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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:=
Storm Surge (25 yr) SS25 0m:=
Storm Surge (100 yr) SS100 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
× psi= operating( )
System Test P1t 1.05Pinc ρcont2 g⋅ href h1−( )⋅ +:= P1t 1.1 103
× psi= operating( )
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=
y 2− u−⋅ cosΦ
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"=
Operational Condition
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"=
Operational Condition
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
Operational Condition
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=
Density corrosion coating ρcorr 915kg m3−
⋅:=
Thermal insulation coating density ρins 4.5pcf:=
Concrete coating density ρcc 3040kg m3−
⋅:=
Content density ρcont 64lb 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 : Hydrotest
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( ) 456.122kg
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( ) 1.851=
if Ws tcc( ) B tcc( )+ 1.1 B tcc( )≤ "FLOAT", "OK!",( ) "OK!"=
Specific Gravity of Product (relative to seawater) SGprod
ρcont
ρsw
:= SGprod 1=
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 371.711kg
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( ) 306.5lb
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 0.547=
From figure 5.11 (Friction Factor = µc)
µc 0.52:=
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 20021
21.5
22
22.5
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 0.52=µ µs soil 1=if
µc otherwise
:=
Friction Factor
Wreq max Ws θ tcc,( )( ):=
Wreq 33.258kg
m=
B 0.25π D tcc( )2
⋅ ρsw⋅:=
B 536.263kg
m=
Ws tcc( ) Wst Wcorr+ Wins+ Wj+ Was+ Wcc+ Wcont+ B−:=
Ws tcc( ) 306.5lb
ft=
if Ws tcc( ) Wreq≤ "Need More Thickness", "OK!",( ) "OK!"=
Safety Factor For Submerged Weight Due To Requirement Weight
SFwWs tcc( )
Wreq
:= SFw 13.715=
Density corrosion coating ρcorr 915kg m3−
⋅:=
Thermal insulation coating density ρins 4.5pcf:=
Concrete coating density ρcc 3040kg m3−
⋅:=
Content density ρcont 4lb 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 3.6m:=
Spectral Peak Period Tp 7.9sec:=
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 : Operation
Wave & Current Data : 100 years return period wave + 100 years 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 0.8m 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( ) 107.642kg
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( ) 1.201=
if Ws tcc( ) B tcc( )+ 1.1 B tcc( )≤ "FLOAT", "OK!",( ) "OK!"=
Specific Gravity of Product (relative to seawater) SGprod
ρcont
ρsw
:= SGprod 0.063=
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 23.232kg
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( ) 72.332lb
ft=
Grain size d50 0.0625mm:=
Roughnes Zo 5.21 106−
m⋅:=
Zero Up Crossing Period According To DNV RP E305 Figure 2.2
Tu 1.2 Tp⋅:= Tu 9.48 s=
From The Soil Parameter Data
A1D tcc( )
Zo
:= A1 1.566 105
×=
B1Zo
D tcc( ):= B1 6.384 10
6−×=
Nikurade equivalent sand roughness parameter
Kb 2.5 d50⋅:= Kb 1.563 104−
× m=
zobKb
30:= zob 5.208 10
6−× m=
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
0.352= φTp
Hs
:= φ 4.164sec
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
0.352=
Us
0.028 Hs⋅
Tn
:= Us 0.036m
s=
From table A.1 Soil parameter can be found as
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 2.319=
From figure 5.11 (Friction Factor = µc)
µc 0.25:=
Sand soil
µs 0.7:=
Average Velocity To Reference Velocity Ratio
UD1
lnZr
Zo
1+
1 B1+( ) ln A1 1+( )⋅ 1− ⋅
Ur⋅:=
UD 0.661m
s= Us 0.036
m
s=
