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SCOPE ............................................................................................................................................................4 REFERENCES.................................................................................................................................................4 OBJECTIVE.....................................................................................................................................................5 DESIGN CONSIDERATIONS ..........................................................................................................................5 WASTE STREAM IDENTIFICATION ..............................................................................................................5 HYDROLOGIC DESIGN ..................................................................................................................................6 BASIC RUNOFF HYDROLOGY ..............................................................................................................6 Design Storms and Return Period Storms, Storm Durations, and Hourly Intensities............................6 Runoff Flow Rate, Based on the Rational Formula...............................................................................9 Calculation of “Time of Concentration" ...............................................................................................10 Runoff Volume Calculation Using Simple Methods ............................................................................11 Storm Runoff Hydrograph...................................................................................................................12 Sewer System Flow Routing; Computerized Models..........................................................................13 HYDRAULIC DESIGN ...................................................................................................................................14 BASIC HYDRAULIC DESIGN CONSIDERATIONS ..............................................................................14 HYDRAULIC DESIGN OF BURIED SEWER PIPES .............................................................................16 HYDRAULIC DESIGN OF OPEN CHANNELS......................................................................................17 CULVERT CROSSINGS OVER OPEN CHANNELS.............................................................................18 HYDROLOGY / HYDRAULICS ENGINEERING SOFTWARE ..............................................................19 STRUCTURAL DESIGN................................................................................................................................20 DETERMINATION OF LOADS IMPOSED ON A BURIED PIPE ...........................................................20 Marston Formula for Earth Portion of the Total Load on Buried Conduits ..........................................21 Effects of Surface Live Loads or Other Surface Loads.......................................................................22 STRUCTURAL DESIGN METHODS FOR SELECTING PIPE WALL THICKNESS..............................25 Rigid Pipe Design ...............................................................................................................................25 Flexible Pipe Design...........................................................................................................................27 Use of HDPE Pipe for Sewers in Plant Areas Where there are Hot Process Streams .......................30 Thermal Effects ..................................................................................................................................37 Corrugated Metal Pipe........................................................................................................................37 Open Channels...................................................................................................................................37 STRUCTURAL ANALYSIS / DESIGN SOFTWARE ..............................................................................38 NOMENCLATURE.........................................................................................................................................39

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APPENDIX A - EXAMPLE PROBLEMS .......................................................................................................67 HYDROLOGIC DESIGN .......................................................................................................................67 Example Problem No. 1, Synthesizing a Local Intensity-Duration-Frequency (IDF) Curve from 30-Minute Storm Data .........................................................................................................................................67 Example Problem No. 2, Calculating Time of Concentration for Use in the Rational Formula ...........69 Example Problem No. 3, Use of the Rational Formula for Runoff Flow Rate .....................................70 Example Problem No.4, Runoff Volume via Simple Runoff Coefficient, and via SCS Curve Number Method ...............................................................................................................................................70 Hydraulic Design ...................................................................................................................................70 Example Problem No. 5, Pipe Flowing Partly Full (Gravity Flow) .......................................................70 Example Problem No. 6, Flow in Small Pipe Network using Rational Method ...................................71 Example Problem No. 7, Open Channel Flow....................................................................................74 Example Problem No. 8, Culvert Sizing .............................................................................................74 Structural Design...................................................................................................................................75 Example Problem No. 9, Calculating Earth Load via Marston Formula, Conventional Cut-and-Cover Pipe in Trench ....................................................................................................................................75 Example Problem No. 10, Load Imposed by Nearby Uniform Distributed Surface Load....................75 Example Problem No. 11, Loads Imposed by Surface Traffic ............................................................76 Example Problem No. 12, Selecting Wall Thickness, Reinforcing Requirements for Reinforced Concrete Pipe ....................................................................................................................................................76 Example Problem No. 13, Selecting Wall Thickness Requirements for Plain (non-reinforced) Concrete Pipe ....................................................................................................................................................77 Example Problem No. 14, Selecting Wall Thickness, Reinforcing Requirements for Vitrified Clay Pipe (VCP) .................................................................................................................................................77 Example Problem No. 15, Selecting Wall Thickness Requirements for Ductile Iron Pipe ..................77 Example Problem No. 16, Selecting Wall Thickness for HDPE Pipe, Smooth Wall Type ..................78 Example Problem No. 17, Selecting Wall Thickness for HDPE Pipe, Profile (Ribbed) Wall Type ......81 APPENDIX B - Formulas for Calculating Hydraulic Radius (R) and Flow Area (A) for Circular Pipes Flowing Partly Full .......................................................................................................................................83 TABLES Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8 Table 9 Table 10 Table 11 Table 12 Table 13 Table 14 Table A-1

Typical Runoff Coefficients For Use In The Rational Formula...........................................10 Estimates Of Manning's “N" For Overland Flow ................................................................11 Overview Of Stormwater Modeling Computer Programs ..................................................14 Manning's Coefficient “N" For Commonly Used Drainage Pipe Materials .........................16 Manning's Coefficient “N" For Commonly Used For Open Channels ................................17 Description Of Parameters Implicit In Marston Coefficient ................................................22 Critical Loading Configurations, Highway Truck Loadings ................................................24 Impact Factors As A Function Of Depth Of Cover, Concrete Pipes ..................................24 Allowances For Casting Tolerances, Ductile Iron (DI) Pipe...............................................29 Kb Values For Various Bedding Angles For Use With Modified Iowa Formula ................33 Treatment Of Design Considerations By Commercial HDPE Pipe Manufacturers ............34 Stiffness Requirements For Plastic Sewer Pipe Parallel Plate Loadings ..........................36 Long Term (50 Year) Elastic Modulus E For HDPE Pipe ..................................................37 Maximum Permissible Velocities For Various Channel Lining Types................................38 Factors For Converting From 30-Minute Duration Storm Depths To Depths For Other Storm Durations, Continental U.S. ..........................................................................67 Table A-2 Factors For Estimating Total Rainfall Depth For Various Recurrence Intervals, Continental U.S. ................................................................................................................67 ExxonMobil Research and Engineering Company – Fairfax, VA

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FIGURES Figure 1 Figure 2 Figure 3-A Figure 3-B Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11-A Figure 11-B Figure 11-C Figure 11-D Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19-A Figure 19-B Figure 20 Figure 21 Figure 22

Example Of Rainfall Depth Map, Continental U.S., From U.S. Weather Bureau's TP 40 10 Year, 1 Hour Storm, Inches ...........................................................................41 Relationship Between Design Return Period And Exceedance Probability ...................42 Example Of Published IDF Curve, Houston TX, From TP 25 (U.S. Weath. Bur.) ..........43 Example Of User Synthesized IDF Curve, Houston TX, From Example No. 1 In Appendix A.....................................................................................................................44 Example Of Hourly Rainfall Distribution Within A Storm, SCS Type II Storm, U.S. .......44 Nomograph For Solution Of “Time Of Concentration" For Overland Flow .....................45 Curve Numbers (CN) For Various Land Use Classifications And Soil Types.................46 Direct Runoff Vs. Rainfall For Various CN (Curve Numbers).........................................46 Example Of Runoff Hydrograph.....................................................................................47 Examples Of Refinery Manhole Seal Arrangements......................................................47 Ratios Of Hydraulic Elements For Circular Conduits Flowing Part Full..........................48 Inlet Control Nomograph For Corrugated Metal Pipe (CMP) Culvert .............................49 Inlet Control Nomograph For Concrete Pipe Culvert......................................................50 Outlet Control Nomograph For CMP Culvert .................................................................51 Outlet Control Nomograph For Concrete Pipe Culvert...................................................52 Illustration Of Earth Loads On Buried Conduit ...............................................................53 Marston Coefficient Cd ..................................................................................................54 Summary Of Standard Methods For Calculating Earth Loads On Buried Conduits .......55 Influence Diagram For Effects Of Distributed Surface Loads On Buried Pipe ...............57 AASHTO HS-20 Truck Loads On Buried Pipe ...............................................................58 Illustration Of “Three Edge Bearing" Test For Use In Indirect Design Of Rigid Pipes ....59 Bedding Factor “Bf" For Concrete Pipe..........................................................................60 Bedding Factor “Bf" For Vitrified Clay Pipe ....................................................................62 Bedding Factor “Bf" For Vitrified Clay Pipe ....................................................................63 Manufacturer Specific Design Charts/Tables For Thickness Design Of HDPE..............64 Soil Modulus E' For Use In Modified Iowa Formula For Flexible Pipe Design................65 Rip-Rap Sizing Requirements For Use As Channel Lining ............................................66

Revision Memo 12/01

DP updated to include information Hydrology / Hydraulics and Structural Design on computer software programs available in the public domain. New guidance also provided on using HDPE pipe in plant areas where there are not process streams. General editorial revisions, including new Nomenclature.

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SCOPE This section covers the hydrologic, hydraulic, and structural design of industrial plant sewers and open channels which serve to convey storm runoff and firewater return flows away from operational areas to a point at which they can be treated and/or released in accordance with applicable law or recovered into the water supply system. The methods customarily used to estimate the quantity and discharge rates for storm runoff, hydraulic design of sewers and open channels, and methods dealing with the structural design of sewers are described in this Design Practice. Firefighting flows are established by company and/or plant practice and are described in the applicable Global Practices. The methods described in this Design Practice are drawn from generally accepted procedures commonly used by civil engineers to design storm sewer systems. While these are expected to be applicable to most routine storm drainage problems, they should not be viewed as the only methods available. The designer is ultimately responsible for selecting the analytical and design methods appropriate to a particular problem, and it is certainly possible that methods other than those described herein may be more applicable to a given problem. This Design Practice does not directly address process wastewaters, their treatment, nor the design of process wastewater sewers except to the extent that process wastewaters are sometimes conveyed along with storm runoff in combined sewers. It should be recognized that disposition of such combined flows can have a major impact on the design of drainage systems, the same as the large flow rates and volumes from storm runoff can impact process wastewater treatment strategy and treatment system design.

REFERENCES DESIGN PRACTICES Section XIX-A Section XIX-A1

Water Pollution Control, Guidelines for Selecting Wastewater Treatment Systems Water Pollution Control, Primary Oil / Water Separators

GLOBAL PRACTICES GP 3-2-1

Sewer Systems

OTHER REFERENCES ACPA Concrete Pipe Design Manual, American Concrete Pipe Association, 1992 ANSI / AWWA C150/A21.50 Thickness Design of Ductile Iron Pipe ANSI / AWWA C906-90 Polyethylene (PE) Pressure PIpe and Fittings, 4 in. through 63 in., for Water Distribution ANSI / AWWA C950-88 Fiberglass Pressure Pipe ASCE No. 77 Design and Construction of Urban Stormwater Management Systems, Manual of Practice No. 77, American Society of Civil Engineers, 1992 ASCE No. 37 Design and Construction of Sanitary and Storm Sewers, Manual of Practice No. 37, American Society of Civil Engineers, 1982 ASTM C 14 - 94 Standard Specification for Concrete Sewer, Storm Drain, and Culvert Pipe ASTM C 76 - 94 Standard Specification for Reinforced Concrete Culvert, Storm Drain, and Sewer Pipe ASTM C 301 - 93 Standard Methods of Testing Clay Pipe ASTM C-497 - 95a Standard Test Methods for Concrete Pipe, Manhole Sections, or Tile ASTM C 700 - 95 Standard Specification for Vitrified Clay Pipe, Extra Strength, Standard Strength, and Perforated Chow, V. T., Handbook of Applied Hydrology, McGraw-Hill Book Company, 1964 Design of Small Dams, U.S. Dept. of the Interior, Bureau of Reclamation, 1974 Holman, J. P., Heat Transfer, 4th ed. NCPI Clay Pipe Engineering Manual, National Clay Pipe Institute, 1974 TP 40 Rainfall Frequency Atlas of the United States, U.S. Dept. of Commerce, Weather Bureau, 1961 TP 25 Rainfall Intensity-Duration-Frequency Curves, U.S. Dept. of Commerce, Weather Bureau, 1955

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OBJECTIVE The primary objective of this Design Practice is to provide the designer with a technical guide relating to:

• •

Calculation of the appropriate design flow in an open channel or pipe (hydrologic design). Sizing of the channel or pipe to handle the design flow (hydraulic design).

•

Determining the required wall thickness for pipes or lining requirements for open channels as necessary to minimize maintenance costs and assure operability over the design life of the conduit (structural design). A secondary objective is to provide the means necessary to compute storm runoff volumes and flow rates. These may be needed in the design of treatment works for combined waste streams (storm flows and other wastewater streams), or for stormwater permitting considerations.

DESIGN CONSIDERATIONS The following factors would be expected to have a bearing on the design, and should be considered at an early stage of the design process.

•

Plant safety; Petrochemical plant sewers can contain hydrocarbon vapors which require special systems to control the risk of explosions. Plant sewers are in general isolated via water seal boxes to prevent vapor releases from drop inlets and to prevent the spread of a fire or explosion between fire risk zones. Seals in plant sewer systems are described in GP 3-2-1.

•

Plant layout and the topography of the area of interest and any tributary area.

•

Possible future expansion of the plant, or changes to the drainage area tributary to the plant.

•

Source of flow in the line or channel; entirely storm runoff, or contaminated storm runoff, or combination of storm runoff with other waste streams (see following section describing categories of wastewater streams).

•

If flow includes waste streams in addition to storm runoff, the chemical quality (e.g., pH, presence and concentrations of solvents, other hydrocarbons, or other corrosive chemicals) that may affect the line's durability or the integrity of joints.

•

The consequences of moderate leakage from joints. If consequences are viewed to be significant, it may impact selection of sewer line materials. For example, HDPE can be made to be continuous and virtually leak proof, and gasketted joints that are for all practical purposes leaktight under nominal sewer line pressures can be specified for jointed pipes.

•

Return period or design storm; the consequences of hydraulically undersizing the line, which could include backing up or ponding of storm water in critical or inconsequential locations. Higher consequences generally imply larger design storm (i.e., selection of a greater return period).

•

Firewater return flows that may be larger than the storm induced runoff for an isolated local area.

WASTE STREAM IDENTIFICATION Waste streams within a plant may be separated into the following categories:

•

Clean water or storm water; storm or firewater runoff from areas that are not normally subject to oil or toxic chemical contamination, including – oil free stormwater – steam turbine condensate – boiler plant condensate blowdown – once-through cooling water and cooling water tower blowdown where possible hydrocarbon contaminants are equivalent to C5 and lighter

•

Oily water or industrial wastewater; oil-contaminated wastewater that is low in sulfides, COD and BOD, including – – – – –

process plant area stormwater runoff and firewater runoff, or runoff from any areas that are normally subject to hydrocarbon or oil contamination normal oily and non-oily process wastewater water drawn off from atmospheric storage tanks ballast water wastewater from plant buildings used for operations or storage, including shop floor drains

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WASTE STREAM IDENTIFICATION (Cont) •

Chemical wastes; acidic, caustic, and other wastes which are not permitted to be released to either sanitary or industrial sewers in the plant, including – waste streams high in acids, alkalis, COD or BOD – laboratory chemical wastes – sour water stripper effluent – slop tank drawoff and flare seal water

•

Sanitary wastewater; waste from toilet facilities, lavatories, showers and floor drains in restrooms, locker rooms, cafeterias, wash rooms, etc. For combined sewers, which are defined as sewers that carry more than one type of wastewater, the design requirements will be controlled by the most stringent requirements of the individual sewers included in the system. The most common type of combined sewer is a combined industrial wastewater/stormwater sewer system. It will be subject to the environmental and permitting considerations for the industrial effluent (which are the subject of Section XIX-A) as well as the wide range in flow rates and runoff volumes associated with storm runoff events, which are the subject of this Section XXIX-C.

HYDROLOGIC DESIGN Hydrologic design involves the determination of flow rates and runoff volumes that would result from precipitation runoff. For the design of the sewer systems, the primary item of interest is the runoff flow rate. Common units of measurement are gpm (gallons per minute), cfs (cubic ft per second), m3/sec (cubic meters per second), MGD (million gallons per day), etc. Conversely, the design of storage and detention systems, which may be a factor in permitting questions for combined sewer systems, is more concerned with runoff volumes. Common units of measurement for runoff volumes are MG (million gallons), acre ft, Km3 (thousand cubic meters), etc. If storm routing studies are anticipated, which consider temporary storage during and after the passage of a runoff event, then both the flow rates and the runoff volumes are of interest. In such cases it is customary to consider both the flow rate and the runoff volume by developing the runoff hydrograph, which provides the instantaneous flow rate (e.g., cfs) as a function of time throughout a runoff event. The area under the runoff hydrograph curve is the runoff volume. Hydrologic design principles discussed in this section are the basis for calculating both runoff flow rates, runoff volumes, and runoff hydrographs. In most industrial sites, runoff that results from rainfall will control the design of pipes and channels, wherein peak flow rate is the item of interest. Snowmelt runoff can be of interest in extreme northern latitudes, or in alpine environments, but the runoff flow rates associated with large melt events are typically small compared to flow rates resulting from rainfall events. By contrast, the runoff volumes produced by snowmelt are typically much larger than runoff volumes from individual return period rain storms. Because the design of plant drainage systems (i.e., conveyances) is tied more toward the flow rates than to volumes, the hydrologic design aspects of drainage systems included in this Design Practice are limited to runoff produced by rainfall events. Depending on the application (conveyance design or temporary detention storage), the methods used to calculate runoff will range from simple ones that produce only peak flow rates or runoff volumes to more sophisticated computerized methods that produce the entire storm runoff hydrograph.

BASIC RUNOFF HYDROLOGY Design Storms and Return Period Storms, Storm Durations, and Hourly Intensities The following terms are commonly used in rainfall runoff determination:

•

Return period storm; a storm which has a defined statistical probability of occurring within a specified return period; example, a “10 year storm". The concept is described in more detail below. “Return period" is often referred to as “recurrence interval".

•

Storm duration; the theoretical beginning and end of the return period storm. Total rainfall depths for storms of specific return periods and specified durations are tabulated and published, usually in a “rainfall atlas" by weather bureaus or similar government agencies.

•

Rainfall intensity or hourly intensity; the instantaneous or hourly average rainfall rate within a given storm, expressed in units of L/T. Average hourly intensities for a storms of specified durations and specified recurrence intervals for various geographic locations are often presented in “intensity-duration-frequency", or “IDF" curves. An IDF curve is specific to a given geographic location, and may be published by government bureaus. Average hourly rainfall intensities are fundamental to calculating runoff flow rates.

•

Total rainfall or total rainfall depth; the total accumulated rainfall for the specified storm duration and return period, measured simply in units of L (generally in. or mm).

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HYDROLOGIC DESIGN (Cont) •

Time of concentration; the time, usually in minutes, that it would take water from the hydraulically most remote location in the catchment area, to arrive at the point of interest.

•

Rainfall hyetograph; the time distribution of rainfall within a storm of defined duration, usually expressed as a plot of rainfall intensity (e.g., in./hr) vs. elapsed time into the storm. All surface hydrologic evaluations are based on statistically defined return period storms. Typically, the design of a hydraulic facility will be specified in terms of a return period storm, such as a “10 year storm." In some cases, in particular those cases in which the volume of runoff is as important as the flow rate, both the return period and the duration have to be specified (e.g., a 10 year, 24 hour storm). The total rainfall amount for storms of various durations and various return periods are tabulated for most locations. In the U.S., the tabulation is generally in the form of rainfall atlases, which provide total rainfall amounts for storm durations from 30 minutes to 24 hours and return periods of 1 to 100 years. Figure 1 is excerpted from TP-40 published by the U.S. Weather Bureau, depicting rainfall amounts for storms of several recurrence intervals and several durations for the United States. Similar maps are maintained by local government agencies for various other locations. A “10 year" storm is the storm which would occur or be exceeded on an average of once every 10 years. Storms are thus defined in accordance with an exceedance probability. It does not mean that a 10 year storm will occur once in every ten year period, although the probability is 65% that at least one 10 year storm will occur in any given ten year period. If the designer wants to be 90% sure that a conduit will not be undersized in any single year, he should design for the 10 year storm (see Figure 2). 95% assurance that the flow would not be exceeded in any single year would require selection of the 20 year storm as the design storm. Normally, the design period is greater than a single year, and is related to the expected service life of the facility in question. Thus, if a designer wanted to be 90% certain that a conveyance or conduit would not be under-sized throughout a 25 year service life, the appropriate design storm would be on the order of a 250 year event. Obviously, such a design criterion would be appropriate only if the anticipated failure consequences are severe. Normally much shorter recurrence intervals are used in sizing drainage systems, as discussed below. Selecting the appropriate return period is a critical first step. Typically, storm sewers are designed for return periods of 2 to 25 years, depending on the consequences of their being undersized, which may involve no more than temporary and tolerable flooding in isolated areas of the plant. However, if expensive equipment would be damaged or if a health/safety risk is posed by the temporary flooding, a greater return period (i.e., larger design storm) should be considered. At one extreme, residential drainage systems are usually designed for return periods of 2 to 5 years, and drainage systems in high value commercial areas are typically designed at 5 to 10 year storms. At the other extreme, large above ground impoundments, which could cause significant damage if they were to overtop, are usually designed for at least the 100 year storm. Exxon's current practice, as reflected in GP 3-2-1 Sewer Systems, calls for storm sewers to be designed for the 10 year storm unless otherwise specified. At sites where storm response flow records have been maintained for a considerable period of time there may exist enough historical data to enable the designer to extrapolate directly to flows associated with other return periods. This is expected to be a rare situation at most industrial sites, since continuous recording flow meters on storm sewers are not likely to exist. For example, it can be shown by statistics that a period of record of about 22 years would be needed in order to be 90% certain that the 10 year flow had been experienced. To be 95% certain, a period of record of about 28 years would be required. Therefore, it is more likely that flow estimates will be prepared based on regional rainfall data than on site specific flow data. Hourly precipitation rates during storms of a specified duration are defined according to a set of rainfall distribution curves. The most commonly used hourly distribution for the U.S. (SCS Type II distribution) places about 55% of the rainfall within the two hour period at the center of a 24 hour storm (see Figure 4). Other hourly distributions of rainfall within a storm are possible, but the hourly distribution within a given storm is of interest only if the designer is attempting to produce a runoff hydrograph. For instantaneous peak flow, all that is needed is the peak rainfall intensity for a specified time period (called “time of concentration," discussed below), an appropriate runoff coefficient, and the catchment area. If only the total runoff volume is desired, all that is needed is the total rainfall amount, an appropriate runoff coefficient, and the catchment area. If more sophisticated storm routing through a sewer system is required, then determination of the runoff hydrograph will be required, including appropriate assumptions regarding hourly rainfall intensity during the storm. For the latter cases, the runoff hydrograph will probably be calculated using one of a number of rainfall-runoff models (e.g., SCS, TR 55, HEC), many of which are included within the comprehensive storm runoff modeling programs described later. Since storm duration does directly affect the runoff volume, it is necessary to specify storm duration as well as return period in cases where detention storage (off-line or on-line) is being considered to reduce peak flow rates.

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HYDROLOGIC DESIGN (Cont) Probably the simplest application, and certainly the most common in the design of drainage structures, is the determination of the peak flow rate. For this application, a quantity called “time of concentration" or “Tc" is defined. This is the time, usually in minutes, that it would take water from the hydraulically most remote location in the catchment area, to arrive at the point of interest (i.e., the “point of concentration"). The hydraulically most remote point is not necessarily the farthest point geographically, as it involves both the distance and the speed at which the water must travel. The latter is dependent on the slope of the terrain or the slope and diameter of the pipes conveying the water to the point of concentration. There are simple methods and formulas to determine time of concentration for any given catchment area, which take into account site topography for undeveloped land, and slow times in site sewers or surface ditches for developed land. Methods to estimate Tc are presented later in this Design Practice. Once the time of concentration is defined by an appropriate means, the parameter of interest is the peak rainfall intensity (usually in in./hr or mm/hr) that would be sustained for a duration equal to that previously defined time of concentration. The theory is that if it would rain at this intensity for this length of time, the entire catchment area would be reporting to the point of concentration, and the runoff flow rate would thus be at its maximum for that particular storm. Since the time of concentration will vary for specific drainage components within a given site, it is generally necessary to have a curve of rainfall intensity for various durations (i.e., various Tc) for various return periods. Such curves are referred to as “Intensity-depth-frequency" curves, or “IDF" curves. They are essential to use of the simpler runoff calculation methods, including the rational formula described below and many PC-based computer programs, and they are unique to a particular location. IDF curves take the general form

id =

(b

where: id D a, b, and n

= = =

a

+ D) n

Intensity of rainfall (in./hr in Customary units, mm/hr in Metric units) Duration of the rainfall, minutes Equation coefficients.

Some methods to compute runoff from rainfall, including some PC-based computer programs, can create IDF curves if the user has the appropriate coefficients. However, it is more common to make use of weather bureau derived IDF curves if these are available, or to synthesize an IDF curve from weather bureau derived relationships linking return periods, storm durations and intensities, as discussed below. Similar to the total rainfall depth curves for various return period storms and durations described previously, many government agencies have also compiled atlases of IDF curves for various locations. In the U.S., these were first consolidated by the U.S. Weather Bureau (1955) into a set of rainfall IDF curves known as TP-25. An example, taken from TP-25 (U.S. Weather Bureau), is presented as Figure 3-A. Since then, many states have updated and fine tuned the IDF curves for their particular region. Similar curves should exist at other locations in developed areas. If the designer has neither a set of published IDF curves for his site, nor adequate historical runoff flow records, but does have the 30-minute total rainfall depth for various return period storms, or can arrive at the 30-minute storm from storms of longer durations, it is possible to generate local IDF curves for use in calculating peak runoff by the Rational Formula. The method as applied in the U.S. is described in a number of texts on hydrology and in design manuals published by some pipe manufacturers. A comparatively simple and straightforward method to produce IDF curves needed for design is described in Example Problem No. 1 in APPENDIX A, and the resulting IDF curve is presented as Figure 3-B.

CAUTION When referring to return period storms, durations, and intensities, confusion sometimes arises due to the units that are used. A very common mistake is to consider that the minimum duration needed in determining a peak flow rate is the storm of one hour duration, simply because the rainfall intensity in the commonly used Rational Formula is usually expressed in in. (or mm) per hour. In fact, the peak hourly intensity for a 30 minute storm is as much as twice the hourly intensity for the 60 minute duration storm of the same return period. This difference is much greater than the difference that would occur by switching from a 10 year to a 25 year return period. Thus, if rainfall intensity is incorrectly chosen as that associated with a 1 hour duration in a catchment area that really has a time of concentration of 17 minutes, the peak flow so determined will be off (short) by more than 100%. What was thought to be a 10 year design flow may in fact be no more than a 1 year flow. When calculating runoff based on rainfall data, it is necessary to have some estimate of the direct runoff coefficient (the fraction of the incipient precipitation that becomes runoff). The formulation of the runoff coefficient will vary with the method used to compute the runoff, but in all cases the more impervious the surface, the higher the coefficient. Industrial areas that have a significant amount of paved areas and equipment surfaces, where runoff is nearly 100%, will tend to have relatively high runoff rates in comparison to rural land. ExxonMobil Research and Engineering Company – Fairfax, VA

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HYDROLOGIC DESIGN (Cont) The methods used to convert rainfall into runoff are for the most part simple and straightforward. Some are customarily carried out using a computer program while others depend only on simple calculations. When seeking to produce a complete runoff hydrograph (plot of flow vs. elapsed time), the designer should bear in mind that a reasonably accurate prediction of the hydrograph will result if the designer knows just three input parameters:

•

The catchment area (acres, meters2, ft2, etc.), usually determined from a topographic map or site drawings.

