MSMA 2 nd Edition DID Malaysia CHAPTER 18 CULVERT

Transcription

1 MSMA nd Edition. 01 DID Malaysia CHAPTER 18 CULVERT 18.1 INTRODUCTION Components Application HYDRAULICS FUNDAMENTALS Flow Conditions Type of Flow Control DESIGN CONSIDERATION DESIGN PROCEDURE FLOW VELOCITY MINIMUM ENERGY CULVERTS REFERENCES APPENDIX 18.A DESIGN FORM, TABLE, CHARTS AND NOMOGRAPH APPENDIX 18.B EXAMPLE CULVERT DESIGN i

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3 MSMA nd Edition. 01 DID Malaysia 18.1 INTRODUCTION A culvert is a relatively short length of conduit used to transport stormwater through an embankment. A culvert acts as an enclosed channel that serves as a continuation for an open channel through the embankment. However, flow through culverts depends on entrance geometry and flow depth at the downstream end. Consequently, flow computations for culverts are more complex than open-channel flow analysis associated with pipes or drains. Culverts are typically designed to pass the design discharge without overtopping the embankment or causing extensive ponding at the upstream end. This Chapter provides guidance and procedures for the hydraulic design of culverts which are based on Hydraulic Design of Highway Culverts, Hydraulic Engineering Circular No (FHWA, 198) Components Major components of a culvert include the barrel, end treatment such as headwalls, endwalls and wingwalls, outlet protection, inlet improvements and debris control structures. Except for the barrel these components are used as the specific situation warrants. End treatments such as headwalls and wingwalls protect the embankment from erosion, serve as retaining walls to stabilize the bank and add weight to counter any buoyancy effects. Ideally, the culvert s centreline should follow the line and grade of natural channel. In many cases this cannot be done and skewing headwalls and wingwalls helps accommodate the natural stream alignment to the culvert alignment. Figure 18.1 shows four types of inlet entrances. a) Projecting Barrel b) Cast In-place Concrete Headwall & Wingwalls c) Precast End Section d) End Mitered to The Slope Figure 18.1: Four Standard End Inlet Treatments Culvert 18-1

4 MSMA nd Edition. 01 DID Malaysia Debris barriers are sometimes constructed on the upstream end to prevent material from entering and clogging the culvert. The barriers are placed far enough away from the entrance so that accumulated debris does not clog the entrance. At the inlet and outlet ends of the culvert endwalls and wingwalls serve as erosion protection for the embankment and inhibit piping along the culverts outside surface. Downstream wingwalls provide a smooth transition between the culvert and the natural stream banks Application Barrels are available in various sizes, shapes and materials. Table 18.1 shows the typically used culvert shapes and their applications. Shape selection depends on construction limitations, embankment height, environment issues, hydraulic performance and cost. The most commonly used culvert materials are corrugated steel, corrugated aluminium and precast or cast-in-place concrete. Factors such as corrosion, abrasion and structural strength determine the selection of material. In cases where the culvert is located in a highly visible amenity area, selection of shape and material may be based on aesthetic as well as functional considerations. Table 18.1: Typical Shapes and Uses Shape Uses Round Common uses Arch For low clearance large waterway opening and aesthetics Low Profile Arch Low-wide waterway enclosures and aesthetics Box Low-wide waterway enclosures 18. HYDRAULICS FUNDAMENTALS Flow Conditions A culvert barrel may flow full over all of its length or partly full. Full flow in a culvert barrel is rare. Generally, at least part of the barrel flows partly full. A water surface profile calculation is the only way to accurately determine how much of the barrel flows full. Full flow or pressure flow - One condition which can create pressure flow in a culvert is the back pressure caused by a high downstream water surface elevation. A high upstream water surface elevation may also produce full flow. It is therefore, regardless of the cause, the capacity of a culvert is affected by upstream and downstream conditions and by the hydraulic characteristics of the culvert. Partly Full or Open channel flow - The appropriate open channel flow regimes, namely subcritical, critical, or supercritical must be determined and accomplished by evaluating the dimensionless Froude number Fr. Fr>1, the flow is supercritical and is characterised as swift. When Fr<1, the flow is subcritical and characterised as smooth and tranquil. If Fr=1, the flow is said to be critical. To analyse free surface flow conditions, a point of known depth and flow (control section) must first be identified. A definable relationship exists between critical depth and critical flow at the dam crest, making it a convenient control section. 18- Culvert

5 MSMA nd Edition. 01 DID Malaysia 18.. Type of Flow Control Inlet and outlet control are the two basic types of flow control which define the control section. The characterisation of pressure, subcritical, and supercritical flow regimes play an important role in determining the location of the control section and thus the type of control. Inlet control - Occurs when the culvert barrel is capable of conveying more flow than the inlet will accept. The control section of a culvert operating under inlet control is located just inside the entrance. Critical depth occurs at or near this location, and the flow regime immediately downstream is supercritical. The upstream water surface elevation and the inlet geometry represent the major flow control. The inlet geometry includes the barrel shape, cross-sectional area, and the inlet edge. Figure 18. show types of inlet control. HW Water Surface A. Projecting End Unsubmerged Inlet HW Water Surface B. Projecting End Submerged Inlet HW Water Surface C. Mitred End Submerged Inlet Figure 18.: Types of Inlet Control Outlet control - Occurs when the culvert barrel is not capable of conveying as much flow as the inlet opening will accept. The control section for outlet control flow in culvert is located at the barrel exit or further downstream. Either subcritical or pressure flow exists in the culvert barrel under this conditions. All the geometric and hydraulic characteristics of the culvert play a role in determining its capacity. These characteristics include all of the factors governing inlet control, water surface elevation at the outlet, and the slope, length, and hydraulic roughness of the culvert barrel. Figure 18. show types of outlet control. (a) Determination of Energy Head (H) The head, H (Figure 18.) or energy required to pass a given flow through a culvert operating under outlet control is made up of three major parts. These three parts are usually expressed in metres of water and include Culvert 18-

