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Hot Pipeline Upheaval Buckling

Calculate high temperature pipeline upheaval buckling using either the Hobbs method, the Pipeng method, or the LRSTAR method.

The Hobbs method can be used for used for pipelines lying on the seabed. The LRSTAR and Pipeng methods are suitable for buried pipelines, and have been developed using the results from finite element analysis (FEA). The LRSTAR method uses a cubic spline fit for the dimensionless Richards length number and Richards weight number. The Pipeng method uses a simple mathematical relationship between the Calladine Length number and the Calladine load number based on beam theory.

The Hobbs method calculates the initiation temperature from the global axial load, the load outside the slip zone, and hence accounts for the expansion of the pipe prior to buckling. The Pipeng method and LRSTAR method calculate the initiation temperature from the axial load in the buckle, and do not account for the expansion of the pipe prior to buckling. The Pipeng method and LRSTAR method are therefore slightly conservative. In addition, the LRSTAR method includes a built in design factor. The LRSTAR method is therefore more conservative than the Pipeng method.

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CALCULATOR : High Temperature Pipeline Hobbs Lateral And Upheaval Buckling Model (Multi Layer Pipe) [PLUS]   ±

Calculate Hobbs upheaval and lateral buckling load and buckling temperature from initial out of straightness for multi layer pipelines.

Buckle conditions can be calculated for either buckle initiation, or post buckle for the selected buckle mode. The global axial load should be the same for buckle initiation and post buckle. Buckling should be checked for lateral buckling modes 1, 2, 3 and 4, and for upheaval buckling. The lowest buckling temperature should be used. Post buckle results are indicative only. The model is not valid outside the elastic range. This calculator is suitable for unburied pipelines lying on the sea bed. It should not be used for buried pipelines.

Tool Input

  • schdtype : Line Pipe Schedule Type
  • diamtype : Line Pipe Diameter Type
    • ODu : User Defined Outside Diameter
    • IDu : User Defined Inside Diameter
  • wtntype : Line Pipe Wall Thickness Type
    • tnu : User Defined Wall Thickness
  • wltype : Pipe Unit Weight Type
  • sectype : Cross Section Type
    • OODu : User Defined Outer Diameter Including Coatings)
    • Zu : User Defined Pipe Z Modulus
    • EIu : User Defined Pipe E x I
    • EAu : User Defined Pipe E x A
    • EAαu : User Defined Pipe E x A x alpha
    • νu : User Defined Pipe Poisson's Ratio
    • WLu : User Defined Pipe Total Weight Per Length
  • buckmode : Buckle Mode
  • buckstage : Buckle Stage
  • WTi : Pipe Liner Wall Thickness
  • ρi : Pipe And Liner Density
  • Ei : Pipe And Liner Elastic Modulus
  • αi : Pipe And Liner Thermal Expansion Coefficient
  • νi : Pipe And Liner Poisson's Ratio
  • WTo : Pipe Coating Wall Thickness
  • ρo : Pipe Coating Density
  • Δi : Initial Out Of Straightness
  • Ta : Ambient Or Installation Temperature
  • Pi : Internal Pressure
  • Nin : Installation Load
  • ρf : Internal Fluid Density
  • ρb : External Fluid Density
  • μa : Axial Friction Factor
  • μl : Lateral Friction Factor

Tool Output

  • ΔT : Delta Temperature At Buckle Inititation
  • Δb : Buckle Amplitude
  • ν : Pipe Poisson Ratio
  • BM : Maximum Bending Moment (Elastic)
  • EA : Pipe E x A
  • EAα : Pipe Expansion Modulus
  • EI : Pipe E x I
  • Fab : Buckle Axial Load
  • Fag : Global Axial Load (Away From Buckle)
  • IID : Pipe Inside Diameter Including Liner
  • Lb : Buckle Half Wave Length
  • Ls : Buckle Slip Length
  • OD : Line Pipe Diameter
  • OD/tn : Line Pipe Diameter Over Wall Thickness Ratio
  • OOD : Pipe Outer Diameter Including Coatings
  • SB : Maximum Bending Stress (Elastic)
  • Tb : Buckle Inititation Temperature
  • W : Total Pipe Weight Per Unit Length
  • Z : Pipe Z Modulus
  • cvg : Convergence Check
  • mlb : Buoyancy Unit Mass
  • mlc : Contents Unit Mass
  • mlp : Pipe Unit Mass Including Liner And Coating
  • tn : Line Pipe Thickness

CALCULATOR : High Temperature Pipeline Pipeng Upheaval Buckling Model (Multi Layer Pipe) [PLUS]   ±

Calculate buried pipeline upheaval buckling initiation temperature from prop height and soil cover height for multi layer pipelines using the Pipeng method.

