Hdd Crossing Calculation 2

6.1 General Information

Determining the loads and stresses that the product pipe will experience as a resultof installation by HDD is an important process and a primary concern for the own-ers and engineers of the pipeline system. HDD contractors, on the other hand, areusually concerned about the loads and stresses on the drilling equipment. It is com-mon for owners and engineers who are unfamiliar with HDD design and construc-tion methods to rely solely on the advice of the contractor as to whether a crossingis feasible. Most HDD contractors will determine that a crossing is feasible if theycan successfully bore and ream the hole and pull the product pipe back throughwithin the specified tolerances and will not consider the pipe itself. As a result, insome HDD crossings, the product pipe did not perform as intended. It is not thatthe HDD contractors intentionally mislead; it is just that they usually look at thecrossing from a different perspective. This is the reason why it is important for theowners and/or engineers to ensure that the HDD contractor is provided with acrossing design that is acceptable for the product pipe.

Due to the relatively recent introduction of HDD construction there is not a lotof literature on the subject of product-pipe installation loads and stresses. However,this is changing as the industry grows. A detailed manual was published in 1995 bythe Pipeline Research Council International1. This manual, which will be referredto as the PRCI Manual throughout this chapter, provides detailed information andmethods for determining the estimated loads and stresses that a steel productpipeline may experience as a result of HDD installation. This chapter utilizes manyof the methods, procedures, and calculations provided in this manual.

Chapter

6

143

HDD Stress Analysis forSteel Product Pipe

� CHAPTER CONTENTS

6.1 General Information6.2 Steel Product-Pipe Stress Analysis

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Source: Horizontal Directional Drilling

The methods provided in the PRCI Manual and this chapter deal with the loadsand stresses on the product pipe, not the total forces experienced by the drill rig.The installation loads experienced by the drill string and reamer are not consideredbecause they do not impact the product pipe. Loads from the above-ground portionof the pull section are omitted because they are seldom critical to the success of aninstallation; if these loads should become critical, the use of pipe side assistancetechniques can essentially counteract their impact. The key point is that these meth-ods estimate the tensile force experienced by the product pipe, not the total forceexerted by the drill rig. There are many variables associated with the pulling loadsthat may occur during HDD construction. These variables often depend on site-specific conditions and individual contractor practices. Some of the principal vari-ables are subsurface conditions, drilling-fluid properties, bore-hole diameter andstability, and effectiveness of buoyancy control measures. The methods that followcannot account for all the possible variables. For this reason the theoretical calcu-lations should be used with caution by someone with some knowledge and experi-ence in HDD design and construction.

6.2 Steel Product-Pipe Stress Analysis

When pipes are installed by HDD, they often experience high tension loads, severebending, and external fluid pressures. Often these installation loads are more se-vere than the design service loads. When selecting the appropriate pipe materialsfor a HDD installation, the designer must consider the pipe properties as well as thebore-hole profile. These two factors should be considered together in order tochoose the best material and profile so that the pipeline can be installed and oper-ated without risk of damage. To ensure that the material and bore-hole profile aresuitable for the proposed application, the installation, operational, and combinedloads and stresses are analyzed.

Installation

When a pipe is installed by HDD construction, it is subjected to tension, bending,and external pressure as it is pulled through the reamed hole. The tension requiredto pull the product pipe into the bore hole comes from the frictional drag betweenthe pipe and the wall of the hole, the fluidic drag as the pipe is pulled through vis-cous drilling fluid, and the effective weight of the pipe as it is pulled through ele-vation changes within the hole. Bending stress results from pulling the rigid pipethrough the curved hole. The pipe will experience external pressure from thedrilling fluid that may result in external hoop stress. This stress may be reduced oreliminated by filling the product pipe with a fluid of equal or greater density. Thestresses and the resulting potential for pipe failure are caused by the combination

144 Chapter 6 � HDD Stress Analysis for Steel Product Pipe



HDD Stress Analysis for Steel Product Pipe

of these loads. This book and the PRCI Manual provide a method to estimate theapplicable loads and stresses and help the engineer determine if the HDD designand material specifications are suitable for the proposed crossing. The followingmethod assumes that the bore hole has been reamed, that the reamed hole is ap-proximately 12 inches larger than the pipe outside diameter, and that the annulusbetween the pipe outside diameter and the reamed hole is filled with drilling fluidof a known or estimated density. This method assumes that the bore hole remainsintact during installation and that no significant formation loads were exerted onthe pipe during the pullback process.

