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CHAPTER 4 LOADS AND SUPPORTING STRENGTHS
The design procedure for the selection of pipe strength requires: I . Determination of Earth Load 2. Determination of Live Load 3. Selection of Bedding 4. Determination of Bedding Factor 5. Application of Factor of Safety 6. Selection of Pipe Strength

TYPES OF INSTALLATIONS
The earth load transmitted to a pipe is largely dependent on the type of installation. Three common types are Trench, Positive Projecting Embankment, and Negative Projecting Embankment. Pipelines are also installed by jacking or tunneling methods where deep installations are necessary or where conventional open excavation and backfill methods may not be feasible. The essential features of each of these installations are shown in Illustration 4.1. Trench. This type of installation is normally used in the construction of sewers, drains and water mains. The pipe is installed in a relatively narrow trench excavated in undisturbed soil and then covered with backfill extending to the ground surface. Positive Projecting Embankment. This type of installation is normally used when the culvert is installed in a relatively flat stream bed or drainage path. The pipe is installed on the original ground or compacted fill and then covered by an earth fill or embankment. Negative Projecting Embankment. This type of installation is normally used when the culvert is installed in a relatively narrow and deep stream bed or drainage path. The pipe is installed in a shallow trench of such depth that the top of the pipe is below the natural ground surface or compacted fill and then covered with an earth fill or embankment which extends above the original ground level. Jacked or Tunneled. This type of installation is used where surface conditions make it difficult to install the pipe by conventional open excavation and backfill methods, or where it is necessary to install the pipe under an existing embankment. A jacking pit is dug and the pipe is advanced horizontally underground.

27

28

Concrete Pipe Design Manual

Illustration 4.1 Essential Features of Types of Installations
GROUND SURFACE TOP OF EMBANKMENT

H

H

Do

pBC Do

Bd Trench TOP OF EMBANKMENT

Positive Projecting Embankment

GROUND SURFACE

H Bd p'Bd

H

Do

Do

Negative Projecting Embankment

Bt Jacked or Tunneled

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Loads and Supporting Strengths

29

BACKGROUND
The classic theory of earth loads on buried concrete pipe, published in 1930 by A. Marston, was developed for trench and embankment conditions. In later work published in 1933, M. G. Spangler presented three bedding configurations and the concept of a bedding factor to relate the supporting strength of buried pipe to the strength obtained in a three-edge bearing test. Spangler’s theory proposed that the bedding factor for a particular pipeline and, consequently, the supporting strength of the buried pipe, is dependent on two installation characteristics: 1. Width and quality of contact between the pipe and bedding. 2. Magnitude of lateral pressure and the portion of the vertical height of the pipe over which it acts. For the embankment condition, Spangler developed a general equation for the bedding factor, which partially included the effects of lateral pressure. For the trench condition, Spangler established conservative fixed bedding factors, which neglected the effects of lateral pressure, for each of the three beddings. This separate development of bedding factors for trench and embankment conditions resulted in the belief that lateral pressure becomes effective only at trench widths equal to or greater than the transition width. Such an assumption is not compatible with current engineering concepts and construction methods. It is reasonable to expect some lateral pressure to be effective at trench widths less than transition widths. Although conservative designs based on the work of Marston and Spangler have been developed and installed successfully for years, the design concepts have their limitations when applied to real world installations. The limitations include: • Loads considered acting only at the top of the pipe. • Axial thrust not considered. • Bedding width of test installations less than width designated in his bedding configurations. • Standard beddings developed to fit assumed theories for soil support rather than ease of and methods of construction. • Bedding materials and compaction levels not adequately defined. This section discusses the Standard Installations and the appropriate indirect design procedures to be used with them. The Standard Installations are the most recent beddings developed by ACPA to allow the engineer to take into consideration modern installation techniques when designing concrete pipe. For more information on design using the Marston/Spangler beddings, see Appendix B.

INTRODUCTION
In 1970, ACPA began a long-range research program on the interaction of buried concrete pipe and soil. The research resulted in the comprehensive finite element computer program SPIDA, Soil-Pipe Interaction Design and Analysis, for the direct design of buried concrete pipe. Since the early 1980’s, SPIDA has been used for a variety of studies, including the development of four new Standard Installations, and a simplified microcomputer design program, SIDD, Standard Installations Direct Design. The procedure presented here replaces the historical A, B, C, and D beddings used in the indirect design method and found in the appendix of this manual, with the four new Standard Installations, and presents a state-of-the-art
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Concrete Pipe Design Manual

method for determination of bedding factors for the Standard Installations. Pipe and installation terminology as used in the Standard Installations, and this procedure, is defined in Illustration 4.2. Illustration 4.2 Pipe/Installation Terminology

Overfill

H

Top Do Crown Haunch Springline Lower Side Di Invert

Bedding Foundation (Existing Soil or Compacted Fill)

Bottom

FOUR STANDARD INSTALLATIONS
Through consultations with engineers and contractors, and with the results of numerous SPIDA parameter studies, four new Standard Installations were developed and are presented in Illustration 4.4. The SPIDA studies were conducted for positive projection embankment conditions, which are the worstcase vertical load conditions for pipe, and which provide conservative results for other embankment and trench conditions. The parameter studies confirmed ideas postulated from past experience and proved the following concepts: • Loosely placed, uncompacted bedding directly under the invert of the pipe significantly reduces stresses in the pipe. • Soil in those portions of the bedding and haunch areas directly under the pipe is difficult to compact. • The soil in the haunch area from the foundation to the pipe springline provides significant support to the pipe and reduces pipe stresses. • Compaction level of the soil directly above the haunch, from the pipe springline to the top of the pipe grade level, has negligible effect on pipe stresses. Compaction of the soil in this area is not necessary unless required for pavement structures.
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Loads and Supporting Strengths • Installation materials and compaction levels below the springline have a significant effect on pipe structural requirements. The four Standard Installations provide an optimum range of soil-pipe interaction characteristics. For the relatively high quality materials and high compaction effort of a Type 1 Installation, a lower strength pipe is required. Conversely, a Type 4 Installation requires a higher strength pipe, because it was developed for conditions of little or no control over materials or compaction. Generic soil types are designated in Illustration 4.5. The Unified Soil Classification System (USCS) and American Association of State Highway and Transportation Officials (AASHTO) soil classifications equivalent to the generic soil types in the Standard Installations are also presented in Illustration 4.5. Illustration 4.3 Standard Trench/Embankment Installation

31

Overfill Soil Category I, II, III H

Do/6 (Min.)

Do

Do (Min.) Haunch - See Illustration 4.4

Springline

Lower Side - See Illustration 4.4 Di

Bedding See Illustrations 4.4 & 4.5 Outer bedding materials and compaction each side, same requirements as haunch

Do/3

Middle Bedding loosely placed uncompacted bedding except Type 4

Foundation

The SPIDA design runs with the Standard Installations were made with medium compaction of the bedding under the middle-third of the pipe, and with some compaction of the overfill above the springline of the pipe. This middle-third area under the pipe in the Standard Installations has been designated as loosely placed, uncompacted material. The intent is to maintain a slightly yielding bedding under the middle-third of the pipe so that the pipe may settle slightly into the bedding and achieve improved load distribution. Compactive efforts in the middlethird of the bedding with mechanical compactors is undesirable, and could
American Concrete Pipe Association • www.concrete-pipe.org

32 Illustration 4.4

Concrete Pipe Design Manual Standard Installations Soil and Minimum Compaction Requirements Haunch and Outer Bedding 95% Category I Lower Side 90% Category I, 95% Category II, or 100% Category III 85% Category I, 90% Category II, or 95% Category lIl 85% Category I, 90% Category II, or 95% Category III No compaction required, except if Category III, use 85% Category III

Installation Bedding Type Thickness Type 1 Do/24 minimum, not less than 75 mm (3"). If rock foundation, use Do/12 minimum, not less than 150 mm (6"). Do/24 minimum, not less than 75 mm (3"). If rock foundation, use Do/12 minimum, not less than 150 mm (6"). Do/24 minimum, not less than 75 mm (3"). If rock foundation, use Do/12 minimum, not less than 150 mm (6") . No bedding required, except if rock foundation, use Do/12 minimum, not less than 150 mm (6").

Type 2

90% Category I or 95% Category II

Type 3

85% Category I, 90% Category II, or 95% Category III No compaction required, except if Category III, use 85% Category III

Type 4

Notes:
1. 2. 3. 4. 5. 6. 7. Compaction and soil symbols - i.e. “95% Category I”- refers to Category I soil material with minimum standard Proctor compaction of 95%. See Illustration 4.5 for equivalent modified Proctor values. Soil in the outer bedding, haunch, and lower side zones, except under the middle1/3 of the pipe, shall be compacted to at least the same compaction as the majority of soil in the overfill zone. For trenches, top elevation shall be no lower than 0.1 H below finished grade or, for roadways, its top shall be no lower than an elevation of 1 foot below the bottom of the pavement base material. For trenches, width shall be wider than shown if required for adequate space to attain the specified compaction in the haunch and bedding zones. For trench walls that are within 10 degrees of vertical, the compaction or firmness of the soil in the trench walls and lower side zone need not be considered. For trench walls with greater than 10 degree slopes that consist of embankment, the lower side shall be compacted to at least the same compaction as specified for the soil in the backfill zone. Subtrenches 7.1 A subtrench is defined as a trench with its top below finished grade by more than 0.1 H or, for roadways, its top is at an elevation lower than 1ft. below the bottom of the pavement base material. 7.2 The minimum width of a subtrench shall be 1.33 Do or wider if required for adequate space to attain the specified compaction in the haunch and bedding zones. 7.3 For subtrenches with walls of natural soil, any portion of the lower side zone in the subtrench wall shall be at least as firm as an equivalent soil placed to the compaction requirements specified for the lower side zone and as firm as the majority of soil in the overfill zone, or shall be removed and replaced with soil compacted to the specified level.

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Loads and Supporting Strengths

33

produce a hard flat surface, which would result in highly concentrated stresses in the pipe invert similar to those experienced in the three-edge bearing test. The most desirable construction sequence is to place the bedding to grade; install the pipe to grade; compact the bedding outside of the middle-third of the pipe; and then place and compact the haunch area up to the springline of the pipe. The bedding outside the middle-third of the pipe may be compacted prior to placing the pipe. As indicated in Illustrations 4.3 and 4.4, when the design includes surface loads, the overfill and lower side areas should be compacted as required to support the surface load. With no surface loads or surface structure requirements, these areas need not be compacted. Illustration 4.5 Equivalent USCS and AASHTO Soil Classifications for SIDD Soil Designations Representative Soil Types SIDD Soil Gravelly Sand (Category 1) USCS, SW, SP, GW, GP Standard AASHTO A1,A3 Percent Compaction Standard Proctor 100 95 90 85 80 61 100 95 90 85 80 49 100 95 90 85 80 45 Modified Proctor 95 90 85 80 75 59 95 90 85 80 75 46 90 85 80 75 70 40

Sandy Silt (Category II)

GM, SM, ML, Also GC, SC with less than 20% passing #200 sieve

A2, A4

Silty Clay (Category III)

CL, MH, GC, SC

A5, A6

SELECTION OF STANDARD INSTALLATION
The selection of a Standard Installation for a project should be based on an evaluation of the quality of construction and inspection anticipated. A Type 1 Standard Installation requires the highest construction quality and degree of inspection. Required construction quality is reduced for a Type 2 Standard Installation, and reduced further for a Type 3 Standard Installation. A Type 4 Standard Installation requires virtually no construction or quality inspection. Consequently, a Type 4 Standard Installation will require a higher strength pipe, and a Type I Standard Installation will require a lower strength pipe for the same depth of installation.

