Part 2-Drainage Design Manual [PDF]

Zitiervorschau

ROAD DESIGN MANUAL FOR ROADS AND BRIDGES

Part II: Drainage Design

April 2016

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

PART 2 – DRAINAGE DESIGN

The Republic of Kenya – Ministry of Roads

1

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Table of Contents

INTRODUCTION ............................................................................................................ 6 1

BASIC PRINCIPLES AND CONCEPT .................................................................. 7

2

PLANNING AND LOCATING OF ROADS AND HIGHWAYS........................... 8 2.1 INTRODUCTION .................................................................................................... 8 2.2 COORDINATION WITH MINISTRIES AND AGENCIES ................................................. 9 2.3 LOCATION AND ALIGNMENT CONSIDERATIONS ................................................... 10 2.3.1 Horizontal Alignment ................................................................................ 10 2.3.2 Vertical Alignment ..................................................................................... 11 2.4 PHYSICAL CONSIDERATIONS............................................................................... 12 2.5 TIDAL AREAS..................................................................................................... 12 2.6 LAND USE CONSIDERATIONS .............................................................................. 12 2.7 LOCATION OF UTILITIES ..................................................................................... 13 2.8 LOCATION OF STORM DRAINAGE FACILITIES ...................................................... 13 2.9 TYPE OF STRUCTURE .......................................................................................... 14 2.10 CONSTRUCTION-RELATED CONSIDERATIONS ..................................................... 14

3

DESIGN STANDARDS AND DESIGN FLOW RETURN PERIODS ................. 16 3.1 3.2

4

THE CONCEPT OF RETURN PERIOD AND DESIGN FREQUENCY .............................. 16 APPLICABLE DESIGN FLOW RETURN PERIODS ..................................................... 16

FLOOD ESTIMATION OF GAUGED RIVERS .................................................. 17 4.1 INTRODUCTION .................................................................................................. 17 4.2 SOURCES OF RIVER FLOW DATA IN KENYA ......................................................... 17 4.3 PROCEDURE ....................................................................................................... 18 4.3.1 Data Preparation ...................................................................................... 18 4.3.2 Frequency Analysis Concepts .................................................................... 19 4.3.3 Plotting Formulas...................................................................................... 19 4.3.4 Distribution Function ................................................................................ 20 4.3.5 Application Example ................................................................................. 21

5

FLOOD ESTIMATION OF NON – GAUGED BASINS ...................................... 23 5.1 INTRODUCTION .................................................................................................. 23 5.2 SPECIFIC DISCHARGE METHOD ........................................................................... 24 5.3 RATIONAL METHOD ........................................................................................... 24 5.3.1 Introduction............................................................................................... 24 5.3.2 Application ................................................................................................ 24 5.3.3 Characteristics .......................................................................................... 25 5.3.4 Equation .................................................................................................... 25 5.3.5 Time of Concentration, Tc ......................................................................... 25 5.3.5.1 5.3.5.2

5.3.6 5.3.7

Kirpich Formula ......................................................................................... 26 Hathaway Formula ..................................................................................... 26

Rainfall Intensity, I .................................................................................... 27 Runoff Coefficient, C ................................................................................. 27 5.3.7.1 5.3.7.2

Undeveloped Basins and Natural Catchments .............................................. 28 Urban Land Use .......................................................................................... 28

5.4 TRRL METHOD ................................................................................................. 29 5.4.1 Introduction............................................................................................... 29 5.4.1 Initial Retention (Y) ................................................................................... 30 5.4.2 Contributing Area Coefficient (CA) ............................................................ 30 The Republic of Kenya – Ministry of Roads

2

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

5.4.3 5.4.4 5.4.5 5.4.6 6

Catchment lag Time (K)............................................................................. 31 Base Time .................................................................................................. 31 Area Reduction Factor .............................................................................. 32 Example (Adopted from TRRL Laboratory Report 706 (4)) ........................ 33

HYDRAULIC DESIGN OF CULVERTS .............................................................. 38 6.1 DEFINITIONS AND SYMBOLS ............................................................................... 38 6.2 PRINCIPLES OF DESIGN ....................................................................................... 40 6.3 DESIGN CRITERIA .............................................................................................. 40 6.3.1 Introduction............................................................................................... 40 6.3.2 Site Criteria ............................................................................................... 40 6.3.2.1 6.3.2.2 6.3.2.3

6.3.3

Design Limitations .................................................................................... 42 6.3.3.1 6.3.3.2 6.3.3.3

6.3.4

Structure Type Selection .............................................................................. 40 Length and Slope ......................................................................................... 41 Debris Control............................................................................................. 41 Allowable Headwater................................................................................... 42 Tailwater Relationship of Channel ............................................................... 42 Maximum Velocity and Minimum Velocity ................................................... 42

Design Features ........................................................................................ 43 6.3.4.1 6.3.4.2 6.3.4.3 6.3.4.4

Culvert Sizes and Shape ............................................................................... 43 Multiple Barrels........................................................................................... 43 Material Selection........................................................................................ 43 Further Reference ........................................................................................ 44

6.4 CULVERT DESIGN HYDRAULICS.......................................................................... 44 6.4.1 Introduction and Calculation Principles........................................................... 44 6.4.2 Inlet and Outlet Control............................................................................. 44 6.4.2.1 6.4.2.2

6.5 6.6 6.7

Inlet Control ................................................................................................ 44 Outlet Control.............................................................................................. 47

DESIGN PROCEDURE .......................................................................................... 52 SOFTWARE APPLICATIONS FOR CULVERT DESIGN ............................................... 58 NOMOGRAPH DESIGN EXAMPLE ......................................................................... 59

7 DRIFTS AND LOW LEVEL CROSSINGS ............................................................... 76 7.1 INTRODUCTION .................................................................................................. 76 7.2 DEFINITION AND TERMINOLOGY ......................................................................... 76 7.2.1 Drifts ......................................................................................................... 76 7.2.2 Causeway .................................................................................................. 77 7.2.3 Submersible Bridges .................................................................................. 78 7.3 APPLICATION CHARACTERISTICS ........................................................................ 79 7.3.1 Basic Characteristics................................................................................. 79 7.3.2 Road Network Considerations ................................................................... 79 7.4 DESIGN CONSIDERATIONS .................................................................................. 79 7.4.1 Site selection ............................................................................................. 79 7.4.2 Hydrological Considerations ..................................................................... 80 7.4.3 Hydraulic Design ...................................................................................... 80 7.5 WORKED EXAMPLE ............................................................................................ 85 8

BRIDGE DESIGN .................................................................................................. 88 8.1 PRINCIPLES AND DESIGN CRITERIA ..................................................................... 88 8.1.1 General Criteria ........................................................................................ 88 8.1.2 Specific Criteria ........................................................................................ 88 8.1.2.1 8.1.2.2 8.1.2.3

Inundation ................................................................................................... 88 Design Floods.............................................................................................. 88 Freeboard .................................................................................................... 89

The Republic of Kenya – Ministry of Roads

3

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

8.1.2.4 8.1.2.5 8.1.2.6 8.1.2.7 8.1.2.8

Flow Distribution ........................................................................................ 89 Relief Openings ........................................................................................... 89 Scour ........................................................................................................... 89 Environmental Considerations ..................................................................... 89 Construction/ Maintenance .......................................................................... 89

8.2 DESIGN PROCEDURE .......................................................................................... 91 8.2.1 Survey Accuracy and Data Collection........................................................ 91 8.2.2 Design Procedure Outline ......................................................................... 92 8.2.3 Hydraulic Performance of Bridges ............................................................ 93 8.2.4 Methodologies ........................................................................................... 96 8.2.4.1 8.2.4.2

HDS-1 Method ............................................................................................. 96 Advanced Computerized Methods, HEC 2, HEC RAS ................................... 96

8.3 BRIDGE SCOUR AND AGGRADATION ................................................................... 97 8.3.1 Introduction............................................................................................... 97 8.3.2 Scour Types ............................................................................................... 97 8.3.2.1 8.3.2.2 8.3.2.3 8.3.2.4 8.3.2.5 8.3.2.6

8.3.3

Long Term Profile Changes ......................................................................... 97 Plan Form Changes ..................................................................................... 98 Contraction ................................................................................................. 98 Local Scour ................................................................................................. 99 Natural Armoring ........................................................................................ 99 Naturally Occurring Scour Resistant Materials ............................................ 99

Scour Analysis Methods............................................................................. 99 8.3.3.1 8.3.3.2

8.3.4.

Method 1 ................................................................................................... 100 Method 2 ................................................................................................... 101

Scour Assessment Procedure ................................................................... 101

8.3.4.1 8.3.4.2

Site Data.................................................................................................... 101 Design Procedure Step by Step .................................................................. 103

8.4 EXAMPLES ....................................................................................................... 105 8.4.1 Example 1: Backwater Calculation HDS-1 .............................................. 105 8.4.2 Example 2 : Riprap at Piers..................................................................... 111 9

RURAL ROADS: ROAD DRAINAGE AND EROSION CONTROL ............... 114 9.1 INTRODUCTION ................................................................................................ 114 9.2 TYPE OF DRAIN ................................................................................................ 114 9.2.1 Choice of Side Drain ............................................................................... 114 9.2.1.2 9.2.1.3 9.2.1.4

Discharge Channels................................................................................... 114 Collection of Water on Embankments......................................................... 114 Economic and Aesthetics............................................................................ 114

9.3 DIMENSIONING OF SIDE DRAINS ....................................................................... 115 9.3.1 Discharge Calculation ............................................................................. 115 9.3.2 Capacity of Side Ditches .......................................................................... 115 9.3.3 Protection of Ditches and Channels from Erosion ................................... 116 9.3.3.1 9.3.3.2

Critical Length Ditches .............................................................................. 116 Method of Protection ................................................................................. 117

9.3.4 Sedimentation Control ............................................................................. 118 9.4 EROSION CONTROL AT SLOPES AND EMBANKMENT........................................... 119 9.4.1 General ................................................................................................... 119 9.4.2 Protection of Slopes ................................................................................ 119 9.4.2.1 9.4.2.2 9.4.2.3 9.4.2.4 9.4.2.5 9.4.2.6

9.5

Topsoiling and Grassing ............................................................................ 119 Surface Treatment with Seeds and Fertilizers ............................................. 119 Gravel or Stone Blanketing ........................................................................ 119 Fascines .................................................................................................... 119 Serrated Slopes .......................................................................................... 120 Other Protection Works ............................................................................. 120

DRAINAGE OF GROUND WATER ........................................................................ 121

The Republic of Kenya – Ministry of Roads

4

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

9.5.1 9.5.2

General .................................................................................................. 121 Drainage Remedies ................................................................................ 121 9.5.2.1 9.5.2.2 9.5.2.3 9.5.2.4

Choice of Proper Alignment ....................................................................... 121 Subsoil Drains ........................................................................................... 121 Blanket Drains........................................................................................... 122 Seepage Remedies...................................................................................... 122

10 URBAN AREAS: ROAD DRAINAGE AND URBAN STORMWATER DRAINAGE .................................................................................................................. 123 10.1 INTRODUCTION................................................................................................ 123 10.2 URBAN HYDROLOGY ....................................................................................... 123 10.2.1 Peak Discharge Calculation .................................................................... 124 10.3 HYDRAULIC CALCULATIONS ............................................................................ 124 10.3.1. Minimum Velocity .................................................................................. 125 10.3.2 Safety Issues ........................................................................................... 125 10.4 TYPES OF URBAN DRAINS ............................................................................ 125 10.4.1 Slotted Drains ....................................................................................... 125 10.4.2 Invert Block Drains (IBD) ....................................................................... 125 10.4.3 Kerbs ....................................................................................................... 125 10.5 INLET STRUCTURES ...................................................................................... 126 10.5.1 Grate Inlets ........................................................................................... 126 10.6 URBAN DRAINAGE NETWORKS ........................................................................ 128 10.6.1 General ........................................................................................................ 128 10.6.2 Design Procedure .................................................................................... 128 10.6.2.1 10.6.2.2

10.7

Summation of Flow Method ....................................................................... 128 Rational Method ........................................................................................ 128

WORKED EXAMPLE OF SEWER NETWORK ........................................................ 129

The Republic of Kenya – Ministry of Roads

5

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Introduction In the past context of Road Design in Kenya the aspects of Hydrology, Hydraulics and Drainage Design – and the issue of water in general - were treated as cross cutting issues. While the design and the hydraulic dimensioning of side drains was considered part of the Geometric Road Design (Part I Rural Road Design Manual), the aspects of Pavement Drainage and Erosion Control were dealt with in the Materials and Pavement Design Manual (Part III Road Design Manual). Classic hydrological and hydraulic calculations concerning catchment runoff and culvert and bridge hydraulics were discussed in the Bridge Design Manual (Part IV Road Design Manual, Draft Version). In addition to that the Road Design Guidelines (2. Draft Version) was used, which covered certain aspects of urban road drainage. This new Drainage Design Manual – as integral part of the updated Kenyan Road Design Manual – aims at integrating all Hydrology and Drainage – related aspects of road and drainage design into one comprehensive volume. An effort was made to harmonise the currently contradictory design recommendations concerning, for instance, the design periods of bridges and culverts in current urban and rural design. However, in cases where the existing established procedures have proven practical and successful, every effort was made to retain established design procedures. As a consequence rural and urban road drainage is still covered in two independent chapters, taking into consideration the more complex nature of urban stormwater design, the larger variety of drainage designs options und specifically urban issues, like scarcity of space, interaction with urban waste water networks and solid waste management. Compared to former drainage manuals environmental issues have been introduced wherever possible. An effort was made to integrate the road drainage design procedure into larger frameworks, like urban drainage master plans and the redefinition of stormwater runoff as a resource – for instance for irrigation in water scarce areas – rather than a problem, which has to be disposed of. The Manual is structures in the following Chapters: In the first Chapter the basic principles and concepts are presented. These principles and concepts reflect the underlying design philosophy applied. The second Chapter concentrates on hydraulic considerations during the planning stage for road design. The third chapter deals with the definition of suitable design flows return periods for hydrological and hydraulic design. Chapter four deals with the analysis of gauges catchments. In Chapter five the most commonly applied methods in Kenya for estimating design flow from ungauged catchments are discussed. Chapter six covers aspects of culvert design, including worked examples based upon the AASHTO design procedures for hand calculations. It also includes the presentation of commonly used hydraulic software for culvert design. Chapter seven concentrates on hydraulic design procedures for drifts and low level crossings. Chapter nine addresses Pavement Drainage for rural roads, including side drainage and subsurface drainage. Chapter ten deals with road pavement drainage. However, it focuses on urban roads and the integration of road drainage into urban stormwater drainage systems.

