free span- as lay- 12 inch-production(kp0-kp6.5) no lock function

APPENDIX 1 - FREE SPAN ANALYSIS - 12INCH PRODUCTION PIPELINE

SU TU NAU PROJECT-DNV RP-F105 FREE SPANNING PIPELINE

Project_info"SU TU NAU FIELD DEVELOPMENT"

"As-Laid Case "

Pipeline_Description "12inch Production Pipeline from STN-N (KP0) to STN-S (KP6.55)"

1.0 INTRODUCTION

This Mathcad sheet has been written in order to calculate in-line and cross flow vortex induced vibration onset and screening lengths of pipelines in accordance withDNV-RPF105Free Spanning Pipelines 2006 (Reference [1]). The sheet calculates the following span limits:VIV onsetFatigue screeningULS criterion (according to Reference [2]) considering both static and dynamic loadingOn-bottom wave and current velocities are calculated using methodology contained within both Reference [1] and Reference [2]. The sheet is set up to perform calculations onan untrenched pipeline configuration. Screening data is always 1 year return period wave data, and 100 year return period current data.Onset lengths can be based upon 1, 10 or 100 year data depending upon the loadcase under consideration. ULS check should consider 100 year current for operatingconditions, and 10 year for temporary conditions, it is a project decision whether maximum wave height and period should be used. Cyclonic conditions will require carefulevaluation of overall velocities and dissemination of these into suitable wave and current components.Sheet performs calculations for the length of the pipeline route of the above for the as-laid, flooded, hydrotest and operating loadcases.For VIV calculations, operating pressures and temperatures are used.Half of any corrosion allowance should be considered - Guidance Note in Section 2.2.5 Reference [1]. NOTE THAT THIS MAY VARY ON A PROJECT BASIS.Corrosion not considered for calculation of effective axial force [and hence frequencies, onset and screening lengths] but is included for stress calculations - Section 6.2.2Reference [1].For ULS criterion check, corrosion allowance is conservatively EXCLUDED when calculating pipeline loading, but INCLUDED when considering pipeline capacity.For ULS criterion check, MAXIMUM wave height and associated period is considered for static loading. Dynamic loading uses SIGNIFICANT values. Design temperaturesand pressures are used.Simplified soils damping criteria are used for this calculationIt is currently assumed that functional loading does not reduced the combined loading effect, refer to Note 1 of Table 4-4 Reference [2].Sheet is set up for single, non-interacting spans only - interacting spans require FE Analysis to determine natural frequencies.Sheet assumes pipe is fully restrained. If this is not the case, an effective axial force may require to be manually input for the operational loadcase.References1. Det Norske Veritas, DNV-RP-F105 - Free Spanning Pipelines, 2006.2. Det Norske Veritas, DNV-OS-F101 - Submarine Pipeline Systems, 20123. Det Norske Veritas, DNV-RP-F109 - On-bottom Stability Design of Submarine Pipelines, 2007.4. Det Norske Veritas, DNV-GL-14 - Free Spanning Pipelines, 1998.5. Det Norske Veritas, DNV-RP-C205 - Environmental Conditions and Environmental Loads April 2010

Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) /73


General Functions / Unit Definition

Find largest value in a column of a matrixmax_find matrix col( ) match max matrix

col matrixcol

0

Matrix trim function trim_rows matrix max_rows( ) submatrix matrix 0 max_rows 0 cols matrix( ) 1 return

0 2Listbox state saving functions Effective Axial Force Pipe Roughness

1 2Equation to use for Seff Span Definition

0 2Loadcase Duration Span Boundary Conditions

val_find val vec( ) lst_vec last vec( )

0 0 return val vec0if

lst_vec lst_vec( )return val veclst_vecif

if val vecii= ii ii 1 ii return val veciiif

ii 1 lst_vecfor otherwise

Value finder - finds the relative position of a value in a vectorof values in terms of which values it lies between.

Appendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 2/73


2D Linear Interpolation linear_interp X Y XYs Xs Ys( ) y_min y_max( ) val_find Y Ys( )

x_min x_max( ) val_find X Xs( )

xvalsXsx_min

Xsx_max

yvalsYsy_min

Ysy_max

x_inter x yv( ) linterp xvalsXYsx_min yv

XYsx_max yv

X

y_inter xv y( ) linterp yvalsXYsxv y_min

XYsxv y_max

Y

XYsx_min y_minreturn x_min x_max=if

x_inter X y_min( )return otherwise

y_min y_max=if

y_inter x_min Y( )return x_min x_max=if

linterp xvalsy_inter x_min Y( )

y_inter x_max Y( )

X

return otherwise

otherwise

3D Linear Interpolation multi_interp X Y Z XYss Xs Ys Zs( ) z_min z_max( ) val_find Z Zs( )

zvalsZsz_min

Zsz_max

xy_1 linear_interp X Y XYssz_min Xs Ys

xy_2 linear_interp X Y XYssz_max Xs Ys

xy_1return z_min z_max=if

linterp zvalsxy_1

xy_2

Z

return otherwise



Modified Parameter Interpolation for Gc G_param_inter M N table( ) mvals table0

m_min m_max( ) val_find M mvals( )

n_min n_max( ) val_find N0.003

0.006

min_offset ii 4 n_min 1

max_offset ii 4 n_max 1

p_1 tablem_min min_offset

p_2 tablem_min max_offset

m_min m_max=if

p_1 linterp mvals tablemin_offset

M

p_2 linterp mvals tablemax_offset

M

otherwise

rmii p_1 n_min n_max=if

rmii linterp0.003

0.006

p_1

p_2

N

otherwise

ii 0 3for

rm

Floating-Point Comparison Operators Less than fp_lt x y( ) if round x 6 round y 6 1 0

Less than or equal to fp_lte x y( ) if round x 6 round y 6 1 0

Equal to fp_eq x y( ) if round x 6 round y 6 = 1 0

Greater than or equal to fp_gte x y( ) if round x 6 round y 6 1 0

Greater than fp_gt x y( ) if round x 6 round y 6 1 0



General Functions / Unit Definition

2.0 INPUT SUMMARY

2.1 Pipeline Properties

Interval for calculations KPStep 100 m

2.1.1 Pipeline Mechanical Properties

pipe_inputs

Pipe Section

Start KP(km)

End KP(km)

Steel OD

D0(mm)

Steel Wall Thickness

tnom(mm)

Internal Coat

Thickness

tint(mm)

Internal Coat

Density

ρint(kg/m3)

Corrosion Allowance

tcor(mm)

Corrosion Coat

Thickness

tcc(mm)

Corrosion Coat

Density

ρcc(kg/m3)

Concretethickness

twc(mm)

ConcreteCoat

Density

ρwc(kg/m3

)

Marine Growth

Thickness

tma(mm)

Marine Growth Density

ρma(kg/m3

)1 0 6.55 323.9 9.5 0 0 3 35.3 200 55 3040 0 1500

2.1.2 Seabed Properties2.1.3 Safety Class Definition



Seabed

KP From KP To Soil TypeSoil Type Integer for Calculations

SeabedRoughness

Associated Roughness

Poisson's Ratio

0 6.55 Medium Sand 1 Medium sand 4.00E-05 0.35

Safety

KP From KP To Safety ClassInteger forCalculation

0 6.55 Low 0



2.1.4 Axial Friction Coefficiens Soil Type: Table 7.3 - 7.4 Section 7.3.1 Page 35 Ref. [1]Seabed Roughness: Table 3.1, Section 3.2.6 Page 19 Ref. [1]White cells are protected, as they calculate the values required by the sheet basedon the selected drop down option.

Axial

KP From KP ToAxial Friction

Coefficient

0 6.55 0.5

2.2 Pipeline Mechanical Properties

Young's modulus of Steel E 207000 MPa Turbulence Intensity Ic 5% Section 3.2.12 Page20 Ref. [1]

Steel density ρs 7850kg m3

Poisson's Ratio of Steel ν 0.3

Field joint infill density ρfj 1025 kg m3

Percentage of Pipeline Diameterused to Calculate Min. Span Gap

e0 30%

Nominal pipe joint length Lpj 12.2m Residual Lay Tension Heff 0kN

Concrete cutback length FJ 470mm Tide and Surge Tsurge 4.09m

SMYS SMYS 450MPa Design Pressure Pdes 0bar

SMTS SMTS 535MPa Operating Pressure Poper 0bar

Young's Modulus of Concrete Ec 30242.52MPa Reference Elevation for Pressure (LAT) elev 20.19m

Linear Thermal Expansion coefficient αe 11.7 106

°C1

Structural Damping ζstr 0.01 Section 6.2.11 Page31,Ref. [1]

Hydrodynamic Damping Section 4.1.8 ζh 0 Section 4.1.9 Page 23 Ref. [1]Steel loss during Operation CA 0%

Redefinition of dimension of user input vectors - Do not modify



Function to convert a distance to a matrix integer KP x( )

x

KPStep

Redefinition of vector dimensions - sheet extracts a large column of data for each variable; this process ensures only the required data set remains, and all theextra zeros on the end are removed.

Set case counter - find number of rows containing data forpipe / headings / bathy data

n_pipe max_find pipe_inputs 0 n_pipe 0.00ip 0 n_pipe

n_SF max_find Safety 0 n_SF 0.00

Trim each matrix such that they are the same size as theactual data set

pipe_inputs trim_rows pipe_inputs n_pipe( )

Safety trim_rows Safety n_SF( )

2.2.7 Pipe Section Data Allocation and Validity Checks

pipe_sec pipe_inputs0

Pipe Sections

pipe_start_kp pipe_inputs1

kmKP Start Points

KP End Points pipe_end_kp pipe_inputs2

km

Steel OD pipe_OD pipe_inputs3

mm

Steel WTtnom pipe_inputs

4 mm

Internal Coat thickness tint pipe_inputs5

mm

Internal Coating Density ρint pipe_inputs6

kg m3

Corrosion Allowance tcorr pipe_inputs7

mm

Corrosion Coating Thickness tcc pipe_inputs8

mm

Corrosion Coating Density ρcc pipe_inputs9

kg m3

Conctete Coating Thickness twc pipe_inputs10

mm

Concrete Coating Density ρwc pipe_inputs11

kg m3



Marine Growth Thicknesstmar pipe_inputs

12 mm

Marine Growth Density ρmar pipe_inputs13

kg m3

KP_input_check kps kpe( ) result 1

result result kpsii kpeii 1=

ii 1 last kps( )for last kps( ) 0if

"Section KP points incorrectly specified"

"KP inputs OK"

result

return

General function for checking KP input validity

KP_pipe_input_check KP_input_check pipe_start_kp pipe_end_kp( )

KP_pipe_input_check "KP inputs OK"2.2.8 Pipe Properties Data Allocation and Function Definition