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Concrete Pipe Design Manual

LOAD PRESSURES
SPIDA was programmed with the Standard Installations, and many design runs were made. An evaluation of the output of the designs by Dr. Frank J. Heger produced a load pressure diagram significantly different than proposed by previous theories. See Illustration 4.6. This difference is particularly significant under the pipe in the lower haunch area and is due in part to the assumption of the existence of partial voids adjacent to the pipe wall in this area. SIDD uses this pressure data to determine moments, thrusts, and shears in the pipe wall, and then uses the ACPA limit states design method to determine the required reinforcement areas to handle the pipe wall stresses. Using this method, each criteria that may limit or govern the design is considered separately in the evaluation of overall design requirements. SIDD, which is based on the four Standard Installations, is a stand-alone program developed by the American Concrete Pipe Association. The Federal Highway Administration, FHWA, developed a microcomputer program, PIPECAR, for the direct design of concrete pipe prior to the development of SIDD. PIPECAR determines moment, thrust, and shear coefficients from either of two systems, a radial pressure system developed by Olander in 1950 and a uniform pressure system developed by Paris in the 1920’s, and also uses the ACPA limit states design method to determine the required reinforcement areas to handle the pipe wall stresses. The SIDD system has been incorporated into PIPECAR as a state-of-the-art enhancement.

DETERMINATION OF EARTH LOAD
Embankment Soil Load. Concrete pipe can be installed in either an embankment or trench condition as discussed previously. The type of installation has a significant effect on the loads carried by the rigid pipe. Although narrow trench installations are most typical, there are many cases where the pipe is installed in a positive projecting embankment condition, or a trench with a width significant enough that it should be considered a positive projecting embankment condition. In this condition the soil along side the pipe will settle more than the soil above the rigid pipe structure, thereby imposing additional load to the prism of soil directly above the pipe. With the Standard Installations, this additional load is accounted for by using a Vertical Arching Factor, VAF. This factor is multiplied by the prism load, PL, (weight of soil directly above the pipe) to give the total load of soil on the pipe.
W = VAF x PL (4.1)

Unlike the previous design method used for the Marston/Spangler beddings there is no need to assume a projection or settlement ratio. The Vertical Arching Factors for the Standard Installations are as shown in Illustration 4.7. The equation for soil prism load is shown below in Equation 4.2. The prism load, PL, is further defined as:
PL = w H + Do(4 - π)

8

Do

(4.2)

American Concrete Pipe Association • www.concrete-pipe.org

Loads and Supporting Strengths where: w = soil unit weight, (lbs/ft3) H = height of fill, (ft) Do = outside diameter, (ft)

35

Illustration 4.6

Arching Coefficients and Heger Earth Pressure Distributions
VAF

a

A3

A6 AF A4 f hI h2 A2 2 A1 b A5 Dm = 1

A6 b A5 d vd A2 2 vh2 uhl e A4 f HAF

c uc

Installation Type VAF

HAF

A1

A2

A3

A4

A5

A6

a

b

c

e

f

u

v

1 2 3 4

1.35 0.45 0.62 0.73 1.35 0.19 0.08 0.18 1.40 0.40 0.18 0.08 0.05 0.80 0.80 1.40 0.40 0.85 0.55 1.40 0.15 0.08 0.17 1.45 0.40 0.19 0.10 0.05 0.82 0.70 1.40 0.37 1.05 0.35 1.40 0.10 0.10 0.17 1.45 0.36 0.20 0.12 0.05 0.85 0.60 1.45 0.30 1.45 0.00 1.45 0.00 0.11 0.19 1.45 0.30 0.25 0.00 0.90 -

Notes: 1. VAF and HAF are vertical and horizontal arching factors. These coefficients represent nondimensional total vertical and horizontal loads on the pipe, respectively. The actual total vertical and horizontal loads are (VAF) X (PL) and (HAF) X (PL), respectively, where PL is the prism load. 2. Coefficients A1 through A6 represent the integration of non-dimensional vertical and horizontal components of soil pressure under the indicated portions of the component pressure diagrams (i.e. the area under the component pressure diagrams). The pressures are assumed to vary either parabolically or linearly, as shown, with the non-dimensional magnitudes at governing points represented by h1, h2, uh1, vh2, a and b. Non-dimensional horizontal and vertical dimensions of component pressure regions are defined by c, d, e, vc, vd, and f coefficients. 3. d is calculated as (0.5-c-e). h1 is calculated as (1.5A1) / (c) (1+u). h2 is calculated as (1.5A2) / [(d) (1+v) + (2e)]
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Concrete Pipe Design Manual

Illustration 4.7 Vertical Arching Factor (VAF)
Standard Installation Minimum Bedding Factor, Bfo

Type 1 Type 2 Type 3 Type 4

1.35 1.40 1.40 1.45

Note: 1. VAF are vertical arching factors. These coefficients represent nondimensional total vertical loads on the pipe. The actual total vertical loads are (VAF) X (PL), where PL is the prism load.

Trench Soil Load. In narrow or moderate trench width conditions, the resulting earth load is equal to the weight of the soil within the trench minus the shearing (frictional) forces on the sides of the trench. Since the new installed backfill material will settle more than the existing soil on the sides of the trench, the friction along the trench walls will relieve the pipe of some of its soil burden. The Vertical Arching Factors in this case will be less than those used for embankment design. The backfill load on pipe installed in a trench condition is computed by the equation: Wd = CdwBd +
2

Do (4 - π) w 8
H Bd

2

(4.3)

The trench load coefficient, Cd, is further defined as: 1 – e – 2Kμ' Cd = 2Kμ' (4.4)

where: Bd = width of trench, (ft) K = ratio of active lateral unit pressure to vertical unit pressure m' = tan ø', coefficient of friction between fill material and sides of trench The value of Cd can be calculated using equation 4.4 above, or read from Figure 214 in the Appendix. Typical values of Kμ' are: Kμ' = .1924 Max. for granular materials without cohesion Kμ' = .165 Max for sand and gravel Kμ' = .150 Max. for saturated top soil Kμ' = .130 Max. for ordinary clay Kμ' = .110 Max for saturated clay As trench width increases, the reduction in load from the frictional forces is offset by the increase in soil weight within the trench. As the trench width increases it starts to behave like an embankment, where the soil on the side of the pipe settles more than the soil above the pipe. Eventually, the embankment condition is reached when the trench walls are too far away from the pipe to help support the soil immediately adjacent to it. The transition width is the width of a trench at a particular depth where the trench load equals the embankment load.

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Loads and Supporting Strengths

37

Once transition width is reached, there is no longer any benefit from frictional forces along the wall of the trench. Any pipe installed in a trench width equal to or greater than transition width should be designed for the embankment condition. Tables 13 through 39 are based on equation (4.2) and list the transition widths for the four types of beddings with various heights of backfill. Negative Projection Embankment Soil Load. The fill load on a pipe installed in a negative projecting embankment condition is computed by the equation:

Wn = CnwBd

2

(4.5)

The embankment load coefficient Cn is further defined as:

Cn =

e

– 2Kμ'

H Bd

–1

– 2Kμ' e
– 2Kμ'
He Bd

when H ≤ He

(4.6)

Cn =

–1

– 2Kμ'

+

H H + e Bd Bd

e

– 2Kμ'

He Bd

when H > He

(4.7)

The settlements which influence loads on negative projecting embankment installations are shown in Illustration 4.8. Illustration 4.8 Settlements Which Influence Loads Negative Projection Embankment Installation
TOP OF EMBANKMENT

H = H' + p'Bd

Plane of Equal Settlement H' H'e Sd + Sf + dc p'Bd Bd Sf + dc Bc Shearing Forces Induced By Settlement Ground Surface Sg

Sf Initial Elevation Final Elevation

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Concrete Pipe Design Manual

The settlement ratio is the numerical relationship between the pipe deflection and the relative settlement between the prism of fill directly above the pipe and adjacent soil. It is necessary to define the settlement ratio for negative projection embankment installations. Equating the deflection of the pipe and the total settlement of the prism of fill above the pipe to the settlement of the adjacent soil, the settlement ratio is:
Sg – (Sd + Sf +dc) (4.8) Sd Recommended settlement ratio design values are listed in Table 40. The projection ratio (p’) for this type of installation is the distance from the top of the pipe to the surface of the natural ground or compacted fill at the time of installation divided by the width of the trench. Where the ground surface is sloping, the average vertical distance from the top of the pipe to the original ground should be used in determining the projection ratio (p’). Figures 194 through 213 present fill loads in pounds per linear foot for circular pipe based on projection ratios of 0.5, 1.0, 1.5, 2.0 and settlement ratios of 0, -0.1, -0.3, -0.5 and -1.0. The dashed H = p’Bd line represents the limiting condition where the height of fill is at the same elevation as the natural ground surface. The dashed H = He line represents the condition where the height of the plane of equal settlement (He) is equal to the height of fill (H). rsd =

Jacked or Tunneled Soil Load. This type of installation is used where surface conditions make it difficult to install the pipe by conventional open excavation and backfill methods, or where it is necessary to install the pipe under an existing embankment. The earth load on a pipe installed by these methods is computed by the equation:

Wt = CtwBt – 2cCtBt
where: Bt = width of tunnel bore, (ft) The jacked or tunneled load coefficient Ct is further defined as:

2

(4.9)

Ct = 1 – e – 2Kμ'

– 2Kμ'

H Bt

(4.10)

In equation (4.9) the Ctw Bt2 term is similar to the Negative Projection Embankment equation (4.5) for soil loads and the 2cCtBt term accounts for the cohesion of undisturbed soil. Conservative design values of the coefficient of cohesion for various soils are listed in Table 41. Figures 147, 149, 151 and 153 present values of the trench load term (Ctw Bt2) in pounds per linear foot for a soil density of 120 pounds per cubic foot and Km’ values of 0.165, 0.150, 0.130 and 0.110. Figures 148, 150, 152 and 154 present values of the cohesion term (2cCtBt) divided by the design values for the coefficient of cohesion (c). To obtain the total earth load for any given height of cover, width of bore or tunnel and type of soil, the value of the cohesion term must be multiplied by the appropriate

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Loads and Supporting Strengths

39

coefficient of cohesion (c) and this product subtracted from the value of the trench load term.

FLUID LOAD
Fluid weight typically is about the same order of magnitude as pipe weight and generally represents a significant portion of the pipe design load only for large diameter pipe under relatively shallow fills. Fluid weight has been neglected in the traditional design procedures of the past, including the Marston Spangler design method utilizing the B and C beddings. There is no documentation of concrete pipe failures as a result of neglecting fluid load. However, some specifying agencies such as AASHTO and CHBDC, now require that the weight of the fluid inside the pipe always be considered when determining the D-load. The Sixteenth Edition of the AASHTO Standard Specifications For Highway Bridges states: “The weight of fluid, Wf, in the pipe shall be considered in design based on a fluid weight of 62.4 lbs/cu.ft, unless otherwise specified.”