USING SIMPLIFIED STATIC STABILITY METHOD :
Wave particle acceleration As 2πUs
Tu
:=
As 0.024 m sec2−
⋅=
Current To Wave Velocity Ratio MUD
Us
:= M 18.26=
Keulegan Carpenter Number KUs Tu⋅
D tcc( ):= K 0.421=
REUD Us+( ) D tcc( )⋅
ν:= RE 5.693 10
5×=
Hidrodynamic Force Coefficients
0 50 100 150 20040
50
60
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 0.421=
M 18.26=
Calibration Factor According To DNV RP E305 Figure 5.12
µ 0.25=µ µs soil 1=if
µc otherwise
:=
Friction Factor
Wreq max Ws θ tcc,( )( ):=
Wreq 87.88kg
m=
B 0.25π D tcc( )2
⋅ ρsw⋅:=
B 536.263kg
m=
Ws tcc( ) Wst Wcorr+ Wins+ Wj+ Was+ Wcc+ Wcont+ B−:=
Ws tcc( ) 72.332lb
ft=
if Ws tcc( ) Wreq≤ "Need More Thickness", "OK!",( ) "OK!"=
Safety Factor For Submerged Weight Due To Requirement Weight
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:=
Wall thickness ts 0.625in:=
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=
Asphalt Was 0.25π Das2
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=
Peak Enhancement Factor 1 year φ1
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=
Significant Flow Velocity
Amplitude at Pipe LevelUs1
0.005 Hs1⋅
Tn
:= Us1 3.592 103−
×m
s=
Wave Spreading Coefficient Rd 1:=
Wave Induced Flow Velocity
( 1 year)Uw1 Us1 Rd⋅:= Uw1 3.592 10
3−×
m
s=
Current Flow Velocity Ratio αUc100
Uw1 Uc100+:= α 0.996=
Reduction of Stability Parameter
(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
⋅ C2⋅ Esteel⋅ Isteel⋅
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)
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_CF 1.0481
s=
fo_CF C1 1 CSF+⋅Esteel Isteel⋅
Wpipe Leff4
⋅
1Seff
PE
+ C3
δCF
D
2
⋅
+
⋅⋅:=Natural Frequency
(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⋅:=
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 21.09m:=
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 64pcf:=
Design Presure Pd 1650psi:=
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 : Hydrotest
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:=
Wall thickness ts 0.625in:=
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 1.731 103
× 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=
Asphalt Was 0.25π Das2
Dj2
−
ρas⋅:= Was 9.91
lb
ft=
Content Weight Wcontentπ
4ID
2ρcontent⋅:= Wcontent 249.778
lb
ft=
Added Mass Weight Waddπ
4D
2⋅ ρsw:= Wadd 360.352
lb
ft=
Effective Weight Wpipe Wsteel Wconc+ Wcorr+ Wcontent+ Wadd+ Was+:=
Wpipe 1.051 103
×lb
ft= Wpipeforce Wpipe g⋅:= Wpipeforce 1.533 10
4× N m
1−⋅=
Submerged Weight Wsub Wpipe 2 Wadd⋅−:= Wsub 329.954lb
ft=
Wsubforce Wsub g⋅:= Wsubforce 4.815 103
× 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
L
D25.842=
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 3.914=
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
:=
Leff 27.626 m=
Euler Buckling PE
1 CSF+( ) π2
⋅ C2⋅ Esteel⋅ Isteel⋅
Leff2
:= PE 6.573 106
× N=
Reduction Velocity Factor for In-Line:
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 0.863= 4.1.8
Stability Parameter Cross-Line Ks_CF
4π Wpipe⋅ ζT_CF⋅
ρsw D2
⋅
:= Ks_CF 0.633=
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 0.751=
Reduction of Stability Parameter
(cros flow)Ksd_CF
Ks_CF
γk
:= Ksd_CF 0.551=
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=
Peak Enhancement Factor 1 year φ1
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=
Significant Flow Velocity
Amplitude at Pipe LevelUs1
0.005 Hs1⋅
Tn
:= Us1 3.592 103−
×m
s=
Wave Spreading Coefficient Rd 1:=
Wave Induced Flow Velocity
( 1 year)Uw1 Us1 Rd⋅:= Uw1 3.592 10
3−×
m
s=
Current Flow Velocity Ratio αUc100
Uw1 Uc100+:= α 0.996=
Reduction of Stability Parameter
(In-line)