Index values for vectors created x_v 0 1pipe_end_kplast pipe_end_kp( )

KPStep Length of the Pipe

Length pipe_end_kplast pipe_end_kp( )KP values to run calculation for KP_vx_v x_v KPStep

Length 6550.00 m

Function to find the index of the section which contains xUsed to transform section data into functions - i.e.replaces an interpolation function to find the value of avariable at any point along the route

x_find x end_val( ) ii 0

lst_val last end_val( )

ii ii 1

ii last end_val( ) x end_valiiwhile

iireturn

pipe_find x( ) x_find x pipe_end_kp( )

Pre-allocate row indices for the pipe section properties KP_indexPIx_v

pipe_find KP_vx_v

Steel OD Do x( ) pipe_ODKP_indexPIKP x( )



Steel WT tnom x( ) tnomKP_indexPIKP x( )

Internal Coat thicknesstint x( ) tintKP_indexPIKP x( )

Internal Coating Density ρint x( ) ρintKP_indexPIKP x( )

Corrosion Allowance tcorr x( ) tcorrKP_indexPIKP x( )

tcc x( ) tccKP_indexPIKP x( )Corrosion Coating Thickness

ρcc x( ) ρccKP_indexPIKP x( )Corrosion Coating Density

twc x( ) twcKP_indexPIKP x( )Conctete Coating Thickness

ρwc x( ) ρwcKP_indexPIKP x( )Concrete Coating Density

Marine Growth Thicknesstmar x( ) tmarKP_indexPIKP x( )

Marine Growth Density ρmar x( ) ρmarKP_indexPIKP x( )

Safety Class

Safety_start_kp Safety0

km

Safety_end_kp Safety1

km

Safety_find x( ) x_find x Safety_end_kp( )

KP_indexSCx_v

Safety_find KP_vx_v

Safety Classsafetyclass Safety

2 safety_class x( ) safetyclassKP_indexSCKP x( )

Integer Safety Class

S_C Safety3

SC x( ) S_CKP_indexSCKP x( )



Seabead properties n_SB max_find Seabed 0

n_SB 0.00last Safety_end_kp( ) 0.00

Seabed trim_rows Seabed n_SB( )

sea_start_kp Seabed0

kmSafety_end_kp0 6550.00 m

sea_end_kp Seabed1

km

Seabed 0.00 6.55 "Medium Sand" 1.00 "Medix_v 0 1

sea_end_kplast sea_end_kp( )

KPStep

KP_vx_v x_v KPStep

sea_find x( ) x_find x sea_end_kp( )Seabed 0.00 6.55 "Medium Sand" 1.00 "

KP_Sea_indexSBx_v

sea_find KP_vx_v

zo Seabed5

zo x( ) zoKP_Sea_indexSBKP x( )

Soil Seabed3

Soil x( ) SoilKP_Sea_indexSBKP x( )

Poisson's Ratio υsoil Seabed6

νsoil x( ) υsoilKP_Sea_indexSBKP x( )

Remove inputs from memory pipe_inputs 0 Safety 0 Seabed 0

Redefinition of dimension of user input vectors - Do not modify





2.3 Operational Data

2.3.1 Water Depth 2.3.2 Trench depth 2.3.3 Internal Pressure Profiles

water_depthKP

[km]Water Depth

[m]

0 37.71

0.01 37.7

0.02 37.7

0.03 37.7

0.04 37.69

0.05 37.69

trench_depthKP

[km]Trench Depth

[m]0 0

6.55 0

OpPresKP

[km]

OperatingPressure

[bar]

Design Pressure

[bar]0 0 0

6.55 0 0

2.3.4 Temperature Profiles 2.3.5 Density Profiles 2.3.6 Empirical KC Section 6.2.5 Page 30. Ref. [1]Temp

KP

[km]

OperatingTemperature

[0C]

DesignTemperature

[0C]0.00 0.00 0.006.55 0.00 0.00

Den

KP

[km]

Contents Density- Op

[kg/m-3]

Contents Density- De

[kg/m-3]0 0 0

6.55 0 0

Emp_KCKP

[km]Empirical KC

0 0.256.55 0.25



Effective Axial Force 2.3.7 Seawater Data 2.3.8 Manual Input - Effective Axial ForceSeffinput

Calculated (Fully Restrained)Manual Input

SaveSEFF "" 0

SWTemp

KP

[km]

Ambient Seawater

Temperature

[0C]

Density

[kg/m-3]

0 19.3 10256.55 19.3 1025

Seffman

KP

[km]

Effective Axial Force -

OPERATING[kN]

Effective AxialForce - DESIGN

[kg/m-3]

0 0 06.55 0 0

Equation to use for effective axial force

WallThick WallThin Wall Approximation (DNV OS F101)

SaveWall "" 0

Loadcase DurationLCinput

Less than 6 monthsMore than 6 months

SaveLC "" 0

Temperature FOR INSTALLATION - this is usedin order to calculate the fully restrained axial force

Pipe Properties Data Processing (No User Input Required)

n_WD max_find water_depth 0 n_WD 655.00

Water depth water_depth trim_rows water_depth n_WD( )

pipe_WD_KP water_depth0

km

pipe_WD water_depth1

m

WD x( ) linterp pipe_WD_KP pipe_WD x( )

Prseures n_OP max_find OpPres 0 n_OP 1.00

OpPres trim_rows OpPres n_OP( )

pipe_POP_KP OpPres0

kmAppendix 1: Free Span Analysis - 12inch Production Pipeline(As-Laid Case) Page 14/73


pop_KP OpPres1

bar

pdes_KP OpPres2

bar

Opreating Prseures Pope x( ) linterp pipe_POP_KP pop_KP x( ) Design Prseures Pde x( ) linterp pipe_POP_KP pdes_KP x( )

This value is using for ULS CheckContent Density

n_Den max_find Den 0 n_Den 1.00

Den trim_rows Den n_Den( )

pipe_Den_KP Den0

km

ρop_Den_KP Den1

kg m3

ρdes_Den_KP Den2

kg m3

Content density Ope ρop x( ) linterp pipe_Den_KP ρop_Den_KP x( ) Content density Des ρdes x( ) linterp pipe_Den_KP ρdes_Den_KP x( )

Temperature n_Tem max_find Temp 0

Temp trim_rows Temp n_Tem( )

pipe_Tem_KP Temp0

km

top_Tem_KP Temp1

°C

tde_Tem_KP Temp2

°C

Temperature Ope Top x( ) linterp pipe_Tem_KP top_Tem_KP x( ) Temperature Des TULS x( ) linterp pipe_Tem_KP tde_Tem_KP x( )



Seawater Temperature n_Sea max_find SWTemp 0

SWTemp trim_rows SWTemp n_Sea( )SWTemp

0.00

6.55

19.30

19.30

1025.00

1025.00

pipe_Tamb_KP SWTemp0

km

tamb_Tamb_KP SWTemp1

°Cpipe_Tamb_KP

0.00

6550.00

m

ρw_Tamb_KP SWTemp2

kg m3

Temperature of Seawater Tamb x( ) linterp pipe_Tamb_KP tamb_Tamb_KP x( ) Denity of water ρw x( ) linterp pipe_Tamb_KP ρw_Tamb_KP x( )

Prseures using for ULS Prseures Operation

pldULS x( ) Pde x( ) Pop x( ) Pope x( )

Empirical constant n_KC max_find Emp_KC 0

Emp_KC trim_rows Emp_KC n_KC( )

pipe_KC_KP Emp_KC0

km

KC Emp_KC1

Emp_KC0.00

6.55

0.25

0.25

kc x( ) linterp pipe_KC_KP KC x( )

Axial Friction n_soil max_find Axial 0 n_soil 0.00

Trim matrix such it is the same size as the actual data set Axial trim_rows Axial n_soil( ) Axial 0.00 6.55 0.50

Give each column of data a relevant name

Section Start Point soil_start Axial0

km



Section End Point soil_end Axial1

km

soil_find x( ) x_find x soil_end( )

Pre-allocate row indices for soil data KP_indexSDx_v

soil_find KP_vx_v

Axial Friction nguyax Axial2

μax x( ) nguyaxKP_indexSDKP x( )

Manual Input - Effective Axial Forcen_Seff max_find Seffman 0

n_Seff 1.00

Seffman trim_rows Seffman n_Seff( )

pipe_Seffm_KP Seffman0

km

Seffman0.00

6.55

0.00

0.00

0.00

0.00

Seffman_onset_KP Seffman

1 kN

Seffman_uls_KP Seffman2

kN

Seffman_onset x( ) linterp pipe_Seffm_KP Seffman_onset_KP x( )

Seffman_uls x( ) linterp pipe_Seffm_KP Seffman_uls_KP x( )

Trench depth n_trench max_find trench_depth 0

trench_depth trim_rows trench_depth n_trench( )

pipe_trench_KP trench_depth0

km

depth_trench_KP trench_depth1

m

dtrench x( ) linterp pipe_trench_KP depth_trench_KP x( )

Remove inputs from memory water_depth 0 OpPres 0 SWTemp 0 Den 0 Temp 0 Emp_KC 0 Axial 0 Seffman 0



trench_depth 0

Pipe Properties Data Processing (No User Input Required)

2.4 Code Data - Boundary Conditions, Safety Factors from DNV RP-F105

Pipe RoughnessTable 5.1 Section 5.4.4 Page 29 Ref. [1]

Span DefinitionTable 2.3, Section 2.6.2 Page 18 Ref. [1]

Span Boundary ConditionsTable 6.1 Section 6.7.8 Page 33 Ref. [1]

roughnessSteel, PaintedSteel, uncoated (not rusted)ConcreteMarine Growth

SaveSteelRough "" 0

Span_DefVery Well Defined - Survey DataWell Defined - FE analysisNot Well Defined

SaveSpan_Def "" 0

BCPinned-PinnedFixed-FixedSingle Span on the SeabedPinned-Fixed

SaveBC "" 0

λ1 1.3 fn12 2.7Ratio between first and secondmodes of crossflow vibrationMode Shape Weighting Factor Section 5.2.7 Page 28 Ref [1] Section 6.8.1 Page 34 Ref [1]



VIV Safety Factors Table 2.3 Section 2.6.2 Page 18 Ref [1] Screening Criteria Safety Factors Table 2.1, Section 2.6.1 Page 18γIL 1.4 γCF 1.4

γf

Low Normal HighVery well defined 1 1 1Well defined 1.05 1.1 1.15Not well defined 1.1 1.2 1.3

Free span typeSafety Class

Table 2-3 Safety factor for natural frequencies, γf

Table 2.3 Section 2.6.2, Page 18 Ref [1]

γf x c( ) γfSpan_Def SC x( ) c 0=if

1 otherwise

Safety Factors Table 2.2 Section 2.6.2, Page 18 Ref [1]