DETERMINATION OF LIVE LOAD
To determine the required supporting strength of concrete pipe installed under asphalts, other flexible pavements, or relatively shallow earth cover, it is necessary to evaluate the effect of live loads, such as highway truck loads, in addition to dead loads imposed by soil and surcharge loads. If a rigid pavement or a thick flexible pavement designed for heavy duty traffic is provided with a sufficient buffer between the pipe and pavement, then the live load transmitted through the pavement to the buried concrete pipe is usually negligible at any depth. If any culvert or sewer pipe is within the heavy duty traffic highway right-of-way, but not under the pavement structure, then such pipe should be analyzed for the effect of live load transmission from an unsurfaced roadway, because of the possibility of trucks leaving the pavement. The AASHTO design loads commonly used in the past were the HS 20 with a 32,000 pound axle load in the Normal Truck Configuration, and a 24,000 pound axle load in the Alternate Load Configuration. The AASHTO LRFD designates an HL 93 Live Load. This load consists of the greater of a HS 20 with 32,000 pound axle load in the Normal Truck Configuration, or a 25,000 pound axle load in the Alternate Load Configuration. In addition, a 640 pound per linear foot Lane Load is applied across a 10 foot wide lane at all depths of earth cover over the top of the pipe, up to a depth of 8 feet. This Lane Load converts to an additional live load of 64 pounds per square foot, applied to the top of the pipe for any depth of burial less than 8 feet. The average pressure intensity caused by a wheel load is calculated by Equation 4.12. The Lane Load intensity is added to the wheel load pressure intensity in Equation 4.13. The HS 20, 32,000 pound and the Alternate Truck 25,000 pound design axle are carried on dual wheels. The contact area of the dual wheels with the ground is assumed to be rectangle, with dimensions presented in Illustration 4.9.

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Concrete Pipe Design Manual

Illustration 4.9 AASHTO Wheel Load Surface Contact Area (Foot Print)
16000 lb. HS 20 Load 12500 lb. LRFD Altemate Load 0.83 ft. (10 in.) a b 1.67 ft. (20 in.)

Illustration 4.10 AASHTO Wheel Loads and Wheel Spacings
LRFD Alternate Load
12000 lb. 12000 lb.

H 20 Load
4000 lb. 4000 lb.

HS 20 Load
4000 lb. 4000 lb.

4 ft.

6 ft.

14 ft.

6 ft.

14 ft.

12000 lb.

12000 lb.

HS 20 & Alternate Loads
16000 lb. 16000 lb. 16000 lb. 16000 lb.

14 ft. to 30 ft.

6 ft. 16000 lb. 16000 lb.

4 ft.

6 ft.

Impact Factors. The AASHTO LRFD Standard applies a dynamic load allowance, sometimes called Impact Factor, to account for the truck load being non-static. The dynamic load allowance, IM, is determined by Equation 4.11: IM = 33(1.0 - 0125H)

100

(4.11)

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Loads and Supporting Strengths where: H = height of earth cover over the top of the pipe, ft.

41

Load Distribution. The surface load is assumed to be uniformly spread on any horizontal subsoil plane. The spread load area is developed by increasing the length and width of the wheel contact area for a load configuration as shown in Illustration 4.13 for a dual wheel. On a horizontal soil plane, the dimensional increases to the wheel contact area are based on height of earth cover over the top of the pipe as presented in Illustration 4.11 for two types of soil. Illustration 4.11 Dimensional Increase Factor, AASHTO LRFD Soil Type LRFD select granular LRFD any other soil Dimensional Increase Factor 1.15H 1.00H

As indicated by Illustrations 4.14 and 4.15, the spread load areas from adjacent wheels will overlap as height of earth cover over the top of the pipe increases. At shallow depths, the maximum pressure will be developed by an HS 20 dual wheel, since at 16,000 pounds it applies a greater load than the 12,500 pound Alternate Load. At intermediate depths, the maximum pressure will be developed by the wheels of two HS 20 trucks in the passing mode, since at 16,000 pounds each, the two wheels apply a greater load than the 12,500 pounds of an Alternate Load wheel. At greater depths, the maximum pressure will be developed by wheels of two Alternate Load configuration trucks in the passing mode, since at 12,500 pounds each, the four wheels apply the greatest load(50,000 pounds). Intermediate depths begin when the spread area of dual wheels of two HS 20 trucks in the passing mode meet and begin to overlap. Greater depths begin when the spread area b of two single dual wheels of two Alternate Load configurations in the passing mode meet and begin to overlap. Since the exact geometric relationship of individual or combinations of surface wheel loads cannot be anticipated, the most critical loading configurations along with axle loads and rectangular spread load area are presented in Illustration 4.12 for the two AASHTO LRFD soil types.

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42
Illustration 4.12

Concrete Pipe Design Manual
LRFD Critical Wheel Loads and Spread Dimensions at the Top of the Pipe for:

Select Granular Soil Fill H, ft H < 2.03 2.03 ≤ H < 2.76 2.76 ≤ H Other Soils H, ft H < 2.33 2.33 ≤ H < 3.17 3.17 ≤ H P, lbs 16,000 32,000 50,000 Spread a, ft a + 1.00H a + 4 + 1.00H a + 4 + 1.00H Spread b, ft b + 1.00H b + 4 + 1.00H b + 4 + 1.00H Illustration 4.13 4.14 4.15 P, lbs 16,000 32,000 50,000 Spread a, ft a + 1.15H a + 4 + 1.15H a + 4 + 1.15H Spread b, ft b + 1.15H b + 4 + 1.15H b + 4 + 1.15H Illustration 4.13 4.14 4.15

Illustration 4.13 Spread Load Area - Single Dual Wheel
1.6 7' Dir ec
b= 0.8

a=

tio

no

f T rav el

3'

Wheel Load Area Spread Load Area

H ft.

Sp

rea

re Sp db

ad

a

American Concrete Pipe Association • www.concrete-pipe.org

Loads and Supporting Strengths
Illustration 4.14 Spread Load Area - Two Single Dual Wheels of Trucks in Passing Mode
Wheel Load Areas
b ft. a Dir ec tio no

43

4.0

Wheel Load Areas

fT

a

rav

el

H ft.
a

re Sp Sp

ad

rea

Distributed Load Area
db

Illustration 4.15 Spread Load Area - Two Single Dual Wheels of Two Alternate Loads in Passing Mode
Wheel Load Areas
b ft. 4.0 Dire c a b tio no fT rav 4.0 ft.

Wheel Load Areas

a

el

H ft.

re Sp Sp rea db

ad

a

Distributed Load Area

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Average Pressure Intensity. The wheel load average pressure intensity on the subsoil plane at the outside top of the concrete pipe is: w= P(1 + IM)

A

(4.12)

where: w = P = A = IM =

wheel load average pressure intensity, pounds per square foot total live wheel load applied at the surface, pounds spread wheel load area at the outside top of the pipe, square feet dynamic load allowance

From the appropriate Table in Illustration 4.12, select the critical wheel load and spread dimensions for the height of earth cover over the outside top of the pipe, H. The spread live load area is equal to Spread a times Spread b. Select the appropriate dynamic load allowance, using Equation 4.11. Total Live Load. A designer is concerned with the maximum possible loads, which occur when the distributed load area is centered over the buried pipe. Depending on the pipe size and height of cover, the most critical loading orientation can occur either when the truck travels transverse or parallel to the centerline of the pipe. Illustration 4.16 shows the dimensions of the spread load area, A, as related to whether the truck travel is transverse or parallel to the centerline of the pipe. Illustration 4.16 Spread Load Area Dimensions vs Direction of Truck
Spread b

Direction of Travel

Spread a

Pipe Pipe Centerline

Unless you are certain of the pipeline orientation, the total live load in pounds, WT, must be calculated for each travel orientation, and the maximum calculated value must be used in Equation 4.14 to calculate the live load on the pipe in
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Spread b

Direction of Travel

Spread a

Loads and Supporting Strengths

45

pounds per linear foot. The LRFD requires a Lane Load, LL, of 64 pounds per square foot on the top of the pipe at any depth less than 8 feet. The total live load acting on the pipe is: WT = (w + LL) L SL (4.13) where: WT = total live load, pounds w = wheel load average pressure intensity, pounds per square foot (at the top of the pipe) LL = lane loading if AASHTO LRFD is used, pounds per square foot 0≤H<8, LL = 64, pounds per square foot H≥8, LL = 0 L = dimension of load area parallel to the longitudinal axis of pipe, feet = outside horizontal span of pipe, Bc, or dimension of load SL area transverse to the longitudinal axis of pipe, whichever is less, feet Total Live Load in Pounds per Linear Foot. The total live load in pounds per linear foot, WL, is calculated by dividing the Total Live Load, WT, by the Effective Supporting Length, Le (See Illustration 4.17), of the pipe:
WL = WT Le (4.14)

where: WL = live load on top of pipe, pounds per linear foot Le = effective supporting length of pipe, feet The effective supporting length of pipe is: Le = L + 1.75(3/4RO) where: RO = outside vertical Rise of pipe, feet Illustration 4.17 Effective Supporting Length of Pipe
Wheel Surface Contact Area

H

L

Pipe Centerline

3Ro

Ro

Le = L + 1.75 (3/4Ro)

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Airports. The distribution of aircraft wheel loads on any horizontal plane in the soil mass is dependent on the magnitude and characteristics of the aircraft loads, the aircraft’s landing gear configuration, the type of pavement structure and the subsoil conditions. Heavier gross aircraft weights have resulted in multiple wheel undercarriages consisting of dual wheel assemblies and/or dual tandem assemblies. The distribution of wheel loads through rigid pavement are shown in Illustration 4.18. If a rigid pavement is provided, an aircraft wheel load concentration is distributed over an appreciable area and is substantially reduced in intensity at the subgrade. For multi-wheeled landing gear assemblies, the total pressure intensity is dependent on the interacting pressures produced by each individual wheel. The maximum load transmitted to a pipe varies with the pipe size under consideration, the pipe’s relative location with respect to the particular landing gear configuration and the height of fill between the top of the pipe and the subgrade surface. For a flexible pavement, the area of the load distribution at any plane in the soil mass is considerably less than for a rigid pavement. The interaction of pressure intensities due to individual wheels of a multi-wheeled landing gear assembly is also less pronounced at any given depth of cover. In present airport design practices, the aircraft’s maximum takeoff weight is used since the maximum landing weight is usually considered to be about three fourths the takeoff weight. Impact is not considered, as criteria are not yet available to include dynamic effects in the design process. Rigid Pavement. Illustration 4.18 Aircraft Pressure Distribution, Rigid Pavement

Fill Height H = 2 Feet

Fill Height H = 6 Feet

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Loads and Supporting Strengths The pressure intensity is computed by the equation:
p(H,X) = CP Rs 2 (4.15)

47

where: P = C = Rs =

Load at the surface, pounds Load coefficient, dependent on the horizontal distance (X), the vertical distance (H), and Rs Radius of Stiffness of the pavement, feet

Rs is further defined as: Rs =
4

(Eh)3 12 (1 – μ2) k

(4.16)

where: E = h = μ = k =

modulus of elasticity of the pavement, pounds per square inch pavement thickness, inches Poisson’s ratio (generally assumed 0.15 for concrete pavement) modulus of subgrade reaction, pounds per cubic inch

