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

Introduction

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=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=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

C_d = \frac{1 – e^{-2K_u\frac{H}{B_d}}}{2K_u}

C_d = \frac{1 - e^{-2K_u\frac{H}{B_d}}}{2K_u}

𝑒 = Base of Natural Logarithm, [2.71828]
𝐾 = Rankine Earth Pressure Coefficient
𝐾 = 𝑡𝑎𝑛² (45-θ/2)
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:

𝑃𝑐 = 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:

\frac{\Delta X}{D_M} = \frac{1}{144} \left( \frac{K_bL_{DL}P_E + K_bP_L}{\frac{2E}{3}(\frac{1}{DR-1} )+F_SE’} \right) \times 100\%

\frac{\Delta X}{D_M} = \frac{1}{144} \left( \frac{K_bL_{DL}P_E + K_bP_L}{\frac{2E}{3}(\frac{1}{DR-1}  )+F_SE'} \right) \times 100\%

∆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]
𝐹𝑆 = Soil Support Factor
𝐷𝑅 = Standard Dimension Ratio DR = D_o /t
𝐷𝑜 = Pipe Outside Diameter [in]
𝑡 = Minimum Pipe Wall Thickness [in]

Parameter Reference Table:

Modulus of Soil Reaction (E’) – Average Values for Iowa Formula

Modulus of Soil Reaction (E’) – Values of E’ for Pipe Embedment

Values of E’n Native Soil Modules of Soil Reaction

Soil Support Factor (Fs)

Pipe Wall Compressive Stress (PE Pipe Crushing):

S=\frac{(P_E+P_S)DR}{288}

S=\frac{(P_E+P_S)DR}{288}

𝑆 = Pipe Wall Compressive Strength, [psi]
𝑃_𝐸 = Vertical Soil Pressure due to Earth Load, [lb/ft²]
𝑃_𝑆 = Vertical Soil Pressure due to Surcharge Load, [lb/ft²]
𝐷𝑅 = Standard Dimension Ratio DR = D_o /t
𝐷_𝑜 = Pipe Outside Diameter [in]
𝑡 = Minimum Pipe Wall Thickness [in]

Case Guide

Part 1: Create Case

Input Parameters

• 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

Part 2: Outputs/Reports

Results

• Vertical Pressure due to Earth Load (lb/ft²)
• Vertical Pressure by Aircraft Load (lb/ft²)
• Bd/Do
• E’n/E
• Fs – Soil Support Factor
• Deflection as % of Pipe Diameter
• Compressive Stress (psi)

References

• “Modulus of Soil Reaction Values for Buried Flexible Pipe”, Journal of the Geotechnical Engineering Division, ASCE, Vol. 103, No GT 1, Howard, A.K. Technical Toolboxes, Inc.
• “Evaluation of Modulus of Soil Reaction E and its Variation with Depth”, Report No. UCB/GT/82-02,
• “Soil Engineering”, Third Edition, Spangler, M.G. and Handy, R.L., Intext Educational Press
• “Structural Mechanics of Buried Pipes”, Watkins, R.K, and Loren, R, A,
• “Polyethylene Pipe Handbook: Design of PE Piping Systems”, Second Edition, Plastic Pipe Institute, Inc.
• API 15LE – Specification for Polyethylene Line Pipe

FAQ