•

The catchment area's imperviousness, estimated based on land use.

•

The rainfall hyetograph for the design storm of interest (i.e., the hourly precipitation rate at various times within the storm). In view of the above, the designer should not be concerned about whether the method selected to produce a runoff hydrograph is the most precise of the several accepted theories. Virtually any generally accepted method will be suitable. What is important is a good understanding of the three parameters described above. Similar guidance exists for those cases in which the entire runoff hydrograph is not required. If the designer seeks only the peak runoff flow rate, then only the catchment area, a runoff coefficient, and the peak rainfall intensity associated with the correct time of concentration are needed. To determine total volume of runoff, only the catchment area, a runoff coefficient, and the total rainfall depth are needed. Runoff Flow Rate, Based on the Rational Formula The Rational Formula, referred to as the Lloyd-Davies method in the United Kingdom, is a simple and widely used means to calculate peak runoff rates for small watersheds. It is not recommended for catchment areas much greater than 200 acres or for any area where ponding in the catchment area might affect peak discharge. Where it is applicable, the Rational Formula relates peak discharge to rainfall intensity by the simple expression Eq. (1)

Q = C i Ac where: Q C i

= = =

Ac

=

Peak discharge ft3/s, Non-dimensional runoff coefficient, Rainfall intensity over a duration equal to the time of concentration, described in detail below, in./hr, Catchment area, acres.

The formula is most convenient when expressed in U.S. units, and then only because 1 acre in./hr = 1.008 cfs. In metric units, the rational formula becomes Q

m3 /sec

= 0.278 C x i mm/hr x A

km 2

Eq. (2)

The method requires a good definition of the limits of the catchment area. Normally this can be developed by defining watershed divides (local high points) on a topographic map. In developed sites, the limits of the various sub-catchment areas will be defined by the grading of the surface and the presence of man-made channels and/or drainage facilities. The normal range of runoff coefficients are described in the following Table 1. For estimating purposes it may be sufficient to use C = 0.5 for unpaved industrial areas, and C = 1.0 for paved areas and equipment surface or roof areas. Tankage areas enclosed by dikes should be excluded from the total area calculation if stormwater release from these areas is controlled by valved drains or if the water percolates into the soil.

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HYDROLOGIC DESIGN (Cont) TABLE 1 TYPICAL RUNOFF COEFFICIENTS FOR USE IN THE RATIONAL FORMULA

RUNOFF COEFFICIENT “C"

BY SURFACE TYPE:

BY LAND USE:

RUNOFF COEFFICIENT “C"

Business

Pavement Asphalt and Concrete

0.70 to 0.95

Downtown

0.70 to 0.95

Brick

0.70 to 0.85

Neighborhood

0.50 to 0.70

Roofs

0.75 to 0.95

Railroad Yards

0.20 to 0.35

Industrial

Lawns Flat, in sandy soil

0.05 to 0.10

Light

0.50 to 0.80

Steep, in clayey soil

0.25 to 0.35

Heavy

0.60 to 0.90

Residential Residential Suburban

0.25 to 0.40

Apartments

0.50 to 0.70

Unimproved Land

0.10 to 0.30

Calculation of “Time of Concentration" As described in the previous section, in order to select the rainfall intensity from the locally applicable “intensity-durationfrequency" curve (IDF) for the return period storm of interest, it is necessary to have calculated the “time of concentration" for the particular catchment area. The hourly intensity for the storm of interest can then be read directly from the IDF curve. Time of concentration can be calculated by means of the Kirpich formula, or similar empirical expressions, for undeveloped portions of the catchment area where overland flow would prevail, and by summing up travel times for flow in discreet conveyances (upstream sewer pipes and ditches) for developed land or industrial sites. The Kirpich formula, in Customary units is as follows: Tc = (11.9 L3 /H) 0.385 where: L

=

H

=

Eq. (3)

Distance in miles, measured along the watercourse to the hydraulically most remote point in the catchment area, Elevation difference from that point to the point of concentration, ft.

The above described formula is for overland flow mainly over bare earth, mowed grass, and roadside ditches. For flow over paved surfaces, it is customary to multiply the Tc calculated via the above expression by 0.4. For flows primarily over grassed areas, the Tc calculated via the above expression should be multiplied by 2.0. The calculation can be made numerically or by means of nomographs such as Figure 5. Time of concentration can also be defined by kinematic wave theory, which couples the continuity equation with bottom slope and friction slope for overland flow. The resulting expression for time of concentration in Customary units is: Tc = 0.938

where: Tc no Lo So ie

no0.6 L o0.6 ie0.4 So0.3

= = = = =

Eq. (4)

Time of concentration, minutes Manning's roughness coefficient for overland flow, given in Table 2 Distance from the farthest point in the catchment area to the point of interest, ft Dimensionless slope of the surface, averaged over the catchment area Excess rainfall rate, in./hr

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HYDROLOGIC DESIGN (Cont) In metric units, the expression is: Tc = 6.99

no0.6 Lo0.6 ie0.4 So0.3

where: L is in meters and ie is in mm/hr

Eq. (5)

Note that the rainfall intensity is included in the expression for Tc. While this is technically more correct than the simpler empirical approaches such as Kirpich's formula, it complicates the calculation by forcing iteration between the above expressions and the IDF curve. TABLE 2 ESTIMATES OF MANNING'S “n" FOR OVERLAND FLOW SURFACE TYPE

MANNING'S “no"

Concrete / asphalt

0.011

Bare sand

0.01

Bare clay / loam

0.02

Hard packed clay

0.03

Light turf

0.02

Lawns

0.025

Dense turf

0.035

Pasture

0.35

Dense shrubbery and forest litter

0.40

For developed sites where upstream areas contribute their flows primarily via pipes and channels, an estimate must be made of the actual flow time in those pipes and channels, plus a quantity referred to as the “inlet time", which is the time required for the water to flow overland from the most remote area within the catchment area to the drop inlet or catch basin. Inlet times in developed industrial areas with closely spaced storm drains are customarily taken as 5 minutes. Once inside the sewer line, flow time depends on flow velocity, which itself depends on flow rate. Initially this may appear to be an overwhelming task requiring a complex iterative procedure, but it should be remembered that the flow velocity is more dependent on conveyance dimensions (pipe diameter, ditch cross section) and gradient, both of which are fixed and known, than on the flow rate. Thus, with a reasonable estimate of the influent flow, sometimes taken as the capacity of the upstream influent pipe or ditch, the travel time can be approximated accurately enough once the conveyance dimensions, gradient, and roughness coefficient for the upstream conveyances are known. Velocities are normally calculated using Manning's Formula, described later. The time of concentration equals the sum of travel times for the various parts of the route from the hydraulically most remote point in the catchment area, including initial inlet time. Note that time of concentration is cumulative as the designer proceeds from the upstream to the downstream areas. The calculations performed to determine Tc for the uppermost reaches need not be redone as the process moves downstream. These times only need to be accumulated as the process moves downstream. For small areas within a plant that may be flowing through a series of laterals to a main or a sub-main, it would not be unusual to calculate a time of concentration as short as 10 minutes. An example problem illustrating the use of the Rational Formula to determine a flow rate is provided as Example Problem No. 3 in APPENDIX A. Runoff Volume Calculation Using Simple Methods If the entire runoff volume is the only parameter of interest, all that is needed is the design storm (return period and duration), catchment area, and a suitable runoff coefficient. Runoff coefficients for this purpose are similar to those described for use in the Rational Formula, and can be viewed in simple terms as the fraction of the incipient rainfall that becomes runoff. A design example is presented below for discussion purpose, and is also included as Example Problem No. 4 in APPENDIX A. The simplest application of the above, on a small industrial catchment area 70 ft x 170 ft (21 m x 52 m), would be to assume a runoff coefficient of 0.9, for a paved industrial area. If the design rainfall amount were specified to be the 10 year 24 hour storm, which for Houston Texas is 8.5 in. (216 mm), the volume of runoff (Vr) would be Vr = 0.9 x (8.5 in./12) x 0.27 acres = 0.172 ac ft = 56,000 gallons (Vr = 0.9 x 0.216 m x 1,092 m2 = 212 m3) ExxonMobil Research and Engineering Company – Fairfax, VA

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HYDROLOGIC DESIGN (Cont) A somewhat more sophisticated approach is the use of the runoff Curve Numbers (CN) as developed by the USDA/SCS. This methodology is intended mainly for use on undeveloped acreage, but it can be applied to other small watersheds. The method takes into account the degree of surface imperviousness in a more rigorous manner than the broad based coefficients used in the Rational Formula. The method takes into account the initial interception and depression storage that occurs as a result of surface irregularities, and it takes into account the rate at which infiltration can consume a portion of the incipient precipitation. Theoretically, these factors are already included in the coefficients used with the Rational Formula, but there is no direct connection between the two methods. For nearly impervious surfaces, such as paved areas within a plant, the CN is very high, and the portion of the runoff that is consumed by the initial depression storage and infiltration during the storm are consequently both very low. Conversely, for unpaved surfaces, or areas covered with vegetation, the above two factors consume a considerable portion of the incipient precipitation. If a particular catchment area includes several types of land use and cover, the CN approach is probably preferred. It is in some ways less judgmental and easier to document, which may be of importance if third party review or approval is involved. Curve Numbers (CNs) for various land uses and various soil types are presented in numerous references (e.g., Design of Small Dams, U.S. Bureau of Reclamation, 1974). An abbreviated summary is included in this Design Practice as Figure 7. The method is fairly easy to use. Surfaces are classified in accordance with their land use, and in accordance with the soil type. The catchment area is broken up into sections of approximately uniform land cover and soil type, and a weighted average CN is developed for the catchment area. The direct runoff (Qd, in.) is then calculated according to the following formula or read directly from a graph such as Figure 7. Qd =

(P

− 0 .2 S ) 2 P + 0 .8 S

where: S

=

P = CN =

Eq. (6)

1000 − 10 CN total precipitation USDA / SCS Curve Number

For the previously described example (10 year, 24 hour storm at Houston, Texas), in an industrial area with CN = 92, the direct runoff (Q) and runoff volume (Vr) would be: Qd =

(8.5 − 0.2 (0.8696 )) 2 (8.5 + 0.8 (0.8696 ))

= 7.5 in.

Vr = 7.5 in./12 x 0.27 acres = 0.169 ac ft = 54,980 gallons Had a CN of 95 been selected, the calculated direct runoff would be 7.9 in., and the corresponding runoff volume would be 57,900 gallons. These two CNs bracket the assumption of a runoff coefficient of 0.9 in the previous method. While the Curve Number method is somewhat more complex than a simple runoff coefficient, it has the advantage of being compatible with most of the methods used to produce complete runoff hydrographs, many of which are included within the more common drainage system modeling programs (e.g., XP-SWMM, TR-55). Storm Runoff Hydrograph There may be occasions when it is desired to produce the complete storm runoff hydrograph for one or more return period storms at a given site. For example, a complete hydrograph is generally needed if the issue is temporary detention of storm flows in on-line or off-line storage, unless it is planned to contain the entire runoff flow. The latter is generally impracticable for return period storms larger than one or two year events, and even then a substantial amount of land is required for the detention basins. Nevertheless, if retention of the entire storm runoff is required, the simpler manual calculation methods described in the previous section would be sufficient. If it is intended to contain only a portion of the runoff, such as the first 30 minutes, synthesis of the entire hydrograph would be required. It should be noted, however, that in cases such as this, it is likely that a sophisticated sewer system routing analysis would be required anyway (discussed in following section). The computer programs that perform system routing also include routines for developing the runoff hydrograph, which is one part of the input required for the storm response modeling. While the techniques to develop a runoff hydrograph are simple enough to be programmed in a BASIC program or a spreadsheet, it is unlikely that these would be used out of context of a formal sewer system routing analysis. Therefore, only the concepts involved in constructing a runoff hydrograph will be described here. Techniques for creating a runoff hydrograph from rainfall are provided in references (SCS National Engineering Handbook, Section 4) and (Design of Small Dams).

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HYDROLOGIC DESIGN (Cont) The input parameters for synthesizing a runoff hydrograph when given only the total rainfall amount (presumably from a rainfall atlas), are similar to those described in the previous sections. Parameters include watershed imperviousness, which is analogous to the runoff coefficient in the Rational Formula. The SCS curve numbers (CNs) are in fact used directly in some hydrograph synthesis methods. Watershed topography is also needed to set lag times for individual sub-drainage areas within the watershed. This is analogous to the time of concentration concept in the Rational Formula. Mini-hydrographs from subdrainage areas of the watershed will not, in most cases, line up peak to peak. Rather, they will be offset by their respective travel times. Finally, the rainfall distribution throughout the storm (i.e., rainfall rate at various points in the storm, also know as the rainfall hyetograph) is needed. This is analogous to the rainfall intensity in the Rational Method, although the Rational Method concerns itself only with the instantaneous peak rainfall intensity applicable to the particular component of interest (i.e., a single pipe or ditch for which the peak flow is desired). The SCS methods used in TR-55 and other urban runoff models builds the watershed hydrograph from a series of dimensionless unit-hydrographs which are determined by the geometry of the particular catchment area. The unit hydrographs for increments within the storm are then converted to runoff hydrographs by means of the runoff coefficients, and are then added together, offset as appropriate according to their time position within the storm, to arrive at a consolidated runoff hydrograph for the entire storm. The result is a plot of flow rate (e.g., cfs) as a function of time from the start of the precipitation event to the effective end of the runoff. The end of runoff occurs some time after the rain has ceased, as would be expected. An example of a runoff hydrograph is presented as Figure 8. The storm runoff hydrograph provides the peak flow, the total runoff volume (area under the hydrograph curve), and the time at which peak flow would occur. Fractional volumes at various points through the storm can also be obtained from the area under the curve. Development of the complete hydrograph may be viewed as an unnecessarily complicated means of obtaining something as simple as a peak flow rate. However, once the designer has obtained or written the necessary program or spreadsheet, it is as easy to obtain the complete hydrograph as to compute a single peak flow. All that is needed is the total storm depth and duration, the weighted runoff curve number (CN), the length and elevation difference (for time of concentration), and the catchment area. Note that these input parameters, or comparable ones, would have been required for the simpler hand calculations using the Rational Formula. Sewer System Flow Routing; Computerized Models Computer modeling of storm sewer systems has been a part of storm drainage and design since the mid-1970s. Several Federal agencies in the U.S. undertook to develop software for this purpose, including the U.S. Army Corps of Engineers with their Storm Treatment and Overflow Runoff Model (STORM) and their previous HEC-1 and HEC-2 series models. The U.S. Soil Conservation Service (SCS) developed their program TR-20 and later specifically adapted it to urban areas in a procedure which has come to be known as TR-55. SCS did not develop computer programs for TR-55, but private vendors have done so and market them as TR-55 solutions. Finally, the U.S. EPA developed the Storm Water Management Model (SWMM) specifically for the analysis of combined sewer systems (storm and sanitary flows) to enable the analysis of response to single storm events. PC based versions of all of these programs are available, either from the sponsoring agencies or from private vendors. Except for the STORM model, the models are well suited to handle the common problem of routing a specific storm though a sewer system, taking into account live storage within the system as well as off-line detention facilities. All of the models, including STORM, can evaluate the potential for drainage design problems such as temporary flooding. A few can take into account the effects of surcharging on sewers (i.e., lines flowing full with the pressure head higher than the top of the pipe). A listing of some of the major features of the most generally accepted models is provided in the following Table 3. Although some of the models purport to be able to predict water quality as a function of time within the runoff hydrograph (referred to as “pollutographs"), the methods to predict storm water quality during passage of a runoff event are best described as being in their infancy. This is due in a large part to the lack of scientifically controlled studies on the pollutant removal efficiencies of detention facilities. While these models may not presently be appropriate for making definitive predictions of water quality in runoff, they are certainly appropriate for determining the hydraulic and hydrologic response of sewer systems to storm events, including determinations of runoff volumes at various points within a storm event. The process of implementing a model, including collecting the necessary input data (pipeline sizes, lengths, gradients, catchment area sizes and characteristics), setting up, and de-bugging the model is a major task. Experience with a few U.S. refineries that have made use of a private vendor version of the SWMM model (XP-SWMM) indicates that it can require 1 to 3 man-months for a 500 acre (200 hectare) site. In view of the cost associated with such an effort for a major refinery or chemical plant, it is clear that use of a sophisticated system model can only be justified when there is no other way to work the problem. In general, the simplest method that provides the desired analysis should be used.

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HYDROLOGIC DESIGN (Cont) TABLE 3 OVERVIEW OF STORMWATER MODELING COMPUTER PROGRAMS ATTRIBUTE Sponsoring agency

STORM

SWMM

HEC-1

STORMCAD

COE/HEC

EPA

SCS

COE/HEC

Haested, Inc

Number of pollutants

6

10

None

None

None

Rainfall/runoff analysis

Y

Y

Y

Y

Y

Sewer system flow routing

N

Y

Y

Y

N

Surcharge

N

Y

N

N

Y

Flow regulators, overflow structures, weirs, etc.

Y

Y

N

N

Y

Storage analysis

Y

Y

Y

Y

N

PC versions available Data and personnel requirements Overall model complexity

➧

TR55

N

Y

Y

Y

Y

Low

High

Medium

Medium

Low

Medium

High

Low

High

Low

STORMCAD is relatively easy to use and is best suited for sizing pipes in a network for the peak flow from a given return period storm, or for evaluating the peak flow capacity of an existing system during various storm events. XP-SWMM is a complex watershed model used mainly for determining flow rates and runoff volumes at any point in the network at any time during a runoff event. It's capabilities and data input requirements are considerably more involved than those associated with STORMCAD. More complete descriptions of these programs are provided in Section XXIX-N.

HYDRAULIC DESIGN The objective of hydraulic design is determination of the conduit dimensions necessary to carry the design flows. For pipes, the critical dimension is the diameter. For open channels, the required dimensions are the channel depth, bottom width and side slopes. Slope or gradient is a factor for both pipes and channels, although the designer normally has less control over gradient as a design variable. Gradient is usually limited by existing topography, i.e., the elevation of the point of interest vs. the elevation that the pipe or ditch must tie into. Materials that a pipe is constructed of, or channel lining materials for the case of open channels, is another variable over which the designer has some control. The pipe material or channel wall determines the conduit's frictional drag properties, which affects the flow capacity for a given set of dimensions and gradient.

BASIC HYDRAULIC DESIGN CONSIDERATIONS Storm drainage systems are normally designed to flow as open channels as opposed to pressurized conduit flow. This concept is easy to accept for open ditches, but it also applies to buried drainage pipes. When buried pipes are flowing as partly full channels, the condition is often referred to as “gravity flow" to distinguish from pressurized flow. Buried pipes behave as open channels as long as they are large enough to not flow full when delivering the design flow. Restricting the design to open channel flow simplifies the design calculations to the extent that the energy grade line and the hydraulic grade line are essentially parallel to the channel bottom, or pipe invert. This creates a minor computational inconvenience when determining the hydraulic radius of a pipe or ditch, which varies with the flow depth, but it allows the gradient to be treated as an independent variable, essentially equal to the pipe slope. As mentioned above, since gradient is for all practical purposes fixed by the site topography, it is convenient to allow it to be treated as an independent variable. The designer then needs only to consider the respective friction coefficients and available diameters of the various pipe materials in order to size the pipe to carry the design flow. Buried sewer lines do in fact pressurize and flow under a condition referred to as “surcharge", which occurs whenever the applied flow is greater than the capacity of the pipe flowing full under gravity flow. Normally, the maximum pressure head that is assumed is the water level ponded over the downstream manhole, or the ground surface elevation at that manhole. Since storm drains can be sized for storms as small as 2-year events, it is not uncommon for them to be surcharged whenever a larger storm is applied. However, calculating the flow capacity during a surcharge condition is a much more complicated undertaking, as it may require treatment of the sewer system as a pipe network, with variable surcharge heads at each junction (manhole). Therefore, sizing the pipes to insure that they flow as individual open channels (i.e., the less than full condition) simplifies the calculations.

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HYDRAULIC DESIGN (Cont) The presence of seals in an industrial sewer can present special problems which need to be considered in design. For example, if the outlet of a manhole into which a pipe flows is higher than the pipe invert, which might be deliberately done to insure a vapor seal, then portions of that pipe may flow as a full conduit with the hydraulic grade line dictated by the tailwater elevation in the manhole. The mere presence of an inverted elbow, which is another common means to effect a vapor seal (see Figure 9), would not cause the pipe to flow as a full conduit so long as the liquid level in the manhole is less than 2/3 the pipe thickness. There are also physical considerations that encourage the designer to restrict sewer design to a non-pressurized condition. While joints in new sewer lines are practically leak proof under the nominal pressures applied to the sewer, sewers (other than force mains) are generally not designed to be leakproof under pressurized flows. Water escaping through joints or defects in a sewer wall during surcharge events often returns to the sewer when the storm has receded, but in the process it can carry with it soil from the outside of the line. This gradually weakens the soil-structure arch that contributes a portion of the sewer's structural strength. This is the classical case of gradual deterioration of the line due to frequent surcharging. Thus, frequent surcharging of buried sewers is generally viewed as a poor practice primarily because it tends to shorten the service life of the system. Another practical constraint on sewer design is the flow velocity. Flow velocity must be kept above a certain minimum to ensure that grit and other debris does not build up in the line or channel. For pipes, which tend to be more difficult to clean than channels, it is customary to keep the flow velocity limits at least 2.5 fps when the pipe is delivering the design flow at its design depth (typically 0.7 times the diameter). At the other extreme, maximum velocities are usually limited by erosion and scour considerations. For pipes, it is customary to limit the maximum velocity to about 10 fps. Occasional bursts of over 10 fps are not likely to cause any damage to pipes in good condition. For channels, the maximum velocity is set by erosion considerations, which are dictated by the material used in the channel lining (if any). Another complication unique to petrochemical plants is that firewater return flows may control the design of the laterals, which might otherwise be sized to carry smaller storm flows. While flow velocity limitations may appear to present another variable to an already complex problem, the velocity when flowing partly full is more dependent on the gradient than on the pipe dimensions. The gradient is often fixed by topographic considerations, simplifying the designer's task somewhat by removing gradient as a variable. Indeed, there are cases in which the designer would like to have the luxury of treating pipe slope as a variable, but more often the gradient will be fixed by other constraints and therefore out of the designer's control. Under these circumstances, the designer need only select the conduit dimensions and check to see that the design flow can be accommodated in the pipe flowing partly full at velocities within the generally accepted limits. If the gradient is too flat to allow the minimum velocity to be attained, use of a smaller or larger pipe will unfortunately not make a large enough difference. That conduit will simply require more frequent maintenance (flushing) than would have been required if a better velocity mix could have been achieved. As a practical matter, topography within an industrial site is usually fairly flat, so the designer will have a fairly narrow band of gradients to consider. For flow in open channels, it is customary to provide some nominal freeboard to keep the flow from jumping out of the channel and to account for undulations in the water surface which might be present if the water is flowing relatively fast. A minimum of one ft or one velocity head (V2/2g) is a customary allowance. If the consequences of the flow jumping the channel are significant at any particular location, it would be reasonable to an increase in the freeboard requirements at that location. Similarly, ride-up on bends in an open channel is accommodated by providing additional freeboard, estimated on the basis of the centrifugal forces on the flowing stream. Flow in buried pipes and in open channels is defined by Manning's Equation (in Customary units), as follows V( fps) =

1.49 2 / 3 1/ 2 R S n

where: n

=

R

=

S

=

Eq. (7)

Manning's roughness coefficient (frictional drag coefficient), which depends on the pipe or ditch material Hydraulic radius, which is the flow area divided by the wetted perimeter, ft. For pipes flowing full, it is simply half the radius, but for pipes flowing partly full it must be calculated and is a function of the flow depth. For open channels it also must be calculated for each flow depth. Pipe or channel gradient (slope) in decimal form (e.g., 1.5% slope is S = 0.015).

In metric units, Manning's Equation is V (m/s ) =

R2 / 3 S1/ 2 n

where R is in meters

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Eq. (8)

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HYDRAULIC DESIGN (Cont) Since the water is incompressible, continuity requires that Q = VA where: A

Eq. (9) =

The cross sectional area of flow. For pipes flowing partly full and for open channels, A also must be calculated as a function of flow depth.

HYDRAULIC DESIGN OF BURIED SEWER PIPES Manning's Equation is used in an iterative process to size the line for given design flow. Except for the fact that R varies with flow depth, the calculation is simple and straightforward. Normally the gradient is fixed, and the design flow has been calculated. The first task is to select a pipe diameter that will deliver the design flow at a flow depth of approximately 0.7 times the diameter. Since the friction coefficient “n" varies with pipe material, it is also necessary to select a trial pipe material. Prior to the advent of PCs and programmable calculators it was customary to select a trial diameter (D), assume a trial depth of 0.7 D, and then read R and A from a table or a chart such as Figure 10 for that trial D. Given S and n, and R and A from the chart, the flow at depth = 0.7 D could be calculated using Manning's Equation. If the calculated flow was smaller than the desired design flow, a larger pipe was selected and the process repeated. Each pipe diameter required a separate trip to the chart to define R and A, which are both functions of D and depth. It is a simple matter to program the expression for R and A into a spreadsheet or a BASIC utility program. The derivation of the algorithms is provided in APPENDIX B. Manning's roughness coefficients have been tabulated for the common materials used in sewer pipes, and a summary is provided in Table 4 below. For the materials commonly used in industrial sewers, it can be observed that the Manning's “n" does not vary much from the from the range of 0.011 to 0.015 listed for concrete, mortar lined cast iron, vitrified clay, and plastic pipe. To account for wear and corrosion that may occur as pipes age, it is customary to select “n" values at the upper end of the range for design purposes. TABLE 4 MANNING'S COEFFICIENT “n" FOR COMMONLY USED DRAINAGE PIPE MATERIALS RANGE OF MANNING'S “n"

COMMON DESIGN VALUE

Asbestos-Cement pipe

0.011 - 0.015

0.013

Brick

0.013 - 0.017

0.015

Cast iron pipe, cement mortar lined and seal coated

0.011 - 0.015

0.015

Concrete pipe

0.011 - 0.015

0.015

Plain

0.022 - 0.026

0.024

Paved invert

0.018 - 0.022

Spun asphalt lined

0.011 - 0.015

MATERIAL

Corrugate metal pipe (1/2 in. x 2-1/2 in. corrugations)

Plastic pipe (smooth)

0.008 - 0.015

0.011 *

Vitrified clay pipe

0.011 - 0.015

0.013

* Plastic pipe manufacturers claim that a value of 0.009 can be used for HDPE pipe and 0.010 for PVC pipe, while ASCE leans toward the higher value within a range of 0.011 to 0.015. Since plastic pipe is generally viewed to be less susceptible to corrosion, pitting, tuberculation or biological growth, it is not necessary to design for the upper limit of the friction coefficient. A value of 0.011 is considered a reasonable compromise. An example problem illustrating the use of Manning's Formula for a buried pipe flowing partly full is provided as Example Problem No. 5 in APPENDIX A.