Tables 46 through 50 present pressure coefficients in terms of the radius of stiffness as developed by the Portland Cement Association and published in the report “Vertical Pressure on Culverts Under Wheel Loads on Concrete Pavement Slabs.” 3 Values of radius of stiffness are listed in Table 52 for pavement thickness and modulus of subgrade reaction. Tables 53 through 55 present aircraft loads in pounds per linear foot for circular, horizontal elliptical and arch pipe. The Tables are based on equations 4.15 and 4.16 using a 180,000 pound dual tandem wheel assembly, 190 pounds per square inch tire pressure, 26-inch spacing between dual tires, 66-inch spacing between tandem axles, k value of 300 pounds per cubic inch, 12-inch, thick concrete pavement and an Rs, value of 37.44 inches. Subgrade and subbase support for a rigid pavement is evaluated in terms of k, the modulus of subgrade reaction. A k value of 300 pounds per cubic inch was used, since this value represents a desirable subgrade or subbase material. In addition, because of the interaction between the pavement and subgrade, a lower value of k (representing reduced subgrade support) results in less load on the pipe. Although Tables 53 through 55 are for specific values of aircraft weights and landing gear configuration, the tables can be used with sufficient accuracy for all heavy commercial aircraft currently in operation. Investigation of the design loads of future jets indicates that although the total loads will greatly exceed present aircraft loads, the distribution of such loads over a greater number of landing gears and wheels will not impose loads on underground conduits greater than by commercial aircraft currently in operation. For lighter aircrafts and/or different rigid pavement thicknesses, it is necessary to calculate loads as illustrated in Example 4.10. Flexible Pavement. AASHTO considers flexible pavement as an unpaved
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surface and therefore live load distributions may be calculated as if the load were bearing on soil. Cover depths are measured from the top of the flexible pavement, however, at least one foot of fill between the bottom of the pavement and top of the pipe should be provided. Railroads. In determining the live load transmitted to a pipe installed under railroad tracks, the weight on the locomotive driver axles plus the weight of the track structure, including ballast, is considered to be uniformly distributed over an area equal to the length occupied by the drivers multiplied by the length of ties. The American Railway Engineering and Maintenance of Way Association (AREMA) recommends a Cooper E80 loading with axle loads and axle spacing as shown in Illustration 4.19. Based on a uniform load distribution at the bottom of the ties and through the soil mass, the live load transmitted to a pipe underground is computed by the equation:
WL = CpoBcIf (4.19)

where: C = po = Bc = If =

load coefficient tire pressure, pounds per square foot outside span of the pipe, feet impact factor

Tables 56 through 58 present live loads in pounds per linear foot based on equation (4.18) with a Cooper E80 design loading, track structure weighing 200 pounds per linear foot and the locomotive load uniformly distributed over an area 8 feet X 20 feet yielding a uniform live load of 2025 pounds per square foot. In accordance with the AREMA “Manual of Recommended Practice” an impact factor of 1.4 at zero cover decreasing to 1.0 at ten feet of cover is included in the Tables. Illustration 4.19 Cooper E 80 Wheel Loads and Axel Spacing
40,000 80,000 80,000 80,000 80,000 52,000 52,000 52,000 52,000 40,000 80,000 80,000 80,000 80,000 52,000 52,000 52,000 52,000
8,000 lb per lin ft

8'

5' 5' 5'

9'

5' 6' 5'

8'

8'

5' 5' 5'

9'

5' 6' 5' 5'

3 Op. cit., p. 28 4 Equation (21) is recommended by WPCF-ASCE Manual, The Design and Construction of Sanitary Storm Sewers.

Based on a uniform load distribution at the bottom of the ties and through the soil mass, the design track unit load, WL, in pounds per square foot, is determined from the AREMA graph presented in Figure 215. To obtain the live load transmitted to the pipe in pounds per linear foot, it is necessary to multiply the unit load, WL, from Figure 215, by the outside span, Bc, of the pipe in feet. Loadings on a pipe within a casing pipe shall be taken as the full dead load, plus live load, plus impact load without consideration of the presence of the casing
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Loads and Supporting Strengths

49

pipe, unless the casing pipe is fully protected from corrosion. Culvert or sewer pipe within the railway right-of-way, but not under the track structure, should be analyzed for the effect of live loads because of the possibility of train derailment. Construction Loads. During grading operations it may be necessary for heavy construction equipment to travel over an installed pipe. Unless adequate protection is provided, the pipe may be subjected to load concentrations in excess of the design loads. Before heavy construction equipment is permitted to cross over a pipe, a temporary earth fill should be constructed to an elevation at least 3 feet over the top of the pipe. The fill should be of sufficient width to prevent possible lateral displacement of the pipe.

SELECTION OF BEDDING
A bedding is provided to distribute the vertical reaction around the lower exterior surface of the pipe and reduce stress concentrations within the pipe wall. The load that a concrete pipe will support depends on the width of the bedding contact area and the quality of the contact between the pipe and bedding. An important consideration in selecting a material for bedding is to be sure that positive contact can be obtained between the bed and the pipe. Since most granular materials will shift to attain positive contact as the pipe settles, an ideal load distribution can be attained through the use of clean coarse sand, wellrounded pea gravel or well-graded crushed rock.

BEDDING FACTORS
Under installed conditions the vertical load on a pipe is distributed over its width and the reaction is distributed in accordance with the type of bedding. When the pipe strength used in design has been determined by plant testing, bedding factors must be developed to relate the in-place supporting strength to the more severe plant test strength. The bedding factor is the ratio of the strength of the pipe under the installed condition of loading and bedding to the strength of the pipe in the plant test. This same ratio was defined originally by Spangler as the load factor. This latter term, however, was subsequently defined in the ultimate strength method of reinforced concrete design with an entirely different meaning. To avoid confusion, therefore, Spangler’s term was renamed the bedding factor. The three-edge bearing test as shown in Illustration 4.20 is the normally accepted plant test so that all bedding factors described in the following pages relate the inplace supporting strength to the three-edge bearing strength.

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Illustration 4.20 Three-Edge Bearing Test
Rigid Steel Member

Bearing Strips

Although developed for the direct design method, the Standard Installations are readily applicable to and simplify the indirect design method. The Standard Installations are easier to construct and provide more realistic designs than the historical A, B, C, and D beddings. Development of bedding factors for the Standard Installations, as presented in the following paragraphs, follows the concepts of reinforced concrete design theories. The basic definition of bedding factor is that it is the ratio of maximum moment in the three-edge bearing test to the maximum moment in the buried condition, when the vertical loads under each condition are equal: Bf = MTEST MFIELD (20)

where: = bedding factor Bf MTEST = maximum moment in pipe wall under three-edge bearing test load, inch-pounds MFIELD = maximum moment in pipe wall under field loads, inch-pounds Consequently, to evaluate the proper bedding factor relationship, the vertical load on the pipe for each condition must be equal, which occurs when the springline axial thrusts for both conditions are equal. In accordance with the laws of statics and equilibrium, MTEST and MFIELD are:
MTEST = [0.318NFS] x [D + t] MFIELD = [MFI] - [0.38tNFI] - [0.125NFI x c] (21) (22)

where: NFS = axial thrust at the springline under a three-edge bearing test load, pounds per foot D = inside pipe diameter, inches t = pipe wall thickness, inches MFI = moment at the invert under field loading, inch-pounds/ft NFI = axial thrust at the invert under field loads, pounds per foot c = thickness of concrete cover over the inner reinforcement, inches
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Loads and Supporting Strengths Substituting equations 4.21 and 4.22 into equation 4.20. Bf = [0.318NFS] x [D + t] [MFI] - [0.38tNFI] - [0.125NFI x C]

51

(23)

Using this equation, bedding factors were determined for a range of pipe diameters and depths of burial. These calculations were based on one inch cover over the reinforcement, a moment arm of 0.875d between the resultant tensile and compressive forces, and a reinforcement diameter of 0.075t. Evaluations indicated that for A, B and C pipe wall thicknesses, there was negligible variation in the bedding factor due to pipe wall thickness or the concrete cover, c, over the reinforcement. The resulting bedding factors are presented in Illustration 4.21. Illustration 4.21 Bedding Factors, Embankment Conditions, Bfe Pipe Diameter 12 in. 24 in. 36 in. 72 in. 144 in. Standard Installation Type 1 Type 2 Type 3 Type 4 4.4 4.2 4.0 3.8 3.6 3.2 3.0 2.9 2.8 2.8 2.5 2.4 2.3 2.2 2.2 1.7 1.7 1.7 1.7 1.7

Notes: 1. For pipe diameters other than listed in Illustration 4.21, embankment condition factors, Bfe can be obtained by interpolation. 2. Bedding factors are based on the soils being placed with the minimum compaction specified in Illustration 4.4 for each standard installation.

Determination of Bedding Factor. For trench installations as discussed previously, experience indicates that active lateral pressure increases as trench width increases to the transition width, provided the sidefill is compacted. A SIDD parameter study of the Standard Installations indicates the bedding factors are constant for all pipe diameters under conditions of zero lateral pressure on the pipe. These bedding factors exist at the interface of the pipewall and the soil and are called minimum bedding factors, Bfo, to differentiate them from the fixed bedding factors developed by Spangler. Illustration 4.22 presents the minimum bedding factors.

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52 Illustration 4.22

Concrete Pipe Design Manual Trench Minimum Bedding Factors, Bfo Minimum Bedding Factor, Bfo 2.3 1.9 1.7 1.5

Standard Installation Type 1 Type 2 Type 3 Type 4

Note: 1. Bedding factors are based on the soils being placed with the minimum compaction specified in Illustration 4.4 for each Standard Installation. 2. For pipe installed in trenches dug in previously constructed embankment, the load and the bedding factor should be determined as an embankment condition unless the backfill placed over the pipe is of lesser compaction than the embankment.

