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
๐๐ = Vertical Soil Pressure, [lb/ft2]
๐ค = Unit Weight of Soil, [lb/,ft2]
๐ป = Height of Soil Above Pipe Crown, [ft]
B. Marston Load (ASCE Manual No.60)
P_m=C_dwB_d
P_m=C_dwB_d
๐๐ = Vertical Soil Pressure, [lb/,ft2]
๐ค = Unit Weight of Soil, [lb/,ft2]
๐ต๐ = Trench Width at Pipe Crown, [ft]
๐ถ๐ = 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}
๐ = Base of Natural Logarithm, [2.71828]
๐พ = Rankine Earth Pressure Coefficient
๐พ = ๐ก๐๐2 (45-ฮธ
/2)
๐ = Angle of Internal Soil Friction,[ยฐ]
๐ข = 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:
๐๐ = 0.6๐๐ + 0.4๐๐
๐๐ = Combined Load or Modified Arching Soil Pressure, [lb/ft2]
Live Load: Multiple 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 = \frac{3F_iW_wH^3}{2\pi r^5}
P_L = \frac{3F_iW_wH^3}{2\pi r^5}
๐๐ฟ = Vertical Soil Pressure due to Live Load [lb/ft2]
๐๐ค = Live Load [lb/ft2] (see table)
๐ป = Soil Height above Pipe Crown [ft]
๐น๐ = Impact Factor
๐ = Distance from the Point of Load Application [ft]
๐ = (โ๐2+๐ป2)
* Simulates a 20-ton truck traffic load, with impact factor
โ Simulates an 80,000 lb./ft railway load, with impact factor
โก 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
ยง Negligible influence of live load on buried pipe
Pipe Deflection is calculated using Spanglerโs 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\%
โ๐ = Horizontal Deflection, in.
๐ท๐ = Mean Diameter, in.
๐พ๐ = Bedding Factor
๐ฟ๐ท๐ฟ = Deflection Lag Factor
๐๐ธ = Vertical Soil Pressure due to Earth Load[lb/ft2]
๐๐ฟ = Vertical Soil Pressure due to Live Load[lb/ft2]
๐ธ = Apparent Modulus of Elasticity of Pipe Material[psi]
๐ธโฒ = Modulus of Soil Reaction[psi]
๐น๐ = Soil Support Factor
๐ท๐
= Standard Dimension Ratio DR = Do /t
๐ท๐ = Pipe Outside Diameter [in]
๐ก = Minimum Pipe Wall Thickness [in]
Parameter Reference Table:
Modulus of Soil Reaction (Eโ) โ Average Values for Iowa Formula
Modulus of Soil Reaction (Eโ) โ Values of Eโ for Pipe Embedment
Values of Eโn 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}
๐ = Pipe Wall Compressive Strength, [psi]
๐๐ธ = Vertical Soil Pressure due to Earth Load, [lb/ft2]
๐๐ = Vertical Soil Pressure due to Surcharge Load, [lb/ft2]
๐ท๐
= Standard Dimension Ratio DR = Do /t
Case Guide
Part 1: Create Case
- Select the Live Load: Multiple Wheel Over Buried PE Pipe – Concentrated Point Load application from the Polyethylene Pipe Module
- To create a new case, click the โAdd Caseโ button
- Enter Case Name, Location, Date and any necessary notes.
- Fill out all required parameters.
- Make sure the values you are inputting are in the correct units.
- Click the CALCULATE button to overview results.
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 โ Trench Width at Pipe Crown
- For Soil:
- Friction Force Coefficient Ku
- Eโ โ Modulus of Soil Reaction
- Eโn- Native Soil Modulus of Soil Reaction
- Deflection Lag Factor (Typically 1.0 โ 1.5)
- Bedding Factor (Typically 0.1)
- Pipe Data
- Do โ 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 โ Pipe Length
- Impact Factor
Part 2: Outputs/Reports
- If you need to modify an input parameter, click the CALCULATE button after the change.
- To SAVE, fill out all required case details then click the SAVE button.
- To rename an existing file, click the SAVE As button. Provide all case info then click SAVE.
- To generate a REPORT, click the REPORT button.
- The user may export the Case/Report by clicking the Export to Excel icon.
- To delete a case, click the DELETE icon near the top of the widget.
Results
- Vertical Pressure due to Earth Load (lb/ft2)
- R โ Distance: Point of Load โ Pipe Crown (ft)
- Vertical Pressure due to Live Load (lb/ft2)
- Bd/Do
- Eโn/E
- Fs โ Soil Support Factor
- Deflection as % of Pipe Diameter
- Compressive Stress (psi)
References
- โModulus of Soil Reaction Values for Buried Flexible Pipeโ, Journal of the Geotechnical Engineering Division, ASCE, Vol. 103, No GT 1, Howard, A.K. Technical Toolboxes, Inc.
- โEvaluation of Modulus of Soil Reaction E and its Variation with Depthโ, Report No. UCB/GT/82-02,
- โSoil Engineeringโ, Third Edition, Spangler, M.G. and Handy, R.L., Intext Educational Press
- โStructural Mechanics of Buried Pipesโ, Watkins, R.K, and Loren, R, A,
- โPolyethylene Pipe Handbook: Design of PE Piping Systemsโ, Second Edition, Plastic Pipe Institute, Inc.
- API 15LE โ Specification for Polyethylene Line Pipe
FAQ
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This property data is a summary of similar materials in the MatWeb database for the category “High Density Polyethylene (HDPE), Injection Molded”.
Each property range of values reported is minimum and maximum values of appropriate MatWeb entries. The comments report the average value, and number of data points used to calculate the average.ย
The values are not necessarily typical of any specific grade, especially less common values and those that can be most affected by additives or processing methods.ย Check Out