ψ trenchonset 1.23=ψ trenchonset 1 0.5∆
D⋅+:=
∆
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 1.0091
s=
fo_IL_ok C1 1 CSF+⋅Esteel Isteel⋅
Wpipe L4( )⋅
1Seff
PE_ok
+ C3
δIL
D
2
⋅
+
⋅⋅:=
Natural Frequency
(In-line)
PE_ok 1.128 107
× N=PE_ok
1 CSF+( ) π2
⋅ C2⋅ Esteel⋅ Isteel⋅
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 0.6261
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 8.443− 106
× N=
Seff Heff ∆P Ai⋅ 1 2 v⋅−( )⋅ − Asteel Esteel⋅ ∆T⋅ αe⋅( )−:=Effective axial force
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
:=In-Line Reduction Factor
CheckCF 1=
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 2.0631
s=
fo_CF_ok C1 1 CSF+⋅Esteel Isteel⋅
Wpipe L4( )⋅
1Seff
PE_ok
+ C3
δCF
D
2
⋅
+
⋅⋅:=
Natural Frequency
(In-line)
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_CF 0.8421
s=
fo_CF C1 1 CSF+⋅Esteel Isteel⋅
Wpipe Leff4
⋅
1Seff
PE
+ C3
δCF
D
2
⋅
+
⋅⋅:=Natural Frequency
(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 0.6261
s=fw 0.127
1
s=fw
1
Tp100
:=Wave Frequency
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 21.6m:=
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 4pcf:=
Design Presure Pd 1100psi:=
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 : Operation
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:=
Wall thickness ts 0.625in:=
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 1.046 103
× psi=
Boundary Condition Cofficient :
Case : Pinned-Pinned C1 1.57:=
C2 1.00:=
C3 0.8:=
C4 4.39:=
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=
Concrete Weight Wconcπ
4D
2Ds 2 tcorr⋅+( )
2−
⋅ ρconc⋅:= Wconc 243.577
lb
ft=
Asphalt Was 0.25π Das2
Dj2
−
ρas⋅:= Was 9.91
lb
ft=
Content Weight Wcontentπ
4ID
2ρcontent⋅:= Wcontent 15.611
lb
ft=
Added Mass Weight Waddπ
4D
2⋅ ρsw:= Wadd 360.352
lb
ft=
Effective Weight Wpipe Wsteel Wconc+ Wcorr+ Wcontent+ Wadd+ Was+:=
Wpipe 816.491lb
ft= Wpipeforce Wpipe g⋅:= Wpipeforce 1.192 10
4× N m
1−⋅=
Submerged Weight Wsub Wpipe 2 Wadd⋅−:= Wsub 95.787lb
ft=
Wsubforce Wsub g⋅:= Wsubforce 1.398 103
× N m1−
⋅=
Dynamic stiffness factor vertical Cv 3000kN m
5−
2⋅:= Table 7.6
C51
8:=
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=
PE 6.338 106
× N=
Reduction Velocity Factor for In-Line:L
D26.467=
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=
Dynamic stiffness factor horizontal Cl 2600kN m
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
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 3.955=
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 28.132 m=
Euler Buckling PE
1 CSF+( ) π2
⋅ C2⋅ Esteel⋅ Isteel⋅
Leff2
:=
Peak Periods Tp100 7.9s:=
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=
Total Modal Damping Ratio ζT_CF ζstr ζsoil_CF+ ζh+:= ζT_CF 0.022=
Stability Parameter In-Line Ks_IL
4π Wpipe⋅ ζT_IL⋅
ρsw D2
⋅
:= Ks_IL 0.671= 4.1.8
Stability Parameter Cross-Line Ks_CF
4π Wpipe⋅ ζT_CF⋅
ρsw D2
⋅
:= Ks_CF 0.492=
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
Ksd_IL
Ks_IL
γk
:= Ksd_IL 0.583=
Reduction of Stability Parameter
(cros flow)Ksd_CF
Ks_CF
γk
:= Ksd_CF 0.428=
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=
Peak Enhancement Factor 1 year φ1
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=
Significant Flow Velocity
Amplitude at Pipe LevelUs1
0.005 Hs1⋅
Tn
:= Us1 3.592 103−
×m
s=
Wave Spreading Coefficient Rd 1:=
Wave Induced Flow Velocity
( 1 year)Uw1 Us1 Rd⋅:= Uw1 3.592 10
3−×
m
s=
Current Flow Velocity Ratio αUc100
Uw1 Uc100+:= α 0.996=
Reduction of Stability Parameter
(In-line)
ψ trenchonset 1.23=ψ trenchonset 1 0.5∆
D⋅+:=
∆
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 1.1481
s=
fo_IL_ok C1 1 CSF+⋅Esteel Isteel⋅