A conservative linear variation is assumed between the minimum bedding factor and the bedding factor for the embankment condition, which begins at transition width. Illustration 4.23 Variable Bedding Factor Bdt Bd Bc Bfe

Bc

Bfo

The equation for the variable trench bedding factor, is: Bfv = [Bfe – Bfo][Bd – Bc] [Bdt – Bc] + Bfo (24)

where: Bc = outside horizontal span of pipe, feet Bd = trench width at top of pipe, feet
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Loads and Supporting Strengths Bdt Bfe Bfo Bfv = = = = transition width at top of pipe, feet bedding factor, embankment minimum bedding factor, trench variable bedding factor, trench

53

Transition width values, Bdt are provided in Tables 13 through 39. For pipe installed with 6.5 ft or less of overfill and subjected to truck loads, the controlling maximum moment may be at the crown rather than the invert. Consequently, the use of an earth load bedding factor may produce unconservative designs. Crown and invert moments of pipe for a range of diameters and burial depths subjected to HS20 truck live loadings were evaluated. Also evaluated, was the effect of bedding angle and live load angle (width of loading on the pipe). When HS20 or other live loadings are encountered to a significant value, the live load bedding factors, BfLL,, presented in Illustration 4.24 are satisfactory for a Type 4 Standard Installation and become increasingly conservative for Types 3, 2, and 1. Limitations on BfLL are discussed in the section on Selection of Pipe Strength. Illustration 4.24 Bedding Factors, BfLL, for HS20 Live Loadings Fill Height, Ft. 12 0.5 2.2 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 Pipe Diameter, Inches 24 1.7 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 36 1.4 1.7 2.1 2.2 2.2 2.2 2.2 2.2 2.2 2.2 48 1.3 1.5 1.8 2.0 2.2 2.2 2.2 2.2 2.2 2.2 60 1.3 1.4 1.5 1.8 2.0 2.2 2.2 2.2 2.2 2.2 72 1.1 1.3 1.4 1.5 1.8 2.2 2.2 2.2 2.2 2.2 84 1.1 1.3 1.4 1.5 1.7 1.8 1.9 2.1 2.2 2.2 96 1.1 1.3 1.3 1.4 1.5 1.7 1.8 1.9 2.0 2.2 108 1.1 1.1 1.3 1.4 1.4 1.5 1.7 1.8 1.9 2.0 120 1.1 1.1 1.3 1.3 1.4 1.5 1.5 1.7 1.8 1.9 144 1.1 1.1 1.1 1.3 1.3 1.4 1.4 1.5 1.7 1.8

Application of Factor of Safety. The indirect design method for concrete pipe is similar to the common working stress method of steel design, which employs a factor of safety between yield stress and the desired working stress. In the indirect method, the factor of safety is defined as the relationship between the ultimate strength D-load and the 0.01inch crack D-load. This relationship is specified in the ASTM Standards C 76 and C 655 on concrete pipe. The relationship between ultimate D-load and 0.01-inch crack D-load is 1.5 for 0.01 inch crack D-loads of 2,000 or less; 1.25 for 0.01 inch crack D loads of 3,000 or more; and a linear reduction from 1.5 to 1.25 for 0.01 inch crack D-loads between more than 2,000 and less than 3,000. Therefore, a factor of safety of 1.0 should be applied if the 0.01 inch crack strength is used as the design criterion rather

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than the ultimate strength. The 0.01 inch crack width is an arbitrarily chosen test criterion and not a criteri for field performance or service limit.

SELECTION OF PIPE STRENGTH
The American Society for Testing and Materials has developed standard specifications for precast concrete pipe. Each specification contains design, manufacturing and testing criteria. ASTM Standard C 14 covers three strength classes for nonreinforced concrete pipe. These classes are specified to meet minimum ultimate loads, expressed in terms of three-edge bearing strength in pounds per linear foot. ASTM Standard C 76 for reinforced concrete culvert, storm drain and sewer pipe specifies strength classes based on D-load at 0.01-inch crack and/or ultimate load. The 0.01-inch crack D-load (D0.01) is the maximum three-edge-bearing test load supported by a concrete pipe before a crack occurs having a width of 0.01 inch measured at close intervals, throughout a length of at least 1 foot. The ultimate D-load (Dult) is the maximum three-edge-bearing test load supported by a pipe divided by the pipe’s inside diameter. D-loads are expressed in pounds per linear foot per foot of inside diameter. ASTM Standard C 506 for reinforced concrete arch culvert, storm drain, and sewer pipe specifies strengths based on D-load at 0.01-inch crack and/or ultimate load in pounds per linear foot per foot of inside span. ASTM Standard C 507 for reinforced concrete elliptical culvert, storm drain and sewer pipe specifies strength classes for both horizontal elliptical and vertical elliptical pipe based on D-load at 0.01-inch crack and/or ultimate load in pounds per linear foot per foot of inside span. ASTM Standard C 655 for reinforced concrete D-load culvert, storm drain and sewer pipe covers acceptance of pipe designed to meet specific D-load requirements. ASTM Standard C 985 for nonreinforced concrete specified strength culvert, storm drain, and sewer pipe covers acceptance of pipe designed for specified strength requirements. Since numerous reinforced concrete pipe sizes are available, three-edge bearing test strengths are classified by D-loads. The D-load concept provides strength classification of pipe independent of pipe diameter. For reinforced circular pipe the three-edge-bearing test load in pounds per linear foot equals D-load times inside diameter in feet. For arch, horizontal elliptical and vertical elliptical pipe the three-edge bearing test load in pounds per linear foot equals D-load times nominal inside span in feet. The required three-edge-bearing strength of non-reinforced concrete pipe is expressed in pounds per linear foot, not as a D-load, and is computed by the equation: T.E.B = WE + WF Bf
+

WL BfLL

x F.S.

(25)

The required three-edge bearing strength of circular reinforced concrete pipe is expressed as D-load and is computed by the equation:

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Loads and Supporting Strengths

55

D-load =

W E + WF Bf

+

WL BfLL

x

F.S. D

(26)

The determination of required strength of elliptical and arch concrete pipe is computed by the equation:

D-load =
where:

W E + WF Bf

+

WL BfLL

x

F.S. S

(27)

S = inside horizontal span of pipe, ft. When an HS20 truck live loading is applied to the pipe, use the live load bedding factor, BfLL, as indicated in Equations 4.25 – 4.27, unless the earth load bedding factor, Bf, is of lesser value in which case, use the lower Bf value in place of BfLL. For example, with a Type 4 Standard Installation of a 48 inch diameter pipe under 1.0 feet of fill, the factors used would be Bf = 1.7 and BfLL = 1.5; but under 2.5 feet or greater fill, the factors used would be Bf= 1.7 and BfLL, = 1.7 rather than 2.2. For trench installations with trench widths less than transition width, BfLL would be compared to the variable trench bedding factor, Bfv. Although their loads are generally less concentrated, the live load bedding factor may be conservatively used for aircraft and railroad loadings. The use of the six-step indirect design method is illustrated by examples on the following pages.

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EXAMPLE PROBLEMS

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Loads and Supporting Strengths

57

EXAMPLE PROBLEMS EXAMPLE 4-1 Trench Installation

H Bd

Bc

Given: A 48 inch circular pipe is to be installed in a 7 foot wide trench with 10 feet of cover over the top of the pipe. The pipe will be backfilled with sand and gravel weighing 110 pounds per cubic foot. Assume a Type 4 Installation. Find: The required pipe strength in terms of 0.01 inch crack D-load. 1. Determination of Earth Load (WE) To determine the earth load, we must first determine if the installation is behaving as a trench installation or an embankment installation. Since we are not told what the existing in-situ material is, conservatively assume a Km' value between the existing soil and backfill of 0.150. From Table 23, The transition width for a 48 inch diameter pipe with a Kμ' value of 0.150 under 10 feet of fill is: Bdt = 8.5 feet Transition width is greater than the actual trench width, therefore the installation will act as a trench. Use Equations 4.3 and 4.4 to determine the soil load.
w H Bd Kμ' = = = = 110 pounds per cubic foot 10 feet 7 feet 0.150 48 + 2 (5) 12 Note: Wall thickness for a 48 inch inside diameter pipe with a B wall is 5-inches per ASTM C 76.

Do =

Do = 4.83 feet

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58

Concrete Pipe Design Manual The value of Cd can be obtained from Figure 214, or calculated using Equation 4.4. 1-e Cd = (2) (0.150) Cd = 1.16
-2 (0.150) 10 7

Equation 4.4 (4.83)2 (4 - π)

(110) Equation 4.3 8 Wd = 6,538 pounds per linear foot We = Wd WE = 6,538 earth load in pounds per linear foot Fluid Load, WF = 62.4 lbs/ft3 2. Determination of Live Load (WL) From Table 42, live load is negligible at a depth of 10 feet. 3. Selection of Bedding Because of the narrow trench, good compaction of the soil on the sides of the pipe would be difficult, although not impossible. Therefore a Type 4 Installation was assumed. 4. Determination of Bedding Factor, (Bfv) The pipe is installed in a trench that is less than transition width. Therefore, Equation 4.24 must be used to determine the variable bedding factor.

Wd = (1.16)(110)(7)2 +

Bc = Do Bc = 4.83 outside diameter of pipe in feet Bd = 7 width of trench in feet Bdt = 8.5 transition width in feet Bfe = 1.7 embankment bedding factor Bfo = 1.5 minimum bedding factor Bfv = (1.7 - 1.5) (7 - 4.83) 8.5 - 4.83 + 1.5 Equation 4.24

Bfv = 1.62
5. Application of Factor of Safety (F.S.) A factor of safety of 1.0 based on the 0.01 inch crack will be applied. 6. Selection of Pipe Strength The D-load is given by Equation 4.26

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59

WE WF WL Bf BfLL D

= = = = = =

6,538 earth load in pounds per linear foot 62.4 fluid load in pounds per cubic foot 0 live load is negligible Bfv Bf = 1.62 earth load bedding factor N/A live load bedding factor is not applicable 4 inside diameter of pipe in feet 6,538 + 62.4 1.62 1.0 4 Equation 4.26

D0.01 =

D0.01 = 1,009 pounds per linear foot per foot of diameter
Answer: A pipe which would withstand a minimum three-edge bearing test load for the 0.01 inch crack of 1,009 pounds per linear foot per foot of inside diameter would be required.

EXAMPLE 4-2 Positive Projection Embankment Installation

H Do

Di

Given: A 48 inch circular pipe is to be installed in a positive projecting embankment condition using a Type 1 installation. The pipe will be covered with 35 feet of 120 pounds per cubic foot overfill. Find: The required pipe strength in terms of 0.01 inch D-load 1. Determination of Earth Load (WE) Per the given information, the installation behaves as a positive projecting embankment. Therefore, use Equation 4.2 to determine the soil prism load and multiply it by the appropriate vertical arching factor.

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Do =

48 + 2 (5) 12

Note: The wall thickness for a 48-inch pipe with a B wall is 5-inches per ASTM C76.

Do = 4.83 outside diameter of pipe in feet w = 120 unit weight of soil in pounds per cubic foot H = 1 height of cover in feet PL = 120 35 + 4.83 (4 - π) 8 4.83 Equation 4.2

PL = 880 pounds per linear foot Immediately listed below Equation 4.2 are the vertical arching factors (VAFs) for the four types of Standard Installations. Using a VAF of 1.35 for a Type 1 Installation, the earth load is:
WE = 1.35 x 20,586 WE = 27,791 pounds per linear foot Equation 4.1

Fluid Load, WF = 62.4 lbs/ft3 2. Determination of Live Load (WL) From Table 42, live load is negligible at a depth of 35 feet. 3. Selection of Bedding A Type 1 Installation will be used for this example 4. Determination of Bedding Factor, (Bfe) The embankment bedding factor for a Type 1 Installation may be interpolated from Illustration 4.21 Bfe36 = 4.0 Bfe72 = 3.8 Bfe48 = Bfe48 72 - 48 72 - 36 = 3.93 (4.0 - 3.8) + 3.8

5. Application of Factor of Safety (F.S.) A factor of safety of 1.0 based on the 0.01 inch crack will be applied. 6. Selection of Pipe Strength The D-load is given by Equation 4.26

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Loads and Supporting Strengths

61

WE WF WL Bf BfLL D

= = = = = =

D0.01 =

27,791 earth load in pounds per linear foot 62.4 fluid load in pounds per cubic foot 0 live load is negligible Bfe Bf = 3.93 earth load bedding factor N/A live load bedding factor is not applicable 4 inside diameter of pipe in feet 27,791 + 62.4 1.0 3.93 4

Equation 4.26

D0.01 = 1,768 pounds per linear foot per foot of diameter

Answer: A pipe which would withstand a minimum three-edge bearing test for the 0.01 inch crack of 1,768 pounds per linear foot per foot of inside diameter would be required.