Stability parameter

η

γk

γs

γonIL

γonCF

Low Normal High

1 0.5 0.25

1 1.15 1.3

VIVULSVIVULSVIVULS

Safety ClassTable 2-2 General safety factors for fatigue

Safety Factor

η

γk

γs1.31

γon,IL

γon,CF

1.11

1.21

γk x c( ) γk0 SC x( )c 0=if

1 otherwise

For ULS criterion γf and γk are equal to 1. γk is also one for safety class low, i.e.temporary loadcases. For operational spanning, they vary as above.For screening, γf is not required, and is set to one in the calculations



Select Appropriate Safety Factors Table 6.1 Section 6.7.8, Page 33 Ref [1]Boundary condition coefficients

Fixed-pinned values for:C1 and C2 taken from DNV GL14C3 to C6 calibrated from literature and DNV GL14

C1

1.57

3.56

3.56

2.45

C2

1.0

4.0

4.0

2.0

C3

0.8

0.2

0.4

0.5

C4 L Leff( )

4.93

14.1

max 14.1 L

Leff

2 8.6

10.2

C5 L Leff( )

1

8

1

12

max 18 Leff

L

2 6

1

1

24

1

8

C6

5

384

1

384

1

384

2

384

C1 C1BC C2 C2BC C3 C3BC

C1 3.56 C2 4.00 C3 0.40

C4 L Leff( ) C4 L Leff( )BC C5 L Leff( ) C5 L Leff( )BC C6 C6BC C6 2.6042 103

2.5 Code Data - Safety Factors from DNV OS-F101

Material Fabrication Factor αfab 1 Table 5.7, Section 5 C307 Page 45 Ref [2]

Functional Load Factor γfLC 1.1 Table 4.4, Section 4 G201Page 39 Ref [2]

Material Resistance Factor γm 1.15 Table 5.4, Section 5 C205 Page 44 Ref [2]

Environmental Load Factor γE 1.3 Table 4.4, Section 4 G201 Page39 Ref [2]

Safety Class Factor γSC 1.04 Table 5.5 Section 5 C206 Page 44 Ref [2]

Condition Load factor γc 1.07 Table 4.5, Section 4, G203,Page 40 Ref [2]

Material Strength factor αU 0.96 Table 5.6 Section 5 C306 Page 45 Ref [2]

Ovality f0 1.5% Table 7.17 Section 4 G314Page 83 Ref [2]



2.6 Environmental Data

Sheet will calculate VIV onset lengths and ULS lengths based on the worst of the following combinations:10yr wave / 1yr current and 1yr wave / 10yr current for temporary cases.100yr wave / 10yr current and 10yr wave / 100yr current for the operating case.Should temporary cases extend beyond 6 months, then 10 year / 100 year data should be used.Note that the screening case considers long term current (10 yr for temporary cases less than 6 months, 100 yr otherwise) with 1 year wave. It is therefore suggested thatall three tables are filled in, to ensure all required data is present. If they are not all available it is conservative to e.g. consider 10year return period data for the 1year input.

RP_1year

KP From[km]

KP to[km]

Wave HightHs(m)

SpectralPeak

Period Tp[s]

Near-bottomvelocityUwd[m/s]

Mean ZeroUp-

CrossingPeriod Tu[s]

Wave /VelocityHeading

Øw(0)

Maximum Waveheight

Hmax[m]

AssociatedPeriodTmax[m]

Near-BottomVelocity

Umaxd[m/s]

Max Wave /

VelocityHeading

Ømax(0)

CurrentVelocityUc[m/s]

CurrentHeading

Øc(0)

0 6.55 3.5 7.8 90 6.94 7.13 90 0.23 90

RP_10year

KP From[km]

KP to[km]

Wave HightHs(m)

SpectralPeak

Period Tp[s]


Mean ZeroUp-



Øw(0)

Maximum Waveheight

Hmax[m]


Near-BottomVelocity

Umaxd[m/s]

Max Wave /

VelocityHeading

Ømax(0)


CurrentHeading

Øc(0)

0 6.55 5.5 10.6 90 10.58 9.65 90 0.53 90



RP_100year

KP From[km]

KP to[km]

Wave HightHs(m)

SpectralPeak

Period Tp[s]


Mean ZeroUp-



Øw(0)

Maximum Waveheight

Hmax[m]


Near-BottomVelocity

Umaxd[m/s]

Max Wave /

VelocityHeading

Ømax(0)


CurrentHeading

Øc(0)

0 6.55 8 14.1 90 14.78 12.79 90 0.73 90

current_data

1 year 10 year 100 year

Height at which Velocity Given zc m 1 1 1

RETURN PERIODPARAMETER VARIABLE UNITS

Data Processing (No User Input Required)

For 1 year Period


Set case counter - find number of rowscontaining data

n_RP1 max_find RP_1year 0

Trim matrix such it is the same size as the actual data set RP_1year trim_rows RP_1year n_RP1( )

KP Starts RP_start_kp1 RP_1year0

km

KP Ends RP_end_kp1 RP_1year1

km



KP index for spectral input table spec_find1 x( ) x_find x RP_end_kp1( )

KP_indexspec1x_v

spec_find1 KP_vx_v RP_1year 0.00 6.55 3.50 7.80 0.0

JONSWAP Spectral Parameters

JONSWAP Significant Wave Height HS_1 RP_1year2

m HS_1 x( ) HS_1KP_indexspec1KP x( )

JONSWAP Peak Wave Period Tp_1 RP_1year3

s Tp_1 x( ) Tp_1KP_indexspec1KP x( )

Near-bottom velocity Uw1_sig_input RP_1year4

m s1

Uw1sig_input x( ) Uw1_sig_inputKP_indexspec1KP x( )

Mean Zero Up-Crossing Period Tu_1_input RP_1year5

s Tu_1_input x( ) Tu_1_inputKP_indexspec1KP x( )

Max Near-bottom velocity Uw1_max_input RP_1year9

m s1

Uw1max_input x( ) Uw1_max_inputKP_indexspec1KP x( )

Angle between Wave and Pipeline Heading: θw_1_calcsig RP_1year6

deg θw_1_sig x( ) θw_1_calcsigKP_indexspec1KP x( )

Extreme Wave Parameters

Expected Max Single Wave Height Hmax_1 RP_1year7

m Hmax_1 x( ) Hmax_1KP_indexspec1KP x( )

Assoc Period of EHmax THmax1 RP_1year8

s Tmax_1 x( ) THmax1KP_indexspec1KP x( )

Angle between Wave and Pipeline Heading: θw_1_max RP_1year10

deg θw_1_max x( ) θw_1_maxKP_indexspec1KP x( )

General Current Parameters




Steady Current Uc1 RP_1year11

m s1

Uc_1 x( ) Uc1KP_indexspec1KP x( )

Angle between Current andPipeline Heading:

θc1 RP_1year12

deg θc_1 x( ) θc1KP_indexspec1KP x( )

For 10 year Period






km


km


KP_indexspec10x_v

spec_find10 KP_vx_v











m s1





m s1











m s1



θc10 RP_10year12


For 100 year Period






km




km


KP_indexspec100x_v

spec_find100 KP_vx_v









m s1





m s1













m s1



θc100 RP_100year12


Height at which Velocity Given



n_curr100 max_find current_data 0 n_curr100 0.00

Trim matrix such it is the same size as the actual data set current_data trim_rows current_data n_curr100( ) current_data 1.00 1.00 1.00

Reference Height (for waves/ currents) zr_c_1 current_data( )0 0 zr_c_1 1.00

zr_c_10 current_data0 1 zr_c_10 1.00

zr_c_100 current_data0 2 zr_c_100 1.00

Remove inputs from memory current_data 0 RP_100year 0 RP_10year 0 RP_1year 0

Data Processing (No User Input Required)



3.0 INITIAL CALCULATIONSIntial Calculation

3.1 Backgound Values for Calculations

L 5m Translate distance used in functions to equivalent integer value KP x( )x

KPStepGuess value for span length

z 0 1 Length

KPStep Two environmental conditions are considered.

This integer is used to store the values for the pair.Integer for calculation points y 0 1

kpz z KPStep Holds the vectors for operating (VIV) and design (ULS) values c 0 1

3.2 Submerged Weight Calculation

Wall thickness t2 x( ) tnom x( ) CA tcorr x( ) Inside Diameter Di x( ) Do x( ) 2 tnom x( ) tint x( ) Used for ULS checks

Total Diameter Dt x( ) Do x( ) 2 tcc x( ) 2 twc x( ) 2 tmar x( ) Concrete Diameter Dc x( ) Do x( ) 2 tcc x( ) 2 twc x( )

Concrete diameter is used for flow velocity calculations - velocities are calculated at the pipe centreline,which will not be moved relative to the seabed by the addition of marine growth.Steel Inner Diameter Dsi x( ) Di x( ) 2 tint x( )

Second Moment of areaOf Steel

lsz

πDo kpz 4 Dsi kpz 4

64 Second Moment of area

Of Concretelconc x( ) π

Dc x( )4

Dc x( ) 2 twc x( ) 4

64

Area of steel As x( )π

4Do x( )

2Dsi x( )

2

Weight of steel Ws x( ) As x( ) ρs g Lpj

Ai x( )π

4Di x( )

2Internal Cross Section Area Weight of Contents Wc x c( ) ρc x( ) ρop x( ) c 0=if

ρdes x( ) c 1=if

Wc Ai x( ) ρc x( ) g Lpj

Wc

Wic x( )π

4Dsi x( )

2Di x( )

2

ρint x( ) g LpjWeight of Internal Coating

Weight of Field Joint Wfj x( )π

4Dc x( )

2Do x( ) 2 tcc x( ) 2

ρfj g 2 FJ



Weight of Corrsion Coat Wcc x( )π

4Do x( ) 2 tcc x( ) 2 Do x( )

2

ρcc x( ) g Lpj

Buoyancy per metre Fb x( )π

4Dt x( )

2 ρw x( ) g Buoyancy per joint FBuoy x( ) Fb x( ) Lpj

Weight of Concrete Coating Wwc x( )π

4Dc x( )

2Do x( ) 2 tcc x( ) 2

ρwc x( ) g Lpj 2 FJ

Weight of Marine Growth Wm x( )π

4Dt x( )

2Dc x( )

2

ρmar x( ) g Lpj

Span Gap e0 x( ) e0 Dc x( )

Submerged Weight(passed into a vector) Wsub x c( )

Wc x c( ) Ws x( ) Wcc x( ) Wm x( ) Wwc x( ) Wic x( ) Wfj x( ) FBuoy x( )

Lpj

Wsubz c

Wsub kpz c



0 2 4 60

20

40

60

80

37.2

37.4

37.6

37.8

Normal Wall ThicknessAnti-corrosion Coating ThicknessConcrete Coating ThicknessInternal Coating ThinknessCorrosion AllowanceWater Depth

