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Pull Force and Installation Stresses Vertical

When pipes are installed by HDD, they often experience high tension loads, severe bending, and external fluid pressures. Often these installation loads are more severe than the design service loads. When selecting the appropriate pipe materials for an HDD installation, the designer must consider the pipe properties as well as the borehole profile. These two factors should be considered together in order to choose the best material and profile so that the pipeline can be installed and operated without risk of damage. To ensure that the material and bore-hole profile are suitable for the proposed application, the installation, operational, and combined loads and stresses are analyzed.

Pipe Weight in Air:

π‘ƒπ‘–π‘π‘’π‘€π‘’π‘–π‘”β„Žπ‘‘Β = 10.68 (𝐷 – 𝑑)𝑑

π‘ƒπ‘–π‘π‘’π‘€π‘’π‘–π‘”β„Žπ‘‘ – Weight of the pipe (lbs/ft)

D – Pipe Outside Diameter (inch)
t – Pipe Wall Thickness (inch)

Pipe Exterior Volume:

Pipe Interior Volume:

Weight of Water in pipe:

(to be calculated only if the pipe is filled with water)

π‘Šπ‘Žπ‘‘π‘’π‘Ÿπ‘ƒβ€’π‘€π‘’π‘–π‘”β„Žπ‘‘Β = π‘ƒπ‘–π‘π‘’π‘–π‘›π‘‘π‘’π‘Ÿπ‘–π‘œπ‘ŸΒ β€’Β π‘£π‘œπ‘™Β βˆ— π‘Šπ‘€π‘’π‘–π‘”β„Žπ‘‘

Wweight – Weight of water (lb/ft3)

Displaced Mud Weight:

π·π‘–π‘ π‘π‘™π‘Žπ‘π‘’π‘šπ‘’π‘‘π‘Šπ‘’π‘–π‘”β„Žπ‘‘Β = 𝑃𝑖𝑝𝑒𝑒π‘₯π‘‘β€’π‘£π‘œπ‘™π‘šπ‘’π‘‘π‘€π‘‘

mudwt = Weight of mud (lb/gal)

Effective Weight of Pipe:

π‘Šπ‘†Β =Β π‘ƒπ‘–π‘π‘’π‘€π‘’π‘–π‘”β„Žπ‘‘Β +Β π‘Šπ‘Žπ‘‘π‘’π‘Ÿπ‘ƒβ€’π‘€π‘’π‘–π‘”β„Žπ‘‘Β βˆ’Β π·π‘–π‘ π‘π‘™π‘Žπ‘π‘’π‘šπ‘’π‘‘π‘Šπ‘’π‘–π‘”β„Žπ‘‘

Straight section A-B

Friction from Soil:

π‘“π‘Ÿπ‘–π‘2Β =Β π‘Šπ‘†πΏ1π‘π‘œπ‘ πœƒπ‘†1πœ‡π‘†π‘œπ‘–π‘™

𝐿1 – Length of the straight section 1
πœƒπ‘†1 – Angle in degrees from horizontal for straight section 1
πœ‡π‘†π‘œπ‘–π‘™ – Average coefficient of friction between pipe and soil. The recommended value is between .21-.3 (Maidla)

Drag Forces from Mud:

π·π‘Ÿπ‘Žπ‘”2Β = πœ‹π·πΏ1πœ‡π‘šπ‘’π‘‘

ΞΌmud – Fluid drag coefficient for steel tube pulled through bentonite mud

Tension on Section:

βˆ†π‘‡2Β = |π‘“π‘Ÿπ‘–π‘2| + π·π‘Ÿπ‘Žπ‘”2Β βˆ’ π‘Šπ‘ πΏ1π‘ π‘–π‘›πœƒπ‘ 1

Cumulative Pull Load:

𝑇2Β = βˆ†π‘‡2Β + 𝑇1

T1 – Pull back as the pipe enters the drill hole (lbf)

Curved Section B-C

(based on Roark’s solution for elastic beam deflection)

ΞΈC1Β – Angle in degrees from horizontal for curved section 1
R1Β – Radius of curvature of curve section 1 (ft)
Larc1Β – Length of curved section 1(ft)
E – Young’s Modulus (psi)

Friction from Soil:

π‘“π‘Ÿπ‘–π‘ = |𝑁3πœ‡π‘†π‘œπ‘–π‘™|

Drag Forces from Mud:

π·π‘Ÿπ‘Žπ‘”3Β = πœ‹π·πΏπ‘Žπ‘Ÿπ‘1πœ‡π‘šπ‘’π‘‘

Tension on Section:

Cumulative Pull Load:

𝑇3Β = βˆ†π‘‡3Β + 𝑇2

Straight Section C-D

Friction from Soil:

π‘“π‘Ÿπ‘–π‘4Β = π‘Šπ‘†πΏπ‘ π‘π‘œπ‘ πœƒπ‘†πœ‡π‘†π‘œπ‘–π‘™

LsΒ – Length of straight section between bends (ft)
ΞΈsΒ – – Angle in degrees from horizontal for straight section between bends