The Pipeng method is based on the dimensionless Calladine load number (Can) and Calladine length number (Cal). The Pipeng model has been determined from finite element analysis (FEA) for a pipeline prop on a stiff foundation. The results fit very closely to the formula

`Can = 2.4688 + 0.09888 (Cal - 2.430718)^2 `
`Cal = li ((Wl) / (EI.hi))^0.25 `
`Can = Nab √((hi) / (EI.Wl)) `

where :

Cal = Calladine length number
Can = Calladine load number
li = length between buckle inflection points
hi = height of buckle above inflection points
EI = pipeline bending stiffness
Wl = pipeline and soil uplift resistance
Nab = axial buckling load

The point Cal = 2.430718 and Can = 2.4688 corresponds to a pipeline with no soil cover. The buckle initiation temperature is calculated from the axial load in the buckle zone. The actual buckling temperature (from the global buckling load) will be slightly higher because of pipeline expansion.

The prop profile and inflection points are calculated from the pipeline installation weight. The soil is assummed to completely fill the space under the pipeline prop. The buckling load is calculated from the total upload resistance (pipeline operating weight + soil weight).

Use the Result Plot option to display buckling temperature versus prop height, or buckling temperature versus soil cover height.

Tool Input

  • soiltype : Soil Cover Type
  • schdtype : Line Pipe Schedule Type
  • diamtype : Line Pipe Diameter Type
    • ODu : User Defined Outside Diameter
    • IDu : User Defined Inside Diameter
  • wtntype : Line Pipe Wall Thickness Type
    • tnu : User Defined Wall Thickness
  • wltypei : Pipe Installation Unit Weight Type
  • wltypeo : Pipe Operating Unit Weight Type
  • sectype : Cross Section Type
    • OODu : User Defined Outer Diameter Including Coatings)
    • EIu : User Defined Pipe E x I
    • EAu : User Defined Pipe E x A
    • EAαu : User Defined Pipe E x A x alpha
    • νu : User Defined Pipe Poisson's Ratio
    • Wiu : User Defined Pipe Installation Weight Per Length
    • Wou : User Defined Pipe Operating Weight Per Length
  • wlstype : Soil Weight Type
    • Wsu : User Defined Soil Weight Or Resistance
  • proptype : Prop Calculation Type
    • Liu : User Defined Inflection Length
    • hiu : User Defined Inflection Height
  • WTi : Pipe Liner Wall Thickness
  • ρi : Pipe And Liner Density
  • Ei : Pipe And Liner Elastic Modulus
  • αi : Pipe And Liner Thermal Expansion Coefficient
  • νi : Pipe And Liner Poisson's Ratio
  • WTo : Pipe Coating Wall Thickness
  • ρo : Pipe Coating Density
  • Hp : Prop Height
  • Hs : Required Soil Cover Height To Top Of Pipe
  • Ta : Ambient Or Installation Temperature
  • Pi : Internal Pressure
  • Nin : Installation Load
  • ρfi : Installation Fluid Density
  • ρfo : Operating Fluid Density
  • ρb : External Fluid Density
  • Su : Soil Undrained Shear Stress
  • ws : Soil Installed Specific Weight
  • fs : Soil Friction Factor

Tool Output

  • ΔT : Delta Temperature At Buckle Inititation
  • ν : Pipe Poisson Ratio
  • Cal : Dimensionless Calladine Length Number
  • Can : Dimensionless Calladine Load Number
  • EA : Pipe E x A
  • EAα : Pipe Expansion Modulus
  • EI : Pipe E x I
  • Fb : Buckle Load
  • Hi : Prop Inflection Height
  • IID : Pipe Inside Diameter Including Liner
  • Li : Prop Inflection Length
  • Mp : Pipe Mass Per Length Including Liner And Coatings
  • OD : Line Pipe Diameter
  • OD/tn : Line Pipe Diameter Over Wall Thickness Ratio
  • OOD : Pipe Outer Diameter Including Coatings
  • Tb : Buckle Inititation Temperature
  • Wi : Installation Pipe Weight Per Unit Length
  • Wo : Operating Pipe Weight Per Unit Length
  • Ws : Soil Weight Per Unit Length
  • Wu : Total Uplift Resistance Per Unit Length
  • lb : Prop Wave Length
  • lp : Prop Half Wave Length
  • tn : Line Pipe Thickness

CALCULATOR : High Temperature Pipeline LRSpur Upheaval Buckling Model (Multi Layer Pipe) [PLUS]   ±

Calculate buried pipeline upheaval buckling required soil cover height from prop height and design temperature for multi layer pipelines using the LRSPUR method (1990).