Wpipe L4( )⋅
1Seff
PE_ok
+ C3
δIL
D
2
⋅
+
⋅⋅:=
Natural Frequency
(In-line)
PE_ok 1.075 107
× N=PE_ok
1 CSF+( ) π2
⋅ C2⋅ Esteel⋅ Isteel⋅
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 0.6071
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 7.758− 106
× N=
Seff Heff ∆P Ai⋅ 1 2 v⋅−( )⋅ − Asteel Esteel⋅ ∆T⋅ αe⋅( )−:=Effective axial force
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
:=In-Line Reduction Factor
CheckCF 1=
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 2.261
s=
fo_CF_ok C1 1 CSF+⋅Esteel Isteel⋅
Wpipe L4( )⋅
1Seff
PE_ok
+ C3
δCF
D
2
⋅
+
⋅⋅:=
Natural Frequency
(In-line)
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_CF 0.9741
s=
fo_CF C1 1 CSF+⋅Esteel Isteel⋅
Wpipe Leff4
⋅
1Seff
PE
+ C3
δCF
D
2
⋅
+
⋅⋅:=Natural Frequency
(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 0.6071
s=fw 0.127
1
s=fw
1
Tp100
:=Wave Frequency
Modulus Elasticity of concrete 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 Densityρas 1300
kg
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 ν 0.3:=
Specified Minimum Yield Strength SMYS 65000psi:=
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≡
Pipeline Design Parameter:
Outer Diameter Ds 28in:= Corrosion Allowance tca 0in:=
Wall thickness ts 0.625in:=
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⋅+:=
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 Ds:=
Specific Local Pressure P1d Pd ρcontent g⋅ h href−( )⋅+:=
Pressure Diference ∆P γp P1d Pe−⋅:= ∆P 116.36 psi=
Soil Parameter : Silty clay
Soil Type Soil 2:= 1 sand= 2 clay=
Void Ratio es 0.6:=
Earth Pressure Coeff Ko 0.5:=
Specified Minimum Tensile Strength SMTS 77000psi:=
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=
(100 year)
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=
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=
Boundary Condition Cofficient :
Case : Pinned-Pinned C1 1.57:=
C2 1.00:=
C3 0.8:=
C4 4.39:=
C51
8:=
C65
384:=
Concrete Stifness Factor :
Submerged Weight Wsub Wpipe 2 Wadd⋅−:= Wsub 80.176lb
ft=
Wsubforce Wsub g⋅:= Wsubforce 1.17 103
× 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=
Dynamic stiffness factor vertical Cv 3000kN m
5−
2⋅:=
Dynamic stiffness factor horizontal Cl 2600kN m
5−
2⋅:=
Dynamic Soil
Stifness verticalKV
Cv
1 ν−
1
3
2
3
ρs
ρsw
⋅+
⋅ D⋅:=
Concrete Weight Wconcπ
4D
2Ds 2 tcorr⋅+( )
2−
⋅ ρconc⋅:= Wconc 243.577
lb
ft=
Asphalt Was 0.25π Das2
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=
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=
Effective Weight Wpipe Wsteel Wconc+ Wcorr+ Wcontent+ Wadd+ Was+:=
Wpipe 800.879lb
ft= Wpipeforce Wpipe g⋅:= Wpipeforce 1.169 10
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
=
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=
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
Pressure Containment
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
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=
d Pe1 Pp2
⋅:=
u1
3
1−
3bb
2⋅ c+
⋅:=
vi1
2
2
27bb
3⋅
1
3bb⋅ c⋅− d+
⋅:=
Φ acosvi−
u3
−
:=
y 2− u−⋅ cosΦ
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=
Reduction Velocity Factor for In-Line:L
D26.957=
Tp100 7.9s:=
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 In-Line Stress
Rangeγs 1.3:=
Safety Factor for Damping γk 1.15:=
Flow Velocity on Pipeline Level:
Assumsed : Linear Wave Theory
Peak Periods
ψαIL 1=
Reduction of Stability Parameter
(In-line)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=
Peak Enhancement Factor 1 year φ1
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=
Significant Flow Velocity
Amplitude at Pipe LevelUs1