The Republic of Kenya – Ministry of Roads

6

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

1

Basic Principles and Concept

The principles and design considerations used in this Manual involve the basic concepts highlighted below: ·

Stormwater is a component of the total water resources of an area and should not be casually discarded but rather, where feasible, should be used to replenish that resource. For example, the use of road runoff for irrigation purposes is currently common practice in many regions of Kenya and should be increased. There should, therefore, be an increasing awareness for reiteration of approaches to basin-wide water and drainage management.

·

Drainage concepts of the past, allow upstream development to increase runoff. As a consequence, downstream development might be unable to accommodate, without significant additional cost, the upstream excess runoff. For design rainfall frequencies (up to 10 years), the peak runoff should not be significantly higher after development of an area than it would be if such development had not taken place.

·

Improvement of the effectiveness of natural systems rather than replacing, downgrading or ignoring them is an objective of current engineering design. In this regards, the basic principles used in this Design Manual include the following: · In areas, where soil and physical conditions permit, the road shall be drained directly into the road reserve. · Where natural watercourse and drainage channels exist the road reserve shall be drained directly into them. · Where conditions necessitate drainage beyond the reserve, additional land shall be acquired for the necessary drainage channels, but this should be the exception rather than the rule.

Two principal systems for handling surface water runoff are recognized. The one on which engineering planning, design and operations have been almost wholly concentrated, the "Minor System", (equally called the "Convenience System") and the larger major storm drainage system, which includes all the natural and man-made drainage facilities in an entire watershed. The "Minor System" is the scheme of kerbs, gutters, inlets, pipes or other conveyances, swales, and appurtenant facilities, all designed to minimize nuisance, inconvenience and hazard from storm runoffs to persons and property. Currently more detailed attention is also being given to the planning and design of the supplementary aspects of the overall "major system", which carry the excess flow over and above the hydraulic capacity of the various components of the minor system. Since many communities and urban areas use less than a 10 years frequency value for their storm drainage facilities, coordination of the highway drainage with that of the local urban area is a primary factor requiring careful consideration. Location studies of a highway through a built up area require close attention to how the proposed highway's drainage requirements can be satisfactorily coordinated with those of the community. Necessarily, both horizontal and vertical location of the proposed highway improvements are of great significance, since most major city streets are likely to have existing storm sewers and underground utilities.

The Republic of Kenya – Ministry of Roads

7

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

2

Planning and Locating of Roads and Highways

2.1 Introduction The planning and locating of highway facilities are the first steps in a challenging process of providing a safe and efficient transportation system. Hydrologic and hydraulic requirements are among the facets, which must be considered during the early phases of the design process. Water and its related resources are important considerations in the planning and locating of highways. Although historically only major drainage features such as large rivers and environmentally sensitive areas have been considered during these early stages, the overall drainage solution must be visualized and studied so that substantial design and construction changes are not required later. The possible effects that highway construction may have on existing drainage patterns, river characteristics, potential flood hazards, and the environment in general, as well as the effects the river and other water features may have on the highway, should be considered at this time. Hydrologic and hydraulic specialists must be actively involved during the initial project phases to ensure that proper consideration is being given to drainage aspects. This involvement should include participation during the highway location selection phase. Early input from these specialists will result in a better design, both hydraulically and economically. It must be emphasized that early studies are not comprehensive, detailed, technical designs. Rather, most are cursory studies to consider obvious drainage related problems that may be encountered or created and what type of data needs to be collected for evaluation of possible impacts. The degree and extent of preliminary hydraulic studies should be commensurate with the cost and scope of the project and the perceived flood hazards that may be encountered. This Chapter of the Design Manual presents a comprehensive overview of possible considerations in the planning and locating of a highway.

The Republic of Kenya – Ministry of Roads

8

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

2.2 Coordination with Ministries and Agencies The overall planning procedure for a new road or highway is a complex process, which involves careful planning between local, regional and national agencies and bodies on all levels and all specific aspects. In this chapter only water related aspects are mentioned, bearing in mind, however, that the overall planning goes far beyond. The hydraulic engineer should be involved in the coordination process with other agencies, which may have water resource data. These national and local agencies have a wealth of information useful to anyone involved in hydraulics or hydrology. This coordination is necessary to find out about plans for water-related projects within the project area, and to inform other agencies about the planned road project. It is important for the hydraulic engineer, therefore, to not only coordinate with these agencies but also to establish a good working relationship with them. In Kenya the agencies to coordinate with are: · Ministry of Water and Irrigation, Nairobi · Water supply/waste water treatment utilities · Regional Basin Management Authorities (TARDA etc..) · Ministry of Energy, KenGen – re. hydropower projects and dams · Ministry of Environment · Ministry of Tourism · Meteorological Department · City Councils and City Engineers re. water or drainage master plans for urban areas · Ministry of Agriculture, or agricultural water user co-operations in the project area · Supranational agencies like UNEP Nairobi · Universities and other training agencies

References: 1) AASHTO Drainage Guideline, Volume I, Guidelines for Hydraulic Considerations in Highway Planning and Location, 1999 2) Road Design Manual, Volume II, Drainage Design, Ministry of Works, Housing and Communications. The Republic of Uganda, 2005

The Republic of Kenya – Ministry of Roads

9

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

2.3 Location and Alignment Considerations 2.3.1 Horizontal Alignment The horizontal alignment of a highway determines where stream crossings will occur and where there will be transverse or longitudinal encroachments. Two aspects of the proposed alignment must be considered. First, the hydraulic engineer must consider how the streams or storm drain systems may affect the roadway, and second, how the roadway may affect the flow characteristics of such streams or systems. Slight changes in alignment can sometimes alter the flooding characteristics significantly. Whether or not changes to the horizontal alignment can be made often depends on whether the project is an improvement to an existing highway or the construction of a highway in a new location. There is often little opportunity to change horizontal alignments when the project is an improvement to an existing highway. The alignment should still be reviewed though, to identify locations where: · · · ·

it is required to protect slopes against scour, abutments moved or skewed differently, drainage structures have to be protected against headcutting, meanders are endangering the highway.

Minor alignment improvements or roadway widening may cause slopes to encroach upon streams. If unavoidable, the hydraulic engineer must be prepared to offer actions to accommodate these encroachments. Changes to the horizontal alignment of the highway at stream crossings can also result in hydraulic consequences. Many older structures were constructed to cross the stream at a right angle to the flow. This sometimes resulted in sharp curves in the roadway approaches to the bridges. Replacement structures are often planned to correct this poor alignment by crossing the stream at a skew. Proper abutment and pier alignment of the replacement structure must be ensured. If the existing substructures are to be used as part of the replacement, their alignment with the channel must be considered. The construction of a highway on a new alignment affords the greatest opportunity for the hydraulic engineer to influence the alignment during the location phase. During this phase, changes can be recommended to locate the highway away from a stream or situate a bridge at a more stable channel location. These recommendations should be made early in the development of a project to avoid delays during the design or right-ofway acquisition phase when the horizontal alignment is difficult to change. During relocation there may also be constraints, which control the alignment. Topographic and cultural features may have to be avoided, resulting in the use of the river environment for the highway. In these cases, the constraints noted in the previous section will often exist. Besides these constraints, there may be other alternatives that should be studied because of other considerations, such as cost-effective designs or land development plans.

The Republic of Kenya – Ministry of Roads

10

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

2.3.2 Vertical Alignment The effect of the vertical alignment, commonly called the profile, on highway drainage facilities is significant and must be assessed in comparing alternate locations. Although the profile usually is of greater interest to the hydraulic engineer than the horizontal alignment, it is normally easier to alter and is not firmly set as early in the project development. The profile is the feature, along with the hydraulic opening, that determines when, as well as where, the highway will be overtopped. By raising or lowering the profile, the frequency of overtopping can be either decreased or increased. Not only does the profile affect the frequency of overtopping, but it also determines the level of upstream flooding. Depressed roadways act as drainage interceptors and may require that upstream surface runoff be accommodated in storm drains or diversion channels. Fills on wide flat areas may intercept surface flows and require special drainage treatments. These problems will be of special concern with large urban expressways and deserve careful evaluation at the location phase. On streams where navigation exists, clearances required for waterway vessels may become the factor controlling vertical alignment. The profile not only affects the flow from streams either over the roadway or through the structure opening, but it also affects the flow of the roadway runoff water. Sag-vertical curves are critical profile areas, as they can serve to trap highway drainage unless adequately sized and spaced outlets or catch basins are provided. Steepness of the highway grade also determines the spacing of inlets in areas where the roadway has kerbs.

The Republic of Kenya – Ministry of Roads

11

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

2.4 Physical Considerations A highway crossing at or near to the confluence of two or more streams represents a complex hydrologic and hydraulic location and should be avoided wherever possible. The hydrology is complicated because several combinations of events should be considered. Large peaks could occur simultaneously on both streams, though this probability is usually small if one watershed is much larger or hydrologically different from the other. Large peaks on one watershed should also be evaluated in combination with lesser events on the other stream, because although headwaters may not be as high as with large runoff events on both, velocities could be higher when only one stream is experiencing a flood due to increased energy gradients caused by a low tailwater. Such locations require an analysis involving the hydraulics of confluences. This includes an analysis of the various combinations of flood events and how they may change flow distributions, hydraulic gradients, headwaters, and velocities. Stream stability can also be more critical at confluences due to middle and point bar formation, which can cause abrupt changes in flow directions. Pier location and alignment and culvert alignment near confluences will have to be carefully analyzed for these effects. While these complexities do not have to be studied in detail during the early planning and location stages, their effects on the location should be recognized and documented. The future potential problems with such sites must be emphasized as well as the positive factors of avoiding these locations. Minor alignment changes may eliminate the problems of a crossing near a confluence.

2.5 Tidal Areas Crossings of tidal waters present the hydraulic engineer with special considerations such as regular changes in water level from astronomically induced tides, storm surges from wind and high waves, or even seismic waves or tsunamis. Tidal inlets and their related marshes may also be highly sensitive environmental areas because of the different and often rare wildlife and biological systems they support. Crossings should be planned which do not significantly alter or restrict the flow, either into or out of these marshes. The altering of flows can affect the ecological nature of the area, as well as the areawide hydraulics. A possible reduction in interior tide heights because of the isolation of an inlet may cause increased velocities, scour, or increased wave heights somewhere else, often along the highway itself. Salinity may be changed, with stratified freshwaters and saltwaters flowing in different directions. This could change the type and extent of vegetation, which in turn could affect the wildlife of the marsh. Again, although these problems might not be solved during the planning and location phase, they will have been recognized and the need for special studies, if necessary, realized. In special cases, extensive studies and specialists in tidal hydraulics might be required to insure that an acceptable design is provided.

2.6 Land Use Considerations The use of land adjacent to the stream must be considered. In rural areas, the most significant consideration is how the crossing may affect property, both upstream and downstream. Upstream, the concern is usually with increased flood stages. The degree and duration of an increased flood stage could affect the present and future land use. In Kenya agricultural land has to be evaluated for increased risks due to flooding. As an example, crops may be impacted by inundation. The Republic of Kenya – Ministry of Roads

12

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Downstream, the hydraulic effects, which are of usual concern are related to increased velocity through the structure. This higher velocity may increase scour immediately below the crossing or increase aggradation downstream. Potential downstream effects are usually more difficult to quantify than upstream effects. In urban areas, the effects of increased flood stages or increased velocities become important considerations. In addition to the impact on future land use, the existing property may suffer extensive physical damage from an increased flood stage. The impact on traffic safety and operation may extend well beyond the stream crossing, as increased flooding may occur on the adjacent street network, inhibiting or obstructing vehicular movement. This may result in extensive delays, more frequent accidents. Many urban areas will have stream or watershed management regulations. These may dictate the limits on the changes, which can be made to the flow characteristics of a watershed.

2.7 Location of Utilities During the location phase, it is important for the hydraulic engineer to be aware of utility locations and types as well as their relationship to the proposed highway project. Locations of overhead power lines, and underwater water and sewer lines and utility facilities such as pumping stations will be found by others. The hydraulic engineer must then evaluate if and how these features may affect the various hydraulic structures or, conversely, be affected by them. If power lines have to be relocated on or buried within an encroachment, their relationship to the projected flood levels must be considered. The reconstruction of a pumping station that could either be flooded or an obstacle to flood flows if not placed at a proper level is another example of what may need to be considered. Even the maintenance of utility facilities may entail hydraulic considerations. Excavating a utility for repairs buried within an encroachment could affect the stability of the embankment or stream and thus expose, even temporarily, the highway to increased erosion potential. The construction of a storm drainage system or the improvement to an existing one can interfere with utilities. Often, in older urban areas, types of utilities and their locations are not accurately documented, if at all. In these cases the hydraulic engineer should coordinate early with all appropriate utility personnel in order to locate as many of the lines as possible to facilitate the later design process as well as provide input to the location process.