Product-Pipe Pull Loads

Product-pipe pull loads are calculated based on an analysis of the designed boreprofile or the actual pilot hole. Figure 6-1 is an example of a bore profile plotted inthe vertical and horizontal planes with horizontal pipe length along the x-axis andvertical distance from the reference line along the y-axis. The entire bore path ismade up of straight and/or curved sections. The bore path should comprise thefewest number of sections possible. However, the design can include as many sec-tions as necessary to define the crossing. There are no upper or lower boundarieson the length of any straight section or the arc length of any curved section. Straightsections are ideally level but may have a very slight curvature. Sections that do notdeviate beyond the bore-hole wall, for this method approximately 12 inches largerthan the product pipe, can be considered straight sections. Curved sections shouldhave one constant radius for the entire sweep of the section. The junction betweena straight and a curved section is considered the start of the curve and is referred toas the point of curvature (PC). The junction where the curve ends and a straight sec-tion begins is referred to as a point of tangent (PT). Straight sections should alwaysjoin curved sections, since there is no reason to divide straight sections.

The estimated pulling load is calculated as a series of straight and curved seg-ments. The forces acting on each segment are calculated sequentially from pipeside to rig side to determine the tensile load at the end of each segment. Normal

6.2 Steel Product-Pipe Stress Analysis 145

Point 3Point 2

Point 1

Angle Product PipeEnters Borehole

L2L1

Point 4

Angle Product PipeExits Borehole

θ Bend Angle

Rad

ius

Point 6 Point 5

Larc2L3

Rad

iusθ Bend Angle

HorizontalDrill Length

Larc1

FIGURE 6-1 HDD Design Profile




practice is to neglect the drag forces from the above-ground portion of the productpipe. This results in the initial tension on the first segment being zero (point 1). Theinitial tension for each of the following segments is equal to the tension at the endof the previous segment (points 2–6). The total tensile load at the end of the pull-back is the sum of the individual forces required to pull the pipe through each ofthe straight and curved segments in the bore hole. The axial load in the product pipeat the end of the pullback process is distributed along the entire product-pipelength. The total axial load is made up of the combined axial loads occurring ineach section of the hole due to the friction between the product pipe and the bore-hole wall plus the dynamic fluid friction needed to make the pipe move through thedrilling mud. Because the bore-hole wall and pipe frictional components arecaused by the shape of the bore hole, the axial tension in the product pipe at anypoint in the bore path can be considered to be confined to that location in the borehole, regardless of which portion of the product pipe is passing that point. This al-lows for worst-case loads anywhere in the bore hole to be calculated only for thecase in which the pipe has just emerged from the hole.

The coefficients used in the calculation of frictional and fluidic drag are usuallyassumed. When the PRCI method was first developed, values for these coeffi-cients were recommendations based on available field data. These coefficientswere intentionally incorporated as variables, allowing them to be modified as bet-ter information became available. Since the development of the PRCI method,calculated pulling loads have been compared against actual field pulling loads onnumerous HDD installations. In most cases the calculated pull loads compared fa-vorably with recorded rig loads. However, in many cases the loads estimated bythe PRCI method exceeded the rig loads as the pullback neared completion. Thisis actually an expected result due to the conservative nature of the PRCI method.Sometimes it is necessary to refine the input parameters used in the following cal-culations to more closely match the calculated and actual loads. Jeffrey S. Puck-ett, P.E., conducted an analysis1 of the calculated versus actual pulling loads us-ing documentation from completed HDD installations. This analysis focused on amore accurate parameter for the fluid-drag coefficient, the input parameter withthe greatest uncertainty. Based on a comparison of the calculated loads and the ac-tual loads it was determined that using a fluid drag coefficient of 0.05 psi pro-duced a substantially greater calculated load than actual load as pullback nearedcompletion. After running several pulling-load calculations using different fluid-drag coefficients, it was determined that a coefficient of 0.025 psi produced closercalculated and actual data. As can be seen from the above comments, using afluid-drag coefficient between 0.025 and 0.05 psi usually provides accurate re-sults. The normal practice is to use 0.05 psi for most applications, since this willprovide accurate yet somewhat conservative results. However, in borderlinecrossings or crossings where drill-rig selection is crucial, a fluid-drag coefficientof 0.025 psi may provide a more useful result.





Calculating the Pull Loads

The first step in calculating the estimated pulling loads is to develop the input datathat will be used in the calculations. This data includes the product-pipe materialproperties, the drilling-fluid properties, and any code or design factors that are ap-plicable. An example of the input data required for calculating estimated pullingloads is provided in Example 6-1 later in this chapter.

Defining the Bore Path The next step is to define the bore path for the crossing.Figure 6-1 defines a typical bore path profile. The values are assigned to the vari-ables based on the profile required to successfully cross the obstacle while reachingthe required depth. The preliminary attempt at determining the values is based onthe definition of the obstacle, the subsurface conditions, and the material propertiesof the product pipe. Using this data and the equations provided in Chapter 8, the de-signer can develop a combination of straight lines and curves that will cross the ob-stacle at the desired depth within the available overall bore length. Figure 6-2 pro-vides an example of a designed bore path where:

L1 = 91 feetLarc1 = 126 feet

LS = 52 feetLarc2 = 126 feet

L2 = 177 feet


FIGURE 6-2 Bore-Path Example




In this example the total bore length is the sum of each segment for a bore-pathlength of 572 feet.