0.005 Hs1⋅
Tn
:= Us1 3.592 103−
×m
s=
Wave Spreading Coefficient Rd 1:=
Wave Induced Flow Velocity
( 100 year)Uw1 Us1 Rd⋅:= Uw1 3.592 10
3−×
m
s=
Current Flow Velocity Ratio αUc100
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
:=
δIL 0D:=Static Deflection
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
:=In-Line Reduction Factor
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=
Reduction Velocity Factor for Cross-Flow:
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=
fo_CF C1 1 CSF+⋅Esteel Isteel⋅
Wpipe Leff4
⋅
1Seff
PE
+ C3
δCF
D
2
⋅
+
⋅⋅:=Natural Frequency
(cross-flow)
δCF 1D:=Static Deflection (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=
VR_CF_onset 3ψproxionst ψtrenchonset⋅
γon_CF
⋅:=Cross-Flow Reduction
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⋅:=
Dj Dcorr:=Density of steel ρs 490pcf:=
Das Dj 2 tas⋅+:=Density of concrete ρconc 190pcf:=
Density of corrosion coating ρcorr 915kg m3−
⋅:=
Asphalt Densityρas 1300
kg
m3
:=
Span length L 21.09m:=
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 64pcf:=
Design Presure Pd 1650psi:=
kinematic viskocity vk 1.076 105−
⋅ ft2
s1−
⋅:=
Poisson Ratio ν 0.3:=
Specified Minimum Yield Strength SMYS 65000psi:=
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≡
Pipeline Design Parameter:
Outer Diameter Ds 28in:= Corrosion Allowance tca 0in:=
Wall thickness ts 0.625in:=
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⋅+:=
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 172.062 psi=
Load Effect Factor for Pressure γp 1.05:= href Ds:=
Specific Local Pressure P1d Pd ρcontent g⋅ h href−( )⋅+:=
Pressure Diference ∆P γp P1d Pe−⋅:= ∆P 1.731 103
× psi=
Soil Parameter : Silty clay
Soil Type Soil 2:= 1 sand= 2 clay=
Void Ratio es 0.6:=
Earth Pressure Coeff Ko 0.5:=
Specified Minimum Tensile Strength SMTS 77000psi:=
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 118m:=
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=
(100 year)
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=
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=
Boundary Condition Cofficient :
Case : Pinned-Pinned C1 1.57:=
C2 1.00:=
C3 0.8:=
C4 4.39:=
C51
8:=
C65
384:=
Concrete Stifness Factor :
Inertia of Concrete
Submerged Weight Wsub Wpipe 2 Wadd⋅−:= Wsub 329.954lb
ft=
Wsubforce Wsub g⋅:= Wsubforce 4.815 103
× 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 24.78kPa=
Dynamic stiffness factor vertical Cv 3000kN m
5−
2⋅:=
Dynamic stiffness factor horizontal Cl 2600kN m
5−
2⋅:=
Dynamic Soil
Stifness verticalKV
Cv
1 ν−
1
3
2
3
ρs
ρsw
⋅+
⋅ D⋅:=
Concrete Weight Wconcπ
4D
2Ds 2 tcorr⋅+( )
2−
⋅ ρconc⋅:= Wconc 243.577
lb
ft=
Asphalt Was 0.25π Das2
Dj2
−
ρas⋅:= Was 9.91
lb
ft=
Content Weight Wcontentπ
4ID
2ρcontent⋅:= Wcontent 249.778
lb
ft=
Added Mass Weight Waddπ
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=
Effective Weight Wpipe Wsteel Wconc+ Wcorr+ Wcontent+ Wadd+ Was+:=
Wpipe 1.051 103
×lb
ft= Wpipeforce Wpipe g⋅:= Wpipeforce 1.533 10
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:=
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
=
Parameter of Soil Stiffness β logK L
4⋅
1 CSF+( ) Esteel⋅ Isteel⋅
:=
β 3.914=
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 27.626 m=
Euler Buckling PE
1 CSF+( ) π2
⋅ C2⋅ Esteel⋅ Isteel⋅
Leff2
:= PE 6.573 106
× N=
Inplace Strength Analysis (based on DnV OS-F101 (DnV 2000)
1. Pressure Containment Requirement
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
Pressure Containment
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
−
:=
y 2− u−⋅ cosΦ
3
60 π⋅
180+
⋅:=
Pressure Collapse Pc y1
3bb⋅−:=
