment to calculate HT. Discharge Channel The proposed downstream discharge channel was dimensioned to avoid labyrinth weir submergence. The resulting water surface elevation and other characteristics of the flow in the discharge channel were calculated using a program developed by the Utah Division of Water Resources entitled “Spillway” (Stauffer and Cole). “Spillway” computes the water surface profile by a two-dimensional direct integration method using a fourth order Runge-Kutta subroutine balancing energy and momentum between spillway sections. The program output confirmed that the flow would be supercritical and sufficiently shallow to preclude weir submergence. Increase in water depth due to air mixture in the water and cavitation parameters were also checked using the methods developed by Falvey (1990). The calculations showed only minor increases in depth due to air mixture, and cavitation parameters were at acceptable levels (i.e., cavitation will not occur).

Design Method Limitations and Discrepancies with Field Conditions

The previously referenced formulas for labyrinth weir discharge provided an excellent means of preparing a preliminary design, and represent some of the most recent research in design methodology for labyrinth spillways, but the support data were limited to the specific

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geometry and approach flow conditions evaluated during their development. These limitations must be carefully considered and addressed in the final design process. Particularly, the methodologies used include the following limitations:

1. Crookston and Tullis (2012a), which was specific to projecting labyrinth weirs, featured

horizontal aprons upstream of the labyrinth that extended a fair distance upstream of the weir, with 180º of converging approach flow upstream.

2. Crookston and Tullis (2013) suggest a tw/P ratio of 1/8, and a crest radius of tw/2. Tullis et al. (1995) used tw of P/6 and a radius of P/12. The only reason for limiting the design to these values is because they are the only ratios and radii tested. Tullis et al. (1995) suggests that a wider wall width will have little effect, but a narrower wall could lower the discharge coefficient by increasing aeration of the nappe. The effect of crest width and radius has not been thoroughly investigated, and none of the design methods include these factors in the calculations. Further physical modeling is necessary to show what range of thicknesses has negligible effect; otherwise, a design formula incorporating these variables is needed.

3. All of the physical models were constructed with the labyrinth connecting to a vertical wall at either end, which contained all flow within the labyrinth. This may not be the case when a spillway is installed through a sloping soil embankment where the top of the abutment walls match the slope of the dam face, and can also act as overflows.

4. The upstream and downstream apexes were of equal width in all of the modeling. This may not be the case, particularly if the weir walls are battered.

5. Downstream channel effects. The models analyzed were located in simple, straight flumes, or had no downstream channel at all, with the water cascading off the testing apparatus after passing over the labyrinth. Care must be taken to prevent submergence of the weir. Tullis et al. (2007) provides a method of calculating the change in flow capacity under submerged conditions.

The Millsite arced labyrinth weir design exceeded some of the geometric limitations associated with the published research (preceding list). Millsite has a 15-inch wide crest for practical reasons (e.g. constructability, cost, etc.), resulting in a wall thickness to wall height ratio (tw/P) of approximately 1/16, which does not match the tested values. Matching the tested values would have required the top of the weir wall to be nearly 2½ feet wide. The wall that the weir attaches to is not vertical, rather it slopes upward matching the slope of the dam face, and provides some additional weir length. Our design also has unequal downstream and upstream apex crest widths due to the battering of the walls. In contrast to the reservoir-type approach condition associated with the research, Millsite has a relatively narrow approach channel where water approaches primarily from one direction and the existing upstream ground elevation adjacent to the spillway is 13½ feet higher than the floor of the labyrinth, only 6 feet below the crest (See Figure 5). In order to more closely approximate the “ideal” approach flow conditions, the ground will be excavated around the spillway structure and sloped away, producing a more uniform, open approach. The effectiveness of these provisions cannot be readily quantified solely through common analytical means. Therefore, some form of system modeling was necessary to determine the proposed spillway design’s true capacity.