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HYDRAULIC DESIGN (Cont) HYDRAULIC DESIGN OF OPEN CHANNELS As in the case of buried pipes, Manning's Equation is also used in an iterative process to arrive at a set of dimensions for open channels. However, in the case of open channels there is an infinite number of combinations of bottom width and side slopes which could be hydraulically satisfactory. Gradient is usually restricted by topography, but it is not uncommon for an open channel to more or less follow the lay of the land (within reason). The intent is to avoid excessive excavation depths while still providing a reasonable bottom gradient, the required flow depth, and a reasonable freeboard allowance. Open channels, by virtue of their large cross section, are capable of conveying considerably greater flows than closed pipes. However, practical limitations on channel cross section include the obvious space limitations which may be applicable in confined areas. In open terrain, side slopes can be laid back at slopes of 1(vt) on 3 (hz), which allows a vegetative cover to be established. 1 on 3 slopes are probably near the limit of what can be practicably mowed, and slopes as flat as 1(vt) on 6(hz) are preferred if regular mowing is contemplated and if space permits. In confined areas, steeper slopes would be required. If side slopes are steeper than about 1.25 (hz): 1 (vt), vegetative linings will be precluded. Rip-rap linings, gabions, or paved lining (concrete or asphalt) may be required for these steeper slopes. Flow area that is lost as the side slopes are steepened generally has to be compensated by a wider bottom width, although channels with steeper side slopes are hydraulically more efficient than extremely broad ditch sections. In any case, both the channel side slopes and the bottom width are dimensions that the designer may choose to vary. Open channel flow is categorized as either sub-critical or super-critical, based on the hydraulic principle that open channel flow with a given specific energy can flow at either of two conjugate depths. The sub-critical, or “tranquil", flow regime is characterized by deeper flow depth and a slower velocity, while the super-critical, or “shooting flow", regime has a shallower depth but a higher velocity. The channel should be designed to assure that the flow will remain either sub-critical or supercritical and will not shift from one to the other except under deliberately controlled conditions. Even if the design results in subcritical flow for the design storm, the conditions that would occur when passing larger events should be checked. The condition of rapid changes from one flow regime to the other is referred to “rapidly varied flow", and it involves hydraulic jumps and “holes" in the water surface. These are inherently difficult to control, which is the reason that changes from one flow regime to the other should be avoided or at least controlled. Similarly, any changes in the channel geometry from one section to the next need to be accomplished gradually to avoid triggering a hydraulic jump or a shift to super-critical flow. Manning's coefficients for various types of open channel linings are tabulated in a number of references. Typical values for Manning's “n" for various open channel conditions that might be encountered in practice are presented in Table 5. TABLE 5 MANNING'S COEFFICIENT “n" FOR COMMONLY USED FOR OPEN CHANNELS CHANNEL CONDITION Lined Channels

Excavated or Dredged Channels

Natural Channels (Minor Streams)

MANNING'S “n"

DESIGN VALUE

Asphalt

0.013 - 0.017

0.015

Concrete

0.011 - 0.020

0.016

Rubble or rip-rap

0.020 - 0.035

0.035

Vegetative cover (grass)

0.030 - 0.040

0.035

Earth, straight and uniform

0.020 - 0.030

0.025

Earth, winding but uniform

0.025 - 0.040

0.035

Rock

0.030 - 0.045

0.045

Unmaintained

0.050 - 0.14

0.1

Fairly regular section

0.03 - 0.07

0.06

Irregular section with pools

0.04 - 0.10

0.07

As is the case with computations for pipe flows, the calculations for flow in open channels can be computerized or can be carried out using nomographs. The problem can easily be set up in a utility BASIC or spreadsheet format. A summary of the derivation of Manning's solution for trapezoidal channels of any dimensions is presented in APPENDIX B. A design example of the solution of Manning's Equation for an open channel problem is presented as Example Problem No. 7 in APPENDIX A.

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HYDRAULIC DESIGN (Cont) Freeboard requirements are generally based on velocity, although a minimum of 1 ft is sometimes specified. relationship to velocity is: Hfb =

A simple

Cfb d , ft

where: Cfb = d

=

Coefficient varying from 1.5 for channels with capacities of 20 ft3/s to 2.5 for channels with capacities of 3000 ft3/s or more Depth of flow, ft.

Superelevation, or “ride-up" on a curve can be calculated as: h=

V 2 Tw g rc

where: h V Tw g rc

= = = = =

Additional elevation, ft Velocity, ft/s Top width of the channel, ft Gravitational constant Radius of curvature, ft.

This expression is also valid for metric units provided consistent units are used.

CULVERT CROSSINGS OVER OPEN CHANNELS A consequence of the use of open channels is the requirement to provide bridges over the channel at various locations. Most often this is accomplished by the used of pre-fabricated pipes, either CMP (corrugated metal pipes) or concrete pipes. The primary design consideration is to provide a waterway opening large enough to allow the design flow to pass through the culvert without backing up water excessively on the upstream side. The depth required to force the water through the pipe must be lower than the roadway elevation (unless overtopping can be tolerated) and low enough so as not to cause upstream backwater effects (ponding) or upstream bank overflows. In general, it is unusual to select a pipe so small that the headwater required to drive the design flow through the pipe is more than twice the diameter of the culvert (total headwater depth measured from the pipe invert). Situations such as this often require consideration of several parallel pipes or shift to a hydraulically more efficient pipe-arch culvert or a bridge. Most culvert design is carried out using a set of nomographs developed by the Federal Highway Administration. The solution considers two possible controlling mechanisms:

•

Inlet control, wherein the flow through the culvert is limited by head losses at the entry point.

•

Outlet control, where the limiting factor is frictional losses incurred as the water flows through the pipe. The condition which requires the greater headwater (upstream side) for a given flow in a given pipe (or set of parallel pipes) is the controlling condition, and the headwater is then determined according to that condition. If the required headwater depth is excessive, then a larger culvert must be considered. Outlet control nomographs can be derived by considering Bernoulli's' equation for conservation of energy, continuity for conservation of mass, and using Manning's equation to relate frictional energy losses to flow velocity. The outlet control nomographs can therefore be adapted to simple spreadsheets or BASIC programs. However, the inlet control solution is based on experimental work on pipes of various diameters and various inlet conditions (e.g., projecting, mitered) that was sponsored by the US. Dept. of Transportation, Federal Highway Administration in the 1950s. Some programmed solutions exist, but it remains common practice to rely on the nomographs, which are reproduced here as Figure 11-A through D. Since the nomographs are needed for the inlet control condition, it is customary to use the parallel set of outlet control nomographs as well. However, the use of the nomographs forces a trial-and-error solution. Nomographs included in Figure 11 are only for circular corrugated metal and circular concrete pipes. There are additional charts provided in other reference for special sections such as elliptical pipes and pipe-arch culverts. (e.g., Design of Small Dams). Typically, the designer will have a design flow, determined as described earlier in this Design Practice. For a starting point, it is reasonable to assume the flow velocity through the culvert will be no more than 10 fps (3 m/s), which allows the selection of a trial pipe size. The pipe is then checked against the “Inlet Control" nomographs, for the pipe type (corrugated metal or concrete pipe) and entry conditions (headwall, mitered pipe, or projecting pipe). The headwater required to deliver the design flow is then read from the nomograph. If the headwater required is greater than what can be accommodated at the crossing (e.g., if the headwater would imply water flowing over the crossing or backing up water such that it flows out of the ditch), then a larger pipe is selected.

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HYDRAULIC DESIGN (Cont) Once a satisfactory solution has been achieved for the inlet control condition, the pipe is checked against the “Outlet Control" nomograph. For this, the length of the pipe is a factor, which is not surprising given the nature of the outlet control solution (friction losses along the pipe). Tailwater, the depth of water at the pipe outlet, is also a parameter. If it is unknown, or can be assumed to be low enough so as not to impeded flow in the pipe, the tailwater is set at 0.85 times the pipe diameter. (The assumption here is that if there is no tailwater, the flow in the pipe will drop through critical depth near its outlet, and 0.85D is a sufficiently accurate representation of this condition) The nomographs require selection of an entrance loss coefficient (Ke), but the solution is generally not sensitive to this. Assuming Ke = 0.9 is the more conservative approach (i.e., greater head loss at entry implies slightly higher total energy losses in the pipe, hence slightly higher headwater requirement). The total head required at the upstream end to drive the design flow through the pipe is the sum of the head determined via the outlet control nomograph plus the applicable tailwater (if any). If this implies a higher headwater elevation than that defined as acceptable by the inlet control nomograph, then the flow is outlet controlled for this pipe diameter and this flow. The process would need to be repeated for the next larger pipe size. Conversely, if the outlet control analysis results in a lower headwater elevation than that previously determined as acceptable for the inlet control condition, then the pipe is inlet controlled, and the pipe diameter selected in the inlet control analysis is adequate. An example problem illustrating the selection of a culvert size for a crossing is provided as Example Problem No. 8 in APPENDIX A. ➧

HYDROLOGY / HYDRAULICS ENGINEERING SOFTWARE A considerable amount of hydrology and hydraulics engineering softare is available in the public domain, which can be used to solve the types of problems discussed in the previous sections. One source of public domain software is the U.S. Department of Transporation Federal Highway Administration (FHWA). The FHWA software can be accessed fromt he world-wide web at www.fhwa.dot.govt/bridge/hyd.htm. The following hydrology and hydraulics engineering software is available on the website: HY7 WSPRO version 061698 (1998) - WSPRO, a water surface profile computation model, can be used to analyze onedimensional, gradually-varied, steady flow in open channels. WSPRO can also be used to analyze flow through bridges and culverts, embankment overflow, and scour at bridges. Minimum requirements: IBM PC/AT or compatible, DOS, 400 Kb memory HY8 Culvert Analysis version 6.1 - Culvert Analysis automates the design methods described in FHWA publications HDS-5, "Hyrdraulic Design of Highway Culverts," HEC-14, "Hydraulic Design of Energy Dissipators for Culverts and Channels," and HEC-19, "Hydrology." Minimum requirements: IBM PC or compatible, DOS 2.1 or higher HY22 Urban Drainage Design Programs - The programs perform the following hydraulic tasks in Metric or Customary units:

•

Drainage of Highway Pavements

• •

Open Channel Flow Characteristics

•

Development of Stage-Storage Relationships

Critical Depth Calculators

•

Reservoir Routing Minimum Requirements: PC or clone, MS-DOS HYDRAIN 6.1 (1999) Integrated Drainage Design Computer System - All the programs included with this release of HYDRAIN can perform calculations and present results using either Customary or Metric units. HYDRAIN contains the following programs:

•

HYDRO generates rainfall estimates, peak runoff estimates, and /or hydrographs.

•

HYDRA is a pipe network hydraulics program used to model an existing storm drain/sewer system or to design a new system. HYDRA generates storm flows by using either the Rational Method or by accepting a hydrograph generated by a HYDRO analysis.

•

WSPRO is a step backwater program for natural channels with an orientation to bridge constrictions. HYDRAIN contains a DOS graphic user interface for use with the WSPRO executable.

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HYDRAULIC DESIGN (Cont) •

HY8 is a program that presents HDS-5 procedures for analysis and design of highway culverts, design of energy dissipators, storm hydrograph generation, and reservoir routing upstream of a culvert. Culvert hydraulics computations for circular, rectangular, elliptical, metal box, high and low profile arch, and arch shapes as well as for a user-defined geometry are performed.

•

NFF is the USGS-developed flood frequency program. It summarizes techniques for estimating peak-flood discharges and associated flood hydrographs for a given recurrence interval or exceedance probability of unregulated rural and urban watersheds.

•

HYCHL is a program which assists in the analysis and design of roadside channels and riprap lining. The program follows the FHWA procedures presented in HEC-11 and HEC-15. Minimum Requirements: IBM XT/PC compatible, DOS 3.0 or higher, 7 Mb disk space, 560 K RAM free.

STRUCTURAL DESIGN The objective of structural design is to determine the pipe type and wall thickness necessary to carry the loads from the overlying soil and any transient or permanent surface loads that may be imposed. For open channels, structural design is limited to providing an adequate lining that can withstand the erosive forces of the design flow. For most pipe materials, structural design has evolved into a set of standards which are published and maintained by the industry groups for each of the more commonly used pipe material types. An exception is the design of plastic pipe, which at the present time has not been consolidated into a single industry standard. For plastic pipe, structural design is often carried out in accordance with individual manufacturers' design manuals. Nevertheless, if a designer already has decided upon a pipe material, he can refer directly to the applicable industry standards or manufacturers' literature, wherein design charts and tables for various depths of burial and soil conditions are addressed. The following discussion provides background into the theory upon which these industry standards and design manuals are based. The structural design of pipes involves two parts, which are to some degree dependent upon each other. The first is the determination of the earth loads and other surface loads such as traffic that are imposed on the pipe. The second is the determination of the stresses in the pipe wall, and selection of a thickness adequate to resist them. The latter determination may be dependent on yield stresses or on deformation considerations, depending on the type of pipe.

DETERMINATION OF LOADS IMPOSED ON A BURIED PIPE The earth loads imposed on pipes are in all cases based ultimately on the dead weight of the overlying soil. In most cases the calculation of earth loads is based either on the Marston Formula, which takes into account the ability of the soil to arch over the pipe, or the simple prism of soil directly over the pipe, neglecting any arching that might occur. The Marston formula was originally published in 1930, based on research into loads on buried rigid pipes carried out at the University of Iowa. It was later expanded in the 1940s to include loads on flexible pipes. Deciding which formulation is more appropriate for use in determining the earth load on a pipe depends on consideration of the pipe's rigidity and the potential for the backfill in the trench to settle, allowing it to mobilize the shear strength along its sides and produce the arching effect. In general, if a pipe is rigid but is buried in a trench that will of settle somewhat relative to the natural ground in which the trench was excavated, the Marston load is the appropriate method for determining the earth load on the crown. Consequently, the Marston load is usually used for rigid pipes (concrete, reinforced concrete, vitrified clay pipe) that are buried in a conventional cut-and-cover installation, even when the backfill overlying the pipe is well compacted. This is the most common field condition, and the primary application of the Marston load. By similar reasoning, if a pipe is flexible enough to compress under the imposed earth loads, then the Marston load should also be applicable. The key factor here is that the backfill is assumed to move downward relative to the natural ground, thereby mobilizing some degree of side shear, and producing the arching effect reflected in the Marston approach. Notwithstanding the above, flexible pipe design can be carried out using either the Marston load, which takes arching into account, or by calculating the dead weight of the simple soil prism directly over the pipe, neglecting arching. Ductile iron pipe, corrugated metal pipe, and steel pipe are customarily designed using the simple soil prism, while some plastic pipe (HDPE) is designed using either method.

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STRUCTURAL DESIGN (Cont) It is commonly assumed, and often stated in the literature, that the prism load is the more conservative approach, i.e., results in a greater calculated load on the pipe crown. A comparison of the two methods shows that this is the case only if the Marston load, calculated on the basis of the ditch width and not the pipe width, is assumed to act over the entire ditch width rather than simply over the pipe crown. As discussed in more detail below, the ditch width dimension that is used in the Marston Formula is customarily assumed to be 3 to 4 ft (1 to 1.2 m) wider than the pipe diameter, thereby providing the construction space necessary to allow alignment of the pipe and placement and compaction of the bedding material adjacent to the pipe. If the material adjacent to the pipe can be assumed to settle the same as the pipe deflection under load, then the assumption of spreading the Marston load over the entire ditch width is valid. Under these circumstances the prism load would be greater, and therefore more conservative. If, however, the fill adjacent to the pipe is more compressible than the pipe, or it settles more than the pipe, then the entire Marston load will be carried on the pipe crown, which is the assumption customarily made for rigid pipes. The presumption that the prism load is more conservative than the Marston load is valid only in context of the relative settlement of the pipe crown and the adjacent soil backfill, and is not solely dependent on the pipe being flexible, as is commonly assumed. Since the calculations are simple enough, the prudent designer may wish to calculate the earth component both ways before deciding on a method in cases where either approach can be used. In making this comparison it is necessary to convert one or the other loads to arrive on a consistent basis. For example, the prism load produces a simple pressure on the crown (p=gH), while the Marston method produces a load per unit length of pipe. The latter can be converted to a pressure to enable comparison to the presumptively more conservative prism load by simply dividing by the pipe diameter or the trench width, depending on the expected compression in the backfill adjacent to the pipe in comparison to the pipe crown. This reasoning leads some flexible pipe manufacturers to endorse a practice of using a design load for flexible pipes that is somewhere between the prism load and the Marston load. Whichever method is used to determine the earth load on the crown, the designer must bear in mind how that load will be used in subsequent calculations for pipe wall thickness. As is described in more detail later, rigid pipe design methods are based on Marston type loads, i.e., weight per unit length of pipe. Conversely, flexible pipe design methods are based on a pressure on the crown (weight per unit area of crown). Surcharges from overlying footings and/or traffic loadings are initially calculated as pressures. If these are being used in a rigid pipe design approach (concrete, reinforced concrete, VCP, some plastic pipe), they are converted to weight per unit length of pipe, as described later. If they are being used in a flexible pipe design approach (ductile iron, corrugated metal, steel, and most plastic pipe applications), they can be used directly as pressure (load per unit area) in the design procedures without conversion. Surface loads, such as passing vehicles, are assumed to be carried down to the pipe crown by elastic theory, most often either a Bousssinesq distribution or a simple stress distribution prism (e.g., 2 (vt):1 (hz) slopes). Most pipe manufacturers also recommend the use of an impact factor, which decreases with depth of burial, to be applied to the traffic induced portion of the distributed loads. The impact factor varies with the pipe material, from 1.3 for concrete pipes and 1.5 for ductile iron pipes with less than 1 ft (0.3 m) of cover, to 1.0 for pipes with 3 or more ft (1 m) of cover. Marston Formula for Earth Portion of the Total Load on Buried Conduits The most common application of the Marston load is for a rigid pipe buried in a trench, via a conventional cut-and-cover construction technique. In such a case, it is assumed that the soil prism that must be carried is the width of the trench, which is always a few feet greater than the pipe diameter. It is also assumed that some arching and redistribution of stress occurs along the walls of the trench as the backfill in the trench settles downward with respect to the natural earth adjacent to the trench. There are variations to the Marston formula that are applicable in special cases such as “tunneled in" pipes or pipes buried at the base of a fill. In these cases the relative settlement is not as described above, and the Marston load is calculated differently. This Design Practice is limited to the more common case of a pipe buried in a trench constructed by conventional cut-and-cover technique. The general form of the Marston Formula is: Wc = Cd w Bd2 where: Cd

w Bd

= = =

Eq. (10) Dimensionless coefficient that depends on the soil type and the trench geometry, Soil unit weight (pcf or kg/m2), Width of the ditch at the pipe crown in units consistent with the unit weight.

The formula produces a load on the conduit, W c, in lb/LF along the pipe. This load may be changed into a vertical pressure (in psi, PSF, or kg/cm2) for some design methods.

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STRUCTURAL DESIGN (Cont) The Marston coefficient Cd takes the form:

Cd =

1− e

æ H ö ç − 2 K u′ ÷ ç B d ÷ø è

2 K u′

where: K u′ H tan φ

=

1 − sin φ 1 + sin φ

=

Ka

= = =

tan φ Depth from the ground surface to the top of the pipe, Soil's frictional strength.

Note that the only place the depth over the pipe appears in the Marston derivation is in the H / Bd ratio in the exponent. The Marston Coefficient has been reduced to a graphical format, as shown in Figure 13. While it is not explicit in many of the references dealing with this formula, the five soil backfill conditions and their corresponding friction angles are as described in Table 6 below: TABLE 6 DESCRIPTION OF PARAMETERS IMPLICIT IN MARSTON COEFFICIENT BACKFILL CONDITION

DESCRIPTION

K u or K u′

f (arctan u)

A

Granular materials without cohesion

0.1924

30°

B

Maximum for sand and gravel

0.165

17°

C

Maximum for saturated topsoil

0.150

14°

D

Maximum for ordinary clay

0.130

11°

E

Maximum for saturated clay

0.110

9°

Ignoring for the moment the small differences in unit weights for sand and clayey backfills, it can be inferred from the above table, or from a plot of the Marston coefficient “Cd" (Figure 13), that the highest load on the conduit results from the curve for backfill condition E, while the lightest load on the conduit results from condition A. For all backfill types, the Marston Coefficient has reached its maximum value by about H/Bd ≅ 15 to 20. For the worst case (maximum load on the pipe), represented by Backfill Condition E, the maximum Marston coefficient is 4. 3 at H/Bd ≅ 20. For the lightest load on the pipe, represented by Backfill Condition A, the Marston coefficient reaches a maximum of 2.6 at H/Bd ≅ 15. The recommendations on the use of the Marston formula as presented by the respective manufacturers associations for the various types of sewer pipes differ in some details. A summary of current practice is presented in Figure 14. The most significant differences are in what is selected for the trench width (Bd, or width of the “ditch" in the Marston Formula). Obviously, the calculated load on the pipe crown is very dependent on this variable. Example Problem No. 9 in APPENDIX A illustrates the use of the Marston Formula to determine the earth component of the load on a buried pipe. Effects of Surface Live Loads or Other Surface Loads Surface loads are assumed to be transmitted to the elevation of the pipe crown by means of elastic theory. When used in conjunction with the Marston load, as would be the case for a rigid pipe, they are converted into a load per unit length that can be added to the Marston earth load to arrive at a total design load on the pipe crown. The fundamental assumption is that the surface loads will be spread out and attenuated on the way down to the pipe crown. Obviously, if the pipe is far enough below the surface, the live loads may be spread out to the extent that they offer no significant additional load on the pipe. If the loads are caused by traffic, it is customary to multiply the static load by an impact factor that varies from a maximum of 1.5 for pipes within 1 ft of the surface to 1.0 for pipes 3 or more ft deep.

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STRUCTURAL DESIGN (Cont) Two general cases of distributed loads are described in this Design Practice, which cover the more common applications expected in a plant. One is a static load that may be imposed by a footing or temporary load such as a crane directly over or near an underground pipe. That case is generally evaluated using influence diagrams such as the one provided as Figure 15. The other case is the standard AASHTO loading for trucks. In theory the approaches are similar to the extent that both take into account the vertical pressure over a finite loaded area at the surface, and then proceed to determine an effective area as a function of depth below the load. A summary of the stress distribution assumptions for truck loadings is provided in Figure 16. More comprehensive discussion of the topic can be found in soil mechanics texts. Distributed Loads, by Newmark's Integration of Boussinesq Equations For a uniform load over a finite area of known dimensions over a pipe of known depth, the general form of the equation is Wsd = Cs p Fi Bc where: Wsd p Fi Bc Cs

= = = = =

Load on the sewer pipe in pounds per unit length, Intensity of the distributed load at the surface, in units of W/L2, Dimensionless impact factor (for traffic or railroad loads, if applicable), Width of the sewer pipe, Dimensionless load coefficient which is a function of dimensions of the loaded area (length and width) in comparison to the depth to the crown of the sewer pipe, as described on Figure 15.

Note that by multiplying by the pipe width Bc, the pressure is converted to a load per unit pipe length. As described in the following sections, structural design methods for selecting pipe wall thickness for rigid pipelines requires a determination of the load on the conduit in pounds or kips per unit length of pipe. The load calculated as described above, wherein the conversion has been made to load per unit length, can be combined directly with the Marston load to determine the total load on the crown so that the wall thickness selection can proceed. For distributed loads that are not centered over the pipe, the effective load can be determined by breaking the area into separate rectangles each of which has one corner over the point in question, and then adding or subtracting the coefficients for the rectangles (i.e., superposition) as appropriate to arrive at the coefficient for the offset loaded area. Note that in assigning a coefficient for each of the rectangles, the coefficients in the table on Figure 15 need to be divided by 4 to account for the fact that the loaded point is under a corner, as opposed to the center, of each of four sub-areas. An example of the load on a buried conduit caused by a rectangular loaded area above and just offset from the pipe is provided as Example Problem No. 10 in APPENDIX A. Distributed Loads for Highway Vehicles If the pavement has been designed for heavy truck traffic, the pavement's effect is to substantially reduce the wheel pressure to the extent that the effects of traffic load on a buried pipe can generally be neglected. This is true for concrete pavements and heavy duty flexible (asphaltic concrete) pavements. Conversely, relatively thin pavements do not reduce the pressure transmitted to an underlying conduit to any significant degree. For the purposes of determining the effect of traffic loads on buried conduits, any gravel roadway or chip-and-seal surface would be treated as an unsurfaced roadway. Since it is more likely that paved roadways within an industrial plant will have been designed for only occasional passage of heavy truck traffic, the methodology used to take such traffic into account when determining loads on a buried pipe is needed, and is presented below. The standard highway truck loading is the AASHTO HS20 Load or the AASHTO Alternate Load. The standard AASHTO HS20 load involves a front axle with two wheels at 4,000 lb (1,800 kg), six ft apart (see Figure 16). Design is however controlled by the rear axle which is 32,000 lb (14,500 kg) carried on two sets of dual wheels, each set loaded to 16,000 pounds (7,250 kg) and centered six ft (2 m) apart. The alternate load is the common tandem set of dual wheels commonly associate with a semi tractor-trailer. In the alternate loading, each of the four sets of dual wheels carries 12,000 lb (7,260 kg), spaced 6 ft (2 m) apart left to right and 4 ft (1.2 m) apart front to back. Finally, if the roadway is a two lane roadway, the design loading condition may need to consider the “passing" condition which places two HS20 trucks next to one another, with the centers of the dual wheels spaced 4 ft (1.2 m) apart. From the above discussion it is obvious that the critical loading condition for any given field application will vary with the depth to the pipe. At shallow depths (less than 1.33 ft) the critical condition will develop as a result of the standard HS20 load (16,000 lb single axle). From 1.33 ft down to 4.1 ft, the critical loading transitions to the passing of two standard 16,000 lb single axles (32,000 lb), and for depths greater than 4.1 ft, the critical load results from passing of two HS20 alternate loading tandem axles (48,000 lb) (21,780 kg). The transition depths have been tabulated and are presented below in Table 7, along with the dimensions of the effective area at various depths in with reference to Figure 16.

