ON-BOTTOM STABILITY 1. Input Parameter

Equivalent Condition

Phase : Installation

Wave/Current Data : 1 yrs return perion wave + 1 yrs return perion current

Soil Type : Clay

1.1 Pipeline Design Parameter

Outer Diameter Ds 12.75in:= Density corr coating ρcorr 940kg m3−

⋅:=

Wall Th ickne ss ts 12.7mm:= Thermal ins. coat. density ρins 0.0005kg m3−

⋅:=

Internal Diameter ID Ds 2 ts⋅−:= Concrete Coating Density ρcc 3044kg m3−

⋅:=

Corrosion Coating thickness tcorr 0.003m:= Content Density ρcont 0:=

Thermal Insulation Coating Thickness tins 0m:= Seawater Density ρsw 1025kg m3−

⋅:=

Jacket Material tj 0m:= Steel Density ρs 7850kg m3−

⋅:=

Asphalt enamels tas 0m:= Asphalt Density ρas 2243kg m3−

⋅:=

tcc 3mm:= 1.2 Environmental Parameter

Significant Wave Height Hs 1.2m:=

Spectral Peak Period Tp 7.5s:=

Water Depth d 70m:=

Current 3m above seabed Ur 0.165m s1−

⋅:=

Kinematic Viscosity of Seawater ν 1.076 105−

⋅ ft2

s1−

:=

1.3 Soil Parameter

Soil Type 1 sand= 2 clay=, soil 2:= medium sand of density ρsoil 326.309kg m3−

⋅:=

Undrained Shear Stress Su 2kPa:=

2. Calculation

2.1 Submerged Weight Calculation

Total Outer Diameter D tcc( ) Ds 2 tcorr⋅+ 2 tins⋅+ 2 tj⋅+ 2 tas⋅+ 2 tcc⋅+:= D tcc( ) 0.336 m=

Total Outside Diameter D tcc( ) 0.336 m=

Internal Diameter Di Ds 2 ts⋅−:= Di 0.298 m=

Dcorr Ds 2 tcorr⋅+:=

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

Submerged Weight = Steel Weight + Corrosion Coat Weight + Thermal Insulation Weight + Jacket Material + Concrete

Coat Weight + Contents Weight - Buoyancy

Ws tcc( ) π

4Ds( )2

ID2

−

ρs⋅ Dcorr( )2

Ds( )2−

ρcorr⋅+ Dins( )2

Dcorr( )2−

ρins⋅+

Dj( )2Dins( )2

−

ρs⋅ Das( )2

Dj( )2−

ρas⋅ D tcc( )2

Das( )2−

ρcc⋅+

Di( )2ρcont⋅ D tcc( )2

ρsw⋅−

+

...

++

...

⋅:=

Ws tcc( ) 19.093kg

m=

Buoyancy B tcc( ) π

4g⋅ D tcc( )2⋅

2 ρsw⋅

g⋅:= B tcc( ) 181.608

kg

m=

2.3 Vertical Stability

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

B tcc( ):= SG tcc( ) 1.105=

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 (relative to seawater) SGsoil

ρsoil

ρsw

:= SGsoil 0.318=

2.3 Find Water Partic le Velocities

Parameter Tnd

g:= Tn 2.672 s= Tp 7.5 s=

Tn

Tp

0.356= ϕTp

Hs

:= ϕ 6.847s

m0.5

=

Peakedness Parameter γ if ϕ 3.6sec

m≤ 5, if ϕ 5

sec

m≥ 1, 3.3,

,

:=

γ 1=

PM 1:=

JONSWAP 3.3 5−:=

Significant Wave Velocity Us

0.021799 Hs⋅

Tn

:=

Zero Up-Crossing Period Tu 1.239122 Tp⋅:= Tu 9.293 s=

2.4 Using Simplified Static Stability Method

Wave particle accel. As 2 π⋅Us

Tu

⋅:= As 6.62 103−

×m

s2

=

Current to wave velocity MUr

Us

:= M 16.852=

KC number KUs Tu⋅

D tcc( ):= K 0.271= Us Tu⋅ 0.091 m=

Reynold's Number Re tcc( )Ur Us+( ) D tcc( )⋅

ν:= Re tcc( ) 5.872 10

4×=

Hydrodynamics Coefficient

CD if Re tcc( ) 3 105

⋅< M 0.8≥∧ 1.2, 0.7,

:= CD 1.2=

CL 0.9:=

CM 3.29:=

Soil Coefficient

Clay Soil

Ratio1

S= Su 2kPa:= Ratio

D tcc( ) Su⋅

Ws tcc( ) g⋅:= Ratio 3.587=

D tcc( ) 0.336 m=

μc 0.25:=

Sand Soil

μs 0.7:=

Friction Coef

μ if soil 1= μs, μc, ( ):= μ 0.25=

Calibration Factor

M 16.852=

K 0.271=

FW 1:=

2.5 Lateral Stability Calculation

Hydrodynamic Forces and Required Submerged Weight

Phase angle range i 0 360..:= θi

i deg⋅:=

Lift Force FL θ tcc, ( ) 1

2

ρsw

g⋅ D tcc( )⋅ CL⋅ Us cos θ( )⋅ Ur+( )2

:=

Drag Force FD θ tcc, ( ) 1

2

ρsw

g⋅ D tcc( )⋅ CD⋅ Us cos θ( )⋅ Ur+( )2

:=

Inertia Force FI θ tcc, ( )π D tcc( )2

⋅

4

ρsw

g⋅ CM⋅ As⋅ sin θ( )⋅:=

Required Submerged Weight Ws θ tcc, ( )FD θ tcc, ( ) FI θ tcc, ( )+ μFL θ tcc, ( )+

μ

FW⋅:=

Result of Calculation

tcc 3 103−

× m=

Wreq max Ws θ tcc, ( )( ):=

Ws tcc( ) 19.093kg

m= Wreq 3.594

kg

m= Wso tcc( ) Ws tcc( ) g⋅:= Wso tcc( ) 187.243

kg

s2

=

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

SFW

Ws tcc( )Wreq

:= SFW 5.313=

Specific Gravity SG tcc( ) 1.105=

Submerged Weight Ws tcc( ) 19.093kg

m=