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Finally, a study by Christensen (2012) was in progress at UWRL at the same time the physical models were being run for this design. Christensen’s study built upon the work of

Crookston by testing weirs with wider sidewall angles (), for 12 and 20º, and included

retesting the =12˚ models initially tested by Crookston. By improving the accuracy in the measurement of the head on the retested models, he showed the discharge coefficient (Cd)

was lower for projecting labyrinths with = 12º than was reported by Crookston, particularly for

low HT/P. The Cd values for = 6º were deemed accurate. Christensen prepared a new

discharge coefficient formula for projecting labyrinth weirs for = 12 and 20º. The formula is of the form shown in equation 4. The coefficients (a through d), and guidance on the proper use of the equation can be found in Christensen (2012). Christensen Coefficient of Discharge for Projecting Labyrinth Weirs

(4)

The Christensen (2012) data were not used for this design, since the study was completed after all of the Millsite model testing was already completed, however, the Christensen data better matched the Millsite model results at low HT/P values than the Crookston and Tullis (2012a) data. Christensen (2012) found that, just like linear labyrinth

weirs, Cd (discharge efficiency) increased with increasing sidewall angle (i.e., = 20º was

hydraulically more efficient than = 6 or 12º); the discharge per cycle, however, increased with decreasing sidewall angle due to improved overall cycle efficiency (i.e. longer weir length per

cycle). Consequently, a labyrinth with = 20º would require a greater overall width and/or a larger cycle arc angle (Ɵ), both of which are not feasible in the case of Millsite. Physical Model In order to verify, or modify, the calculated spillway capacity due to the incongruences between the modeled conditions used in developing the design calculations, and the actual conditions, a physical model of the proposed design was tested at the Utah Water Research Laboratory (UWRL) at Utah State University (USU). The approach topography was modeled in AutoCAD Civil3D, based on aerial survey data, and included the proposed cuts around the spillway. Several different scenarios were prepared for differing quantities and locations of cut around the spillway. Cross-sections were produced at 20 foot intervals and utilized to prepare a physical model of the actual approach conditions around the model spillway. The discharge channel downstream of the labyrinth was not included as part of this model since our calculations showed that the channel flows were supercritical and shallow enough to preclude any submergence or significant backwater effects on the weir. Physical Model Study Overview The physical model (1:30) study of the arced-labyrinth weir spillway and approach flow channel was conducted at the Utah Water Research Laboratory at Utah State University in May and June of 2012 to determine discharge capacity, and identify the influence of various upstream channel excavation schemes with respect to spillway discharge capacity. A partial list of prototype and model labyrinth weir geometric details are summarized in Table 3.

P

Hd

cbP

Ha

C T

T

d ln1

2

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Table 3. Prototype and model 3-cycle, half-round crest,

arced labyrinth weir geometric details.

Geometric Parameter Prototype Scaled model

Weir height (P) 19.5 ft 7.8 in

Weir wall thickness (tw) 15 in 0.5 in

Cycle sidewall length (lc) 78.5 ft 31.4 in

Total weir length (L) 493.1 ft† 197.25 in†

Inlet sidewall angle (α) 12.16° 12.16°

Outlet sidewall angle (α’) 17.16° 17.16°

† overflow abutment wall length not included

Model Justification

The justification for the model study was based on the following: 1. The published 12° arced labyrinth weir data (Crookston 2010) used for the Millsite arced

labyrinth weir preliminary design featured a horizontal upstream and downstream apron with 180° of flow convergence approaching the weir; the Millsite approach channel will be more channelized featuring a variable, excavated rock topography.

2. The wall height (P) and wall thickness (tw) varied between the published study and the Millsite design geometries.

3. The physical model was used to verify the head-discharge relationship for the prototype arced labyrinth weir design with various upstream approach channel topographies. In an effort to balance the cost of upstream approach channel rock removal vs. adequate hydraulic performance of the arced labyrinth weir, 7 different upstream channel topographies were tested featuring variable amounts of upstream channel excavation. A horizontal apron condition was also tested for comparison with the Crookston and Tullis (2012) data. The maximum water level under the PMF must not exceed the dam crest elevation during the design flood (~30,000 cfs). The influence of the backwater profiles associated with each upstream topography option on the required reservoir elevation was evaluated.