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STRUCTURAL DESIGN (Cont) TABLE 7 CRITICAL LOADING CONFIGURATIONS, HIGHWAY TRUCK LOADINGS H, ft

Pw, lb

Condition

ALL, Distributed Loaded Area

H < 1.33 ft

16,000

One set of dual wheels

(0.83 + 1.75 H) x (1.67 + 1.75H)

1.33 < H < 4.1 ft

32,000

Passing dual wheels (2 trucks)

(0.83 + 1.75 H) x (5.67 + 1.75H)

H > 4.1 ft

48,000

Passing tandem dual sets (2 trucks)

(4.83 + 1.75 H) x (5.67 + 1.75H)

Having determined the effective loaded area at the pipe crown as described above, the unit pressure applied to the pipe crown is calculated as follows: wL =

Pw (1 + lf ) ALL

where: wL

=

Pw = ALL = If =

Average pressure intensity, in units of weight per unit area (psf if Table 7 and Figure 16 are used), Wheel load, Distributed liveload area on the plane at the outside top of the pipe, Impact factor, described in the following Table 8.

Note that the loads calculated above are at this point still expressed as pressures, and have not been converted to loads per unit length of pipe for use in rigid pipe design. Impact factors used in this calculation are tabulated below. TABLE 8 IMPACT FACTORS AS A FUNCTION OF DEPTH OF COVER, CONCRETE PIPES THICKNESS OF COVER, H

IMPACT FACTOR, If

H < 1 ft

0.30

1 ft < H < 2 ft

0.20

2 ft < H < 3 ft

0.10

H > 3 ft

0.00

Ductile iron pipe manufacturers and plastic pipe manufacturers commonly use a fixed impact factor of 1.5 regardless of depth. In this configuration, the analogous If would be 0.5. The pressure wL still has to be converted into a load per unit length of pipe to be compatible with the other loads on the pipe for rigid pipe design. This is accomplished by determining an “effective supporting length of pipe", calculated according to the following expression. æ 3 Bc ö L e = L ALL + 1.75 ç ÷ è 4 ø

where: Bc = LALL

Outside diameter of the pipe (or height in the case of elliptical pipes), = Length of ALL along the longitudinal axis of the pipe (refer again to Figure 16).

The load on the pipe, in units of weight per unit length of pipe, is then calculated as: Wt = w L L e SL where: SL

=

Outside horizontal span of the pipe or the width of ALL, whichever is less.

Note that W t is now in units of weight per unit length of pipe, and can be combined with other loads on the pipe (Marston load for earth component, other distributed loads) to arrive at a total design load on the pipe crown. Had the design procedure been based on flexible pipe design methods, the conversion would not be necessary. An example describing the calculation of a truck loading on a pipe is presented as Example Problem No. 11 in APPENDIX A.

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STRUCTURAL DESIGN (Cont) STRUCTURAL DESIGN METHODS FOR SELECTING PIPE WALL THICKNESS While the methodology used in determining the loads on the pipe is generally based on the Marston load or the simple prism of earth directly over the pipe, plus whatever distributed live loads may exist, other structural design principles vary significantly according to the pipe material. A summary of the design procedure for each type of sewer pipe are described below. The structural design approach depends first on whether the pipe is considered rigid or flexible. The main difference is that rigid pipes are assumed to be capable of carrying the imposed vertical loads on them with no assistance from the earth material adjacent to the pipe. Rigid pipes include cast iron, concrete, reinforced concrete, and vitrified clay pipe. Flexible design assumes that the pipe deforms enough to press outward against the soil adjacent to the pipe, and in so doing mobilizes some lateral resistance from the soil, which then helps to carry the imposed vertical load. Flexible pipes include steel (tubular and corrugated metal), all plastic and fiberglass reinforced plastic pipe, and ductile iron pipe. The latter might be viewed as rigid, similar to the cast iron pipes which they have for the most part supplanted. However, most ductile iron pipe used in sewers is internally lined with a cement mortar lining. The deformation limits of the lining are much smaller than the deformation needed to mobilize the complete strength of ductile iron. Ductile iron is therefore designed in accordance with the procedures for flexible pipes. Pipe structural design is further broken down further into “direct" and “indirect" design methods. In direct design, the stresses in the pipe of a given trial diameter and wall thickness are calculated and compared to allowable yield stresses. Such an analysis would consider both the geometry of the system and the material properties of the sewer pipe and surrounding soil mass. Depending on the degree of sophistication in the assumptions dealing with soil response, the direct design methods can be analytically complicated. Their application is usually limited to flexible pipe design, and to large diameter reinforced concrete pipe for which the simpler methods may produce overly conservative designs. Indirect methods rely on long established empirical methods based on laboratory testing of standard dimensioned pipes (pipe diameter, wall thickness, reinforcing arrangement), which result in tabulated ultimate loads for the various sizes of pipe. The strengths are measured in terms of the ultimate “three edge bearing" tests. Indirect design for unreinforced concrete and vitrified clay pipe is based on the ultimate crushing load (i.e., rupture) for pipes tested in accordance with the standard three edge bearing test, while loading for reinforced concrete pipe is usually based on the three edge bearing load that causes a crack 0.01 in. wide to open. Indirect design is applied most often to rigid pipes. Indirect design methods are based on applying field loads calculated by means of the Marston formula to pre-defined pipe sections for which the load carrying performance has been established via laboratory standard loading tests. The method can result in conservative designs for pipes greater than 48 in. in diameter. In such cases a more precise analysis can be made using a direct design method based on the principles of soil structure interaction. Such methods are considerably more complex than the commonly applied indirect methods described below for rigid pipes, although advances in PC applications are making such analyses more common. Nevertheless, soil-structure interaction analyses are beyond the scope of this Design Practice. Direct method design for rigid pipe is therefore not discussed in any further detail. Rigid Pipe Design In general, rigid pipe design is based on the indirect method, which is applicable to concrete, reinforced concrete, and vitrified clay pipe. Indirect methods are also applicable to cast iron pipes, but these are seldom used in direct burial applications today, and have been supplanted by ductile iron, which is designed according to flexible pipe methods. However, understanding of rigid pipe design as it applies to cast iron may still be of use in an evaluation of an existing installation. The goal is to determine the required dimensions, essentially the necessary wall thickness required for a given pipe diameter and a given field loading condition. The indirect design methods are based on a standardized laboratory test in which prototype pipe specimens are loaded to failure (or to a specified crack width short of failure for reinforced concrete pipe) in accordance with a standardized arrangement. Based on the results of standardized tests, ASTM C 700, C 14, and C 76 provide tables for the load (in pounds per linear ft of pipe length) that a pipe of given dimensions and wall thickness is presumed capable of carrying. Pipes meeting these industry standard specifications are fabricated and marketed by various manufacturers. It is presumed that if a pipe of given dimensions (wall thickness and diameter) claims to meet the applicable standard, then the pipe could be counted on to carry at least the specified load (in pounds per linear ft of pipe) that the standard says a pipe of those dimension should be capable of carrying. That is the essence of the indirect design method. To use the indirect method, the designer first calculates the combined earth and surcharge loads, in pounds or kips per linear ft of pipe length (note, not per ft of width), applies a safety factor which depends on the pipe type, applies a bedding factor that reflects the anticipated field conditions for support at the base of the pipe, and proceeds into the tables in the industry standards in search of a pipe that has at least that load capacity.

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STRUCTURAL DESIGN (Cont) To understand the bedding factor, it is first necessary to understand the standard crushing test to which prototype pipes are subjected. The test is referred to as “three edge bearing" test. Diagrams of the apparatus used to perform the test and a photograph of a typical test in progress are provided in Figure 17. It can be observed that the pipe is supported on a cradle formed by two strips that are set apart only enough to insure that the pipe does not squeeze out of the jig as it is loaded to failure. The load on the top is for all practical purposes a concentrated line load. From a stress concentration perspective, the load on the bottom is very nearly a concentrated line load. This is representative of the most severe loading to which a pipe could be subjected, second only to a true point load on the top and on the bottom, which be impossible to effect safely in the laboratory. The bedding factors that are applied to design are based on reasonable assumptions regarding how close the field loading condition will be to the “three edge bearing" laboratory condition described above. The bedding factor serves to reduce the load imposed on the pipe by taking into account the field loading condition, which may or may not be as severe as the nearly 2-point loading imposed in the “three edge bearing" test. Higher bedding factors imply a less severe crushing strength requirement, and therefore allow a thinner wall requirement for a given diameter. At the extreme, for a pipe resting on essentially a flat hard surface with essentially no support under its haunches, the field loading would approximate the “three edge bearing" loading condition, and a bedding factor of nearly unity (Bf = 1.1) would be used. At the other extreme, a pipe that is fully encased in reinforced concrete, both over the crown and under its base, would have a bedding factor as high as 4.5. Note that Bf appears in the denominator, and a larger Bf implies a less severe field loading condition in comparison to the laboratory three-edge bearing test. Bedding factors for the various pipe support conditions are provided in Figure 18 for concrete pipe and Figure 19 for vitrified clay pipe (VCP). These concrete pipe bedding factors apply to concrete and reinforced concrete pipes. Note that the bedding factors for the most optimistic case (Class A) are dependent on the pipe type, while the factors for the other classes of bedding are the same for concrete and clay pipes. Class D bedding, essentially consisting of the pipe resting on a flat hard bottom, used to be referred top as “impermissible" for concrete pipe. The bedding described as Class D is defined as that in which little or no care is exercised to shape the foundation to fit the lower portion of the conduit or to refill all spaces under and around the conduit. Clay pipe manufacturers made no such restriction, and current handbooks published by concrete pipe manufacturers' groups no longer discourage this practice quite so strongly. However, the bedding factor associated with this type of bedding remains at a pessimistic value of 1.1, implying that the load is assumed to be nearly equivalent to the three-edge bearing test. Indirect design for plain concrete pipes and vitrified clay pipes is based on the ultimate crushing strength determined in a three edge bearing test described in ASTM C 497 (ASTM C 497M for metric sizes and loads). Reinforced concrete design is based on a variation of the three edge bearing test in that the load carrying capacity is not based on the ultimate crushing strength, but is instead based on the load that causes a crack 0.01" (0.3 mm) in width to open. This load is further normalized by dividing by the pipe diameter, and is referred to as the “D-load" strength. The application to design is similar, except that the factor of safety used when design reinforced concrete pipes based on “D-load" tests is customarily taken as 1.0, while the factor of safety for plain concrete and VCP, which are based on ultimate crushing load, is customarily set at 1.25 and 1.5 respectively. For plain concrete pipes and vitrified clay pipes, the required three-edge bearing strength is determined as follows: Req' d "3 - Edge" Bearing Strength =

Design Load x Safety Factor Bedding Factor

The 3-edge bearing strength is the ultimate load per liner ft of pipe that the pipe can support at incipient rupture. Tables of 3-edge bearing strengths for plain concrete pipes with diameters from 4 in. to 36 in. and wall thicknesses from 5/8 in. to 4.75 in. are provided in ASTM C 14. Corresponding 3-edge bearing strengths for plain concrete pipes in metric sizes (100 to 900 mm) are provided in ASTM C 14M. Tables of 3-edge bearing strengths for clay pipes with diameters from 3 in. to 42 in. (75 to 1050 mm) for standard and extra strength pipes are provided in ASTM C 700. For reinforced concrete pipe, the analogous D-load required strength is determined by the following formula: Req' d " D - Load" Strength =

Design Load x Safety Factor Bedding Factor x Diameter

In the above expression, the diameter “D" is in feet. The D-load strength is pounds per liner ft of pipe per ft of diameter that will produce a 0.01 in. (0.3 mm) crack. Tables of D-load strengths applicable to reinforced concrete pipes with diameters ranging from 12 in. to 96 in. and thicknesses from 1.75 in. to 9.75 in. are provided in ASTM C 76. Corresponding D-load strengths for reinforced concrete pipes in metric sizes (1500 to 3600 mm) are provided in ASTM C 76M. Examples of wall thickness determinations based on the indirect design method for reinforced concrete, plain concrete, and vitrified clay pipes are presented respectively as Example Problems No. 12, 13 and 14 in APPENDIX A.

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STRUCTURAL DESIGN (Cont) Flexible Pipe Design Design performance limits for flexible sewer pipe may be expressed in terms of stress or strain in the pipe wall, crushing or buckling of the wall, or deflection. The most common limit is deflection. Typically, a deflection limit is established to provide a factor of safety against structural failure or any type of distress that might tend to limit the service life of the pipe. This limit will vary with different pipe materials and different pipe manufacturing processes. Pipes must be able to deflect without cracking, and without liner failure, joint leaks, excessive strain or other distress. Finally, they should be designed with a reasonable factor of safety. Deflection limits for ductile iron pipes serve to illustrate this. While ductile iron pipe is capable of deflecting as much as 20% before the wall material goes into yield, the deflection limit is usually set at about 3%. The basis for this is that ductile iron pipes are usually provided with a cement mortar lining (CML), which must not be permitted to crack. Conversely, flexible lined and coated steel pipe, flexible coated and CML “lined in-place" steel pipe, fiberglass pipe and thermoplastic pipe (PVC, ABS, HDPE) are usually designed for a maximum deflection of 5%. The deflection limits of the lining therefore set the deflection limits of this particular type of pipe. The load carried by a flexible pipe in a narrow trench may be calculated by the Marston Formula, described previously. A more conservative design that is often used for flexible pipe is to assume that the dead load carried by the pipe is the “prism load", which is simply the column of soil directly over the pipe. Under normal installations, it is assumed that the prism load is the maximum load that can be developed, although the designer is advised to verify this on a case basis. Recommendations regarding selection of the Marston load or the prism load will vary by pipe type and sometimes by manufacturer. While the principles involved in flexible pipe design are common to all types of flexible pipe, the design procedures and details are specific to each type. These procedures are generally provided either in industry standards developed by a consortium of manufacturers of a given pipe, as is the case for ductile iron pipe, or provided separately by the manufacturers, as is the case for most plastic pipe. Design procedures for the more common classes of flexible pipe are therefore described separately. Ductile Iron Pipe The design of ductile iron pipe is based on the following criteria, which help to simplify the design:

•

Earth load is based on the prism load concept, not the Marston load. This is generally viewed as a very conservative assumption for flexible pipe.

•

Truck loads are based on a single AASHTO H-20 loading, with 16,000 lb wheel loads and an impact factor of 1.5 regardless of depth.

•

External load design includes calculation of both ring bending stress and deflection, with ring bending stress limited to 48 ksi, providing a safety factor of at least 2.0 based on ultimate bending stress.

•

Deflection of the pipe is limited to 3% for CML (cement mortar lined) pipe, which provides a safety factor of at least 2.0 against applicable performance limits on the lining. Unlined pipe and pipe with flexible linings can withstand greater deflections.

•

Five trench types have been defined, to reflect the range of possible laying conditions. These take into account not only the conditions under the bottom of the pipe, as in rigid pipe design. They also take into account the stiffness of the soil backfill immediately surrounding and supporting the pipe walls. There are additional criteria for ductile iron pipe used in pressure service, but these do not apply to use of this pipe in normal gravity drainage applications. The trench load used in design (Pv) is expressed as vertical pressure in psi, and is the sum of earth load (Pe) and truck load (Pt). The earth load is simply the weight of the earth above the pipe to the ground. Earth load is calculated as Pe =

λ Hg 144

where: Pe γ Hg

= = =

Earth load, psi Unit weight of backfill, lb/ft3 Depth from ground surface to pipe crown, ft.

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STRUCTURAL DESIGN (Cont) Truck load is calculated as Pt =

Csf R P F 12 D

where: Pt = Csf = R

=

Pw = F = D =

Truck load, psi, A surface load factor for a single concentrated wheel load centered over an effective pipe length of 3 ft, A reduction factor which takes into account the fact that the part of the pipe directly below the wheels is aided in carrying the truck load by adjacent parts of the pipe that receive little or no direct load from the wheels, Wheel load (16,000 lb for this case), Impact factor (set at 1.5), Outside diameter of the pipe, in.

The earth load Pe and the truck load Pt are added together to produce the total vertical load Pv, in units of pressure, that is assumed to be acting on the pipe. While loads can be calculated for individual cases, tabulated values for earth loads, truck loads, and their resulting combined trench load are provided for various depths and various pipe sizes in ANSI / AWWA C150 / A21.50-91 Thickness Design of Ductile Iron Pipe. The required wall thickness is then calculated via the expressions below. Thickness is based on maximum ring bending stress of 48 ksi, which provides factors of safety under trench loading of at least 1.5 based on ring yield strength and at least 2.0 based on ultimate ring strength. Wall thickness based on ring yield is calculated by means of the expression on the left, while thickness required to limit deflection is calculated by means of the expression to the right: Based on Ring Yield:

Pv

Based on Limiting Deflection:

1

f = x ö æDö æD 3 ç ÷ ç − 1÷ ø ètø èt

Kb −

where: Pv

=

f tw Do E E′

= = = = =

Kb Kx ∆x

= = =

t1

=

Pv

Kx æ ç ç 8E ç ç æD ç E′ ç − ç ç tw è è

3

ö 1÷÷ ø

ö ÷ ÷ + 0.732 ÷ ÷ ÷ ÷ ø

ù é ú ê ú 8E ∆x / D ê + 0.732 E′ú = ê 3 12 K x ê æ D ú ö ú ê çç − 1÷÷ úû êë è t1 ø

Combined trench load, in psi (prism earth load plus truck load), calculated as described above, Maximum bending stress, 48 ksi, Net wall thickness, in., Outside diameter, in., Modulus of elasticity of the pipe material (24 x 106 psi), Soil modulus of reaction, also in psi, and defined for various pipe laying (essentially bedding) conditions, Bending moment coefficient, Deflection coefficient, also defined as a function of pipe laying conditions, Deflection in in., and for the customary limit of 3% to protect the cement mortar lining, ∆x/D will be 0.03, Minimum manufacturing thickness, which includes manufacturing tolerances, and is set at t + 0.08 in.

While these equations could be solved by an iterative approach, the manual solution of these equations for bending stress and deflection to determine net thickness is difficult and time consuming. Consequently, the equations have been solved and reduced to design tables giving diameter-thickness ratios for a wide range of trench loads and for the five standard laying conditions. The tables are presented in ANSI / AWWA C150 / A21.50-91. With these tables, a designer need only know the trench load and the intended laying condition to determine net thickness required for bending stress and deflection controlled design.

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STRUCTURAL DESIGN (Cont) Once the controlling net thickness has been determined, certain allowances are added to obtain the calculated total thickness requirement. To obtain the minimum manufacturing thickness, which is a parameter in the deflection expression above, a service allowance (0.08 in.) is added to provide an additional safety factor for unknowns. Then a casting tolerance is added to provide the latitude needed by the manufacturing process and to prevent the possibility of significant minus deviation from the design thickness. Casting tolerance is dependent on the pipe size as described below. TABLE 9 ALLOWANCES FOR CASTING TOLERANCES, DUCTILE IRON (DI) PIPE PIPE DIAMETER, in.

CASTING TOLERANCE, in.

3-8

0.05

10 - 12

0.06

14 - 42

0.07

48

0.08

54 - 64

0.09

An example of the thickness design for a ductile iron pipe is provided as Example Problem No. 15 in APPENDIX A. HDPE Pipe

At present, the various manufacturers of HDPE pipe have not incorporated their respective design methods into a single industry standard, although this effort is currently in progress under the direction of the Plastic Pipe Institute (PPI). Until a uniform industry standard is promulgated for HDPE pipe, it is necessary to rely on a mix of design procedures specified by the several pipe manufacturers and theoretical formulas applicable to flexible pipe in general. Various manufacturers of HDPE pipe prefer slightly different design methods to arrive at design loads, but the wall thickness is in all cases based on SDR (standard dimension ratios) which relate wall thickness to pipe diameter. HDPE pipe is manufactured to industry standard wall thicknesses, and standard SDRs. SDR is a key parameter in plastic pipe design, and is defined as the ratio of the outside diameter of the pipe (OD) to the wall thickness (t). SDR (or DR) =

OD t

The manufacturer of PlexcoR and SpiroliteR pipe (Chevron) recommends the use of either the Marston formula or the simpler prism load for determining earth loads, and recommends determination of other distributed loads and traffic loads the same as described earlier in this Design Practice. The manufacturer of DriscopipeR (Phillips) recommends use of the simpler soil prism (dead weight of soil directly over the pipe), and adds any distributed surface loads and traffic loads essentially as described previously. One additional design consideration in plastic pipe is the potential for a vacuum load. While such a uniform load has virtually no impact on stronger pipes, it could lead to buckling of a plastic pipe if it is large enough. Further, since HDPE can be made into a long continuous line that can flow under siphon conditions for part of its length, negative loads could be significant. However, for applications to gravity sewers than cannot create negative pressure conditions, this type of loading will not be further considered. Finally, two factors unique to HDPE and other thermoplastic sewer pipes are effluent temperature and long term creep. The strength and stiffness of the plastic which forms the pipe wall vary with temperature, and the elastic modulus also depends on level of applied stress and duration. If a sewer line will be subjected to hot effluent, the temperature of the liquid will be an important design consideration. Since elastic modulus is a factor in the design of flexible pipe, the stress level in the pipe and the intended service life (usually set at 50 years) are also considered in design process.

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STRUCTURAL DESIGN (Cont) ➧

Use of HDPE Pipe for Sewers in Plant Areas Where there are Hot Process Streams

It is noted that the melting point for HDPE pipe is only 450°F (230°C). Consequently, the use of HDPE pipe for sewers in plant areas with hot process fluids needs careful consideration due to the potential for ruptures of process equipment/piping to cause large volumes of hot petroleum product to flow into the sewer system. Whether HDPE pipe can be considered suitable in these areas depends on the following:

• •

maximum credible spill size

•

product temperature

• •

response time for the application of firewater

•

magnitude of external service loads

pipe wall thickness

type of backfill material placed around the pipe

•

consequence of a collapsed sewer pipe When cement stabilized sand (or equivalent engineered cohesive material) is used as bedding/backfill around the pipe, HDPE sewers may be used in areas where the maximum temperature of the unit process streams do not exceed 400°F (205°C). In areas where there is a process stream above 400°F (205°C), spill scenarios should be developed and assessed to determine if HDPE sewers may be used. HDPE sewers may not be used where the spill scenario temperature is more than 650°F (343°C). In addition, the mid-wall temperature of the pipe should not be allowed to exceed 350°F (177°C) for the duration of exposure. For spill scenarios where the process stream is 400-650°F (205-343°C), then determining whether HDPE can be used should be based on a risk assessment considering the combined probability of the spill and subsequent failure (plugging / collapse due to high temperature) of the pipe and the resulting consequences. If the risk with HDPE pipe is unacceptable, then only cast iron or concrete sewer pipe that is suitable for the high temperature spill scenarios should be used in the area. The probability of an HDPE sewer line collapse due to high temperature can be minimized if the predicted average pipe wall thickness remains below 350°F (177°C) throughout the period of exposure. In previous risk assessment applications, the probability of a sewer line collapse when following this criteria, in combination with normal process equipment maintenance practices, has been judged to be "Remote" per the ExxonMobil Risk Assessment Matrix. When determining the average pipe wall temperature for a spill scenario, a heat transfer analysis assuming transient heat flow in a semi-infinite solid should be used. An example calculation technique, from Heat Transfer 4th ed. By J.P. Holman, is shown below:

æ xm T (xm, t) = To + (Ti - To) erf ç ç2 a t d ex è

ö ÷ ÷ ø

where: T (x,t) = Pipe wall temperature at depth x and time t Ti = Initial pipe wall temperature (°C) To = Temperature of the process stream (°C) xm = Mid wall depth (m) ad = Thermal diffusivity tex = Exposure time (sec.) æ ö xm ÷ is obtained from tables in the reference erf ç ç2 a t ÷ d ex ø è

For new design applications, the figure below can be used to establish the minimum pipe wall thickness that should be specified as function of the spill scenario temperature. In the figure it is assumed that the exposure time is a maximum of 15 min., which is considered a reasonable response time for firewater application. The initial temperature of the buried pipe is also assumed to be at a maximum of 90°F (32°C). The pipe wall thickness should be increased if the predicted exposure time is longer than 15 min. Shown in the figure is an adjustment factor that can be used if the exposure is 30 min. instead of 15 min.

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STRUCTURAL DESIGN (Cont) Minimum Required Wall Thickness for 15 min. Exposure 1.2

Pipe Wall Thickness (in.)

1

0.8

Mid pipe wall temperature at maximum 350°F (177°C)

0.6

0.4

For a 30 min. Exposure Case - increase the required pipe wall thickness by 35%

0.2

.

0 0

200

400

600

800

Process Stream Temperature (°F)

DP29Cfa

There are three stress conditions and one deformation condition that are evaluated. The first stress condition is almost trivial, and consists of simple wall crushing. However, in conjunction with the intended design life and expected temperature, this will impact the elastic modulus to be selected for use in the other loading conditions. The total load on the crown is assumed to be carried in compression at the spring line, one half on each side. The second stress condition is wall buckling under a uniform hydrostatic load, such as might be imposed by the ground water in the soil matrix. This condition is evaluated based on elastic buckling of an unrestrained ring, and it depends directly on the elastic modulus. Since the latter is known to be a function of service life and service temperature, tables or charts are provided by the pipe manufacturers to define the elastic modulus for various service conditions. Finally, the pipe is evaluated in context of constrained wall buckling, which is more in line with the design of other flexible pipes, and takes into account the lateral constraint provided by the soil surrounding the pipe. Vertical deformation under design load is also evaluated as ring deflection. A brief overview of the equations relating to each condition is presented below.

CAUTION When calculating stresses in pipe walls, it is important to be sure that the loads and stresses are being determined on a consistent basis. Loads on pipe crown, when determined in accordance with Marston theory, are based on load per unit length of pipe. Distributed surface loads and/or traffic loads may have been converted to a similar basis. Conversely, the prism load commonly used to define the earth portion of the load on a plastic pipe is expressed in units of pressure, and distributed or traffic loads must be on the same basis to be applicable. Most plastic pipe manufacturers' literature determines pipe wall thickness on the basis of pressure on the crown, not load per unit length. Wall Crushing

The compressive stress (e.g., in psi) for a smooth wall pipe the wall is calculated according to S =

PL Do 2t

where: PL Do t

= = =

Vertical load on the pipe, in units of pressure, Outside diameter in units of length, Wall thickness, also in units of length.

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STRUCTURAL DESIGN (Cont) Note the caution in the preceding paragraph with regard to external loads on the crown which need to be expressed in units of pressure. For profile wall plastic pipes (i.e., ribbed walls), the derivation is similar to the above except that the “t" term is replaced by an average cross sectional area term “A" which is in units of L2/unit length of pipe. Since HDPE pipe is normally specified according to standard dimension ratio, SDR = OD/t, the above expression could be written: S =

(SDR ) PL 2

At least one pipe manufacturer prefers to make this calculation via the expression: S =

(SDR − 1) PL 2

Examination of that expression implies that the manufacturer considers the vertical pressure on the crown to act over a width that is slightly less than OD, namely Dm or the “mean diameter." (Dm = OD - t). Since t is typically small in comparison to OD, this difference does not produce a significant difference in the calculated stress. Wall thickness must be great enough to maintain this stress below the allowable sustained compression stress, which varies with manufacturer but is restricted to no more than about 50% of the compressive yield strength of the material. Instantaneous yield strength of HDPE is about 1500 psi (10.3 mPa). One manufacturer recommends that the wall be thick enough such that the compressive stress is no higher than 800 psi (5.1 mPa), which implies the same safety factor. The designer needs to check against the yield strength that applies at the expected service temperature for pipes that will be subjected to high temperature liquids. Unconstrained Wall Buckling

Unconstrained buckling, also referred to as “unrestrained" or “hydrostatic" buckling, is governed by the following equation: Pc =

24 E l (1 − u2 ) Dm3

where: Pc

E

= =

I = u = Dm =

Critical buckling pressure, which can act on the crown or in any direction in the case of hydrostatic loading, Elastic modulus of the pipe material, which is a function of the temperature, stress level, and the desired service life, Pipe's moment of inertia per unit length of pipe, equal to t3/12, where t is wall thickness, Poisson's ratio (0.45 for long-term loading of polyethylene), Mean diameter, equal to the pipe outside diameter less approximately one wall thickness.

