DAFTAR PUSTAKA A - Institut Teknologi Bandungdigilib.itb.ac.id/files/disk1/629/jbptitbpp-gdl-ratnapuspi-31432-7... · DAFTAR PUSTAKA A Abidin, Zenal. ... Veritas Offshore Technology

DDAAFFTTAARR PPUUSSTTAAKKAA

Abidin, Zenal. “Analisis On-Bottom Stability dan Instalasi Pipa Bawah Laut di Daerah

Shore Approach” Tugas Akhir Mahasiswa Program Studi Teknik Kelautan Institut

Teknologi Bandung.

American Petroleum Institute. 1993. “API RP2A Recommended Practices for Planning,

Designing, and Constructing Fixed Offshore Platform – LRFD”. Dallas: API

Production Dept.

Bai, Yong. 2001. “Pipelines and Risers”. Amsterdam: Elsevier Science.

Dalrymple.Dean. 1991. “Water Wave Mechanics for Engineers and Scientist”. New Jersey:

World Scientific.

Mouselli, A.H. 1985. “Offshore Pipelines Design, Analysis and Method”. Oklahoma: Penn

Well Books.

Thales Geosolutions (Singapore) Pte Ltd. 2002. “Free Spans Analysis Methodology”. Field

Report 28” East Java Gas Pipeline for PT. Komaritim.

Veritas Offshore Technology and Services A/S. Februari 2006. “DNV RP F105 Free

Spanning Pipelines”. Norway: DNV Publisher.

Veritas Offshore Technology and Services A/S. Agustus 2005. “DNV RP C203 Fatigue

Design of Offshore Steel Structure”. Norway: DNV Publisher.

Veritas Offshore Technology and Services A/S. Oktober 1988. “DNV RP E305 On Bottom

Stability Design of Submarine Pipelines”. Norway: DNV Publisher.

Veritas Offshore Technology and Services A/S. Oktober 2007. “DNV OS F101 Submarine

Pipelines Systems”. Rev Oktober 2003 Norway: DNV Publisher.

Veritas Offshore Technology and Services A/S. April 1981. “DNV 1981 Rules for

Submarine Pipelines Systems”. Norway: DNV Publisher.

http://www.gulfmex.org

Concrete Coating Thickness tcc 1.75in:=

Corossion Allowance tCA 0in:=

Asphalt enamel tas 0.197in:=

Thermal Insulation Thickness ttherm 0in:=

Internal Diameter Di OD 2ts−:= Di 26.75in=

Total Outside Diameter Dtot OD 2 tcorr tcc+ ttherm+ tas+( )⋅+:=

Dtot 32.13in=

Input Factor

Material Strength Factor

Normally = 1; su 1:=

Supplementary Req.αu = 2;

αU 0.96 su 1=if

1 otherwise

:= αU 0.96=

Maximum Fabricator Facor

Manufacturing Process Seamless =1;

UO &TRB & ER =2;

UOE =3;

fm 3:=

αfab 1 fm 1=if

0.93 fm 2=if

0.85 otherwise

:= αfab 0.85=

WALL THICKNESSCALCULATION

Definition kPa 1000Pa:= MPa 1000kPa:= pcf 1lb ft3−

⋅:= K 1C= kN 1000N:=

Data pipa:

Steel Pipe Outer Diameter OD 28in:= OD 28in=

Limit State Category 1 FLS= 2 ULS=

LSC 2:=

Safety Class Design SCD "Normal"=

Pipeline fabrication PF "ERW/DSAW"=

Poisson Ratio ν 0.3:=

Wall Thickness

Steel Pipe Thickness ts 0.625in:= ts 15.875mm=

Corrossion Coating Thickness tcorr 0.118in:=

lc 1:=

2 2=1 1=

Location Definition

1 The area where no frequent human activity is anticipated along the pipeline route.

2 The part of the pipeline/riser in the near platform (manned) area or in areas with

frequent human activity. The extent of location class 2 should be based on appropriate risk

analyses. If no such analyses are performed a minimum distance of 500 m shall be adopted.

Location Class

cf 2:=

5 E=4 D=3 C=2 B=1 A=

Klasifikasi

Classification of fluids

Category Description

A Typical non-flammable water-based fluids.

B Flammable and/or toxic substances which are liquids at ambient temperature and

atmospheric pres-sure conditions. Typical examples would be oil petroleum products.

Methanol is an example of a flammable and toxic fluid.

C Non-flammable substances which are non-toxic gas-es at ambient temperature and

atmospheric pressure conditions. Typical examples would be nitrogen, carbon dioxide,

argon and air.

D Non-toxic, single-phase natural gas.

E Flammable and/or toxic fluids which are gases at ambient temperature and

atmospheric pressure conditions and which are conveyed as gases and/or liquids.

Typical examples would be hydrogen, natural gas (not otherwise covered under

category D), ethane, ethylene, liquefied petroleum gas (such as propane and butane),

natural gas liquids, ammonia, and chlorine.

Fuid Calssification

Tamb 25C:=Ambient Temperature

Top 29.4C:=Max Operating Temperature

γz 2.5:=Resistance Strain Factor

γ inc 1.1:=Usage factor incidental pressure

γm 1.15=γm 1 LSC 1=if

1.15 otherwise

:=

FLS = 1;

SLS/ULS/ALS = 2

Material Resistance Factor

Modulus of Elasticity (Modulus Young) E 3 107

psi⋅:=

Characteristic Material Properties

Characteristic Yield Stress fy SMYS fytemp−( ) αU⋅:= fy 6.24 104

× psi=

Characteristic Tensile Stress fu SMTS futemp−( ) αU⋅:= fu 7.392 104

× psi=

Density

Steel Density ρst 490pcf:=

Corrosion Coating Density ρcorr 57.122pcf:=

Concrete Coating Density ρconc 189.781pcf:=

Thermal insulation Density ρtherm 0pcf:=

Asphalt density ρas 1300kg

m3

:=

Safety Class

Safety class Definition

1. Low Where failure implies low risk of human injury and minor environmental and

economic consequences. This is the usual classification for installation phase.

2. Normal For temporary conditions where failure implies risk of human injury, significant

environmental pollution or very high economic or political consequences. This

is the usual classification for operation outside the platform area.

3. High For operating conditions where failure implies high risk of human injury,

significant environmental pollution or very high economic or political

consequences. This is the usual classification during operation in location

class 2.

1 1= 2 2= 3 3=

Klasifikasi sc 2:=

Safety Class Resistence Factor

γsc1 1.046 sc 1=if

1.138 sc 2=if

1.308 otherwise

:=γsc1 1.138=

Pressure Containtment-->

γsc2 1.04 sc 1=if

1.14 sc 2=if

1.26 otherwise

:=γsc2 1.14=

other

Material Grade (API5L X-52)

Specified Minimum Yield Stress SMYS 65000psi:=

Specified Minimum Tensile Stress SMTS 77000psi:=

fytemp 0MPa:=

futemp 0MPa:=

Dbodmin 4− mm=

Dbodmin min Dbodmin minbod,( ):=

minbod 3.2− mm 60.3mm OD≤ 610mm≤if

4− mm 610mm OD< 1422mm≤if

:=

Dbodmin min Dbodmax 0.5− mm,( ):=

Dbodmin 3.556− mm=

Dbodmin 0.75− % OD⋅ dpb 1= OD 60.3mm<∧if

0.75− % OD⋅ dpb 2= OD 60.3mm<∧if

0.75− % OD⋅ dpb 1= 60.3mm OD≤ 610mm≤∧if

0.75− % OD⋅ dpb 2= 60.3mm OD≤ 610mm≤∧if

1− % OD⋅ dpb 1= 610mm OD< 1422mm≤∧if

0.5− % OD⋅ dpb 2= 610mm OD< 1422mm≤∧if

:=

Welded = 2

OD 711.2mm=dpb 2:=SMLS = 1

Diameter Pipe Body Minimum

Dbodmax 3.556mm=

Dbodmax min Dbodmax maxbod,( ):=

maxbod 3.2mm 60.3mm OD≤ 610mm≤if

4mm 610mm OD< 1422mm≤if

:=

Dbodmax max Dbodmax 0.5mm,( ):=

Content Density ρcont1 0kg m3−

⋅:= installation

ρcont2 1025kg m3−

⋅:= systemtest

ρcont3 64.074kg m3−

⋅:= operating

Sea Water Density ρsw 1025kg m3−

⋅:=

Tolerance For Diameter & Out Of Roundness

Diameter Pipe Body Maximum

SMLS = 1 dpb 2:= OD 711.2mm=

Welded = 2

Dbodmax 0.75% OD⋅ dpb 1= OD 60.3mm<∧if

0.75% OD⋅ dpb 2= OD 60.3mm<∧if

0.75% OD⋅ dpb 1= 60.3mm OD≤ 610mm≤∧if

0.75% OD⋅ dpb 2= 60.3mm OD≤ 610mm≤∧if

1% OD⋅ dpb 1= 610mm OD< 1422mm≤∧if

0.5% OD⋅ dpb 2= 610mm OD< 1422mm≤∧if

:=

Dbodmax 3.556mm=

Dmin 27.843 in=Dmin OD min Dendmin Dbodmin,( )+:=Diameter Minimum

Dmax 28.14in=Dmax OD max Dendmax Dbodmax,( )+:=Diameter Maximum

tfab 1mm=tfab 1mm:=Wall Thickness Fabrication

Dendmin 1.6− mm=

Dendmin min Dendmin minend,( ):=

minend 1.6− mm OD 60.3mm< 6.3mm OD≤ 610mm≤∨if

Dendmin otherwise

:=

Dendmin min Dendmin 0.5− mm,( ):=

Dendmin 1.6− mm=

Dendmin 0.5− % OD⋅ dpe 1= OD 60.3mm<∧if

0.5− % OD⋅ dpe 2= OD 60.3mm<∧if

0.5− % OD⋅ dpe 1= 60.3mm OD≤ 610mm≤∧if

0.5− % OD⋅ dpe 2= 60.3mm OD≤ 610mm≤∧if

2− mm dpe 1= 610mm OD< 1422mm≤∧if

1.6− mm dpe 2= 610mm OD< 1422mm≤∧if

:=

Welded = 2

OD 711.2mm=dpe 2:=SMLS = 1

Diameter Pipe End Minimum

Dendmax 1.6mm=

Dendmax min Dendmax maxend,( ):=

maxend 1.6mm OD 60.3mm< 6.3mm OD≤ 610mm≤∨if

Dendmax otherwise

:=

Dendmax max Dendmax 0.5mm,( ):=

Dendmax 1.6mm=

Dendmax 0.5% OD⋅ dpe 1= OD 60.3mm<∧if

0.5% OD⋅ dpe 2= OD 60.3mm<∧if

0.5% OD⋅ dpe 1= 60.3mm OD≤ 610mm≤∧if

0.5% OD⋅ dpe 2= 60.3mm OD≤ 610mm≤∧if

2mm dpe 1= 610mm OD< 1422mm≤∧if

1.6mm dpe 2= 610mm OD< 1422mm≤∧if

:=

Welded = 2

OD 711.2mm=dpe 2:=SMLS = 1

Diameter Pipe End Maximum

Hm100 3.6m:=

Water Depth (Deepest water depth) d 118m:= d 387.139ft=

Reference Height Above Seabed Zr 3m:=

Elevation of the reference point (positive upwards) href OD:=

Elevation of the local pressure point (positive upwards h1 d:=

Highest Astronomical Tid HAT 2.44m:=

Storm Surge (1 yr) SS1 0m:=



Reference Water Depth dmax d HAT+ SS100+Hm100

2+:= dmax 122.24m=

dmax2 d HAT+ SS1+Hm1

2+:= dmax2 121.44m=

Characteristic Wall Thickness

Used when failure is likely to occur in connection with a low capacity (i.e. system effects are

present)

When there is negligible corrosion

(Mill Pressure Test, Installation,

and System Pressure Test Condition)

t1 ts tfab−:= t1 0.586in=

When there is corrosion

(Operation Condition)t1_2 ts tfab− tCA−:= t1_2 0.586in=

Used when failure is likely to occur in an extreme load effect at a location with average

thickness

When there is negligible corrosion

(Mill Pressure Test, Installation,

and System Pressure Test Condition)

t2 ts:= t2 0.625in=

When there is corrosion

(Operation Condition)t2_2 ts tCA−:= t2_2 0.625in=

Current and Wave Data

Spectral Peak Period (1 yr) Tp1 5.9s:=

Spectral Peak Period (100 yr) Tp100 7.9s:=

Maximum Wave Height (1yr) Hm1 2m:=

Maximum Wave Height (25yr) Hm25 2.8m:=

Maximum Wave Height (100yr)

External Pressure Design Pemax2 ρsw g⋅ dmax2( )⋅:= Pemax2 177.046psi=

Pemax ρsw g⋅ dmax( )⋅:= Pemax 178.213psi=

CALCULATION

Pressure Containment

Mill Pressure Condition

Minimum of Yield Stress & Tensile Stress fcb min fy

fu

1.15,

:= fcb 6.24 104

× psi=

Yielding Limit Stress Pby

2 t1⋅

OD t1−fy⋅

2

3

⋅:= Pby 3.078 103

× psi=

Bursting Limit Stress Pbb

2 t1⋅

OD t1−

fu

1.15⋅

2

3

⋅:= Pbb 3.171 103

× psi=

Pressure Containment Resistance Pb1 min Pby Pbb,( ):= Pb1 3.078 103

× psi=

ResistancePb1

γsc1 γm⋅2.352 10

3× psi=

Pressure Containment Check Check_Containment_press "OK"

Pb1

γsc1 γm⋅P1t≥if

"NOT OK" otherwise

:=

Check_Containment_press "OK"=

Pressure Data

Pressure Design Pd 1100psi:=

Incidental Pressure Pinc γ inc Pd⋅:= Pinc 1.21 103

× psi=

Local Pressure

Design P1di Pd ρcont1 g⋅ href h1−( )⋅ +:= P1di 1.1 103

× psi= instalasi( )

P1do Pd ρcont3 g⋅ href h1−( )⋅ +:= P1do 1.089 103

× psi= operating( )

Incidental P1ii Pinc ρcont1 g⋅ href h1−( )⋅ +:= P1ii 1.21 103

× psi= instalasi( )

