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