Drag Forces from Mud:

π·π‘Ÿπ‘Žπ‘”4Β = πœ‹π·πΏπ‘ πœ‡π‘šπ‘’π‘‘

Tension on Section:

βˆ†π‘‡4Β = |π‘“π‘Ÿπ‘–π‘4| + π·π‘Ÿπ‘Žπ‘”4Β βˆ’ π‘Šπ‘ πΏπ‘ π‘ π‘–π‘›πœƒπ‘ 

Cumulative Pull Load:

𝑇2Β = βˆ†π‘‡4Β + 3

Curved Section D-E

ΞΈC2Β – Angle in degrees from horizontal for curved section 2
R2Β – Radius of curvature of curve section 2 (ft)
Larc2Β – Length of curved section 2(ft)

Friction from Soil:

π‘“π‘Ÿπ‘–π‘ = |𝑁3πœ‡π‘†π‘œπ‘–π‘™|

Drag Forces from Mud:

π·π‘Ÿπ‘Žπ‘”3Β = πœ‹π·πΏπ‘Žπ‘Ÿπ‘2πœ‡π‘šπ‘’π‘‘

Tension on Section:

Cumulative Pull Load:

𝑇3 = βˆ†π‘‡3 + 𝑇2

Straight Section E-F

Friction from Soil:

π‘“π‘Ÿπ‘–π‘6Β = π‘Šπ‘†πΏ2π‘π‘œπ‘ πœƒπ‘†2πœ‡π‘†π‘œπ‘–π‘™

Drag Forces from Mud:

π·π‘Ÿπ‘Žπ‘”6Β = πœ‹π·πΏ2πœ‡π‘šπ‘’π‘‘

Tension on Section:

βˆ†π‘‡6Β = |π‘“π‘Ÿπ‘–π‘6| + π·π‘Ÿπ‘Žπ‘”6Β + π‘Šπ‘ πΏ1π‘ π‘–π‘›πœƒπ‘ 12 – Length of the straight section 2

ΞΈS2Β –Β  Angle in degrees from horizontal for straight section 2

Cumulative Pull Load:

𝑇6Β = βˆ†π‘‡6Β + 𝑇5

Total pull load of the pipe:

π‘‡π‘‘π‘œπ‘‘π‘Žπ‘™Β = βˆ†π‘‡2Β + βˆ†π‘‡3Β + βˆ†π‘‡4Β + βˆ†π‘‡5Β + βˆ†π‘‡6

TtotalΒ  – Total pull load of the pipe (lbf)

Maximum Pull Force, F:

ID – Internal Pipe Diameter (inch)
fs – Safety Factor
F – Maximum pull force (lbf)

Tensile Stress at a Point:

Allowable Tensile Stress:

π‘‡π‘†π‘‘π‘Ÿπ‘’π‘ π‘ β€’π‘Žπ‘™π‘™π‘œπ‘€Β = 0.9π‘†π‘€π‘Œπ‘†

Bending Stress at a point:

Allowable Bending Stress:

Hoop Stress at a point:

Allowable Hoop Stress:

Unity Check – Tensile and Bending Stress:

Unity Check – Tensile, Bending & Hoop Stress:

Input Parameters

Drill Path/Borehole Design*:

  • Elevation Profile
    • Pipe Entry (ft)
    • Pipe Exit (ft)
  • Downslope: Straight Section A – B
    • Pipe Entry Angle A – B [degree]
    • Measured Length [ft]
  • Downslope: Curved Section B – C
    • Bend Angle B – C [degree]
    • Radius of Curvature B – C [ft]
    • Measured Length [ft]
  • Straight Section C – D
    • Horizontal Angle[degree]
    • Measured Length [ft]
  • Downslope: Curved Section D – EΒ  HDDPT Steel
    • Horizontal Angle[degree]
  • Radius of Curvature D – E
    • Measured Length [ft]
  • Straight Section E – F
    • Bend Angle[degree]
    • Measured Length [ft]
  • Upslope: Curved Section F – G
    • Bend Angle F – G [degree]
  • Radius of Curvature F – G [ft]
    • Measured Length [ft]
  • Upslope: Straight Section G –H
    • Bend Angle G – H [degree]
    • Radius of Curvature G – H [ft]
    • Measured Length [ft]
  • Upslope: Straight Section H- I
    • Pipe Exit Angle H – I [degree]
    • Measured Length [ft]

*The design changes based on borehole design (section configuration)

Pull Load and Maximum Allowable Pull Force:

  • Pipe Outside Diameter (in)
  • Pipe Wall Thickness(in)
  • Pipe Grade
  • SMYS – Specified Minimum Yield Strength(psi)
  • Poisson’s Ratio
  • Young’s Modulus of Elasticity(psi)
  • Code Design Factor
  • Code SMYS
  • Coefficient of Friction: Pipe – Soil (0.21 – 0.3)
  • Coefficient of Friction: Pipe – Rollers (0.1)
  • Fluid Drag Coefficient (0.03 – 0.05) (psi)
  • Mud Weight (lbs./gal)
  • Water Weight(lbs./ft3)
  • Pipe Filled with Water:
    • Pipe Above Ground Section of Roller?
    • Pipe Section Above Ground Section on Rollers (ft)
    • Angle of Pipe Above Ground on Rollers (Β°)
    • Maximum Load Factor
    • Safety Factor
      • Note: Point A is Pipe Entry Point

Outputs/Reports

  • Straight Section A-B (ft)
  • Curved Section B-C (ft)
  • Straight (Downslope) Section C-D (ft)
  • Curved Section D-E (ft)
  • Straight Section E-F (ft)
  • Total Length of the Borehole (ft)
  • Effective Submerged Weight (lb./ft)
  • Pull Load Section on Rollers (lb)
  • Pull Load Straight Section A-B (lb)
  • Pull Load at Point B (lb)
  • Pull Load Curved Section B-C (lb)
  • Pull Load at Point C (lb)
  • Pull Load Straight (Downslope) Section C-D (lb)
  • Pull Load at Point D (lb)
  • Pull Load Curved Section D-E (lb)
  • Pull Load at Point E (lb)
  • Pull Load Straight Section E-F (lb)
  • Total Pull Load at Point F (lb)
  • Maximum Allowable Pull Force (lb)
  • Allowable Tensile Stress (psi)
  • Total Tensile Stress (psi)

Pass/Fail:

Select Point of Interest (B)

  • Tensile Stress(psi)
  • Allowable Tensile Stress(psi)
  • Bending Stress(psi)
  • Allowable Bending Stress(psi)
  • Hydrostatic Mud Pressure(psi)
  • External Hoop Stress(psi)
  • Allowable Elastic Hoop Buckling
  • Combined Load Interaction at Point
  • Unity Check: Tensile and Bending
  • Unity Check: Tensile, Bending, and External Hoop

Select Point of Interest (C)

  • Tensile Stress(psi)
  • Allowable Tensile Stress(psi)
  • Bending Stress(psi)
  • Allowable Bending Stress(psi)
  • Hydrostatic Mud Pressure(psi)
  • External Hoop Stress(psi)
  • Allowable Elastic Hoop Buckling
  • Combined Load Interaction at Point
  • Unity Check: Tensile and Bending
  • Unity Check: Tensile, Bending, and External Hoop

Select Point of Interest (D)

  • Tensile Stress(psi)
  • Allowable Tensile Stress(psi)
  • Bending Stress(psi)
  • Allowable Bending Stress(psi)
  • Hydrostatic Mud Pressure(psi)
  • External Hoop Stress(psi)
  • Allowable Elastic Hoop Buckling
  • Combined Load Interaction at Point
  • Unity Check: Tensile and Bending
  • Unity Check: Tensile, Bending, and External Hoop

Select Point of Interest (E)

  • Tensile Stress(psi)
  • Allowable Tensile Stress(psi)
  • Bending Stress(psi)
  • Allowable Bending Stress(psi)
  • Hydrostatic Mud Pressure(psi)
  • External Hoop Stress(psi)
  • Allowable Elastic Hoop Buckling
  • Combined Load Interaction at Point
  • Unity Check: Tensile and Bending
  • Unity Check: Tensile, Bending, and External Hoop

Select Point of Interest (F)

  • Tensile Stress(psi)
  • Allowable Tensile Stress(psi)
  • Bending Stress(psi)
  • Allowable Bending Stress(psi)
  • Hydrostatic Mud Pressure(psi)
  • External Hoop Stress(psi)
  • Allowable Elastic Hoop Buckling
  • Combined Load Interaction at Point
  • Unity Check: Tensile and Bending
  • Unity Check: Tensile, Bending, and External Hoop

Related Links

Pipeline HUB β€” User Resources

Table of Contents
Table of Pages
  1. Pipeline HUB User Resources
  2. AC Mitigation PowerTool
  3. API Inspector's Toolbox
  4. Crossings Workflow
  5. Horizontal Directional Drilling PowerTool
  6. Hydrotest PowerTool
  7. Pipeline Toolbox
  8. PRCI AC Mitigation Toolbox
  9. PRCI RSTRENG
  10. RSTRENG+
  11. Ad-hoc Analysis
  12. Database Import
  13. Data Availability Dashboard
  14. ESRI Map
  15. Report Builder
  16. Crossings Workflow
  17. Hydrotest PowerTool
  18. Investigative Dig PowerTool
  19. Hydraulics PowerTool
  20. External Corrosion Direct Assessment Procedure - RSTRENG
  21. Canvas
  22. Definitions

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