The model study objectives included determining the head-discharge relationship (including IDF, SDH, and 100-year flood events) for various upstream approach channel topographies, document the approach flow velocity field using the 2-D velocity probe for two upstream topographies and along the dam embankment near the spillway for riprap sizing, and demonstrating the spillway performance to representatives from the Utah Division of Water Resources and the Natural Resources Conservation Service (NRCS) via a witness test.

Model Details The laboratory-scale arced labyrinth weir was constructed in an elevated head box that simulated a 480-ft wide by 320-ft long prototype footprint. The model included the approach channel, arced labyrinth weir, and part of the dam embankment. The labyrinth weir was fabricated using 1/2-inch thick high-density polyethylene (HDPE) sheeting. The model featured vertical (non-battered) weir walls with a wall thickness based on the prototype wall thickness at the crest (the prototype has battered walls). Plan views of the model are shown in Figure 7. Topographic cross sectional templates and road base were used to simulate the

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approach channel options in the model. Seven different approach channel topographies (varied amounts of excavation) were tested; three representative excavation options are shown in Figure 8.

Figure 7. Overview of (a) model and head box, and

(b) labyrinth weir layouts (model inches).

Figure 8. Schematics of three representative approach channel topographical options [Topo 1, minimum excavation (a); Topo 2, medium excavation (b), Topo 3, maximum excavation (c)].

Instrumentation Flow measurement was provided by calibrated magnetic flow meters (±0.25%), traceable to the National Institute of Standard and Technology (NIST) by weight. Water levels were measured using a precision point gage installed in a stilling well that was hydraulically connected to a floor pressure tap in the head box. The pressure tap was installed in a region

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of negligible velocity head, making the upstream piezometric and total heads equivalent. Approach flow velocity data were collected in a rectangular grid pattern (typically at 60% of the local water depth) using a Flow Tracker 2-D velocity probe. Model Scale For a model to properly simulate hydraulic conditions in the prototype it is necessary to maintain geometric, kinematic, and dynamic similitude. Geometric similitude is achieved by carefully building the model to a selected scale ratio. The selection of the model scale has a direct impact on the ability to maintain kinematic and dynamic similitude. If the model is built too small, similarity is not maintained and the results obtained from the model may not directly apply to the prototype; a 1:30 scale model was used. Spillway models are typically modeled using Froude-scaling, which is based on the ratio of inertia to gravity forces and expressed as

the Froude Number (F=V / gy ) (y is the flow depth, g is the gravitational acceleration

constant, and V is velocity). Similarity is achieved and inertial and gravity forces scaled properly by operating the model so that the Froude number in the model is the same as the Froude number in the prototype. Discharge, velocity, pressure, and time can be scaled using Froude scaling.

Experimental Results The weir discharge coefficient data (Cd) were calculated per the standard weir equation (Eq. 1). Cd vs Ht/P data for the three representative topography options as well as the horizontal upstream apron are presented in Figure 9, along with the Christensen (2012) data