P1io Pinc ρcont3 g⋅ href h1−( )⋅ +:= P1io 1.199 103


System Test P1t 1.05Pinc ρcont2 g⋅ href h1−( )⋅ +:= P1t 1.1 103


Plastic Collapse Pressure Pp 2 fy⋅ αfab⋅t2

OD⋅:= Pp 2.368 10

3× psi=

Ovalisation fo

Dmax Dmin−

OD:= fo 1.062%=

The Charactristic Resistance for External Pressure Solution

b Pe1−:= b 733.29− psi=

c Pp2

Pp Pe1⋅ fo⋅OD

t2

⋅

+

−:= c 6.433− 106

× psi2

=

ddd Pe1 Pp2

⋅:= ddd 4.111 109

× psi3

=

u1

3

1−

3b

2⋅ c+

⋅:= u 2.204− 106

× psi2

=

v1

2

2

27b

3⋅

1

3b⋅ c⋅− ddd+

⋅:= v 1.255 109

× psi3

=

Σv−

u3

−

:= Σ 0.383−=

Operational Condition

Yielding Limit Stress Pby

2 t1_2⋅

OD t1_2−fy⋅

2

3

⋅:= Pby 3.078 103

× psi=

Bursting Limit Stress Pbb

2 t1_2⋅

OD t1_2−

fu

1.15⋅

2

3

⋅:= Pbb 3.171 103

× psi=

Pressure Containment Resistance Pb2 min Pby Pbb,( ):= Pb2 3.078 103

× psi=

Pb2

γsc1 γm⋅2.352 10

3× psi=

Pressure Containment Check Check_Containment_press "OK"

Pb2

γsc1 γm⋅P1io≥if

"NOT OK" otherwise

:=

Check_Containment_press "OK"=

System Collapse Criteria

Construction and System Pressure Test Condition

Elastic Collapse Pressure Pe1

2 E⋅t2

OD

3

⋅

1 ν2

−

:= Pe1 733.29psi=

fo 1.062%=

The Charactristic Resistance for External Pressure Solution

b Pe1−:= b 733.29− psi=

c Pp2

Pp Pe1⋅ fo⋅OD

t2_2

⋅

+

−:= c 6.433− 106

× psi2

=

ddd Pe1 Pp2

⋅:= ddd 4.111 109

× psi3

=

u1

3

1−

3b

2⋅ c+

⋅:= u 2.204− 106

× psi2

=

v1

2

2

27b

3⋅

1

3b⋅ c⋅− ddd+

⋅:= v 1.255 109

× psi3

=

Σv−

u3

−

:= Σ 0.383−=

Φ acos Σ( ):= Φ 1.964rad=

y 2− u−⋅ cosΦ

3

60 π⋅

180+

⋅:= y 388.405psi=

Φ acos Σ( ):= Φ 1.964rad=


3

60 π⋅

180+

⋅:= y 388.405psi=

Pc1 y1

3b⋅−:= Pc1 632.835psi=

Pc1

γm γsc2⋅482.711psi=

System Collapse Check Sys_Coll_Check1 "OK" Pemax2

Pc1

γm γsc2⋅≤if

"NOT OK" otherwise

:=

Sys_Coll_Check1 "OK"=


Elastic Collapse Pressure Pe1

2 E⋅t2_2

OD

3

⋅

1 ν2

−

:= Pe1 733.29psi=

Plastic Collapse Pressure Pp 2 fy⋅ αfab⋅t2_2

OD⋅:= Pp 2.368 10

3× psi=

Ovalisation fo

Dmax Dmin−

OD:=

Pb3 min Pby Pbb,( ):= Pb3 3.29 103

× psi=

Flow stress parameter accounting

for strain hardeningβ 0.5

OD

t2

15<if

60OD

t2

−

9015

OD

t2

≤ 60≤if

0OD

t2

60>if

:=

β 0.169=

αc 1 β−( ) βfu

fy

⋅+:= αc 1.031=

"True" effective axial force (axial

force in pipe wall)Nf 450kN:= dari hasil analisis instalasi

Effective axial force Sf Nfπ

4P1t OD 2t2−( )

2⋅

⋅ Pemax2 OD

2⋅

−

−:=

Sf 1.681− 103

× kN=

Designed effective axial forces γF 1.2:= (Functional load factor-->system check)

γc 1.00:= (Condition load effect factor-->installation condition)

Pc2 y1

3b⋅−:= Pc2 632.835psi=

Pc2

γm γsc2⋅482.711psi=

System Collapse Check Sys_Coll_Check1 "OK" Pemax

Pc2

γm γsc2⋅≤if

"NOT OK" otherwise

:=

Sys_Coll_Check1 "OK"=

Combined Loading-Load Controlled Condition

Instalation Condition

Plastic moment resistance Mp fy OD t2−( )2

⋅ t2⋅:= Mp 3.302 103

× kN m⋅=

Characteristic plastic axial force

resistanceSp fy π⋅ OD t2−( )⋅ t2⋅:= Sp 1.492 10

4× kN=

Pressure Containment Pby

2 t2⋅

OD t2−fy⋅

2

3⋅:= Pby 3.29 10

3× psi=

Pbb

2 t2⋅

OD t2−

fu

1.15⋅

2

3⋅:= Pbb 3.389 10

3× psi=

Pby 3.29 103

× psi=

Pbb

2 t2_2⋅

OD t2_2−

fu

1.15⋅

2

3⋅:= Pbb 3.389 10

3× psi=

Pb4 min Pby Pbb,( ):= Pb4 3.29 103

× psi=

Flow stress parameter accounting

for strain hardeningβ 0.5

OD

t2_2

15<if

60OD

t2_2

−

9015

OD

t2

≤ 60≤if

0OD

t2_2

60>if

:=

β 0.169=

αc 1 β−( ) βfu

fy

⋅+:=αc 1.031=

"True" effective axial force (axial

force in pipe wall)H 0kN:= (residual lay tension-->from instalation

analysis)

Thermal expansion coefficent αTh 1.17 105−

⋅ C1−

:=

Effective axial force

Sf H P1ii P1di−( )π

4OD 2t2_2−( )

2⋅

⋅ 1 2ν−( )⋅− π OD t2_2−( )⋅ t2_2⋅ E⋅ αTh⋅ Top Tamb−( )⋅ − +:=

Sf 479.254− kN=

Sd γF γc⋅ Sf⋅:= Sd 2.017− 103

× kN=

Moment Designed Mf 650kN m⋅:= dari hasil analisis instalasi

Md γF γc⋅ Mf⋅:= Md 7.8 105

× N m⋅=

Effective axial forces and internal/external overpressure check

Eff_Ax_Frc_Check_axt "OK" γsc2 γm⋅Md

αc Mp⋅

⋅ γsc2 γm⋅Sd

αc Sp⋅

⋅

2

+

2

γsc2 γm⋅Pemax2

Pc1

⋅

2

+ 1≤if

"NOT OK" otherwise

:=

Eff_Ax_Frc_Check_axt "OK"=


Plastic moment resistance Mp fy OD t2_2−( )2

⋅ t2_2⋅:= Mp 3.302 103

× kN m⋅=

Characteristic plastic axial force

resistanceSp fy π⋅ OD t2_2−( )⋅ t2_2⋅:= Sp 1.492 10

4× kN=

Pressure Containment at Operational

ConditionPby

2 t2_2⋅

OD t2_2−fy⋅

2

3⋅:=

Prop_Check "NOT OK"=

Prop_Check "OK" Pemax2

Ppr

γm γsc2⋅≤if

"NOT OK" otherwise

:=Propagating Buckling Check

Ppr 138.19psi=

Ppr 35 fy⋅ αfab⋅t2

OD

2.5

⋅:=Propagating Buckling Criterion

Construction and Pressure Test Condition

Propagation Buckling Check

Kesimpulan_Eff_Ax_For "OK"=

Kesimpulan_Eff_Ax_For "OK" Eff_Ax_Frc_Check_int "OK"= Eff_Ax_Frc_Check_ext "OK"=∧if

"NOT OK" otherwise

:=

Eff_Ax_Frc_Check_ext "OK"=

Eff_Ax_Frc_Check_ext "OK" γsc2 γm⋅Md

αc Mp⋅

⋅ γsc2 γm⋅Sd

αc Sp⋅

⋅

2

+

2

γsc2 γm⋅Pemax

Pc2

⋅

2

+ 1≤if

"NOT OK" otherwise

:=

Eff_Ax_Frc_Check_int "OK"=

Eff_Ax_Frc_Check_int "OK" γsc2 γm⋅Md

αc Mp⋅

2

⋅ γsc2 γm⋅Sd

αc Sp⋅

⋅

2

+

2

γsc2 γm⋅Pemax

Pc2

⋅

+ 1≤if

"NOT OK" otherwise

:=

Effective axial forces and internal/external overpressure check

dari hasil analisis instalasiMd 0N m⋅:=Moment Designed

Sd 564.082− kN=Sd γF2 γc2⋅ Sf⋅:=

(Condition load effect factor-->uneven seabed

condition)γc2 1.07:=

(Functional load factor-->system check)γF2 1.1:=Designed effective axial forces


Ppr 35 fy⋅ αfab⋅t2_2

OD

2.5

⋅:=Propagating Buckling Criterion

Ppr 138.19psi=

Propagating Buckling Check Prop_Check "OK" Pemax

Ppr

γm γsc2⋅≤if

"NOT OK" otherwise

:=

Prop_Check "NOT OK"=

Density corrosion coating ρcorr 915kg m3−

⋅:=

Thermal insulation coating density ρins 4.5pcf:=

Concrete coating density ρcc 3040kg m3−

⋅:=

Content density ρcont 0lb ft3−

⋅:=

Seawater density ρsw 64lb ft3−

⋅:=

Steel density ρs 490lb ft3−

⋅:=

Asphalt density ρas 1300kg m3−

⋅:=

Concrete coating thickness tcc 1.75in:=

ENVIRONMENTAL PARAMETER :

Significant Wave Height Hs 2m:=

Spectral Peak Period Tp 5.9sec:=

Water Depth d 76m:=

ON-BOTTOM STABILITY CALCULATIONDURING OPERATION PHASE

pcf lb ft3−

⋅:= C K≡ kPa 103

Pa≡ MPa 106

Pa≡ N newton≡ kN 103

N≡

Equivalent Condition

Phase : instalasi

Wave & Current Data : 1 year return period wave + 1 year retun period current

PIPELINE DEIGN PARAMETER :

Outer Diameter Ds 28in:=

Wall thickness ts 0.625in:=

Internal Diameter ID Ds 2 ts⋅−:=

Corrosion coating Thickness tcorr 3mm:=

Thermal Insulation coating thickness tins 0in:=

Jacket material tj 0in:=

Asphalt enamels tas 5mm:=

D tcc( ) 0.816m=

Total Outside Diameter D tcc( ) 32.13 in=

Internal Diameter Di Ds 2 ts⋅−:= Di 26.75 in=

Dcorr Ds 2 tcorr⋅+:=

Dins Dcorr 2 tins⋅+:= Dj Dins 2 tj⋅+:= Das Dj 2 tas⋅+:=

Submerged Weight = Steel Weight+Corr. coat. weight+Thermal Insulation+Jacket material+

Concrete coating weight+Content weight-Buoyancy

Steel Weight Wst 0.25π Ds2

ID2

−

⋅ ρs⋅:=

Wst 272.188kg

m=

Corrosion Coating Weight Wcorr 0.25π Dcorr2

Ds2

−

⋅ ρcorr⋅:=

Wcorr 6.159kg

m=

Thermal Insulation Wins 0.25π Dins2

Dcorr2

−

ρins⋅:=

Wins 0kg

m=

Current 3 m above seabed Ur 0.7m sec1−

⋅:=

Zr 3m:=

Kinematic Viscosity of Seawater ν 1.076 105−

⋅ ft2

sec1−

⋅:=

Angle Between Wave Direction And Pipeline Direction φwave 90deg:=

Angle Between Current Direction And Pipeline Direction φcurr 90deg:=

SOIL PARAMETER :

Soil type 1 sand= 2 clay=, soil 2:=

Undrained Shear Stress Su 0.435psi:=

ρsoil 1860kg m3−

⋅:=

CALCULATIONS :

Submerged Weight :

This section calculates provided weight by pipeline properties section

Total Outside Diameter D tcc( ) Ds 2tcorr+ 2tins+ 2 tj⋅+ 2 tas⋅+ 2 tcc⋅+:=

Ws tcc( ) 84.41kg

m=

Bouyancy B tcc( )π

4g⋅ D tcc( )

2⋅

ρsw

g⋅:=

B tcc( ) 360.352lb

ft=

Vertical Stability :

Specific Gravity SG tcc( )Ws tcc( ) B tcc( )+

B tcc( ):= SG tcc( ) 1.1≥

SG tcc( ) 1.157=

if Ws tcc( ) B tcc( )+ 1.1 B tcc( )≤ "FLOAT", "OK!",( ) "OK!"=

Specific Gravity of Product (relative to seawater) SGprod

ρcont

ρsw

:= SGprod 0=

Specific Gravity of Soil (elative to seawater) SGsoil

ρsoil

ρsw

:= SGsoil 1.814=

Jacket Material Wj 0.25π Dj2

Dins2

−

ρs⋅:=

Wj 0kg

m=

Asphalt Was 0.25π Das2

Dj2

−

ρas⋅:=

Was 14.748kg

m=

Concrete Coating Weight Wcc 0.25π D tcc( )2

Das2

−

⋅ ρcc⋅:=

Wcc 327.579kg

m=

Content Weight Wcont 0.25π Di2

⋅ ρcont⋅:=

Wcont 0kg

m=

Buoyancy B 0.25π D tcc( )2

⋅ ρsw⋅:=

B 536.263kg

m=

Submerged Weight Ws tcc( ) Wst Wcorr+ Wins+ Wj+ Was+ Wcc+ Wcont+ B−:=

Ws tcc( ) 56.721lb

ft=

Kb 1.563 104−

× m=Kb 2.5 d50⋅:=

Nikurade equivalent sand roughness parameter

B1 6.384 106−

×=B1Zo

D tcc( ):=

A1 1.566 105

×=A1D tcc( )

Zo

:=

From The Soil Parameter Data

Tu 8.095 s=Tu 1.372 Tp⋅:=

Zero Up Crossing Period According To DNV RP E305 Figure 2.2

Zo 5.21 106−

m⋅:=Roughnes

d50 0.0625mm:=Grain size

FIND WATER PARTICLE VELOCITIES :