The above listed expression appears in slightly different forms in various pipe manufacturers' literature, but is based on fundamental Euler buckling of an unrestrained ring, as described in many engineering mechanics texts. It is sometimes referred to as Love's Equation. Unrestrained, or “hydrostatic", buckling applies only in a limited set of circumstances, including:

•

A line that can operate under vacuum, such as might occur due to pump start-up or shut-off, separation of flow column running downhill, or flow under siphon conditions.

•

External hydrostatic load such as elevated groundwater table over an ungrouted PE or PVC slipliner.

•

A partially full line under water and not constrained by firm earth backfill, or in soft marine deposits or marshland soil that is incapable of providing any significant lateral support. For most direct burial applications where backfill is provided around the pipe, or for slipline applications that are post-grouted, the unconstrained buckling analysis described above will not apply. Rather, the following constrained analysis will apply.

Constrained Wall Buckling This condition is evaluated in accordance with the Modified Iowa Formula developed by Spangler and Watkins, and is used for design of flexible pipes which can be assumed to rely on lateral restraint provided by the surrounding soil. This complicated soil-structure interaction problem depends on the soil and pipe moduli, bedding conditions, and pipe dimensions. The general form of the expression is as follows:

∆X =

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STRUCTURAL DESIGN (Cont) where: ∆X Kb Dt

= = =

We

=

Dm Ep I

= = =

E′

=

Horizontal deflection, outward, which is resisted by the soil, in., Bedding constant dependent on the width of the sewer pipe bedding, Deflection lag factor, empirically determined, ranging from 1.25 to 2.5, which compensates for the time dependent consolidation characteristics of the soil. Values of 1.25 to 1.5 are commonly used for HDPE pipe. Applied load on the crown derived from the Marston load or soil prism load plus any other loads applied to the sewer, lb/in., Mean pipe diameter, in., Pipe's modulus of elasticity in tension, psi, Pipe section's moment of inertia per unit length, in.4/in., taken as t3/12, Modulus of soil reaction, also in psi, described in tables presented on Figure 21.

Note that manufacturers' design guides may refer to the Modified Iowa Formula and express it in terms of ∆X / D, with all other terms except W e the same as in the above expression. However, in place of W e, which is a Marston based load in weight per unit pipe length, the manufacturers' expressions will usually have P or Pt, which is a pressure in weight per unit area, arrived at by dividing the Marston load W e by the pipe diameter D. The expressions are therefore equivalent. The bedding factor Kb in the Iowa formula is based on the bedding angle, which is the angle subtended from the center of the pipe to the effective edges of bearing material adjacent to the pipe haunches. Customary values for Kb are provided in Table 10. TABLE 10 Kb VALUES FOR VARIOUS BEDDING ANGLES FOR USE WITH MODIFIED IOWA FORMULA BEDDING ANGLE, DEGREES

Kb

0

0.110

30

0.108

45

0.105

60

0.102

90

0.096

120

0.090

180

0.083

Since there are design assumptions implied in the terms in the Iowa Formula, some discussion of those terms is in order. The first term in the denominator, ‘E I’ (pipe stiffness factor) reflects the influence of the inherent stiffness of the sewer pipe. The second term, 0.061 E′r3, reflects the influence of the passive earth pressure on the sides of the pipe. This second term may predominate in the case of large-diameter pipe, with the result that a very lightweight pipe may appear satisfactory. Since the pipe wall must have sufficient local strength in bending and thrust to develop and utilize the passive resistance pressure on the sides of the pipe, it is recommended as a practical measure that the value of EI should never be less than about 10-15% of the term 0.61 E′r3. E′ values for use in the expression are tabulated on Figure 21. These are average values that do not necessarily reflect field variables, so a degree of judgement by the designer is in order. Structural design of all flexible pipes, including plastic pipes, requires definition of the critical deflection limit for the specific pipe considered. For plastic pipes, the typical allowable long-term deflection limits are 5% of diameter. A comparison of the applicable mathematical expressions for the various stress evaluations is provided in Table 11.

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TABLE 11 TREATMENT OF DESIGN CONSIDERATIONS BY COMMERCIAL HDPE PIPE MANUFACTURERS THEORETICAL CONSIDERATION

CHEVRON PLEXCO AND SPRIOLITE DESIGN MANUALS

PHILLIPS DRISCOPIPE DESIGN MANUAL

Wall Crushing, compressive stress S: S = W c/2t or S = Pl Do/2t Where Wc is load on crown per unit length, and Pt is load on crown expressed as pressure; t is pipe wall thickness, Do is outside diameter of pipe.

(SDR − 1) Pt 2

S =

PL Do for Plexco (smooth wall) or 288 t

SA =

S =

PL Do for Sprirolite (ribbed) 288 A

where Pt is external pressure on crown, psi.

where S is and P are in psf, t and Do, in. Design goal is to maintain S ≤ 800 psi for service at ambient temperature (78.4°F).

Designer calculates FS =

1500 psi SA

While no minimum value for FS is specified, design guide implies that compressive yield strength at 78.4°F is about 1500 psi.

Hydrostatic (unrestrained buckling, critical radial pressure:

Pc =

24 El 2

(1 − u ) Dm

3

Euler load for unrestrained ring buckling.

Constrained Buckling, critical vertical buckling load:

æ 1 çç 2 (1 − u ) è SDR −

2E

Pcr =

3

ö ÷ , and P = Pcr foval 1 ÷ø

where foval is dependent on % deflection, nearly linear to 0.55 @ 6% deflection, then 0.35 @ 10% deflection. Mfgr suggests apply FS = 2 against buckling, and points out that E is time and temperature dependent; u = 0.45 for HDPE.

Pwc =

5.65 N

R′ B′ E′

El Dm3

where E′ is soil’s modulus of reaction in psi, based on soil type and compaction condition (see Figure 21), Dm is pipe average diameter in in., R is a buoyancy factor R = 1 - 0.333 (H′/H) where H′ is height of groundwater and H is total height of cover, E and I are pipe material modulus and moment of inertia (per unit length), N is a safety factor, customarily set to 2, and B″ is defined as:

B′ =

1 1 + 4e −0.065H

The origins of this expression are found in an AWWA standard C-950 which is actually for fiberglass reinforced thermoplastic pipe. A simpler method is provided, as P = fofsPcr wherein fo and Pcr are as defined above in “unrestrained buckling”, and fs is a “support factor” that ranges from 1 to about 4, and varies with SDR and soil condition. Only two soil conditions are provided, “loose soil” and “compacted soil”. The value of fs must be read from a graph provided in the manufacturer’s design manual (see Figure 20). It is unclear what safety factor, if any Is implied in this alternate method. Note however that the implication is that good soil restraint can increase the buckling load by as much as a factor of 3.

Pc =

Pc =

2.32 E (SDR )3

for round pipes, and

2 E( t / D)3 æ Dmin ç (1 − u2 ) çè Dmax

ö ÷ ÷ ø

3

for deflected shape

A simplified burial design is provided in the form of a chart, reproduced on Figure 20. This assumes no external loads. More detailed pipe design is based on the following relationship:

Pcb = 0.8

E′ Pc

where Pc is the unrestrained buckling load calculated as described above, and E′ the soil modulus of reaction (in psi) defined in accordance with the Modified Iowa Formula (see Figure 21). The manufacturer endorses selecting a wall thickness sufficient to achieve a safety factor of 2, expressed as:

FS =

Pcb Pt

where Pr is the total external pressure applied to the pipe (earth load plus other surcharge and/or traffic loads). A separate safety factor designed to preclude buckling is applied by inverting the above expression for Pcb as follows:

E′ =

Pcb 2 , 0.64 Pc

which is the soil modulus necessary to prevent buckling. This modulus is then increased by FS = 2 to arrive at a minimum allowable soil modulus to be achieved in the field: E′min = E′ x FS. The specification is then written to require that the backfill material and compaction will be sufficient to achieve the require E′min

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STRUCTURAL DESIGN (Cont) TABLE 11 (Cont) TREATMENT OF DESIGN CONSIDERATIONS BY COMMERCIAL HDPE PIPE MANUFACTURERS THEORETICAL CONSIDERATION

CHEVRON PLEXCO AND SPRIOLITE DESIGN MANUALS

PHILLIPS DRISCOPIPE DESIGN MANUAL

Ring Bending (vertical deflection) via Modified Iowa Formula: Extensive research carried out in the 1940s by Prof. Spangler at the Iowa Engineering Experiment Station, resulted in expressions for deflection and wall thickness for a specified deflection

∆X =

t =

3

Dt K b We Dm3 Ep l + 0.061 E′Dm 1 E

3

and

Calculate deflection by means of

é ê ∆X P ê = ê Dm 144 ê 2E ê ë 3

ù ú ú KL ú 3 æ ö ú 1 çç ÷÷ + 0.061E′ ú − SDR 1 è ø û

Rather than calculate the pipe deflection, this manufacturer makes the assumption that the pipe deflection will be identical to the soil backfill surrounding the pipe acting under the influence of the vertical soil pressure at the pipe crown, according to

εsoil =

for Plexco (smooth wall) pipe, or

æ 12 KWr 3 ö ç − 0.732 E′ r 4 ÷ ç ∆X ÷ è ø

Terms are as defined previously in the text on page 34.

é ù ú ∆X P êê KL ú = Dm 144 ê 1.24 (RSC) ′ú + 0 . 061 E ê ú Dm ë û

Pipe vertical deflection, assumed to be equal to soil strain calculated above, is compared to allowable deflections tabulated for various SDRs, as follows: SDR

for Spirolite (ribbed wall) pie RSC is the ring stiffness constant for ribbed wall pipe, and is calculated as RSC = 6.44 E l/Dm2 Then calculate ring bending strain ε via

ε = fd

∆Y C Dm Dm

where ε is wall strain, in %, Dm is mean diameter (OD-t), C is the distance from the outer fiber to the wall centroid, in in., and is calculated as C = 0.53 t for Plexco (smooth wall) pipe, and C = H - Z for Spirolite (ribbed) pipe, where H = wall height (in.) and Z = pipe wall centroid (in.). fd is an elliptical deformation correction factor, which would be 4.28 if the pipe deformation were truly elliptical. Because buried plastic pipe rarely has a perfectly elliptical shape, it is common practice to assume fd = 6

Pt E′min

Allowable Ring Defl.

32.5

8.1%

26.0

6.5%

21.0

5.2%

19.0

4.7%

17.0

4.2%

15.5

3.9%

13.5

3.4%

11.0

2.7%

The above tabulated allowable ring deflections are based on limiting outer fiber tangential strain to 1.5% or less, which is viewed to be conservative. A final check is made to determine what degree of compaction is necessary to achieve the above calculated soil strain, εsoil, based on empirical date presented in Figure 20. The backfill compaction specification is set accordingly.

Calculated ring bending strains are then compared to an allowable strain, taken conservatively as 4.2%.

Other Plastic Pipe (ABS, RPM, PVC)

Thermoplastic pipe other than HDPE is also designed according to flexible pipe methods. The design process is more standardized however, and is not as dependent on individual manufacturer's literature. The most common procedure is that based on a standardized laboratory load test, which determines “pipe stiffness" or load-deflection characteristics via a “parallel plate test." In the U.S., the standard test is ASTM C 2412. In this test a short length of pipe is loaded between two rigid parallel plates that are moved together at a controlled rate. Load and deflection data are recorded. The parallel-plate loading test determines pipe stiffness (PS) at a prescribed deflection (∆Y) which is arbitrarily set at 5% of original pipe diameter. Note that this is not to be considered a field deflection limit. The pipe stiffness is defined as the value obtained by dividing the force (F) per unit length of pipe by the deflection in the same units at the prescribed deflection, and is expressed in psi, as follows:

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STRUCTURAL DESIGN (Cont) PS =

F El = ∆Y 0.149 Dm3

where: F ∆Y E I Dm t

= = = = = =

Force per unit length, lb/in., Prescribed deflection, in., Modulus o elasticity, lb/ft2, t3/12, Mean radius of the pipe, in., Mean wall thickness, in.

Minimum required pipe stiffness values for various types and sizes of plastic pipe are specified in the various ASTM specifications for plastic sewer pipe, as shown in Table 12. A quantity defined as the “stiffness factor" (SF) is equivalent to EI as used in the Modified Iowa formula to determine approximate deflections under applied loads in the field. SF = E l =

F 0.149 Dm3 = 0.149 Dm3 (PS) ∆Y

The stiffness factor or ‘E I’ is used in the Modified Iowa Formula (page 31) to determine approximate field deflections under earth loads. Approximate values of horizontal deflections (∆X) for field loadings can be calculated using the Modified Iowa Formula. A correction factor must be applied to the calculated horizontal deflections to accurately predict the vertical deflection for low pipe to soil stiffness ratios. The formula can be simplified to permit a calculation of approximate deflection based on pipe stiffness as follows: ∆X =

DL K b Wc 0.149 PS + 0.061 E′

TABLE 12 STIFFNESS REQUIREMENTS FOR PLASTIC SEWER PIPE PARALLEL PLATE LOADINGS MATERIAL

ASTM SPECIFICATION

ABS Composite

D 2680

ABS Plain

D 2751

SDR 23.5 SDR 35 SDR 42

RPM (fiberglass)

PVC

D 3262

D 2729

D 2729

D 3033 D 3034

(PVC-12454)

NOMINAL DIAMETER, in.

REQ'D STIFFNESS @ 5% DEFLECTION, psi

8 - 15

200

4 and 6

150

3

50

4 and 6

45

8, 10 and 12

20

8 to 18

Varies, 99 to 17

20 to 108

10

3

19

4

11

5

9

6

8

3

24

4

13

5

12

6

10

SDR 41

6 to 15

28

SDR 35

4 to 15

46

SDR 41

6 to 15

28

SDR 35

4 to 15

46

(PVC-13364)

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STRUCTURAL DESIGN (Cont) ➧

Thermal Effects

HDPE pipe has a coefficient of thermal expansion that is about an order of magnitude greater than concrete or iron pipe, although its modulus of elasticity is much less. Nevertheless, the potential exists for inducing large axial stresses and strains which would need to be considered in design if a pipe will be subjected to temperature fluctuations. These factors are beyond the scope of this Design Practice. The designer is referred to publications produced by pipe manufacturers for assistance with problems of this nature. Table 13 provides modulus for two commonly used grades of HDPE pipe at what is considered normal ambient temperature (73°F, 23°C) and at one elevated temperature (140°F, 60°C). TABLE 13 LONG TERM (50 YEAR) ELASTIC MODULUS E FOR HDPE PIPE HDPE GRADE

60

TEMPERATURE °F 73

140

PE

2408

27,600 psi

22,600 psi

14,900 psi

PE

3208

38,700 psi

28,200 psi

18,700 psi

Corrugated Metal Pipe

Corrugated metal pipe (CMP) is manufactured in a variety of gages, corrugation depths, and corrugation spacings. For larger sizes which are built up from sheets, the longitudinal seam formed by bolting or riveting curved sheets should be checked for crushing strength. Tables of seam strengths for various metal gages and bolt or rivet sizes and spacing can be found in manufacturers' handbooks. Corrugated metal pipe may be designed for a limiting deflection using the Modified Iowa Formula (page 31) or by the manufacturers' handbook figures and charts. A design deflection limit of 5% of initial diameter is commonly specified. Open Channels

The analogous structural consideration for open channels is simply to insure that the side slopes and bottom remain reasonably intact when delivering the design flow. This is accomplished by evaluating the resistance of the channel lining to erosive flow velocities. Correlations for both permissible velocities and for permissible shear force (tractive force) exist, but the velocity correlations are simpler and are adequate for most applications. Acceptable velocities for various ditch linings are presented in Table 14 below.

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STRUCTURAL DESIGN (Cont) TABLE 14 MAXIMUM PERMISSIBLE VELOCITIES FOR VARIOUS CHANNEL LINING TYPES VELOCITY CHANNEL MATERIAL ft/s

m/s

Fine sand

2

(0.6)

Coarse sand

4

(1.2)

Fine gravel, < 20 mm or 3/4 in.

6

(1.8)

Earth (unlined)

2

(0.6)

Sandy silt

3.5

(1.1)

Silty clay

6

(1.8)

Bermuda grass in sand

6

(1.8)

Bermuda grass in silty clay

8

(2.4)

Kentucky bluegrass in sand

5

(1.5)

Kentucky bluegrass in silty clay

7

(2.1)

10

(3.0)

Soft sandstone

8

(2.4)

Soft shale

3.5

(1.1)

20

(6.1)

Clay Grass-lined earth

Sedimentary rock

Hard rock (igneous or metamorphic) Paved linings Concrete, asphalt

20 + 6 to 25

(6.1+) (1.8 to 7.6)

Rip-rap lined (varies w/ rock size, see Figure 22)

➧

STRUCTURAL ANALYSIS / DESIGN SOFTWARE

➧

Structural engineering software is available, which can be used to evaluate certain types of buried pipe subject to evaluate certain types of buried pipe subject to internal and external loadings. Some structural analysis / design software can be obtained through the world-wide web at www.fhwa.dot.govt/bridge/hyd.htm. The web site is mainted by the U.S. Department of Transportation Federal Highway Administration and is linked to the American Concrete Pipe Associates. The following programs are available: CANDE-89

This software is for the structural analysis and design of buried culverts and other soil-structure stystems. The CANDE methodology incorporates the soil mass with the structure into an incremental static, plane-strain boundary value problem. Three solutions are available: 1. closed for plan strain solution for circular conduit in elastic halfspace 2. 2D finite element solution iwth automated mesh generation 3. 2D finite element solution with user defined mesh. Minimum requirements: IMB XT/AT compatible, 640 K RAM, 2Mb hard disk, DOS 3.2 or higher. BOXCAR 1.0

BOXCAR is a program for the structural analysis and design of reinforced concrete box culvert sections. Load analysis includes box weight, soil weight, internal fluid forces, live loads, and user-specified surcharges. Design criteria include ultimate flexure, diagonal tension, service load crack control, and service load fatigue. Minimum requirements: DOS, IBM PC or compatible.

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STRUCTURAL DESIGN (Cont) PIPECAR 2.1

PIPECAR is a program for structural analysis and design of circular and horizontal reinforced concrete pipe. Load analysis includes pipe weight, soil weight, internal fluid load, live loads, and internal pressures up to 50 ft. of head. Pipe can be designed according to AASHTO "Standard Specifications for Highway Bridges" (13th Ed.) or to ASCE "Standard Practice for Direct Design of Buried Precast Concrete Pipe using Standard Installations (SIDD)." MInimum requirements: DOS 2.0 or higher, 640 k RAM plus math coprocessor.

NOMENCLATURE a, b, and n ad A

= = =

Ac ALL Bc Bci Bd C Csf Cd Cfb

= = = = = = = = =

Cs

=

CN d D Dm Do Dt

= = = = = =

E

=

Ep

= =

Equation coefficients Thermal diffusity The cross sectional area of flow. For pipes flowing partly full and for open channels, A also must be calculated as a function of flow depth. Catchment area, acres Distributed liveload area on the plane at the outside top of the pipe Width of the sewer pipe Outside diameter of the pipe (or height in the case of elliptical pipes) Width of the ditch at the pipe crown in units consistent with the unit weight Non-dimensional runoff coefficient A surface load factor for a single concentrated wheel load centered over an effective pipe length of 3 ft Dimensionless coefficient that depends on the soil type and the trench geometry Coefficient varying from 1.5 for channels with capacities of 20 ft3/s to 2.5 for channels with capacities of 3000 ft3/s or more Dimensionless load coefficient which is a function of dimensions of the loaded area (length and width) in comparison to the depth to the crown of the sewer pipe. USDA / SCS Curve Number Depth of flow, ft Duration of the rainfall, in minutes Mean diameter, equal to the pipe outside diameter less approximately one wall thickness Outside diameter in units of length Deflection lag factor, empirically determined, ranging from 1.25 to 2.5, which compensates for the time dependent consolidation characteristics of the soil. Elastic modulus of the pipe material, which is a function of the temperature, stress level, and the desired service life Pipe's modulus of elasticity in tension, psi Soil modulus of reaction, also in psi, and defined for various pipe laying (essentially bedding) conditions

= = = = = = = =

Maximum bending stress Force per unit length, lb/in. Dimensionless impact factor (for traffic or railroad loads, if applicable) Gravitational constant Additional elevation for a trapezoidal channel, ft Elevation difference in ft from that point to the point of concentration Depth from ground surface to pipe crown, ft Height of freeboard, ft

E′ f F Fi g h H Hg Hfb

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NOMENCLATURE (Cont) i id ie I If Kb Kb Kx L

= = = = = = = = =

Lo LALL n no p P Pc Pe Pt Pv Pw PL Q Qd rc R

= = = = = = = = = = = = = = = =

Rf

=

S So SL t tex tw t1 tan F Tc Ti To

= = = = = = = = = = =

Tw

=

Rainfall intensity in over a duration equal to the time of concentration, in./hr Intensity of rainfall, in./hr (mm/hr) Excess rainfall rate, in./hr Pipe's moment of inertia per unit length of pipe, equal to t3/12 Impact factor Bending moment coefficient Bedding constant dependent on the width of the sewer pipe bedding Deflection coefficient, also defined as a function of pipe laying conditions Distance, measured along the watercourse to the hydraulically most remote point in the catchment area, miles Distance from the farthest point in the catchment are to the point of interest, ft Length of ALL along the longitudinal axis of the pipe (refer again to Figure 16) Manning's roughness coefficient (frictional drag coefficient), for pipe or open channel flow Manning's roughness coefficient for overland flow Intensity of the distributed load at the surface, in units of W/L2 Total precipitation Critical buckling pressure, which can act on the crown or in any direction in the case of hydrostatic loading Earth load, psi Truck load, psi Combined trench load, in psi (prism earth load plus truck load), calculated as described above Wheel load, lbs. Vertical load on the pipe, psi Peak discharge ft3/s, Direct runoff, in. Radius of curvature, ft Hydraulic radius, which is the flow area divided by the wetted perimeter, ft. For pipes flowing full, it is simply half the radius, but for pipes flowing partly full it must be calculated and is a function of the flow depth. For open channels it also must be calculated for each flow depth. A reduction factor which takes into account the fact that the part of the pipe directly below the wheels is aided in carrying the truck load by adjacent parts of the pipe that receive little or no direct load from the wheels Pipe or channel gradient (slope) in decimal form (e.g., 1.5% slope is S = 0.015). Dimensionless slope of the surface, averaged over the catchment area Outside horizontal span of the pipe or the width of ALL, whichever is less Wall thickness, in units of length Exposure time, sec. Net wall thickness, in. Minimum manufacturing thickness, which includes manufacturing tolerances, in. Soil's frictional strength Time of concentration, minutes Initial pipe wall temperature Temperature of the process stream, °C Top width of the channel, ft

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NOMENCLATURE (Cont) u

= =

Poisson's ratio

w

= = =

Velocity, ft/s Volume of runoff, gallons (m3) Soil unit weight (pcf or kg/m2)

wL We

= =

Average pressure intensity, in units of weight per unit area (psf if Table 7 and Figure 16 are used)

Wsd ∆Y

= =

Applied load on the crown derived from the Marston load or soil prism load plus any other loads applied to the sewer, lb/in. Load on the sewer pipe in pounds per unit length Prescribed deflection, in.

γ

=

Unit weight of backfill, lb/ft3

∆x

=

Deflection in in.

∆X Xm

=

Horizontal deflection, outward, which is resisted by the soil, in.

=

Mid wall depth, m

u′ V Vr

tan φ

FIGURE 1 EXAMPLE OF RAINFALL DEPTH MAP, CONTINENTAL U.S., FROM U.S. WEATHER BUREAU'S TP 40 10 YEAR, 1 HOUR STORM, INCHES .8 .6 .6 1

.8

1

1

1.2

1.4

1.4

1.4

.6

1.4

1.6 1.8 2

.6

1.2 1 1 1 1.2 1.6

.6 .6 .8

.8

1.2

1.2

.6 .6

2.2 2.4 2.6 .6 .8 .6

2.8

1.2 1.2 3 1 1 1 1 1.2 1.4 1.8

3 2.2 2 1.6 1.4 1.4 1.6 1.8

2

2.4

3.6

2.6

3.4 3.8

2.8 2.6 3

3.8

2.8

3 3

3 3.2

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FIGURE 2 RELATIONSHIP BETWEEN DESIGN RETURN PERIOD AND EXCEEDANCE PROBABILITY 1000 800 600 500 95

400 300 200

90

Design Return Period, Td Years

100 85 50 75 70 25 60

50 10 40 5

2

Theoretical Probability (%) of not being Exceeded in Td Years

1 1

2

5

10

25

50

100

Design Period, T d Years Relationship between design return period, T years, design period, Td, and probability of not being exceeded in T d years.

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FIGURE 3-A EXAMPLE OF PUBLISHED IDF CURVE, HOUSTON TX, FROM TP 25 (U.S. WEATH. BUR.) 20.0 15.0

10.0 8.0 6.0 Return Period (Years) 100

4.0

25 50

Rainfall Intensity in Inches Per Hour

5

10

2.0 2

1.0 0.8 0.6 0.4

0.2

0.1 .08 .06 .04

.02 5

10

15

20 30 Minutes

40 50 60

2

Duration

3

4

5

6 8 10 12 Hours

Note: Frequency analysis by method of extreme values, after Gumbel

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FIGURE 3-B EXAMPLE OF USER SYNTHESIZED IDF CURVE, HOUSTON TX, FROM EXAMPLE NO. 1 IN APPENDIX A

10

10 yr 5 yr 2 yr 1 1

10

100

1000

Duration, min.

DP29Cf3b

FIGURE 4 EXAMPLE OF HOURLY RAINFALL DISTRIBUTION WITHIN A STORM, SCS TYPE II STORM, U.S. 100

80

% of Total Rainfall

Rainfall Intensity, in./hr

100

60

Appoximately 55% of the Rainfall Occurs During the 2 Hr Period Around the Center of the Storm

40

Approximately 70% of the Rainfall Occurs between Hour 8 and Hour 14

20 0 0

4

8

12

16

Elapsed Time Into Storm, hrs.

