Live Load: Single Wheel Over Buried PE Pipe - Concentrated Point Load

This calculation determines the deflection or structural damage to the repeated load application on buried PE pipes with adequate soil cover subjected to concentrated point multiple wheel loads. However, it does not take into account concentrated heavy loading, inadequate cover, or unstable soils.

Dead/Earth Load

A. Prism Load

𝑃_𝑝 = 𝑤𝐻

𝑃_𝑝 = Vertical Soil Pressure,[lb/ft²]

𝑤 = Unit Weight of Soil,[lb/ft²]

𝐻 = Height of Soil Above Pipe Crown,[ft]

B. Marston Load (ASCE Manual No.60)
𝑃_𝑚 = 𝐶_𝑑𝑤𝐵_𝑑
𝑃_𝑚 = Vertical Soil Pressure,[lb/ft²]
𝑤 = Unit Weight of Soil,[lb/ft²]
𝐵_𝑑 = Trench Width at Pipe Crown,[ft]
𝐶_𝑑 = Load/Trench Coefficient

𝑒 = Base of Natural Logarithm,[2.71828]

𝐾 = Rankine Earth Pressure Coefficient

𝐾 = 𝑡𝑎𝑛²  

𝜃 = Angle of Internal Soil Friction, [°]

𝑢 = Coefficient of Friction between Backfill and Trench Sides

C. Combined Prism and Marston Load
For flexible pipe, a more conservative method is to use a soil pressure load in between prism and Marston load:
𝑃_𝑐 = 0.6𝑃_𝑚 + 0.4𝑃_𝑝 𝑃_𝑐 = Combined Load or Modified Arching Soil Pressure, [lb/ft²]

Live Load: Single Wheel over Buried PE Pipe – Concentrated Point Load
The Boussinesq Equation gives the pressure at any point in a soil mass under a concentrated surface load. The Boussinesq Equation may be used to find the pressure transmitted from a wheel load to a point that is not along the line of action of the load. Pavement effects are neglected.

𝑃_𝐿 − Vertical Soil Pressure due to Live Load [lb/ft²]

𝑊_𝑤 − Live Load [lb/ft²] (see table)

𝐷 − Outside Pipe Diameter [in]

𝐹𝑖 − Impact Factor

𝐿 − Pipe Length [ft]

𝐶_𝐻 − Load Coefficient

* Simulates a 20-ton truck traffic load, with impact factor
† Simulates an 80,000 lb./ft railway load, with impact factor
‡ Applies to 180,000 lb. dual-tandem gear assembly, with 26 in. spacing between tires and 66 in. center to center spacing between fore and aft tire under a rigid 12 in. pavement, with impact factor
§ Negligible influence of live load on buried pipe

  Pipe Deflection is calculated using Spangler’s Modified Iowa Formula:

∆𝑋 = Horizontal Deflection[in]

𝐷_𝑀 = Mean Diameter[in]

𝐾_𝑏 = Bedding Factor

𝐿_𝐷𝐿 = Deflection Lag Factor

𝑃_𝐸 = Vertical Soil Pressure due to Earth Load[lb/ft²]

𝑃_𝐿 = Vertical Soil Pressure due to Live Load]lb/ft²]

𝐸 = Apparent Modulus of Elasticity of Pipe Material[psi]

𝐸′ = Modulus of Soil Reaction[psi]

𝐹_𝑆 = Soil Support Factor

𝐷𝑅 = Standard Dimension Ratio DR 

𝐷_𝑜 = Pipe Outside Diameter [in]

𝑡 = Minimum Pipe Wall Thickness [in]

 

• Modulus of Soil Reaction (E’) – Average Values for Iowa Formula (see table in section 2.0)
• Modulus of Soil Reaction (E’) – Values of E’ for Pipe Embedment (see table in section 2.0)
• Values of E’n Native Soil Modules of Soil Reaction (see table in section 2.0)
• Soil Support Factor (see table in section 2.0)

Pipe Wall Compressive Stress

𝑆 = Pipe Wall Compressive Strength [psi]

𝑃_𝐸 = Vertical Soil Pressure due to Earth Load[lb/ft²]

𝑃_L = Vertical Soil Pressure due to Live Load [lb/ft²]

𝐷𝑅 = Standard Dimension Ratio DR 

𝐷_𝑜 = Pipe Outside Diameter [in]

𝑡 = Minimum Pipe Wall Thickness [in]

 

Input Parameters

1. To create a new case, click the “Add Case” button
2. Select the Live Load: Single Wheel Over Buried PE Pipe – Concentrated Point Load application from the Polyethylene Pipe – Design & Stress Analysis module list.
3. Enter Case Name, Location, Date and any necessary notes.
4. Fill out all required fields.
5. Make sure the values you are inputting are in the correct units.
6. Click the CALCULATE button.

• Reference: ASTM F 1962
  • HDPE Typical Apparent Modulus of Elasticity
  • Duration Time
• Reference: Allowable Compressive Strength
  • For PE Pipe Material Designation Code:
• Reference: Safe Deflection Limits for Pressurized Pipe
  • Pipe DR/SDR
• Reference: Typical Impact Factor for Paved Road
  • Depth of Cover
  • Select Earth/Dead Load Calculation Method
• Pipe Soil Envelope Data
  • Unit Weight of Soil
  • Soil Height above Pipe Crown
  • Bd – Trench Width at Pipe Crown
  • For Soil:
  • Friction Force Coefficient Ku
  • E’ – Modulus of Soil Reaction
  • E’n- Native Soil Modulus of Soil Reaction
  • Deflection Lag Factor (Typically 1.0 – 1.5)
  • Bedding Factor (Typically 0.1)
• Pipe Data
  • Do – PE Pipe Outside Diameter
  • PE Pipe DR or SDR
  • PE Pipe Apparent Modulus of Elasticity
  • Safe Deflection as % of Diameter
  • Allowable Compressive Stress
• Live Load
  • Wheel Load
  • L – Pipe Length
  • Impact Factor

 

Outputs/Reports

1. View the results.
2. If an input parameter needs to be edited be sure to hit the CALCULATE button after the change.
3. To SAVE, fill out all required case details then click the SAVE button.
4. To rename an existing file, click the SAVE As button. Provide all case info then click SAVE.
5. To generate a REPORT, click the REPORT button.
6. The user may export the Case/Report by clicking the Export to Excel/PowerPoint icon.
7. To delete a case, click the DELETE icon near the top of the widget.

• Vertical Pressure due to Earth Load
• L/2H
• Do/2H
• Ch – Load Coefficient
• Vertical Pressure due to Live Load
• Bd/Do
• E’n/E
• Fs – Soil Support Factor
• Deflection as % of Pipe Diameter
• Compressive Stress

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