TUGAS AKHIR
BAB 4 STUDI KASUS
BAB
4 STUDI KASUS
4.1
Deskripsi Permasalahan
Permasalahan yang dibahas dalam tugas akhir ini adalah free span yang terjadi pada pipa bawah laut. Berdasarkan hasil survei yang ada, diketahui bahwa terdapat sejumlah free spans yang harus diperbaiki untuk melindungi jalur pipa terhadap vibrasi/getaran dan fatigue. Dalam studi kasus pada tugas akhir ini dilakukan penilaian bahaya fatigue dari free span yang tidak memenuhi kriteria Vortex Induced Vibration (VIV) yang didasarkan pada DNV (2007). Lingkup pekerjaan yang dilakukan adalah : •
Review desain pipa bawah laut (ketebalan pipa, buckling, dan kestabilan pipa).
•
Identifikasi span pipa berdasarkan data elevasi pipa bawah laut yang dihimpun secara survei.
•
Penilaian terhadap spans untuk kriteria vortex induced vibration.
•
Menghitung bahaya fatigue.
4.2
Deskripsi Lokasi Pipa
Studi kasus yang dibahas pada Tugas Akhir ini diambil dari proyek jaringan pipa transmisi gas The 28” East Java Gas Pipeline. Jalur pipa ini menghubungkan Central Processing Plant (CPP) di Pulau Pagerungan Besar (Pulau Kangean) yang letaknya di sebelah timur Pulau Madura menuju Onshore Facility Receiver (OFR), Porong di daratan Jawa Timur. Jalur ini telah terpasang dan telah beroperasi sejak tahun 1993. Total panjang pipa ini adalah 420 km yang terbagi menjadi 2 seksi, 360 km di lepas pantai dan 60 km di darat. Peta lokasi jaringan pipa dapat dilihat pada Gambar 4.1.
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-1
TUGAS AKHIR
BAB 4 STUDI KASUS
Gambar 4.1 Peta lokasi pipeline [sumber: Field report 28” East Java Gas Pipeline].
4.3
Data-Data Pipa
Data proyek yang didapatkan merupakan data yang akan dipergunakan untuk desain jaringan pipa bawah laut, data tersebut meliputi data material dan data lingkungan.
4.3.1
Data Pipa
Data-data pipa yang didapatkan dapat dilihat pada Tabel 4.1. Tabel 4.1 Data Pipa [sumber: Field report 28” East Java Gas Pipeline].
Pipa Baja Parameter
Nilai
Satuan
Diameter Luar
28
inch
Ketebalan Pipa
0.625
inch
Spesifikasi Baja
API 5L
Kelas Baja
X65
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-2
TUGAS AKHIR
BAB 4 STUDI KASUS
SMYS (Specified Minimum Yield Strength)
65000
psi
Yield Strength
4570
kg/m3
SMTS
77000
psi
Young Modulus
3 x 107
psi
Poisson’s Ratio
0.3
Density
490
lb/ft3
Coefficient of Themal Expansion
6.5 x 106
/ °F
Steel Potensial
- 0.85
volt
Internal Corrosion Allowance
Nil
External Corrosion Protection Coating a. CPP – PC.10 Material
Asphalt Enamel
Thickness
0.005
m
Density
1300
kg/m3
b. PC. 10 – ORF Material
Polyethylen
Thickness
0.003
m
Density
915
kg/m3
20
tahun
Design Life Design Life
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-3
TUGAS AKHIR
BAB 4 STUDI KASUS
Data-data Concrete coating thickness dapat dilihat pada Tabel 4.2. Tabel 4.2 Data Concrete Coating Thickness [sumber: Field report 28” East Java Gas Pipeline].
Concrete Thickness Metocean Zone Inch
mm
Zone Ia
2.75
70
Zone Ib
3.91
99
Zone II
1.75
44
Zone III
1.75
44
Zone IV
1.75
44
4.3.2
Data Desain dan Operasional
Tabel 4.3 menyajikan data-data desain dan operasional dari pipa. Tabel 4.3 Data Desain dan Operasional Pipa [sumber: Field report 28” East Java Gas Pipeline].
Unit
CPP Inlet
ORF Outlet
psi
1100
kPa
7584.2
900 6205.3
°F
75
°C
23.9
85 29.4
Designed Temperature
°C
100
100
Gas Gravity/Effluent SG
-
0.65
0.65
Density of Content
lb/ft3
4
Keterangan Operating Pressure
Operating Temperature
4.3.3
Data Elevasi Pasang Surut
Terdapat informasi yang cukup penting pada elevasi pasang surut. Tabel 4.4 meyajikan nilai elevasi penting pada perhitungan pipa.