6 MSMA nd Edition. 01 DID Malaysia HW Water Surface H W.S. TW=h 0 (a) Culvert Flowing Full, Submerged Outlet HW H W.S. (b) Culvert Flowing Full, Unsubmerged Outlet HW Hydraulic Grade Line H W.S. (c) Culvert Flowing Full, for Part of Length HW H W.S. (d) Culvert not flowing full Figure 18.: Type of Outlet Control a velocity head, H v, an entrance loss, H e and a friction loss, H f. The energy head is expressed in equation form as: H = H v + H e + H f (18.1) The velocity head, H v is given by, V H v = g (18.) 18- Culvert

7 MSMA nd Edition. 01 DID Malaysia where V is the mean velocity in the culvert cell and g is the acceleration due to gravity. The mean velocity is the discharge, Q, divided by the cross-sectional area A of the cell. The entrance loss is expressed as, V H e = K e g (18.) The entrance loss coefficient, K e, depends on the inlet geometry primarily through the effect it has on contraction of the flow. Values of K e determined from experiment, range from 0. for a well rounded entrance, through for a square edged inlet in a vertical headwall to 0.9 for a sharp pipe (e.g. corrugated steel) projecting from an embankment. K e coefficients are given on Design Chart 18.A1. Since most engineers are familiar with Manning s n, the following expression is used to calculate the friction loss, H f along the conduit: where, H f gn L V = x 1. R g (18.) n = Manning s friction factor; L = Length of culvert cell (m); V = Mean velocity of flow in culvert cell (m/s); g = Acceleration due to gravity (9.80 m/s ); R = Hydraulic radius (m) = A/W p; A = Area of flow for full cross-section (m ); and W p = Wetted perimeter (m). Substituting in Equation 18.1 and simplifying, we get for full flow: gn L V H = 1+ Ke + 1. R g (18.) Figure 18. shows the terms of Equation 18., the energy line, the hydraulic grade line and the headwater depth, HW. The energy line represents the total energy at any point along the culvert cell. The hydraulic grade line is defined as the pressure line to which water would rise in small vertical pipes attached to the culvert wall along its length. The difference in elevation between these two lines is the velocity head, V /g. By referring to Figure 18. and using the culvert invert at the outlet as datum, we get: Then, and, h V LS = h + Hv + He + H g f (18.) h V LS- h = H v + H e + H g f (18.7) V LS h = H v + H e + H f H = h - (18.8) g Culvert 18-

8 MSMA nd Edition. 01 DID Malaysia From the development of this energy equation and Figure 18., H is the difference between the elevation of the hydraulic grade line at the outlet and the energy line at the inlet. Since the velocity head in the entrance pool is usually small under ponded conditions, the water surface of the headwater pool elevation can be assumed to equal the elevation of the energy line. V 1/g V /g W.S. V 1 HW h1 Energy Line He H f LS V S Hydraulic Grade Line L Hv h W.S. Datum Figure 18.: Hydraulics of Culvert Flowing Full under Outlet Control for High Tailwater. Equation 18. can be readily solved for H by the use of the full flow nomographs in Appendix 18.A, Design Charts 18.A9 to 18.A11 (b) Determination of Headwater Depth (HW o ) Headwater depth, HW 0 can be determined from an equation for outlet control: HW 0 = H + h 0 LS (18.9) where, H = Head (m) determined from Design Charts 18.A9 to 18.A11 or from Equation 18.8; h 0 = Greater of TW and (h c + D)/, in which h D; h c = Critical depth (m) from the Design Charts 18.A7 and 18. A8 in Appendix 18.A; D = Culvert height (m); L = Length of culvert (m); and S = Slope of cell (m/m). (c) Determination of h o The determination of h 0 is an important factor in calculating both the headwater depth and the hydraulic capacity a culvert flowing under outlet control. Tailwater depth, TW is the depth from the culvert invert at the outlet to the water surface in the outlet channel. Engineering judgement is required in evaluating possible tailwater depths. Tailwater is often controlled by a downstream obstruction or by water levels in another stream. A field inspection should be made to check on downstream conditions and flood levels. The Slope Area Method can be used to calculate flow depths, if downstream conditions do not provide an obvious control. Fortunately, most natural streams are wide compared to the culvert and the depth of water in the natural channel is considerably less than critical depth in the culvert section. In such cases the natural tailwater does not govern. Two tailwater conditions can occur with culverts operating under outlet control, (i) tailwater above the top of the opening and (ii) tailwater at or below top of opening: 18- Culvert