2.8 Location of Storm Drainage Facilities The location of storm drainage facilities is another item, which should be considered during the early phases of a project. Collection systems, the main pipes, pumping stations, and particularly the outfall alternatives should be tentatively located. Collection points should be located early in the project development, especially for large systems, chiefly for right-of-way considerations. Another reason, however, is the possibility of combining the collection of storm water from several watersheds or for connecting to an existing system. The capacity of existing systems to accept the flows from these collection points as well as water quality considerations would be the main concerns at this point in the project. If a project is an improvement to an existing highway, collection points will have been in existence for several years. The possibility of altering, adding, or deleting points should not be overlooked however, as a more cost-effective and hydraulically efficient system may be possible. Storm drain collection pipes are commonly located The Republic of Kenya – Ministry of Roads

13

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

parallel to the highway. However, consideration should be given to the terrain, and the possibility of construction problems with this generally accepted solution. Sometimes, a route with less excavation or other advantages may be available. The location of outfall alternatives is the most important consideration for storm drainage systems made during the planning and location phases. Drainage must be discharged into natural or constructed drainage features capable of conveying this flow in a safe and efficient manner. Sinkholes or other low-lying areas without a natural outlet must be avoided. With constructed facilities, such as irrigation canals, it is advisable to obtain written agreements for the discharge and assurance the facility will remain in perpetuity. Existing outfalls must be checked for present as well as future adequacy and whether or not downstream problems such as erosion or flooding could occur. Proposed outlet locations should be checked for the same considerations, as well as ensuring the legality of creating a flow where none, or very little, has previously existed. Coordination with the local community will often be necessary when tying into existing outfalls. New outfalls may also need to be coordinated as the community may have plans in progress utilizing the outfall area for other purposes. Highways on new locations in urban areas may significantly affect existing surface runoff patterns and storm drainage systems. Depressed highways will most likely cut through existing storm drains while highways on fills will isolate drainage areas. Early and careful attention to these types of projects is needed or alternates suggested to ensure a feasible system for accommodating disrupted drainage patterns can be designed.

2.9 Type of Structure The location of a stream crossing may influence and limit the type of structure that can be used. Decisions made during the preliminary phases of project development should not constrain the final recommendations of the hydraulic engineer. Detailed surveys and comprehensive hydrologic and hydraulic studies are needed to make conclusive recommendations. Even then, the hydraulic engineer may recommend alternate types and shapes, depending on the site. Sometimes there will be critical crossing sites, such as those within a designated flood insurance area that may require detailed studies early in the project development. This may be because requirements for acquiring permits in these areas are such that plans must be more specific than usual at earlier stages of the project. When this is the case, a final structure type can be provided. There are many considerations to be made before selecting a final design alternative. These include hydrologic, hydraulic, environmental, economic, construction, and maintenance factors.

2.10 Construction-Related Considerations Problems during construction will be minimized when important drainage or other waterrelated factors are considered during the location and planning phases of the project. The occurrence of erosion and sediment, and how to control it, must be considered, at least in broad terms, during the early phases of location. The hydraulic engineer, along with other specialists, may be involved in the identification of groundwater flows and potential unstable slopes because of underground water so that proper measures can be taken to prevent problems before they occur. The time of the year and the total construction time should be taken into consideration in considering impacts. Certain elements, such as embankments along a stream, should be completed before the anticipated flood season. In some sections of the country, work cannot be performed as the stream may serve as an irrigation supply requiring that flows The Republic of Kenya – Ministry of Roads

14

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

not be interrupted and that pumping and distribution systems not be contaminated with sediment. The use of temporary structures must also be planned. Often a temporary crossing can be smaller than normal if it is only going to be utilized during the months. If it will be used for more than one year, perhaps it needs to be sized for a flood of greater magnitude. This consideration may change the concept of the project or at least the type of structure designed. Many construction-related hydraulic problems are ones of scheduling. Although they will be studied in more detail during the design phase, they should be initially considered, at least in a preliminary manner, as early as possible.

References 1) AASHTO Drainage Guideline, Volume I, Guidelines for Hydraulic Considerations in Highway Planning and Location, 1999

The Republic of Kenya – Ministry of Roads

15

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

3

Design Standards and Design Flow Return Periods

3.1 The Concept of Return Period and Design Frequency A design frequency shall be selected to match the facility’s cost, amount of traffic, potential flood hazard to property, expected level of service, political considerations, and budgetary constraints, considering the magnitude and risk associated with damages from larger flood events. With long highway routes having no practical detour, where many sites are subject to independent flood events, it may be necessary to increase the design frequency at each site to avoid frequent route interruptions from floods. In selecting a design frequency, potential upstream land use that could reasonably occur over the anticipated life of the drainage facility shall be considered. Hydrologic analysis should include the determination of several design flood frequencies for use in the hydraulic design. These frequencies are used to size different drainage structures to allow for an optimum design, that considers both risk of damage and construction cost. Consideration shall be given to what frequency flood was used to design other structures along a highway corridor. Since it is not economically feasible to design a structure for the maximum runoff a catchment area is capable of producing, a design frequency must be established. The frequency with which a given flood can be expected to occur is the reciprocal of the probability or chance that the flood will be equalled or exceeded in a given year. If a flood has a 20 percent chance of being equalled or exceeded each year, over a long period of time, the flood will be equalled or exceeded on an average of once every five years. This is called the return period or recurrence interval (RI). The designer should note that the 5-year flood is not one that will necessarily be equaled or exceeded every five years. There is a 20 percent chance that the flood will be equaled or exceeded in any year; therefore, the 5-year flood could conceivably occur in several consecutive years. The same reasoning applies to floods with other return periods.

3.2 Applicable Design Flow Return Periods Currently the following design Periods are used in Kenya: Table 3.1 Applicable Design Flow Return Periods Return Period years Box Culverts and Bridges 5 Pipe culverts for small roads 10 Pipe culverts for large roads 50 Box culverts 100 Bridges 1 year return period, Drifts and low level crossings overtopping not more than 10 cm supercritical flow and 15 cm for subcritical flow.

The Republic of Kenya – Ministry of Roads

16

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

4

Flood Estimation of Gauged Rivers

4.1 Introduction The use of measures river flow data is the first choice for hydraulic design of drainage structures, especially large bridges. However, the availability of measured water levels and river flow in Kenya varies over space and time. Generally there are more hydrometric stations in the western part of the country than towards the coast. In areas where irrigations schemes are in operation, highly exact data of river flow and, possibly, information on peak discharges are available. For the design of large structures the optimum use of measured river flow data is strongly recommended. Flood water runoff estimation methods solely based upon empirical rainfall – runoff models (as described in Chapter 5 of this Manual) do not provide sufficient secure information for safe design.

4.2 Sources of River flow Data in Kenya Due to the recent restructuring of Kenya’s water sector in information on river flow can be found at two agencies: ·

The River Basin Management Agencies e.g. TARDA

·

Ministry of Water and Irrigation, Nairobi

Recently measured stream data can best be obtained from the regional basin authorities. However, detailed extended water levels or discharge data has to be obtained from the Ministry of Water and Irrigation, located in Nairobi, where the historic data sets are recorded in data base format. Dept. of Meteorology, Nairobi, is a further source of measured river flow information.

The Republic of Kenya – Ministry of Roads

17

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

4.3 Procedure 4.3.1 Data Preparation The analysis of gauged data is done by statistical methods provided sufficient data are available at the site to permit a meaningful statistical analysis to be made. It is suggested that at least 10 years of record are necessary to warrant a statistical analysis by method presented therein. Before analyzing data, it is necessary to arrange it in a systematic manner. Data can be arranged in a number of ways depending on the specific characteristics that are to be examined. An arrangement of data by a specific characteristic is called a distribution or a series. The most common arrangement of hydrologic data is by magnitude of the annual peak discharge. This arrangement is called an annual series. Another method used in flood data arrangement is the partial-duration series. This procedure uses all peak flows (for instance all flows above the discharge of approximately bank-full stage) above some base value. Partial-duration series are used primarily in defining annual flood damages when more than one event that causes flood damages can occur in any year. The partial-duration series avoids a problem with the annual-maximum series. Annual maximum series analyses ignore floods that are not the highest flood of that year even though they are larger than the highest floods of other years. While partial-duration series produce larger sample sizes than annual maximum series, they require a criterion that defines independence of the discharges to be considered for the frequency analysis. The difference between the results of the two methods is large at the lower flows and becomes very small at the higher peak discharges. If the recurrence interval of these peak flows is computed as the order divided by the number of events (not years), the recurrence interval of the partial-duration series can be computed in terms of the annual series by the equation:

TB =

1 ln T A - ln(TA - 1)

(Eqn. 4.1)

where:

TB and T A are the recurrence intervals of the partial-duration series and annual series, respectively. Comparison between analyses results of the two methods shows that the maximum deviation between the two series occurs for flows with recurrence intervals less than 10 years. At this interval the deviation is about 5 percent and for the 5-year discharge, the deviation is about 10 percent. For the less frequent floods, the two series approach one another. When using the partial-duration series, one must be especially careful that the selected flood peaks are independent events. This is a tough practical problem since secondary flood peaks may occur during the same flood as a result of high antecedent moisture conditions. In this case, the secondary flood is not an independent event. One should also be cautious with the choice of the lower limit or base flood since it directly affects the computation of the properties of the distribution (i.e., the mean, the variance and standard deviation, and the coefficient of skew) all of which may change the peak flow determinations. The Republic of Kenya – Ministry of Roads

18

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

For this reason, it is probably best to utilize the annual series and convert the results to a partial-duration series through use of Equation 4.1. For the less frequent events (greater than 5 to 10 years), the annual series is entirely appropriate and no other analysis is required. 4.3.2 Frequency Analysis Concepts Future floods cannot be predicted with certainty. Therefore, their magnitude and frequency are treated using probability concepts. To do this, a sample of flood magnitudes are obtained and analyzed for the purpose of estimating a population that can be used to represent flooding at that location. The assumed population is then used in making projections of the magnitude and frequency of floods. It is important to recognize that the population is estimated from sample information and that the assumed population, not the sample, is then used for making statements about the likelihood of future flooding. The purpose of this section is to introduce concepts that are important in analyzing sample flood data in order to identify a probability distribution that can represent the occurrence of flooding.

4.3.3 Plotting Formulas When making a flood frequency analysis, it is common to plot both the assumed population and the peak discharges of the sample. To plot the sample values on frequency paper or as computer chart in a logarithmic form, it is necessary to assign an exceedence probability to each magnitude. A plotting position formula is used for this purpose. A number of different formulas have been proposed for computing plotting position probabilities, with no unanimity on the preferred method. A general formula for computing plotting positions is:

P=

i-a n - a - b +1

(Eqn. 4.2)

where:

i = the rank of the ordered flood magnitudes, with the largest flood having a rank of 1 n = the record length a and b = constants for a particular plotting position formula The Weibull, Pw ( a = b =0), Hazen, Ph ( a = b =0.5), and Cunnane, Pc ( a = b =0.4) are three possible plotting position formulas:

i n +1 i - 0 .5 Ph = n PW =

Pc =

(Eqn. 4.3 (a)) (Eqn. 4.3 (b))

i - 0.4 n + 0.2

(Eqn 4.3 (c))

The data are plotted by placing a point for each value of the flood series at the intersection of the flood magnitude and the exceedance probability computed with the plotting position formula. The Republic of Kenya – Ministry of Roads

19

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

4.3.4 Distribution Function Flood frequency analysis uses sample information to fit a population, which is a probability distribution. Several cumulative frequency distributions are commonly used in the analysis of hydrologic data, and as a result they have been studied extensively. The frequency distributions that have been found most useful in hydrologic data analysis are the Normal Distribution, the Log-Normal Distribution, the Gumbel Extreme Value Distribution, and the log-Pearson Type III distribution. A very good approximation for most common distribution function is the Simplified Frequency Formula as introduced by Chow (Ref.1) YT = X+ s * k

(Eqn. 4.4)

Where: YT = expected maximum event at given return period X = mean value of values in sample s = Standard deviation of values in sample k = frequency factor, depending on return period and sample size as show in Table 4.1 Table 4.1: Gumbel k values for different Sample Size and Return Periods, after Chow (1) Return Periods Sample size n 2 5 10 25 50 10 -0.136 1.058 1.848 2.846 3.587 15 -0.144 0.967 1.702 2.631 3.320 20 -0.148 0.918 1.624 2.516 3.178 25 -0.151 0.887 1.575 2.444 3.088 30 -0.153 0.866 1.540 2.393 3.025 35 -0.154 0.850 1.515 2.355 2.978 40 -0.156 0.837 1.495 2.326 2.942 45 -0.157 0.827 1.479 2.302 2.913 50 -0.157 0.819 1.466 2.283 2.889

The Republic of Kenya – Ministry of Roads

20

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

4.3.5 Application Example Table 4.2: Maximum Discharge Calculation for Gumbel Equation after Chow (1) Length of record 15 years Mean measured maximal instantaneous discharge 48.74 m3/s 3 Standard Deviation 22.56 m /s

Rank I i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Treturn

Year 1987 1988 1981 1986 1984 1980 1983 1977 1989 1990 1979 1978 1985 1976 1982 1975 k for N = 15

2 5 10 25 50

Max. measured maximal instantaneous discharge in any year 3 m /s 94 83.7 68.9 68.5 64.9 55.5 48.9 47.9 44.6 43.7 38.9 28.9 27.4 23.9 22.6 17.6

Probability P = i/(15+1) 0.0625 0.125 0.1875 0.25 0.3125 0.375 0.4375 0.5 0.5625 0.625 0.6875 0.75 0.8125 0.875 0.9375 1

Treturn 1/P years 16.0 8.0 5.3 4.0 3.2 2.7 2.3 2.0 1.8 1.6 1.5 1.3 1.2 1.1 1.1 1.0

Q est.= 48.47 + k*22.56

-0.144 0.967 1.702 2.631 3.32

The Republic of Kenya – Ministry of Roads

45.5 70.6 87.1 108.1 123.6

21

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Figure 4.1 : Measured and calculated Flood flow for different Return Periods Measured and Calculated Flood Flow for Different Return Periods 140