for = 12º, Ɵ = 10, weir thickness = 1 inch, weir height = 8 inches arced labyrinth weirs as a reference. The weir length used in the Cd calculations was limited to the labyrinth weir itself; the overflow abutment wall lengths were not included. According to the data in Figure 9, the thinner-walled Millsite labyrinth weir installed on the horizontal apron was less efficient (smaller Cd values) than the 25% thicker labyrinth weir (same wall height) tested on a horizontal apron by Christensen (2012) (with the exception of a few low HT/P <0.15 values which may have been effected by variations in the nappe aeration behavior). This may be due, in part, by the fact that the nappe separates from the half-round crest (creating an aerated nappe) more easily with a thinner weir wall; a clinging nappe (no air pocket between the nappe and weir wall) is hydraulically more efficient than an aerated nappe. The upswing in the discharge coefficient for the “No Topography” option at higher values of HT/P is likely due to the sloping overflow abutment walls, which effectively added additional weir length as the head increased. The effects of these overflow walls can be seen in the Cd results for the scenarios with the topography in place as well (See Figure 9). Because the effect of the overflow abutment walls is inherent in the measured Cd values, the length of the weir may remain constant in the standard weir equation no matter what the head is, making final design calculations much simpler.

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Figure 9. Cd vs. Ht/P data corresponding to various approach channel topographies, abutment wall detail option (A or B), and reference data.

(a) (b)

Figure 10. Labyrinth weir model overview photos with (a) horizontal apron and (b) topography upstream. As expected, the addition of the upstream topography (all options) diminished the discharge efficiency of the labyrinth weir spillway relative to the horizontal apron case. With

the topography in place, the reservoir approach flow was relatively channelized (not the 180 converging approach flow condition as existed with the horizontal apron), resulting in a decreased discharge efficiency (smaller Cd values). The data in Figure 9 also show minor differences between the experimental data from the various topographical options.

Based on the fact that all of the Millsite labyrinth weir topographical configurations tested are less efficient than the Christensen (2012), the length of the Millsite labyrinth weir may need to be increased in order to pass the design flood without exceeding the freeboard

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height. It was necessary to perform a reservoir routing analysis using the discharge coefficients determined from the models to determine if this was the case. The results of the reservoir routing analysis are discussed in the “Application of Model to Design” section below. Approach Flow Velocity Data Approach flow velocity measurements were documented with Topo 2 at two different discharges (Q = 15,000 and 26,000 cfs); the direction and magnitudes are presented in Figure 11. Note that the velocity vector data correspond to the grid point and not the tip of the velocity vector arrow.

Figure 11. Approach flow velocity data for Topo 2 for (a) Q = 26,000cfs and (b) Q = 15,000cfs.

As can be observed in Figure 11, the channelized flow is directed towards the center of the spillway, and slightly to the right (in the figure above), particularly during higher flows. The arcing of the labyrinth opened up the cycles, improving the orientation of the walls in the central cycles relative to the oncoming flow, thus producing the increased efficiency of the arced labyrinth, but the topography limits the gains by restricting the flows to the right and left sides of the labyrinth, and altering the angle of approach of the flows to a less efficient orientation (flow perpendicular to the weir is the most efficient).

Application of Model to Design

Selection Of Excavation Option The first five tests made it apparent that it was not necessary to excavate much of the hillside adjacent to the right abutment, since excavating varying amounts of it had little to no effect on the discharge coefficient. The approach flows were channelized in such a way that it produced ineffective flows in the region of the hillside, even if it were removed. Excavating 2 feet of the flat surrounding the spillway, and sloping the ground outwards from the base of the spillway was effective in reducing the losses in discharge capacity from an average reduction of approximately 14% (minimal excavation scenario) to about 9%. Subsequent tests involved excavating deeper in the flat surrounding the spillway. Excavating 4 feet out from the flat resulted in higher discharge coefficients as well, lowering the average capacity reduction to about 6½ percent, but excavating 6 feet produced minimal additional capacity. The

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diminishing returns appear to be due to the fact that the discharge curve was approximating the discharge curve of the labyrinth model with a horizontal apron, meaning the primary controlling factor was no longer the topography, but the narrow crest width. Figure 12 shows the capacity of some of the modeled scenarios relative to the calculated capacity of the arced labyrinth using the Crookston formula. It can be seen that the excavation scenarios are bounded roughly by the flat approach apron scenario above and by the scenario of doing minimal excavation around the spillway below. As more material is cut, the capacity approaches its upper bound until no additional gains can be made through more excavation.