9 MSMA nd Edition. 01 DID Malaysia (i) Tailwater above the top of opening when the tailwater, TW in the outlet channel is above the top of the culvert outlet, Figure 18. (a); h o = TW (18.10) The relationship of h 0 to the other terms in Equation 18.9, for this situation, is illustrated on Figure 18.. HW H LS D S TW=h 0 L Figure 18.: Determination of h o for High Tailwater. (ii) Tailwater at or below top of opening when the tailwater in the outlet channel is at or below the top of the culvert outlet, as on Figure 18. (b), 18. (c) and 18. (d), h 0 is more difficult to determine. Full flow depth at the outlet, Figure 18. (b), will occur only when the flow rate is sufficient to give critical depths equal or higher than the height of the culvert opening. For all such flows the hydraulic grade line will pass through the top of the culvert at the outlet and the head, H can be added to the level of the top of the culvert opening in calculating HW 0. When critical depth is less than the height of the culvert opening, the water surface drops as shown on Figures 18. (c) and 18. (d), depending on the flow. For the condition shown on Figure 18. (c), the culvert must flow full for of its length. Flow profile computations show that the hydraulic grade line, if extended as a straight line from the point where the water breaks away from the top of the culvert, will be at a height approximately halfway between critical depth and the top of the culvert, at the culvert outlet. i.e.: ( + D) h h = c o (18.11) This level should be used if it is greater than TW. The head, H can be added to this level in calculating HW 0. The relationship of h 0 to the other terms in Equation 18.9 for this situation is illustrated on Figure 18.. As the discharge decreases the situation approaches that of Figure 18. (d). For design purposes, this method is satisfactory for calculated headwater depths above 0.7D. For smaller values of headwater, more accurate result can be obtained by flow profile calculations or by the use of the capacity charts from Hydraulic Engineering Circular No 10 (US Federal Highway Administration, 197). HW H LS D S hc TW L h 0 = Greater of hc + D and TW Figure 18.: Determination of h o for Tailwater below Top of Opening. Culvert 18-7

10 MSMA nd Edition. 01 DID Malaysia 18. DESIGN CONSIDERATION Headwater - Headwater is the water surface in the upstream of culvert. The available headwater may be limited by the height of the surrounding ground or the elevation at which the road formation cuts through the HGL. The most economical culvert is one which utilize all of the available headwater to pass the design discharge. However, it is not always possible to utilize all of the available headwater due to constraints that limit the upstream water level. The following factors should be considered in the selection of the design headwater: Limits on backwater not to cause inundation of the properties upstream; and The outlet velocity and the potential scours. Multiple Cells - The culvert shape selected will best fit the waterway of channel or stream. In narrow deep channel, a small number of large diameter pipes or box culverts are usually appropriate. In flat areas of no well defined waterway, the flood may be larger in volume, but shallow depth. A number of separate culverts spread over the width of the flooded area may be more appropriate. Special consideration should be given to multiple cell culverts where the approach flow is of high velocity, particularly if supercritical. Culvert in Flat Terrain - In flat terrain, drainage channels are often not well defined. Multiple culverts can be considered to have a common headwater elevation. It is also necessary to construct levee banks to achieve the design headwater at the culvert location provide no danger of increased flooding of upstream properties. The approval of the local drainage authority must be obtained prior to construction of such levee bank. 18. DESIGN PROCEDURE The approach is to analyse a culvert for various types of flow control and then design for the control which produces the minimum performance. Design for minimum performance ignores transient conditions which might result in periods of better performance. The benefit of designing for minimum performance are ease of design and assurance of adequate performance under the least favourable hydraulic conditions. The design engineer should be familiar with all the equations in the previous Section before using these procedures. Following the design method without an understanding of culvert hydraulics can result in an inadequate, unsafe, or costly structures. The procedures does not address the effect of storage. The design procedure is summarised on the Culvert Design Flowchart, Figure 18.7 The steps in culvert sizing are as follows:. Step 1: Assemble Site Data The following data are required for the design of culvert: Site survey and locality map; Embankment cross-section; Roadway profile; Photographs, aerial photographs; Details from field visit (sediment, debris and scour at existing structure); Design data for nearby structures; Studies by other authorities near the site, including small dams, canals, weirs, floodplains, storm drains; and Recorded and observed flood data. Step : Determine Design Flood Discharge Determine ARI of design flood and hence the design flood discharge Q, Please refer Chapter Culvert

11 MSMA nd Edition. 01 DID Malaysia Yes hc + D h c + D h o = HWo = H+ho-SoL Consider Option: Scour Protection Energy Dissipator If Change of Culvert Size, Repeat Design Steps HW i = Headwater for inlet control HW o = Headwater for outlet control ` Figure 18.7: Design Flow Chart Culvert 18-9

12 MSMA nd Edition. 01 DID Malaysia Step : Commence Summarising Data on Design Form The information obtained from step 1 and step are put into Design form Chart 18.A1 in Appendix 18.A. Step : Select Trial Culvert Choose culvert material, shape, size and entrance type. The initial trial size of culvert is determined, either by arbitrary selection or by assuming a velocity (say m/s) and calculating a culvert area from A = Q/V Step : Determine Inlet Control Headwater Depth, HW i Use inlet Control Design Charts 18.A to 18.A. The nomographs cover various culvert types and inlet configurations. Each nomographs has an example on it which is self-explanatory. Using the trial culvert size, the relevant nomograph can be used to calculate HW i given a known Q. They can also be used in reverse to calculate Q given a known HW i. It should be noted that where the approach velocity is considerable, the approach velocity head can be calculated and deducted from the calculated HW i to give the actual physical head required. Step : Determine Depth, h 0 for Outlet control Calculate both (h c + D)/ and the tailwater, TW from known flood levels, downstream controlling levels or from the Slope Area Method. If it is clear that the downstream tailwater conditions do not control, take h 0 = (h c + D)/. h c can be calculated from Design Charts 18.A7. or 18.A8. If h c exceeds D then take h c as D. h 0 is the larger of TW or (h c + D)/ Step 7: Determine Outlet Control Headwater Depth at Inlet, HW 0 Determine entrance loss coefficient, K e from Design Table 18.A1., Appendix 18.A. Calculate the losses through the culvert, H using the outlet control nomographs, Design Charts 18.A9 to 18.A11 (or Equation 18. if outside the range). As with the inlet control nomographs, these nomographs cover various culvert types and each nomograph has an selfexplanatory example on it. If the Manning s n value of the culvert under consideration differs from the Manning n value shown on the nomograph, this can be allowed for by adjusting the culvert length as follows: n1 L1 = L (18.1) n where, L 1 = Adjusted culvert length; L = Actual culvert length; n 1 = Desired Manning n value; and n = Manning n value given on the nomograph. Calculate HW 0 = H + h 0 LS As with inlet control, where the approach velocity is considerable, the approach velocity head can be calculated and deducted from the calculated HW 0 to give the actual physical head required Culvert