Discharge in m3/s

120 100 80

Measured

60

Calculated

40 20 0 1

10

100

Return Period in log y

References 1) Chow, V.T. ; ‘Handbook of Applied Hydrology’, McGraw Hill. 1964 2) Fiddes, D.; ‘The Prediction of Storm Rainfall in East Africa’ TRRL Report 623, Crowthorne, 1974 3) Fiddes, D. and Watkins,L.H.; ’Highway and Urban Hydrology in the Tropics’, Pentech, 1984 4) Fiddes, D. ‘The East African Flood Model’, TRRL Report 706, Crowththorne 1976 5) Federal Highway Administration: Hydrology, , HEC No. 19, 1984 6) Rainfall Frequency Atlas of Kenya, Ministry of Water Development, 1978

The Republic of Kenya – Ministry of Roads

22

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

5

Flood Estimation of Non – Gauged Basins

5.1 Introduction The estimation of storm water runoff from un-gauged catchments on the basis of rainfall – runoff models is the most common exercise carried out by hydrologists as far as road drainage issues are concerned. This due to the fact, that only very few catchments in Kenya are gauged on a regular basis. The small and medium sized catchments often crossed or even created by road embankments are usually not measured and estimation techniques have to be applied. The basis of all flood flow estimations should be the site visit, which represents an essential step in the design procedure of culverts (see Chapter 6), drifts (see Chapter 7) and bridges (see Chapter 8). High water marks should be identified and surveyed as part of the field inspection. Interviews with local inhabitants usually provide information on historic flood events. It has to be mentioned however, that only people who live nearby the crossing can provide good quality information on the flooding behaviour of specific rivers. Many flood events in Africa happen at night after heavy late-afternoon rainfall and most people will try not to leave their home during such conditions. The observed high water marks should be used as a calibration tool for all storm water run off estimation results achieved on the basis of basic (Rational Method) or more complex rainfall runoff models. Often existing structures upstream or downstream of the planned crossing point can provide further information on flood flow. If no measured flow at the crossing point is available the following methods can be used to estimate the design rainfall: · · ·

Specific Discharge Method Rational Method TRRL Method

These three methods, which are frequently used in Kenya are described in more detail below.

The Republic of Kenya – Ministry of Roads

23

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

5.2 Specific Discharge Method The specific Discharge Method is based upon transferring the specific storm water discharge calculated as l/s/ha or m3/s/km2 from similar, gauged, catchments in the project region to the actual project site. Catchment size, form, exposure and slope should be of comparable nature for both catchments, as well as the overall climatic and topographic conditions. The un - gauged catchments is in some cases an upstream sub - catchment of a larger measured river basin. In this case the probable contribution of the sub - catchment to the total measured riverflow can be estimated on the basis of the respective surface areas of the catchments. However, specific basin characteristics have to be considered in order to avoid over - or under design.

5.3 Rational Method 5.3.1 Introduction The Rational Method is most accurate for estimating the design storm peak runoff for small catchments. This method, while first introduced in 1889, is still widely used. Even though it has come under frequent criticism for its simplistic approach, no other drainage design method has achieved such widespread use. Carefully applied, it can be used for large catchments up to 200km2, provided an area reduction factor is applied. Confirmation of the estimated storm water runoff with the TRRL method described below is strongly recommended. 5.3.2 Application Some precautions shall be considered when applying the Rational Method: ·

The first step in applying the Rational Method is to obtain a good topographic map and define the boundaries of the catchment area in question. A field inspection of the area should also be made to determine if the natural drainage divides have been altered.

·

In determining the runoff coefficient C value for the catchment area, thought shall be given to future changes in land use (deforestation, bush fires) that might occur during the service life of the proposed facility that could result in an inadequate drainage system. Also, the effects and the life span of upstream detention structures must be taken into account. Restrictions to the natural flow such as highway crossings and dams that exist in the catchment area shall be investigated to see how they affect the design flows.

The Republic of Kenya – Ministry of Roads

24

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

5.3.3 Characteristics Characteristics of the Rational Method that generally limit its use include: ·

The rate of runoff resulting from any rainfall intensity is a maximum when the rainfall intensity lasts as long or longer than the time of concentration. That is, the entire catchment area does not contribute to the peak discharge until the time of concentration has elapsed.

This assumption limits the size of the drainage basin that can be evaluated by the Rational Method. For large catchment areas, the time of concentration can be so large that constant rainfall intensities for such long periods do not occur and shorter more intense rainfalls can produce larger peak flows. ·

The fraction of rainfall that becomes runoff (C) is independent of rainfall intensity or volume.

This assumption is only reasonable for impervious areas, such as streets, rooftops, and parking lots. For pervious areas, the fraction of runoff does vary with rainfall intensity and the accumulated volume of rainfall. Thus, the application of the Rational Method requires the selection of a coefficient that is appropriate for the storm, soil, and land use conditions. Many guidelines and tables have been established, but seldom, if ever, have they been supported with empirical evidence. 5.3.4 Equation The rational formula estimates the peak rate of runoff at any location in a catchment area as a function of the catchment area, runoff coefficient, and the mean rainfall intensity for a duration equal to the time of concentration. The rational formula is expressed as: Q = 0.0278 CIA

(Eqn.5.1)

where: Q C I A

= maximum rate of runoff, m3/s = runoff coefficient, representing a ratio of runoff to rainfall = average rainfall intensity for a duration equal to the time of concentration TC, for a selected return period, mm/hr = catchment area tributary to the design location, km2

5.3.5 Time of Concentration, Tc The time of concentration is the time required for water to flow from the hydraulically most remote point of the catchment area to the point under investigation. Use of the Rational Method requires the time of concentration tc for each design point within the catchment area. The duration of rainfall is then set equal to the time of concentration and is used to estimate the design average rainfall intensity (I). Pipe or open channel flow time can be estimated from the hydraulic properties of the conduit or channel. An alternative way to estimate the overland flow time is to estimate overland flow velocity and divide the velocity into the overland travel distance.

The Republic of Kenya – Ministry of Roads

25

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

For design conditions in rural and agricultural areas which do not involve complex drainage conditions, like steep slopes and mixed landuse, the following two equations are recommended for use in Kenya. 5.3.5.1

Kirpich Formula

tC = 0.0663 * L0.77* S

– 0.385

(Eqn. 5.2)

where: tC = time of concentration (hr) L = main stream length (km), and S = overall catchment slope in m/m 5.3.5.2

Hathaway Formula

tC = 1.44

(

L. N S

) 0.47, (Eqn.5.3)

where: tC = L = S= N=

time of concentration (min.) catchment length (m) catchment slope (m/m) catchment roughness factor, see table below

Table 5.1: Catchment Roughness Factor in Hathaway’s Formula (5)

Soil types

N

Smooth and impermeable Bare and compacted Plantations and agricultural areas Bush and shrubs, low vegetation Forest

0.02 0.10 0.20 0.40 0.60

Usually the Kirpich Formula provides shorter results for tc, and thus results in more conservative and more costly design parameters. For catchment areas with considerable vegetated areas (Hathaway N: 0.2 – 0.6) the Hathaway Formula is recommended.

For urban areas the following formula, based upon the American SCS method, is recommended.

tC =

((8.7*L3)/(H*1010))0.385 * 60 +te

(Eqn: 5.4)

where L= H= tC = te =

length of the critical path of the catchment (m) difference in elevation between the watershed and the design point (m) time of concentration (min.) time of entry, usually taken as 2 to 5 minutes. The greater value of 5 minutes is used where the ground is rather flat and the figure of 2 minutes where the grades are steep.

The Republic of Kenya – Ministry of Roads

26

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Three common errors should be avoided when calculating tc : ·

First, application of simplified general equations such as Kirpich for determining tc can result in too short of a time of concentration particularly when the average basin slope varies significantly from the mean channel slope as in steep mountainous areas. Neglecting the overland flow time can also dramatically shorten the time of concentration thus increasing the design peak runoff. Computing tc for two reaches of main channel, from the low point to the 0.7 point, then from there to the end of the channel, has been found to give better results.

·

Second, in some cases runoff from a portion of the catchment area that is highly impervious may result in a greater peak discharge than would occur if the entire area were considered. In these cases, adjustments can be made to the catchment area by disregarding those areas where flow time is too slow to add to the peak discharge. Sometimes it is necessary to estimate several different times of concentration to determine the design flow that is critical for a particular application.

·

Third, when designing a drainage system, the overland flow path is not necessarily perpendicular to the contours shown on available mapping. Especially in urban areas, the land will be graded and swales will intercept the natural contour and conduct the water to the streets, which reduces the time of concentration. Care shall be exercised in selecting overland flow paths in excess of 100 meters in urban areas and 200 meters in rural areas.

5.3.6 Rainfall Intensity, I The rainfall intensity (I) is the average rainfall rate in mm/hr for a duration equal to the time of concentration for a selected return period. Once a particular return period has been selected for design and a time of concentration calculated for the catchment area, the rainfall intensity can be determined from Rainfall-Intensity-Duration curves. RainfallIntensity-Duration curves for use in Kenya can found in the ‘Rainfall Frequency Atlas of Kenya’, which is currently in the process of being updated. 5.3.7 Runoff Coefficient, C The runoff coefficient (C) is the variable of the Rational Method least susceptible to precise determination and requires judgment and understanding on the part of the designer. In determining the run-off coefficient, the designer should use his knowledge of local conditions to take account of the following parameters: · Catchment area · Slope · Soil type · Vegetation · Land use and probable changes during the design life of the road.

It is stressed that future changes in land use can have a dramatic effect on the runoff from a catchment and careful consideration should be given to possible changes in vegetation cover or future developments within the catchment.

The Republic of Kenya – Ministry of Roads

27

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

5.3.7.1 Undeveloped Basins and Natural Catchments In the 1970s considerable research concerning the definition of runoff coefficient from natural catchments in Kenya has been carried out by TTRL (see Section 5.4). It is recommended to use the Contributing Area Coefficient (CA) as described in 5.4.2, Eqn. 5.8, below. 5.3.7.2 Urban Land Use For urban Land use the following coefficients are recommended. Table 5.2 Recommended Runoff Coefficient C for Various Urban Land Uses, after (5) Business: Downtown areas 0.70-0.95 Neighborhood areas 0.50-0.70 Residential: Single-family areas 0.30-0.50 Multi units, detached 0.40-0.60 Multi units, attached 0.60-0.75 Suburban 0.25-0.40 Residential (0.5 hectare lots or more) 0.30-0.45 Apartment dwelling areas 0.50-0.70 Industrial: Light areas 0.50-0.80 Heavy areas 0.60-0.90 Parks, cemeteries 0.10-0.25 Playgrounds 0.20-0.40 Railroad yard areas 0.20-0.40 Unimproved areas 0.10-0.30

The Republic of Kenya – Ministry of Roads

28

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

5.4 TRRL Method 5.4.1 Introduction While catchments up to 200km2 can be calculated with the Rational Method (it is recommended to check the result with the TRRL method) runoff from catchments having a larger area should be calculated with the TRRL Method, which has for a long time been the most widely used flood estimation method for ungauged catchment in the East African Region.The TRRL method is based upon the Hydrograph Method, which attempts to relate the form of a typical hydrograph to the estimated peak discharge. Additional information on hydrographs, unit hydrographs and the attached flood estimation methods can be found in (Ref.1,2,3,4,5). Adapted to African conditions, it has proofed applicable to use the relatively stable ratio of the peak flow (Q) divided by the average flow (Q) measured over the base time as means for calculating peak discharge.

F=

Q Q

(Eqn. 5.5)

The peak flow can therefore be simply estimated if the average flow during the base time of the hydrograph can be calculated. The total volume of runoff is given by:

RO = ( P - Y )C A * A * 10 3 ( m 3 )

(Eqn. 5.6)

Where: P = rainfall (mm) during time period equal to the base time Y = initial retention CA = contributing are coefficient A = catchment area (km2) If the hydrograph base time is measured to a point on the recession curve at which the flow is one tenth of the peak flow, then the volume under the hydrograph is approximately 7 per cent less than the total run off given by Eqn. 5.6 The average flow (Q ) is therefore given by:

Q=

0.93 * RO 3600 * TB

(Eqn. 5.7)

Where: TB = hydrograph base time (hrs.) Estimates of Y and CA are required to calculate RO and lag time K to calculate TB.

The Republic of Kenya – Ministry of Roads

29

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

5.4.1 Initial Retention (Y) In arid and semi arid zones an initial retention of 5 mm could be considered. Elsewhere zero initial retention could be assumed. 5.4.2 Contributing Area Coefficient (CA) Contributing area coefficient is a coefficient that reflects the effects of the catchment wetness and the land use. A grassed catchment at field capacity is taken as a standard value of contributing area coefficient. The design value of the contributing area coefficient could be estimated from the following equation.