EXAMPLE 4-3 Negative Projection Embankment Installation

H Bd

Bc

Given: A 72 inch circular pipe is to be installed in a negative projecting embankment condition in ordinary soil. The pipe will be covered with 35 feet of 120 pounds per cubic foot overfill. A 10 foot trench width will be constructed with a 5 foot depth from the top of the pipe to the natural ground surface. Find: The required pipe strength in terms of 0.01 inch D-load 1. Determination of Earth Load (WE) A settlement ratio must first be assumed. The negative projection ratio of this installation is the height of soil from the top of the pipe to the top of the natural ground (5 ft) divided by the trench width (10 ft). Therefore the negative projection ratio of this installation is p' = 0.5. From Table 40, for a negative projection ratio of p' = 0.5, the design value of the settlement ratio is -0.1.

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62

Concrete Pipe Design Manual Enter Figure 195 on the horizontal scale at H = 35 feet. Proceed vertically until the line representing Bd = 10 feet is intersected. At this point the vertical scale shows the fill load to be 27,500 pounds per linear foot for 100 pounds per cubic foot fill material. Increase the load 20 percent for 120 pound material since Figure 195 shows values for 100 pound material. Wn = 1.20 x 27,500 Wn = 33,000 pounds per linear foot WE = Wn WE = 33,000 earth load in pounds per linear foot Fluid Load, WF = 62.4 lbs/ft3 2. Determination of Live Load (WL) From Table 42, live load is negligible at a depth of 35 feet. 3. Selection of Bedding No specific bedding was given. Assuming the contractor will put minimal effort into compacting the soil, a Type 3 Installation is chosen. 4. Determination of Bedding Factor, (Bfv) The variable bedding factor will be determined using Equation 4.24 in the same fashion as if the pipe were installed in a trench. Note: The wall thickness for a 72-inch pipe with a B wall is 7-inches per ASTM C 76. 12 Bc = 7.17 outside diameter of pipe in feet Bd = 10 trench width in feet Bdt = 14.1 transition width for a Type 3 Installation with Kμ'=0.150 Bfe = 2.2 embankment bedding factor (taken from Illustration 4.21) Bfo = 1.7 minimum bedding factor (taken from Illustration 4.22) (2.2 - 1.7) (10 - 7.17) + 1.7 Equation 4.24 Bfv = 14.1 - 7.17 Bfv = 1.9 5. Application of Factor of Safety (F.S.) A factor of safety of 1.0 based on the 0.01 inch crack will be applied. 6. Selection of Pipe Strength The D-load is given by Equation 4.26 72 + 2 (7)

Bc =

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33,000 earth load in pounds per linear foot 62.4 fluid load in pounds per cubic foot 0 live load is negligible Bfv Bf = 1.9 earth load bedding factor N/A live load bedding factor is not applicable 6 inside diameter of pipe in feet 33,000 + 62.4 1.0 D0.01 = 6 1.9

WE WF WL Bf BfLL D

= = = = = =

Equation 4.26

D0.01 = 2,895 pounds per linear foot per foot of diameter
Answer: A pipe which would withstand a minimum three-edge bearing test load for the 0.01 inch crack of 28,95 pounds per linear foot per foot of inside diameter would be required.

EXAMPLE 4-4 Jacked or Tunneled Installation
H

Bc

Bt

Given: A 48 inch circular pipe is to be installed by the jacking method of construction with a height of cover over the top of the pipe of 40 feet. The pipe will be jacked through ordinary clay material weighing 110 pounds per cubic foot throughout its entire length. The limit of excavation will be 5 feet. Find: The required pipe strength in terms of 0.01 inch crack D-load. 1. Determination of Earth Load (WE) A coefficient of cohesion value must first be assumed. In Table 41, values of the coefficient of cohesion from 40 to 1,000 are given for clay. A conservative value of 100 pounds per square foot will be used. Enter Figure 151, Ordinary Clay, and project a horizontal line from H = 40 feet on the vertical scale and a vertical line from Bt = 5 feet on the horizontal scale. At the intersection of these two lines interpolate

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Concrete Pipe Design Manual between the curved lines for a value of 9,500 pounds per linear foot, which accounts for earth load without cohesion. Decrease the load in proportion to 110/120 for 110 pound material since Figure 151 shows values for 120 pound material.
110 Wt = 120 x 9,500 Wt = 8,708 pounds per linear foot

Enter Figure 152, Ordinary Clay, and project a horizontal line from H = 40 feet on the vertical scale and a vertical line from Bt = 5 feet on the horizontal scale. At the intersection of these two lines interpolate between the curved lines for a value of 33, which accounts for the cohesion of the soil. Multiply this value by the coefficient of cohesion, c = 100, and subtract the product from the 8,708 value obtained from figure 151. Wt = 8,708 –100 (33) Wt = 5,408 pounds per linear foot WE = Wt WE = 5,408 earth load in pounds per linear foot Note: If the soil properties are not consistent, or sufficient information on the soil is not available, cohesion may be neglected and a conservative value of 8,708 lbs/ft used. Fluid Load, WF = 62.4 lbs/ft3 2. Determination of Live Load (WL) From Table 42, live load is negligible at 40 feet. 3. Selection of Bedding The annular space between the pipe and limit of excavation will be filled with grout. 4. Determination of Bedding Factor (Bfv) Since the space between the pipe and the bore will be filled with grout, there will be positive contact of bedding around the periphery of the pipe. Because of this beneficial bedding condition, little flexural stress should be induced in the pipe wall. A conservative variable bedding factor of 3.0 will be used. 5. Application of Factor of Safety (F.S.) A factor of safety of 1.0 based on the 0.01 inch crack will be applied. 6. Selection of Pipe Strength The D-load is given by Equation 4.26.

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WE WF WL Bf BfLL D

= = = = = =

D0.01 =

5,408 earth load in pounds per linear foot 62.4 fluid load in pounds per cubic foot 0 live load is negligible Bfv Bf = 3.0 earth load bedding factor N/A live load bedding factor is not applicable 4 inside diameter of pipe in feet 5,408 + 62.4 1.0 3.0 4

Equation 4.26

D0.01 = 451 pounds per linear foot per foot of diameter Answer: A pipe which would withstand a minimum three-edge bearing test load for the 0.01 inch crack of 451 pounds per linear foot per foot of inside diameter would be required.

EXAMPLE 4-5 Wide Trench Installation

H Bd

Bc

Given: A 24 inch circular non reinforced concrete pipe is to be installed in a 5 foot wide trench with 10 feet of cover over the top of the pipe. The pipe will be backfilled with ordinary clay weighing 120 pounds per cubic foot. Find: The required three-edge bearing test strength for nonreinforced pipe and the ultimate D-load for reinforced pipe. 1. Determination of Earth Load (WE) To determine the earth load, we must first determine if the installation is behaving as a trench installation or an embankment installation. Assume that since the pipe is being backfilled with clay that they are using in-situ soil for backfill. Assume a Kμ’ value between the existing soil and backfill of 0.130. We will assume a Type 4 Installation for this example. From Table 17, the transition width for a 24 inch diameter pipe with a Kμ’ value of 0.130 under 10 feet of fill is: Bdt = 4.8
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Concrete Pipe Design Manual

Since the transition width is less than the trench width, this installation will act as an embankment. Therefore calculate the prism load per Equation 4.2 and multiply it by the appropriate vertical arching factor (VAF). Do = 24 + 2 (3) 12 Note: The wall thickness for a 24-inch pipe with a B wall is 3-inches per ASTM C76.

Do = 2.5 outside diameter of pipe in feet w = 120 unit weight of soil in pounds per cubic foot H = 10 height of cover in feet PL = 120 10 + 2.5 (4 - π) 8 2.5 Equation 4.2

PL = 3,080 pounds per linear foot Immediately listed below Equation 4.2 are the vertical arching factors (VAF) for the four types of Standard Installations. Using a VAF of 1.45 for a Type 4 Installation, the earth load is:

WE = 1.45 x 3,080 WE = 4,466 pounds per linear foot
Fluid Load, WF = 62.4 lbs/ft3

Equation 4.1

2. Determination of Live Load (WL) From Table 42, live load is negligible at a depth of 10 feet. 3. Selection of Bedding A Type 4 Installation has been chosen for this example 4. Determination of Bedding Factor, (Bfe) Since this installation behaves as an embankment, an embankment bedding factor will be chosen. From Illustration 4.21, the embankment bedding factor for a 24 inch pipe installed in a Type 4 Installation is: Bfe = 1.7 5. Application of Factor of Safety (F.S.) A factor of safety of 1.0 based on the 0.01 inch crack will be applied. 6. Selection of Pipe Strength The D-load is given by Equation 4.26.

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WE WF WL Bf BfLL D

= = = = = =

4,466 earth load in pounds per linear foot 62.4 fluid load in pounds per cubic foot 0 live load is negligible Bfe Bf = 1.7 earth load bedding factor N/A live load bedding factor is not applicable 2 inside diameter of pipe in feet

The ultimate three-edge bearing strength for nonreinforced concrete pipe is given by Equation 4.25 TEB = 1.5 1.7 TEB = 3,941 pounds per linear foot 4,466 + 62.4 Equation 4.25

The D-load for reinforced concrete pipe is given by Equation 2.46. 1.0 Equation 4.26 D0.01 = 4,466 + 62.4 2 1.7 D0.01 = 1,314 pounds per linear foot per foot of diameter

Answer: A nonreinforced pipe which would withstand a minimum three-edge bearing test load of 3,941 pounds per linear foot would be required.

EXAMPLE 4-6 Positive Projection Embankment Installation Vertical Elliptical Pipe

H

pB'C B'c

Given: A 76 inch x 48 inch vertical elliptical pipe is to be installed in a positive projection embankment condition in ordinary soil. The pipe will be covered with 50 feet of 120 pounds per cubic foot overfill.

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68 Find:

Concrete Pipe Design Manual The required pipe strength in terms of 0.01 inch crack D-load. 1. Determination of Earth Load (WE) Note: The Standard Installations were initially developed for circular pipe, and their benefit has not yet been established for elliptical and arch pipe. Therefore, the traditional Marston/Spangler design method using B and C beddings is still conservatively applied for these shapes. A settlement ratio must first be assumed. In Table 40, values of settlement ratio from +0.5 to +0.8 are given for positive projecting installation on a foundation of ordinary soil. A value of 0.7 will be used. The product of the settlement ratio and the projection ratio will be 0.49 (rsdp approximately 0.5). Enter Figure 182 on the horizontal scale at H = 50 feet. Proceed vertically until the line representing R x S = 76" x 48" is intersected. At this point the vertical scale shows the fill load to be 41,000 pounds per linear foot for 100 pounds per cubic foot fill material. Increase the load 20 percent for 120 pound material. Wc = 1.20 x 41,000 Wc = 49,200 per linear foot WE = 49,200 earth load in pounds per linear foot WE = Wc Fluid Load, WF = 62.4 lbs/ft3 2. Determination of Live Load (WL) From Table 44, live load is negligible at a depth of 50 feet. 3. Selection of Bedding Due to the high fill height you will more than likely want good support around the pipe, a Class B bedding will be assumed for this example. 4. Determination of Bedding Factor (Bfe) First determine the H/Bc ratio.
H Bc Bc = 50 48 + 2 (6.5) = 12 Note: the wall thickness for a 72" x 48" elliptical pipe is 6.5" per ASTM C507.