13 MSMA nd Edition. 01 DID Malaysia If HW 0 is less than 0.7D and the culvert is under outlet control, then the culvert may be flowing only part full and using (h c + D)/ to calculate h 0 may not be applicable. If required, more accurate results can be obtained by flow profile calculations or the use of Hydraulic Engineering Circular No 10 (as discussed in Section 18.. under (ii) tailwater depth at or below top of opening). Step 8: Determine Controlling Headwater, HW c Compare HW i and HW 0 and use the higher: If HW i > HW 0 the culvert is under inlet control and HW c = HW i; and If HW 0 > HW i the culvert is under outlet control and HW c = HW 0. Step 9: Calculate Outlet Velocity, V 0 The average outlet velocity will be the discharge divided by the cross-sectional area of flow at the culvert outlet. The cross-sectional area of flow depends, in turn, on the flow depth at the outlet. If inlet control is the controlling headwater, the flow depth can be approximated by calculating the normal depth, y n, for the culvert cross-section using Manning s Equation. The flow area, A is calculated using y n and the outlet velocity: Q V o = (18.1) A The outlet velocity computed utilising the normal depth, y n will usually be high, because the normal depth is seldom reached in the relatively short length of average culvert. If outlet control is the controlling headwater, the flow depth can be either critical depth h c, the tailwater depth TW (if below the top of the culvert), or the full depth D of the culvert depending on the following Use relationships: h c, if h c > TW; Use TW, if h c < TW < D; and Use D, if D < TW. Calculate flow area using appropriate flow depth and then outlet velocity using Equation Step 10: Review Results Compare alternative design with the site constraints and assumptions. If any of the following conditions are not met, repeat steps to 9: The culvert must have adequate cover; The final length of the culvert should be close to the approximate length assumed in design; The headwalls and wingwalls must fit the site; The allowable headwater should not be exceeded; and The allowable overtopping flood frequency should not be exceeded. The performance of the culvert should also be considered, (i) with floods larger than the design flood to ensure such rarer floods do not pose unacceptable risks to life or potential for major damage and (ii) with smaller floods than the design flood to ensure that there will be no unacceptable problems of maintenance. If outlet velocity is high, scour protection or an energy dissipater may be required. Culvert 18-11

14 MSMA nd Edition. 01 DID Malaysia Step 11: Improved Designs Under certain conditions more economic designs may be achieved by consideration of the following: The use of an improved inlet for culverts operating under inlet control; and Allowing ponding to occur upstream to reduce the peak discharge, if a large upstream headwater pool exists. 18. FLOW VELOCITY Culvert usually increase the flow velocity in the natural water course. When culverts flow full, the highest velocity occurs near the outlet and may cause erosion. Check on outlet velocity must be carried out in the culvert design discharging into unlined waterway. Inlet Control - The outlet velocity for a pipe culvert flowing with inlet control can be obtained from the Colebrook-White equation, Design Chart 18.A1, Appendix 18.A for pipe roughness k=. For other pipe material charts of appropriate k values should be used. Chart 18.A and 18.A for circular and box culvert respectively can be used to obtain velocity for part full flow. This approach assumes that the outlet flow depth corresponding to uniform flow. The depth of flow should be checked against critical depth as determined from Design Charts 18.A7 and 18.A8 for circular and box culverts respectively. Outlet Control - For outlet control, the average outlet velocity will be equal to the discharge divided by the crosssectional areas of flow at the outlet. Erosion of Conduit - Very fast flow of higher than 7.m/s in full flow pipe, and 1m/s in open conduit can cause cavitation and erosion to the conduit. Maximum recommended flow velocities for Precast concrete pipes and precast box culvert are 8.0m/s, while for insitu concrete and hard packed rock of 00mm minimum is.0m/s. Scour at Inlets and Outlets - Scour can occur upstream of the culvert caused by high velocity and acceleration of flow as it leaves the natural channel and enters the culvert. Upstream wing walls, aprons, cut-off walls and embankment paving assist protecting the embankment and stream bed at the upstream end of a culvert. The flow of high velocity emerging from culvert can cause erosion and scour in the bed immediately downstream. Scour protection such as concrete apron, rock riprap, rock mattresses, or concrete filled mattresses may be considered. Siltation - Flow velocity about m/s and below will cause settlement of fine to medium sand particles and siltation occurs. Higher velocity may be obtained by increase the slope and hence to be self-cleansing. Self cleansing may also be obtained by graded culverts to the average grade of the water course upstream and downstream of the culvert, and levels must represent the average stream levels before the culvert was built. 18. MINIMUM ENERGY CULVERTS The tranquil flow occur in conduit laid on natural grade of low slope of a fraction of one per thousand as in most coastal areas. The Minimum Energy Culvert concept is to concentrate the flow in a narrow, deep cross section flowing with critical velocity under maximum design flow, taking advantage of the minimum specific energy under critical flow condition. This maximises the flow per unit length of waterway crossing. By keeping the flow outside the supercritical region, the designer avoids the energy loss in a hydraulic jump and the need for erosion protection, hence safe cost. Here, the design requires knowledge of: Design discharge; Average natural slope of terrain; Flood Levels; and Survey details of flood plain adjacent to culvert Culvert