Pc 467.347 psi=
Pe 172.062 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 1.147 105
× psi=
γk 1.15:=
Flow Velocity on Pipeline Level:
Assumsed : Linear Wave Theory
Peak Periods Tp100 7.9s:=
Significant Wave Height Hs100 3.6 m=
Natural Peiode Tnh
g:= Tn 3.469 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
0.439= and γ 2.616=
Significant Flow Velocity
Amplitude at Pipe LevelUs100
0.028 Hs100⋅
Tn
:= Us100 0.029m
s=
Wave Spreading Coefficient Rd 1:=
Total Modal Damping Ratio ζT_CF ζstr ζsoil_CF+ ζh+:= ζT_CF 0.022=
Stability Parameter In-Line Ks_IL
4π Wpipe⋅ ζT_IL⋅
ρsw D2
⋅
:= Ks_IL 0.863= 4.1.8
Stability Parameter Cross-Line Ks_CF
4π Wpipe⋅ ζT_CF⋅
ρsw D2
⋅
:= Ks_CF 0.633=
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 In-Line Stress
Rangeγs 1.3:=
Safety Factor for Damping
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
:= ψαIL 1=
Reduction of Stability Parameter
(In-line)Ksd_IL
Ks_IL
γk
:= Ksd_IL 0.751=
Reduction of Stability Parameter
(cros flow)Ksd_CF
Ks_CF
γk
:= Ksd_CF 0.551=
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=
( )
Wave Induced Flow Velocity
( 100 year)Uw100 Us100 Rd⋅:= Uw100 0.029
m
s=
Peak Enhancement Factor 1 year φ1
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
0.56= and γ 2.039=
Significant Flow Velocity
Amplitude at Pipe LevelUs1
0.005 Hs1⋅
Tn
:= Us1 2.883 103−
×m
s=
Wave Spreading Coefficient Rd 1:=
Wave Induced Flow Velocity
( 100 year)Uw1 Us1 Rd⋅:= Uw1 2.883 10
3−×
m
s=
Current Flow Velocity Ratio αUc100
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_2 3.766=VR_IL_2 VR_IL_end 2 Ay2⋅−:=
VR_IL_end 3.899=
VR_IL_end 4.5 0.8 Ksd_IL⋅−( ) Ksd_IL 1<if
3.7 Ksd_IL 1≥if
:=
VR_IL_1 1.897=VR_IL_1 10 Ay1⋅ VR_IL_onset+:=
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
:=In-Line Reduction Factor
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⋅:=Inline VIV Amplitude (Ay/D)
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
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 0.626
1
s=
Keulegan Carpenter Number KCUw100
fw D⋅:= KC 0.281=
Static Deflection δIL 0D:=
Natural Frequency
(In-line)fo_IL C1 1 CSF+⋅
Esteel Isteel⋅
Wpipe Leff4
⋅
1Seff
PE
+ C3
δIL
D
2
⋅
+
⋅⋅:=
fo_IL 0.6261
s=
Reduced Velocity VRIL
Uc100 Uw1+
fo_IL D⋅:=
VRdIL VRIL γf⋅:=
VRdIL 1.887=
In-Line Amplitude Response Ayo 0.068:= AyoAmplitude
Diameter
=
Stress Range for In-Line Direction
In-Line Stress Range SIL 2 AIL⋅ Ayo⋅ ψαIL⋅ γs⋅:=
SIL 1.399 108
× Pa=
Reduction Velocity Factor for Cross-Flow:
In-Line Unit Stress Amplitude
VRCF
Uc100 Uw1+
fo_CF D⋅:=Reduced Velocity
fo_CF 0.8421
s=
fo_CF C1 1 CSF+⋅Esteel Isteel⋅
Wpipe Leff4
⋅
1Seff
PE
+ C3
δCF
D
2
⋅
+
⋅⋅:=Natural Frequency
(cross-flow)
δCF 1D:=Static Deflection (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=
VR_CF_onset 3ψproxionst ψtrenchonset⋅
γon_CF
⋅:=Cross-Flow Reduction
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)
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=
Mstatic_ok Mstatic:=
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
:=
Stress Range for Cross-Flow Direction
Cross-Flow Stress Range SCF 2 ACF⋅ Azo⋅ Rk⋅ γs⋅:=
SCF 0 psi=
Summary Stress Range
In-Line Stress Range SIL 2.029 104
× psi=
Cross-Flow Stress Range SCF 0 psi=
In-Line Stress Dynamic
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 1.029= αc 1.2<
Bursting Pressure (containment) Pb2
3
2 ts⋅
Ds ts−⋅ min fy
fu
1.15,
⋅:=
Pb 3.22 103
× psi=
Design Pressure Differential
Pressure Load Factor γp 1.05=
Depth Reference href 0.711 m=
Design Pressure Pd 1.65 103
× psi=
Design Pressure Differential ∆Pd γp Pd ρcontent g⋅ h href−( )⋅+ ρsw g⋅ h⋅− ⋅:=
∆Pd 1.731 103
× psi=