Figure 12. Relative Discharge Capacities (Physical Model vs. Crookston Formula).

Using the new stage-discharge curve created using the Millsite-specific physical model data, the design flood was routed through Millsite reservoir. A hydrology program developed by the Utah Division of Water Resources entitled “STORM” was used to route the storm. It was found that the 2-ft, 4-ft, and 6-ft excavation options all returned maximum water elevations within 1 inch of each other. The 6-ft excavation option met the freeboard requirements, with a maximum water elevation of less than 1/2 inch below the dam crest elevation, but the other two options were also less than 1 inch above the dam crest elevation. In conclusion, in was determined that rather than do more rock excavation, or widen the spillway by 1 ft, which is all that was required, the option with the least excavation would be

60%

65%

70%

75%

80%

85%

90%

95%

100%

105%

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Re

lati

ve C

apac

ity

(%)

(HT/P)

Relative Discharge Capacity (Compared to Calculated Capacity using Crookston Formula)

Model w/2' Cut (Final Design) Calculated Capacity

Model w/Flat Apron In-Flume Calculated Capacity

Minimal Excavation (Do Nothing) Model w/4' Cut

Model w/6' Cut

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used, and the crest of the dam would be raised by 0.1 feet, allowing the spillway to remain as originally designed. A variation of 0.1 feet undoubtedly is within the margin of error of the program and model, and as such might be ignored; but without further evidence of the direction and magnitude of the error, the reservoir elevation values were taken at face value. Figure 13 shows the inflow and outflow hydrographs for the reservoir, and Figure 14 shows the stage-discharge curve from the preliminary design calculations, compared to the discharge-curve from the chosen excavation option (2 feet of cut). Refer back to Figures 4, 5 and 8b for the final design configuration.

Figure 13. Millsite reservoir hydrographs.

0

1

2

3

4

5

6

7

0

5000

10000

15000

20000

25000

30000

35000

0 10 20 30 40 50 60

Hea

d (

ft)

Flo

w (

cfs)

Time (hrs)

Inflow/Outflow Hydrograph

Inflow Hydrograph

Outflow Hydrograph(Spillway)Head

Max Head = 7.6 ft

Peak Spillway Flow = 29,870 cfs

Peak Inflow = 31,520 cfs Volume = 29,164 ac-ft

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Figure 14. Calculated Stage-Discharge Curve Using Crookston Formula vs. Modeled Stage-Discharge Curve of Final Design.

Summary

Labyrinth weirs are a highly efficient means of increasing discharge capacity and storage capacity in reservoirs. Their high discharge capacity relative to other spillway types allows these spillways to pass much larger flows within a smaller footprint, resulting in a cost-effective design.

There are multiple research studies available to aid in the design of labyrinth spillways, of which the following are among the most useful: 1. Lux and Hinchliff (1985), Lux (1989) – Design methodology, 2. Tullis, et al (1995) – Design methodology (“Tullis Method”), 3. Falvey (2003) – Labyrinth weir design manual,

4. Willmore (2004) – Corrections to discharge formula coefficients for = 6 and 8 degrees in Tullis Method,

5. Tullis et al. (2007) – Submergence effects, 6. Crookston (2010) – Design methodology, including both in-channel and arced, protruding

labyrinth weirs, 7. Crookston and Tullis (2011) – Design and Analysis Toolbox, 8. Crookston and Tullis (2012 a,b,c) – Arced weirs, Reservoir Applications, Nappe

Interference and Local Submergence 9. Crookston and Tullis (2013a) – Design and Analysis of Labyrinth weirs: Discharge

Relationships. 10. Crookston and Tullis (2013b) – Design and Analysis of Labyrinth weirs: Nappe Aeration,

Instabilities, and Vibration. 11. Christensen (2012) – Additional data building on Crookston’s research, including larger

sidewall angles.