= 5.08 outside diameter of pipe in feet

H/Bc = 9.84

From Table 59, for an H/Bc ratio of 9.84, rsdp value of 0.5, p value of 0.7, and a Class B bedding, an embankment bedding factor of 2.71 is obtained. Bfe = 2.71

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Loads and Supporting Strengths 5. Application of Factor of Safety (F.S.) A factor of safety of 1.0 based on the 0.01 inch crack will be applied. 6. Selection of Pipe Strength The D-load is given by Equation 4.27
WE WF WL Bf BfLL S = = = = = = 49,200 earth load in pounds per linear foot 62.4 fluid load in pounds per cubic foot 0 live load is negligible Bfe Bf = 2.71 earth load bedding factor N/A live load bedding factor is not applicable 4 inside diameter of pipe in feet 49,200 + 62.4 1.0 2.71 4

69

D0.01 =

Equation 4.27

D0.01 = 4,539 pounds per linear foot per foot of diameter

Answer: A pipe which would withstand a minimum three-edge bearing test load for the 0.01 inch crack of 4,539 pounds per linear foot per foot of inside horizontal span would be required.

EXAMPLE 4-7 Highway Live Load

Bc B

Given: A 24 inch circular pipe is to be installed in a positive projection embankment under an unsurfaced roadway and covered with 2.0 feet of 120 pounds per cubic foot backfill material. Find: The required pipe strength in terms of 0.01 inch crack D-load. 1. Determination of Earth Load (WE) Per the given information, the installation behaves as a positive projecting embankment. Therefore, use Equation 4.2 to determine the soil prism load and multiply it by the appropriate vertical arching factor.
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Concrete Pipe Design Manual

12 Do = 2.5 outside diameter of pipe in feet w = 120 unit weight of soil in pounds per cubic foot H = 2 height of cover in feet PL = 120 2 + 2.5 (4 - π) 8 2.5

Do =

24 + 2 (3)

Note: The wall thickness for a 24-inch pipe with a B wall is 3-inches per ASTM C76.

Equation 4.2

PL = 680 pounds per linear foot Assume a Type 2 Standard Installation and use the appropriate vertical arching factor listed below Equation 4.2.
VAF = 1.4 WE = 1.40 x 680 WE = 952 pounds per linear foot

Equation 4.1

Fluid Load, WF = 62.4 lbs/ft3 2. Determination of Live Load (WL) Since the pipe is being installed under an unsurfaced roadway with shallow cover, a truck loading based on AASHTO will be evaluated. From Table 42, for D = 24 inches and H = 2.0 feet, a live load of 1,780 pounds per linear foot is obtained. This live load value includes impact. WL = 1,780 pounds per linear foot 3. Selection of Bedding A Type 2 Standard Installation will be used for this example. 4. Determination of Bedding Factor, (Bfe) a.) Determination of Embankment Bedding Factor From Illustration 4.21, the earth load bedding factor for a 24 inch pipe installed in a Type 2 positive projecting embankment condition is 3.0. Bfe = 3.0 b.) Determination of Live Load Bedding Factor, (BfLL) From Illustration 4.24, the live load bedding factor for a 24 inch pipe under 2 feet of cover is 2.2. BfLL = 2.2 5. Application of Factor of Safety (F.S.) A factor of safety of 1.0 based on the 0.01 inch crack will be applied.

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Loads and Supporting Strengths 6. Selection of Pipe Strength The D-load is given by equation 4.26

71

WE WF WL Bf BfLL D

= 952 earth load in pounds per linear foot = 62.4 fluid load in pounds per cubic foot = 1,780 live load in pounds per linear foot = Bfe Bf = 3 earth load bedding factor = 2.2 live load bedding factor is not applicable = 2 inside diameter of pipe in feet 952 + 62.4 3.0 + 1,780 2.2 1.0 4 Equation 4.26

D0.01 =

D0.01 = 597.3 pounds per linear foot per foot of diameter
Answer: A pipe which would withstand a minimum three-edge bearing test for the 0.01 inch crack of 563 pounds per linear foot per foot of inside diameter would be required.

EXAMPLE 4-8 Highway Live Load per AASHTO LRFD

Bc B

Given: A 30-inch diameter, B wall, concrete pipe is to be installed as a storm drain under a flexible pavement and subjected to AASHTO highway loadings. The pipe will be installed in a 6 ft wide trench with a minimum of 2 feet of cover over the top of the pipe. The AASHTO LRFD Criteria will be used with Select Granular Soil and a Type 3 Installation. Find: The maximum 0.01” Dload required of the pipe. 1. Determination of Earth Load (WE) Per review of Table 19, the 6 ft. trench is wider than transition width. Therefore, the earth load is equal to the soil prism load multiplied by the appropriate vertical arching factor.
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Note: The wall thickness for a 30-inch pipe with a B wall is 3.5-inches per ASTM C76. 12 Do = 3.08 outside diameter of pipe in feet w = 120 unit weight of soil in pounds per cubic foot H = 2 height of cover in feet 3.08 (4 - π) PL = 120 2 + 3.08 8 PL = 861 pounds per linear foot Do =
Illustration 4.7 lists the vertical arching factors (VAFs) for the four types of Standard Installations. Using a VAF of 1.40 for a Type 3 Installation, the earth load is: WE = 1.40 x 861 WE = 1,205 pounds per linear foot Equation 4.1

30 + 2 (3.5)

The weight of concrete pavement must be included also. Assuming 150 pounds per cubic foot unit weight of concrete, the total weight of soil and concrete is: WE = 1,205 + 150 x 1.0 x 3.08 WE = 1,655 pounds per linear foot Fluid Load, WF = 62.4 lbs/ft3 2. Review project data. A 30-inch diameter, B wall, circular concrete pipe has a wall thickness of 3.5 inches, per ASTM C76 therefore Bc = 30 + 2 (3.5) 12

Bc = 3.08 And Ro, the outside height of the pipe, is 3.08 feet. Height of earth cover is 2 feet. Use AASHTO LRFD Criteria with Select Granular Soil Fill. 2. Calculate average pressure intensity of the live load on the plane at the outside top of the pipe. From Illustration 4.12, the critical load, P, is 16,000 pounds from an HS 20 single dual wheel, and the Spread Area is: A A A A I.M. I.M. w w w = = = = = = = = = (Spread a)(Spread b) (1.67 + 1.15x2)(0.83 + 1.15x2) (3.97)(3.13) 12.4 square feet 33(1.0-0.125H)/100 0.2475 (24.75%) P(1+IM)/A 16,000(1+0.2475)/12.4 1,610 lb/ft2
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Loads and Supporting Strengths 3. Calculate total live load acting on the pipe.
3.13

73

WT = (w + LL)LSL Assuming truck travel transverse to pipe centerline. LL L Spread b Bc SL WT = = = = 64 Spread a = 3.97 feet 3.13 feet 3.08 feet, which is less than Spread b, therefore = 3.08 feet = (1,610 + 64) 3.97 x 3.08 = 20,500 pounds
3.97

3.97

Assuming truck travel parallel to pipe centerline. = 64 LL Spread a = 3.97 feet L = Spread b = 3.13 feet Bc = 3.08 feet, which is less than Spread a, therefore = 3.08 feet SL = (1,610 + 64) 3.08 x 3.13 = 16,100 pounds WT WT Maximum = 20,500 pounds; and truck travel is transverse to pipe centerline 4. Calculate live load on pipe in pounds per linear foot, (WL) Ro Le Le WL WL = = = = = 3.08 feet L + 1.75 (3/4Ro) 3.97 + 1.75(.75 x 3.08) = 8.01 feet WT/Le 20,500/8.01 = 2,559 pounds per linear foot

3.13

The pipe should withstand a maximum live load of 2,559 pounds per linear foot. 5. Determination of Bedding Factor, (Bfe) a) Determination of Embankment Bedding Factor The embankment bedding factor for a Type 3 Installation may be interpolated from Illustration 4.21 Bfe24 = 2.4 Bfe36 = 2.3 36 - 30 Bfe30 = (2.4 - 2.3) + 2.3 34 - 24 Bfe30 = 2.3

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Concrete Pipe Design Manual b) Determination of Live Load Bedding Factor From Illustration 4.24, the live load bedding factor for a 30 inch pipe under 3 feet of cover (one foot of pavement and two feet of soil) can be interpolated BfLL24 = 2.4 BfLL36 = 2.2 Therefore BfLL30 = 2.3 6. Application of Factor of Safety (F.S.) A factor of safety of 1.0 based on the 0.01 inch crack will be applied. 7. Selection of Pipe Strength
1,655 earth load in pounds per linear foot 62.4 fluid load in pounds per cubic foot 2,559 live load in pounds per linear foot Bfe Bf = 2.35 earth load bedding factor 2.3 live load bedding factor is not applicable 2.5 inside diameter of pipe in feet 1,655 + 62.4 2,559 1.0 + D0.01 = Equation 4.26 2.35 2.3 2.5 D0.01 = 727 pounds per linear foot per foot of diameter WE WF WL Bf BfLL D = = = = = =

Answer: A pipe which would withstand a minimum three-edge bearing test for the 0.01 inch crack of 727 pounds per linear foot per foot of inside diameter would be required.

EXAMPLE 4-9 Aircraft Live Load Rigid Pavement

H Bc

Given: A 12 inch circular pipe is to be installed in a narrow trench, Bd = 3ft under a 12 inch thick concrete airfield pavement and subject to heavy
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Loads and Supporting Strengths commercial aircraft loading. The pipe will be covered with 1.0 foot (measured from top of pipe to bottom of pavement slab) of sand and gravel material weighing 120 pounds per cubic foot. Find: The required pipe strength in terms of 0.01 inch crack D-load.

75

1. Determination of Earth Load (WE) Per review of Table 13, the 3 ft. trench is wider than transition width. Therefore, the earth load is equal to the soil prism load multiplied by the appropriate vertical arching factor.