Specific Local Pressure Pld Pd ρcontent g⋅ h href−( )⋅+:=
Pld 1.821 103
× 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=
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 Densityρas 1300
kg
m3
:=
Span length L 21.6m:=
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 4pcf:=
Design Presure Pd 1100psi:=
kinematic viskocity vk 1.076 105−
⋅ ft2
s1−
⋅:=
Poisson Ratio ν 0.3:=
Specified Minimum Yield Strength SMYS 65000psi:=
Specified Minimum Tensile Strength SMTS 77000psi:=
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
Pipeline Design Parameter:
Outer Diameter Ds 28in:= Corrosion Allowance tca 0in:=
Wall thickness ts 0.625in:=
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
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 172.062 psi=
Load Effect Factor for Pressure γp 1.05:= href Ds:=
Specific Local Pressure P1d Pd ρcontent g⋅ h href−( )⋅+:=
Pressure Diference ∆P γp P1d Pe−⋅:= ∆P 985.559 psi=
Soil Parameter : Silty clay
Soil Type Soil 2:= 1 sand= 2 clay=
Poissons ratio
Void Ratio es 0.6:=
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 118m:=
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=
(100 year)
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=
Earth Pressure Coeff Ko 0.5:=
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=
Boundary Condition Cofficient :
Case : Pinned-Pinned C1 1.57:=
C2 1.00:=
C3 0.8:=
C4 4.39:=
C51
8:=
Wpipe 816.491lb
ft= Wpipeforce Wpipe g⋅:= Wpipeforce 1.192 10
4× N m
1−⋅=
Submerged Weight Wsub Wpipe 2 Wadd⋅−:= Wsub 95.787lb
ft=
Wsubforce Wsub g⋅:= Wsubforce 1.398 103
× 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 7.863kPa=
Dynamic stiffness factor vertical Cv 3000kN m
5−
2⋅:=
Dynamic stiffness factor horizontal Cl 2600kN m
5−
2⋅:=
Corrosion Weight Wcorrπ
4Ds 2 tcorr⋅+( )
2Ds
2−
⋅ ρcorr⋅:= Wcorr 4.139
lb
ft=
Concrete Weight Wconcπ
4D
2Ds 2 tcorr⋅+( )
2−
⋅ ρconc⋅:= Wconc 243.577
lb
ft=
Asphalt Was 0.25π Das2
Dj2
−
ρas⋅:= Was 9.91
lb
ft=
Content Weight Wcontentπ
4ID
2ρcontent⋅:= Wcontent 15.611
lb
ft=
Added Mass Weight Waddπ
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=
Effective Weight Wpipe Wsteel Wconc+ Wcorr+ Wcontent+ Wadd+ Was+:=
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
1. Pressure Containment Requirement
Inplace Strength Analysis (based on DnV OS-F101 (DnV 2000)
PE 6.338 106
× N=PE
1 CSF+( ) π2
⋅ C2⋅ Esteel⋅ Isteel⋅
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⋅
1 CSF+( ) Esteel⋅ Isteel⋅
:=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
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
Material Resistance Factor γm 1.15:=
Safety Class Resistance Factor γSC 1.138:=
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:=
Pressure Containment
Yielding Limit State Requirement
Yielding
Limit
State Req
Req_yield 1 Pli Pe−( )D ts tfab− tca−( )−
2 ts tfab− tca−( )⋅⋅ η SMYS fytemp−( )⋅≤if
0 otherwise
:=
Req_yield 1=
AIL 1.107 105
× psi=
Reduction Velocity Factor for In-Line:L
D26.467=
Modal Damping Ratio
Structural Damping ζstr 0.01:= 6.2.11
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:=
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
−
:=
y 2− u−⋅ cosΦ
3
60 π⋅
180+
⋅:=
Pressure Collapse Pc y1
3bb⋅−:=
Pc 467.347 psi=
Pe 172.062 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
⋅:=
Safety Factor for In-Line Stress
Rangeγs 1.3:=
Safety Factor for Damping γk 1.15:=
Flow Velocity on Pipeline Level:
Assumsed : Linear Wave Theory
Peak Periods Tp100 7.9s:=
Significant Wave Height Hs100 3.6 m=
Natural Peiode Tnh
g:= Tn 3.469 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
0.439= and γ 2.616=