Straight Sections After defining the input data and the bore path, the calcula-tions begin with the straight section of pipe, assuming that the pipe is pulled fromthe left to the right (as viewed in Figure 6-2). The modeling and calculation processmust be done from the pipe side to the rig side. As stated earlier, it is usually as-sumed that the load at point 1 is zero. When using this assumption the first calcu-lated load is at the end of the first straight section, or point 2. Each straight sectionis modeled with variables as shown in Figure 6-3.

For any straight section the tension at T2 is calculated from the static forcebalance:

Equation 6-1where:

T2 = the tension (or pull load) at the rig side of the straight section required toovercome the drag and friction in pounds

T1 = the tension (or pull load) at the pipe side of the straight section, usually as-sumed to be zero, in pounds

| fric| = the friction between the pipe and soil in pounds

The +/– term is (–) if T2 is downhole, (+) if T2 is uphole, and (0) if the hole ishorizontal.

Equation 6-2where:DRAG = the fluidic drag between the pipe and the drilling fluid in pounds

Equation 6-3DRAG D Lmud

= π µ* * *1

fric W LS S soil

= ( )* *cos *1 1

θ µ

T T fric DRAG W LS2 1

= + + ± * * sin θ


FIGURE 6-3 Straight Section




where:WS = the effective (submerged) weight of the pipe plus any internal contents (if

filled with water) in foot-poundsL1 = the length of the straight section in feetπ = the angle of the straight section relative to the horizontal plane (zero is hor-

izontal and 90 degrees is vertical)µsoil = the average coefficient of friction between the pipe and soil; the recom-

mended value is 0.21 to 0.30 (Maidla)µ mud = the fluid-drag coefficient for steel pipe pulled through the drilling mud; the

recommended value is 0.025 to 0.05D = the outside diameter of the pipe in inches

Curved Sections Each curved section is modeled with variables as shown inFigure 6-4.

The variables that are different than those in the straight sections are:

R1 = the radius of curvature of the curved section between points 2 and 3 in feetθc1 = the angle of the curved section in degreesθ1 = the angle from horizontal of T2 at the right end of the section in degreesθ2 = the angle from horizontal of T3 at the left end of section in degreesθ = (θ1 + θ2)/2 in degrees

Larc1 = R1 × θc1 in feet

The values N, N1, and N2 are the contact forces at the center, right, and left pointsof the section. The values fric, fric1, and fric2 are the frictional forces at the center,


FIGURE 6-4 Curved Section




right, and left points of the section. The curved sections are modeled as three-pointbeams. For the bent pipe to fit in the bore hole it must bend enough to place its cen-ter at a point that reflects the displacement (h):

Equation 6-4

This method is not completely accurate, however, since the objective is to deter-mine the normal contact forces and then calculate the frictional forces, it is an ac-ceptable estimation. The vertical component of the distributed weight and the arclength of the pipe section are used to find N. From Roark’s2 solution for elasticbeam deflection:

Equation 6-5

where:

Equation 6-6

Equation 6-7

Equation 6-8

Equation 6-9

Equation 6-10UL

jarc=

I D tt

= −( )π * *3

8

j EI

T=

*

1

2

YL

jU

arc=

− −

1812

11

2

2

2* *

cosh

XL j Uarc= −

312 2 2

* * tanh

N

T h W Y

X

Scl

=−

* *cos *θ2

h R c= −

* cos12

1θ





E = Young’s Modulus for steel (2.9 x 107 psi).t = Pipe wall thickness in inches

Equations 6-5 and 6-8 both require a value for T, which is the average value ofT2 and T3. This requires an iterative solution to solve for T3. One method is tochange the variable T to an assumed average value and solve the problem untilthe required accuracy is obtained. The assumed average value of T should bewithin 10 percent of the actual average of T2 and T3

where the values:

and should be with 10 percent. If not within

10 percent use a new assumed value for Tavg and solve again. Using computerprograms makes this a relatively easy task. For a curved section fric becomes:

Equation 6-11

The reactions at the end of the curved section are assumed to be N/2, and endfriction forces are assumed to be fric/2. For positive values of N (defined as down-ward-acting as in Figure 6-4) the bending resistance and/or buoyancy of the pipe issufficient to require a normal force acting against the top of the hole in order forthe pipe to displace downward by an amount equal to h. Where N is negative, thesubmerged pipe weight is sufficient to carry the pipe to the bottom of the curvedsection, where an upward-acting normal force is felt at the point of contact. Re-gardless of the value of N, all friction values are positive, acting in opposition toT3. The estimated forces acting along the curved path of the pipeline are added asif they were acting in a straight line. As a result T3 becomes:

Equation 6-12

The load at point 3 then becomes ∆T3 + T2 in pounds of force.