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-4
TUGAS AKHIR
BAB 4 STUDI KASUS
Tabel 4.4 Data Elevasi Pasang Surut [sumber: Field report 28” East Java Gas Pipeline].
Data (m) Elevation
Unit
HHWL
m
+ 2.44
LLWL
m
- 2.44
Storm Surge
m
0.09
4.3.4
1 years
Data Kondisi Tanah
Tabel 4.5 menggambarkan kondisi tanah detail sepanjang jalur pipa. Tabel 4.5 Deskripsi Tanah [sumber: Field report 28” East Java Gas Pipeline].
KP Deskripsi Tanah Dari
Ke
0
13.6
13.6
22
22
42
42
45
45
66
66
72
72
78
78
87
87
110
110
121
Yellowish grey carbonate fine SAND with shell and coral fragments Very soft light brown silty/sandy CLAY Yellowish grey/brown fine to coarse SAND with progressively increasing amount of gravel (shell and coral) Very soft light brown sandy CLAY Greenish grey silty/clayey fine to coarse SAND, with occasionally traces of gravel White greenish grey silty/clayey fine to medium SAND (0-0.6 m) overlaying dark brown clayey SILT White and greenish grey silty/clayey fine to coarse SAND with shell fragments White and greenish grey silty/clayey fine to coarse (<1 m) ovelaying clayey SILT Very soft to soft greenish grey sandy CLAY, overlaying with greenish grey silty SAND at KP 92 Greenish grey silty/clayey fine to coarse SAND
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-5
TUGAS AKHIR
BAB 4 STUDI KASUS
121
135
135
160
160
165
165
350
4.3.5
Very soft greenish gray sandy CLAY Very soft dark grey greenish CLAY, occasionally overlaying with greenish grey silty SAND or SILT (<0.6 m) Fine SAND (0.6 m) with traces of coarse sand and gravel, overlaying coralline SAND Very soft to soft grey/green CLAY with occasionally scattered shell fragments
Data Kedalaman Perairan
Tabel 4.6 menyajikan data kedalaman perairan di lokasi penempatan pipa. Tabel 4.6 Data Kedalaman Perairan [sumber: Field report 28” East Java Gas Pipeline].
Kedalaman Perairan (LAT) Zona
KP (km)
A. Shore Approach
Min (m)
Max (m)
0 – 1.2
-4.5
32
I-a (1)
1.2 – 6
28
50
I-a (2)
6 – 23
23
42
I-b (1)
23 – 28.5
10
32
I-b (2)
28.5 – 39.5
9
36
I-b (3)
39.5 – 42
9
35
II-a
42 – 80
26
96
II-b
80 – 140
80
109
II-c
140 – 180
76
118
III
180 – 285
61
76
IV
285 – 345
23
61
V
345 – 349.66
10
23
B. Shore Approach
349.66 – 354.75
-2.2
10
LF.2 – PC.10
352.75 – 357.01
-1.5
-3.7
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-6
TUGAS AKHIR
4.3.6
BAB 4 STUDI KASUS
Data Arus dan Gelombang
Data arus dan gelombang yang ditinjau terbagi kedalam 4 zona. Diasumsikan bahwa arus diukur 3 m dari dasar laut. Tabel 4.7 Data Arus [sumber: Field report 28” East Java Gas Pipeline].
KP
Design Basis (1year)
Design Basis (100 years)
Zona From
To
Uc (m/s)
Uc (m/s)
0.9
1.2
0.9
1
1.2
6
1.2
1.3
6
23
0.6
0.7
23
2.85
1.2
1.3
28.5
39.5
0.6
0.7
39.5
42
0.8
0.9
42
64.4 0.3
0.4
64.4
80
80
96.6
96.6
120.9 0.7
0.8
120.9
130.9
158.3
190
140
142.8
142.8
158.3
0.7
0.8
158.3
190
III
190
285
0.4
0.5
IV
285
345
0.5
0.6
Ia
Ib
II a
II b
II c
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-7
TUGAS AKHIR
BAB 4 STUDI KASUS
Tabel 4.8 Data Gelombang Signifikan [sumber: Field report 28” East Java Gas Pipeline].
