Live Load: Multiple Wheel Not Over Buried PE Pipe – Concentrated Point Load

Introduction

This calculation determines the deflection or structural damage to the repeated load application not over buried pipe i.e. parallel. 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=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: Multiple Wheel Not 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 = \frac{3F_iW_wH^3}{2\pi r^5} \~\
r = \sqrt{x^2 + \left( H + \frac{\frac{D}{12}}{2} \right)^2 – \left( \frac{\frac{D}{12}}{2} \right)^2}

P_L = \frac{3F_iW_wH^3}{2\pi r^5} \\~\\
r = \sqrt{x^2 + \left( H + \frac{\frac{D}{12}}{2} \right)^2 - \left( \frac{\frac{D}{12}}{2} \right)^2}

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

𝑊_𝑤 = Live Load [lb/ft²] (see table)

𝐻 = Soil Height above Pipe Crown [ft]

𝐹_𝑖 = Impact Factor

𝑟 = Distance from the Point of Load Application [ft]

For standard H-20 and H-20 highway vehicle loading, the contact area is normally taken for dual wheels, that is, 16,000 lb. over a 10 in. by 20 in. area. 

* 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

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
• Live Load
  • Wheel Load
  • L – Pipe Length
  • Impact Factor

Part 2: Outputs/Reports

Results

• Vertical Pressure due to Earth Load (lb/ft²)
• R – Distance: Point of Load – Pipe Crown (ft)
• Vertical Pressure due to Live 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