Total Pulling Loads

The total force (or pulling load) required to pull the pipe through the bore hole isthe sum of the required force for all the straight and curved sections in the pipeline.Example 6-1 is an example of the pulling-load calculations for the HDD crossingprovided in Figure 6-2.

∆T fric DRAG W LS arc

c3 1

122

= + ±

* * *sinθ

fric Nsoil

= *µ

T T

Tavg avgassumed

avgassumed

−*100T

T Tavg

=+

2 3

2






EXAMPLE 6-1A HDD Pull Loads





EXAMPLE 6-1B HDD Pull Loads





EXAMPLE 6-1C HDD Pull Loads





EXAMPLE 6-1D HDD Pull Loads





EXAMPLE 6-1E HDD Pull Loads





EXAMPLE 6-1F HDD Pull Loads




Calculating the Installation Stresses

The installation stresses experienced by product pipes are often the worst-case loadevents that the pipe will experience over its life. As a result, the installation stressesoften dictate the material properties of the product pipe. During HDD installationthe worst-case stress condition is located where tensile, bending, and hoop stressesoccur at the same time. Generally these are areas of tight radius bends; high ten-sion, which is usually closer to the drill rig; and high external pressure, which isusually at the deepest point. The approach used in this book and the PRCI Manualis taken from the API Recommended Practice 2A-WSD. For this approach select alocation in the drill-path profile that is suspected of being a critical stress location.The first step is to calculate the individual stresses for the tensile, bending, andhoop stresses and compare the calculated values against allowable levels for thesestress states. If all are within allowable limits, the next step is to check the com-bined stress state. The combined stress state is compared in two interaction equa-tions presented as unity checks. The combined stresses in the interaction equationmust be less than 1.0 for the pipe to be safe from bending or hoop collapse in allregimes (plastic, elastic, and transition).

Example 6-2 is an example of the installation stress calculations for the HDDcrossing provided in Figure 6-2.

Calculating Operating Loads and Stresses

Except for elastic bending, the operating loads and stresses experienced in a pipeinstalled by HDD are not different from those experienced by pipes installed bycut-and-cover techniques. The same methods and procedures for calculating andlimiting stresses can be applied to HDD installations except for elastic bending. Apipeline installed by HDD will contain elastic bends. The pipe is not bent to fit inthe drilled hole as is a pipe installed by cut and cover to fit the ditch. The pipe bend-ing stresses imposed by HDD construction are usually not excessive. However, thebending stresses should be checked in combination with other longitudinal andhoop stresses to ensure that the allowable stress limits are not exceeded. The equa-tions for bending and hoop stress (also provided in Example 6-2) are:

Equation 6-13

Equation 6-14stressp D

thoop=

( )( )∆ *

*2

stressE D

Rbending=

( )( )

*

*24






EXAMPLE 6-2A Installation Stress





EXAMPLE 6-2B Installation Stress





EXAMPLE 6-2C Installation Stress





EXAMPLE 6-2D Installation Stress





EXAMPLE 6-2E Installation Stress





EXAMPLE 6-2F Installation Stress





EXAMPLE 6-2G Installation Stress




The term ∆p is the difference between the hydrostatic pressure caused by thegroundwater acting on the pipe and the internal pressure from the fluid or gas in-side the pipe. The thermal stress calculation from ASME/ANSI B31.42 is:

Equation 6-15

where:k = the coefficient of thermal expansion (for steel 0.0000065 inches per inch

per degree F)T1 = installed temperature in degrees FT2 = operating temperature in degrees F

According to ASME/ANSI B31.4 the maximum shear stress in the pipelineshould not exceed 45 percent of the SMYS of the pipe. Maximum shear may becalculated using the following equation (Timoshenko and Gere):

Equation 6-16

where:Equation 6-17

ν = Poisson’s ration (0.3 for steel)

When performing this analysis all tensile stresses are positive and all compres-sive stresses are negative. The product pipe will experience the maximum shearstress on the compressive side of the bend at the maximum distance from thebend’s neutral axis. Example 6-3 is an example of the operating-stress calculationsfor the HDD crossing provided in Figure 6-2.

Chapter 6 Footnotes1 Jeffery S. Puckett, PE (2000). Analysis of Theoretical Versus Actual HDD Pulling Loads.

stress stress stress strelong bending thermal

= + + ssshoop

* ν

shearstress stress

imum

hoop long

max=

−2

stress E k T Tthermal

= ( ) −( )* *1 2






EXAMPLE 6-3 Operating Stress

( )




Hdd Crossing Calculation 2

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