Live Load: Cooper E-80 Railroad Load on Buried PE Pipe

This calculation based on normal RR loading and analyzed for depths of cover from 6 to 14 feet. The calculation only accounts for up to 80,000 lb/ft railway load, with impact factor.

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: Cooper E-80 Railroad Load on Buried PE Pipe
𝑃_𝐿 = 𝐹_𝐸80(𝐻)

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

𝐹_𝐸80 = Live Load Transfer to Pipe [lb/ft²] (see table)

𝐻 = Soil Height above Pipe Crown [ft]

* 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: Cooper E-80 Railroad Load on Buried PE Pipe 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

 

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
• Vertical Pressure due to Cooper E-80 Load
• Bd/Do
• E’n/E
• Fs – Soil Support Factor
• Deflection as % of Pipe Diameter
• Compressive Stress

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