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FIGURE 5 NOMOGRAPH FOR SOLUTION OF “TIME OF CONCENTRATION" FOR OVERLAND FLOW H (ft) 500 Tc (min.) 200

400 300 200 150

Example:

150

Height = 100 ft Length = 3,000 ft Time of Concentration = 14 min.

100 80

Height of Most Remote Point Above Outlet

100

L (ft) 10,000

60 50 40

50

5,000

40 30

Maximum Length of Travel

3,000

20

10

5

2,000 1,500 1,000

Time of Concentration

30 25

500

4

20 15 10 8 6 5 4

300

3

3 200

2

150

2

100 1 1

Notes: (1) (2) (3) (4) (5)

(6)

Use nomograph Tc for natural basins with well defined channels, overland flows on bare earth and mowed grass roadside channels. For overland flow, grassed surfaces, multiply Tc by 2. For overland flow, concrete or asphalt surfaces, multiply Tc by 0.4. For concrete channels, multiply Tc by 0.2. Solution may be made by equation: 0.385

Tc

=

11.9 L3 H

Tc L H

= = =

Time of concentration, hrs. Length of longest watercourse, miles Elevation difference, ft

Based on recommendations by the USBPR (1963 - C). DP29Cf05

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FIGURE 6 CURVE NUMBERS (CN) FOR VARIOUS LAND USE CLASSIFICATIONS AND SOIL TYPES CN for Hydrologic Soil Group Soil Type

Land Use Description

A

B

C

D

Industrial districts

Avg., 72% impervious

81

88

91

93

Commercial and business areas

Avg., 85% impervious

89

92

94

95

98

98

98

98

Paved, with curbs and storm sewers

98

98

98

98

Gravel

76

85

89

91

Dirt

72

82

87

89

Paved parking lots, roads, driveways, etc. Streets and roads

Residential

65

77

85

90

92

1/3 acre

30

57

72

81

86

1 acre

20

51

68

79

84

Without conservation treatment

77

81

88

91

With conservation treatment

62

71

78

81

Good condition

68

78

86

89

Poor condition

39

61

74

80

Meadow

Good condition

30

58

71

78

Wood or forest land

Thin stand, poor cover, no mulch

45

66

77

83

Good cover, litter and brush cover the soil

25

55

70

77

Good condition, > 75% grass cover

39

61

74

80

Fair condition, 50% to 75% grass cover

49

69

79

84

Avg. lot size

Agricultural land

Avg. % impervious

1/8 acre

Cropland Pasture or range

Open spaces, lawns, parks, golf courses, etc.

FIGURE 7 DIRECT RUNOFF VS. RAINFALL FOR VARIOUS CN (CURVE NUMBERS) 8

SOIL GROUP 7 Q=

Direct Runoff (Q) in Inches

6

(P – 0.2 S)2 P + 0.8 S

100

A

High infiltration rate; deep well-drained sands and gravels

B

Moderate infiltration rate when thoroughly wet; moderately deep well-drained soils of moderately fine to moderately coarse texture

C

Slow infiltration rate when wet; chiefly moderately deep, well-drained soils of moderately fine to moderately coarse texture

D

Very slow infiltration rate; chiefly soils with high swelling potential, permanently high groundwater table, soils with a hardpan or claypan at or near the surface and shallow soils over nearly impervious materials

5 Curve Number CN =

1000 10 + S

95 90

4

80

85

70

75

3

60

65

2

50

55 1

45

40

35

30

0 0

1

2

3

4

5

6

7

DESCRIPTION

8

Rainfall (P) in Inches

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FIGURE 8 EXAMPLE OF RUNOFF HYDROGRAPH 0 Loss – (Constant Rate Assumption)

Precipitation, in.

.5

1.5 70

Examples:

Time, Hours

% of D Lg + 2

Ordinate

Net Hydrograph g

6

63.2*

19.*7*

54,290

7

73.7

24.9

68,510

8

84.2

25.8

71,000

9

94.8

23.4

64,330

TCV = 9.5 Hours D

60

50

Discharge, sec-ft x 103

Portion of Dimensionless Graph Computation

Excess Rainfall

1.0

D 2

40

= 4 Hours

Lg

= 7.5 Hours

Vol. = 26,150 Second-Feet-Days D = 9.5 Hours Lg + 2

3

Lg

D

* 6 x 100 9.5

TCV

30

9.5

** Ordinate = 54,290 x

26,150 20

10

6

12

18

24

30

36

42

48

54

Time, hrs.

60

66

72 DP29Cf08

FIGURE 9 EXAMPLES OF REFINERY MANHOLE SEAL ARRANGEMENTS

MH Outlet

From CB

Flanged Elbow

Outlet Invert 6" Min Seal (At the MH Wall)

To MH/ Lateral

Outlet Invert 6" Min Seal

12" Debris Pocket

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FIGURE 10 RATIOS OF HYDRAULIC ELEMENTS FOR CIRCULAR CONDUITS FLOWING PART FULL

Ratios of Hydraulic Elements for Circular Conduit 1.0

0.9 Area, A

Ratio of Depth to Diameter d / D

0.8

0.7

0.6 Discharge, Q 0.5

0.4 Hydraulic Radius, R 0.3 Velocity, V

0.2

0.1

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Ratios V / V f, Q / Qf, A / Af, R / Rf Note: (1) (2) (3)

Elements Vf, Qf, and Rf, are for pipe flowing full. Values shown for ratios A/Af and R/Rf are independent of friction factor. Values shown for ratios V/Vf and Q/Qf are for constant friction factor with depth.

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FIGURE 11-A INLET CONTROL NOMOGRAPH FOR CORRUGATED METAL PIPE (CMP) CULVERT 10,000

180

8,000

Example

156

6,000 5,000

D = 36 in. (3.0 ft) Q = 66 cfs

144

4,000

132

3,000

168

120

(1) (2) (3)

2,000

108

H D 1.8 2.1 2.2

(1) 6. H (ft)

5.

5.4 6.3 6.6

4.

(2) 6. 5.

6. 5. 4.

3. 3.

1,000

3.

800 84

(3)

4.

*D, ft

96

600 500

2.

400 72

2.

2.

1.5

1.5

48

42

1.5

D

200 Example

100 80 60 50 40

36

30

33

20

27

H D

Scale (1) (2) (3)

30

Headwater Depth in Diameters ( H )

54

Discharge (Q), CFS

Diameter of Culvert (D), in.

300

60

Entrance Type

Headwall Mitered to conform to slope Projecting

10

1.0

1.0

.9

.9

21

6 5 4 3

18

1.0 .9

.8

.8 .8

.7

8 24

.7 .7

To use scale (2) or (3) project horizontally to scale (1), then use straight inclined line through D and Q scales, or reverse as illustrated.

.6

.6 .6

2 15

H

D

.5

1.0

12

49 of 84

Headwater Depth for Corrugated-Metal Pipe Culverts with Entrance Control. (U.S. Bureau of Public Roads.) 288–D–2909.

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FIGURE 11-B INLET CONTROL NOMOGRAPH FOR CONCRETE PIPE CULVERT To use scale (2) or (3), project horizontally to scale (1), then use straight inclined line through D and Q scales, or reverse as illustrated. 180

10,000

168

8,000

156

6,000 5,000

144

(2)

(1)

Example

6.

D = 42 in. (3.5 ft) Q = 120 cfs

4,000 132 3,000

(1) (2) (3)

120 2,000 108

H D 2.5 2.1 2.2

6.

5. 5.

6.

H (ft)

5.

8.8 7.4 7.7

4.

*D, ft

96

(3)

4.

3.

4.

3.

3.

1,000 800

54

300

Example

200

100 48

42

80 60 50 40

36

30

33 20 30 27 24

21

2.

1.5

1.5

1.0

1.0

.9

.9

.8

.8

.7

.7

.6

.6

.5

.5

1.5

1.0 .9

.8 10 8 6 5

H D

Scale (1) (2) (3)

Entrance Type Square edge with headwall Groove end with headwall Groove end projecting

.7

4 18

2. 2.

400

H ) D

60

600 500

Headwater Depth in Diameters (

Diameter of Culvert (D), in.

72

Discharge (Q), CFS

84

.6

3 2

15

H 1.0

12

D .5

Headwater Depth for Concrete Pipe Culverts with Entrance Control. (U.S. Bureau of Public Roads.) 288–D–2908.

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FIGURE 11-C OUTLET CONTROL NOMOGRAPH FOR CMP CULVERT 2000 H

H

1000 800

Line

Turning

0.85 D

.4

Low Tailwater

High Tailwater

.5 .6

600

120

500

108

.8

400

96

1.0

300

84 72

50

66

Length (L),ft

60

2

100

50

Head (H), ft

200

100 80 60 50 40 Q = 35 30

Diameter (D), in.

Discharge (Q), cfs

54

Ke = 0.5

L = 120 Ke = 0.9

42

200 200 Ke = 0.9

33

8

D = 27 400

500 500

18 20

3

2

466.18 n2 L

2.5204 (1 + Ke) 15

5 4

10

400

24

8 6

H = 7.5

300

21 10

4

6

300

Example 30

3

5

36

27 20

100

48

12

Equation:

HT = HT Ke D n L Q

= = = = = =

D4

+

D 16/3

Q 10

2

Head, ft Entrance loss coefficient Diameter of pipe, ft Manning's roughness coefficient Length of culvert, ft Design discharge rate, cfs

Head for Corrugated - Metal Pipe Culverts Flowing Full, n = 0.024. (U.S. Bureau of Public Roads.) 288 - D - 2911. DP29Cf11c

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FIGURE 11-D OUTLET CONTROL NOMOGRAPH FOR CONCRETE PIPE CULVERT Pressure Line

2000

HT

HT

1000 800

Line

Turning

0.85 D

.4

Low Tailwater

High Tailwater

.6

120 108

600

.8 96

400

84

300

72 50

Discharge (Q), cfs

Q = 70

Diameter (D), in.

66 200

100

Example

60

2 Length (L), ft

54 L = 110

D = 48 48

Ke = 0.5

50

200 100 300 200

42

400 300

36

50 40 30

20

33

500

6

Ke = 0.1

8

30 500 27

Ke = 0.2

10

Ke = 0.5

24 21

466.18 n2 L

2.5204 (1 + Ke) Equatoin:

HT =

D4

+

D

16/3

Q

20

2

10

15

8 6

5 400

18

10

12

HT Ke D n L Q

= = = = = =

Head, ft Entrance loss coefficient Diameter of pipe, ft Manning's roughness coefficient Length of culvent, ft Design discharge rate, cfs

5 4

3

4

80 60

1.0

HT = 0.94

Head (H), ft

500

100

.5

Head for concrete Pipe Culverts Flowing Full, n = 0.012. (U.S. Bureau of Public Roads.) 288 – D – 2910. DP29Cf11d

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FIGURE 12 ILLUSTRATION OF EARTH LOADS ON BURIED CONDUIT

A

P

Bd

F H

B

F

W c Load on Pipe

C

D Side Fill Bc

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FIGURE 13 MARSTON COEFFICIENT Cd 1.0

1.5

2.0

3.0

4.0

5.0

30 25

Cd (Graph on Left)

20

2

15

1.5 A

B C

D E

Values of

H H or Bt Bd

10 9 8

1.0 0.9 0.8

7

0.7

6

0.6

5

0.5

4

0.4

3

0.3

Cd for Kµ and Kµ ′

2

A = B C D E

1.5

= = = =

0.1924 for granular materials without cohesion 0.165 max for sand and gravel 0.150 max for saturated top soil 0.130 ordinary max for clay 0.110 max for saturated clay

0.2

0.15

Cd (Graph on Right) 0.1 0.10

0.15

0.20 0.25 0.30

0.40

0.50 0.6 0.7 0.8 0.9 1.0

1.5

Values of Coefficient Cd or Ct DP29Cf13

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FIGURE 14 SUMMARY OF STANDARD METHODS FOR CALCULATING EARTH LOADS ON BURIED CONDUITS PIPE TYPE, SIZE

SKETCH

Concrete and Reinforced Concrete

h

If " Cut & Cover " W c = Cd γ Bd2

Bd

Concrete and reinforced concrete pipe are "rigid" in context of determining pipe wall thickness

All sizes

Cast Iron (CI)

Load on Conduit Crown is the lesser of...

Bd = OD +2'

Wc = Cd γ Bd2 or

All sizes

Marston formula is used to determine earth loads, including the standard means of reducing loads on the conduit when tunnel installations by taking into account the contribution of the cohesion on the walls.

Concrete Pipe Design Manual, pp. 27-41, by Am. Concrete Pipe Assn., 1985

If " Tunnelled In " Wc = Ct Bc (γ Bc – 2c) Where: c = cohesion Ct = Marston coefficient with B = Bc

h

Cast iron pipe is "rigid" in context of determining pipe wall thickness

REFERENCE

Superimposed loads (e.g., footing, truck) are brought down to the top of the pipe using Boussinesque or equivalent elastic methods.

h

Bc

COMMENTS

Bc

h

Wc = Cd γ Bc2

Standards for cast iron pipe in direct burial mode are probably obsolete to the extent that this material is seldom used anymore in direct burial. Cast iron pipe may be used within a building down to grade, but at the point it will likely tie into DIP, concrete pipe, VCP or other common direct burial pipe.

"Thickness Design of Cast-Iron Pipe," ASA A21. 1-1967

Marston load is used to determine the trench (dead weight of earth) component, with one caveat, as follows. First the standard Marston load is calculated for the normal "ditch" end earth condition, wherein the width is taken as the ditch width at the crown of the pipe (generally at least 2 feet wider than the pipe diameter). Then a comparison is made to the "positive projecting" condition wherein a larger coefficient is used, but the width is taken as the pipe diameter, which is smaller than the trench width. The smaller earth load is then used for designing the pipe. Superimposed loads as truck loads are distributed down to the pipe crown via elastic methods such as Boussinesque. DP29Cf14a

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FIGURE 14 (Cont) SUMMARY OF STANDARD METHODS FOR CALCULATING EARTH LOADS ON BURIED CONDUITS PIPE TYPE, SIZE

SKETCH

COMMENTS

γ = Soil Unit Weight

Ductile Iron (DI)

h

Bd = OD +2'

h Bc

DIP is considered "flexible" for pipe wall thickness design

φ < B"

φ > 18"

Wc = Cd γ Bd2

Wc = γ Bch

h Bc Wc = γ Bch Plastic (HDPE)

h Bc Wc = γ h Bc

All sizes Bd

h Bc Wc = Cd γ Bd2

"Thickness Design of Ductile Iron Pipe," ASA A21.5-65.

"Thickness Design of Ductile Iron Pipe," ANSI C-50/A21.50-91.

"Design of Ductile Iron Current standard for earth Pipe," by Ductile Iron load is the simple prism w = Pipe Research Assn. γhΦ , directly over the pipe. Superimposed loads are distributed down to the pipe by elastic methods, but the results are presented in tabular format, as previously done (see above). Design method varies by manufacturer.

Bc

Plastic pipe is considered "flexible" for pipe wall thickness design

Older standards (c.a. 1965) used Marston formula for Φ up to 8", and simple prism w = γ hΦ of Φ > 18". For pipe sizes in between 8" and 18", pro-rated between the two methods. Superimposed truck loads calculaed via elastic stress distribution, although tables were used to present the results for varying depth of cover conditions.

REFERENCE

Driscopipe, "Systems Design," pp. 40-46, Phillips Driscopipe, 1991

Driscopipe (Phillips) recommends simple prism over the pipe w = γhΦ , where: Φ is pipe OD. Other superimposed loads are brought down to the pipe crown via elastic distribution (Boussinesque, or equivalent). Plexco (Chevron) acknowledges that the simple prism load is the easiest to calculate, but points out that it fails to take advantage of the arching that is known to occur, especially with the flexible pipes. They then suggest that the Marston formula is the most common means to take arching into account for the trench loads (earth dead weight). Elastic distribution methods (e.g. Boussinesque) for other superimpodes loads. In Marston formula, the trench width at the pipe crown (the standard Marston approach) is used, not the smaller pipe width.

Plexco/Spirolite "Engineering Manual, 2. System Design", pp. 3350, Chevron Chemicals, Performance Pipe Division, 1993.

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FIGURE 15 INFLUENCE DIAGRAM FOR EFFECTS OF DISTRIBUTED SURFACE LOADS ON BURIED PIPE VALUES OF LOAD COEFFICIENTS, Cs, FOR CONCENTRATED AND DISTRIBUTED SUPERIMPOSED LOADS VERTICALLY CENTERED OVER SEWER PIPEa

D 2H

M 2H

or

L 2H

or

Bc 2H

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.2

1.5

2.0

5.0

0.1 0.2 0.3 0.4

0.019 0.037 0.053 0.067

0.037 0.072 0.103 0.131

0.053 0.103 0.149 0.190

0.067 0.131 0.190 0.241

0.079 0.155 0.224 0.284

0.089 0.174 0.252 0.320

0.097 0.189 0.274 0.349

0.103 0.202 0.292 0.373

0.108 0.211 0.306 0.391

0.112 0.219 0.318 0.405

0.117 0.229 0.333 0.425

0.121 0.238 0.345 0.440

0.124 0.244 0.355 0.454

0.128 0.248 0.360 0.460

0.5 0.6 0.7 0.8

0.079 0.089 0.097 0.103

0.155 0.174 0.189 0.202

0.224 0.252 0.274 0.292

0.284 0.320 0.349 0.373

0.336 0.379 0.414 0.441

0.379 0.428 0.467 0.499

0.414 0.467 0.511 0.546

0.441 0.499 0.546 0.584

0.463 0.524 0.584 0.615

0.481 0.544 0.597 0.639

0.505 0.572 o.628 0.674

0.525 0.596 0.650 0.703

0.540 0.613 0.674 0.725

0.548 0.624 0.688 0.740

0.9 1.0 1.2 1.5 2.0

0.108 0.112 0.117 0.121 0.124

0.211 0.219 0.229 0.238 0.244

0.306 0.318 0.333 0.345 0.355

0.391 0.405 0.425 0.440 0.454

0.463 0.481 0.505 0.525 0.540

0.524 0.544 0.572 0.596 0.613

0.574 0.597 0.628 0.650 0.674

0.615 0.639 0.674 0.703 0.725

0.647 0.673 0.711 0.742 0.766

0.673 0.701 0.740 0.774 0.800

0.711 0.740 0.783 0.820 0.849

0.742 0.774 0.820 0.861 0.894

0.766 0.800 0.849 0.894 0.930

0.784 0.816 0.868 0.916 0.956

aInfluence coefficients for solution of Holl's and Newmark's integration of the Boussinesq equation for vertical stress.

Uniform Load p, lb/ft2, Acting on Area D x M

A

H

J

D M B

G

F Ground Surface

C

E

D

Diagram for obtaining stress at point A caused by load in shaded area BCDE (ASCE, 1969).

H I

Bc Bc

Distributed superimposed load vertically centered over sewer pipe (psf x 47.9 = Pa) (ASCE, 1969).

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FIGURE 16 AASHTO HS-20 TRUCK LOADS ON BURIED PIPE AASHTO HS20 Load 4000 lb 4000 lb

AASHTO HS20 Load 4000 lb 4000 lb

6 ft

AASHTO Alternate Load 12000 lb 12000 lb

6 ft 14 ft

14 ft

12000 lb

12000 or 16000 lb

4 ft 12000 lb

HS20 and Alternate Loads 16000 lb

16000 lb

16000 lb

0.83 ft (10 in.)

16000 lb 14 ft to 30 ft

1.67 ft (20 in.) Wheel Load Surface Contact Area (ft x 0.304 8 = m; in. x 25.4 = mm; lb x 0.453 6 = kg) Am. Concrete Pipe Assoc., 1988).

6 ft 4 ft 6 ft 16000 lb 16000 lb Live Load Spacing (ft x 0.304 8 = m; lb. x 0.453 6 = kg) (Am. Concrete Pipe Assoc., 1988)

Wheel Load Areas

Direction of Travel 1.67 ft (20 in.)

0.83 ft

4.0 ft

Direction of Travel

1.67 ft

0.83 ft (10 in.) 1.67 ft

Wheel Load Areas Wheel Load Area H

Distributed Load Area H ft (5.67 + 1.75 H) ft (1.67 + 1.75 H) ft

Distributed Load Area – Single Dual Whell (ft x 0.304 8 = m; in. x 25.4 = mm) (Am. Concrete Pipe Assoc., 1988).

Direction of Travel Wheel Load Areas 1.67 ft 1.67 ft Wheel Load Areas

Distributed Load Area

(0.83 + 1.75 H) ft

(0.83 + 1.75 H) ft

Distributed Load Area – Two HS20 Trucks Passing (ft x 0.304 8 = m) (Am. Concrete Pipe Assoc., 1988).

0.83 ft 4.0 ft

0.83 ft L H

H ft 3Bc 4

Bc

(5.67 + 1.75 H) ft (4.83 + 1.75 H) ft

Distributed Load Area

Distributed Load Area – Alternate Loads in Passing Mode (ft x 0.304 8 = m) (Am. Concrete Pipe Assoc., 1988).

3Bc 4 Effective Supporting Length of Pipe (Am. Concrete Pipe Assoc., 1988). Le = L + 1.75

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FIGURE 17 ILLUSTRATION OF “THREE EDGE BEARING" TEST FOR USE IN INDIRECT DESIGN OF RIGID PIPES

Rigid Steel Member

Pipe Wall

Bearing Strips

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DRAINAGE SYSTEMS DESIGN PRACTICES

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FIGURE 18 BEDDING FACTOR “Bf" FOR CONCRETE PIPE 1-1/4 Bc

1/4 D 4" min.

Bc + 8" min. 12" min.

1-1/4 Bc Bc + 8" min. 1/8 H 6" min.

Densely Compacted Backfill Bc

Plain or Reinforced Concrete 2000 psi min.

1/4 Bc d (See Notes)

Bc

Compacted Granular Material

Concrete Cradle Class A Reinforced As = 1.0% Bf = 4.8 Reinforced As = 0.4% Bf = 3.4 Pain Bf = 2.8

d

Concrete Arch

12"

12" Bc

Fine Granular Fill Material 2" min.

0.6 Bc Shaped Subgrade with Granular Foundation

Densely Compacted Backfill

Bc

Compacted Granular Material

d

Granular Foundation Class B Bf = 1.9

1/8 H 6" min.

1/8 H 6" min.

Bc

0.5 Bc

Lightly Compacted Backfill

Bc

1/6 Bc

Compacted Granular Material or Densely Compacted Backfill

Shaped Subgrade

d

Granular Foundation Class C Bf = 1.5

Loose Backfill

1/8 H 6" min.

See next page for Legend and Notes Bc

Flat Subgrade

Class D Bf = 1.1

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December, 2001

FIGURE 18 (Cont) BEDDING FACTOR “Bf" FOR CONCRETE PIPE

Depth of Bedding Material Below Pipe D

d (min.)

27" & Smaller 30" to 60" 66" & Larger

3" 4" 6"

Legend Bc H D d As

= = = =

Outside diameter Backfill cover above top of pipe Inside diameter Depth of bedding material below pipe = Area of tranverse steel in the cradle of arch expressed as a percentage of area of concrete at invert or crown.

Notes: For Class A beddings, use d as depth of concrete below pipe unless otherwise indicated by soil or design conditions. For Class B and C beddings, subgrades should be excavated or over excavated, if necessary, so a uniform foundation free of protruding rocks may be provided. Special care may be necessary with Class A or other unyielding foundations to cushion pipe from shock when blasting can be anticipated in the area. DP29Cf18b

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FIGURE 19-A BEDDING FACTOR “Bf" FOR VITRIFIED CLAY PIPE Load Factors – Class A 1.25 Bc or Bc + 8 in. (200 mm) Min. 12 in. (300 mm) Min.

Hand Placed Backfill Bc

Bc/4

Concrete

Bc/4, 4 in. (100 mm) Min.

Load Factors: 2.2 Native Backfill Material Lightly Tamped 2.8 ASTM D448 = 67 Crushed Stone 3.4 Reinforced Concrete, p = 0.4% 1.25 Bc or Hand Placed Backfill

Figure 1 Class A-1

5 in. (125 mm) Min.

Bc + 8 in. (200 mm) Min.

Concrete

12 in. (300 mm) Min.

Hand Placed Backfill

Bc/4, 4 in. (100 mm) Min. Bc

Concrete

Bc

Bc/2

Bedding

3/4 Bc

Bc/8 Max., Bc/15 Min.

Bedding Bc/8, 4 in. (100 mm) Min. Load Factors: 2.8 Plain Concrete 3.4 Reinforced Concrete, p = 0.4%

Load Factor 2.7

Figure 2 Class A-ll

Bc/8, 4 in. (100 mm) Min.

Figure 3 Class A-III 6 in. (150 mm) Min.

1.5 Bc or Bc + 8 in. (200 mm) Min.

Bc/4, 5 in. (125 mm) Min. Concrete

Bc/6, 5 in. (125 mm) Min.

Concrete

Bc

Bc Bc/8 Max., Bc/15 Min.

Bedding

Bc/15 Min.

Const. Joint Load Factor 3.2 Figure 4 Class A-IV

Bc/8 Max., 4 in. (100 mm) Min.

Load Factor 4.5 Figure 5 Class A-V

Bc/4, 4 in. (100 mm) Min. DP29Cf19a

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FIGURE 19-B BEDDING FACTOR “Bf" FOR VITRIFIED CLAY PIPE Load Factors – Class B,C and D

12 in. (300 mm) Min.

Hand Placed Backfill Bc

Bc/2

Bedding

Bc/8, 4 in. (100 mm) Min. Load Factor 1.9 Figure 6 Class B

Hand Placed Backfill

12 in. (300 mm) Min.

12 in. (300 mm) Min.

Hand Placed Backfill Bc

Bc

Bc/6 Min. Bedding

Bc/8, 4 in. (100 mm) Min. Load Factor 1.5

0.5 Bc

Figure 8 Class C

Load Factor 1.5 Shaped Bottom Figure 7 Class C

Hand Placed Backfill

12 in. (300 mm) Min.