Minimum Required Submerged Weight Calculation According To DNV RP E305

Natural Period Parameter According

To DNV RP E305 Figure 2.2 Tnd

g:= Tn 2.784 s=

Tn

Tp

0.472= φTp

Hs

:= φ 4.172sec

m=

Peakness Parameter γ 5 φ 3.6sec

m≤if

1 φ 5sec

m≥if

3.3 otherwise

:=

γ 3.3=

Assuming There's No Reduction For Directional And Spreading Factor R = 1, Us* = Us

Wave Induced Current Velocity Perpendicular To The Pipe According To DNV RP E305 Figure 2.1

Tn

Tp

0.472=

Us

0.0057 Hs⋅

Tn

:= Us 4.095 103−

×m

s=

From table A.1 Soil parameter can be found as

Hidrodynamic Force Coefficients

Drag Coefficient CD 1.2 RE 3 105−

⋅< M 0.8≥∧if

0.7 otherwise

:=

CD 0.7=

Lift Coefficient CL 0.9:=

Inertia Coefficient CM 3.29:=

Soil Friction Coefficient

Clay soil

ratio1

S= ratio

D tcc( ) Su⋅

Ws tcc( ) g⋅:= ratio 2.957=

From figure 5.11 (Friction Factor = µc)

µc 0.24:=

Sand soil

µs 0.7:=

zobKb

30:= zob 5.208 10

6−× m=

Average Velocity To Reference Velocity Ratio

UD1

lnZr

Zo

1+

1 B1+( ) ln A1 1+( )⋅ 1− ⋅

Ur⋅:=

UD 0.579m

s= Us 4.095 10

3−×

m

s=

USING SIMPLIFIED STATIC STABILITY METHOD :

Wave particle acceleration As 2πUs

Tu

:=

As 3.179 103−

× m sec2−

⋅=

Current To Wave Velocity Ratio MUD

Us

:= M 141.274=

Keulegan Carpenter Number KUs Tu⋅

D tcc( ):= K 0.041=

REUD Us+( ) D tcc( )⋅

ν:= RE 4.756 10

5×=

0 50 100 150 20036

37

38

39

Ws θ tcc,( )lb

ft

θ

deg

RESULT OF CALCULATION

Ws θ tcc,( ) FwFD θ tcc,( ) FI θ tcc,( )+ µ FL θ tcc,( )⋅+

µ

⋅:=Required Submerged Weight

FI θ tcc,( ) 0.25ρsw

gπ⋅ D tcc( )

2⋅ CM⋅ As⋅ sin θ( )⋅:=Inertia Force

FD θ tcc,( ) 0.5ρsw

gD tcc( )⋅ CD⋅ Us cos θ( )⋅ UD+( )

2⋅:=Drag Force

FL θ tcc,( ) 0.5ρsw

gD tcc( )⋅ CL⋅ Us cos θ( )⋅ UD+( )

2⋅:=Lift Force

θ i i deg⋅:=

i 0 180..:=Phase Angle Range

Hydrodynamic Forces vs Required Submerged Weight :

LATERAL SABILITY CALCULATION :

Fw 1:=

if K>50 & M>=0.8, Fw=1.2K 0.041=

M 141.274=

Calibration Factor According To DNV RP E305 Figure 5.12

µ 0.24=µ µs soil 1=if

µc otherwise

:=

Friction Factor

Wreq max Ws θ tcc,( )( ):=

Wreq 56.995kg

m=

B 0.25π D tcc( )2

⋅ ρsw⋅:=

B 536.263kg

m=

Ws tcc( ) Wst Wcorr+ Wins+ Wj+ Was+ Wcc+ Wcont+ B−:=

Ws tcc( ) 56.721lb

ft=

if Ws tcc( ) Wreq≤ "Need More Thickness", "OK!",( ) "OK!"=

Safety Factor For Submerged Weight Due To Requirement Weight

SFwWs tcc( )

Wreq

:= SFw 1.481=


⋅:=



⋅:=


⋅:=


⋅:=


⋅:=


⋅:=



Significant Wave Height Hs 2m:=


Water Depth d 76m:=


pcf lb ft3−

⋅:= C K≡ kPa 103

Pa≡ MPa 106


N≡


Phase : Hydrotest

Wave & Current Data : 1 year return period wave + 1 year retun period current









D tcc( ) 0.816m=








ID2

−

⋅ ρs⋅:=

Wst 272.188kg

m=


Ds2

−

⋅ ρcorr⋅:=

Wcorr 6.159kg

m=


Dcorr2

−

ρins⋅:=

Wins 0kg

m=


⋅:=

Zr 3m:=


⋅ ft2

sec1−

⋅:=



SOIL PARAMETER :



ρsoil 1860kg m3−

⋅:=

CALCULATIONS :

Submerged Weight :



Ws tcc( ) 456.122kg

m=

Bouyancy B tcc( )π

4g⋅ D tcc( )

2⋅

ρsw

g⋅:=

B tcc( ) 360.352lb

ft=



B tcc( ):= SG tcc( ) 1.1≥

SG tcc( ) 1.851=



ρcont

ρsw

:= SGprod 1=


ρsoil

ρsw

:= SGsoil 1.814=


Dins2

−

ρs⋅:=

Wj 0kg

m=


Dj2

−

ρas⋅:=

Was 14.748kg

m=


Das2

−

⋅ ρcc⋅:=

Wcc 327.579kg

m=


⋅ ρcont⋅:=

Wcont 371.711kg

m=


⋅ ρsw⋅:=

B 536.263kg

m=


Ws tcc( ) 306.5lb

ft=

Kb 1.563 104−

× m=Kb 2.5 d50⋅:=


B1 6.384 106−

×=B1Zo

D tcc( ):=

A1 1.566 105

×=A1D tcc( )

Zo

:=


Tu 8.095 s=Tu 1.372 Tp⋅:=


Zo 5.21 106−

m⋅:=Roughnes

d50 0.0625mm:=Grain size





g:= Tn 2.784 s=

Tn

Tp

0.472= φTp

Hs

:= φ 4.172sec

m=


m≤if

1 φ 5sec

m≥if

3.3 otherwise

:=

γ 3.3=



Tn

Tp

0.472=

Us

0.0057 Hs⋅

Tn

:= Us 4.095 103−

×m

s=




⋅< M 0.8≥∧if

0.7 otherwise

:=

CD 0.7=




Clay soil

ratio1

S= ratio

D tcc( ) Su⋅



µc 0.52:=

Sand soil

µs 0.7:=

zobKb

30:= zob 5.208 10

6−× m=


UD1

lnZr

Zo

1+

1 B1+( ) ln A1 1+( )⋅ 1− ⋅

Ur⋅:=

UD 0.579m

s= Us 4.095 10

3−×

m

s=



Tu

:=

As 3.179 103−

× m sec2−

⋅=


Us

:= M 141.274=


D tcc( ):= K 0.041=


ν:= RE 4.756 10

5×=

0 50 100 150 20021

21.5

22

22.5

Ws θ tcc,( )lb

ft

θ

deg



µ



gπ⋅ D tcc( )




2⋅:=Drag Force



2⋅:=Lift Force

θ i i deg⋅:=




Fw 1:=

if K>50 & M>=0.8, Fw=1.2K 0.041=

M 141.274=



µc otherwise

:=

Friction Factor


Wreq 33.258kg

m=

B 0.25π D tcc( )2

⋅ ρsw⋅:=

B 536.263kg

m=


Ws tcc( ) 306.5lb

ft=



SFwWs tcc( )

Wreq

:= SFw 13.715=


⋅:=



⋅:=


⋅:=


⋅:=


⋅:=


⋅:=



Significant Wave Height Hs 3.6m:=


Water Depth d 76m:=


pcf lb ft3−

⋅:= C K≡ kPa 103

Pa≡ MPa 106


N≡


Phase : Operation

Wave & Current Data : 100 years return period wave + 100 years retun period current









D tcc( ) 0.816m=








ID2

−

⋅ ρs⋅:=

Wst 272.188kg

m=


Ds2

−

⋅ ρcorr⋅:=

Wcorr 6.159kg

m=


Dcorr2

−

ρins⋅:=

Wins 0kg

m=


⋅:=

Zr 3m:=


⋅ ft2

sec1−

⋅:=



SOIL PARAMETER :



ρsoil 1860kg m3−

⋅:=

CALCULATIONS :

Submerged Weight :



Ws tcc( ) 107.642kg

m=

Bouyancy B tcc( )π

4g⋅ D tcc( )

2⋅

ρsw

g⋅:=

B tcc( ) 360.352lb

ft=



B tcc( ):= SG tcc( ) 1.1≥

SG tcc( ) 1.201=



ρcont

ρsw

:= SGprod 0.063=


ρsoil

ρsw

:= SGsoil 1.814=


Dins2

−

ρs⋅:=

Wj 0kg

m=


Dj2

−

ρas⋅:=

Was 14.748kg

m=


Das2

−

⋅ ρcc⋅:=

Wcc 327.579kg

m=


⋅ ρcont⋅:=

Wcont 23.232kg

m=


⋅ ρsw⋅:=

B 536.263kg

m=


Ws tcc( ) 72.332lb

ft=

Grain size d50 0.0625mm:=

Roughnes Zo 5.21 106−

m⋅:=


Tu 1.2 Tp⋅:= Tu 9.48 s=


A1D tcc( )

Zo

:= A1 1.566 105

×=

B1Zo

D tcc( ):= B1 6.384 10

6−×=


Kb 2.5 d50⋅:= Kb 1.563 104−

× m=

zobKb

30:= zob 5.208 10

6−× m=





g:= Tn 2.784 s=

Tn

Tp

0.352= φTp

Hs

:= φ 4.164sec

m=


m≤if

1 φ 5sec

m≥if

3.3 otherwise

:=

γ 3.3=



Tn

Tp

0.352=

Us

0.028 Hs⋅

Tn

:= Us 0.036m

s=



⋅< M 0.8≥∧if

0.7 otherwise

:=

CD 0.7=




Clay soil

ratio1

S= ratio

D tcc( ) Su⋅



µc 0.25:=

Sand soil

µs 0.7:=


UD1

lnZr

Zo

1+

1 B1+( ) ln A1 1+( )⋅ 1− ⋅

Ur⋅:=

UD 0.661m

s= Us 0.036

m

s=



Tu

:=

As 0.024 m sec2−

⋅=


Us

:= M 18.26=


D tcc( ):= K 0.421=


ν:= RE 5.693 10

5×=


0 50 100 150 20040

50

60

Ws θ tcc,( )lb

ft

θ

deg



µ



gπ⋅ D tcc( )




2⋅:=Drag Force



2⋅:=Lift Force

θ i i deg⋅:=




Fw 1:=

if K>50 & M>=0.8, Fw=1.2K 0.421=

M 18.26=



µc otherwise

:=

Friction Factor


Wreq 87.88kg

m=

B 0.25π D tcc( )2

⋅ ρsw⋅:=

B 536.263kg

m=


Ws tcc( ) 72.332lb

ft=



SFwWs tcc( )

Wreq

:= SFw 1.225=

Econc 2.999 1010

Pa⋅:=

Dj Dcorr:=Density of steel ρs 490pcf:=

Das Dj 2 tas⋅+:=Density of concrete ρconc 190pcf:=

Density of corrosion coating ρcorr 915kg m3−

⋅:=

Asphalt Density ρas 1300kg

m3

:=

Span length L 22m:=

Internal Pipe area Aiπ

4ID

2⋅:= Ai 0.363 m

2=

Cross Section Steel Area Asteelπ

4Ds

2ID

2−

⋅:= Asteel 0.035 m

2=

Density of Content ρcontent 0pcf:=

Design Presure Pd 0psi:=

kinematic viskocity vk 1.076 105−

⋅ ft2

s1−

⋅:=

Poisson Ratio v 0.3:=

Specified Minimum Yield Strength SMYS 65000psi:=

Specified Minimum Tensile Strength SMTS 77000psi:=

FREE SPAN ANALYSIS

SCREENING FATIGUE Phase : Installation

kN 103N≡ kPa 10

3Pa≡ MPa 10

6Pa≡ pcf lb ft

3−⋅≡ C K≡ kJ 10

3J≡

Pipeline Design Parameter:

Outer Diameter Ds 28in:= Corrosion Allowance tca 0in:=


Internal Diameter ID Ds 2 ts⋅−:= ID 26.75 in=

Corrosion Coating thickness tcorr 3mm:=

Concrete Coating tcc 1.75in:=

Asphalt enamel tas 5mm:=

Total Diameter D Ds 2 tcorr⋅+ 2 tcc⋅+ 2 tas⋅+:= D 32.13 in=

Modulus Elasticity of steel Esteel 2.068 1011

Pa⋅:=

Dcorr Ds 2 tcorr⋅+:=Modulus Elasticity of concrete

(100 year)Ts100 7.9sec:= Tp100 1.05Ts100:= Tp100 8.295s=

Current Velocity :

(1 year) Uc1 0.7m

s:=

(100 year) Uc100 0.8m

s:=

External Pressure Pe ρsw g⋅ h⋅:= Pe 110.819 psi=

Load Effect Factor for Pressure γp 1.05:= href 1m:=

Specific Local Pressure P1d Pd ρcontent g⋅ h href−( )⋅+:=

Pressure Diference ∆P γp P1d Pe−⋅:= ∆P 116.36 psi=

Boundary Condition Cofficient :

Case : Pinned-Pinned C1 1.57:=

C2 1.00:=

C3 0.8:=

C4 4.39:=

C51

8:=

Effective (residual) Lay Tension Heff 0kN:=

Temperature expansion Coefficient αe 1.17 105−

⋅1

K:=

Span Height e 1m:=

Environmental Parameter :

Density of Seawater ρsw 64pcf:=

Water Depth h 76m:=

Design Temperature Td 100C:=

Laying Temperature Tsw 20C:=

Temperature Difference ∆T Td Tsw−:= ∆T 80 C=

Significant Wave Height :

(1 year) Hs1 2m:=

(100 year) Hs100 3.6m:=

Peak Period :

(1 year) Ts1 5.9sec:= Tp1 1.05Ts1:= Tp1 6.195 s=

Wconcπ

4D

2Ds 2 tcorr⋅+( )