C A = C S * CW * C L

(Eqn. 5.8)

Where: CS = the standard value of contributing area coefficient for a grassed catchment at field capacity CW = the catchment wetness factor CL = the land use factor The three factors are given in Tables 5.3, 5.4, and 5.5 Table 5.3: Standard Contributing Area Coefficient (wet zone catchment, short grass cover) after (4)

Soil Type Catchment Slope Very Flat Moderate Rolling

Slightly Impeded

Well Drained

Drainage

< 1.0 % 1-4 % 4-10 %

0.09 0.10

0.15 0.38 0.45

10-20 %

0.11

0.50

Mountainous >20 %

0.12

Hilly

Impeded Drainage 0.30 0.40 0.50

Note: The soil types are based on the soil map contained in the Hand Book of Natural Resources of East Africa

Table 5.4: Catchment Wetness Factor, after (4)

Rainfall Zone

Catchment Wetness Factor Perennial Streams

Ephemeral Streams

Wet Zone

1.0

1.0

Semi Arid Zone Dry Zones (except West. Uganda)

1.0 0.75

1.0 0.50

West Uganda

0.60

0.30

The Republic of Kenya – Ministry of Roads

30

Draft Document – December 2009

DESIGN MANUAL for ROADS and BRIDGES PART 2 – Drainage Design 2009 Table 5.5: Land Use Factor (base assumes short grass cover), after (4)

Land Use

Land Use Factor

Largely bare soil

1.50

Intense cultivation (particularly in valleys) Grass cover

1.50 1.00

Dense vegetation (particularly in valleys) Ephemeral steam, sand filled valley

0.50 0.50

Swamp filled valley Forest

0.33 0.33

5.4.3 Catchment lag Time (K) The appropriate value of lag time can be estimated from Table 5.6. In assessing which category to place a given catchment, it should be remembered that generally only small areas either side of the stream are contributing to the flood hydrograph. It is these areas, therefore, which must be assessed. Table 5.6: Catchment Lag Time, after (4)

Catchment Type

Lag Time (K) in hrs

Arid Very steep small catchments (slope > 20 %)

0.1 0.1

Semi arid scrub (large bare soil patches) Poor pasture

0.3 0.5

Good pasture Cultivated land (down to river bank)

1.5 3.0

Forest, overgrown valley bottom Papyrus swamp in valley bottom

8.0 20.0

5.4.4 Base Time The rainfall time (TP) is the time during which the rainfall intensity remains at high level. This can be approximated by the time during which 60 per cent of the total rainfall occurs. Using the general intensity duration frequency equation as given in Ref.4:

i=

(Eqn.5.9)

a ( 0 .33 + t p ) c

the time to give 60 per cent of the total rainfall is given by solving the above equation.

t p æ 24.33 ö ç ÷ 0 .6 = 24 çè t p + 0.33 ÷ø

c

(Eqn. 5.10)

Values for the various rainfall zones of East Africa are given in Table 5.7

The Republic of Kenya – Ministry of Roads

31

Draft Document – December 2009

DESIGN MANUAL for ROADS and BRIDGES PART 2 – Drainage Design 2009 Table 5.7: Rainfall Time (TP) for East African 10 year Storm, after (4)

Index 'c'

Rainfall time (T P) (hr)

Inland zone Coastal zone

0.96 0.76

0.75 4.0

Kenya Aberdare Uluguru Zone

0.85

2.0

Zone

The flood wave attenuation (TA) can be estimated from equation 5.11

TA =

0.028L 1

Q 4S

1

(Eqn. 5.11)

2

Where: L = length of main stream (km)

Q = average flow during base time (m3/s) S = average slope along main stream The base time is, therefore, estimated from equation 5.12:

TB = TP + 2.3K + T A

(Eqn. 5.12)

It is noted that Q appears in eqn. 5.12. as part of TA . So an iterative or trial end error solution is required. If initially TA is assumed zero, two iterations could be adequate. Knowing Q and F, the peak flow is calculated using Eqn. 5.5 5.4.5 Area Reduction Factor The use of an area reduction factor Area Reduction Factor ARF is advised. The following formula is widely used:

ARF = 1 - 0.04T

1

3

A

1

2

with T = TB, base time (h),and A = catchment area in km2

The Republic of Kenya – Ministry of Roads

32

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

5.4.6 Example (Adopted from TRRL Laboratory Report 706 (4)) A 10 year average recurrence interval design flood is required for a catchment that has the following details. a) Area: 10 square kilometres b) Land slope: 6 % C) Channel slope: 3% d) Channel length: 4 km e) Grid reference: 5oS 35o E f) Catchment type: Poor pasture From Table 5.6, lag time (K) = 0.5 h From Table 5.3, standard contributing area coefficient CS = 0.45 From Table 5.4, catchment wetness factor CW = 0.5 From Table 5.5, land use factor CL = 1.0 Therefore, the design value for CA = 0.23 Initial retention Y = 0 From Table 5.7, TP = 0.75 hrs. Using Eqn. 5.12 with TA = 0 TB = 0.75 + 2.3 (0.5) = 1.9 hrs. Rainfall during base time is given by: c

RTB

10 T æ 24.33 ö ÷÷ * R 24 = B çç 24 è TB + 0.33 ø

Where R

10

24

= daily rainfall of 10 years average recurrence interval

and c = 0.96 (Table 5.7) Using rainfall maps: Map 5.1: Daily point rainfall of Average recurrence interval 2 year = 63 mm Map 5.2:10:2 yr ratio = 1.49 Remark: For rainfall base data of longer return period use of the ‘Rainfall Frequency Atlas of Kenya (ref.6) is recommended.

Daily rainfall of average recurrence interval 10 yr = (63*1.49) = 94 mm

R1.9 =

1.9 æ 24.33 ö ç ÷ 24 è 1.9 + 0.33 ø

0.96

* 94 = 73.79mm

The Republic of Kenya – Ministry of Roads

33

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Area Reduction Factor is given by

ARF = 1 - 0.04T

1

3

A

1

2

= 0.84

Average Rainfall P = 73.79 x 0.84 = 61.98

RO = C A ( P - Y ) A *103 (Q ) =

TA

0.93 * RO = 19.38 m3/s 3600 * TB

0.028L 1

(Q) 4 S

1

= 0.31 hrs 2

TB (2nd approximation) = 1.9 + 0.31 = 2.21 hrs. 0.96

* 94 = 75.75

m m

R2.2.1

2.21 æ 24.33 ö = ç ÷ 24 è 2.21 + 0.33 ø

ARF = 0.84 Therefore P = 63.63 mm

Q = 17.11 m3/sec TA = 0.32 hrs (no change) Therefore Q = F * Q For K less than 0.5 hour F = 2.8 For K more than 1 hour, F = 2.3 For the case at hand, therefore, F = 2.8 Therefore, Q = 2.8 * 17.11 = 47.91 m3/sec

The Republic of Kenya – Ministry of Roads

34

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

References 1) Chow, V.T. ; ‘Handbook of Applied Hydrology’, McGraw Hill. 1964 2) Fiddes, D.; ‘The Prediction of Storm Rainfall in East Africa’ TRRL Report 623, Crowthorne, 1974 3) Fiddes, D. and Watkins,L.H.; ’Highway and Urban Hydrology in the Tropics’, Pentech, 1984 4) Fiddes, D. ‘The East African Flood Model’, TRRL Report 706, Crowththorne 1976 5) Federal Highway Administration: Hydrology, , HEC No. 19, 1984 6) Rainfall Frequency Atlas of Kenya, Ministry of Water Development, 1978

The Republic of Kenya – Ministry of Roads

35

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Map 5.1: Daily point Rainfall of Average Recurrence Interval 2 years, after Ref. (4).

The Republic of Kenya – Ministry of Roads

36

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Map 5.2: 10:2 Ratio for Different Rainfall Zones in East Africa, after Ref. (4)

The Republic of Kenya – Ministry of Roads

37

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

6

Hydraulic Design of Culverts

6.1 Definitions and Symbols A culvert is a structure that is designed hydraulically to take advantage of submergence to increase hydraulic capacity. It is also a structure used to convey surface runoff through embankments. A culvert can be a structure, as distinguished from bridges, that is usually covered with an embankment and is composed of structural material around the entire perimeter. These include steel and concrete pipe culverts and concrete box culverts. However, a culvert can also be a structure supported on spread footings with the streambed serving as the bottom of the culvert. These include some multi-plate steel structures and concrete slab culverts. This chapter provides procedures for the hydraulic design of highway culverts that are based on FHWA and AASHTO practice. It also refers to the method of culvert analysis using HY8 culvert analysis software. This chapter only aims at covering the hydraulic design of culverts. For structural issues or aspects concerning the construction procedure of culvert the reader is referred to: · Design Manual for Roads and Bridges, Part 6a – Bridge and Culvert Design, 2009 · Standard Culvert and Drifts Manual, Part 6b, Construction Drawings · Standard Small Span Concrete Bridges, Section 1 A Construction The following are concepts that are important in culvert design: Critical depth The depth at which the specific energy of a given flow rate is at a minimum. For a given discharge and cross-section geometry, there is only one critical depth. Charts 6-3 and 6-7 at the end of this chapter contain critical depth charts for circular pipe and rectangular sections, respectively. Crown The crown of the culvert is the inside top of the culvert. Flow Type Seven culvert flow types are presented that assist in determining the flow conditions at a particular site. Diagrams of these flow types are provided in Figures 6-1 to 6-7 in this chapter. Free Outlet Free Outlet describes a tailwater equal to or lower than critical depth. For culverts with free outlets, a lowering of the tailwater has no effect on the discharge or the backwater profile upstream of the tailwater. Improved Inlet Has an entrance geometry that decreases the flow constriction at the inlet and thus increases the capacity of culverts. These inlets are referred to as either side- or slopetapered (walls or bottom tapered). Invert Is the flowline of the culvert (inside bottom).

The Republic of Kenya – Ministry of Roads

38

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Normal flow Normal flow occurs in a channel reach when the discharge, velocity, and depth of flow do not change throughout the reach. The water surface profile and channel bottom slope will be parallel. This type of flow will exist in a culvert operating on a steep slope if the culvert is sufficiently long enough. Submerged A submerged outlet occurs where the tailwater elevation is higher than the crown of the culvert. A submerged inlet occurs where the headwater is greater than 1.2D. To provide consistency within this chapter the following symbols are used. These symbols are selected for their wide use in culvert publications. Symbol Definition A AHW B D d dc g H Hb HE Hf HL Ho Hv ho HW KE L n P Q R S TW V Vd Vo Vu g t

Units

Area of cross section of flow Allowable HW m Barrel width m Culvert diameter or barrel height Depth of flow m Critical depth of flow Acceleration due to gravity Sum of HE + Hf + Ho Bend headloss Entrance headloss Friction headloss Total energy losses Outlet or exit headloss Velocity headloss Hydraulic grade line height above outlet invert Headwater depth (subscript indicates section) Entrance loss coefficient Length of culvert Manning’s roughness coefficient Wetted perimeter Rate of discharge Hydraulic radius (A/P) Slope of culvert Tailwater depth above invert of culvert Mean velocity of flow with barrel full Mean velocity in downstream channel Mean velocity of flow at culvert outlet Mean velocity in upstream channel Unit weight of water Tractive force Pa

The Republic of Kenya – Ministry of Roads

39

m² mm or m m m/s2 m m m m m m m m m m m m m m3/s m m/m m m/s m/s m/s m/s N/m

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

6.2 Principles of Design The following principles are specific to culverts: · All culverts shall be hydraulically designed. · Overtopping flood selected is generally consistent with the class of highway and the risk at the site. In our case, it shall conform to the requirements of Chapter 3: Design Standards and Design Flow Return Periods · Survey information shall include topographic features, channel characteristics, highwater information, existing structures, and other related site-specific information. · Culvert location in both plan and profile shall be investigated to avoid sediment buildup in culvert barrels. · The cost savings of multiple use (e.g.- utilities, stock and wildlife passage, and land access) shall be weighed against the advantages of separate facilities. · Culverts shall be designed to accommodate debris or proper provisions shall be made for debris maintenance. · Material selection shall include consideration of materials availability, and the service life including abrasion and corrosion potentials. · Culverts shall be located and designed to present a minimum hazard to traffic and people. · The detail of documentation for each culvert site shall be commensurate with the risk and importance of the structure. Design data and calculations shall be assembled and retained for future reference.

6.3

Design Criteria

6.3.1 Introduction Listed below by categories are the design criteria that should be considered for the hydraulic design of culverts. For culvert types, designs and construction drawings currently used in Kenya reference is made the following documents: · Standard Culvert and Drifts Manual, Part 1, Construction Drawings · Standard Small Span Concrete Bridges, Section 1 A Construction 6.3.2 Site Criteria 6.3.2.1 Structure Type Selection The type of drainage structure specified for a particular location is often determined based on economic considerations. The following can serve as a guide in the selection of the type of structure, proceeding from the most expensive to the least expensive. Note that bridges are included in the text of this section to allow for a more complete progression in the treatment of this topic. The Republic of Kenya – Ministry of Roads

40

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Bridges are used where they are more economical than a culvert, perhaps due to the need to bury a culvert under a high level of fill. They are also employed to satisfy land use requirements, to mitigate environmental harm possible with a culvert, to avoid floodway or irrigation canal encroachments, and to accommodate large debris. For more information the reader is referred to Design Manual for Roads and Bridges Part 6 A, Bridge and Culvert Design, 2009. Culverts are used where bridges are not hydraulically required, where debris is tolerable, and where they are more economical than a bridge. Culverts can be concrete box culverts, reinforced concrete pipe culverts, or corrugated metal culverts. Concrete box culverts are constructed with a square or rectangular opening, and with wingwalls at both ends. They are usually specified for larger flows, where the area of the opening is larger than that available for manufactured concrete or metal pipe culverts. They may also be used where the cost estimate indicates that concrete box culverts constructed on site are less expensive than manufactured and/or imported pipe culverts. An alternative sometimes employed is to use metal arch pipe, and for larger openings this can be more economic than concrete. Although metal pipe culverts are usually less expensive than concrete pipe culverts, a cost estimate may indicate that this is not the case. Certain corrosive soils can create problems with metal pipes, and this would have a tendency to create a shift in favour of concrete pipes. However, the corrosive effects are mitigated through the application of bitumen coating to the metal pipes. This adds slightly to the cost of the metal pipe. The use of headwalls and/or wingwalls with pipe culverts is generally dependent on factors such as the slope and stability of the channel. Pipe culverts can often be placed particularly on lower volume roads without headwalls or wingwalls. 6.3.2.2 Length and Slope · ·

The culvert invert shall be aligned with the channel bottom and the skew angle of the stream, and The culvert entrance shall match the geometry of the roadway.