Wall Thickness

Distance Along Pipeline (km)

Thic

knes

s (m

m)

Wat

er D

epth

(m)



0 2 4 61

0.5

0

0.5

1

37.2

37.4

37.6

37.8

Operating PressureDesign PressureWater Depth

Pressure Profile


Pres

sure

(bar

g)

Wat

er D

epth

(m)



0 2 4 60

5

10

15

20

37.2

37.4

37.6

37.8

Operating TemperatureDesign TemperatureAmbient TemperatureWater Depth

Temperature Profile


Tem

pera

ture

(°C)

Wat

er D

epth

(m)



0 2 4 6987

987.417

987.833

988.25

988.667

989.083

989.5

Submerged Weight (VIV)Submerged Weight (ULS)

Submerged Weight


Subm

erge

d W

eigh

t (k

N)

3.3 Required ValuesSection 6.2.5 Page 30 Ref. [1]

Concrete Stiffness Enhancement Factor CSF x( ) kc x( )Ec lconc x( )

E lsKP x( )

0.75

Effective Mass me Ca x c( )

WsubKP x( ) c

Fb x( )

gCa

π

4 Dt x( ) 2 ρw x( )

Pcr L x( )

1 CSF x( ) C2 π2

E lsKP x( )

L2

Section 1.14.1 Page 11 Ref. [1]Critical Buckling Load



Leff L K x( ) L

β logK 30 Do x( ) 4

1 CSF x( ) E lsKP x( )

L 30 Do x( )if

logK L

4

1 CSF x( ) E lsKP x( )

L 30 Do x( )if

4.73

0.066 β2 1.02β 0.63

β 2.7if

4.73

0.036β2 0.61β 0.63

β 2.7if

BC 2=if

1 BC 2if

Section 6.7.9 Page 33 Ref. [1]Function for Effective Span Length

Euler (Bar) buckling length limit Eulerlimit K x Seff( ) 200 Do x( ) Pop x( ) 0=if

root Pcr Leff L K x( ) x( ) Seff L otherwise



3.4 Effective Axial Force

μaxz

μax kpz Axial Friction

Sfr x c( ) Pi x( ) Pop x( )

ΔT x c( ) max 0 °C Top x( ) Tamb x( ) c 0=if

max 0 °C TULS x( ) Tamb x( ) c 1=if

Seff Heff 1 2 ν Pi x( )π

4 Di x( )

2 αe ΔT x c( ) E As x( ) Seffinput 0= Wall 1=if

Heff Pi x( )π

4 Di x( )

2 2 Pi x( ) ν

As x( )

4

Dsi x( )

tnom x( )1

αe ΔT x c( ) E As x( ) Seffinput 0= Wall 0=if

Seffman_onset x( ) c 0=if

Seffman_uls x( ) otherwise

Seffinput 1=if

Seffreturn

Limiter to ensure no negativetemperature assumed for temporarycases

Section 6.4.3 Page 31 Ref. [1]

Return a vector for fully restrainedforce along the line

Sfrz c

Sfr kpz c

Pipeline Section from KP 0 to KP 2.18

z1 0 1 round2180m

KPStep

Total Friction Force available from left hand end εlH1z1 c

if z1 0 μaxz1

Wsubz1 c

KPStep εlH1

z1 1 c 0

Total Friction Force available from right hand endεrH1

c

εfCy if y round2180m

KPStep

= 0 μaxy

Wsuby c

KPStep εfCy 1

y round2180m

KPStep

round2180m

KPStep

1 0for



Fff1z1 c

max εlH1z1 c

εrH1z1 c

Pipeline Section from KP 2.18 to KP 4.36

z2 round2180m

KPStep

round2180m

KPStep

1 round4360m

KPStep


if z2 round2180m

KPStep

μaxz2

Wsubz2 c

KPStep εlH2

z2 1 c 0


c


KPStep

= 0 μaxy

Wsuby c

KPStep εfCy 1

y round4360m

KPStep

round4360m

KPStep

1 round2180m

KPStep

for

Fff2z2 c

max εlH2z2 c

εrH2z2 c



Pipeline Section from KP 4.36 to KP 6.55z3 round

4360m

KPStep

round4360m

KPStep

16550m

KPStep


if z3 round4360m

KPStep

μaxz3

Wsubz3 c

KPStep εlH3

z3 1 c 0


c


KPStep

= 0 μaxy

Wsuby c

KPStep εfCy 1

y round6550m

KPStep

round6550m

KPStep

1 round4360m

KPStep

for

Fff3z3 c

max εlH3z3 c

εrH3z3 c



Total Friction Force Fff

z cFff1

z c0 z round

2180m

KPStep

if

Fff2z c

round2180m

KPStep

z round4360m

KPStep

if

Fff3z c

otherwise

Effective axial force is the lesser of friction force or full restraint force. Seffz c

max Fffz c

Sfrz c

0 2 4 61

0.5

0

0.5

1

Fully Restrained Effective Axial ForceActual Effective Axial Force

Effective axial force

Effective axial force (kN)

Pres

sure

(bar

g)



WDt x( ) WD x( ) TsurgeTotal Water depth

Pe x( ) WDt x( ) g ρw x( )External Pressure

Pipe Surface Roughness kpipe x( ) kp 0.005m tmar x( ) 0mmif

kpipe m otherwise

kp

Intial Calculation

4.0 Metocean Calculations 4.1 Wave Spectra

Wave Induced Velocities - Heights and Periods

4.1.1 JONSWAP Spectrum

Angular Spectral Peak Frequency ωp Tp( )2 π

Tp JONSWAP Peak

Enhancement Factorχunit Hs Tp( )

Tp

Hs

m0.5

sec Section 3.3

Peak Enhancement Factor γ Hs Tp( ) if χunit Hs Tp( ) 3.6 5 if 3.6 χunit Hs Tp( ) 5 e5.75 1.15 χunit Hs Tp( )

1

Section 3.3.3 Ref. [1]

Generalised Phillips' Constant αp Hs Tp( )5

16

Hs2

ωp Tp( )4

g2

1 0.287 ln γ Hs Tp( )( ) Section 3.3.3 Page 20 Ref. [1]

Spectral Width Parameter sigma ω Tp( ) if ω ωp Tp( ) 0.07 0.09

Wave Number Start value k 1 m1

k ω x( ) root k WD x( )ω

2WD x( )

gcoth k WD x( )( ) k

Section 3.3.5

Frequency Transfer Function G ω x( )ω cosh k ω x( ) Dc x( ) e0 x( )

sinh k ω x( ) WD x( )( )k ω x( ) WD x( ) 707if

0 otherwise




Spectral Density Function Sηη ω Hs Tp( ) αp Hs Tp( ) g2

ω5

e

5

4ω

ωp Tp( )

4

γ Hs Tp( )e

0.5ω ωp Tp( )

sigma ω Tp( ) ωp Tp( )

2

Section 3.3.3

Wave induced velocity spectrum SUU ω Hs Tp x( ) G ω x( )2

Sηη ω Hs Tp( ) Section 3.3.5

Spectral MomentsSection 3.3.6 Page 21 Ref. [1] M0 Hs Tp x( )

0s1

∞ s1

ωSUU ω Hs Tp x( )

d M2 Hs Tp x( )

0s1

∞ s1

ωSUU ω Hs Tp x( ) ω2

d

Significant Flow Velocity atPipe Centreline Us Hs Tp x( ) 2 M0 Hs Tp x( ) Section 3.3.6 Page 21 Ref. [1]

Zero Up Crossing Period Tu Hs Tp x( ) 2 πM0 Hs Tp x( )

M2 Hs Tp x( ) Section 3.4.4 Page 21 Ref. [1]

Wave energy spreading function kw s( )1π

Γ 1 s

2

Γ1

2s

2

w β s( ) kw s( ) cos β( )s

βπ

2if

0 otherwise

Wave directionality and spreading reduction factor for each wave direction

Section 3.4.3 Page 21 Ref. [1]RD θw x RD 0

rdπ

2

π

2βw β s( ) sin θw β 2

d

RD rd rd RDif

s 2 3 8for

1 Year significant wave velocity Uw1_sig_calc x( ) RD θw_1_sig x( ) x Us HS_1 x( ) Tp_1 x( ) x



1 Year significant wave velocityTu_1_sig x( ) Tu HS_1 x( ) Tp_1 x( ) x

10 Year significant wave velocityUw10_sig_calc x( ) RD θw_10_sig x( ) x Us HS_10 x( ) Tp_10 x( ) x

10 Year zero up-crossing period Tu_10_sig x( ) Tu HS_10 x( ) Tp_10 x( ) x

100 Year significant wave velocity Uw100_sig_calc x( ) RD θw_100_sig x( ) x Us HS_100 x( ) Tp_100 x( ) x

100 Year zero up-crossing period Tu_100_sig x( ) Tu HS_100 x( ) Tp_100 x( ) x

4.2 Short term wave conditions - Linear Wave Theory

Wave length λ Tmax x( ) rootg

2π λtanh

2π WD x( )

λ

1

2

Tmax λ 1m 1000m

Section 3.2.2.3, Page 25 Ref. [5]Wave Number k Tmax x( )

2π

λ Tmax x( )

Maximum Wave Induced Water ParticleVelocity - calculated at the top of pipe. Uwmax Hmax Tmax x( ) 0m s

1

π Hmax

Tmax

cosh k Tmax x( ) Dt x( ) sinh k Tmax x( ) WD x( )( )[ ]on error Table 3-1 Section 3.5.2.6, Page 32 Ref. [5]

1 Year maximum wave velocity Uw1_max_calc x( ) RD θw_1_max x( ) x Uwmax Hmax_1 x( ) Tmax_1 x( ) x

10 Year maximum wave velocity Uw10_max_calc x( ) RD . θw_10_max x( ) x Uwmax Hmax_10 x( ) Tmax_10 x( ) x

100 Year maximum wave velocity Uw100_max_calc x( ) RD θw_100_max x( ) x Uwmax Hmax_100 x( ) Tmax_100 x( ) x

Wave Induced Velocities - Heights and Periods



Wave - Induced Velocities - Input at Given Reference Height

4.3 Wave-Induced Velocity Directional Calculation

Collapse this section if wave heights and periods are input. It is not required, and nor are the results used.