2−

⋅ ρconc⋅:= Wconc 243.577

lb

ft=


Dj2

−

ρas⋅:= Was 9.91

lb

ft=

Content Weight Wcontentπ

4ID

2ρcontent⋅:= Wcontent 0

lb

ft=

Added Mass Weight Waddπ

4D

2⋅ ρsw:= Wadd 360.352

lb

ft=

Effective Weight Wpipe Wsteel Wconc+ Wcorr+ Wcontent+ Wadd+ Was+:=

Wpipe 800.879lb

ft= Wpipeforce Wpipe g⋅:= Wpipeforce 1.169 10

4× N m

1−⋅=

Submerged Weight Wsub Wpipe 2 Wadd⋅−:= Wsub 80.176lb

ft=

Wsubforce Wsub g⋅:= Wsubforce 1.17 103

× N m1−

⋅=

Dynamic stiffness factor vertical Cv 3000kN m

5−

2⋅:= Table 7.6

Dynamic stiffness factor horizontal Cl 2600kN m

5−

2⋅:=

C65

384:=

Concrete Stifness Factor :

Inertia of Concrete Iconcπ

64D

4Ds 2 tcorr⋅+( )

4−

⋅:= Iconc 8.787 10

3−× m

4=

Inertia of Steel Isteelπ

64Ds

4ID

4−

⋅:= Isteel 2.097 10

3−× m

4=

Empirical Constant of

Slippage of corrosion and

concrete coating

coat 3:= 1 asphalt= 2 PP= 3 PE=

kc 0.33 coat 1=if

0.25 coat 2= coat 3=∨( )if

:= kc 0.25=

Stiffness of Concrete Coating CSF kc

Econc Iconc⋅

Esteel Isteel⋅

0.75

⋅:= CSF 0.172=

Mass of Pipe :

Steel Weight Wsteelπ

4Ds

2ID

2−

⋅ ρs⋅:= Wsteel 182.902

lb

ft=

Corrosion Weight Wcorrπ

4Ds 2 tcorr⋅+( )

2Ds

2−

⋅ ρcorr⋅:= Wcorr 4.139

lb

ft=

Concrete Weight

Reduction Velocity Factor for In-Line:L

D26.957=

Modal Damping Ratio

Structural Damping ζstr 0.01:=

Soil Damping Horizontal

(in-line)ζsoil_IL 0.02:= Table 7.4

Soil Damping Vertical

(cross-flow)ζsoil_CF 0.012:=

Hidrodynamic Damping ζh 0.00:=

Total Modal Damping Ratio ζT_IL ζstr ζsoil_IL+ ζh+:= ζT_IL 0.03=

Total Modal Damping Ratio ζT_CF ζstr ζsoil_CF+ ζh+:= ζT_CF 0.022=

Dynamic Soil

Stifness verticalKV

Cv

1 v−

1

3

2

3

ρs

ρsw

⋅+

⋅ D⋅:= 7.4.10

KV 2.105 104

×kN

m2

=

Dynamic Soil

Stifness verticalKL Cl 1 v+( )⋅

1

3

2

3

ρs

ρsw

⋅+

⋅ D⋅:=

KL 1.66 104

×kN

m2

=

K max KV KL,( ):= K 2.105 104

×kN

m2

=

Parameter of Soil Stiffness β logK L

4⋅

1 CSF+( ) Esteel⋅ Isteel⋅

:=

β 3.987=

Effective of Soil Stiffness Leff4.73

0.066− β2

⋅ 1.02 β⋅+ 0.63+

L⋅

β 2.7≥if

4.73

0.036 β2

⋅ 0.61 β⋅+ 1.0+

L⋅

β 2.7<if

:= 6.7.9

Leff 28.529 m=

Euler Buckling PE

1 CSF+( ) π2

⋅ C2⋅ Esteel⋅ Isteel⋅

Leff2

:= PE 6.163 106

× N=

Significant Wave Height Hs100 3.6 m=

Natural Peiode Tnh

g:= Tn 2.784 s=

Peak Enhancement Factor 100 year φ100

Tp100

Hs100

m0.5

s⋅:= φ100 4.164=

γ 5 φ100 3.6≤if

exp 5.75 1.15 φ100⋅−( ) 3.6 φ100< 5<if

1 φ100 5≥if

:=

γ 2.616=

From Figure 3-2, with :Tn

Tp100

0.352= and γ 2.616=

Significant Flow Velocity

Amplitude at Pipe LevelUs100

0.028 Hs100⋅

Tn

:= Us100 0.036m

s=

Wave Spreading Coefficient Rd 1:=

Wave Induced Flow Velocity

( 100 year)Uw100 Us100 Rd⋅:= Uw100 0.036

m

s=

Stability Parameter In-Line Ks_IL

4π Wpipe⋅ ζT_IL⋅

ρsw D2

⋅

:= Ks_IL 0.658= 4.1.8

Stability Parameter Cross-Line Ks_CF

4π Wpipe⋅ ζT_CF⋅

ρsw D2

⋅

:= Ks_CF 0.483=

Safety Factor for Fatigue, onset value

for in-line & cross flow VIVγon_IL 1.10:= Table 2.1

γon_CF 1.20:=

Safety Factor for In-Line γIL 1.4:= Table 2.1

Safety Factor for Cross-Flow γCF 1.4:=

Safety Factor for Natural Frequency γf 1.2:=

Safety Factor for Damping γk 1.15:= Table 2.2

Flow Velocity on Pipeline Level:

Assumsed : Linear Wave Theory

Peak Periods Tp100 7.9s:=

Ksd_IL

Ks_IL

γk

:= Ksd_IL 0.572=

Reduction of Stability Parameter

(cros flow)Ksd_CF

Ks_CF

γk

:= Ksd_CF 0.42=

Turbulence Intensity Ic

σc

Uc

= σcstandard deviation of the velocity

fluctuations

Ucthe 10min or 30min average

(mean)

velocity (1 Hz sampling rate)Ic 5%:=

Relative Direction θrel 60deg:=

Reduction Function RIθ1 1 π2 π

22 θrel⋅−

⋅ Ic 0.03−( )⋅

−:=

RIθ1 0.982=

RIθ2 1Ic 0.03−( )

0.17−:=

RIθ2 0.882=


Tp1

Hs1

m0.5

s⋅:= φ1 4.381=

γ 5 φ1 3.6≤if

exp 5.75 1.15 φ1⋅−( ) 3.6 φ1< 5<if

1 φ1 5≥if

:=

γ 2.039=

From Figure 3-2, with:Tn

Tp1

0.449= and γ 2.039=



0.005 Hs1⋅

Tn

:= Us1 3.592 103−

×m

s=



( 1 year)Uw1 Us1 Rd⋅:= Uw1 3.592 10

3−×

m

s=

Current Flow Velocity Ratio αUc100

Uw1 Uc100+:= α 0.996=


(In-line)

∆

D0.46=∆

1.25 d⋅ e−

DD⋅:=

d 1.1 e⋅:=Trench effect

Correction Factor

ψproxionst 1=

4.4.6ψproxionst1

54 1.25

e

D⋅+

⋅

e

D0.8<if

1 otherwise

:=Seabed proximity Correction Factor

Reduction Velocity Factor for Cross-Flow:

fo_IL_ok 1.2371

s=

fo_IL_ok C1 1 CSF+⋅Esteel Isteel⋅

Wpipe L4( )⋅

1Seff

PE_ok

+ C3

δIL

D

2

⋅

+

⋅⋅:=

Natural Frequency

(In-line)

PE_ok 1.036 107

× N=PE_ok

1 CSF+( ) π2


L2

:=Euler Buckling

for pinned-pinned boundary condition Leff is to be replaced by L in the above expressions

also for PE (euler buckling load) see Para 6.8.8, note no.2 table 6-1.

fo_IL 0.4141

s=

fo_IL C1 1 CSF+⋅Esteel Isteel⋅

Wpipe Leff4

⋅

1Seff

PE

+ C3

δIL

D

2

⋅

+

⋅⋅:=Natural Frequency

(In-line)

δIL 0D:=Static Deflection

Seff 6.829− 106

× N=

Seff Heff ∆P Ai⋅ 1 2 v⋅−( )⋅ − Asteel Esteel⋅ ∆T⋅ αe⋅( )−:=Effective axial force

VR_IL_onset 1.066=

VR_IL_onset1

γon_IL

Ksd_IL 0.4<if

0.6 Ksd_IL+

γon_IL

0.4 Ksd_IL< 1.6<if

2.2

γon_IL

Ksd_IL 1.6≥if

:=In-Line Reduction Factor

CheckCF 1fo_CF_ok

γCF

Uc100 Uw1+

VR_CF_onset D⋅γCF⋅>if

0 otherwise

:=

- Passed if Check-CF = 1

- Failed if Check-CF = 0

Cross flow Criteria:

Screening Fatigue Criteria for Cross-Flow:

CheckIL 1=

CheckIL 1fo_IL_ok

γIL

Uc100

VR_IL_onset D⋅1

L

D

250−

⋅1

α⋅>if

0 otherwise

:=

- Passed if Check-IL = 1

- Failed if Check-IL = 0

In-Line Criteria:

Screening Fatigue Criteria for In-Line:

fo_CF_ok 2.2631

s=

fo_CF_ok C1 1 CSF+⋅Esteel Isteel⋅

Wpipe L4( )⋅

1Seff

PE_ok

+ C3

δCF

D

2

⋅

+

⋅⋅:=

Natural Frequency

(In-line)



fo_CF 1.0481

s=

fo_CF C1 1 CSF+⋅Esteel Isteel⋅

Wpipe Leff4

⋅

1Seff

PE

+ C3

δCF

D

2

⋅

+


(cross-flow)

δCF 1D:=Static Deflection (cross-flow)

VR_CF_onset 3.074=

VR_CF_onset 3ψproxionst ψtrenchonset⋅

γon_CF

⋅:=Cross-Flow Reduction

Factor

fo_IL 0.4141

s=fw 0.127

1

s=fw

1

Tp100

:=Wave Frequency

ψ trenchonset 1.23=ψ trenchonset 1 0.5∆

D⋅+:=

CheckCF 1=

Econc 2.999 1010

Pa⋅:=




⋅:=


m3

:=

Span length L 21.09m:=


4ID

2⋅:= Ai 0.363 m

2=


4Ds

2ID

2−

⋅:= Asteel 0.035 m

2=




⋅ ft2

s1−

⋅:=




FREE SPAN ANALYSIS

SCREENING FATIGUE Phase : Hydrotest

kN 103N≡ kPa 10

3Pa≡ MPa 10

6Pa≡ pcf lb ft

3−⋅≡ C K≡ kJ 10

3J≡










Pa⋅:=



Current Velocity :

(1 year) Uc1 0.7m

s:=

(100 year) Uc100 0.8m

s:=




Pressure Diference ∆P γp P1d Pe−⋅:= ∆P 1.731 103

× psi=



C2 1.00:=

C3 0.8:=

C4 4.39:=

C51

8:=



⋅1

K:=

Span Height e 1m:=



Water Depth h 76m:=





(1 year) Hs1 2m:=

(100 year) Hs100 3.6m:=

Peak Period :


Wconcπ

4D

2Ds 2 tcorr⋅+( )

2−


lb

ft=


Dj2

−

ρas⋅:= Was 9.91

lb

ft=


4ID

2ρcontent⋅:= Wcontent 249.778

lb

ft=


4D

2⋅ ρsw:= Wadd 360.352

lb

ft=


Wpipe 1.051 103

×lb


4× N m

1−⋅=


ft=


× N m1−

⋅=


5−

2⋅:= Table 7.6


5−

2⋅:=

C65

384:=



64D

4Ds 2 tcorr⋅+( )

4−

⋅:= Iconc 8.787 10

3−× m

4=


64Ds

4ID

4−

⋅:= Isteel 2.097 10

3−× m

4=



concrete coating


kc 0.33 coat 1=if

0.25 coat 2= coat 3=∨( )if

:= kc 0.25=


Econc Iconc⋅

Esteel Isteel⋅

0.75

⋅:= CSF 0.172=

Mass of Pipe :


4Ds

2ID

2−

⋅ ρs⋅:= Wsteel 182.902

lb

ft=


4Ds 2 tcorr⋅+( )

2Ds

2−


lb

ft=

Concrete Weight

L

D25.842=

Modal Damping Ratio









Dynamic Soil

Stifness verticalKV

Cv

1 v−

1

3

2

3

ρs

ρsw

⋅+

⋅ D⋅:= 7.4.10

KV 2.105 104

×kN

m2

=

Dynamic Soil


1

3

2

3

ρs

ρsw

⋅+

⋅ D⋅:=

KL 1.66 104

×kN

m2

=

K max KV KL,( ):= K 2.105 104

×kN

m2

=


4⋅


:=

β 3.914=


0.066− β2

⋅ 1.02 β⋅+ 0.63+

L⋅

β 2.7≥if

4.73

0.036 β2

⋅ 0.61 β⋅+ 1.0+

L⋅

β 2.7<if

:=

Leff 27.626 m=

Euler Buckling PE

1 CSF+( ) π2


Leff2

:= PE 6.573 106

× N=

Reduction Velocity Factor for In-Line:


Natural Peiode Tnh

g:= Tn 2.784 s=


Tp100

Hs100

m0.5

s⋅:= φ100 4.164=

γ 5 φ100 3.6≤if

exp 5.75 1.15 φ100⋅−( ) 3.6 φ100< 5<if

1 φ100 5≥if

:=

γ 2.616=


Tp100

0.352= and γ 2.616=



0.028 Hs100⋅

Tn

:= Us100 0.036m

s=



( 100 year)Uw100 Us100 Rd⋅:= Uw100 0.036

m

s=



ρsw D2

⋅

:= Ks_IL 0.863= 4.1.8



ρsw D2

⋅

:= Ks_CF 0.633=



γon_CF 1.20:=








Ksd_IL

Ks_IL

γk

:= Ksd_IL 0.751=


(cros flow)Ksd_CF

Ks_CF

γk

:= Ksd_CF 0.551=


σc

Uc


fluctuations


(mean)




22 θrel⋅−

⋅ Ic 0.03−( )⋅

−:=

RIθ1 0.982=

RIθ2 1Ic 0.03−( )

0.17−:=

RIθ2 0.882=


Tp1

Hs1

m0.5

s⋅:= φ1 4.381=

γ 5 φ1 3.6≤if

exp 5.75 1.15 φ1⋅−( ) 3.6 φ1< 5<if

1 φ1 5≥if

:=

γ 2.039=


Tp1

0.449= and γ 2.039=



0.005 Hs1⋅

Tn

:= Us1 3.592 103−

×m

s=



( 1 year)Uw1 Us1 Rd⋅:= Uw1 3.592 10

3−×

m

s=


Uw1 Uc100+:= α 0.996=


(In-line)