6.3.2.3 Debris Control Where experience or physical evidence indicates the watercourse will transport a heavy volume of controllable debris, · · ·

for culverts located in mountainous or steep regions, for culverts that are under high fills, and where clean out access is limited;

access must be available to clean out the debris control device.

The Republic of Kenya – Ministry of Roads

41

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

6.3.3

Design Limitations

6.3.3.1 Allowable Headwater Allowable Headwater is the depth of water that can be ponded at the upstream end of the culvert that will be limited by one or more of the following: · will not damage up stream property, · not higher than 300 mm below the edge of the shoulder, · equal to an HW/D not greater than 1.5, · no higher than the low point in the road grade 6.3.3.2 Tailwater Relationship of Channel · The hydraulic conditions downstream of the channel determine the tailwater depth relationship for different discharges. · Backwater curves at sensitive locations or single cross sections should be used. For important structures several downstream cross sections are required. · Critical depth and equivalent hydraulic grade line can be used if the culvert outlet is operating with a free outfall. · The high water elevation that has the same frequency as the design flood if events are known to occur concurrently (statistically dependent) should be used to evaluate the influence of confluences. 6.3.3.3 Maximum Velocity and Minimum Velocity The maximum velocity at the culvert exit shall be consistent with the velocity in the natural channel or shall be mitigated with channel stabilization and energy dissipation. It is generally recommended to limit the exit velocity below 3m/s. The minimum velocity in the culvert barrel should result in a tractive force (t=gdS) greater than critical t of the transported streambed material at low flow rates. When streambed material size is not known 0.8 meters per second should be used as approximation. If clogging is probable, consider installation of a sediment trap or size culvert to facilitate cleaning.

The Republic of Kenya – Ministry of Roads

42

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Design Features 6.3.4.1 Culvert Sizes and Shape The culvert size and shape selected is to be based on engineering and economic criteria related to site conditions. The following absolute minimum sizes shall be used to avoid maintenance problems and clogging: Urban areas: Cross drainage min. 450 mm Rural areas: Cross drainage min. 900 mm, 600 mm for access culverts.

Land use requirements can dictate a larger or different barrel geometry than required for hydraulic considerations 6.3.4.2 Multiple Barrels Multiple barrel culverts should fit within the natural dominant channel with only minor widening of the channel to avoid conveyance loss through sediment deposition in some of the barrels. When the approach flow is supercritical, either a single barrel or special inlet treatment is required to avoid adverse hydraulic jump effects. It is good practice to install one barrel at the flow line of the stream while other barrels are set slightly higher to reduce sedimentation. Where ever possible double cell pipe culverts should be replaced with single cell box culverts in order to avoid the problem of piling up of debris against the ineffective middle section. 6.3.4.3 Material Selection Concrete is the preferred material for construction of culverts, however, other materials may be more suitable for a particular location, hydraulic roughness, bedding condition, or project. In evaluating the suitability of alternate materials, the selection process shall be based on a comparison of the total cost of alternate materials over the design life of the structure that is dependent upon the following: · · · · · · · ·

durability (service life) cost availability construction and maintenance ease structural strength traffic delays abrasion and corrosion resistance, and water tightness requirements

A pipe material other than concrete may be accepted as an alternate if the substitution is supported by evidence that the hydraulic capacity, strength, durability, abrasion, and corrosion resistance of the concrete pipe specified is equaled or exceeded. In addition, any substitution must be analyzed in terms of cost and availability. Corrugated metal pipe, if permitted, shall be protected at the ends by headwalls. Use of corrugated metal pipes with projecting ends is not recommended.

The Republic of Kenya – Ministry of Roads

43

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

6.3.4.4 Further Reference For further design features, reference is made the commonly used culvert and bridge design specification documents used in Kenya: · Standard Culvert and Drifts Manual, Part 1, Construction Drawings · Standard Small Span Concrete Bridges, Section 1 A Construction · Design Manual for Roads and Bridges Part 6 A, Bridge and Culvert Design, 2009.

6.4 Culvert Design Hydraulics 6.4.1 Introduction and Calculation Principles An exact theoretical analysis of culvert flow is extremely complex because the following is required: · analyzing non-uniform flow with regions of both gradually varying and rapidly varying flow, · determining how the flow type changes as the flow rate and tailwater elevations change, · applying backwater and drawdown calculations, energy, and momentum balance, · applying the results of hydraulic model studies, and · determining if hydraulic jumps occur and if they are inside or downstream of the culvert barrel The procedures in this chapter use the following principles: · Control Section The location where there is a unique relationship between the flow rate and the upstream water surface elevation. Inlet control is governed by the inlet geometry. Outlet control is governed by a combination of the culvert inlet geometry, the barrel characteristics, and the tailwater. · Minimum Performance Is assumed by analyzing both inlet and outlet control and using the highest headwater. The culvert may operate more efficiently at times (more flow for a given headwater level), but it will not operate at a lower level of performance than calculated. 6.4.2 Inlet and Outlet Control A culvert may flow with either inlet or outlet control over its full design discharge range. Alternatively flow through the culvert may vary with discharge from inlet to outlet control. The designer should check both inlet and outlet control to determine the governing headwater depth. The following sections are aimed to guide the designer on these issues. 6.4.2.1 Inlet Control Culverts flowing with inlet control usually lie on relatively steep gradients and flow only partly full. Guidance for the sizing of culverts for inlet control are adapted from publications by the U.S. Bureau of Public Roads, and from AASHTO model drainage manual. For inlet control, the control section is at the upstream end of the barrel (the inlet). The flow passes through critical depth near the inlet and becomes shallow, high velocity The Republic of Kenya – Ministry of Roads

44

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

(supercritical) flow in the culvert barrel. Depending on the tailwater, a hydraulic jump may occur downstream of the inlet. Headwater depth is measured from the inlet invert of the inlet control section to the surface of the upstream pool. The inlet area is the cross-sectional area of the face of the culvert. Generally, the inlet face area is the same as the barrel area. Inlet edge configuration describes the entrance type. Some typical inlet edge configurations include thin edge projecting, mitred edges, square edges in a headwall, and beveled edges. Inlet shape is usually the same as the shape of the culvert barrel. Typical shapes are rectangular, circular, elliptical, and arch. It is necessary to check for additional control section if the shape of inlet is different from that of the barrel. Flow with inlet control can be further subdivided into different flow regions depending on whether inlet is submerged or unsubmerged. Hydraulically, three regions of flow are known: unsubmerged, transition, and submerged types of flow regions. Unsubmerged Zone For headwater below the inlet crown, the entrance operates as a weir (see Figure 6.1). A weir is a flow control section where the upstream water surface elevation can be predicted for a given flow rate. The relationship between flow and water surface elevation can be determined by model tests of the weir geometry or by measuring prototype discharges.

Figure 6.1: Unsubmerged Flow Inlet Control

Submerged Zone For headwaters above the inlet, the culvert operates as an orifice (see Figure 6.2). An orifice is an opening, submerged on the upstream side and flowing freely on the downstream side, which functions as a control section.

The Republic of Kenya – Ministry of Roads

45

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Figure 6.2: Submerged Flow Inlet Control

Transition Zone The transition zone is located between the unsubmerged and the submerged flow conditions where the flow is poorly defined. This zone is approximated by plotting the unsubmerged and submerged flow equations and connecting them with a line tangential to both curves as shown in Figure 6.11 Nomographs applicable for Inlet Control The inlet control flow versus headwater curves, which are established using the above procedure, are the basis for constructing the inlet control design nomographs. Note that in the inlet control nomographs, Hw is measured to the total upstream energy grade line including the approach velocity head. Inlet control nomographs are given in Chart 6.1, 6.2 and 6.6.

The Republic of Kenya – Ministry of Roads

46

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

6.4.2.2 Outlet Control Outlet control has depths and velocity that are subcritical. The control of the flow is at the downstream end of the culvert (the outlet). The tailwater depth is assumed to be critical depth near the culvert outlet or in the downstream channel, whichever is higher. In a given culvert, the type of flow is dependent on all of the barrel factors such as barrel roughness, barrel area, barrel length, barrel slope and so on. Outlet control flow is illustrated in Figure 6.3.

Figure 6.3 Outlet Control

Figure 6.4 Submerged Pipe Flowing Full, Inlet Control

The Republic of Kenya – Ministry of Roads

47

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Outlet controlled culvert flows are calculated with an energy (total head) equation. Occasionally a backwater calculation through the culvert is required. The energy equations are expressed below based on schematic diagram of Figure 6.3. Ignoring the outlet velocity head, the energy equation between u/s and d/s ends of the culvert: (Eqn.6.1)

Hw + SoL = Tw + H where: Hw: depth from the inlet invert to the energy grade line, m So : slope of channel L : length of channel Tw: tailwater depth H : head losses Losses are composed of :

(Eqn.6.2)

HL = HE + Hf + Hv + Hb + Hj + Hg

where: HL = total energy loss, m HE = entrance loss, m HF = friction losses, m HV = exit loss (velocity head), m Hb = bend losses, m Hj = losses at junctions, m Hg = losses at grates, m Velocity

(Eqn.6.3)

V = Q/A

where: V = average barrel velocity, m/s Q = flow rate, m3/s A = cross sectional area of flow with the barrel full, m2 Velocity Head

Hv = V2/2g

(Eqn.6.4)

where: g = acceleration due to gravity, 9.8 m/s2 Entrance Loss (Eqn.6.5a)

HE = KE (V2/2g) where: KE = entrance loss coefficient, see Table 6.2

The Republic of Kenya – Ministry of Roads

48

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Friction Loss HF = [(19.63n2L)/R1.33] [V2/2g)

(Eqn.6.5b)

where: n = Manning’s roughness coefficient L = length of the culvert barrel, m R = hydraulic radius of the full culvert barrel = A/P, m P = wetted perimeter of the barrel, m exit Loss Ho = 1.0 [(V2/2g) - (Vd2/2g)]

(Eqn.6.5c)

where: Vd= channel velocity downstream of the culvert, m/s (usually neglected, resulting in equation (6.5d)). Ho = HV = V2/2g

(Eqn.6.5d)

Barrel Losses H = HE + Ho+HF

H = [1 + Ke + (19.63n2L/R1.33)] [V2/2g]

(Eqn.6.6)

The energy grade line represents the total energy at any point along the culvert barrel. Equating the total energy at sections 1 and 2, upstream and downstream of the culvert barrel in Figure 6.3, the following relationship results: (Eqn.6.7)

HW o + ( Vu2/2g) = TW + (Vd2/2g) + HL where:

HW o= headwater depth above the outlet invert, m Vu = approach velocity, m/s TW = tailwater depth above the outlet invert, m Vd = downstream velocity, m/s HL = sum of all losses (equation 6.2) The hydraulic grade line is the depth to which water would rise in vertical tubes connected to the sides of the culvert barrel. In full flow, the energy grade line and the hydraulic grade line are parallel lines separated by the velocity head except at the inlet and the outlet. Nomographs applicable to outlet control Nomographs (full flow) - The nomographs were developed assuming that the culvert barrel is flowing full and: · · · ·

·

TW > D, Outlet Control (see figure 6.3) or; dc > D, Inlet Control (see figure 6.4); Vu is small and its velocity head can be considered a part of the available headwater (HW) used to convey the flow through the culvert; Vd is small and its velocity head can be neglected; and, Equation 6.7 will appear in same form as equation 6.1. With rearrangement it becomes:

The Republic of Kenya – Ministry of Roads

49

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

(Eqn.6.8)

HW = TW + H - SoL where: HW H SoL

= depth from the inlet invert to the energy grade line, m = is the value read from the nomographs (or equation 9.6), m = drop from inlet to outlet invert, m

Nomographs (Partly full flow) Equations (6.1) through (6.8) were developed for full barrel flow. The equations also apply to the flow situations which are effectively full flow conditions, if TW < dc, Figure 6-5.

Figure 6.5: Partly full flow Backwater calculations may be required that begin at the downstream water surface and proceed upstream. If the depth intersects the top of the barrel, a full flow extends from that point upstream to the culvert entrance.