Bc

Load Factor 1.1 Flat or Unshaped Trench Bottom Figure 9 Class D DP29Cf19b

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FIGURE 20 MANUFACTURER SPECIFIC DESIGN CHARTS/TABLES FOR THICKNESS DESIGN OF HDPE MAXIMUM BURIAL DEPTH, ft IN DRY SOIL OF 100 lb/ft3

MAXIMUM EXTERNAL PRESSURE psi

MAXIMUM DEFLECTION, % AFTER INSTALLATION

SOIL MODULUS, psi*

SOIL MODULUS, psi*

SOIL MODULUS, psi*

SDR 1000

2000

3000

1000

2000

3000

1000

2000

3000

32.5

25

32

37

17

22

26

1.7

0.9

0.6

26

33

45

52

23

31

36

2.3

1.2

0.8

21

46

61

71

32

42

49

3.2

1.6

1.1

19

52

69

81

36

48

56

3.6

1.8

1.2

17

61

121

181

42

84

126

4.2

2.1

1.4

15.5

56

112

168

39

78

117

3.9

2.0

1.3

13.5

49

98

147

34

68

102

3.4

1.7

1.1

11

39

78

117

27

54

81

2.7

1.4

0.9

9.3

33

68

101

23

47

70

2.3

1.2

0.8

8.3

30

61

89

21

42

62

2.1

1.1

0.7

7.3

26

52

79

18

36

55

1.8

0.9

0.6

*assumes no external loads

Plot of Vertical Stress - Strain Data for Typical Trench Backfill (Except Clay) from Actual Test*

Support Factor 26

Pt = Vertical Soil Pressure (Ib/ft2)

4000

17

11

7

5 90% Standard Density

3000

80% Standard Density

Compacted Soil

E' = Soil Modulus Pt E' = ε

4

s

3

* Test Performed at the Utah State University Experiment Station

2000

fs 2

Zone of Critical Void Ratio

1000

Compacted Soil 70% Standard Density

Loose Soil

Loose Soil

0 0

1

2

3

4

εs Vertical Soil Strain (Percent)

5

6

1 32.5 21

13.5

9

SDR DP29Cf20

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FIGURE 21 SOIL MODULUS E′ FOR USE IN MODIFIED IOWA FORMULA FOR FLEXIBLE PIPE DESIGN BUREAU OF RECLAMATION AVERAGE VALUES OF E′ FOR IOWA FORMULA (INITIAL DEFLECTION) E′ FOR DEGREE OF BEDDING COMPACTION, lb/in.2 Slight, 95% Proctor, >70% relative density

No data available: consult a competent soils engineer, otherwise, use E' = 0

Fine-grained soils (LL < 50) soils with medium to no plasticity CL, ML, ML-CL, with less than 25% coarse grained particles

50

200

400

1,000

Fine-grained soils (LL < 50) soils with medium to no plasticity CL, ML, ML-CL, with more than 25% coarse grained particles

100

400

1,000

2,000

200

1,000

2,000

3,000

Crushed rock

1,000

3,000

3,000

3,000

Accuracy in terms of percentage deflection4

± 2%

± 2%

± 1%

± 0.5%

Coarse-grained soils with fines GM, GC, SM, SC3 contains more than 12% fines Coarse-grained soils with little or no fines GW, GP, SW, SP3 contains less than 12% fines

1 ASTM D-2487, USBR Designation E-3 2 LL = Liquid Limit 3 Or any borderline soil beginning with one of these symbols (i.e., GM-GC, GC-SC). 4 For ≥1% accuracy and predicted deflection of 3%, actual deflection would be between 2% and 4%.

Note: Values applicable only for fills less than 50 ft (15 m). Table does not include any safety factor. For use in predicting initial deflections only; appropriate Deflection Lag Factor must be applied for long-term deflections. If bedding falls on the borderline between tow compaction categories, select lower E' value, or average the two values. Percentage Proctor based on laboratory maximum dry density from test standards using 12,500 ft-lb/ft3 (598,000 J/m2) (ASTM D-698, AASHTO T-99, USBR Designation E-11). 1 psi = 6.9 Kpa. DUNCAN-HARTLEY SOIL REACTION MODULUS

TYPE OF SOIL

DEPTH OF COVER, ft

E′ FOR STANDARD AASHTO RELATIVE COMPACTION, lb/in.2 85%

90%

95%

100%

Fine-grained soils with less than 25% sand content (CL, ML, CL-ML)

0-5 5 - 10 10 - 15 15 - 20

500 600 700 800

700 1,000 1,200 1,300

1,000 1,400 1,600 1,800

1,500 2,000 2,300 2,600

Coarse-grained soils with fines (SM, SC)

0-5 5 - 10 10 - 15 15 - 20

600 900 1,000 1,100

1,000 1,400 1,500 1,600

1,200 1,800 2,100 2,400

1,900 2,700 3,200 3,700

Coarse-grained soils with little or no fines (SP, SW, GP, GW)

0-5 5 - 10 10 - 15 15 - 20

700 1,000 1,050 1,100

1,000 1,500 1,600 1,700

1,600 2,200 2,400 2,500

2,500 3,300 3,600 3,800

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FIGURE 22 RIP-RAP SIZING REQUIREMENTS FOR USE AS CHANNEL LINING

26 170

3:1 160

2:1

20

1 1/2:1

18

1:1

150

1.2

1.4

d

1.0

=

.8

16

Side Slope (H:V)

1.0

Coefficient (C) for Stone Size Correction

k

4:1

22

0.8

Stone Diameter in Feet

12:1 or Bottom

24

140

Total Depth of Flow in Feet

Stone Weight, in Pounds 20 60 600 1000 1500 3000 5000 2000 4000 1 510 40 100 200 400 800

180

Velocity (V) in Feet Per Second

Unit Weight of Rock (W) in Pounds Per Cubic Ft

190

14 12 10 For Stone Weighing 165 Lbs. Per Cu. Ft 8

.6

6 .4 4 2

.2

0 0

0 0

.2 .4 .6 Velocity Against Stone (FPS) Mean Velocity in Channel (FPS)

=

.8 Vs

1.0

1

2

3

4

Equivalent Spherical Diameter of Stone, (K) in Feet

Vm

Note: (1) Adapted from USBPR (1970-b). (2) Stone size (K) is the diameter in feet of an equivalent spherical stone having the same weight as the 50% (median) stone size, by weight, of well-graded stones with a unit weight of 165 pounds per cubic foot. (3) When the depth of flow exceeds about 10 feet, use 0.4 of the total depth. (4) When the unit weight of the stone is not 165 PCF, the size (K) should be corrected by Creager's Equation: Kw =

102.5 = C.K W - 62.5

Where:

(5)

K = Stone size in graphs Kw = Corrected stone size for stone of unit weight W pounds per cubic foot C = Correction cofficient For determining the stone size at the point of impingement, the velocity vs should be multiplied by a factor varying between 1 and 2 (depending upon the severity of the attack by the current) before entering into the graph. DP29Cf22

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APPENDIX A - EXAMPLE PROBLEMS HYDROLOGIC DESIGN Example Problem No. 1, Synthesizing a Local Intensity-Duration-Frequency (IDF) Curve from 30-Minute Storm Data

The 30-minute rainfall amount for the return period of interest must be known and is used as a starting point. That total rainfall amount is then converted to longer or shorter durations by multiplying by the factors in the following table for the continental U.S. A similar table of conversion factors would have to be obtained from the local weather authorities for other locations. TABLE A-1 FACTORS FOR CONVERTING FROM 30-MINUTE DURATION STORM DEPTHS TO DEPTHS FOR OTHER STORM DURATIONS, CONTINENTAL U.S. DURATION

DEPTH FACTOR (in., total)

2 hrs

1.60

90 min

1.50

60 min

1.26

30 min

1.00

15 min

0.72

10 min

0.57

5 min

0.37

The rainfall hourly intensity (in. per hour) for any other storm duration is then determined by multiplying by the appropriate depth factor to convert the specified duration into an implied hourly rate. For example, if the 30 minute total rainfall is 2.7 in., then the corresponding 10 minute total rainfall would be 0.57 x 2.7 in. = 1.54 in. Since this amount of rain would have fallen in a 10 minute period, the implied hourly intensity is 1.54 x (60 min/10 min) = 9.2 in./hour (six 10 minute periods in an hour). This intensity (9.2 in./hour) is the value that would be used in the Rational Formula to calculate the runoff from a catchment area whose time of concentration (see above) is 10 minutes. Alternatively, this value could be plotted along with hourly intensities for other durations to develop an IDF curve for the location. The process is described in more detail later in this example problem. If intensity-duration data are required for return periods other than the one for which rainfall data is available, the total rainfall depth for differing return periods can usually be approximated by data published by local government bureaus. In the U.S., the factors presented in the following table can be used to convert total rainfall depths from one return period to another. Note that a similar table providing conversion factors for various return periods would have to be obtained from the local weather authorities for other locations. TABLE A-2 FACTORS FOR ESTIMATING TOTAL RAINFALL DEPTH FOR VARIOUS RECURRENCE INTERVALS, CONTINENTAL U.S. RECURRENCE INTERVAL (YEARS)

FACTOR

2 yr

1.0

5 yr

1.3

10 yr

1.6

25 yr

1.9

50 yr

2.2

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APPENDIX A - EXAMPLE PROBLEMS (Cont) Note that the above factors are average factors suitable for estimating purposes or for use when more comprehensive rainfall data is unavailable. Such an approach would apply to well developed areas such as the U.S. and most of Europe where rainfall records are abundant. It may also applicable to more remote sites, again assuming that rainfall records are available and assuming the conversion factors such as those presented in the above table have been compiled by government bureaus. However, the values in these tables are regional averages, and as such will not necessarily conform precisely to site specific rainfall data collected over several years, even for a site within the continental U.S. If rainfall data has been tabulated by government authorities for a particular site, use of that data is obviously preferable to the factors provided in tables such as that provided above. To produce intensity-duration curves for a different return period storm, the 30-minute duration storm of the desired return period would either be read directly from published local data or would be estimated using the above table and the 30-minute storm of the known recurrence interval. Then intensities for durations other than 30 minutes would be calculated as described previously. Presentation of intensity-duration data for storms of several return periods (frequencies) on the same graph would result in a complete IDF curve (intensity-duration-frequency). Based on the above described methodology, the following illustrates development of IDF curves for Houston, Texas, for durations ranging from 5 minutes to 2 hours and recurrence intervals of 2, 5 and 10 years, given only the 10 year 1 hour storm amount of 3.4 in., taken from maps provided in U.S. Weather Bureau's TP-40 (1961). 1. Calculate the 2 and 5 year one-hour rainfall amounts from the factors presented in Table A-2 Given then

2.

10 yr, 1 hr storm = 5 yr, 1 hr storm =

(Note, TP-40 would give 2.9 in., which is a more accurate value. However, for this example, continue to use 2.8) and 2 yr, 1 hr storm = 3.4 x 1.0/1.6 = 2.1 in. (TP-40 would give 2.35 in.; use 2.1 for this example) Determine corresponding 30-minute total rainfall depths using factors in Table A-1 10 yr, 30 minute

3.

3.4 in. 3.4 x 1.3/1.6 = 2.8 in.

=

3.4 in. / 1.26 = 2.7 in. (note converting back to 30-minute duration, therefore divide) 5 yr, 30 minute = 2.8 in. / 1.26 = 2.2 in. 2 yr, 30 minute = 2.1 in. / 1.26 = 1.7 in. Determine the hourly intensities for other return periods using the factors in Table A-1

Calculation is shown for 2 year storms; 2 yr, 30 min rainfall total is 1.7 in. over 30 minutes total time.

DURATION

FACTOR (TABLE 1)

CALCULATION (2 YR STORMS SHOWN)

2 YR

5 YR

10 YR

HOURLY INTENSITY,

HOURLY INTENSITY,

HOURLY INTENSITY,

in./hr

in./hr

in./hr

5 min

0.37

0.37 x 1.7 in. x (60 min/5 min) =

7.5 iph

9.8

12.0

10 min

0.57

0.57 x 1.7 in. x (60 min/10 min) =

5.8 iph

7.6

9.3

15 min

0.72

0.72 x 1.7 in. x (60 min/15 min) =

4.9 iph

6.4

7.8

30 min

1.00

1.00 x 1.7 in. x (60 min/30 min) =

3.4 iph

4.4

5.4

1 hr

1.26

1.26 x 1.7 in. x (60 min/60 min) =

2.1 iph

2.7

3.4

2 hr

1.60

1.60 x 1.7 in. x (60 min/120 min) =

1.4 iph

1.8

2.2

The hourly intensities for the 5 and 10 year 30 minute storms, with total depths of 2.2 and 2.7 in. respectively, were determined by multiplying the 2 year storm values by 1.3 and 1.6 respectively (Table A-2) to arrive at the hourly intensities shown in the right two columns. The results can be combined into an IDF plot such as Figure 3B. Such a plot can be used to interpolate hourly intensities for a range of storm durations, as is customarily needed in order to calculate runoff flow rates using the Rational Formula.

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APPENDIX A - EXAMPLE PROBLEMS (Cont) Example Problem No. 2, Calculating Time of Concentration for Use in the Rational Formula

Overland flow example Given a 10 acre area, mostly undeveloped, within an industrial site, where flow is mainly via overland grassed surfaces which are not mowed or otherwise maintained. The longest watercourse length is 900 ft, and the elevation difference along it is 6 ft (dimensions from topographic map or survey). Determine the time of concentration either by use of the nomograph in Figure 5 or directly via the Kirpich formula. By the Kirpich formula (see Eq. 3), 0.385

æ 11.9 L3 ö ÷ Tc = ç ç ∆H ÷ è ø

where: Tc = Time for concentration, hrs. L = Length of the longest watercourse in miles, ∆H = Elevation difference along the watercourse, ft. Calculated Tc = 0.17 hrs, or 10 minutes. Since the undeveloped land is not maintained, the value calculated by the above method should be doubled. Time of concentration for this catchment area, or this portion of a larger catchment area, is therefore 2 x 0.17 hrs = 0.34 hrs or 20 minutes.

While it is difficult to imagine a paved area this large, the calculated concentration time would be multiplied by 0.4, if the area were paved but not confined in discrete paved channels and ditches. If the flow were conveyed in channels, then the calculated concentration time would be multiplied by 0.2, resulting in a Tc of only 2 minutes. However, for this latter condition, the assumption of overland flow is probably no longer valid, and the determination of time of concentration should be carried out as described below. Time of Concentration via Pipe and Ditch Flow Travel Times

For developed land in which storm runoff is conveyed mainly by ditches and buried storm sewers, the time of concentration to be used for determining the flow at any subsequent downstream point is determined by summing up discrete travel times for the route from the most distant point in the catchment area. Consider a paved industrial site where the flows are collected in sub-laterals which feed into lateral storm drains that feed into mains. Determine the time of concentration for the flow reporting to the main, if the length of the catchment area is 1000 ft, and the most remote sublateral feeding into the lateral is 50 ft in length, and receives its inflow through a drop inlet that drains a paved area that is 80 ft by 50 ft. The sub-laterals and laterals have are at a nominal grade of 0.5% fixed by topography, and assume they have been sized such that they flow at a velocity of 3 fps when delivering their respective design flows. The time for runoff to travel by overland flow from the edges of each sub-catchment area to the respective drop inlet is called the “inlet time". Inlet time will vary with the surface slope, the nature of the surface cover, and the length of the overland flow path. In general, the higher the rainfall intensity, the shorter the inlet time. Inlet time is usually selected, somewhat arbitrarily, to be anywhere from 5 to 15 minutes. In densely developed areas, where impervious surfaces shed their water directly to storm sewers through closely spaced inlets, an inlet time of 5 minutes is often reported. Times shorter than 5 minutes present problems in that the shortest duration presented on IDF curves is typically 5 minutes. Five minutes should be taken as the minimum inlet time for use in design unless there is reason to select a longer inlet time (e.g., if calculation of travel time using the Kirpich formula indicates a longer time, the calculated value should be used. However, for closely spaced inlets in a paved industrial area, it is not likely that the Kirpich formula would result in inlet times greater than 5 minutes unless the surface slope is extremely flat.) Adopting an inlet time of 5 minutes, the time of concentration is then determined by adding travel times within the pipe conduits. Since the sub-laterals are 50 ft long, travel time to the lateral would be 50/3.5 fps = 14 seconds (0.2 minutes), which could almost be ignored in view of the assumption regarding inlet time. Travel to the main in the lateral (1000 ft long) would require 4.8 minutes, which implies a combined Tc for the catchment area of 10 minutes (5 minutes inlet, 0.2 minutes in the sub-lateral, and 4.8 minutes in the lateral enroute to the main).

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APPENDIX A - EXAMPLE PROBLEMS (Cont) Example Problem No. 3, Use of the Rational Formula for Runoff Flow Rate

Assume for this problem that design for a 10 year flow in Houston, Texas is desired, and it had been determined by the methods described in the body of the Design Practice that Tc is 10 minutes. The U.S. Weather Bureau IDF curve (from TP-25) gives 7.2 in./hr as the intensity for a storm of 10 minutes duration for Houston, while the user developed IDF described in Example Problem No.1 indicates 9.2 iph as the appropriate value. Note that a 10 year-one hour storm for the same location produces 3.4 in. of rain, for an hourly intensity of only 3.4 iph, which if used would result in an underestimate of the flow for this particular component by a factor of about 3. Assuming a mainly paved industrial area with C = 0.9, and a catchment area of 100 x 120 ft (30 x 37 m) (equals 0.27 acres), which might represent the catchment area for four storm drains, and adopting the user developed value of 9.2 iph as the intensity, the 10 year flow via the Rational Formula (see Eq. 1) would be Q = 0.9 x 9.2 iph x 0.27 = 2.23 cfs (1000 gpm) Using the metric equivalent formula (see Eq. 2), and assuming the equivalent intensity is 9.2 x 25.4 = 234 mm/hr, A = 30 m x 37 m = 1110 m2 = 0.00111 km2, Q = 0.278 x 0.9 x 234 mm/hr x 0.00111 km2 = 0.065 m3/sec. For the 2-year event, the IDF curve presents an intensity of 5.8 iph, and the corresponding flow would be 631 gpm. To place this flow in perspective, a 12-in. pipe, at a slope of 0.6%, could carry a flow of about 2.3 cfs while flowing about 2/3 full. Methods to calculate flow capacities in pipes are described later in this Design Practice. Example Problem No.4, Runoff Volume via Simple Runoff Coefficient, and via SCS Curve Number Method

For the small industrial catchment area described above, assume the runoff coefficient is 0.9, for a paved industrial area. If the design storm of interest were specified to be the 10 year 24 hour storm, which for Houston Texas is 8.5 in., the volume of runoff for the 24 hour period would be Vr = 0.9 x (8.5 in./12) x 0.27 acres = 0.172 ac ft = 56,000 gallons The metric equivalent, with total storm depth = 8.5 x 25.4 = 216 mm and A = 1,110 m2, V = 0.9 x 0.216 m x 1,110 m2 = 216 m3 For the previously described example (10 year, 24 hour storm at Houston, Texas with total rainfall depth 8.5 in.), in an industrial area with CN = 92, the runoff as read from Figure 7 or calculated from the expression provided there would be (Q) = 7.5 in.. Runoff volume would be Vr = 7.5 in./12 x 0.27 acres = 0.169 ac ft = 54,980 gallons Had a CN of 95 been selected, calculated direct runoff would be 7.9 in., and the corresponding runoff volume would be 57,900 gallons. These two CNs bracket the assumption of a runoff coefficient of 0.9 in the previous method.

HYDRAULIC DESIGN Example Problem No. 5, Pipe Flowing Partly Full (Gravity Flow)

Given a gradient fixed by other constraints at 0.008, and the design flow is 2.23 cfs, what nominal diameter concrete pipe would be required? The requirement is to deliver 2.23 cfs at a flow depth of approximately 0.7D, and to do so with a velocity between 2.5 and 10 fps. Assume n = 0.013. Trial D = 8 in., has R = 0.197 ft and A = 0.261 ft2 when flowing at 0.7D (= 5.4 in. deep). Manning's equation, with S = 0.008 gives V = 3.47 fps, and Q = 0.91 cfs. Therefore, pipe is too small. Check the next larger size. Trial D = 12 in., has R = 0.296 ft and A = 0.587 ft2 when flowing at 0.7D (= 8.4 in. deep). Manning's equation gives V = 4.55 fps and Q = 2.67 cfs. Therefore, pipe is satisfactory. If the gradient had been considerably smaller, say 0.003, the 12" pipe would be undersized (Q = 1.64 cfs), and an 18" pipe would be required (Q = 4.83 cfs). However, the velocity when flowing 0.7 D would drop to 3.65 fps, which is still adequate, but illustrates the impact of gradient on flow velocity. Performing the same example in metric units, with Q = 2.23 cfs = 0.063 m3/sec, and using manual solution of Manning's equation and Figure 10, targeting a pipe that will flow 0.063 m3/sec at 0.7 D depth.

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APPENDIX A - EXAMPLE PROBLEMS (Cont) Try 250 mm pipe. First calculate pipe flowing full condition. For full pipe, A = ≈ (0.2502)/4 = 0.0491 m2, R = D/4 = 0.250/4 = 0.0625 m, V

1 2 / 3 1/ 2 1 R S = (0.0625 )2 / 3 (0.008 )1/ 2 = 1.08 m/s n 0.013

From Figure 10, V @ 0.7 D ≈ 1.18 x V full, so V = 1.18 x 1.08 m/sec = 1.27 m/sec From Figure 10, A @ 0.7 D ≈ 0.75 Afull, so A = 0.75 x 0.0491 m2 = 0.0368 m2 ; Q = VA = 1.27 x 0.0368 = 0.047m3/sec; too small; try next larger size. Try 280 mm pipe. Afull = 0.0616 m2, Rfull = D/4 = 0.070 m ; Vfull = 1.17 m/sec From Figure 10, V @ 0.7 D ≈ 1.18 x V full, so V = 1.18 x 1.17m/sec = 1.38 m/sec; A = 0.75 x 0.0616 = 0.046 m2 Q = VA = 1.38 x 0.046 = 0.063 m3/sec; OK Note:

280 mm pipe ≈ 11 in. ID.

Example Problem No. 6, Flow in Small Pipe Network using Rational Method

This example problem is based on the conditions which might exist in the uppermost reach of a sewer network within an industrial plant. Inlets 1 and 2 might represent the drop inlets common to a process unit, with tributary areas about 50 ft x 60 ft. The analysis would probably be performed today using any of a number of PC based computer programs (see Table 3 in the main body of this Design Practice). For illustration of manual calculations for larger networks, refer to water resources or civil engineering texts.

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APPENDIX A - EXAMPLE PROBLEMS (Cont) C = 0.8 Area = 0.07 Acres Inlet 1

Area = 0.07 Acres C = 0.7

Pipe 1 8 in. HDPE

L = 60 ft S = 0.5% n = 0.010

Inlet 2 Pipe 2 8 in. HDPE L = 60 ft S = 0.5% n = 0.010

Outfall Pipe 4

Junction J-1

Pipe 3 10" HDPE L= 1000 ft S= 0.53% n= 0.010

Inlet 3 Area = 0.30 Acre C = 0.6

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APPENDIX A - EXAMPLE PROBLEMS (Cont) Given an industrial watershed with 3 inlets, connected via pipelines with dimensions and grades as shown in the sketch above, and watershed data as described below. Calculate the flows reporting to Junction J-1 for a 10-year event, using the IDF curve presented in Figure 3-A as the source of the applicable rainfall intensities. INLET

TRIBUTARY AREA

RUNOFF COEFFICIENT

1

0.07 acre

0.8

2

0.07 acre

0.7

3

0.30 acre

0.6

Assume “inlet time" is fixed and is 5 minutes for each inlet. To solve the problem, first obtain the rainfall intensities from the curve for the 10 year storm in Figure 3-A. These have been tabulated below: DURATION

RAINFALL INTENSITY in./hr

5 min

8.1

15 min

6.4

30 min

4.7

60 min

3.5

Intensities corrresponding to intermediate durations will be determined by linear interpolation. The inlet flows for the respective sub-watersheds (Inlets 1, 2 and 3) are shown in the following table. The corresponding travel times in the various pipes are then calculated using velocities determined via methods described in Example Problem No. 5. In this case the “system time" equals the inlet time (5 minutes) plus the longest of the respective pipe travel times. The longest travel time (Pipe 3, from Inlet 3) sets the “system time" of concentration for flows at Junction J-1. This flow can then be used to size or evaluate the adequacy of Pipe No. 4.

NODE

C•A

INLET INTENSITY

INLET FLOW, = CiA

AVG VEL. IN PIPE

TRAVEL TIME

SYSTEM TIME

SYSTEM INTENSITY

(in./hr.)

ft3/s

ft/s

(min.)

(min.)

(in./hr.)

SYSTEM ΣC•A

SYSTEM FLOW, ΣCA•i ft3/s

Inlet I-1

0.8 x 0.07 = 0.056

8.1

0.454

2.08

2.40

7.40

—

—

—

Inlet I-2

0.7 x 0.07 = 0.049

8.1

0.397

1.81

2.76

7.76

—

—

—

Inlet I-3

0.6 x 0.30 = 0.180

8.1

1.458

3.64

4.58

9.58

← controls

—

—

—

—

—

—

9.58

7.32

0.285

2.09

Jct. J-1

—

The system intensity of 7.32 iph for a system time of 9.58 minutes at Junction J-1 is obtained by interpolating from the data in the rainfall intensity table. Note that the flow of 2.09 cfs at Junction J-1 is based on the time of concentration for the entire system upstream of that point, and is less than the 2.31 cfs that would result if the flows from each pipe had simply been added together. In general, the farther downstream in the system, the “system time" will be increasing and the corresponding rainfall intensity will be decreasing. However, flow will generally be increasing due to the inclusion of additional inlets and drainage areas. In some designs a single intensity for storm sewers, set somewhat arbitrarily as the 10 year 1-hr intensity, has been used. In this example problem, that intensity is equivalent to 3.5 in./hr, and it would produce a calculated flow at Junction J-1 of 0.285 x 3.5 iph = 1.00 cfs. This is about half of the actual 10 year flow at that junction, and it would correspond to actual return frequency of less than 1 year using this rainfall data. Selecting a single intensity can therefore result in underdesign (i.e., temporary flooding) in all areas above the point that corresponds to a system time of 1 hour, and results in overdesign (uneconomically large pipe sizes) for all areas downstream of that point. Since most industrial sites can be expected to have system times well below 1 hour, at least within the individual upstream areas that are tributary to mains, the condition of frequent flooding is the more likely consequence of using a single valued intensity. These drawbacks may be acceptable in some cases, provided the designer is aware of the principles involved.