D⋅+:=

∆

D0.46=∆

1.25 d⋅ e−

DD⋅:=


Correction Factor

ψproxionst 1=

4.4.6ψproxionst1

54 1.25

e

D⋅+

⋅

e

D0.8<if

1 otherwise



fo_IL_ok 1.0091

s=


Wpipe L4( )⋅

1Seff

PE_ok

+ C3

δIL

D

2

⋅

+

⋅⋅:=

Natural Frequency

(In-line)

PE_ok 1.128 107

× N=PE_ok

1 CSF+( ) π2


L2

:=Euler Buckling



fo_IL 0.6261

s=


Wpipe Leff4

⋅

1Seff

PE

+ C3

δIL

D

2

⋅

+


(In-line)


Seff 8.443− 106

× N=


VR_IL_onset 1.228=

VR_IL_onset1

γon_IL

Ksd_IL 0.4<if

0.6 Ksd_IL+

γon_IL

0.4 Ksd_IL< 1.6<if

2.2

γon_IL

Ksd_IL 1.6≥if


CheckCF 1=

CheckCF 1fo_CF_ok

γCF

Uc100 Uw1+


0 otherwise

:=





CheckIL 1=

CheckIL 1fo_IL_ok

γIL

Uc100

VR_IL_onset D⋅1

L

D

250−

⋅1

α⋅>if

0 otherwise

:=



In-Line Criteria:


fo_CF_ok 2.0631

s=


Wpipe L4( )⋅

1Seff

PE_ok

+ C3

δCF

D

2

⋅

+

⋅⋅:=

Natural Frequency

(In-line)



fo_CF 0.8421

s=


Wpipe Leff4

⋅

1Seff

PE

+ C3

δCF

D

2

⋅

+


(cross-flow)


VR_CF_onset 3.074=


γon_CF


Factor

fo_IL 0.6261

s=fw 0.127

1

s=fw

1

Tp100

:=Wave Frequency

Econc 2.999 1010

Pa⋅:=




⋅:=


m3

:=



4ID

2⋅:= Ai 0.363 m

2=


4Ds

2ID

2−

⋅:= Asteel 0.035 m

2=




⋅ ft2

s1−

⋅:=




FREE SPAN ANALYSIS

SCREENING FATIGUE Phase : Operation

kN 103N≡ kPa 10

3Pa≡ MPa 10

6Pa≡ pcf lb ft

3−⋅≡ C K≡ kJ 10

3J≡










Pa⋅:=



Current Velocity :

(1 year) Uc1 0.7m

s:=

(100 year) Uc100 0.8m

s:=





× psi=



C2 1.00:=

C3 0.8:=

C4 4.39:=



⋅1

K:=

Span Height e 1m:=



Water Depth h 76m:=





(1 year) Hs1 2m:=

(100 year) Hs100 3.6m:=

Peak Period :


Concrete Weight Wconcπ

4D

2Ds 2 tcorr⋅+( )

2−


lb

ft=


Dj2

−

ρas⋅:= Was 9.91

lb

ft=


4ID


lb

ft=


4D

2⋅ ρsw:= Wadd 360.352

lb

ft=


Wpipe 816.491lb


4× N m

1−⋅=


ft=


× N m1−

⋅=


5−

2⋅:= Table 7.6

C51

8:=

C65

384:=



64D

4Ds 2 tcorr⋅+( )

4−

⋅:= Iconc 8.787 10

3−× m

4=


64Ds

4ID

4−

⋅:= Isteel 2.097 10

3−× m

4=



concrete coating


kc 0.33 coat 1=if

0.25 coat 2= coat 3=∨( )if

:= kc 0.25=


Econc Iconc⋅

Esteel Isteel⋅

0.75

⋅:= CSF 0.172=

Mass of Pipe :


4Ds

2ID

2−

⋅ ρs⋅:= Wsteel 182.902

lb

ft=


4Ds 2 tcorr⋅+( )

2Ds

2−


lb

ft=

PE 6.338 106

× N=


D26.467=

Modal Damping Ratio









5−

2⋅:=

Dynamic Soil

Stifness verticalKV

Cv

1 v−

1

3

2

3

ρs

ρsw

⋅+

⋅ D⋅:= 7.4.10

KV 2.105 104

×kN

m2

=

Dynamic Soil


1

3

2

3

ρs

ρsw

⋅+

⋅ D⋅:=

KL 1.66 104

×kN

m2

=

K max KV KL,( ):= K 2.105 104

×kN

m2

=


4⋅


:=

β 3.955=


0.066− β2

⋅ 1.02 β⋅+ 0.63+

L⋅

β 2.7≥if

4.73

0.036 β2

⋅ 0.61 β⋅+ 1.0+

L⋅

β 2.7<if

:= 6.7.9

Leff 28.132 m=

Euler Buckling PE

1 CSF+( ) π2


Leff2

:=



Natural Peiode Tnh

g:= Tn 2.784 s=


Tp100

Hs100

m0.5

s⋅:= φ100 4.164=

γ 5 φ100 3.6≤if

exp 5.75 1.15 φ100⋅−( ) 3.6 φ100< 5<if

1 φ100 5≥if

:=

γ 2.616=


Tp100

0.352= and γ 2.616=



0.028 Hs100⋅

Tn

:= Us100 0.036m

s=



( 100 year)Uw100 Us100 Rd⋅:= Uw100 0.036

m

s=




ρsw D2

⋅

:= Ks_IL 0.671= 4.1.8



ρsw D2

⋅

:= Ks_CF 0.492=



γon_CF 1.20:=







Ksd_IL

Ks_IL

γk

:= Ksd_IL 0.583=


(cros flow)Ksd_CF

Ks_CF

γk

:= Ksd_CF 0.428=


σc

Uc


fluctuations


(mean)




22 θrel⋅−

⋅ Ic 0.03−( )⋅

−:=

RIθ1 0.982=

RIθ2 1Ic 0.03−( )

0.17−:=

RIθ2 0.882=


Tp1

Hs1

m0.5

s⋅:= φ1 4.381=

γ 5 φ1 3.6≤if

exp 5.75 1.15 φ1⋅−( ) 3.6 φ1< 5<if

1 φ1 5≥if

:=

γ 2.039=


Tp1

0.449= and γ 2.039=



0.005 Hs1⋅

Tn

:= Us1 3.592 103−

×m

s=



( 1 year)Uw1 Us1 Rd⋅:= Uw1 3.592 10

3−×

m

s=


Uw1 Uc100+:= α 0.996=


(In-line)


D⋅+:=

∆

D0.46=∆

1.25 d⋅ e−

DD⋅:=


Correction Factor

ψproxionst 1=

4.4.6ψproxionst1

54 1.25

e

D⋅+

⋅

e

D0.8<if

1 otherwise



fo_IL_ok 1.1481

s=


Wpipe L4( )⋅

1Seff

PE_ok

+ C3

δIL

D

2

⋅

+

⋅⋅:=

Natural Frequency

(In-line)

PE_ok 1.075 107

× N=PE_ok

1 CSF+( ) π2


L2

:=Euler Buckling



fo_IL 0.6071

s=


Wpipe Leff4

⋅

1Seff

PE

+ C3

δIL

D

2

⋅

+


(In-line)


Seff 7.758− 106

× N=


VR_IL_onset 1.076=

VR_IL_onset1

γon_IL

Ksd_IL 0.4<if

0.6 Ksd_IL+

γon_IL

0.4 Ksd_IL< 1.6<if

2.2

γon_IL

Ksd_IL 1.6≥if


CheckCF 1=

CheckCF 1fo_CF_ok

γCF

Uc100 Uw1+


0 otherwise

:=





CheckIL 1=

CheckIL 1fo_IL_ok

γIL

Uc100

VR_IL_onset D⋅1

L

D

250−

⋅1

α⋅>if

0 otherwise

:=



In-Line Criteria:


fo_CF_ok 2.261

s=


Wpipe L4( )⋅

1Seff

PE_ok

+ C3

δCF

D

2

⋅

+

⋅⋅:=

Natural Frequency

(In-line)



fo_CF 0.9741

s=


Wpipe Leff4

⋅

1Seff

PE

+ C3

δCF

D

2

⋅

+


(cross-flow)


VR_CF_onset 3.074=


γon_CF


Factor

fo_IL 0.6071

s=fw 0.127

1

s=fw

1

Tp100

:=Wave Frequency

Modulus Elasticity of concrete Econc 2.999 1010

Pa⋅:=




⋅:=

Asphalt Densityρas 1300

kg

m3

:=

Span length L 22m:=


4ID

2⋅:= Ai 0.363 m

2=


4Ds

2ID

2−

⋅:= Asteel 0.035 m

2=




⋅ ft2

s1−

⋅:=



FREE SPAN ANALYSIS

ULTIMATE LIMIT STATE (ULS) CRITERIA Phase : Installation

kN 103N≡ kPa 10

3Pa≡ MPa 10

6Pa≡ pcf lb ft

3−⋅≡ C K≡ kJ 10

3J≡










Pa⋅:=Dcorr Ds 2 tcorr⋅+:=

Ts100 7.9sec:= Tp100 1.05Ts100:= Tp100 8.295s=

Current Velocity :

(1 year) Uc1 0.7m

s:=

(100 year) Uc100 0.8m

s:=


Load Effect Factor for Pressure γp 1.05:= href Ds:=



Soil Parameter : Silty clay

Soil Type Soil 2:= 1 sand= 2 clay=

Void Ratio es 0.6:=

Earth Pressure Coeff Ko 0.5:=




⋅1

K:=

Span Height e 1m:=



Water Depth h 76m:=





(1 year) Hs1 2m:=

(100 year) Hs100 3.6m:=

Peak Period :


(100 year)


64D

4Ds 2 tcorr⋅+( )

4−

⋅:= Iconc 8.787 10

3−× m

4=


64Ds

4ID

4−

⋅:= Isteel 2.097 10

3−× m

4=



concrete coating


kc 0.33 coat 1=if

0.25 coat 2= coat 3=∨( )if

:= kc 0.25=


Econc Iconc⋅

Esteel Isteel⋅

0.75

⋅:= CSF 0.172=

Mass of Pipe :


4Ds

2ID

2−

⋅ ρs⋅:= Wsteel 182.902

lb

ft=


4Ds 2 tcorr⋅+( )

2Ds

2−


lb

ft=

Unit Weight of water γwater 10kN m3−

⋅:=

Submerged Unit weight of soil γsoil_sub 7kN m3−

⋅:=

Total Unit weight of soil γsoil γsoil_sub γwater+:= γsoil 17 kN m3−

⋅=

Undrained Shear Strength Su 50kN m2−

⋅:=

Vertical soil settlement (soil

embedment)v 10mm:=

Over-Consolidation Ratio OCR 1 Soil 2=if

0 otherwise

:= OCR 1=



C2 1.00:=

C3 0.8:=

C4 4.39:=

C51

8:=

C65

384:=



ft=


× N m1−

⋅=

Effective Span Length :

Load Distribution Width b 2 D v−( ) v⋅⋅ v 0.5 D⋅≤if

D v 0.5 D⋅>if

:=

b 0.18 m=

Support Length Ratio Lsh/L (silty clay) Lsr 0.3:=

Effective mean Stress σs1

21 Ko+( )⋅ b⋅ γsoil_sub⋅

Wsubforce

3 b⋅1

0.5

Lsr

+

⋅+:=

σs 6.735kPa=


5−

2⋅:=


5−

2⋅:=

Dynamic Soil

Stifness verticalKV

Cv

1 ν−

1

3

2

3

ρs

ρsw

⋅+

⋅ D⋅:=


4D

2Ds 2 tcorr⋅+( )

2−


lb

ft=


Dj2

−

ρas⋅:= Was 9.91

lb

ft=


4ID

2ρcontent⋅:= Wcontent 0

lb

ft=


4D

2⋅ ρsw:= Wadd 360.352

lb

ft=

Span Height Ratioe

D1.225=

Added Mass

CoefficientCa 0.68

1.6

1 5e

D

⋅+

+

e

D0.8<if

1e

D0.8≥if

:=

Ca 1=


Wpipe 800.879lb


4× N m

1−⋅=

Incidental Pressure Factor γinc 1.10:=

Incidental Pressure Pinc γinc Pd⋅:= Pd 0 psi=

Pinc 0 psi=

Specific Local Pressure Pli Pinc ρcontent g⋅ h D−( )⋅+:=

Pli 0 psi=

Material Strength Factor αU 0.96:=

Anisotropy Factor αA 0.95:=

Material Resistance Factor γm 1.15:=

Safety Class Resistance Factor γSC 1.138:=

KV 2.105 104

×kN

m2

=

Dynamic Soil

Stifness verticalKL Cl 1 ν+( )⋅

1

3

2

3

ρs

ρsw

⋅+

⋅ D⋅:=

KL 1.66 104

×kN

m2

=

K max KV KL,( ):= K 2.105 104

×kN

m2

=


4⋅


:=

β 3.987=


0.066− β2

⋅ 1.02 β⋅+ 0.63+

L⋅

β 2.7≥if

4.73

0.036 β2

⋅ 0.61 β⋅+ 1.0+

L⋅

β 2.7<if

:= 6.7.9

Leff 28.529 m=

Euler Buckling PE

1 CSF+( ) π2


Leff2

:= PE 6.163 106

× N=

Inplace Strength Analysis (based on DnV OS-F101 (DnV 2007)

1. Pressure Containment Requirement

c Pp2

Pp Pe1⋅ fo⋅D

ts tca−( )⋅+

−:=

bb Pe1−:=Analytical Pressure Collapse

(three degree polynom)

fo 0.003:=Ovalisation

Pp 2 fy⋅ αfab⋅ts tca−

D

⋅:=

αfab 0.85:=Maximum Fabrication Factor

fy SMYS fytemp−( ) αU⋅:=Characteristic Yield Strength

Pe1

2 Esteel⋅ts tca−

D

3

⋅

1 ν2

−

:=

Pressure Collapse

External Pressure Requirement (System Collapse Check)