6219

6220

6221

6222

6223

6224

6225

6226

6227

0 10000 20000 30000

Ele

vati

on

(ft

)

Capacity (cfs)

Stage-Discharge Curves of Final Design Configuration

Calculated

Modeled

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The preceding list includes those studies that provide some of the most thorough and up-to-date work on labyrinth weirs, particularly protruding labyrinth weirs, but it is not a complete list. Research is ongoing and the designer should be attentive to the developing knowledge base and most recent studies in order to produce an effective design. It is also critical that the limitations of the research be understood. A design cannot go beyond the parameters used within the research (such as HT/P ratios, w/P ratios, crest type, approach and discharge conditions) without creating uncertainty in the design. In such a case numerical analysis in finite element software may be useful, but often physical models can further reduce uncertainty, and address or identify multiple design concerns or discrepancies between the design and design method. Even when physical modeling is completed, it is necessary to bear in mind the limitations of the data, and the extent of their applicability. Designs cannot vary significantly from the models or else uncertainty again develops. In this instance physical modeling showed that the arced labyrinth weir was less efficient because of the approach conditions and the width of the crest, but the side weirs aided in regaining some of the lost flow capacity. Testing multiple depths and configurations of excavation in the approach channel made it possible to determine the design requiring the least amount of excavation that would still meet the design flow. In the end, using an approach channel design requiring a relatively small amount of excavation (Figure 8b), combined with a minute raise in the dam crest (0.1 ft), the original labyrinth weir configuration proved sufficient to pass the design flood. It was apparent though that in addition to the approach conditions, the crest width and radius can have a significant effect on the discharge capacity, due to aeration of the nappe, and more research in this regard seems merited.

Acknowledgements

This research was completed with the generous assistance of the Natural Resource Conservation Service (NRCS), the Utah Department of Water Resources (UDWR), and the staff at the Utah Water Research Laboratory (UWRL).

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Nomenclature A Inside apex width Ac Apex centerline length [Ac = (A + D)/2] Ac/lc Crest ratio

Sidewall angle

’ Outlet sidewall angle

’ = + θ ∕ 2θ = Θ∕ N

B Length of labyrinth weir (apron) in flow direction Cd Discharge coefficient D Outside apex width ε’ Cycle efficiency g Acceleration constant of gravity h depth of flow over the weir crest HT Total upstream head measured relative to the weir crest (unsubmerged) HT/P Headwater ratio Lc Total centerline length of labyrinth weir lc Centerline length of weir sidewall Lc-cycle Centerline length for a single labyrinth weir cycle M Magnification ratio, Lc-cycle/w N Number of labyrinth weir cycles P Weir height Q Discharge over weir R Arc radius, Rcrest Radius of rounded crest (e.g., R = tw / 2) r Circle center to channel width midpoint distance r’ = R - r r’ Segment height tw Thickness of weir wall Θ Arced labyrinth weir angle, Θ = W’∕ R Ɵ Cycle arc angle W Width of channel W’ Width of arced labyrinth spillway, W’ = RΘ w Width of a single labyrinth weir cycle

w’ Cycle width for an arced labyrinth weir spillway. w’ = R w/P Cycle width ratio