15 MSMA nd Edition. 01 DID Malaysia Base on the above information and the following assumptions, a plan and longitudinal section of the culvert is drawn; The energy line parallels the natural fall of the terrain; and Energy losses at entry and exit of culvert are disregarded due to smooth transitions. To avoid the formation of standing eddies, the expansion of exit stream bed should be smaller than the entry angle. Using the following equations: H s,c = 1.d c, Q = bd c (gd c ) (18.1a) (18.1b) Corresponding values of b, d c and H s can be tried and compared. PLAN 1 b 1 bc 1 ELEVATION 1 v g Energy Line d 1 dc Culvert Water Surface Culvert and Channel Bottom Figure 18.8: Characteristic Flow Line of Minimum Energy Culvert Culvert 18-1

16 MSMA nd Edition. 01 DID Malaysia REFERENCES 1. DID Malaysia (000). Urban Stormwater Management Manual for Malaysia. Department of Irrigation and Drainage.. U.S. Federal Highway Administration (197). Capacity Chart for the Hydraulic Design of Highway Culverts, Hydraulic Engineering Circular No.10, Washington DC.. U.S. Federal Highway Administration (197). Hydraulic Design of Highway Culverts, Hydraulic Engineering Circular No., Washington DC Culvert

17 MSMA nd Edition. 01 DID Malaysia APPENDIX 18.A DESIGN FORM, TABLE, CHARTS AND NOMOGRAPH PROJECT : HYDROLOGICAL AND CHANNEL INFORMATION SKETCH EL. Q 1 = TW 1 = ALLOWABLE HW= Q = TW = (Q = Design Discharge) 1 (Q = Check Discharge) 1 EL. S 0 = L = MEAN STREAM VELOCITY = MAX. STREAM VELOCITY = CULVERT DESCRIPTION (Entrance Type) Q SIZE INLET CONT. HWi D HW HEADWATER COMPUTATION OUTLET CONTROL HW 0= H + h 0-LS 0 hc + D Ke H hc TW h 0 LS 0 HW 0 ENGINEER : DATE : STATION : TW EL. CONTROLLING HW OUTLET VELOCITY SUMMARY AND RECOMMENDATIONS: COST COMMENTS Design Chart 18.A1: Design Form for Culvert Calculation Culvert 18-1

18 MSMA nd Edition. 01 DID Malaysia Design Table 18.A1: Entrance Loss Coefficients Pipe, Concrete Type of Barrel And Inlet Loss Coefficients Projecting from fill, socket end 0. Projecting from fill, square cut end Headwall or headwall and wingwalls Socket end of pipe 0. Square-edge Rounded (radius = 1/1 D) 0. Mitred to conform to fill slope 0.7 End-section conforming to fill slope (standard precast) Bevelled edges,.7 or bevels 0. Side-tapered or slope-tapered inlets 0. Pipe, or Pipe-Arch, Corrugated Steel Projecting from fill 0.9 Headwall or headwall and wingwalls, square edge Mitred to conform to fill slope 0.7 End-section conforming to fill slope (standard prefab) Bevelled edges,.7 or bevels Side-tapered or slope-tapered inlets 0. Box, Reinforced Concrete Headwall Square-edged on edges Rounded on edges to radius of 1/1 barrel dimension, Or bevelled edges on sides 0. Wingwalls at 0 to 7 to barrel Square-edged at crown 0. Crown edge rounded to radius of 1/1 barrel dimension Or bevelled top edge 0. Wingwalls at 10 to to barrel Square-edged at crown Wingwalls parallel (extension of sides) Square-edged at crown 0.7 Side-tapered or slope-tapered inlet 0. Projecting Square-edged 0.7* Bevelled edges,.7 or bevels 0.* * Estimated K e 18-1 Culvert

19 MSMA nd Edition. 01 DID Malaysia D (m) Q N (m /s) HW Example D = 0 m Q = 1.7 m /s N Inlet HW D HW(m) (1).0.08 () () D (1) () () Q N = 1.7 m /s Example D = 0 m Inlet Type (1) Headwall with Square Edge () Headwall with Socket End () Projecting with Socket End D Design Chart 18.A: Inlet Control Nomograph Concrete Pipe Culvert Culvert 18-17

20 MSMA nd Edition. 01 DID Malaysia Height of Box D (m) D = m Example Q (m /s per metre span) NB 70 Example HW 0.00 x 0m Box Q = 8.0m /s D 0 (1) () () Q 0 =.0m /s per m NB Inlet HW HW D (m) 7 0 (1)..0 ().8.8 () Angle of Wingwall Flare 1.0 Ratio of Dischange to Width Q =.0m /s per m NB B = Span per cell Head Water Depth in Terms of Height ( HW/D ) Wingwall Flare HW/D Scale (headwall) 0 (parallel) B D Design Chart 18.A: Inlet Control Nomograph Box Culvert Culvert

21 MSMA nd Edition. 01 DID Malaysia SPCSP Sizes D (m) C M P Sizes D = 0.90 m Q N (m /s) Q N Example D = 0.90 m Q = 1.8 m /s N Inlet HW HW(m) D (1) () () = 1.8 m /s Example Inlet Edges (1) Headwall () Mitred () Projecting (1) () () HW D D Design Chart 18.A: Inlet Control Nomograph Corrugated Metal Pipe (CMP) Culvert Culvert 18-19

22 MSMA nd Edition. 01 DID Malaysia Relative Depth y/d Q/Q F V/VF R/RF y D Q = Part - full Discharge Q F= Full Flow Discharge V = Part - full Velocity V F = Full Flow Velocity R = Part - full Flow Hydraulic Radius R F= Full Flow Hydraulic Radius Q/Q F V/V R/R F F Relative Discharge Q/Q, Relative Velocity V/V F F, Relative Hydraulic Radius R/R F Design Chart 18.A: Relative Discharge, Velocity and Hydraulic Radius in Part-full Pipe Flow. y/d 1.0 B/D NOTE : Q/Q = 1 Corresponds to Full Flow F with Top Slab Fully Wetted Q/Q > 1 Disregards All Effects F of Top Slab Q/Q F 0. V/V F 0. Part - Full Flow Box Culverts 0. y D 0.1 B 0 Q/Q F V/V F Q/Q and V/V F F Design Chart 18.A: Relative Discharge, Velocity and Hydraulic Radius in Part-full Box Culvert Flow 18-0 Culvert

