Distributed Static Surcharge Load: Directly Beneath a Surcharge Load

Introduction

In this approach the active earth force is calculated due to simultaneous effect of both the soil weight and the surcharge of strip load over the pipe to determine earth pressures.

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:

𝑃_𝑐 = 0.6𝑃_𝑚 + 0.4𝑃_𝑝

𝑃_𝑐 = Combined Load or Modified Arching Soil Pressure, [lb/ft²]

Distributed Static Surcharge Load Over PE Pipe

This method is using Boussinesq equation for pressure acting on pipe crown.

P_{dp} = P_a + P_b + P_c + P_d \
P_i = I_CW_i

P_{dp} = P_a + P_b + P_c + P_d \\
P_i = I_CW_i

𝑃_𝑑𝑝 = Subcharge Distributed Load Pressure at Point on Pipe Crown [lb/,ft²]
𝑃_𝑎 = Sub Area a Subcharge Load [lb/ft²]
𝑃_𝑏 = Sub Area b Subcharge Load [lb/ft²]
𝑃_𝑐 = Sub Area c Subcharge Load [lb/ft²]
𝑃_𝑑 = Sub Area d Subcharge Load [lb/ft²]

𝑃_𝑖 = Sub Area Subcharge Load at ith Area [a,b,c or d]
𝐼_𝐶 = Influence Coefficient
𝑤_𝑖 = Distributed Surcharge Pressure Acting over ith Area [a,b,c or d]

Influence coefficient is selected from the table below:

𝐻 = Vertical Distance from Surface to Crown of Pipe, [ft]
𝑀 = Horizontal Distance Normal to Pipe Centerline, from the Center of Load Area, [ft]
𝑁 = Horizontal Distance Parallel to Pipe Centerline, from the Center of Load Area, [ft]

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
• 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
• Static Load
  • Distributed Surcharge Pressure
  • N – Length
  • M – Length
  • M1 – Length

Part 2: Outputs/Reports

Results

• Vertical Pressure due to Earth Load (lb/ft²)
• N/H
• M/H
• M1/H
• Influence Factor for Ic = F (N/H, M/H)
• Influence Factor for Ic = F (N/H, M1/H)
• Vertical Pressure by Surcharge 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

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