Note: The wall thickness for a 12-inch pipe with a B wall is 2-inches per ASTM C76. 12 Do = 1.33 outside diameter of pipe in feet w = 120 unit weight of soil in pounds per cubic foot H = 1 height of cover in feet 1.33 (4 - π) PL = 120 1 + 1.33 Equation 4.2 8 PL = 182 pounds per linear foot Do =
Immediately listed below Equation 4.2 are the vertical arching factors (VAFs) for the four types of Standard Installations. Using a VAF of 1.40 for a Type 2 Installation, the earth load is: WE = 1.40 x 182 WE = 255 pounds per linear foot Equation 4.1

12 + 2 (2)

The weight of concrete pavement must be included also. Assuming 150 pounds per cubic foot unit weight of concrete, the total weight of soil and concrete is: WE = 255 + 150 x 1.0 x 1.33 WE = 455 pounds per linear foot Fluid Load, WF = 62.4 lbs/ft3 2. Determination of Live Load (WL) It would first be necessary to determine the bearing value of the backfill and/or subgrade. A modulus of subgrade reaction, k = 300 pounds per cubic inch will be assumed for this example. This value is used in Table 53A and represents a moderately compacted granular material, which is in line with the Type 2 Installation we are using. Based on the number of undercarriages, landing gear configurations and gross weights of existing and proposed future aircrafts, the Concorde is a reasonable commercial aircraft design loading for pipe placed under airfields. From Table 53A, for D = 12 inches and H = 1.0 foot, a live load of 1,892 pounds per linear foot is obtained. WL = 1892 pounds per linear foot
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Concrete Pipe Design Manual 3. Selection of Bedding Since this installation is under an airfield, a relatively good installation is required, therefore use a Type 2 Installation. 4. Determination of Bedding Factor, (Bfe) a.) Determination of Embankment Bedding Factor From Illustration 4.21, the embankment bedding factor for a 12 inch pipe installed in a positive projecting embankment condition is 3.2. Bfe = 3.2 b.) Determination of Live Load Bedding Factor From Illustration 4.24, the live load bedding factor for a 12 inch pipe under 2 feet of cover (one foot of pavement and one foot of soil) is 2.2. BfLL = 2.2 5. Application of Factor of Safety (F.S.) A factor of safety of 1.0 based on the 0.01 inch crack will be applied. 6. Selection of Pipe Strength The D-load is given by Equation 4.26

WE WF WL Bf BfLL D

= 455 earth load in pounds per linear foot = 62.4 fluid load in pounds per cubic foot = 1,892 live load in pounds per linear foot = Bfe Bf = 3.2 earth load bedding factor = 2.2 live load bedding factor is not applicable = 1 inside diameter of pipe in feet 455 + 62.4 + 1,892 1.0 Equation 4.26

D0.01 =

3.2 2.2 4 D0.01 = 1,002 pounds per linear foot per foot of diameter

Answer: A pipe which would withstand a minimum three-edge bearing test for the 0.01 inch crack of 1,002 pounds per linear foot per foot of inside diameter would be required.

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EXAMPLE 4-10 Aircraft Live Load Rigid Pavement

H

20'

p1 = 943psf

p2 = 290psf

290psf

Bc = 10.25'

Given: A 68 inch x 106 inch horizontal elliptical pipe is to be installed in a positive projecting embankment condition under a 7 inch thick concrete airfield pavement and subject to two 60,000 pound wheel loads spaced 20 feet, center to center. The pipe will be covered with 3-feet (measured from top of pipe to bottom of pavement slab) of sand and gravel material weighing 120 pounds per cubic foot. Find: The required pipe strength in terms of 0.01 inch crack D-load. 1. Determination of Earth Load (WE) Note: The Standard Installations were initially developed for circular pipe, and their benefit has not yet been established for elliptical and arch pipe. Therefore, the traditional Marston/Spangler design method using B and C beddings is still conservatively applied for these shapes. A settlement ratio must first be assumed. In Table 40, values of settlement ratio from +0.5 to +0.8 are given for positive projecting installations on a foundation of ordinary soil. A value of 0.7 will be used. The product of the settlement ratio and the projection ratio will be 0.49 (rsdp approximately 0.5). Enter Figure 187 on the horizontal scale at H = 3 ft. Proceed vertically until the line representing R x S = 68" x 106" is intersected. At this point the vertical scale shows the fill load to be 3,400 pounds per linear foot for 100 pounds per cubic foot fill material. Increase the load 20 percent for 120 pound material. Wd = 3,400 x 1.2 Wd = 4,080 pounds per linear foot outside span of pipe is:
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Concrete Pipe Design Manual
106 + 2 (8.5) Note: The wall thickness for a 68"x106" ellipitical pipe is 8.5-inches per ASTM C76. 12

Bc =

Bc = 10.25 feet Assuming 150 pounds per cubic foot concrete, the weight of the pavement is: Wp = 150 x 7/12 x 10.25 Wp = 897 pounds per linear foot WE = Wd + Wp WE = 4,977 pounds per linear foot

Fluid Load, WF = 62.4 lbs/ft3 2. Determination of Live Load (WL) Assuming a modulus of subgrade reaction of k = 300 pounds per cubic inch and a pavement thickness of h = 7 inches, a radius of stiffness of 24.99 inches (2.08 feet) is obtained from Table 52. The wheel spacing in terms of the radius of stiffness is 20/2.08 = 9.6 Rs, therefore the maximum live load on the pipe will occur when one wheel is directly over the centerline of the pipe and the second wheel disregarded. The pressure intensity on the pipe is given by Equation 4.15:

P(X,H) =

CxP

Rs2 The pressure coefficient (C) is obtained from Table 46 at x = 0 and H = 3 feet.
For x/Rs = 0 and H/Rs = 3/2.08 = 1.44, C = 0.068 by interpolation between H/Rs = 1.2 and H/Rs = 1.6 in Table 46. (2.08)2 p1 = 943 pounds per square foot p1 = (0.068)(60,000) Equation 4.15

In a similar manner pressure intensities are calculated at convenient increments across the width of the pipe. The pressure coefficients and corresponding pressures in pounds per square foot are listed in the accompanying table.
x/Rs 0.8 0.058 804

Point Pressure Coefficient C Pressure psf

0.0 0.068 943

0.4 0.064 887

1.2 0.050 693

1.6 0.041 568

2.0 0.031 430

2.4 0.022 305

2.8 0.015 208

For convenience of computing the load in pounds per linear foot, the pressure distribution can be broken down into two components; a

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Loads and Supporting Strengths uniform load and a parabolic load.

79

The uniform load occurs where the minimum load is applied to the pipe at:
x = Rs
1 2

Bc Rs =

5.13 2.08

x = 2.5 Rs

The pressure, p2, is then interpolated between the points 2.4 and 2.8 from the chart x/Rs above, and equal to 290 pounds per square foot. The parabolic load (area of a parabola = 2/3ab, or in this case 2/3 (p1p2)Bc has a maximum pressure of 653 pounds per foot. Therefore the total love load, (WL) is equal to: WL = p2 x Bc + 2/3 (p1-p2)Bc WL = 290 x 10.25 + 2/3(943-290)10.25 WL = 7,435 pounds per linear foot 3. Selection of Bedding A Class B bedding will be assumed for this example. 4. Determination of Bedding Factor, (Bfe) a.) Determination of Embankment Bedding Factor From Table 60, a Class B bedding with p = 0.7, H/Bc = 3 ft/10.25 ft. = 0.3, and rsdp = 0.5, an embankment bedding factor of 2.42 is obtained. Bfe = 2.42 b.) Determination of Live Load Bedding Factor Live Load Bedding Factors are given in Illustration 4.24 for circular pipe. These factors can be applied to elliptical pipe by using the span of the pipe in place of diameter. The 106" span for the elliptical pipe in this example is very close to the 108" pipe diameter value in the table. Therefore, from Illustration 4.24, the live load bedding factor for a pipe with a span of 108 inches, buried under 3.5 feet of fill (3 feet of cover plus 7 inches of pavement is approx. 3.5 feet) is 1.7. BfLL = 1.7 5. Application of Factor of Safety (F.S.) A factor of safety of 1.0 based on the 0.01 inch crack will be applied.
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Concrete Pipe Design Manual 6. Selection of pipe strength The D-load given is given by Equation 4.27
49,277 earth load in pounds per linear foot 62.4 fluid load in pounds per cubic foot 7,435 live load in pounds per linear foot Bfe Bf = 2.42 earth load bedding factor 1.7 live load bedding factor 106/12 8.83 inside span of pipe in feet 4,977 + 62.4 7,435 1.0 + Equation 4.27 D0.01 = 2.42 1.7 8.83 D0.01 = 728 pounds per linear foot per foot of diameter WE WF WL Bf BfLL S S = = = = = = =

Answer: A pipe which would withstand a minimum three-edge bearing test load for the 0.01 inch crack of 728 pounds per linear foot per foot of inside horizontal span would be required. EXAMPLE 4-11 Railroad Live Load

H

BL

Given: A 48 inch circular pipe is to be installed under a railroad in a 9 foot wide trench. The pipe will be covered with 1.0 foot of 120 pounds per cubic foot overfill (measured from top of pipe to bottom of ties). Find: The required pipe strength in terms of 0.01 inch crack D-load. 1. Determination of Earth Load (WE) The transition width tables do not have fill heights less than 5 ft. With only one foot of cover, assume an embankment condition. An installation directly below the tracks such as this would probably require good granular soil well compacted around it to avoid settlement of the tracks. Therefore assume a Type 1 Installation and multiply the soil
American Concrete Pipe Association • www.concrete-pipe.org

Loads and Supporting Strengths prism load by a vertical arching factor of 1.35.

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Note: The wall thickness for a 48-inch pipe with a B wall is 5-inches per ASTM C76. 12 Do = 4.83 outside diameter of pipe in feet w = 120 unit weight of soil in pounds per cubic foot H = 1 height of cover in feet 4.83 (4 - π) PL = 120 1 + 4.83 Equation 4.2 8 PL = 880 pounds per linear foot Do =
PL = 880 pounds per linear foot Immediately listed below Equation 4.2 are the vertical arching factors (VAFs) for the four types of Standard Installations. Using a VAF of 1.35 for a Type 1 Installation, the earth load is: WE = 1.35 x 880 WE = 1,188 pounds per linear foot Fluid Load, WF = 62.4 lbs/ft3 2. Determination of Live Load (WL) From Table 56, for a 48 inch diameter concrete pipe, H = 1.0 foot, and a Cooper E80 design load, a live load of 13,200 pounds per linear foot is obtained. This live load value includes impact. WL = 13,200 pounds per linear foot 3. Selection of Bedding Since the pipe is in shallow cover directly under the tracks, a Type 1 Installation will be used. 4. Determination of Bedding Factor, (Bfe) a.) Determination of Embankment Bedding Factor The embankment bedding factor for 48 inch diameter pipe in a Type 1 Installation may be interpolated from Illustration 4.21.
Bfe36 = 4.0 Bfe72 = 3.8 72 - 48 (4.0 - 3.8) + 3.8 Bfe = 72 - 36 Bfe = 3.93

48 + 2 (5)

Equation 4.1

b.) Determination of Live Load Bedding Factor From Illustration 4.24, the live load bedding factor for a 48 inch pipe installed under 1 foot of cover is: BfLL = 1.5
American Concrete Pipe Association • www.concrete-pipe.org

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Concrete Pipe Design Manual 5. Application of Factor of Safety (F.S.) A factor of safety of 1.0 based on the 0.01 inch crack will be applied. 6. Selection of Pipe Strength The D-load is given by Equation 4.26 = 1,188 earth load in pounds per linear foot = 62.4 fluid load in pounds per cubic foot = 13,200 live load in pounds per linear foot = Bfe Bf = 3.93 earth load bedding factor = 1.5 live load bedding factor is not applicable = 4 1,188 + 62.4 13,200 1.0 + D0.01 = Equation 4.26 3.93 1.5 4 D0.01 = 2,276 pounds per linear foot per foot of diameter WE WF WL Bf BfLL D

Answer: A pipe which would withstand a minimum three-edge bearing test for the 0.01 inch crack of 2,276 pounds per linear foot per foot of inside diameter would be required.

American Concrete Pipe Association • www.concrete-pipe.org

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