23 MSMA nd Edition. 01 DID Malaysia Design Chart 18.A7: Critical Depth in a Circular Pipe Culvert 18-1

24 MSMA nd Edition. 01 DID Malaysia B (m) Q (m /s) N B =.00 m Example Q/N = 11. m /s h c = 1.0 m h c (m) h c = 0.7 Q ( NB (h >D) c / hc B D Critical Depth Rectangular Section Design Chart 18.A8: Critical Depth in a Rectangular (Box) Section 18- Culvert

25 MSMA nd Edition. 01 DID Malaysia Q (m /s) N D (m) H (m) Q = m /s N D = 0 m Turning Line K e = L = 17 m K e = 0. K e= Length (m) Example H =.0 m Ke 0. Wingwall Angle & Edge Finish - Socket End (Projecting or Headwall) - Bevelled Inlet (.7 or ) - Square (Cut) End (Proj. or Headwall) - Prefabricated End Section D Outlet Control Conrete Pipe Culvert Flowing Full n = 0.01 Design Chart 18.A9: Outlet Control Nomograph Concrete Pipe Culvert Flowing Full with n = 0.01 Culvert 18-

26 MSMA nd Edition. 01 DID Malaysia Q (m /s) N A (m ) QExample H =.80 m N = m /s Turning Line K e = 0. K e = K e = 0.7 L =1 m K e = Length (m) Ke Wingwall Angle & Edge Finish or 90 Bevelled Edge - 0 to 7 Bevelled Edge - 90 Square Edge - 10 to Square Edge Projecting Square Edge H (m) B D NOTE: A=BD A = Cross-sectional Area per Cell If B/D = to.0 Calculate H from E 7. Design Chart 18.A10: Outlet Control Nomograph Concrete Box Culvert Flowing Full with n = Culvert

27 MSMA nd Edition. 01 DID Malaysia Q (m /s) N D (m) H (m) Q N=1 m /s D=0.70 m Turning Line L=1 m K =0.9 e K = e K = e K =0.9 e 10 0 Example Length (m) H=.9 m K e Wingwall Angle & Edge Finish 0. - Side-tapered or Slope-tapered - Bevelled Edge - Headwall or Wingwalls, Square Edge - Prefabricated End Section Mitred Parallel to Fill Slope Projecting D Outlet Control Corrugated Steel Pipe Flowing Full n=0.0 Design Chart 18.A11: Outlet Control Nomograph Corrugated Metal Pipe (CMP) Flowing Full with n = 0.0 Culvert 18-

28 MSMA nd Edition. 01 DID Malaysia HYDRAULIC GRADIENT, % DISCHARGE Q, L/s DIAMETER D, mm VELOCITY VELOCITY, V, m/s M/S Design Chart 18.A1: Hydraulic Design of Pipes Colebrook-White Formula k = 0 mm 18- Culvert

29 MSMA nd Edition. 01 DID Malaysia APPENDIX 18.B EXAMPLE CULVERT DESIGN 18.B1 Pipe Culvert (Inlet Control) Problem: Figure 18.B1 shows a proposed culvert located near a road intersection to be sized to accommodate a given design flow of.8m /s. Road level as well as culvert inflow and outflow inverts are as given. Determine a suitable pipe culvert (k = mm) and calculate the velocity to check if erosion will be a problem IL Flow IL Culvert Location 9.91 IL Flow IL Figure 18.B1: Culvert Location and Levels Solution: Reference Calculation Output STEP 1: Data Flow Q =.8m /s Culvert length, L = m Natural waterway inverts level: Inlet = 7.98m Outlet = 7.0m Acceptable upstream flood level = 9.7m Proposed pavement level = 0.8m Minimum freeboard = 0.0m Estimated downstream tailwater level = 8.0m Maximum headwater height, HW max, is the lesser of: i) =.0m ii) = 1.7m Therefore maximum headwater height, HW max = 1.7 m HW max = 1.7m Culvert 18-7

30 MSMA nd Edition. 01 DID Malaysia STEP : Assume Inlet Control Estimate required waterway flow area by assuming flow velocity, V =.0m/s. Use Design Chart 18.A Use Design Chart 18.A Estimated flow area, A = Q/V =.0m i) Try 10mm diameter reinforced concrete pipe (RCP), D = 1.m Enter Design Chart 18.A with Q/N =.8/1 =.8m /s; Inlet Type (1): Obtain HW i /D = 1.10m HW i = 1.81m > 1.7m maximum. Not acceptable. ii) Try RCP 1800 mm diameter Enter Design Chart 18.A with Q/N =.8/1 =.8m /s; Inlet Type (1): Obtain HW i /D = 0.9m HW i = 1.9m < 1.7m But maximum culvert height available only 1.7m HW i > HW max, not acceptable Use Design Chart 18.A iii) Try twin lines, /100mm diameter Enter Design Chart 18.A with Q/N =.8/ =.0m /s; Inlet Type (1): Obtain HW i /D = 1.m HW i = 1.70m < 1.7m Use /100mm diameter pipes HW i <HW max, ok Use Design Chart 18.A7 STEP : Check Outlet Control TW = = 0m< D (1.0m) Enter Design Chart 18.A7 with D = 1.0m; Q/N =.8/ =.m /s h c = 0m< D (1.0m) (h c +D)/ = ( )/ = 0.9m > TW = 0m Use Design Chart 18.A9 Calculate HW o for outlet control: Enter Design Chart 18.A9 with D = 1.0 m; Q/N =.8/ =. m /s; K e = ; and L = m Obtain H = m Fall of culvert invert, L S = = 0.8m hence: HW o = (h c +D)/ + H - L S = = 1.0m HW i (Inlet control) = 1.70m greater than HW o (Outlet control) = 1.0m Inlet Control HW i <HW max, ok Therefore inlet control governs Culvert