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APPENDIX A - EXAMPLE PROBLEMS (Cont) Example Problem No. 7, Open Channel Flow

Assume that the gradient is fixed by other constraints at 0.008, and the design flow has been determined to be 900 cfs. What bottom width would be required if side slopes need to be held no steeper than 1(vt) on 3(hz), and a grass lining is to be applied? Excavation depths of more than 6 ft are to be avoided. The above conditions imply a Manning's “n" of 0.035. Iterative solutions of Manning's equation result in a nominal depth of 5.03 ft if the bottom width is set at 8 ft. The flow velocity is 7.7 fps, resulting in a velocity head (V2/2g) of 0.9 ft. The nominal 1 ft of freeboard would control, and the channel bottom should be set at 6 ft below grade. It will flow with about 1 ft of freeboard when delivering the design flow. The design flow for this section is sub-critical, but it is not far from the critical flow (1150 cfs). The design should be checked for the condition of a larger flow which might be super-critical, to determine if there might be adverse consequences should the flow become rapidly varying (i.e., extremely turbulent). The flow velocity of 7.7 fps is near the upper limit of allowable velocities in grass lined channels, and would only be permissible if the soil materials into which the channel is cut are clayey (refer to Table 14). Example Problem No. 8, Culvert Sizing

Height of road above ditch bottom is 15 ft. Assume for this application that it is acceptable to pond water as deep as 14 ft on the upstream side of the crossing. The roadway has a 40 ft top width, and 2.5:1 side slopes down to the ditch bottom, resulting in a culvert length of 115 ft. Assume that a CMP is the preferred pipe if it will work, and that it will have a headwall at the inlet. Design flow is 900 cfs. What is the minimum acceptable pipe diameter? Solution: First approximation is flow area required 900 cfs/10 fps = 90 ft2 → D ≈ 10 ft. Try 9 ft. Enter inlet control nomograph with 9 ft diameter (108 in.), and read HW/D = 1.5 for headwall inlet, → HW=13.5 ft, OK (i.e., < 14 ft) Next check the outlet control nomograph. With D = 9 ft (108 in.), L = 115 ft, Ke = 0.9, 7.9 ft of head over tailwater is required (tailwater taken as Tw = 0.85D = 7.65 ft), for a total head of 7.9 + 7.64 = 15.5 > 14 ft; 9 ft pipe is too small. Try D = 10 ft, L = 115 ft, Ke = 0.9. The outlet control nomograph requires 5.5 ft of head over tailwater for this condition. Since no tailwater elevation has been specified, assume again that Tw = 0.85 D = 8.5 ft (minimum tailwater is assumed to be approximately equal to critical depth in pipe), for a total head of 8.5 + 5.5 = 14 ft. OK Since the 9 ft pipe was satisfactory in inlet control, it is not necessary to re-check the 10 ft pipe for inlet control. However, for the purpose of instruction, the 10 ft pipe with the same headwall type entrance would require an inlet HW/D of 1.2, which implies inlet HW of 10 * 1.2 = 12 ft, which is within the design requirement (< 14 ft), but it is obvious that the pipe is still outlet controlled. Had a pipe larger than 10 ft been required, the design would have been forced to elliptical pipe arch culvert or a set of smaller diameter parallel pipes.

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APPENDIX A - EXAMPLE PROBLEMS (Cont) STRUCTURAL DESIGN Example Problem No. 9, Calculating Earth Load via Marston Formula, Conventional Cut-and-Cover Pipe in Trench

36" ID (≈ 3.5 ft OD) concrete pipe, buried in trench with Bd = 6.5 ft Backfill assumed to be saturated clay (Soil E in Marston curves), at unit weight γ = 120 pcf. Calculate H/Bd = 6/6.5 = 0.92, → Cd = 0.83 from graph or via formula. Then Marston formula W c = Cd γ Bd2 gives

H = 6 ft

Wc = 0.83 x 120 pcf x (6.5 ft)2 = 4,208 lb/LF of pipe where: LF

=

linear

Bd = 6.5 ft

Bc = 3.5 ft

Example Problem No. 10, Load Imposed by Nearby Uniform Distributed Surface Load

Calculate the load/LF on the crown of a pipe that is 6 ft below and is offset as shown from a 4 ft x 6 ft area loaded at 3000 psf. Referring to Figures, and superpositioning the rectangles shown at right,

3.5' OD

J C D H

produces a net shape factor of 0.046, as illustrated below: RECTANGLE

M

M/2H

D

D/2H

Cso

Cs/4

SUM

+ AJDF

8.5

0.71

5.6

0.47

0.395

0.099

+ 0.099

- AJCG

8.5

0.71

1.7

0.14

0.134

0.033

- 0.033

- AHEF

2.6

0.22

5.6

0.47

0.148

0.037

- 0.037

+ AHBG

2.6

0.22

1.7

0.14

0.051

0.013

+ 0.013

Net

0.046

6'

B

A

4'

3000 psf

D

G E

M

F 3' 3000 psf

Impact factor is 1.0 (static load). Incremental load to be added to Marston load for use in calculating stress on pipe crown would be Wsd = 0.046 x 3,000 psf x 1.0 x 3.5 ft (OD) = 483 lb/LF of pipe

H = 6'

This is the peak load imposed by the distributed surface load. It would be imposed only for a limited distance along the pipe. For design purposes it can be added to the Marston load as though it continues indefinitely along the pipe. The total design load would therefore be 4,208 + 483 = 4,691 lb/LF of pipe.

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APPENDIX A - EXAMPLE PROBLEMS (Cont) Example Problem No. 11, Loads Imposed by Surface Traffic

For the pipe described in the previous problem, determine the additional load on the crown if the pipe crosses under a two-lane road at right angles, such that two HS20 trucks could pass one another directly over the pipe. Although the road is paved, it is basically a light duty asphaltic concrete pavement intended for only occasional heavy truck traffic. Since this pavement is not considered stiff enough to effect any significant distribution of the truck load, it is assumed to have no impact. The calculation of the load caused by the truck(s) is carried out as though the pavement were not present. First determine the Impact factor. Since H > 3 ft, there is no effect from impact (refer to Table 7), and Impact factor is therefore If = 0.0. Next determine the critical truck wheel loading configuration, which depends on thickness of cover over the pipe. Since H > 4 ft, the critical loading configuration is P = 48,000 lb over ALL = (4.83 + 1.75 x 6 ft) x (5.67 + 1.75 x 6 ft) (refer to Table 6 and Figure 16). ALL = 15.33 ft x 16.17 ft = 247.9 sq. ft. Referring again to Figure 16, the 15.33 ft dimension is in the direction of truck travel, and the 16.17 ft dimension is along the axis of the pipe. wL =

48,000 lbs (1 + 0.0) P(1 + lf ) → wL = = 194 lb/ft2 ALL 247.8 ft 2

The load must be converted from a pressure to load per unit length of pipe. The first step is to determine the total load imposed on the pipe by means of WT = wL L SL where: L SL

= =

Length of ALL parallel to the longitudinal axis of the pipe (16.17 ft in this case), Outside span of the pipe or width of ALL transverse to the axis of the pipe, whichever is less. SL is 3.5 ft (pipe OD) in this case.

WT = 194 psf x 16.17 ft x 3.5 ft = 10,980 lb Note that the pipe is carrying only about one fourth of the total load imposed by the passing tandem dual wheels of two trucks. The load per unit length of pipe for inclusion in the total design load is wL =

WT Le

where: Le

=

Le

=

wL

=

3 Bc or in this case, 4 3 x 3.5 ft 16.17 ft + 1.75 = 20.8 ft 4 10,980 lb/20.8 ft = 528 lb/LF of pipe

L + 1.75

This load can be added directly to the Marston load (earth component), and any other surface loads that may be imposed on the pipe, to arrive at a total design load for determining the necessary pipe wall thickness. Example Problem No. 12, Selecting Wall Thickness, Reinforcing Requirements for Reinforced Concrete Pipe

Reinforced concrete pipe is designed in accordance with the procedures for rigid pipes. Given that ID has been set at 36" by hydraulic requirements, and imposed loads have been determined as described above. These design loads are: Earth load (via Marston Formula) = 4208 lb/LF of pipe Surface structure loads (via elastic influence charts) = 483 lb/LF of pipe Traffic load (via AASHTO, passing HS20 trucks) = 528 lb/LF of pipe Total design load = 5219 lb/LF of pipe Assume that the pipe will be installed in a shaped and compacted granular bed, (Class B bedding, Bf = 1.9; refer to Figure 18), which requires the pipe to be placed in a compacted granular bed that extends up to the pipe mid-section. Select the most economic reinforced concrete pipe wall thickness and reinforcing arrangement. To determine trial section capacities, use the D0.01 -Load as the criterion.

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APPENDIX A - EXAMPLE PROBLEMS (Cont) D - Loadreq’d =

Design load x FS Bf x Diam ( ft )

→ D - loadreq’d =

5219 lbs/LF x 1.0 1.9 x 3 ft

= 916 lb/LF/ft diameter

Safety factor 1.0 was selected because the design is being specified in accordance with the D0.01 -load (load required to open a 0.01 in. crack). The bedding factor 1.9 was selected based on the bedding conditions that will be specified in the field. Refer to ASTM C 76 “Reinforced Concrete Culvert, Storm Drain, and Sewer Pipe", and observe that Class I pipes are inadequate (maximum D0.01 -load is 800 lb/LF/ft diameter). Proceed to Class II pipes (max D0.01-load = 1000 lb). Choose any of three suitable wall configurations in Table 2 (Class II RCP) according to whichever is least expensive and available from local pipe manufacturers. Wall A Thickness = 3 in., w/inner cage steel at 0.14 in2 and outer cage 0.08 in2 per LF of wall Wall B Thickness = 4 in., w/inner cage steel at 0.12 in2 and outer cage 0.07 in2 per LF of wall, or Wall C Thickness = 4.75 in., w/inner cage steel at 0.07 in2 and outer cage 0.07 in2 per LF of wall Example Problem No. 13, Selecting Wall Thickness Requirements for Plain (non-reinforced) Concrete Pipe

Plain concrete pipe is designed in accordance with the procedures for rigid pipes. The design load and bedding parameters as described in Example Problem No. 12 apply. Design of plain concrete pipe is based on Three Edge Bearing load (T.E.B. load). Can use safety factor of 1.25 to 1.5 for select 1.25. Req’d T.E.B. Strength =

Design Load x Safety Factor 5219 x 1.25 = Bedding Factor 1 .9

= 3,433 lb/LF pipe

Referring to Table 1 in ASTM C 14 “Concrete Sewer, Storm Drain, and Culvert Pipe", it can be observed that the thinnest wall available (4 in., Class I pipe), with T.E.B. strength of 3300 lb/LF, is just short of the required 3,433 lb/LF. The next thicker wall (4.75 in. for Class II) will be satisfactory. Since the Class I wall was close, the designer may want to explore whether upgrading the bedding to Class A, which would enable the use of Class I (thinner wall) pipe, would be economically justified. Since the minimum requirement for Class A bedding would be to pour a concrete cradle extending one fourth of the pipe depth, and in so doing remove the need to place and compact the granular bedding material required for Class B, this may result in a more economical design. In general, when the pipe class is just short of the required T.E.B. load, it is worthwhile to evaluate whether an upgrade in bedding class is economically warranted. Example Problem No. 14, Selecting Wall Thickness, Reinforcing Requirements for Vitrified Clay Pipe (VCP)

Vitrified clay pipe (VCP) is designed in accordance with the procedures for rigid pipes. All parameters as described in Example Problems 12 and 13 for concrete pipes. Design is based on Three Edge Bearing load (T.E.B. load). Use safety factor of 1.5 for VCP. Req’d T.E.B. Strength =

Design Load x Safety Factor 5219 x 1.25 = Bedding Factor 1 .9

= 4,120 lb/LF pipe

Bedding factors, referred to as “Load Factor", and bedding classes for clay pipe are similar to those for concrete pipe, although there are differences in the Class A details. Bedding factors for clay pipe are presented in Figure 19. For Class B bedding, the details and the bedding factor are the same as for concrete pipe, namely Bf=1.9. Referring to Table 1 in ASTM C 700 “Extra Strength and Standard Strength Clay Pipe and Perforated Pipe", it can be observed that the standard strength pipe would exhibit a T.E.B. load of only 4,000 lb/LF. The extra strength clay pipe, with T.E.B strength at 6,000 lb/LF, would be satisfactory. As discussed above for the plain concrete pipe, the standard pipe is close enough to the required bearing strength that an improvement in the assumed bedding condition might result in a more economical design if this would allow selection of the standard strength pipe. Example Problem No. 15, Selecting Wall Thickness Requirements for Ductile Iron Pipe

Ductile iron pipe (DIP) is designed in accordance with the procedures for flexible pipes. Relying on the design standard published as ANSI/AWWA C150/A21.50.91, the earth load is calculated as a simple prism load, and the traffic load is determined in accordance with the standard AASHTO H20 truck loading.

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APPENDIX A - EXAMPLE PROBLEMS (Cont) Determine the wall thickness requirements for a 36" ID ductile iron pipe, installed in a trench 6 ft below grade, and passing under a roadway that might be subjected to truck traffic. Assume that the surface distributed load also is present. Pipe bedding conditions are the same as described previously for the concrete, reinforced concrete and vitrified clay pipe, which consists of the pipe bedded in granular material and supported on its sides by compacted fill up to half its height. The above described bedding condition is best described as Laying Condition “Type 4" in the AWWA standard, i.e., pipe resting on a granular layer and adjacent side fill placed in a controlled manner with deliberate compaction. Since that would result, in this particular case, in a design for which deflection limits are not a factor, the pipe laying Condition “Type 3" will be used in this example. The primary difference between “Type 3" and “Type 4" is the degree of backfill compaction assumed for the fill adjacent to the pipe. From Table 50.1 in C150/A21.50.91, Pe = 5.0 psi note this value obtained from the table includes applicable impact factors From Table 50.1 in C150/A21.50.91, Pt = 1.7 psi; and applicable stress distribution The ductile iron pipe standard does not present a method for calculating other distributed loads. The elastic distribution method described earlier can nevertheless be used. Pdistrib = 0.46 x 3000 psf (from p. A-5) = 0.97 psi ≈ 1.0 psi Total trench load Pv = 5.0 + 1.7 + 1.0 psi = 7.7 psi Enter Table 50. 9 for diameter-thickness ratios for laying condition Type 3. For bending stress, find required D/t = 186; From Table 50.5, D of a 36" pipe is 38.3 in., ∴ treq'd = 38.3/186 = 0.21" For deflection design, (also Table 50.3), D/t1 req'd > 200 → t1req'd = 38.3/200 = 0.19" Deduct service allowance from deflection design thickness, 0.19" - 0.08" = 0.11" req'd for deflection design The thicker wall requirement (bending stress in this case, at t = 0.21") controls. Select net thickness and add all allowances t = 0.21” 0.08” + service allowance Minimum thickness 0.28” 0.07” for 36 in. pipe + casting allowance Total calculated thickness 0.35” The lowest class DIP (pressure class 150) has a wall thickness of 0.38" for 36" pipe, and is therefore suitable for this application. Example Problem No. 16, Selecting Wall Thickness for HDPE Pipe, Smooth Wall Type

For the conditions described in Example Problem No. 11, determine the wall thickness requirement for a smooth wall HDPE pipe with 36 in. O.D. Depth to pipe crown in 6', and assume a permanent ground water table may exist coincident with the ground surface. Assume the sewer will be installed in moderately dense clayey soil subgrade, with an E' moduls of ~ 1000 psi (refer to Figure 21). Determine the required wall thickness for two conditions; ambient affluent temperature at 73°F and sustained effluent temperature of 140°F. Flow is entirely gravity flow, and there is no chance for this line to operate under siphon or vacuum loading. Ambient temperature case (73°F) Recapping loads applied to pipe crown from Example Problem No. 11,

Earth load

4208

lb/LF pipe

Structure live load ladjacent footing

483

lb/LF pipe

Traffic load

528

lb/LF pipe

5219

lb/LF pipe

Convert load per unit length into pressure on crown 5219

lb / 3 ft crown width = 1740 psf = 12.08 psi applied LF pipe

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APPENDIX A - EXAMPLE PROBLEMS (Cont) Use procedures described in PlexcoR design manuals as these are closer to industry guidelines under development at Plastic Pipe Institute (PPI). Check for wall crushing: æ OD ö ÷ Start with thinnest wall pipe, SDR = 32.5 çç SDR = ÷ t wall ø è

For SDR 32.5, wall thickness t =

36" 32.5

= 1.108”

Wall crushing is based on applied load per unit area. S =

1740 psf x 36" 288 x 1.108"

= 196 psi, OK, well below 800 psi guideline which has an implied safety factory of 2.

Unconstrained (i.e., hydrostatic) buckling not applicable, as pipe will be buried in firm backfill and will not be exposed to vacuum loading conditions. Check for constrained buckling: Note: crown loads, modulii, and buckling pressures are in “psi". Pcr required = 12.08 psi based on loads applied to crown (see above); use N (safety factor) = 2 Pcr =

5.65 N

R B′ E′

El 3 Dm

H′ H H′ = groundwater height above crown, H = total backfill height above crown

where R = bouyancy correction = 1 - 0.333

in which and

æ6ö R = 1 - 0.333 ç ÷ è6ø

B′ =

1 1 + 4 e −0.065 H

= 0.67

= 0.27

E = 28,200 psi for PE 3408 @ 73°F l =

t3 1.1083 ,= 12 12

= 0.1133 in.3

Dm = mean Diam = OD -

1 (2t) = 36” - 1.08” = 34.89” 2

E′ = soil modulus = 1000 psi solves to Pcr = 10.42 psi; not enough, need 12.08 Try next thicker wall, SDR 26, t =

l

=

(1.385" )3 12

36" 26

= 1.385”

= 0.2212 in.3

Dm = 36" - 1.385" = 34.62" Pcr = 13.25 psi; OK, 12.08 required ExxonMobil Research and Engineering Company – Fairfax, VA

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APPENDIX A - EXAMPLE PROBLEMS (Cont) Using alternative design methodology, P = fofs Pcr where Pcr is simple unrestrained (Euler) buckling load, fo is ovality correction factor given by: fo =

é (1 − % deflection) ù ê ú 2 ëê (1 + % deflection ) ûú

3

and fs = soil support factor given in Figure 20

Assuming 5% deflection, fo =

Pcr =

2E 1 − u2

é 1 − 0.05 ù ê ú 2 êë (1 + 0.05 ) úû

3

= 0.64

3

æ ö 1 çç ÷÷ , with u = 0.45@73° = 28,200 psi SDR − 1 è ø

For SDR - 32.5, Pcr = 2.26 psi

For SDR = 26, Pcr = 4.53 psi

For compacted soil, Figure 20 gives Ff

= 3 if SDR = 32.5

and Ff

P = 0.64 x 3 x 2.26 psi = 4.33 psi

= 2. 7 for SDR = 26

P = 0.64 x 2.7 x 4.53 psi = 7.83 psi

Both of the above are insufficient. By trial, determine that SDR - 21 is required to achieve the required 12.08 psi. Note: This alternative method tends to give overly conservative wall thickness and is used mainly for screening evaluation. Design should be based on the longer form solution described previously. Check for pipe deflection (via modified Iowa equation) With SDR = 26, based on previous “long form" constrained buckling analysis, é ê ∆x P ê = ê Dm 144 ê 2 E ê ë 3

where: P K L

= = =

ù ú ú KL ú 3 æ ö ú 1 çç ÷÷ + 0.061E′ ú − SDR 1 è ø û

Load applied to crown, psf Bedding factor, typically 0.1 Viscoelastic deflection lag factor, typically 1.25 to 1.5 for HDPE

é ê ∆x 1740 ê = ê Dm 144 ê 2 x 28,200 ê 3 ë

ù ú ú 0 .1 x 1 .5 ú 3 æ 1 ö ú çç ÷÷ + 0.061 x 1000 ú è 26 − 1 ø û

= 0.029 = 2.9%

Manufacturers literature defines 7% as the allowable limit for SDR 26; therefore, SDR 26 is OK High temperature case (140°F)

Check for constrained buckling, start with SDR 26 pipe At 140°F, E = 18,700 psi All other factors are same as ambient (73°F) case Pcr =

5.65 2

0.67 x 0.27 x 1000 x

18,700 x 0.212 34.623

= 12.0 psi; close enough to 12.08, OK

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APPENDIX A - EXAMPLE PROBLEMS (Cont) é ê ∆x 1740 ê = ê Dm 144 ê 2 x 18,700 ê 3 ë

Check for pipe deflection;

ù ú ú 0 .1 x 1 .5 ú 3 æ 1 ö ú çç ÷÷ + 0.061 x 1000 ú − 26 1 è ø û

= 0.029 = 2.9%, OK

Note that deflection is not extremely sensitive to changes in pipe modulus, as it is mainly governed by soil modulus. Example Problem No. 17, Selecting Wall Thickness for HDPE Pipe, Profile (Ribbed) Wall Type

Assume loading condition, all other factors, are the same as in Example Problem 16. Find class rating of SpiroliteR pipe necessary to satisfy stress, buckling and deflection criteria for ambient temperature case (73°F) and for elevated temperature case (140°F). Note:

RSC = ring stiffness constant -

6.44 E l 2 Dm

= class rating

Available class ratings for 36" ID pipe are 40, 63, 100, 160. Refer to manufacturers literature for dimensional parameters for specific classes. Ambient temperature case (73°F)

Check pipe crushing

PL Do 288 A

S = where: PL Do A

= = =

Crown load in lb/ft2 Pipe outside diameter, in. Pipe x-sectional area, in.

Try Class 40 From manufacturer's literature, wall thickness incl. ribs = 1.86" ; therefore, DO = 36" + 2 x 1.86" = 39.72" A = 0.309 in.2/in. (also from manufacturer's literature) S =

1740 x 39.72 288 x 0.309

= 777 psi < 800 psi, OK

S =

1740 x 39.72 288 x 0.309

Check constrained buckling From manufacturer's literature, for class 40 SpiroliteR pipe I Z Dm R′ B′ E E′ N Pwc =

=

5.65 N

5.65 2

= = = = = = = =

0.078 in3 0.42" 36" + 2 x Z = 36 + 2 (0.42) = 36.84" 0.67 as in Example Problem 16 0.27 as in Example Problem 16 28,200 psi (pipe) as in Example Problem 16 1000 psi (soil) as in Example Problem 16 factor of safety = 2 as in Example Problem 16 R B′ E′

E l 3 Dm

0.67 x 0.27 x 1000 x

28,200 x 0.078 36.843

= 7.97 psi; not enough, need 12.08 psi

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APPENDIX A - EXAMPLE PROBLEMS (Cont) Try next class (Class 63) From manufacturers literature,

I Z Dm

so Pwc =

5.65 2

= = =

0.107 0.47 36 + 2 x 0.47 = 36.94

0.67 x 0.27 x 1000 x

28,200 x 0.107 36.943

= 9.30, need 12.08 psi Try Class 100 I Z Pwc

= = =

0.171 0.58 so Dm = 36 + 2 (0.58) = 37.16 11.65 psi, close enough to 12.08 psi, OK

Check deflection: Recall that RSC = 100 for Class 100 pipe é ù ù é ú 1740 ê ú P êê KL 0 .1 x 1 .5 ∆x ú = = ú = 0.028 = 2.8% ê 1 . 24 x 100 Dm 144 ê 1.24 RSC 144 ú ú ê ′ 0 . 061 E + + 0 . 061 x 1000 ê ú úû Dm ëê 37.16 ë û

Manufacturer's literature lists 4.2% as allowable for profile pipe; OK High temperature case (140°F)

E

= 18,700 psi, all other factors unchanged; start with Class 100 pipe (from ambient temperature

case) Pwc =

5.65 2

0.67 x 0.27 x 1000 x

18,700 x 0.171 37.163

= 9.49 psi; too low; need 12.08 psi Try next class (Class 160) From manufacturer's literature, I = 0.276, Z = 0.66, so Dm = 36 + 2 (0.66) = 37.32" and Pwc = 11.97, close enough to 12.08 psi, OK Check deflection for Class 160 pipe @ 140°F ù é ú ∆x 1740 ê 0 .1 x 1 .5 = ú ê Dm 144 ê 1.24 x 160 + 0.061 x 1000 ú úû ëê 37.32

= 0.027 = 2.7%, OK, less than 4.2%

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ExxonMobil Proprietary CIVIL WORKS

Section XXIX-C

DRAINAGE SYSTEMS DESIGN PRACTICES

Page 83 of 84

December, 2001

APPENDIX B - FORMULAS FOR CALCULATING HYDRAULIC RADIUS (R) AND FLOW AREA (A) FOR CIRCULAR PIPES FLOWING PARTLY FULL

D

Pipe Flowing Less Than Half Full, D = pipe diameter, r = pipe radius, y = depth below mid-point Atotal = A1 – A2 where: A1 = (πD2/4)/2 = πD2/8 and

0,0

()

y A2 = y √ r2 – y2 + r2 arctan x

X r

A2

y

where: x = √ r2 – y2 + y is as shown R = Atotal /Pwetted Pwetted = P1 – P2

A Total

where: P1 = πD/2 and P2 = π

Pwetted

D 2

α° ( 90° )

or π

D 2

α

( π/2 ) , and α = arctan ( yx )

Pipe Flowing More Than Half Full, D = pipe diameter, r = pipe radius, y = depth above mid-point Atotal = A1 – A2 where: A1 = (πD2/4)/2 = πD2/8 and y

r

A2

()

y A2 = y √ r2 – y2 + r2 arctan x where: x =

0,0

√ r2 – y2 and y is as shown

x R = Atotal /Pwetted Pwetted = P1 + P2

A1

where: P1 = πD/2 and D D α° or π P2 = π 2 2 90°

( )

α

( π/2 ) , and α = arctan ( yx )

Pwetted

DP29CAB1

Flow area and hydraulic radii determined as described above can be used in Manning's equation to calculate flow rates in pipes of given diameter, roughness coefficient (n) and gradient (s) for any partial depth of flow, via Qcfs = A flow x V = A flow

1.49 1/ 2 2 / 3 s R n

which can be easily adapted to BASIC, QBASIC or standard spreadsheet programs such as Excel or Lotus 123, taking the necessary care to define angles in radian or degree measure as appropriate.

ExxonMobil Research and Engineering Company – Fairfax, VA

ExxonMobil Proprietary Section XXIX-C

CIVIL WORKS

Page 84 of 84

DRAINAGE SYSTEMS DESIGN PRACTICES

December, 2001

APPENDIX B FORMULAS FOR CALCULATING HYDRAULIC RADIUS (R) AND FLOW AREA (A) FOR CIRCULAR PIPES FLOWING PARTLY FULL (Cont)

T Z left

Z rt t

t

y

B DP29CAB2

+ Zrt ö æZ A flow = ( y B) + y 2 ç left ÷ 2 è ø R =

A flow = Wp

Vfps =

A flow æ 2 B + y ç 1 + Zleft + ç è

1.49 1/ 2 0.667 s R n

ö 1 + Zrt2 ÷ ÷ ø

Manning’s Equation

Qcfs = V Aflow Manning roughness coefficient, dependant upon channel lining material Hydraulic radius, a function of flow depth and channel geometry, calculated as describe above s = Channel bed slope Zleft = Left channel bank slope, ft/ft, i.e., horizontal distance required to drop 1 ft in elevation Zrt = Right channel bank slope, ft/ft, i.e., horizontal distance required to drop 1 ft in elevation B = Channel bottom width, ft y = Flow depth, ft Because flow area and wetted perimeter are both functions of flow depth (y) solution must be solved iteratively. A convenient means is to specify the required flow (Q), assume a set of trial dimensions, assume a flow depth and calculate Q. Compare to the required Q and repeat the process, zeroing in on a flow depth that achieves the required flow. Once a satisfactory flow depth is obtained, it is a simple matter to calculate whether the flow is sub-critical or super-critical for those channel dimensions. The flow that is critical for the assumed channel section and depth is where:

n R

= =

32.2 A 3flow T

Qcrit =

where: T

=

Width of surface = B + y Zleft + y Zrt

If the flow being evaluated is greater than Qc, the channel would be flowing in a super-critical condition. Conversely, if the flow being evaluated is less than Qc, the channel would be flowing in a sub-critical condition. The above expressions can be easily adapted to BASIC, QBASIC or standard spreadsheet programs such as Excel or Lotus.

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