Significant Wave Velocity Maximum Wave Velocity

1 Year Uw1_sig_dir x( ) RD θw_1_sig x( ) x Uw1sig_input x( ) Uw1_max_dir x( ) RD θw_1_max x( ) x Uw1max_input x( )



Significant Wave Velocity Zero Up-Crossing Period

1 Year Uw_1z

Uw1_sig_dir z KPStep( ) HS_1 z KPStep( ) 0=if

Uw1_sig_calc z KPStep( ) otherwise

Tu_1z

Tu_1_sig z KPStep( ) Tu_1_input z KPStep( ) 0=if

Tu_1_input z KPStep( ) otherwise

10 Year Uw_10z



Tu_10z



100 Year Uw_100z



Tu_100z



Maximum Wave Velocity

1 Year Uw_max_1z

Uw1_max_dir z KPStep( ) Hmax_1 z KPStep( ) 0=if

Uw1_max_calc z KPStep( ) otherwise



10 Year Uw_max_10z



100 Year Uw_max_100z



Wave - Induced Velocities - Input at Given Reference Height

Current Velocities

4.4 Current Velocity Directional Calculation

Reduction Factor Rc θc sin θc Elevation aboveseabed

zed x( )e0 x( ) 0.5 Dc x( )

m Section 3.4.1 Page 21 Ref. [1]

For current in the inner zone, assuming logarithmic profile - refer to Section 3.2.6 Page 19 Ref. [1]

Average current velocity across the pipeassuming a total pipe diameter Dt :

Uc U θc zr x Rc θc Uln zed x( )( ) ln zo x( )

ln zr ln zo x( ) Section 3.2.6 Page 19 Ref. [1]

1 Year Current Uc_1z

Uc Uc_1 z KPStep( ) θc_1 z KPStep( ) zr_c_1 z KPStep





Current Velocities

5.0 SOIL PARAMETERS



Soil Calculation

5.1 Definition of Dynamic and Static Soil Stiffnesses

Crossflow added mass coefficient

CV0

CL0

KV0

CV CL KV,S

(kN/m5/2) (kN/m5/2) (kN/m/m)Loose 10500 9000 250Medium 14500 12500 530Dense 21000 18000 1350Very Soft 600 500 50 - 100Soft 1400 1200 160 - 260Firm 3000 2600 500 - 800Stiff 4500 3900 1000 - 1600Very Stiff 11000 9500 2000 - 3000Hard 12000 10500 2600 - 4200

Sand

Clay

Table 7-5 and Table 7-6 Dynamic stiffness factor and static stiffness for pipe-soil interaction in sand and clay.

Soil Type


CoeffCFRES

2

2.5

8

8.5

10

1

5.5

0

0.5

0.5

KvSTAT x( ) KVSoil x( )

kN m2

CaCF Vrxf( ) linterp CoeffCFRES0

CoeffCFRES1

Vrxf

5.2 Modal Damping Ratios NB Simplified soils damping criteria is used for this calculation

soil x( ) if Soil x( ) 2 Soil x( ) if Soil x( ) 4 3 if 4 Soil x( ) 6 4 if 6 Soil x( ) 8 5 "error" Create correct soil type reference integer

L/D Ratio - to reduce sizeof below matrices

R L x( )L

Dt x( )



Table 7-3 Modal soil damping ratios (in %) for sand.

L/D L/D<40 100 >160 <40 100 >160

Loose 3.0 2.0 1.0 2.0 1.4 0.8Medium 1.5 1.5 1.5 1.2 1.0 0.8Dense 1.5 1.5 1.5 1.2 1.0 0.8

Horizontal (in-line) direction

Vertical (cross-flow) directionType

Table 7-4 Modal soil damping ratios (in %) for clay.

L/D L/D<40 100 >160 <40 100 >160

Very Soft - Soft 4.0 2.0 1.0 3.0 2.0 1.0Firm - Stiff 2.0 1.4 0.8 1.2 1.0 0.8Very Stiff - Hard 1.4 1.0 0.6 0.7 0.6 0.5

Horizontal (in-line) direction

Vertical (cross-flow) directionClay Type

The values given in Table 7-3 and Table 7-4 above are interpolated below to give accurate soil damping values

ζs.in L x c( )

if R L x( ) 40 3 if R L x( ) 160 1 3R L x( ) 40

60

1.5

1.5

if R L x( ) 40 4 if R L x( ) 160 1 4R L x( ) 40

60

if R L x( ) 40 2 if R L x( ) 160 0.8 2R L x( ) 40

100

if R L x( ) 40 1.4 if R L x( ) 160 0.6 1.4R L x( ) 40

150

%ζs.xf L x c( )

if R L x( ) 40 2 if R L x( ) 160 0.8 2R L x( ) 40

100

if R L x( ) 40 1.2 if R L x( ) 160 0.8 1.2R L x( ) 40

300

if R L x( ) 40 1.2 if R L x( ) 160 0.8 1.2R L x( ) 40

300

if R L x( ) 40 3 if R L x( ) 160 1 3R L x( ) 40

60

if R L x( ) 40 1.2 if R L x( ) 160 0.8 1.2R L x( ) 40

300

if R L x( ) 40 0.7 if R L x( ) 160 0.5 0.7R L x( ) 40

600

%

Total damping ratiosSection 4.1.9 Ref. [1]

Inline ζT.inline L x c( ) ζstr ζs.in L x c( )soil x( )

ζh

Crossflow ζT.xflow L x c( ) ζstr ζs.xf L x c( )soil x( )

ζh

Soil Calculation



6.0 ONSET SPAN LENGTHS

6.1 Onset Reduced Velocities

Current flow ratio - Section 4.1.7

ααtz

Uc_10z

Uc_10z

Uw_1z

ααo

z

Uc_100z

Uc_100z

Uw_1z

Temporary Screening Operating Screening

Screening Current : wave ratio Guidance Note, Section 2.3.1, Page 15 Ref. [1]

Screening Current Ucscrz

Uc_10z

LCinput 0=if

Uc_100z

otherwise

ααscrz

ααtz

LCinput 0=if

ααoz

otherwise

Temporary Onset Operating Onset

Check both 10yr wave / 1yr current and 1yr wave / 10yr current Check both 100yr wave / 10yr current and 10yr wave / 100yr current

ααoiaz

Uc_1z

Uc_1z

Uw_10z

ααoib

z

Uc_10z

Uc_10z

Uw_1z

ααoa

z

Uc_10z

Uc_10z

Uw_100z

ααob

z

Uc_100z

Uc_100z

Uw_10z



Selection of correct wave and current velocities, along with current:wave ratio.

Wave induced velocities Current velocities Current : wave ratio

Uwonsetz y

Uw_10z

y 0=if

Uw_1z

y 1=if

LCinput 0=if

Uw_100z

y 0=if

Uw_10z

y 1=if

LCinput 1=if

Uconsetz y

Uc_1z

y 0=if

Uc_10z

y 1=if

LCinput 0=if

Uc_10z

y 0=if

Uc_100z

y 1=if

LCinput 1=if

ααonz y

ααoiaz

y 0=if

ααoibz

y 1=if

LCinput 0=if

ααoaz

y 0=if

ααobz

y 1=if

LCinput 1=if

1 year / 10 year data ifduration less than 6 months

10 year / 100 year data ifduration longer than 6 months

Buoyancy ratio ρsratio x c( )

WsubKP x( ) c

Fb x( )

Fb x( ) Inline Added Mass Coefficient Ca x( ) 0.68

1.6

1 5e0 x( )

Dt x( )

e0 x( )

Dt x( )0.8if

1 otherwise


Also Section 3.2.15 Page 20 Ref. [1]

6.2 Reduced Velocities

Inline Stability Parameter Cross-Flow Onset Vibration Reduced Velocity

Section 4.4.6 Page 26 Ref. [1]Ksin L x c( )

4π me Ca x( ) x c ζT.inline L x c( )

ρw x( ) Dt x( ) 2 γk x c( )

ψproxi x( )1

54 1.25

e0 x( )

Dt x( )

e0 x( )

Dt x( )0.8if

1 otherwise



In-line Onset Vibration Reduced Velocity Section 4.3.5 Ref. [1] Section 4.4.7 Page 26 Ref. [1]

VRILon L x c( )1.0

γonILc

Ksin L x c( ) 0.4if

0.6 Ksin L x c( )

γonILc

0.4 Ksin L x c( ) 1.6if

2.2γonIL

c

otherwise

ΔID x( ) dD min1.25 dtrench x( ) e0 x( )

Do x( )1

dtrench x( ) 0mif

dD 0 dtrench x( ) 0mif

ψtrench x( ) 1 0.5 ΔID x( )

VRCFon x c( )3 ψproxi x( ) ψtrench x( )

γonCFc

Crossflow Stability Parameter Section 4.1.8 Page 23 Ref. [1]

Kscf L x c( )4π me CaCF VRCFon x c( ) x c ζT.xflow L x c( )

ρw x( ) Dt x( ) 2 γk x c( )

Section 7.4.10 Page 37 Ref. [1]Modified Soil Stiffnesses

Inline KIL x c( ) CLSoil x( )

kN m2.5

1 νsoil x( ) 2

3ρsratio x c( )

1

3

Dt x( ) Crossflow KCF x c( )

CVSoil x( )

kN m2.5

1 νsoil x( )

2

3ρsratio x c( )

1

3

Dt x( )

6.3 Inline Vibration Onset Span Lengths

Simplify formulae me_ILz

me Ca kpz kpz 0 Leff_IL L x( ) Leff L KIL x 0 x EulILz

Eulerlimit KIL kpz 0 kpz Seffz 0

The frequency is a function of the loadcase (represented by x), the span length (L) and the environmental conditions (y). Static deflection ignored for inline direction

Inline Structural Frequency Section 6.7.2 Page 32 Ref. [1] Inline Onset Frequency Section 4.1.5 Page 23 Ref. [1]

IL1 L x( ) C1 1 CSF x( )E ls

KP x( )

me_ILKP x( )

Leff_IL L x( )4

1Seff

KP x( ) 0

Pcr Leff_IL L x( ) x

IL2 L x y( ) γf x 0 Uconset

KP x( ) yUwonset

KP x( ) y

VRILon L x 0 Dt x( )



At the onset of VIV the two frequencies are equal. The other boolean expressions assist in making the calculation robust

Given Im L( ) 0= L 0m L EulILKP X( )

IL1 L X( ) IL2 L X Y( )= LILon L X Y( ) Find L( )

Find the minimum span length from the two environmental conditions for each loadcase

LILonerrz y

1000 m Lil 30m z 0=if

Lil LILonerrz 1 y

otherwise

Lil2 LILon Lil z KPStep y( )return

on error

IL2 15m 0.5km y 1.52

1.27

s1.00

LILon_matz y

LILonerrz y

0.999 Re

IL1 LILonerrz y

kpz IL2 LILonerr

z ykpz y

1.001if

1000m LILonerrz y

otherwise

LILonz

min LILon_matz 0

LILon_matz 1

Due to the nature of the equations specified by DNV, a solution is not always attainable. The Find command may not therefore always return a solution.