31 MSMA nd Edition. 01 DID Malaysia STEP : Flow Velocity For 100mm diameter pipes: A = (πd )/ = 7m S = 0.8/ = 0.01 (= 1.% ) Use Design Chart 18.A1 From Colebrook-White s Chart for k = mm (Chart 18.A1) Q f =.0m /s V f =.80m/s Use Design Chart 18.A Because the culvert does not flow full it is necessary to use part-full flow relationships plotted in Design Chart 18.A: Q/Q f =./. = 0.71 and from Design Chart 18.A, V/V f = 0.9 and V = 0.9 x.80 =.m/s y/d = 8 and y = 8 x 1.0 y = 0.71m < h c = 0m STEP : Summary Use /100mm diameter concrete pipes with square edge entrance. Pipes will flow with inlet control with headwater height of 1.70m and headwater at RL 9.8m. Outlet velocity =.m/s and the possibility of scour or the formation of a hydraulic jump at the outlet must be checked. Use /100mm mm diameter pipes with square edge entrance. HW=9.8m 0.8m Embankment D=100mm IL=7.98m Ls Culvert L=m IL=7.0m Profile Section Culvert 18-9

32 MSMA nd Edition. 01 DID Malaysia 18.B Box Culvert (Inlet Control) Problem: Using the same data as provided for the previous pipe culvert (Example 18.B1), calculate a suitable box culvert size and check for the effects of the outlet velocity. Solution: Reference Calculation Output STEP 1: Data Flow Q =.8m /s Culvert length, L = m Natural waterway inverts level: Inlet = 7.98m Outlet = 7.0m Acceptable upstream flood level = 9.7m Proposed pavement level = 0.8m Minimum freeboard = 0.0m Estimated downstream tailwater level = 8.0m Maximum headwater height, HW max, is the lesser of: i) =.0m ii) = 1.7m Therefore maximum headwater height, HW max = 1.7 m HW max = 1.7m STEP : Assume Inlet Control Estimate required waterway flow area by assuming flow velocity, V =.0m/s. Estimated flow area, A = Q/V =.0m Use Design Chart 18.A Try 100mm (wide) and 100mm (high) box culvert Enter Design Chart 18.A with D = 1.m; Q/NB =.8/(1x1.) =.m /s/m; Inlet Type (1): Obtain HW i /D = 1.m HW i = 1.70m > 1.7m maximum, which is acceptable HW i <HW max, ok Use Design Chart 18.A8 STEP : Check Outlet Control TW = = 0m< D (1.0m) Enter Design Chart 18.A8 with B = 1.0m; Q/N =.8/1 =.80m /s h c = 1.00m< D (1.0m) (h c +D)/ = ( )/ = 1.10m > TW = 0m 18-0 Culvert

33 MSMA nd Edition. 01 DID Malaysia Use Design Chart 18.A10 Calculate headwater for outlet control (HW o ): Enter Design Chart 18.A10 with A = 1. x 1. = 1.80 m ; Q/N =.8/1 =.8 m /s; K e = ; and L = m Obtain H = 0.7m Fall of culvert invert, L S = = 0.8m hence: HW o = (h c +D)/ + H - L S = = 1.7m HW i (Inlet control) = 1.70m greater than HW o (Outlet control) = 1.7m Inlet Control HW i <HW max, ok Therefore inlet control governs. STEP : Flow Velocity Hydraulic radius R = Area/wetted perimeter R = 1.8/((1.+1.)) = 0.m Equivalent D = x 0. = 1.m and S = 0.8/ = 0.01 (= 1.% ) Use Design Chart 18.A1 From Colebrook-White s Chart for k = mm (Chart 18.A1) V f =.0m/s Q f = 1.8 x.0 = 8.10m /s Use Design Chart 18.A Because the culvert does not flow full it is necessary to use part-full flow relationships plotted in Design Chart 18.A: Q/Q f =.8/8.1 = 9 and from Design Chart 18.A B/D = 1., V/V f = 1.0 and V = 1.0 x.0 =.7m/s y/d = 7 and y = 7 x 1.0 y = 8 < h c = 1.00m Culvert 18-1

34 MSMA nd Edition. 01 DID Malaysia STEP : Summary Use 100mm (wide) by 100mm (high) concrete box culvert with square edges. Culvert will flow with inlet control with headwater height of 1.70m and headwater at RL 9.8m. Use 100mm (wide) by 100 (high) box culvert with square edges. Outlet velocity =.7m/s and the possibility of scour or the formation of a hydraulic jump at the outlet must be checked. 0.8m IL=7.98m HW=9.8m Ls Embankment Culvert L=m Profile D=100mm IL=7.0m B=100mm Section 18- Culvert

35 MSMA nd Edition. 01 DID Malaysia 18.B Pipe Culvert (Outlet Control) Problem: Figure 18.B shows a different culvert crossing located at a road junction to be sized to accommodate a given design flow of 0.90m /s. Road level as well as culvert inflow and outflow inverts are as given. Determine a suitable pipe culvert (k = mm) and calculate the velocity to check if erosion will be a problem. Culvert Location IL Flow IL IL.090 Flow IL Figure 18.B: Culvert Location and Levels Solution: Reference Calculation Output STEP 1: Data Flow Q = 0.90m /s Culvert length, L = m Natural waterway inverts level: Inlet =.0m Outlet =.09m Acceptable upstream flood level = 7.0m Proposed pavement level = 7.90m Minimum freeboard = 0.0m Estimated downstream tailwater level =.9m Maximum headwater height, HW max, is the lesser of: i) =.0m ii) =.0m Therefore maximum headwater height, HW max =.0 m HW max =.0m Culvert 18-