2. Local Buckling Requirement

Req_yield 1=

Req_burst 1 Pli Pe−( )D ts tfab− tca−( )−

2 ts tfab− tca−( )⋅⋅

η

1.15SMYS futemp−( )⋅≤if

0 otherwise

:=

Bursting

Limit

State Req

Bursting Limit State Requirtement

Req_yield 1=

Req_yield 1 Pli Pe−( )D ts tfab− tca−( )−

2 ts tfab− tca−( )⋅⋅ η SMYS fytemp−( )⋅≤if

0 otherwise

:=Yielding

Limit

State Req

Yielding Limit State Requirement


futemp 0MPa:=Derating Value to Tensile Strength

fytemp 0MPa:=Derating Value to Yield Strength

η2 αU⋅

3 γm⋅ γSC⋅ γinc⋅:=Usage Factor for Pressure

Containment

tfab 5% ts⋅:=Fabrication Wall Thickness

Modal Damping Ratio

Structural Damping ζstr 0.01:= 6.2.11


(in-line)ζsoil_IL 0.02:= table 7.4






d Pe1 Pp2

⋅:=

u1

3

1−

3bb

2⋅ c+

⋅:=

vi1

2

2

27bb

3⋅

1

3bb⋅ c⋅− d+

⋅:=

Φ acosvi−

u3

−

:=


3

60 π⋅

180+

⋅:=

Pressure Collapse Pc y1

3bb⋅−:=

Pc 467.347 psi=

Pe 110.819 psi=

External Pressure Req Req_ext 1 Pe

Pc

1.1 γm⋅ γSC⋅≤if

0 otherwise

:=

Req_ext 1=

Pipe Member Subjected to Bending Moment, Effective Axial Force, & Internal

Overpressure

In-Line Unit Stress Amplitude AIL C4 1 CSF+( )⋅D Ds ts−( )⋅ Esteel⋅

Leff2

⋅:=

AIL 1.076 105

× psi=


D26.957=

Tp100 7.9s:=


Natural Peiode Tnh

g:= Tn 2.784 s=


Tp100

Hs100

m0.5

s⋅:= φ100 4.164=

γ 5 φ100 3.6≤if

exp 5.75 1.15 φ100⋅−( ) 3.6 φ100< 5<if

1 φ100 5≥if

:=

γ 2.616=


Tp100

0.352= and γ 2.616=



0.028 Hs100⋅

Tn

:= Us100 0.036m

s=



( 100 year)Uw100 Us100 Rd⋅:= Uw100 0.036

m

s=



ρsw D2

⋅

:= Ks_IL 0.658= 4.1.8



ρsw D2

⋅

:= Ks_CF 0.483=



γon_CF 1.20:=




Safety Factor for In-Line Stress

Rangeγs 1.3:=

Safety Factor for Damping γk 1.15:=



Peak Periods

ψαIL 1=


(In-line)Ksd_IL

Ks_IL

γk

:= Ksd_IL 0.572=


(cros flow)Ksd_CF

Ks_CF

γk

:= Ksd_CF 0.42=


σc

Uc


fluctuations


(mean)

velocity (1 Hz sampling rate)

Ic 5%:=



22 θrel⋅−

⋅ Ic 0.03−( )⋅

−:=

RIθ1 0.982=

RIθ2 1Ic 0.03−( )

0.17−:=

RIθ2 0.882=


Tp1

Hs1

m0.5

s⋅:= φ1 4.381=

γ 5 φ1 3.6≤if

exp 5.75 1.15 φ1⋅−( ) 3.6 φ1< 5<if

1 φ1 5≥if

:= γ 2.039=


Tp1

0.449= and γ 2.039=



0.005 Hs1⋅

Tn

:= Us1 3.592 103−

×m

s=



( 100 year)Uw1 Us1 Rd⋅:= Uw1 3.592 10

3−×

m

s=


Uw100 Uc100+:= α 0.957=

Reduction Function for reduced

In-Line VIV in Wave Induced

Flow

ψαIL 0.0 α 0.5<if

α 0.5−( )

0.30.5 α< 0.8<if

1.0 α 0.8>if

:=


Seff 6.829− 106

× N=

Seff Heff ∆P Ai⋅ 1 2 ν⋅−( )⋅ − Asteel Esteel⋅ ∆T⋅ αe⋅( )−:=Effective axial force

0

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

0,09

0,1

0 1 2 3 4 5

VR_IL_2 3.886=VR_IL_2 VR_IL_end 2 Ay2⋅−:=

VR_IL_end 4.042=

VR_IL_end 4.5 0.8 Ksd_IL⋅−( ) Ksd_IL 1<if

3.7 Ksd_IL 1≥if

:=

VR_IL_1 1.991=VR_IL_1 10 Ay1⋅ VR_IL_onset+:=

VR_IL_onset 1.066=

VR_IL_onset1

γon_IL

Ksd_IL 0.4<if

0.6 Ksd_IL+

γon_IL

0.4 Ksd_IL< 1.6<if

2.2

γon_IL

Ksd_IL 1.6≥if


Ay1 0.092=Ay1 max 0.18 1

Ksd_IL

1.2−

⋅ RIθ1⋅ Ay2,

:=

Ay2 0.078=Ay2 0.13 1Ksd_IL

1.8−

⋅ RIθ2⋅:=Inline VIV Amplitude (Ay/D)

ψproxionst1

54 1.25

e

D⋅+

⋅

e

D0.8<if

1 otherwise

:= 4.4.6

ψproxionst 1=

Trench effect

Correction Factord 1.1 e⋅:=

∆1.25 d⋅ e−

DD⋅:=

∆

D0.46=

ψ trenchonset 1 0.5∆

D⋅+:= ψ trenchonset 1.23=

Wave Frequency fw1

Tp100

:= fw 0.1271

s= fo_IL 0.414

1

s=

Keulegan Carpenter Number KCUw100

fw D⋅:= KC 0.351=

Natural Frequency

(In-line)fo_IL C1 1 CSF+⋅

Esteel Isteel⋅

Wpipe Leff4

⋅

1Seff

PE

+ C3

δIL

D

2

⋅

+

⋅⋅:=

fo_IL 0.4141

s=

Reduced Velocity VRIL

Uc100 Uw1+

fo_IL D⋅:=

VRdIL VRIL γf⋅:=

VRdIL 2.854=

In-Line Amplitude Response Ayo 0.086:= AyoAmplitude

Diameter

=

Stress Range for In-Line Direction

In-Line Stress Range SIL 2 AIL⋅ Ayo⋅ ψαIL⋅ γs⋅:=

SIL 1.659 108

× Pa=


In-Line Unit Stress Amplitude ACF AIL:=

Seabed proximity Correction Factor

VRdCF VRCF γf⋅:=

VRCF

Uc100 Uw1+

fo_CF D⋅:=Reduced Velocity

fo_CF 1.0481

s=


Wpipe Leff4

⋅

1Seff

PE

+ C3

δCF

D

2

⋅

+


(cross-flow)


0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 2 4 6 8 10 12 14 16 18

VR_CF_2 9=

VR_CF_2 VR_CF_end7

1.3

Az1( )⋅−:=

VR_CF_end 16:=

VR_CF_1 7=VR_CF_1 77 VR_CF_onset−( )

1.151.3 Az1−( )⋅−:=

VR_CF_onset 3.074=


γon_CF


Factor

Az2 1.3=Az2 Az1:=

Az1 1.3=

Az1 0.7 KC 10<if

0.7 0.01 KC 10−( )⋅+[ ][ ] α 0.8≤ 10 KC≤ 30≤∧if

0.9 KC 30>if

1.3 α 0.8>if

:=Cross-Flow VIV Amplitude

(Az/D)

Md 1.102 103

× kJ=

Md max Mdyn Mstatic_ok,( ):=Design Bending Moment

Mstatic_ok Mstatic:=

Mstatic 1.102− 103

× kJ=

Mstatic C5

Wsub Leff2

⋅

1Seff

PE

+

⋅ g⋅:=Static Bending Moment

Mdyn 500.244 kJ=

Mdyn max σdynIL σdynCF,( )2 Isteel⋅

Ds ts−⋅:=Dynamic Bending Moment

due to VIV or direct wave act.

Bending Moment

σdynCF 0 psi=

σdynCF1

2SCF:=Cross-Flow Stress Dynamic

σdynIL 1.203 104

× psi=

σdynIL1

2max SIL 0.4SCF

AIL

ACF

⋅,

:=In-Line Stress Dynamic

SCF 0 psi=Cross-Flow Stress Range

SIL 2.406 104

× psi=In-Line Stress Range

Summary Stress Range

SCF 0 psi=

SCF 2 ACF⋅ Azo⋅ Rk⋅ γs⋅:=Cross-Flow Stress Range

Stress Range for Cross-Flow Direction

Rk 1 0.15 Ksd_CF⋅−( ) Ksd_CF 4≤if

3.2 Ksd_CF1.5−

⋅

Ksd_CF 4>if

:=Amplitude Reduction due to

Damping

AzoAmplitude

Diameter

=Azo 0:=In-Line Amplitude Response

VRdCF 1.128=

Moment Plastic Limit Mp fy π⋅ Ds ts−( )2

⋅ ts⋅:= Mp 1.037 107

× J=

Yield Stress Characteristic fy 6.24 104

× psi=

Tensile Stress Characteristic fu αU αA⋅ SMTS futemp−( )⋅:=

fu 7.022 104

× psi=

Strain Hardening Adjusment

Parameterqh

Pld Pe−( )Pp

Pli Pe>if

0 otherwise

:=

B 0.4 qh+( )D

ts

15<if

0.4 qh+( )

60D

ts

−

45⋅

15D

ts

≤ 60≤if

0 otherwise

:=

αc 1 B−( ) Bfu

fy

⋅+:=

αc 1.01= αc 1.2<

Bursting Pressure (containment) Pb2

3

2 ts⋅

Ds ts−⋅ min fy

fu

1.15,

⋅:=

Pb 3.22 103

× psi=

Design Pressure Differential

Pressure Load Factor γp 1.05=

Depth Reference href 0.711 m=

Design Pressure Pd 0 psi=

Design Pressure Differential ∆Pd γp Pd ρcontent g⋅ h href−( )⋅+ ρsw g⋅ h⋅− ⋅:=

∆Pd 116.36− psi=

Specific Local Pressure Pld Pd ρcontent g⋅ h href−( )⋅+:=

Pld 0 psi=

Momen and Axial Plastic Limit

Axial Plastic Limit Sp fy π⋅ Ds ts−( )⋅ ts⋅:= Sp 1.492 107

× N=

Requirement for Pipe Member Subjected to Bending Moment, Effective Axial Force, &

Internal Overpressure

Req_1 1 γSC γm⋅Seff

αc Sp⋅

2

⋅ γSC γm⋅Md

αc Mp⋅1

∆Pd

αc Pb⋅

2

−⋅

⋅+∆Pd

αc Pb⋅

2

+ 1≤if

0 otherwise

:=

Req_1 1=

Pipe Member Subjected to Bending Moment, Effective Axial Force, & External

Overpressure

Req_2 1 γSC γm⋅Md

αc Mp⋅

⋅ γSC γm⋅Seff

αc Sp⋅

2

+

2

γSC γm⋅Pe

Pc

⋅

2

+ 1≤if

0 otherwise

:=

Req_2 1=

Propagation Buckling Requirement

Propagating Pressure Ppr 35fy αfab⋅

γm γSC⋅⋅

ts tfab− tca−

D

2.5

⋅:=

Ppr 65.852 psi=

Propagating Pressure Req Req_prop 1 Ppr Pc<if

0 otherwise

:=

Req_prop 1=

Modulus Elasticity of concrete Econc 2.999 1010

Pa⋅:=




⋅:=


kg

m3

:=



4ID

2⋅:= Ai 0.363 m

2=


4Ds

2ID

2−

⋅:= Asteel 0.035 m

2=




⋅ ft2

s1−

⋅:=



FREE SPAN ANALYSIS

ULTIMATE LIMIT STATE (ULS) CRITERIA Phase : Hydrotest

kN 103N≡ kPa 10

3Pa≡ MPa 10

6Pa≡ pcf lb ft

3−⋅≡ C K≡ kJ 10

3J≡











Ts100 7.9sec:= Tp100 1.05Ts100:= Tp100 8.295s=

Current Velocity :

(1 year) Uc1 0.7m

s:=

(100 year) Uc100 0.8m

s:=





× psi=



Void Ratio es 0.6:=





⋅1

K:=

Span Height e 1m:=



Water Depth h 118m:=





(1 year) Hs1 2m:=

(100 year) Hs100 3.6m:=

Peak Period :


(100 year)

Iconcπ

64D

4Ds 2 tcorr⋅+( )

4−

⋅:= Iconc 8.787 10

3−× m

4=


64Ds

4ID

4−

⋅:= Isteel 2.097 10

3−× m

4=



concrete coating


kc 0.33 coat 1=if

0.25 coat 2= coat 3=∨( )if

:= kc 0.25=


Econc Iconc⋅

Esteel Isteel⋅

0.75

⋅:= CSF 0.172=

Mass of Pipe :


4Ds

2ID

2−

⋅ ρs⋅:= Wsteel 182.902

lb

ft=


4Ds 2 tcorr⋅+( )

2Ds

2−


lb

ft=


⋅:=


⋅:=


⋅=


⋅:=


embedment)v 10mm:=


0 otherwise

:= OCR 1=



C2 1.00:=

C3 0.8:=

C4 4.39:=

C51

8:=

C65

384:=


Inertia of Concrete


ft=


× N m1−

⋅=



D v 0.5 D⋅>if

:=

b 0.18 m=




Wsubforce

3 b⋅1

0.5

Lsr

+

⋅+:=

σs 24.78kPa=


5−

2⋅:=


5−

2⋅:=

Dynamic Soil

Stifness verticalKV

Cv

1 ν−

1

3

2

3

ρs

ρsw

⋅+

⋅ D⋅:=


4D

2Ds 2 tcorr⋅+( )