0 2 4 620.5

20.65

20.8

Inline Span Length (Onset Criteria)

Inline Vibration Onset Span Lengths

KP (km)

Min

imum

Allo

wabl

e Sp

an L

engt

h (m

)

Represent above results in graphical form

6.4 Crossflow Vibration Onset Span Lengths

Deflection Load per unit length, taken as weight per unit length qz c Wsubz c

Section 6.7.2 and Section 6.7.7 Page 32-33 Ref. [1]



Simplify formulae me_CF x( ) me CaCF VRCFon x 0 x 0 Leff_CF L x( ) Leff L KCF x 0 x EulCFz

Eulerlimit KCF kpz 0 kpz Seffz 0

Crossflow Structural Frequency

CF1 L x( ) C1 1 CSF x( )E ls

KP x( )

me_CF x( ) Leff_CF L x( )4

1Seff

KP x( ) 0

Pcr Leff_CF L x( ) x C3

C6

qKP x( ) 0 Leff_CF L x( )

4

E lsKP x( )

1 CSF x( )

1

1Seff

KP x( ) 0

Pcr Leff_CF L x( ) x

Dt x( )

2

Crossflow Onset Frequency CF2z y γf kpz 0 Uconset

z yUwonset

z y

VRCFon kpz 0 Dt kpz Section 4.1.5 Page 23 Ref. [1]

At the onset of VIV the two frequencies are equal. The other boolean expressions assist in making the calculation robust

Given L 0m CF1 L X( ) CF2KP X( ) Y= L EulCFKP X( )

Im L( ) 0=L

CF1 L X( )d

d0 LCFon L X Y( ) Find L( )

Solve to find onset length

LCFonerrz y

1000 m Lcf 30m z 0=if

Lcf LCFonerrz 1 y

otherwise

LCFon Lcf z KPStep y( )return

on error

LCFon_matz y

LCFonerrz y

0.999 Re

CF1 LCFonerrz y

kpz CF2z y

1.001if

1000m LCFonerrz y

otherwise

LCFonz

min LCFon_matz 0

LCFon_matz 1



0 2 4 626.6

26.75

26.9

CrossFlow Span Length (Onset Criteria)

Crossflow Vibration Onset Span Lengths

KP (km)

Min

imum

Allo

wabl

e Sp

an L

engt

h (m

)

6.0 SCREENING Screening Criteria

6.1 Inline

Compare Frequency calculation for effective span length and actual span length Section 2.3.3 Page 15 Ref. [1]

ILscr L x( )

UcscrKP x( )

VRILon L x 0 Dt x( )1 L

250 Dt x( )

1

ααscrKP x( )

γIL Range of Applicability Table 1.1



Given Im L( ) 0= ILscr L X( ) IL1 L X( )= 0m Leff_IL L X( ) 200 Do X( ) L 0mL

IL1 L X( )d

d

0 L EulILKP X( )

Lilsc L X( ) Find L( )

LILscrerrz

1000 m Lil 25m z 0=if

Lil LILscrerrz 1

otherwise

Lilsc Lil z KPStep( )return

on error LILscrz

LILscrerrz

0.999 Re

ILscr LILscrerrz

kpz IL1 LILscrerr

zkpz

1.001if

1000m LILscrerrz

otherwise



0 2 4 622.3

22.35

22.4

22.45

22.5

Inline Span Length (Screening Criteria)

Inline Vibration Screening Span Lengths

KP (km)

Min

imum

Allo

wabl

e Sp

an L

engt

h (m

)

6.2 Crossflow

Crossflow screening requirement CFsrcz

Ucscrz

Uw_1z

VRCFon z KPStep 0 Dt z KPStep( )γCF Section 2.3.4 Page 15 Ref. [1]

Given CFsrcKP X( ) CF1 L X( )= L 0mL

CF1 L X( )d

d

0 L EulILKP X( )

Im L( ) 0= Lxfsc L X( ) Find L( )

LCFscrerrz

1 m Lcf 30m z 0=if

Lcf LCFscrerrz 1

otherwise

Lxfsc Lcf z KPStep( )return

on error LCFscrz

LCFscrerrz

0.999 Re

CF1 LCFscrerrz

z KPStep CFsrcz

1.001if

1000m LCFscrerrz

otherwise



0 2 4 625.8

25.838

25.875

25.913

25.95

Crossflow Span Length (Screening Criteria)

Crossflow Vibration Screening Span Lengths

KP (km)

Min

imum

Allo

wabl

e Sp

an L

engt

h (m

)

Screening Criteria

7.0 SIMPLIFIED ULS CRITERION CHECK ULS Criteria

7.1 Current Conditions

Dynamic stress calculations consider significant wave height and zero up-crossing period. Static (or instantaneous) stresses, are found using maximum wavevelocities and associated periods. Code requirement is that the worse of 100yr wave / 1yr current or 1yr wave / 100yr current is considered for the operating case(Section 2.5.5). 100 year return period can be reduced to 10 year if duration of loadcase is less than 6 months.

Currents Significant Wave velocity Significant Wave Heading



UcULSz y

Uc_1z

y 0=if

Uc_100z

LCinput 1=if

Uc_10z

otherwise

y 1=if

UwsigULSz y

Uw_1z

y 1=if

Uw_100z

LCinput 1=if

Uw_10z

otherwise

y 0=if

θrel_sigz y

θw_1_sig z KPStep( ) y 1=if

θw_100_sig z KPStep( ) LCinput 1=if

θw_10_sig z KPStep( ) otherwise

y 0=if

Spectral Peak Periods Maximum Wave Heading

TuULSz y

Tu_1z

y 1=if

Tu_100z

LCinput 1=if

Tu_10z

otherwise

y 0=if

θrel_maxz y

θw_1_max z KPStep( ) y 1=if

θw_100_max z KPStep( ) LCinput 1=if

θw_10_max z KPStep( ) otherwise

y 0=if

Single Wave Associated Period

UwmaxULSz y

Uw_max_1z

y 1=if

Uw_max_100z

LCinput 1=if

Uw_max_10z

otherwise

y 0=if

TwmaxULSz y

Tmax_1 z KPStep( ) y 1=if

Tmax_100 z KPStep( ) LCinput 1=if

Tmax_10 z KPStep( ) otherwise

y 0=if



Combined Current Velocity UtotULSz y

UcULSz y

UwsigULSz y

Flow Regime Velocity ratio αULS x y( )

UcULSKP x( ) y

UtotULSKP x( ) y

KC No. KCuls x y( )

UwsigULSKP x( ) y

Dt x( )TuULS

KP x( ) y

Limiting span for whichresults can be found

Eulerlimit x( ) min 200 Do x( ) Eulerlimit KvSTAT x( ) x SeffKP x( ) 1

Unit Diameter Stress Amplitude

AIL L x( ) C4 L Leff L KvSTAT x( ) x( )( )1 CSF x( ) Dt x( ) Do x( ) tnom x( ) E

L2

Section 6.7.5 Page 33 Ref. [1]Inline

Cross - flow ACF L x( ) C4 L Leff L KvSTAT x( ) x( )( )1 CSF x( ) Dt x( ) Do x( ) tnom x( ) E

L2

7.2 Cross Flow Response Model Section 4.4.4 RP F105

Simplify Formulae meCFULS x( ) me CaCF VRCFon x 1 x 1 LeffCFULS L x( ) Leff L KCF x 1 x

CFULS L x( ) C1 1 CSF x( )E ls

KP x( )

meCFULS x( ) LeffCFULS L x( )4

1Seff

KP x( ) 1

Pcr LeffCFULS L x( ) x C3

C6

qKP x( ) 1 LeffCFULS L x( )

4

E lsKP x( )

1 CSF x( )

1

1Seff

KP x( ) 1

Pcr LeffCFULS L x( ) x

Dt x( )

2



Reconstructing Figure 4-4 Section 4.4.3 Page 25 Ref. [1] Plateaux definition

Az1 x y( )

az1 0.9 fn12 15if

az1 0.9 0.5 fn12 1.5 1.5 fn12 2.3if

az1 1.3 2.3 fn12if

αULS x y( ) 0.8if

az1 0.9 KCuls x y( ) 30if

az1 0.7 0.01 KCuls x y( ) 10 10 KCuls x y( ) 30if

az1 0.7 KCuls x y( ) 10if

αULS x y( ) 0.8if

az1 Dt x( )

VRx L z y( ) 0

UtotULSz y

CFULS L z KPStep( ) Dt z KPStep( )γf z KPStep 1 on error

VRCF1 x y( ) 77 VRCFon x 1

1.151.3 Az1 x y( )

Dt x( )

VCFR2 x y( ) 167

13

Az1 x y( )

Dt x( )

Reduced velocity Section 4.1.5 Page 23 Ref. [1]

AyCF1 x y( )

2.0

VRCFon x 1

VRCF1 x y( )

VCFR2 x y( )

16

0

0.15

Az1 x y( )

Dt x( )

Az1 x y( )

Dt x( )

0

Vector representing five 'points'of Figure 4.4 Page 25 Ref. [1]

Translate the function into a matrix AyCF1z y

AyCF1 z KPStep y( )

Obtain a point along the 'curve' onFigure 4-4 Page 25 Ref. [1] for eachwave/current velocity

AyCF L z y( ) 0 VRx L z y( ) 2if

max 0 linterp AyCF1z y

0

AyCF1z y

1

VRx L z y( )

otherwise



7.3 Inline Response Model Section 4.3.5 Page 24 Ref. [1]

Correction for unsteadiness of flow Section 5.4.5 Page 29 Ref. [1] Correction for proximity to fixed boundary Section 5.4.6 Ref. [1]

ψKCα x y( )

0.85 0.15αULS x y( )

2 αULS x y( ) 0.5if

0.6 0.15 otherwise

KCuls x y( ) 40if

0.856

KCuls x y( )

αULS x y( )

2 αULS x y( ) 0.5if

0.66

KCuls x y( ) otherwise

40 KCuls x y( ) 5if

KCuls x y( )

51.05

αULS x y( )

2 1

αULS x y( ) 0.5if

KCuls x y( )

50.8 1 otherwise

otherwise

ψprox_CD x( ) 0.9

0.5

1 5e0 x( )

Dt x( )

e0 x( )

Dt x( )0.8if

1 otherwise

Correction for trenching effects Section 5.4.7Page 30 Ref. [1]

ψtrench_CD x( ) 12

3ΔID x( )

Correction for crossflow vibrations Section 5.4.8Page 30 Ref. [1]

ψVIV_CD L z y( ) 1 1.043 2 AyCF L z y( ) 0.65

Basic coefficient for steady flow Section 5.4.4Page 29 Ref. [1]

CdkD x( ) 0.65kpipe x( )

Dt x( )

104

if

0.6529

13

4

13log

kpipe x( )