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References

Christensen, N., (2012). “Arced Labyrinth Weirs.” MS Thesis, Utah State University. Crookston, B.M. (2010). “Labyrinth Weir Hydraulics.” Dissertation, Utah State University. Crookston, B.M. and B.P. Tullis (2012a). “Arced Labyrinth Weirs.” J. Hydraul. Eng., 138(6), pp. 555-562. Crookston, B.M. and Tullis, B.P. (2012b). “Discharge efficiency of reservoir-application-specific labyrinth weirs.” J. Irrig. Drain. Engr., ASCE, 138(6). 564-568. Crookston, B.M. and Tullis, B.P. (2012c). “Labyrinth weirs: Nappe interference and local submergence.” J. Irrig. Drain. Engr., ASCE, 138(8). Crookston, B.M. and Tullis B.P. (2013a). “Hydraulic Design and Analysis of Labyrinth Weirs. I: Discharge Relationships.” J. of Irrig. Drain. Engr., ASCE, 139(5), 363-370. Crookston, B.M. and Tullis B.P. (2013b). “Hydraulic Design and Analysis of Labyrinth Weirs. II: Nappe Aeration, Instability, and Vibration.” J. of Irrig. Drain. Engr., ASCE, 139(5). 371-370. Falvey, Henry T., (1990). Cavitation in Chutes and Spillways: Engineering Monograph No. 42. United States Department of the Interior, Bureau of Reclamation, Denver, Colorado. Falvey, Henry T., (2003). Hydraulic Design of Labyrinth Weirs. ASCE Press, Reston, Virginia. Houston, K.L., (1983). “Hydraulic Model Study of Hyrum Dam Auxiliary Labyrinth Spillway”. Report No. GR-82-7, U.S. Bureau of Reclamation, Denver, Colorado. Jensen, Donald, (2003). “2002 Update for Probable Maximum Precipitation, Utah 72 Hour Estimates to 5,000 sq. mi. – March 2003” (USUL). Utah Climate Center, Utah State University, Logan, Utah. Jensen, Donald (1995). “Probable Maximum Precipitation Estimates for Short Duration, Small Area Storms in Utah – October 1995” (USUS). Utah Climate Center, Utah State University, Logan, Utah. Lux, F., and Hinchliff, D.L., (1985). “Design and Construction of Labyrinth Spillways”, 15

th Congress ICOLD, Vol.

IV, Q59-R15, Lausanne, Switzerland, 249-274. National Engineering Handbook, Part 634 – Hydraulic Engineering, Section 14 – Chute Spillways, Chapter 2c – Box Inlets, National Resource Conservation Service. National Engineering Handbook, Part 630 – Hydrology, National Resource Conservation Service. Paxon, G., Campbell, D., and Monroe, J., (2011). “Evolving Design Approaches and Considerations for Labyrinth Spillways”, 31

st Annual USSD Conference, U.S Society on Dams, Denver, Colorado.

Paxson, G., and Savage, B. (2006). “Labyrinth Spillways: Comparison of Two Popular U.S.A. Design Methods and Consideration of Non-standard Approach Conditions and Geometries.” International Junior Researcher and Engineer Workshop on Hydraulic Structures, J. Matos and H. Chanson (Eds), Report CH61/06, Div. of Civil Eng., The University of Queensland, Brisbane, Australia. Savage, B.M., Frizell, K. and Crowder, J. (2004). “Brains versus Brawn: The Changing World of Hydraulic Model Studies.” ASDSO 2004 Annual Conference Proceedings. Stauffer, Dr. Norman E. and Cole, David. “Spillway” water profile analysis program. Division of Water Resources, State of Utah.

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Taylor, G., (1968). “The performance of labyrinth weirs.” PhD thesis, University of Nottingham, Nottingham, England. Tullis, J.P., Nosratollah, A., and Waldron, D., (1995). “Design of Labyrinth Spillways”, American Society of Civil Engineering, Journal of Hydraulic Engineering, 121(3), 247-255. Willmore, C. (2004). “Hydraulic characteristics of labyrinth weirs.” M.S. report, Utah State University, Logan, Utah.

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Appendix

Project Photographs

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Fig. A-1. Millsite labyrinth weir model with embankment retaining wall option A and no upstream topography.

Fig. A-2. Millsite labyrinth weir model with embankment retaining wall option B, Topo 4, and Ht/P = 0.142.

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Fig. A-3. Millsite labyrinth weir model with embankment retaining wall option B, Topo 6, and Ht/P = 0.265.

Fig. A-4. Millsite labyrinth weir model with embankment retaining wall option B, Topo 6, and Ht/P = 0.51.