2−


lb

ft=


Dj2

−

ρas⋅:= Was 9.91

lb

ft=


4ID


lb

ft=


4D

2⋅ ρsw:= Wadd 360.352

lb

ft=

Span Height Ratioe

D1.225=

Added Mass

CoefficientCa 0.68

1.6

1 5e

D

⋅+

+

e

D0.8<if

1e

D0.8≥if

:=

Ca 1=


Wpipe 1.051 103

×lb


4× N m

1−⋅=

Incidental Pressure Factor γinc 1.10:=

Incidental Pressure Pinc γinc Pd⋅:= Pd 1.65 103

× psi=

Pinc 1.815 103

× psi=

Specific Local Pressure Pli Pinc ρcontent g⋅ h D−( )⋅+:=

Pli 1.986 103

× psi=

Material Strength Factor αU 0.96:=

Anisotropy Factor αA 0.95:=



KV 2.105 104

×kN

m2

=

Dynamic Soil

Stifness verticalKL Cl 1 ν+( )⋅

1

3

2

3

ρs

ρsw

⋅+

⋅ D⋅:=

KL 1.66 104

×kN

m2

=

K max KV KL,( ):= K 2.105 104

×kN

m2

=


4⋅


:=

β 3.914=


0.066− β2

⋅ 1.02 β⋅+ 0.63+

L⋅

β 2.7≥if

4.73

0.036 β2

⋅ 0.61 β⋅+ 1.0+

L⋅

β 2.7<if

:= 6.7.9

Leff 27.626 m=

Euler Buckling PE

1 CSF+( ) π2


Leff2

:= PE 6.573 106

× N=



bb Pe1−:=Analytical Pressure Collapse

(three degree polynom)



D

⋅:=



Pe1


D

3

⋅

1 ν2

−

:=

Pressure Collapse



Req_yield 1=



η


0 otherwise

:=

Bursting

Limit

State Req


Req_yield 1=



0 otherwise

:=Yielding

Limit

State Req



futemp 0MPa:=Derating Value to Tensile Strength

fytemp 0MPa:=Derating Value to Yield Strength

η2 αU⋅

3 γm⋅ γSC⋅ γinc⋅:=Usage Factor for Pressure

Containment

tfab 5% ts⋅:=Fabrication Wall Thickness

ζT_IL 0.03=ζT_IL ζstr ζsoil_IL+ ζh+:=Total Modal Damping Ratio

ζh 0.00:=Hidrodynamic Damping

ζsoil_CF 0.012:=Soil Damping Vertical

(cross-flow)

table 7.4ζsoil_IL 0.02:=Soil Damping Horizontal

(in-line)

6.2.11ζstr 0.01:=Structural Damping

Modal Damping Ratio

L

D25.842=Reduction Velocity Factor for In-Line:

c Pp2

Pp Pe1⋅ fo⋅D

ts tca−( )⋅+

−:=

d Pe1 Pp2

⋅:=

u1

3

1−

3bb

2⋅ c+

⋅:=

vi1

2

2

27bb

3⋅

1

3bb⋅ c⋅− d+

⋅:=

Φ acosvi−

u3

−

:=


3

60 π⋅

180+

⋅:=


3bb⋅−:=

Pc 467.347 psi=

Pe 172.062 psi=


Pc


0 otherwise

:=

Req_ext 1=


Overpressure


Leff2

⋅:=

AIL 1.147 105

× psi=

γk 1.15:=





Natural Peiode Tnh

g:= Tn 3.469 s=


Tp100

Hs100

m0.5

s⋅:= φ100 4.164=

γ 5 φ100 3.6≤if

exp 5.75 1.15 φ100⋅−( ) 3.6 φ100< 5<if

1 φ100 5≥if

:=

γ 2.616=


Tp100

0.439= and γ 2.616=



0.028 Hs100⋅

Tn

:= Us100 0.029m

s=





ρsw D2

⋅

:= Ks_IL 0.863= 4.1.8



ρsw D2

⋅

:= Ks_CF 0.633=



γon_CF 1.20:=





Rangeγs 1.3:=

Safety Factor for Damping



Flow


α 0.5−( )

0.30.5 α< 0.8<if

1.0 α 0.8>if

:= ψαIL 1=


(In-line)Ksd_IL

Ks_IL

γk

:= Ksd_IL 0.751=


(cros flow)Ksd_CF

Ks_CF

γk

:= Ksd_CF 0.551=


σc

Uc


fluctuations


(mean)


Ic 5%:=



22 θrel⋅−

⋅ Ic 0.03−( )⋅

−:=

RIθ1 0.982=

( )


( 100 year)Uw100 Us100 Rd⋅:= Uw100 0.029

m

s=


Tp1

Hs1

m0.5

s⋅:= φ1 4.381=

γ 5 φ1 3.6≤if

exp 5.75 1.15 φ1⋅−( ) 3.6 φ1< 5<if

1 φ1 5≥if

:=

γ 2.039=


Tp1

0.56= and γ 2.039=



0.005 Hs1⋅

Tn

:= Us1 2.883 103−

×m

s=



( 100 year)Uw1 Us1 Rd⋅:= Uw1 2.883 10

3−×

m

s=


Uw100 Uc100+:= α 0.965=

Seff 8.444− 106

× N=

Seff Heff ∆P Ai⋅ 1 2 ν⋅−( )⋅ − Asteel Esteel⋅ ∆T⋅ αe⋅( )−:=Effective axial force

0

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

0 1 2 3 4 5


VR_IL_end 3.899=


3.7 Ksd_IL 1≥if

:=


VR_IL_onset 1.228=

VR_IL_onset1

γon_IL

Ksd_IL 0.4<if

0.6 Ksd_IL+

γon_IL

0.4 Ksd_IL< 1.6<if

2.2

γon_IL

Ksd_IL 1.6≥if


Ay1 0.067=Ay1 max 0.18 1

Ksd_IL

1.2−

⋅ RIθ1⋅ Ay2,

:=

Ay2 0.067=Ay2 0.13 1Ksd_IL

1.8−


RIθ2 0.882=

RIθ2 1Ic 0.03−( )

0.17−:=

ACF AIL:=

Seabed proximity Correction Factor ψproxionst1

54 1.25

e

D⋅+

⋅

e

D0.8<if

1 otherwise

:=

ψproxionst 1=

Trench effect


∆1.25 d⋅ e−

DD⋅:=

∆

D0.46=



Wave Frequency fw1

Tp100

:= fw 0.1271

s= fo_IL 0.626

1

s=

Keulegan Carpenter Number KCUw100

fw D⋅:= KC 0.281=

Static Deflection δIL 0D:=

Natural Frequency


Esteel Isteel⋅

Wpipe Leff4

⋅

1Seff

PE

+ C3

δIL

D

2

⋅

+

⋅⋅:=

fo_IL 0.6261

s=


Uc100 Uw1+

fo_IL D⋅:=

VRdIL VRIL γf⋅:=

VRdIL 1.887=


Diameter

=



SIL 1.399 108

× Pa=


In-Line Unit Stress Amplitude

VRCF

Uc100 Uw1+

fo_CF D⋅:=Reduced Velocity

fo_CF 0.8421

s=


Wpipe Leff4

⋅

1Seff

PE

+ C3

δCF

D

2

⋅

+


(cross-flow)


0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 2 4 6 8 10 12 14 16 18

VR_CF_2 9=

VR_CF_2 VR_CF_end7

1.3

Az1( )⋅−:=

VR_CF_end 16:=


1.151.3 Az1−( )⋅−:=

VR_CF_onset 3.074=


γon_CF


Factor

Az2 1.3=Az2 Az1:=

Az1 1.3=

Az1 0.7 KC 10<if

0.7 0.01 KC 10−( )⋅+[ ][ ] α 0.8≤ 10 KC≤ 30≤∧if

0.9 KC 30>if

1.3 α 0.8>if


(Az/D)

σdynIL1

2max SIL 0.4SCF

AIL

ACF

⋅,

:=

σdynIL 1.014 104

× psi=

Cross-Flow Stress Dynamic σdynCF1

2SCF:=

σdynCF 0 psi=

Bending Moment

Dynamic Bending Moment

due to VIV or direct wave act.Mdyn max σdynIL σdynCF,( )

2 Isteel⋅

Ds ts−⋅:=

Mdyn 421.821 kJ=

Static Bending Moment Mstatic C5

Wsub Leff2

⋅

1Seff

PE

+

⋅ g⋅:=

Mstatic 1.614− 103

× kJ=


Design Bending Moment Md max Mdyn Mstatic_ok,( ):=

Md 1.614 103

× kJ=

VRdCF VRCF γf⋅:=

VRdCF 1.402=

In-Line Amplitude Response Azo 0:= AzoAmplitude

Diameter

=

Amplitude Reduction due to

DampingRk 1 0.15 Ksd_CF⋅−( ) Ksd_CF 4≤if

3.2 Ksd_CF1.5−

⋅

Ksd_CF 4>if

:=


Cross-Flow Stress Range SCF 2 ACF⋅ Azo⋅ Rk⋅ γs⋅:=

SCF 0 psi=


In-Line Stress Range SIL 2.029 104

× psi=

Cross-Flow Stress Range SCF 0 psi=

In-Line Stress Dynamic


⋅ ts⋅:= Mp 1.037 107

× J=


× psi=


fu 7.022 104

× psi=


Parameterqh

Pld Pe−( )Pp

Pli Pe>if

0 otherwise

:=

B 0.4 qh+( )D

ts

15<if

0.4 qh+( )

60D

ts

−

45⋅

15D

ts

≤ 60≤if

0 otherwise

:=

αc 1 B−( ) Bfu

fy

⋅+:=

αc 1.029= αc 1.2<

Bursting Pressure (containment) Pb2

3

2 ts⋅

Ds ts−⋅ min fy

fu

1.15,

⋅:=

Pb 3.22 103

× psi=




Design Pressure Pd 1.65 103

× psi=


∆Pd 1.731 103

× psi=


Pld 1.821 103

× psi=



× N=




αc Sp⋅

2

⋅ γSC γm⋅Md

αc Mp⋅1

∆Pd

αc Pb⋅

2

−⋅

⋅+∆Pd

αc Pb⋅

2

+ 1≤if

0 otherwise

:=

Req_1 1=


Overpressure


αc Mp⋅

⋅ γSC γm⋅Seff

αc Sp⋅

2

+

2

γSC γm⋅Pe

Pc

⋅

2

+ 1≤if

0 otherwise

:=

Req_2 1=


Propagating Pressure Ppr 35fy αfab⋅

γm γSC⋅⋅

ts tfab− tca−

D

2.5

⋅:=

Ppr 65.852 psi=

Propagating Pressure Req Req_prop 1 Ppr Pc<if

0 otherwise

:=

Req_prop 1=

Econc 2.999 1010

Pa⋅:=




⋅:=


kg

m3

:=



4ID

2⋅:= Ai 0.363 m

2=


4Ds

2ID

2−

⋅:= Asteel 0.035 m

2=




⋅ ft2

s1−

⋅:=




FREE SPAN ANALYSISkN 10

3N≡ kPa 10

3Pa≡ MPa 10

6Pa≡ pcf lb ft

3−⋅≡ C K≡ kJ 10

3J≡

ULTIMATE LIMIT STATE (ULS) CRITERIA Phase : Operation











Modulus Elasticity of concrete

Ts100 7.9sec:= Tp100 1.05Ts100:= Tp100 8.295s=

Current Velocity :

(1 year) Uc1 0.7m

s:=

(100 year) Uc100 0.8m

s:=







Poissons ratio

Void Ratio es 0.6:=



⋅1

K:=

Span Height e 1m:=



Water Depth h 118m:=





(1 year) Hs1 2m:=

(100 year) Hs100 3.6m:=

Peak Period :


(100 year)

C65

384:=



64D

4Ds 2 tcorr⋅+( )

4−

⋅:= Iconc 8.787 10

3−× m

4=


64Ds

4ID

4−

⋅:= Isteel 2.097 10

3−× m

4=



concrete coating


kc 0.33 coat 1=if

0.25 coat 2= coat 3=∨( )if

:= kc 0.25=


Econc Iconc⋅

Esteel Isteel⋅

0.75

⋅:= CSF 0.172=

Mass of Pipe :


4Ds

2ID

2−

⋅ ρs⋅:= Wsteel 182.902

lb

ft=



⋅:=


⋅:=


⋅=


⋅:=


embedment)v 10mm:=


0 otherwise

:= OCR 1=



C2 1.00:=

C3 0.8:=

C4 4.39:=

C51

8:=

Wpipe 816.491lb


4× N m

1−⋅=


ft=


× N m1−

⋅=



D v 0.5 D⋅>if

:=

b 0.18 m=




Wsubforce

3 b⋅1

0.5

Lsr

+

⋅+:=

σs 7.863kPa=


5−

2⋅:=


5−

2⋅:=


4Ds 2 tcorr⋅+( )

2Ds

2−


lb

ft=


4D

2Ds 2 tcorr⋅+( )

2−


lb

ft=


Dj2

−

ρas⋅:= Was 9.91

lb

ft=


4ID


lb

ft=


4D

2⋅ ρsw:= Wadd 360.352

lb

ft=

Span Height Ratioe

D1.225=

Added Mass

CoefficientCa 0.68

1.6

1 5e

D

⋅+

+

e

D0.8<if

1e

D0.8≥if

:=

Ca 1=


αA 0.95:=Anisotropy Factor

αU 0.96:=Material Strength Factor

Pli 1.221 103

× psi=

Pli Pinc ρcontent g⋅ h D−( )⋅+:=Specific Local Pressure

Pinc 1.21 103

× psi=

Pd 1.1 103

× psi=Pinc γinc Pd⋅:=Incidental Pressure

γinc 1.10:=Incidental Pressure Factor



PE 6.338 106

× N=PE

1 CSF+( ) π2


Leff2

:=Euler Buckling

Leff 28.132 m=

Leff4.73

0.066− β2

⋅ 1.02 β⋅+ 0.63+

L⋅

β 2.7≥if

4.73

0.036 β2

⋅ 0.61 β⋅+ 1.0+

L⋅

β 2.7<if

:=Effective of Soil Stiffness

β 3.955=

β logK L

4⋅


:=Parameter of Soil Stiffness

K 2.105 104

×kN

m2

=K max KV KL,( ):=

KL 1.66 104

×kN

m2

=

KL Cl 1 ν+( )⋅1

3

2

3

ρs

ρsw

⋅+

⋅ D⋅:=Dynamic Soil

Stifness vertical

KV 2.105 104

×kN

m2

=

KV

Cv

1 ν−

1

3

2

3

ρs

ρsw

⋅+

⋅ D⋅:=Dynamic Soil

Stifness vertical



D

⋅:=



Pe1


D

3

⋅

1 ν2

−

:=

Pressure Collapse



Req_yield 1=



η


0 otherwise

:=

Bursting

Limit

State Req




Fabrication Wall Thickness tfab 5% ts⋅:=

Usage Factor for Pressure

Containmentη

2 αU⋅

3 γm⋅ γSC⋅ γinc⋅:=

Derating Value to Yield Strength fytemp 0MPa:=

Derating Value to Tensile Strength futemp 0MPa:=



Yielding

Limit

State Req



0 otherwise

:=

Req_yield 1=

AIL 1.107 105

× psi=


D26.467=

Modal Damping Ratio

Structural Damping ζstr 0.01:= 6.2.11


(in-line)ζsoil_IL 0.02:= table 7.4




Analytical Pressure Collapse

(three degree polynom)bb Pe1−:=

c Pp2

Pp Pe1⋅ fo⋅D

ts tca−( )⋅+

−:=

d Pe1 Pp2

⋅:=

u1

3

1−

3bb

2⋅ c+

⋅:=

vi1

2

2

27bb

3⋅

1

3bb⋅ c⋅− d+

⋅:=

Φ acosvi−

u3

−

:=


3

60 π⋅

180+

⋅:=


3bb⋅−:=

Pc 467.347 psi=

Pe 172.062 psi=


Pc


0 otherwise

:=

Req_ext 1=


Overpressure


Leff2

⋅:=


Rangeγs 1.3:=

Safety Factor for Damping γk 1.15:=





Natural Peiode Tnh

g:= Tn 3.469 s=


Tp100

Hs100

m0.5

s⋅:= φ100 4.164=

γ 5 φ100 3.6≤if

exp 5.75 1.15 φ100⋅−( ) 3.6 φ100< 5<if

1 φ100 5≥if

:=

γ 2.616=


Tp100

0.439= and γ 2.616=



0.028 Hs100⋅

Tn

:= Us100 0.029m

s=





ρsw D2

⋅

:= Ks_IL 0.671= 4.1.8



ρsw D2

⋅

:= Ks_CF 0.492=


for in-line & cross flow VIVγon 1.10:= table 2.1

γon_IL 1.10:= γon_CF 1.20:=





Uw100 Uc100+:= α 0.965=



Flow


α 0.5−( )

