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Mekelweg 2. 2638 CO Delft 14th WEGEMT. Trondheim Norway
21st - 25th of January 1991
EXERCISE
on
Upheaval Creep of Buried Heated Pipelines
by
Preben Terndrup Pedersen Department of Ocean En^neering The Tecfanical University of Denmark
DK-2800 Lyngby, Denmark
In the exercise session Thurs(îay January 24th a numerical design procedure will be demonstrated. The numrical analjrsis methods are based on the theory presented in Refe. / I / and /2/. These calculation procedures are programmed in Fortran such that the programs can be run on IBM compatible PC's.
The programs to be used for the exercise haye bem develpped at the Depart-ment of Ocean Engineering, Tedmical University of Denioark with financial support from Maersk Olie og Gas. There programs are not freeware. Therefore, tfaey should not be copied aad used outside this WEGEMT course. The purpose with the exercise is to demonstrate some pf the steps which are involved in design against upheaval buckling independent of the applied software.
It can be mentioned that several organizations have very recently developed similar computer programs which can be used as design tools against upheaval buckling. Examples pf such organizations are Lloyd Register of Shipping and SHELL Research R V / 3 / .
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in RM/FORTRAN and share the same input- and output-files as wdl as graphics output That means that the same input-data-files can be used in both prognuns (with regard to input-files; see later).
The two prP^ams consist of the following source-codes: - START: MAIRFOR SUB.FOR FÛN.FOR GRAPHIC.FOR INPÜT.FOR OUTPUT.FOR
(main pro-am and main subroutine) (subroutines performing analy^) (functions called by subroutines) (graphics subroutines)
(input subroutines) (output subroutines)
- BUCK: BUCK_MN.FOR (main program and main subroutine) BUCK_SB.FOR (subroutines performing analysis) BUCK_FN.FOR (functions called by subroutines) BUCK_GP.FOR (graphics subroutines)
BUCK_IN.FOR (input subroutines) BUCK_OUT.FOR (output subroutines) FD.FOR (finite difference solution)
- and they share the same mclude-file COMFILE.FOR containing COMMON declarations.
These source files are compiled and linked to graphics and mathematical l i -braries/modiiles, into run-files that are named:
START:EXE and BUCK.EXE respectivdy.
- The program START calculates the upheaval teanperatiure for an elastic impofect pipeline by solving a set of transcendent analytical equations as given in / I / . The loading is constant along the pipeline. This is a good approximation for small upheaval aiiq)Iitudes, and the program is therefore best suited for calculating allowable upheaval temperatures for sznall valü@ of this amplitude. Another reason for this is that the results do not depend very much on the moment-curvature relations for small values pf the upheaval clearance.
The constant loading along the pipe can be determined either by a user-de-fined value, by use of Kyriatódes formulae (see page 19 in Ref. /I/) or by using the fomaùlae of C J . Fnmann Clausen (see Fig. 3 in Ref. /2/). Fpr the last two cases an average value of the distributed load are determined.
The program BUCK also calculates the upheaval temperature but the pipe need not be elastic^ the friction coefficient can be assumed to have a bilinear characteristic close to reality, and the load from the weight of the cover and the pipe will vary along the pipe, and with the upheaval clearance. The üpheavaled part of the pipe is modelled with the finite difference method and the equiltiirmm for a given upheaval length is determined by iterations from an analytically calculated linear starting gütós (START), as described in Ref. /2/.
This program is suited for larger upheaval amplitudes for 2 reasons:
1) The non-linear effects are taken into account here and not in program START.
2) The same results as with program START can be found for small upheaval clearances but it takes mucfa Ipnger time, and the non-linear capabilities are not needed here, at stated above. The succes of runs with BUCK is detemnined by convergence of the iter-ations, and Unfortunately this has in some cases shown tp be difficult to obtain, especially when the problan is strongly non-linear. Rdaxations has been included in the methpd, but that has not cleared thè problem com-pletely.
Apart from a longer computational time than START, this incomplete con-vergence seems to be the only disadvantage of program BUCK.
To run the programs simply type:
drive> START <enter> or
drive> BUCK <enter> (assimiing no re-direction),
you will thai be prompted for names of ijaput- and outputrfiles, form of Pütpüt as wdl as some loading data. YOii wûl be prOmipted whether or not
answer NO (0) to this also, the program will use C J . Frimann Clausâis formulas for the soil load.
The data-input file contains all the needed inf(»mation except those g i y ^ interactively iri the start of the run. It is an ordinary ASCII text file, whidi can be edited, printed and copied as any other file. The data m this file is read unformated by tbe programs, that irieans any legal FORTRAN-format may be iised.
The only difference between the two programs in connection with the input-file, is that in program START the upheaval clearance is used directly, whereas the upheaval length is used in BUCK, and the a»rresponding clears ance is determined from the length. This means that an input-file for START should be corrected from upheaval dearances into upheaval buckling lengths before using the same file with program BUCK.