Significant Flow Velocity
Amplitude at Pipe LevelUs100
0.028 Hs100⋅
Tn
:= Us100 0.029m
s=
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=
Stability Parameter In-Line Ks_IL
4π Wpipe⋅ ζT_IL⋅
ρsw D2
⋅
:= Ks_IL 0.671= 4.1.8
Stability Parameter Cross-Line Ks_CF
4π Wpipe⋅ ζT_CF⋅
ρsw D2
⋅
:= Ks_CF 0.492=
Safety Factor for Fatigue, onset value
for in-line & cross flow VIVγon 1.10:= table 2.1
γon_IL 1.10:= 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:=
Current Flow Velocity Ratio αUc100
Uw100 Uc100+:= α 0.965=
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
:= ψαIL 1=
Reduction of Stability Parameter
(In-line)Ksd_IL
Ks_IL
γk
:= Ksd_IL 0.583=
Reduction of Stability Parameter
(cros flow)Ksd_CF
Ks_CF
γk
:= Ksd_CF 0.428=
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:=
Wave Spreading Coefficient Rd 1:=
Wave Induced Flow Velocity
( 100 year)Uw100 Us100 Rd⋅:= Uw100 0.029
m
s=
Peak Enhancement Factor 1 year φ1
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
0.56= and γ 2.039=
Significant Flow Velocity
Amplitude at Pipe LevelUs1
0.005 Hs1⋅
Tn
:= Us1 2.883 103−
×m
s=
Wave Spreading Coefficient Rd 1:=
Wave Induced Flow Velocity
( 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_2 3.878=VR_IL_2 VR_IL_end 2 Ay2⋅−:=
VR_IL_end 4.033=
VR_IL_end 4.5 0.8 Ksd_IL⋅−( ) Ksd_IL 1<if
3.7 Ksd_IL 1≥if
:=
VR_IL_1 1.984=VR_IL_1 10 Ay1⋅ VR_IL_onset+:=
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
:=In-Line Reduction Factor
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⋅:=Inline VIV Amplitude (Ay/D)
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=
Reduction Velocity Factor for Cross-Flow:
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
Correction Factord 1.1 e⋅:=
∆1.25 d⋅ e−
DD⋅:=
∆
D0.46=
ψ trenchonset 1 0.5∆
D⋅+:= ψ trenchonset 1.23=
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
(In-line)fo_IL C1 1 CSF+⋅
Esteel Isteel⋅
Wpipe Leff4
⋅
1Seff
PE
+ C3
δIL
D
2
⋅
+
⋅⋅:=
fo_IL 0.5941
s=
Reduced Velocity VRIL
Uc100 Uw1+
fo_IL D⋅:=
VRdIL VRIL γf⋅:=
VRdIL 1.987=
In-Line Amplitude Response Ayo 0.09:= AyoAmplitude
Diameter
=
Stress Range for In-Line Direction
In-Line Stress Range SIL 2 AIL⋅ Ayo⋅ ψαIL⋅ γs⋅:=
δCF 1D:=Static Deflection (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=
VR_CF_onset 3ψproxionst ψtrenchonset⋅
γon_CF
⋅:=Cross-Flow Reduction
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)
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
:=
Stress Range for Cross-Flow Direction
Cross-Flow Stress Range SCF 2 ACF⋅ Azo⋅ Rk⋅ γs⋅:=
SCF 0 psi=
Summary Stress Range
Pld 1.111 103
× psi=
Momen and Axial Plastic Limit
Axial Plastic Limit Sp fy π⋅ Ds ts−( )⋅ ts⋅:= Sp 1.492 107
× N=
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
:=
Mstatic 644.638− kJ=
Mstatic_ok Mstatic:=
Design Bending Moment Md max Mdyn Mstatic_ok,( ):=
Md 644.638 kJ=
Design Pressure Differential
Pressure Load Factor γp 1.05=
Depth Reference href 0.711 m=
Design Pressure Pd 1.1 103
× psi=
Design Pressure Differential ∆Pd γp Pd ρcontent g⋅ h href−( )⋅+ ρsw g⋅ h⋅− ⋅:=
∆Pd 985.559 psi=
Specific Local Pressure Pld Pd ρcontent g⋅ h href−( )⋅+:=
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
Propagation Buckling Requirement
Req_2 1=
Req_2 1 γSC γm⋅Md
αc Mp⋅
⋅ γSC γm⋅Seff
αc Sp⋅
2
+
2
γSC γm⋅Pe
Pc
⋅
2
+ 1≤if
0 otherwise
:=
Pipe Member Subjected to Bending Moment, Effective Axial Force, & External
Overpressure
Req_1 1=
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
:=
Requirement for Pipe Member Subjected to Bending Moment, Effective Axial Force, &
Internal Overpressure
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