0.30.5 α< 0.8<if

1.0 α 0.8>if

:= ψαIL 1=


(In-line)Ksd_IL

Ks_IL

γk

:= Ksd_IL 0.583=


(cros flow)Ksd_CF

Ks_CF

γk

:= Ksd_CF 0.428=


σc

Uc


fluctuations


(mean)


Ic 5%:=




( 100 year)Uw100 Us100 Rd⋅:= Uw100 0.029

m

s=


Tp1

Hs1

m0.5

s⋅:= φ1 4.381=

γ 5 φ1 3.6≤if

exp 5.75 1.15 φ1⋅−( ) 3.6 φ1< 5<if

1 φ1 5≥if

:=

γ 2.039=


Tp1

0.56= and γ 2.039=



0.005 Hs1⋅

Tn

:= Us1 2.883 103−

×m

s=



( 100 year)Uw1 Us1 Rd⋅:= Uw1 2.883 10

3−×

m

s=

( ) ( )

0

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

0,09

0,1

0 1 2 3 4 5


VR_IL_end 4.033=


3.7 Ksd_IL 1≥if

:=


VR_IL_onset 1.076=

VR_IL_onset1

γon_IL

Ksd_IL 0.4<if

0.6 Ksd_IL+

γon_IL

0.4 Ksd_IL< 1.6<if

2.2

γon_IL

Ksd_IL 1.6≥if


Ay1 0.091=Ay1 max 0.18 1

Ksd_IL

1.2−

⋅ RIθ1⋅ Ay2,

:=

Ay2 0.078=Ay2 0.13 1Ksd_IL

1.8−


RIθ2 0.882=

RIθ2 1Ic 0.03−( )

0.17−:=

RIθ1 0.982=

RIθ1 1 π2 π

22 θrel⋅−

⋅ Ic 0.03−( )⋅

−:=Reduction Function

SIL 1.785 108

× Pa=


In-Line Unit Stress Amplitude ACF AIL:=

Seabed proximity Correction Factor ψproxionst1

54 1.25

e

D⋅+

⋅

e

D0.8<if

1 otherwise

:= 4.4.6

ψproxionst 1=

Trench effect


∆1.25 d⋅ e−

DD⋅:=

∆

D0.46=



Effective axial force Seff Heff ∆P Ai⋅ 1 2 ν⋅−( )⋅ − Asteel Esteel⋅ ∆T⋅ αe⋅( )−:=

Seff 7.698− 106

× N=

Static Deflection δIL 0D:=

Natural Frequency


Esteel Isteel⋅

Wpipe Leff4

⋅

1Seff

PE

+ C3

δIL

D

2

⋅

+

⋅⋅:=

fo_IL 0.5941

s=


Uc100 Uw1+

fo_IL D⋅:=

VRdIL VRIL γf⋅:=

VRdIL 1.987=


Diameter

=




0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 2 4 6 8 10 12 14 16 18

VR_CF_2 9=

VR_CF_2 VR_CF_end7

1.3

Az1( )⋅−:=

VR_CF_end 16:=


1.151.3 Az1−( )⋅−:=

VR_CF_onset 3.074=


γon_CF


Factor

Az2 1.3=Az2 Az1:=

Az1 1.3=

Az1 0.7 KC 10<if

0.7 0.01 KC 10−( )⋅+[ ][ ] α 0.8≤ 10 KC≤ 30≤∧if

0.9 KC 30>if

1.3 α 0.8>if


(Az/D)

KC 0.281=KCUw100

fw D⋅:=Keulegan Carpenter Number

fo_IL 0.5941

s=fw 0.127

1

s=fw

1

Tp100

:=Wave Frequency

In-Line Stress Range SIL 2.589 104

× psi=

Cross-Flow Stress Range SCF 0 psi=

In-Line Stress Dynamic σdynIL1

2max SIL 0.4SCF

AIL

ACF

⋅,

:=

σdynIL 1.295 104

× psi=

Cross-Flow Stress Dynamic σdynCF1

2SCF:=

σdynCF 0 psi=

Bending Moment

Dynamic Bending Moment

due to VIV or direct wave act.Mdyn max σdynIL σdynCF,( )

2 Isteel⋅

Ds ts−⋅:=

Mdyn 538.384 kJ=

Static Bending Moment Mstatic C5

Wsub Leff2

⋅

1Seff

PE

+

⋅ g⋅:=

Natural Frequency

(cross-flow)fo_CF C1 1 CSF+⋅

Esteel Isteel⋅

Wpipe Leff4

⋅

1Seff

PE

+ C3

δCF

D

2

⋅

+

⋅⋅:=

fo_CF 0.9821

s=

Reduced Velocity VRCF

Uc100 Uw1+

fo_CF D⋅:=

VRdCF VRCF γf⋅:=

VRdCF 1.203=

In-Line Amplitude Response Azo 0:= AzoAmplitude

Diameter

=

Amplitude Reduction due to

DampingRk 1 0.15 Ksd_CF⋅−( ) Ksd_CF 4≤if

3.2 Ksd_CF1.5−

⋅

Ksd_CF 4>if

:=


Cross-Flow Stress Range SCF 2 ACF⋅ Azo⋅ Rk⋅ γs⋅:=

SCF 0 psi=


Pld 1.111 103

× psi=



× N=


⋅ ts⋅:= Mp 1.037 107

× J=


× psi=


fu 7.022 104

× psi=


Parameterqh

Pld Pe−( )Pp

Pli Pe>if

0 otherwise

:=

B 0.4 qh+( )D

ts

15<if

0.4 qh+( )

60D

ts

−

45⋅

15D

ts

≤ 60≤if

0 otherwise

:=

Mstatic 644.638− kJ=


Design Bending Moment Md max Mdyn Mstatic_ok,( ):=

Md 644.638 kJ=




Design Pressure Pd 1.1 103

× psi=


∆Pd 985.559 psi=


Req_prop 1=

Req_prop 1 Ppr Pc<if

0 otherwise

:=Propagating Pressure Req

Ppr 65.852 psi=

Ppr 35fy αfab⋅

γm γSC⋅⋅

ts tfab− tca−

D

2.5

⋅:=Propagating Pressure


Req_2 1=


αc Mp⋅

⋅ γSC γm⋅Seff

αc Sp⋅

2

+

2

γSC γm⋅Pe

Pc

⋅

2

+ 1≤if

0 otherwise

:=


Overpressure

Req_1 1=


αc Sp⋅

2

⋅ γSC γm⋅Md

αc Mp⋅1

∆Pd

αc Pb⋅

2

−⋅

⋅+∆Pd

αc Pb⋅

2

+ 1≤if

0 otherwise

:=



Pb 3.22 103

× psi=

Pb2

3

2 ts⋅

Ds ts−⋅ min fy

fu

1.15,

⋅:=Bursting Pressure (containment)

αc 1.2<αc 1.02=

αc 1 B−( ) Bfu

fy

⋅+:=

6.7.2

4.4.6

Wave Height

(m) Kejadian Frek Relatif CDF PDF

T life(20 th)

(s)

ts

(m)

Ds

(m)

Dtot

(m)

Es

(Psi)

Is

(m4) C γf γk γs

0.000 - 0.490 10043613 5.1927E-01 5.1927E-01 2.7330E-01 6.3072E+08 0.016 0.711 0.816 3.00E+07 2.10E-03 4.30E+11 1.20 1.15 1.30

0.500 - 0.990 7417485 3.8349E-01 9.0276E-01 2.0184E-01 6.3072E+08 0.016 0.711 0.816 3.00E+07 2.10E-03 4.30E+11 1.20 1.15 1.30

1.000 - 1.490 1640910 8.4837E-02 9.8760E-01 4.4651E-02 6.3072E+08 0.016 0.711 0.816 3.00E+07 2.10E-03 4.30E+11 1.20 1.15 1.30

1.500 - 1.990 217635 1.1252E-02 9.9885E-01 5.9221E-03 6.3072E+08 0.016 0.711 0.816 3.00E+07 2.10E-03 4.30E+11 1.20 1.15 1.30

2.000 - 2.490 20994 1.0854E-03 9.9993E-01 5.7127E-04 6.3072E+08 0.016 0.711 0.816 3.00E+07 2.10E-03 4.30E+11 1.20 1.15 1.30

2.500 - 2.990 1266 6.5454E-05 1.0000E+00 3.4449E-05 6.3072E+08 0.016 0.711 0.816 3.00E+07 2.10E-03 4.30E+11 1.20 1.15 1.30

3.000 - 3.490 0 0.0000E+00 1.0000E+00 0.0000E+00 6.3072E+08 0.016 0.711 0.816 3.00E+07 2.10E-03 4.30E+11 1.20 1.15 1.30

m h

(m)

Hs

(m)

Tp

(s)

Tn

(s) Tn/Tp γ

Ud

m/s

Us

m/s St

fs

(1/s)

fn_IL

(1/s)

fn_CF

(1/s) Vr_IL Vr_CF Vrd_IL Vrd_CF

3 90.2 0.245 2.195 3.033 1.382 2.000 0.8 8.08E-05 0.200 0.196 0.263 0.260 3.728 3.771 4.474 4.525

3 90.2 0.745 3.827 3.033 0.792 2.000 0.8 3.68E-03 0.200 0.197 0.263 0.260 3.745 3.788 4.494 4.546

3 90.2 1.245 4.947 3.033 0.613 2.000 0.8 1.23E-02 0.200 0.199 0.263 0.260 3.785 3.829 4.542 4.595

3 90.2 1.745 5.857 3.033 0.518 2.000 0.8 4.60E-02 0.200 0.207 0.263 0.260 3.942 3.988 4.731 4.785

3 90.2 2.245 6.644 3.033 0.456 2.000 0.8 8.14E-02 0.200 0.216 0.263 0.260 4.107 4.155 4.929 4.985

3 90.2 2.745 7.346 3.033 0.413 2.000 0.8 1.30E-01 0.200 0.228 0.263 0.260 4.335 4.385 5.202 5.262

3 90.2 3.245 7.987 3.033 0.380 2.000 0.8 1.94E-01 0.200 0.244 0.263 0.260 4.630 4.684 5.556 5.620

Ay/D Az/D L

(m)

Leff

(m) Leff/D

e

(m) e/D CSF

AIL

(psi) Ks_IL Ks_CF Ksd_IL Ksd_CF Rk

0.120 0.000 144.000 149.502 183.213 0.78 0.955882353 0.172 3916.4659 0.403 0.403 0.350 0.350 0.947435

0.118 0.000 144.000 149.502 183.213 0.78 0.955882353 0.172 3916.4659 0.403 0.403 0.350 0.350 0.947435

0.116 0.000 144.000 149.502 183.213 0.78 0.955882353 0.172 3916.4659 0.403 0.403 0.350 0.350 0.947435

0.112 0.000 144.000 149.502 183.213 0.78 0.955882353 0.172 3916.4659 0.403 0.403 0.350 0.350 0.947435

0.040 0.000 144.000 149.502 183.213 0.78 0.955882353 0.172 3916.4659 0.403 0.403 0.350 0.350 0.947435

0.000 0.112 144.000 149.502 183.213 0.78 0.955882353 0.172 3916.4659 0.403 0.403 0.350 0.350 0.947435

0.000 0.115 144.000 149.502 183.213 0.78 0.955882353 0.172 3916.4659 0.403 0.403 0.350 0.350 0.947435

S-IL

(psi)

S-IL

(MPa) Ni-IL

S-CF

(psi)

S-CF

(Mpa) Ni-CF ni D fat - IL D fat-CF

1157.706 8.425 7.19E+08 0.000 0.000 #DIV/0! 6.42E+07 8.932E-02 0

1138.411 8.285 7.56E+08 0.000 0.000 #DIV/0! 1.12E+08 1.483E-01 0

1119.116 8.144 7.96E+08 0.000 0.000 #DIV/0! 1.24E+08 1.558E-01 0

1080.526 7.863 8.85E+08 0.000 0.000 #DIV/0! 1.31E+08 1.477E-01 0

385.902 2.808 1.94E+10 0.000 0.000 #DIV/0! 1.36E+08 7.015E-03 0

0.000 0.000 #DIV/0! 1080.526 7.863 8.85E+08 1.44E+08 0.000E+00 1.63E-01

0.000 0.000 #DIV/0! 1109.468 8.074 8.17E+08 1.54E+08 0.000E+00 1.88E-01

Total 0.548147 0.350622

Life time 1.824328 2.852072

Documents

DAFTAR PUSTAKA A - Institut Teknologi Bandungdigilib.itb.ac.id/files/disk1/629/jbptitbpp-gdl-ratnapuspi-31432-7... · DAFTAR PUSTAKA A Abidin, Zenal. ... Veritas Offshore Technology