36 MSMA nd Edition. 01 DID Malaysia STEP : Assume Inlet Control Estimate required waterway flow area by assuming flow velocity, V =.0m/s. Estimated flow area, A = Q/V = 0.m Try 00mm diameter concrete pipe, D = 0m Use Design Chart 18.A Enter Design Chart 18.A with D = 0m; Q/N = 0.90/1 = 0.90m /s; Inlet Type (1): Obtain HW i /D =.80m HW i = 1.8m for inlet control This depth is less than the limit of.0m HW i <HW max, ok STEP : Check Outlet Control Use Design Chart 18.A9 TW =.9.09 = 1.0m> D (0m), the culvert is flowing full with a submerged outlet. Enter Design Chart 18.A9 with D = 0m; Q/N = 0.90/1 = 0.90m /s; K e = ; and L = m Obtain H = 1.m Fall of culvert invert, L S =.0.09 = 0.1m hence: HW o = TW + H - L S = =.m Note that because.m > 1.8m for inlet control, the culvert is under outlet control. HW o >HW max, not acceptable However the design is unacceptable because HW max =.0m Use Design Chart 18.A Use Design Chart 18.A9 Return to Step using 70mm pipe diameter in Design Chart 18.A Obtain HW i /D = 1.m HW i = 1. x 0.7 = 1.09m for inlet control Now check for outlet control. Re-enter Design Chart 18.A9 with D = 0.7m and obtain H = 0.8m HW o = TW + H - L S = = 1.77m HW o (Outlet control) = 1.77m greater than HW i (Inlet control) = 1.09m Therefore outlet control governs. HW i <HW max, ok Outlet control HW o <HW max, ok 18- Culvert

37 MSMA nd Edition. 01 DID Malaysia STEP : Flow Velocity With HW and TW both well above the crown of the pipe and a moderate slope of 0.1/ = the pipe will flow full hence: V = Q/A = x 0.9/(.1 x 0.7 ) =.0m/s The velocity must be checked against erosion at outlet. STEP : Summary Use single line of 70mm diameter concrete pipe with square edge entrance. Pipe will flow full under outlet control with headwater height of 1.77m and headwater at RL 7.07m. Use concrete pipe 70mm diameter with square edge. Outlet velocity =.0m/s and the possibility of scour or the formation of a hydraulic jump at the outlet must be checked. 7.90m HW=7.07m Embankment TW=.9m D=70mm IL=.0m Ls Culvert IL=.09m L=m Profile Section Culvert 18-

38 MSMA nd Edition. 01 DID Malaysia 18.B Box Culvert (Outlet Control) Problem: Using the same data as provided for the previous pipe culvert (Example 18.B), calculate a suitable box culvert size and check for the effects of the outlet velocity. Solution: Reference Calculation Output STEP 1: Data Flow Q = 0.90m /s Culvert length, L = m Natural waterway inverts level: Inlet =.0m Outlet =.09m Acceptable upstream flood level = 7.0m Proposed pavement level = 7.90m Minimum freeboard = 0.0m Estimated downstream tailwater level =.9m Maximum headwater height, HW max, is the lesser of: i) =.0m ii) =.0m Therefore maximum headwater height, HW max =.0 m HW max =.0m STEP : Assume Inlet Control Estimate required waterway flow area by assuming flow velocity, V =.0m/s. Estimated flow area, A = Q/V = 0.m Use Design Chart 18.A Try 70mm (wide) and 00mm (high) box culvert Enter Design Chart 18.A with D = 0m and Q/NB = 0.90/(1x0.7) = 1.m /s/m; Inlet Type (1): Obtain HW i /D = 1.0m HW i = 1. x 0 = 0.9m <.0 maximum, which is acceptable HW i <HW max, ok 18- Culvert

39 MSMA nd Edition. 01 DID Malaysia STEP : Check Outlet Control TW = 1.m (see Example 18.B) > m hence the culvert is flowing full with a submerged outlet. Calculate H from Design Chart 18.A10, noting that B/D=1., so the chart is applicable: Use Design Chart 18.A10 Enter Design Chart 18.A10 with A = 0.7 x 0 = 0.m ; Q/N = 0.90/1 = 0.90m /s; K e = ; and L = m Obtain H = 0.7m Fall of culvert invert, L S =.0.09 = 0.1m hence: HW o = TW + H - L S = = 1.7m HW o (Outlet control) = 1.7m greater than HW i (Inlet control) = 0.9m Outlet control HW o <HW max, ok Therefore outlet control governs. STEP : Flow Velocity As the culvert flows full, V = Q/A = 0.9/(0.7 x 0) =.00m/s The velocity must be checked against erosion at outlet. Culvert 18-7

40 MSMA nd Edition. 01 DID Malaysia STEP : Summary Use a single 70mm (wide) by 00mm (high) concrete box culvert with square edges entrance. The culvert will flow with outlet control with headwater height of 1.7m and headwater at RL 7.0m and outlet velocity =.00m/s and the possibility of scour or the formation of a hydraulic jump at the outlet must be checked. 7.90m Use 70mm (wide) by 00mm (high) box culvert with square edges. HW=7.0m Embankment TW=.9m IL=.0m Ls Culvert L=m IL=.09m D=00mm B=70mm Profile Section 18-8 Culvert