Bdow is shown an example of an input-file: (START-version)
1 0.20 12.25 3 0.01 0.02 0.03 8 0.30 0.50 0.70 0.90 1,10 1.30 1.50 1.70 1000.0 0.00 (start of input-file) Number of different impöfection heights
List of found, iniperf. heights in ascending order Length of foundation imperfection
Number of différait upheaval dearances
List of pipdine upheaval clear, in ascending order
Number of different trenching cpver depths List of trenchv cover depths in ascending order
(max 60) m' m (max 60)
M
(max 60)M
Mass density of submerged trenching cover Cementation or flow of stressed soil
[kg/m^] (0/1, cement:O.0)
3.00 Properties of sand (0/1/2/3/4: refer to repport) 0.50 Coeffident of friction for distributed forces
0.50 Coeffident of friction for concentrated fprces
0.0001 Deformation limit for fuÜy mobilised friction
M
2,leH-ll Youngs naodulus of sted [N/m^]
0.30 Poissons ratip
3.50e-l-08 Yield stress [N/m2]
1.00 Strain hardening factor (1.0: elastic, >1.Q: plastic)
0.11e-04 Coeffident of thermal expandPn [l/'C]
7860.00 Mass density of sted pipe
[kg/ml
3000.00 Mass density of cpnorete layer [kg/m^]
ft
600.00 Mass density of foam material [kg/<]
1000.00 Mass density of wrapping material [kg/ni3]
0.2191 Outa- diameter of sted pipe [m]
0.0143 Wall thickness of steel pipe
M
0.0500 Wall thickness of conaete layer [m]
0.0300 Wall thickness of foam layer [m]
0.0050 Wall thickness of wrapping layer [m]
0.01 "Height" of pipeline transverse imperfection [m]
1025.00 Mass density of sea water
[kg/ml
850.00 Mass density Pf prodiict (oil/gas) [kg/m^]
n
2.00 Mass density of atm air [kg/m3]
9.82 Gravity acceleration [m/sec^]
35.00 Water depth
M
2.07e+07 Internal pressure in pipeline [N/m2]
25 Number pf intervals used in finite diff. solution 1.00e-04 Allowed relative error used in (spme) iterations
(end of input-file)
- The putpiit file contains an echo pf the input file and if wanted table of pipeline shape, distribution of bending moment, loading and axial force äkmg the pipeline, for each equilibrium found. An example . is shown bdow: (START-version)
PIPELINE AND FOUNDATION PROPERTIES
Hdght of foundation imperfection Length pf foundation unperfection Clearance between foundatipn and pipe
Depth of trenching cover
Mass daisity of trenching cover inaterial CemaatatiOn or flow of sand
Sand friction angle
0,2ÖOÖE-l-00 m 0.i225E+02 m O.lOOOE-01 m 0.2000B-01 m 0.3000E-01 m 0.3000E-i-00 ni 0.5000E+00 m 0.7000E-I-00 m 0.9000E+00 m O.llOOE+01 m 0.1300E+01 m 0-1500E+01 m 0.1700E-I-01 m 0.1000E-h04 kg/m^ cementation 0.3500E4^2 deg
Coef; of friction for distributed forces Coef. pf friction for concentrated forces Deform, limit for fully mobilised friction Youngs modulus
Poissons ratio Yidd stress
Strain hardening factpr Coef. of thermal expansion Mass density of stell
Mass density of concrete Mass density of foam maitenal Mass density of wrs^plng material Outer diameter of stell pipe Wall thickness of sted pipe Wall thickness of concrete layer Wall thicknesis Pf foaim layer Wall thickness of wrapping lay^
0.5000E+00 0.5000E+00 O.lOPOE-03 m 0.2100E+12 N/m^ 0.3000E+00 0.3500E-I-09 N/m^ 0.1000E-(-01 O.llOOE-04 l / ' C 0-7860E-I-04 kg/m^ 0.3Ô00E+04 kg/m^ 0.6000E-I-03 kg/rn^ 0.1000E-K)4 kg/m^ 0.2101E+00 m 0.1430B-01 m 0.5000E-01 m 0.3000E-01 m 0.5000E-02 m
"Hdght" of pipeline transverse impafection O.lOOOB-01 m Mass density of sea water
Mass density of product (oil/gas) Mass density of atm. air
Gravity acceleration Wata: depth
Internal pressure in pipeline
0.1025E-i-04 0.8500E+03 0.2000E-I-01 0,9820E-H01 0.3500E-I-02 0.2070E+08 kg/m^ kg/m' m/s^ m N/m^ No of dements in finite difference solution
Allowed error in itarations
25
O.lOOOE-03
RELATED PROPERTIES
Wdght of stèd pipe Weaght of foam layer Weight of wrapping alyer Wdght of concrete laya^ Wdght of product
Bouyancy of pipe
TOTAL WEIGHT OF PIPELINE
0.7I01E-I-03 N/m 0.1383E+03 N/m 0.4382E-I-Q2 N/m 0.1569E4-04 N/m 0.2379E-i-03 N/m 0.1197E+04 N/m 0.1503E-I-04 N/m Cross sectional area (Sted pipe)
Cross sect, moment of inertia (sted pipe)
0.9201E-02 m' 0.4847E-04 m'
< tablés of equilibrium propâties are not induded here> (end of output-file)
R^reocës
/ I / Pedersen, P. Terndrup & Jensen, J.J.: "Upheaval Creep of Buried Heated Pipdines with Imtial Imperfections". Marine Structures, Vol. 1, pp U - 22, 1988.
/2/ Pedersen, P. Terndrup k Michelsen, J.: "Large Deflection Upheaval Buckling of Marine Pipelines". Proceedings of the Behaviour of Offshore Structures (BOSS), Trondhdm, Vol. 3, pp 965 - 980. June 1988.
/3/ Kleva, F.J.; van Hdvofrt, L . C and Sluyternianv A - C ; "A Dedicated Finite Element Model for Analyzing Upheaval Buckling Response of Submarine Pipelines". Proceedings 22nd Annual Offshore Technology Confaence, papa no 6333, pp 529 - 537, May 1990.