The Republic of Kenya – Ministry of Roads

50

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Nomographs: FHWA Approximation It has been found that the hydraulic grade line pierces the plane of the culvert outlet at a point one-half way between critical depth and the top of the barrel or (dc + D)/2 above the outlet invert. For such situation, TW should be used if higher than (dc + D)/2. Generally, the following equation should be used: (Eqn.6.9)

HW =ho+ H -SoL where: ho = the larger of TW or (dc + D)/2, m

Adequate results are obtained down to a HW = 0.75D. For lower headwaters, backwater calculations are required. (See Figure 6.6 if TW < dc and Figure 6.7 if TW > dc)

Figure 6.6 Flow Condition, TW < dc

Figure 6.7 Flow Condition, TW > dc

The Republic of Kenya – Ministry of Roads

51

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

6.5 Design Procedure The following design procedure provides a convenient and organized method for designing culverts for a constant discharge, considering inlet and outlet control. The computation form has been provided as Figure 6-10 to guide the user. It contains blocks for the project description, designer’s identification, hydrologic data, culvert dimensions and elevations, trial culvert description, inlet and outlet control HW, culvert barrel selected, and comments. The overall procedure is resumed in Flowchart 6-1 at the end of this section Step 1:

Assemble Site Data and Project File

A: Hydrographic Survey, Data include · topographic, site, and location maps · embankment cross section · roadway profile · photographs · field visit (sediment, debris) and · design data of nearby structures B: Studies by other agencies including Ministry of Water Resources C: Environmental constraints contained in environmental review documents D: Design criteria. Review Chapter 3: for applicable design criteria, and prepare risk assessment, if necessary. Step 2:

Determine Hydrology

Minimum data required—drainage area maps, rainfall intensities at design return period Step 3:

Design Downstream Channel

Minimum data are cross section of channel and the rating curve for channel Step 4:

Summarize Data on Design Form (see Form 6-1)

Use data from Steps 1-3 Step 5:

Design Limitations

A: See Section 6.3. subchapter Design Features. B: Choose culvert material, shape, size, and entrance type Step 6 :

Select Design Discharge Qd

A: See Section 6.3: subchapter Design Limitations B: Determine flood frequency C: Determine Q from Rational Method or TRRL Method D: Divide Q by the number of barrels

The Republic of Kenya – Ministry of Roads

52

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Step 7:

Determine Inlet Control Headwater Depth (HWi)

Use the inlet control nomograph (Chart 6-1, 6-2 or 6-6) (NOTE: A plastic sheet with a matte finish can be used for marking such that the nomographs can be preserved.) A: Locate the size or height on the scale B: Locate the discharge · ·

for a circular shape use discharge for a box shape use Q per meter of width

C: Locate HW/D ratio using a straightedge · ·

extend a straight line from the culvert size through the flow rate mark the first HW/D scale. Extend a horizontal line to the desired scale, read HW/D, and note on Charts

D: Calculate headwater depth (HW) · ·

·

multiply HW/D by D to obtain HW to energy gradeline neglecting the approach velocity HW i = HW including the approach velocity HWi = HW - approach velocity head

Step 8:

Determine Outlet Control Headwater Depth at Inlet (HWoi)

A: Calculate the tailwater depth (TW) using the design flow rate and normal depth (single section) or using a water surface profile B: Calculate critical depth (dc) using appropriate chart (Chart 6-3 or 6-7) · ·

locate flow rate and read dc dc cannot exceed D

C: Calculate (dc + D)/2 D: Determine (ho) ho = the larger of TW or (dc + D/2) E: Determine entrance loss coefficient (KE) from Table 6-2 F: Determine losses through the culvert barrel (H) · range · · · and ·

use nomograph charts or equation 6.5 or 6.6 if outside locate appropriate KE scale locate culvert length (L) or (L1): use (L) if Manning’s n matches the n value of the culvert use (L1) to adjust for a different culvert n value (Eqn.6-10)

L1 = L(n1/n)2 Where: L1 L n1 n

= adjusted culvert length, m = actual culvert length, m = desired Manning n value = Manning n value on chart

The Republic of Kenya – Ministry of Roads

53

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

§ § § ·

mark point on turning line use a straightedge and connect size with the length

read (H) § §

use a straightedge connect Q and turning point and

·

read (H) on Head Loss scale

G: Calculate outlet control headwater (HW) ·

use equation 6.11, if Vu and Vd are neglected (Eqn. 6.11)

HW oi = H + ho - SoL ·

use equation 6.1, 6.4c, and 6.6 to include Vu and Vd.

· if HWoi is less than 1.2D and control is outlet control § § § § Step 9:

the barrel may flow partly full the approximate method of using the greater tailwater or (dc+ D)/2 may not be applicable backwater calculations should be used to check the result and if the headwater depth falls below 0.75D, the approximate method shall not be used

Determine Controlling Headwater (HWc)

Compare HW i and HW oi, use the higher · · Step 10:

HWc = HWi, if HW i > HW oi HWc = HWoi, if HW oi > HWi

Þ the culvert is in inlet control Þ the culvert is in outlet control

Compute Discharge over the Roadway (Qr )

Calculate depth above the roadway (HWr) HWr = HWc - HWov HW ov = height of road above inlet invert · If HWr £ 0, Qr = 0 · If HWr > 0, determine Qr

Step 11:

Compute Total Discharge (Qt)

The Republic of Kenya – Ministry of Roads

54

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Qt

(Eqn.6.12)

= Qd + Qr

Step 12:

Calculate Outlet Velocity (Vo) and Depth (dn)

If inlet control is the controlling headwater : a. Calculate flow depth at culvert exit · use normal depth (dn) · use water surface profile b. Calculate flow area (A) c. Calculate exit velocity (Vo) = Q/A If outlet control is the controlling headwater: a. Calculate flow depth at culvert exit · use (dc) if dc > TW · use (TW) if dc < TW < D · use (D) if D < TW b. Calculate flow area (A) c. Calculate exit velocity (Vo) = Q/A Step 13:

Review Results

Compare alternative design with constraints and assumptions, if any of the following are exceeded, repeat Steps 5 through 12 · · · · · Step 14:

the barrel must have adequate cover the length should be close to the approximate length the headwalls and wingwalls must fit site conditions the allowable headwater should not be exceeded and the allowable overtopping flood frequency should not be exceeded Plot Performance Curve

Repeat Steps 6 through 12 with a range of discharges Use the following upper limit for discharge · · · ·

Step 15:

Q100 if Qd £ Q100 Q500 if Qd > Q100 Qmax if no overtopping is possible Qmax = largest flood that can be estimated

Related Designs

Consider the following options (See Sections 6.3: Design Features) The Republic of Kenya – Ministry of Roads

55

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

· · · Step 16:

Tapered inlets if culvert is in inlet control and has limited available headwater Energy dissipators if Vo is larger than the normal V in the downstream channel Sediment control storage for sites with sediment concerns such as alluvial fans

Documentation

Prepare report and file with background information

The Republic of Kenya – Ministry of Roads

56

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

T able 6-2 Entrance Loss Coefficient (Outlet Control, Full or Partially Full) He = Ke (V2/2g) Type of Structure and Design of Entrance Pipe, concrete Mitered to conform to fill slope End-section conforming to fill slope* Projecting from fill, square cut end Headwall or headwall and wingwalls Square-edge Rounded (radius = 1/12D) Socket end of pipe (groove-end) Projecting from fill, socket end (groove-end) Beveled edges, 33.7˚ or 45˚ bevels Side- or slope-tapered inlet Pipe, or pipe-arch, corrugated metal Projecting from fill (no headwall) Mitered to conform to fill slope, paved or unpaved slope Headwall or headwall and wingwalls square-edge End-section conforming to fill slope Beveled edges, 33.7˚ or 45˚ bevels Side- or slope-tapered inlet Box, Reinforced Concrete Wingwalls parallel (extension of sides) square-edged at crown Wingwalls, 10˚ to 25˚ or 30˚ to 75˚ to barrel, square-edged at crown Headwall parallel to embankment (no wingwalls) Square-edged on 3 edges Rounded on 3 edges to radius of 1/12 barrel dimension Beveled edges on 3 sides Wingwalls at 30˚ to 75˚ to barrel, crown edge rounded to radius of 1/12 barrel dimension, or beveled top edge Side- or slope-tapered inlet

The Republic of Kenya – Ministry of Roads

57

Coefficient ke 0.7 0.5 0.5 0.5 0.2 0.2 0.2 0.2 0.2 0.9 0.7 0.5 0.5 0.2 0.2 0.7 0.5

0.5 0.2 0.2 0.2 0.2

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

6.6 Software Applications for Culvert Design As culvert hydraulics are extremely complicated various software products are freely available to assist the lengthy process of culvert design as described above. The most widely use applications have been developed by the American Federal Highway Authority (HY8) or the Hydraulic Engineering Corps (HEC). HEC RAS 4 can be applied for all kinds of water level calculations concerning floodplain crossings, multiple culvert calculations and bridge hydraulics. The application of these software tools is highly recommended for checking the design results reached by the Nomograph Method described below.

The Republic of Kenya – Ministry of Roads

58

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

6.7 Nomograph Design Example The following example problem follows the Design Procedure Steps described in Section 6.5 Step 1 Assemble Site Data and Project File

A:

Site survey project file contains:

Figure 6-8 Cross-Section

· ·

roadway profile and embankment cross section (see Figure 6-8)

Site visit notes indicate · no sediment or debris problems and · no nearby structures B:

Studies by other agencies – none

C:

Environmental risk assessment shows · no buildings near floodplain · no sensitive floodplain values and · convenient detours exist

D:

Design criteria · 50-year frequency for design and · 100-year frequency for check

Step 2:

Determine Hydrology

TRRL equations yield · Q50 = 11.3 m3/s · Q100 = 14.16m3/s

The Republic of Kenya – Ministry of Roads

59

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Step 3:

Design Downstream Channel (see figure 6-9)

Figure 6-9 Cross-Section of Channel (Slope = 0.05 m/m)

Point 1 2 3 4 5 6 7 8

Station, m 3.7 6.7 9.8 10.4 11.9 12.5 15.5 18.6

Elevation, m 54.86 53.34 53.19 52.58 52.58 53.19 53.34 54.86

Q (m3/s)

TW (m)

2.83 5.66 8.50 11.33 14.16

0.43 0.63 0.76 0.85 0.93

The Republic of Kenya – Ministry of Roads

60

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Step 4: Summarize Data on Design Form (see Figure 6-10)

Figure 6.10: Completed Design Form

The Republic of Kenya – Ministry of Roads

61

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Step 5: Select Design Alternative Shape Size Material Entrance

– -

Box 2135 mm by 1830 mm Concrete Wingwalls, 45o bevel, rounded

Step 6: Select Design Discharge (Qd = Q50 = 11.33 m3/s) Step 7: Determine Inlet Control Headwater Depth (HWi) Use inlet control nomograph - Chart 6-6 a. D = 1.83 m b. Q/B = 11.33/2.13 = 5.32 c. HW/D = 1.27 for 45o bevel d. HWi = (HW/D)D = (1.27)1.83 = 2.32 m (Neglect the approach velocity) Step 8: Determine Outlet Control Headwater Depth at Inlet (HWoi) a. TW = 0.85 m for Q50 = 11.33 m3/s b. dc = 1.43 m from Chart 6-7 c. (dc + D)/2 = (1.43 + 1.83)/2 = 1.63 m d. ho = the larger of TW or (dc + D/2) ho = (dc + D)/2 = 1.63 m e. KE = 0.2 from Table 6-2 f. Determine (H) - use Chart 6-8 · KE scale = 0.2 · culvert length (L) = 90 m · n = 0.012 same as on chart · area = 3.90 m2 · H = 0.85 m g. HWoi = H + ho - SoL = 0.85 + 1.63 - (0.05)90 = - 2.02 m HWoi is less than 1.2D, but control is inlet control, outlet control computations are for comparison only Step 9: Determine Controlling Headwater (HWc) · HWc = HW i = 2.32 m > HWoi = - 2.02 m · The culvert is in inlet control Step 10: Compute Discharge over the Roadway (Qr) a. Calculate depth above the roadway: HWr = HWc - HWov = 2.32 – 2.59 = - 0.27m b. If HWr £ 0, Qr = 0 Step 11: Compute Total Discharge (Qt) Qt = Qd + Qr = 11.33 m3/s + 0 = 11.33 m3/s The Republic of Kenya – Ministry of Roads

62

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Step 12: Calculate Outlet Velocity (Vo) and Depth (dn) Inlet Control a. Calculate normal depth (dn): Q = (1/n)A R2/3 S1/2 = 11.33 m3/s = (1/0.012)(2.13*dn)[(2.13*dn/(2.13+2dn)]2/3(0.05).5 = (2.13*dn)[2.13*dn/(2.13+2dn)]2/3 = 0.608 try dn = 0.6 m, 0.675 > 0.608 use dn= 0.55 m, 0.596 » 0.608 b. A = (2.13)0.55 = 1.17 m2 c. Vo = Q/A = 11.33/1.17 = 9.68 m/s Step 13: Review Results Compare alternative design with constraints and assumptions, if any of the following are exceeded repeat, Steps 5 through 12 · barrel has (2.59 m – 1.83 m) = .76 m of cover · L = 90 is OK, since inlet control · headwalls and wingwalls fit site · allowable headwater (2.59 m) > 2.32 m is ok and · overtopping flood frequency > 50-year Step 14: Plot Performance Curve Use Q100 for the upper limit, Steps 6 through 12 should be repeated for each discharge used to plot the performance curve, these computations are provided on the computation form, Figure 6-11 that follows this example. Step 15: Related Designs Consider the following options (see Section 6.3: Design Features) a. Consider tapered inlets, culvert is in inlet control and has limited available headwater · No flow routing, a small upstream headwater pool exists · Consider energy dissipators since Vo= 9.5 m/s > 6 m/s in the channel · No sediment problem

downstream

Step 16: Documentation Report prepared and background filed

The Republic of Kenya – Ministry of Roads

63

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Figure 6-11 Performance Curve for Design Example

The Republic of Kenya – Ministry of Roads

64

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

CHART 6.1

The Republic of Kenya – Ministry of Roads

65

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

CHART 6.2

The Republic of Kenya – Ministry of Roads

66

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

CHART 6-3 – CRITICAL DEPTH – CIRCULAR PIPE

This curves are obtained from the following formula :

With : 3 Q – Discharge (m /s) 2 g - gravity constant (m/s ) Dc – Critical depth (m) q, qr - See sketch (degree, radian)

The Republic of Kenya – Ministry of Roads

67

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

CHART 6.4

The Republic of Kenya – Ministry of Roads

68

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

CHART 6.5

The Republic of Kenya – Ministry of Roads

69

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

CHART 6.6

The Republic of Kenya – Ministry of Roads

70

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Chart 6-7

1,6

1,4

Critical Depth-dc (Meters)

1,2 1

0,8

dc CANNOT EXCEED TOP OF PIPE

0,6

0,4 0,2

0 0

1

2

3 Q/B

4

5

6

5

4,5

Critical Depth-dc (Meters)

4

3,5

3

dc CANNOT EXCEED TOP OF PIPE

2,5

2

1,5

1 5

10

15

The Republic of Kenya – Ministry of Roads

20 Q/B

71

25

30

35

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

CHART 6.8

Q=flow (m3/s) B=base of section (m) Dc=0.467 (Q/B ) 2/3

The Republic of Kenya – Ministry of Roads

72

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Assemble Site data, profile, cross-section, design criteria, hydrology, channels… Using one of the nomographs Using (Chart 6-1,one 6-2oforthe 6-3nomographs according to 7-1, 7-2 orto7-3 according the(Chart type of culvert) determine to theand type of culvert) determine HW/D HW. HW/D and HW.