Dt x( )

104 kpipe x( )

Dt x( )

102

if

1.05kpipe x( )

Dt x( )10

2if

Total Drag Coefficient Section 5.4.3 Page 29 Ref. [1]

CD L x y( ) CdkD x( ) ψKCα x y( ) ψprox_CD x( ) ψtrench_CD x( ) ψVIV_CD L KP x( ) y( )

Translate the function into a matrix

Structural frequency, Section 5.4.3Page 29 Ref. [1]

ILULS L x( ) C1 1 CSF x( )E ls

KP x( )

me Ca x( ) x 1 Leff L KIL x 1 x 4

1Seff

KP x( ) 1

Pcr Leff L KIL x 1 x x



Design Reduced Velocity,Section 4.1.5 Page 23 Ref. [1] VRd L x y( ) 0

UtotULSKP x( ) y

ILULS L x( ) Dt x( )γf x 1

on error

Reduction Factor, Section 4.3.7Page 25 Ref. [1]

ψαIL x y( ) if αULS x y( ) 0.5 0 if 0.5 αULS x y( ) 0.8αULS x y( ) 0.5

0.3 1

Reconstructing Figure 4-2 Page 25 Ref. [1]

Reduction Factors

0 RIθ 1 RIθ1 x y( ) RIθ min 1 π2 π

22 θrel_sig

KP x( ) y

Ic 0.03 1

RIθ1 max RIθ 0

RIθ2 RIθ min 1Ic 0.03

0.17 1

RIθ2 max RIθ 0

Normalised VIV Amplitudes

Ay2 L x( ) 0.13 1min 1.799 Ksin L x 1

1.8

RIθ2

Dt x( ) Ay1 L x y( ) Dt x( ) max 0.18 1Ksin L x 1

1.2

RIθ1 x y( )Ay2 L x( )

Dt x( )

Cut-off Velocities VRIL1 L x y( ) 10Ay1 L x y( )

Dt x( )

VRILon L x 1 VRILend L x( ) if Ksin L x 1 1 4.5 0.8 Ksin L x 1 3.7

VRIL2 L x( ) VRILend L x( ) 2Ay2 L x( )

Dt x( )

Vector representing four'points' of Figure 4.2Page 25 Ref. [1]

AYOD L x y( )

VRILon L x 1

VRIL1 L x y( )

VRIL2 L x( )

VRILend L x( )

0

Ay1 L x y( )

Dt x( )

Ay2 L x( )

Dt x( )

0

Obtain a 'curve' on Figure 4-2 Page 25 Ref. [1] for each wave/current velocity

AyOD L x y( ) max 0 linterp AYOD L x y( )0

AYOD L x y( )1

Re VRd L x y( )



7.4 Stress Calculations

Crossflow dampingreduction factor

Rk L x( ) 1 0.15 Kscf L x 1 Kscf L x 1 4if

3.2 Kscf L x 1 1.5 Kscf L x 1 4if


Maximum inline unit diameter stress amplitude SIL L x y( ) 2 AIL L x( ) AyOD L x y( ) ψαIL x y( ) γs1 Section 4.3.3 Page 24 Ref.[1]

Maximum crossflow unit diameter stress amplitude SCF L x y( ) 2 ACF L x( ) AyCF L KP x( ) y( ) Rk L x( ) γs1 Section 4.4.3 Page 25 Ref. [1]

7.4.1 Inertia Force Coefficients

Basic Inertia Coefficient forfree concrete coated pipe

f α( ) 1.6 2 α α 0.5if

0.6 otherwise

Section 5.4.10Page 30 Ref. [1]

CMO x y( ) f αULS x y( ) 52 f αULS x y( ) KCuls x y( ) 5

Correction for Pipe RoughnessSection 5.4.11 Page 30 Ref. [1]

ψk_CM x( ) 0.75 0.434 logkpipe x( )

Dt x( )

Correction for TrenchEffects

ψtrench_CM x( ) 11

3ΔID x( )

Correction for Seabed Proximity Section 5.4.13 Page 30 Ref. [1] Total Coefficient of Inertia Section 5.4.9 Page 30 Ref. [1]

ψproxi_CM x( ) 0.840.8

1 5e0 x( )

Dt x( )

e0 x( )

Dt x( )0.8if

1 otherwise

CM x y( ) CMO x y( ) ψk_CM x( ) ψproxi_CM x( ) ψtrench_CM x( )

Translate the function into a matrix

Section 5.4.9 Page 30 Ref. [1] CMz y

CM z KPStep y( )



7.4.2 Peak Combined Drag and Inertia Loading This calculates the static load, and therefore considers the maximum wave and associated period

Horizontal Acceleration AmplitudeAwave z y( )

2 π

TwmaxULSz y

UwmaxULSz y

Wave Induced Velocity wrtWave Phase Angle

Wave Induced Acceleration wrtWave Phase Angle

Awave θ z y( ) Awave z y( )( ) sin θ( )Uwave θ z y( ) UwmaxULS

z y

cos θ( )

Drag Force wrt Wave Phase Angle Fdraguls L z y θ( )1

2ρw z KPStep( ) Dt z KPStep( ) CD L kpz y Uwave θ z y( ) UcULS

z y Uwave θ z y( ) UcULS

z y

Inertia Force wrt Wave Phase AngleFM z y θ( )

π

4ρw z KPStep( ) Dt z KPStep( ) 2 CM

z y Awave θ z y( )

Horizontal Force (Drag + Inertia)FH θ L z y( ) Fdraguls L z y θ( ) FM z y θ( )

The maximum horizontal hydrodynamicforce occurs when the first derivative isequal to zero.

FHmax L z y( ) fd1

2ρw z KPStep( ) Dt z KPStep( ) CD L kpz y

fmπ

4ρw z KPStep( ) Dt z KPStep( ) 2 CM

z y

fhi fd Uwave θ z y( ) UcULSz y

Uwave θ z y( ) UcULSz y

fm Awave θ z y( )

i i 1

θ 0deg 2deg 90degfor

max fh( )return

Static Span effective LengthLeffULS L x( ) Leff L KvSTAT x( ) x( )

Resultant Moment Mwave L x y( ) C5 L LeffULS L x( ) FHmax L KP x( ) y( ) LeffULS L x( )

2

1Seff

KP x( ) 1

Pcr LeffULS L x( ) x

Section 6.7.6 / 6.7.10 Page 33 Ref. [1]



Associated Stress σFM_MAX L x y( )Mwave L x y( ) Do x( ) t2 x( )

2 lsKP x( )


σdynIN L x y( )1

2max 0.4 SCF L x y( )

AIL L x( )

ACF L x( ) SIL L x y( )

σFM_MAX L x y( )Dynamic Inline Bending Stress Section 2.5.12 Page 18 Ref. [1]

Dynamic Crossflow Bending Stress σdynCF L x y( )1

2SCF L x y( ) Section 2.5.8 Page 17 Ref. [1]

7.4.3 Peak Combined Drag and Inertia Loading

Calculates the static load, and therefore considers the maximum wave and associated period

Static, Functional [Vertical] BendingMoment due to Submerged Weight

Mfunc L x( ) C5 L LeffULS L x( ) Wsub

KP x( ) 1LeffULS L x( )

2

1Seff

KP x( ) 1

Pcr LeffULS L x( ) x

γfLC γc Section 6.7.10 Page 33 Ref. [1]

Environmental [Horizontal] BendingMoment due to in-line VIV

Section 2.5.7 / Section 2.5.8 Page 17 Ref. [1]MDILVIV L x y( ) σdynIN L x y( )

2 lsKP x( )

Do x( ) tnom x( )

2

γE

Environmental [Vertical] Bending Moment due to cross-flow VIV

MDCFVIV L x y( ) σdynCF L x y( )

2 lsKP x( )

Do x( ) tnom x( )

2

γE Section 2.5.7 / Section 2.5.8 Page 17 Ref. [1]



7.5 Preliminary Load-Controlled Combined Loading Check Calculations

Operating Temperature for Stress De-Rating (Valid for Toper < 200 oC)

Yield strength temperature de-rating Taken from Section 5, B604 if no other information exists

Yield Stress Temperature De-rating fy_temp x( ) ifTULS x( )

°C50 0 if

TULS x( )

°C100

TULS x( )

°C50

0.6TULS x( )

°C100

0.4

30

MPa

Tensile Stress Temperature De-rating fu_temp x( ) ifTULS x( )

°C50 0 if

TULS x( )

°C100

TULS x( )

°C50

0.6TULS x( )

°C100

0.4

30

MPa

Characteristic Yield Strength fy x( ) SMYS fy_temp x( ) αU Equation 5.5 Section 5 C302 - Page 44 Ref. [2]

Characteristic Tensile Strength fu x( ) SMTS fu_temp x( ) αU Equation 5.6 Section 5 C302 - Page 44 Ref. [2]

Design Moment MSd L x y( ) Mfunc L x( ) MDCFVIV L x y( ) 2 MDILVIV L x y( )2

Equation 4.5 Section 4 G201 - Page 39 Ref. [2]

Design differential effective axoiavle froprrceessure SSd x( ) SeffKP x( ) 1

γfLC γc Equation 4.7 Section 4 G201 - Page 39 Ref. [2]

Design differential overpressure Δpd x( ) pldULS x( ) Pe x( )

Characteristic plasticmoment resistance

Mp x( ) fy x( ) Do x( ) t2 x( ) 2 t2 x( ) Equation 5.21 Section 5 D605 - Page 48 Ref. [2]

Characteristic plastic axialforce resistance

Sp x( ) fy x( ) π Do x( ) t2 x( ) t2 x( ) Equation 5.20 Section 5 D605 - Page 48 Ref. [2]

fcb x( ) min fy x( )fu x( )

1.15

Limit strength Equation 5.9 Section 5 D202 - Page 38 Ref. [2]



pb x( )2 t2 x( )

Do x( ) t2 x( )fcb x( )

2

3

Yield Limit State Equation 5.8 Section 5 D202 - Page 38 Ref. [2]

Plastic Collapse Pressure pp x( ) fy x( ) αfab2 t2 x( )

Do x( ) Equation 5.11 Section 5 D401 - Page 46 Ref. [2]

7.6 Internal Overpressure

Equation 5.24 - Section 5 D605 Page 48Ref. [2]

Flow stress parameter Account for effect of D/t ratio

βio x( ) beta 0.5Do x( )

t2 x( )15if

beta

60Do x( )

t2 x( )

90 15

Do x( )

t2 x( ) 60if

beta 0Do x( )

t2 x( )60if

αc_io x( ) 1 βio x( ) βio x( )fu x( )

fy x( ) αp2 x( ) 1 βio x( )

pldULS x( ) Pe x( )

pb x( )0.7if

1 3 βio x( ) 1pldULS x( ) Pe x( )

pb x( )

otherwise

Equation 5.22 - Section 5 D605Page 48 Ref. [2]