The LRSPUR method is based on the dimensionless Richards weight number (Riw) and Richards length number (Ril). The LRSPUR model uses a cubic spline which has been fitted to the results of finite element analysis (FEA) for a pipeline prop on a stiff foundation.

`Ril = li √((Nab)/(EI)) `
`Riw = (EI.Wl) / (hi.Nab^2) `

where :

Riw = Richards length number
Riw = Richards weight number
li = length between buckle inflection points
hi = height of buckle above inflection points
EI = pipeline bending stiffness
Wl = pipeline and soil uplift resistance
Nab = axial buckling load

The buckle initiation temperature is calculated from the axial load in the buckle zone. The actual buckling temperature (from the global buckling load) will be slightly higher because of pipeline expansion.

The prop profile and inflection points are calculated from the pipeline installation weight. The soil is assumed to completely fill the space under the pipeline prop. The soil height is calculated from the total upload resistance (pipeline operating weight + soil weight).

Use the Result Plot option to display buckling temperature versus prop height, or buckling temperature versus soil cover height. The LRSTAR or LRSPUR method is conservative.

Tool Input

  • soiltype : Soil Cover Type
  • schdtype : Line Pipe Schedule Type
  • diamtype : Line Pipe Diameter Type
    • ODu : User Defined Outside Diameter
    • IDu : User Defined Inside Diameter
  • wtntype : Line Pipe Wall Thickness Type
    • tnu : User Defined Wall Thickness
  • wltypei : Pipe Installation Unit Weight Type
  • wltypeo : Pipe Operating Unit Weight Type
  • sectype : Cross Section Type
    • OODu : User Defined Outer Diameter Including Coatings)
    • EIu : User Defined Pipe E x I
    • EAu : User Defined Pipe E x A
    • EAαu : User Defined Pipe E x A x alpha
    • νu : User Defined Pipe Poisson's Ratio
    • Wiu : User Defined Pipe Installation Weight Per Length
    • Wou : User Defined Pipe Operating Weight Per Length
  • wlstype : Soil Weight Type
  • proptype : Prop Calculation Type
    • Liu : User Defined Inflection Length
    • hiu : User Defined Inflection Height
  • WTi : Pipe Liner Wall Thickness
  • ρi : Pipe And Liner Density
  • Ei : Pipe And Liner Elastic Modulus
  • αi : Pipe And Liner Thermal Expansion Coefficient
  • νi : Pipe And Liner Poisson's Ratio
  • WTo : Pipe Coating Wall Thickness
  • ρo : Pipe Coating Density
  • Hp : Prop Height
  • Td : Design Temperature
  • Ta : Ambient Or Installation Temperature
  • Pi : Internal Pressure
  • Nin : Installation Load
  • ρfi : Installation Fluid Density
  • ρfo : Operating Fluid Density
  • ρb : External Fluid Density
  • Su : Soil Undrained Shear Stress
  • ws : Soil Installed Specific Weight
  • fs : Soil Friction Factor

Tool Output

  • ΔT : Delta Temperature At Buckle Inititation
  • ν : Pipe Poisson Ratio
  • EA : Pipe E x A
  • EAα : Pipe Expansion Modulus
  • EI : Pipe E x I
  • Fb : Buckle Load
  • Hi : Prop Inflection Height
  • Hs : Required Soil Cover Height To Top Of Pipe
  • IID : Pipe Inside Diameter Including Liner
  • Li : Prop Inflection Length
  • Mp : Pipe Mass Per Length Including Liner And Coatings
  • OD : Line Pipe Diameter
  • OD/tn : Line Pipe Diameter Over Wall Thickness Ratio
  • OOD : Pipe Outer Diameter Including Coatings
  • Ril : Dimensionless Richards Length Number
  • Riw : Dimensionless Richards Weight Number
  • Wi : Installation Pipe Weight Per Unit Length
  • Wo : Operating Pipe Weight Per Unit Length
  • Ws : Soil Weight Per Unit Length
  • Wu : Total Uplift Resistance Per Unit Length
  • cvg : Convergence Check
  • lb : Prop Wave Length
  • lp : Prop Half Wave Length
  • tn : Line Pipe Thickness