Select design discharge Qd

Select design alternative : Shape, size, material…

END Is The approach velocity V neglectable ?

Considerdesign design option options Consider depending on on the the results. depending results. See7.3 6.3:: Design See Design Features features

Yes

No Yes Do you have enough values to plot performance curve ? No

Hwi = HW-V²/2g

Hwi = HW

Yes Compute the Tailwater depth TW Compute the Tailwater depth (see 6.3 Design Limitations) TW (See 7.3 DESIGN LIMITATIONS)

Yes Calculate critical depth (dc) using chart Calculate6-3 critical or 6-7depth (dc) using chart 7-3 or 7-7

Are results in agreement with constraints and assumptions ?

Ho= Max (TW,dc+D/2) Compute Outlet velocity Vo and depth dn

Determine Ke (see Table 6-2) Determine Ke (See Table 7-2)

Compute total discharge : Qt=Qd+Qr

Compute drainage over roadway Qr. Yes

Determine lossloss H through the culvert using Detrmine H through the culvert Eqn. using 6.5 forEquation a full barrel 7.5(Y=Q/Section for a full barrel.(V=Q/Section)

Qr=0

Calculate outlet control headwater HWoi=H+Ho-SoL

No

HWc-HWov>0 ? (HWov=height of road above inlet invert)

HWc= HWi Inlet control

HWi>Hwoi ? No

HWc= Hwoi Outlet control

Flowchart 6-1 Design of Culverts (See Procedure in section 6-5)

The Republic of Kenya – Ministry of Roads

Yes

Yes HWoi>1.2D ?

No Approximation has to be checked (see Step 8)

73

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Form 6-1

The Republic of Kenya – Ministry of Roads

74

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

References 1) J.M Norman, R.J. Houghtalen, W.J. Johnston, "Hydraulic Design of Highway Culverts," HDS No. 5, FUWA-IP-85-15, FUWA, Washington, D.C. 20590,1985 2) G.K. Young, J.S. Krolak, HYDRAIN - Integrated Drainage Design Computer System, Volumes 1-6, FUWA-RD-88-120, FUWA, 1987. 3) A. Ginsberg, HY8 - Culvert Analysis Microcomputer Program, Applications Guide, FHWA-EPD-87-101, and software available from McTrans Center, 512 Weil Hall, University of Florida, Gainesville, Florida 32611. 4) "Guidelines for the Hydraulic Design of Culverts," Task Force on Hydrology and Hydraulics, Subcommittee on Design, American Association of State Highway and Transportation Officials, 341 National Press Bldg., Washington, D.C. 20045, 1975. 5) G.L. Bodhaine, Measurement of Peak Discharge at Culverts by Indirect Methods, Techniques of Water-Resources Investigations of the USGS, Chapter A3, 1982. 6) G. Reihsen and L.J. Harrison, "Debris Control Structures," BEC No. 9, Hydraulics Branch, Bridge Division, Office of Engineering, FHWA, Washington, D.C. 20590, August 1971. 7) S.W. Jens, "Design of Urban Highway Drainage - The State of the Art," FHWA-TS-79225, Hydraulics Branch, Bridge Division, Office of Engineering, FHWA, Washington, D.C. 20590, August 1979 8) "Design of Small Canal Structures," Bureau of Reclamation, Denver, Co., 1974. 9) 'Culvert Design System," FHWA-TS-80-245, Hydraulics Section, Wyoming Highway Department, Cheyenne, Wyoming 82006, December 1980. 10) "Design Charts For Open Channel Flow," HDS No. 3, Hydraulics Branch, Bridge Division, Office of Engineering, FHWA, Washington, D.C. 20590, 1973. 11) J.N. Bradley, "Hydraulics of Bridge Waterways," HDS No. 1, Second Edition, Hydraulics Branch, Bridge Division, Office of Engineering, FHWA, Washington, D.C. 20590, September 1973. 12) J.O. Shearman, W.H. Kirby, V.R. Schneider, and H.N. Flippo, "Bridge Waterways Analysis Model, "FHWA-RD-86-108, FHWA, Washington, D.C. 13) H.W. King and E.F. Brater, "Handbook of Hydraulics, 'I Sixth Edition, McGraw-Hill Book Co., 1976. 14) FHWA Hydraulic Design Series No. 5 (HDS5), Hydraulic Design of Highway Culverts. 15) AASHTO Highway Drainage Guidelines, 1992.

The Republic of Kenya – Ministry of Roads

75

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

7 Drifts and Low Level Crossings 7.1 Introduction Design flows at river crossings often substantially exceed the capacity of small to medium type culvert structures as described in Chapter 7. However, due to economic or technical constraints it is not always possible to construct high level bridges at these locations. Low level crossings, which also come under the name of drifts, fords, irish crossing or vented drifts, can offer a cost effective alternative. It is the aim of this chapter to provide assistance to the engineer concerning: · the choice of type of low level crossing · the technical and economic aspects to be taken into consideration, and · the hydrological and hydraulic design process

7.2 Definition and Terminology A Low Level River Crossings (LLRC) is a submersible road structure, designed in such way as to experience no or limited damage when overtopped. This type of structure is appropriate when the inundation of a road for short periods is acceptable. Different names of Low Level Crossings are used in many part of the world, such as: · · · · · · · · · ·

Low Level River Crossing Low Level Bridge Submersible Crossing Irish Crossing Causeway Vented Causeway Drift Ford Submersible bridge etc..

In order to clearly define the different type of structures the following classification of LLRC is proposed: 7.2.1 Drifts A drift is defined as a specifically prepared surface for vehicles to drive over when crossing a river. A drift does not contain any openings underneath the surface for allowing passing water through. The surface layer may consist of gravel, concrete, grouted stone concrete blocs held together longitudinally with polyester, galvanised steel or stainless steel cables. Drifts are also referred to in the literature as Fords.

The Republic of Kenya – Ministry of Roads

76

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Figure 7.1: Example of drifts

7.2.2 Causeway A vented causeway (also referred to as a causeway) in essence also consists of a suitable surface layer over which vehicles may drive, but contains openings underneath allowing water to pass through the structure. These openings may be of circular or rectangular shape and can be formed by means of pre-cast pipes or portal culverts, corrugated iron void formers, short spun decks etc. Vented causeways are also referred to in the literature as Vented Fords Vented causeways with several openings under the actual roadway could have the following functions: ·

To reduce the water level upstream of the structure

·

To raise the tailwater level, so less embankment protection is required on the downstream side

·

To act as anti – ponding structures

The Republic of Kenya – Ministry of Roads

77

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Figure 7.2: Example of vented causeways

7.2.3 Submersible Bridges A submersible bridge is defined as a structure consisting of a short – span deck (typically between 4 and 7.5 m) supported by a sub structure consisting of two abutments and any number of piers. The height of the deck above the riverbed is usually lass than 2m. Additional information on low level crossing structures can be found under Section 5.8 , Design Manual for Roads and Bridges, Part 6 a Bridge and Culvert Design

The Republic of Kenya – Ministry of Roads

78

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

7.3 Application Characteristics 7.3.1 Basic Characteristics · ·

LLRC are designed to be inundated from time to time Construction costs are considerably lower than those for a conventional bridge

LTRC are appropriate under the following circumstances: · · ·

when short-term disruption of traffic is acceptable when alternative routes exists which can be taken during flood periods where high level crossings are not economically justified

The following limitations of LLRC have to be taken into consideration: · · ·

The fact that the crossing might not be usable from time to time The risk that drivers might try to use the crossings during flood flow and and of being washed away The level of maintenance, which might be required after flooding events.

7.3.2 Road Network Considerations If a particular community has only one access road only and the access road crosses a river without a structure, the decision whether to construct a LLRC or a high – level bridge depends on the acceptability of short periods of inaccessibility, the construction costs and the economic justification of the options. With large rivers, attention should be paid to the total road network in the area, the number and locations of river crossing structures, as well as the levels of these structures in terms of design return period. Rather than designing all river crossing structures for the same return period, variations in the return periods used for design can be considered. In this way the number of accessible structures during flooding will be reduced, whilst alternatives remain available. In contrast with the first option a situation may occur where all the structures under consideration are overtopped at the same time.

7.4 Design Considerations 7.4.1 Site selection As with all river crossing structures LLRC should be located within a straight section of the river where the river flow is as uniform as possible. Riverbanks on the outside of bends tend to erode which might lead to the floodwater by-passing the structure during flooding. Where the width of a river channel varies, the advantages of locating the structure in a narrower section should be compared to those associated with location I a wider section. Benefits of a narrower section are shorter length and, therefore, lower construction costs. Benefits of narrower section also cover the possibility that the narrower section is associated with less weathered in-situ material, which may offer better foundation conditions.

The Republic of Kenya – Ministry of Roads

79

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Benefits of a wider section in the river are that flow velocity is relatively low with shallower depth. These two benefits reduce the risk that the structure maybe damaged and increases the safety of vehicles crossing the structure. Crossing the river at a skew should be avoided. A skew approach, coupled with the possible blocking of opening with debris tends to direct the full force of the river towards on of the riverbanks, which increases the possibility of the approach being washed away. The structure should be straight. A horizontally curved structure will be subject to similar problems of undesirable concentration of flow. 7.4.2 Hydrological Considerations Design flow return periods are to chosen from Chapter 3. The recommended methods for design flood calculations are explained in Chapter 4 and 5 of the Design Manual. Generally is it not required to achieve high accuracy of flood water estimation as the structure is designed to be overtopped. In many cases it is thus sufficient to apply the Rational Method for flood calculation. If the theoretical submergence period is of concern, the TRRL Method has to be applied in order estimate the duration of flood flow above a certain flood level, associated with a specific flood return period. 7.4.3 Hydraulic Design In this section the design procedure for both, standard drifts and vented drifts are discussed. The capacity of a structure is determined as the sum of the discharge that could be accommodated over the structure within acceptable depth, and the discharge to be accommodated underneath the structure. The sum is then compared to the design discharge, Qdesign, in order to evaluate the adequacy of the structure. Flow over the structure

Decide on the maximum flow depth over the structure through which a vehicle will still be able to pass safely (l00 mm for supercritical flow due to the high momentum transfer associated with the velocities, and 150 mm for subcritical flow over the structure. Determine the discharge that could be accommodated over the structure. As a first assumption, especially if the slope in the direction of flow is 2 to 3% as recommended elsewhere, assume this flow to be supercritical. For supercritical channel flow over the structure: Qover

= ( Aover 5/3 * So 0.5 )/ (n Pover2/3)

(Eqn. 7.1)

Where: Qover

= the discharge that could be accommodated over the structure within the selected flow depth (m3/s)

Aover

= area of flow over structure at the flow depth selected m

So

= slope in direction of flow, for example 0,02 or 0,03 mlm

The Republic of Kenya – Ministry of Roads

80

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

NCONC = Manning n-value. For a concrete deck nCONC can be taken as 0,016 s/ml/3 wetted perimeter at the flow depth selected (m) Aover and Pover are calculated as follows: Aover = A1 + A2 + A3, or

(Eqn.:7.2)

Pover = P1 + P2 + P3, or

(Eqn.: 7.3)

AI, A2, A3 d K K2

= = = =

areas defined in Figure 7.4 (m2) depth of flow over the structure (m) the K value for vertical curve 1 the K value for vertical curve 3

With K being a vertical road alignment parameter, defined as the horizontal length of road required for a 1 % change in the gradient of the road.

Figure 7.3: Cross section through river at drift

The Republic of Kenya – Ministry of Roads

81

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

Figure 7.4: Cross section through structure at drift The vertical road alignment, K (K1 and K3) should not be confused with K1nl and Kout following below. The symbol K is used because it is the symbol used in vertical road design methodology. Note that in the calculation of the flow over the structure the effect of guide-blocks are for simplicity reasons ignored. Flow through the structure Flow under the structure is in essence flow through a culvert opening as discussed in section 6.5. However, as the bridge deck represents an obstacle to flow over the structure a slightly adapted way of culvert calculation is recommended for the flow through the structure. Assume outlet control The flow passing through the structure is defined as Qunder , where Qunder = Vunder * A eff

(Eqn.: 7.4)

(Eqn.: 7.5)

where: Acff

= the effective inlet area through the structure (m2) = Acell (the effective inlet area through the structure)

The Republic of Kenya – Ministry of Roads

82

Draft Document – December 2009

PART 2 – Drainage Design 2009

DESIGN MANUAL for ROADS and BRIDGES

LB

= the total width of the deck of the structure (m)

Vunder

= the average velocity of flow through the structure (m/s)

C

= factor that reflects the transition losses

Determine the total energy height (Hj) upstream of the structure and the water level at the outlet of the structure: Assumption: Since the water is dammed by the structure, the velocity v1 = 0 m/s H1 = h +x+ D

(Eqn.: 7.6)

Where: x

= the thickness of the deck (depending on the structural design) (m)

D

= the height of the soffit of the deck above the river invert level (m)

By applying the conservation of energy principle, determine the depth upstream of the structure, h, that is required to pass the flow rate, Qover: h = (v22/2g) + d

(Eqn.: 7.7)

with v2 = Qover/Aover

(Eqn.: 7.8)

H2 = D - LbSo

(Eqn.: 7.9)

where: LB

= the total width of the deck of the structure (m)

So

= slope of the conduit underneath the structure (m/m)

C is a factor representing the local or transition losses due to flow convergence/divergence at the inlet/outlet: C = ∑(K inl. + Koutl.) each cell

(Eqn.: 7.10)

Kinl and Koutl. Are determined as followed for rectangular sections: :: Kinl. at outlet control Koutl. at outlet control

Sudden transition Gradual transition Sudden transition Gradual transition

Kinl = 0.5 Kinl = 0.25 Koutl.= 1.0 Koutl. = 1.0 for 45º