Equation 5.23 - Section 5 D605 Page 48 Ref. [2]

Interaction Ratio Equation 5.19(a) -Section 5 D607 Page 47 Ref. [2] UCio L x y( ) γm γSC

MSd L x y( )

αc_io x( ) Mp x( )

γm γSC SSd x( )

αc_io x( ) Sp x( )

2

2

αp2 x( )pldULS x( ) Pe x( )

αc_io x( ) pb x( )

2

Design Moment forInternal Overpressure MDio x( )

1 αp2 x( )pldULS x( ) Pe x( )

αc_io x( ) pb x( )

2

γm γSC SSd x( )

αc_io x( ) Sp x( )

2

γm γSCαc_io x( ) Mp x( )



7.7 External Overpressure

Elastic Collapse PressureCharacteristic Collapse Pressure Equation 5.10 - Section 5 D401 Page 46

Ref. [2]Equation 5.11 - Section 5 D401Page 46 Ref. [2] guess pc 1barg

pel x( )

2 Et2 x( )

Do x( )

3

1 ν2

pc x( ) root pc pel x( ) pc2

pp x( )2

pc pel x( ) pp x( ) f0

Do x( )

t2 x( ) pc

Interaction Ratio Equation 5.28(a) - Section 5 D607Page 48 Ref. [2]UCeo L x y( ) γm γSC

MSd L x y( )

αc_io x( ) Mp x( )

γm γSC SSd x( )

αc_io x( ) Sp x( )

2

2γm γSC Pe x( ) 0

pc x( )

2

Design moment forexternal overpressure

MDeo x( )

1γm γSC Pe x( ) 0

pc x( )

2

γm γSC SSd x( )

αc_io x( ) Sp x( )

2

γm γSCαc_io x( ) Mp x( )

7.8 Results

Select internal or external overpressure UC L x y( ) if pldULS x( ) Pe x( ) UCio L x y( ) UCeo L x y( )

and associated moment Md x( ) if pldULS x( ) Pe x( ) MDio x( ) MDeo x( )

Solve to find Given Im Lu( ) 0= UC Lu X Y( ) 1= Lu 1m Mfunc Lu X( ) 0 LlimULS Lu X Y( ) Find Lu( )

LULSz y 1 m LU LCFon0 z 0=if

LU LULSz 1 y

otherwise

luls LlimULS LU z KPStep y( )

luls

on error LULSz

min LULSz 0 LULS

z 1



0 2 4 647.5

47.6

47.7

47.8

47.9

48

Span Length (ULS Criteria)

Span Lengths Following ULS Criterion

KP (km)

Min

imum

Allo

wabl

e Sp

an L

engt

h (m

)

ULS Criteria

8.0 VALIDITY CHECKS / RESULT PROCESSING

Validity Checks / Result Collation / Data Saving

8.1 Validity Checks

Maximum length for response model validity MaxmODL x( ) 140 Do x( ) Section 6.7.1 Page 32 Ref [1]



Crossflow deflection δCF x z( ) C6

Wsubz 0

LCFonz

4

E lsKP x( )

1 CSF x( ) 1 C2

Seffz 0

LCFonz

2

1 CSF x( ) π2

E lsKP x( )

1

Section 6.7.7 Page 33 Ref [1]

Max allowable deflection δcheck x z( ) if δCF x z( ) 2.5 Dt x( ) "Invalid" "" Section 6.7.1 Page 32 Ref [1]

Section 6.7.1 Page 32 Ref [1]Check that Euler buckling is not influencing EulerIL x z( ) "" if

Seffz 0

Pcr LILonz

x 0.5 "" "Influenced by Euler limit"

on error

EulerCF x z( ) "" if

Seffz 0

Pcr LCFonz


on error

Bar buckling influenceon screening spans

eulils x z( ) if

Seffz 0

Pcr LILscrz


eulcfs x z( ) if

Seffz 0

Pcr LCFscrz


Model length validity limiton onset spans

mlilo x z( ) if LILonz

200 Do x( ) ">200Do limit" ""

mlcfo x z( ) if LCFonz

200 Do x( ) ">200Do limit" ""

Model length validity limiton screening spans

mlils x z( ) if LILscrz

200 Do x( ) ">200Do limit" ""

mlcfs x z( ) if LCFscrz

200 Do x( ) ">200Do limit" ""



If current flow ratio lessthan 0.5 inline VIV can beignored

ILVIVo z( ) if ααonz 0

0.5 "a<0.5 - IL VIV may be ignores" ""

Section 1.9.1 Page 10 Ref [1]

ILVIVs z( ) if ααscrz

0.5 "a<0.5 - IL VIV may be ignores" ""

If D/t > 45, Load Controlled Check not Valid

Determine which combination of environmental loading has been used bb z( ) 0 LULSz

LULSz 0=if

1 otherwise

zz z( ) 0 LILonz

LILon_matz 0

=if

1 otherwise

Include in results table z 0 1 Length

KPStep KPz z KPStep Dtv

zif

Do KPz tnom KPz 45 "OK" "Invalid D/t ratio"

lilonz if concat mlilo KPz z EulerIL KPz z ILVIVo z( ) ""= "OK" concat mlilo KPz z EulerIL KPz z ILVIVo z( )

lilscrz if concat mlils KPz z eulils KPz z ILVIVs z( ) ""= "OK" concat mlilo KPz z EulerCF KPz z ILVIVs z( )

lcfonz if concat mlcfo KPz z EulerCF KPz z δcheck KPz z ""= "OK" concat mlcfo KPz z EulerCF KPz z δcheck KPz z aaz KPz

lcfscrz if concat mlcfs KPz z eulcfs KPz z ""= "OK" concat mlcfs KPz z eulcfs KPz z

Create large matrix to pass to output table

results augment KP LILon LCFon lilon lcfon LILscr LCFscr lilscr lcfscr LULS Dtv

Validity Checks / Result Collation / Data Saving



9.0 RESULTS

Location for Detailed Span results Location 5km

Extract Data for Desired Location

loc roundLocation

KPStep

SpanVIVloc stack LILonloc

LCFonloc

LILscrloc

LCFscrloc

"NA"

Menv L x y( ) MDCFVIV L x y( )

2MDILVIV L x y( )

2

SpanULSloc stack "NA" "NA" "NA" "NA" LULSloc

Spansloc augment SpanVIVloc SpanULSloc

VIVloc stack

Seffloc 0

kN

Uconsetloc zz loc( )

m s1

Uwonset

loc zz loc( )

m s1

ααonloc 0

Wsub

loc 0

kN m1

CSF loc KPStep( ) VRILon LILonloc

loc KPStep 0

VRCFon loc KPStep 0 δCF loc KPStep zz loc( )( )

m

2.5

ULSloc stack

Mfunc LULSloc

loc KPStep kN m

Menv LULSloc

loc KPStep bb loc( ) kN m

MSd LULS

locloc KPStep bb loc( ) kN m

Seff

loc 1

kN

UcULSloc bb loc( )

m s1

UwmaxULS

loc bb loc( )

m s1

Eulerlimit KCF loc KPS

SaveLC LCinput 1 0.00 SaveBC BC 1 2.00 SaveSEFF Seffinput 1 0.00

SaveSteelRough roughness 1 2.00 SaveSpan_Def Span_Def 1 2.00 SaveWall Wall 1 1.00

Extract Data for Desired Location

9.1 Tabulated Span Lengths



freespan

INLINE CROSSFLOW INLINE CROSSFLOW

0 22.45 25.92 OK OK 47.91 OK

100 22.45 25.91 OK OK 47.89 OK

200 22.45 25.91 OK OK 47.91 OK

300 22.46 25.92 OK OK 47.93 OK

400 22.47 25.93 OK OK 47.96 OK

500 22.46 25.92 OK OK 47.93 OK

600 22.44 25.91 OK OK 47.88 OK

700 22.45 25.91 OK OK 47.89 OK

800 22.45 25.92 OK OK 47.91 OK

900 22.44 25.90 OK OK 47.87 OK

1000 22.42 25.88 OK OK 47.82 OK

1100 22.42 25.88 OK OK 47.82 OK

ULS RESULTS

CHECKKP

SCREENING SPAN LIMITSSCREENING RESULTS

CHECK ULS SPAN LIMITS



results

9.2 Charted Span Lengths

0 2 4 60

10

20

30

40

Inline Screening Span LengthsCrossflow Screening Span LengthsULS Span Lengths

Summary of Allowable Spans Lengths

Distance Along Pipe (km)

Min

imum

Allo

wabl

e Sp

an L

engt

h (m

)

LILscrz

LCFscrz

LULSz

kpz

km



9.3 Detailed Results at Specified Location

SU TU NAU FIELD DEVELOPMENT

As-Laid Case

12inch Production Pipeline from STN-N (KP0) to STN-S (KP6.55)

VIV ULS

m 22.35 NA

m 25.81 NA

m NA 47.59

0.50

VRILon m/s 1.18

Crossflow Onset [Reduced] Velocity

Concrete Stiffness Factor

VRCFon m/s 2.19

CSF

0.21

Maximum Allowable Span Length at Location Specified Symbol

Inline Onset [Reduced] Velocity

-----

Submerged Weight

Crossflow Screening Allowable Span Length

ULS Allowable Span Length

----

Wsub

PROJECTLOADCASEPIPELINE DESCRIPTION

Onset Steady Current Velocity Uc m/s

Effective Axial Force

0.99

Onset Wave Induced Velocity Uw m/s 0.62

Onset current flow ratio αα 0.25

kN/m

Unit

VIV Onset Allowabe Spans

LULS

Load Case

ValueSymbol Unit

Inline Screening Allowable Span Length LILscr

LCFscr

Sef f op kN 0.00

MPa 15.92

σCF m 0.04

Allowable Deflection

Crossflow Onset Deflection

Crossflow Soil Stiffness KV MPa 21.04

Inline Soil Stiffness

σmax m 1.26

KL

0.99

-4.16

Submerged Weight

Pressure Difference

3.51

2.82

Drag Coefficient

Inertia Coefficient

Euler Buckling Limit

ULS Allowabl Spans

ValueUnitSymbol

Functional moment

357.09

0.00

0.48

0.30

Environmental moment

Design moment

Effective Axial Force

Steady Current Velocity

Maximum Wave Velocity

64.78

kN.m

kN.m

kN.m

kN

m/s

m/s

m

193.24

210.21

Mf

Me

Md

Sef f ULS

Uc

Uw

----

CD

Cm

Wsub

ΔP

----

----

kN/m

bar

Detailed_Results "Updated Successfully"


free span- as lay- 12 inch-production(kp0-kp6.5) no lock function

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