KP
Wave Data Angle of
Zona From
1 year significant
100 years significant
wave
wave
To
Attack
Hs (m)
Tp (m)
Hs (m)
Tp (m)
Deg
0.9
1.2
2.1
6
3.8
8.1
90
1.2
6
2.1
6
3.8
8.1
90
6
23
2.2
6.1
3.9
8.3
90
23
28.5
1.6
5.6
2.8
6.6
90
28.5
39.5
1.0
4.0
1.6
4.5
90
39.5
42
1.8
5.8
3.3
7.3
90
42
80
2.6
6.5
4.3
8.7
90
80
140
2.6
6.5
4.3
8.7
90
140
190
2.0
5.9
3.6
7.9
90
III
190
285
1.5
5.2
2.6
6.5
90
IV
285
345
1.3
5.0
2.3
6.2
90
Ia
Ib
II
4.3.7
Data Properti Air Laut
Tabel 4.9 merupakan tabel yang menyajikan data propeti air laut tempat penempatan pipa. Tabel 4.9 Data Properti Air Laut [sumber: Field report 28” East Java Gas Pipeline].
Description
Unit
Data
Seawater Density
lb/ft3
64
Seawater Reststivity
ohm – cm
20
Seabed Temperature
°C
20
Sediment Resistivity
ohm – cm
150
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-8
TUGAS AKHIR
4.4
BAB 4 STUDI KASUS
Analisis Desain Pipa
Berikut ini adalah analisis-analisis yang dilakukan pada proses pendesainan struktur jaringan pipa bawah laut. 4.4.1
Analisis Ketebalan Pipa
Jaringan pipa pada proyek ini mempergunakan diameter 28 in. Hasil ini merupakan hasil perhitungan yang didapatkan dari process engineering. Oleh karena itu, review design ketebalan dinding pipa dilakukan untuk pipa dengan diameter 28 in. Dalam melakukan review design ini digunakan standar DNV-OS-F101. Ketebalan pipa yang digunakan ini akan di cek sehingga dapat diketahui apakah pipa sudah memenuhi syarat pressure containment, system collapse criteria, combined loading-load controlled condition, dan propagation buckling check. Input yang digunakan untuk perhitungan ketebalan pipa adalah: Steel pipe outer diameter
: OD
= 28 in
Kedalaman
: d
= 118 m
Kedalaman maksimum
: dmax
= 122.24 m (kondisi operasional)
dmax2 Safety class resistance factor : γsc1 γsc2
= 121.44 m (kondisi instalasi dan hydrotest) = 1.138 (untuk kriteria pressure containment) = 1.14 (untuk kriteria buckling)
Material resistance factor
: γm
= 1.15
Rasio tekanan insidental
: γinc
= 1.1
Content density
: ρcont1
= 0 pcf
ρcont2
= 64 pcf
ρcont3
= 4 pcf
Poisson’s ratio
: ν
= 0.3
Modulus elatisitas
: E
= 3 x 107 psi
Ovalisation
: fo
= 1.062 %
Characteristic yield stress
: fy
= 6.24 x 104 psi
Characteristic tensile stress : fu
= 7.392 x 104 psi
Karakteristik tebal pipa
= 0.586 in (untuk kriteria pressure containment)
: t1 t2
ANALISIS FREE SPAN PIPA BAWAH LAUT
= 0.625 in (untuk kriteria buckling)
4-9
TUGAS AKHIR
BAB 4 STUDI KASUS
Tabel 4.10 sampai Tabel 4.13 merupakan hasil dari perhitungan ketebalan pipa. •
Pressure containment
Tabel 4.10 Perhitungan Pressure Containment.
No. Keterangan 1
Nilai
Mill pressure condition
Yielding limit stress
Pby =
2 ⋅ t1 2 ⋅ f y ⋅ OD − t1 3
3.078 × 103 psi
Bursting limit state
Pbu =
2 ⋅ t1 f 2 ⋅ u ⋅ OD − t1 1.15 3
3.171× 103 psi
Pressure containment
Pb1 = min (Pby , Pbu )
resistance
Resistance
System test Pressure containment check 2
Rumus
Pb1
2.352 × 103 psi
γ sc1⋅γ m Plt = Pt + ρ cont 2 .g.d Pb1
γ sc1⋅γ m
3.078 × 103 psi
≥ Plt
1.1 × 10 3 psi
Ok!
Operational condition
Resistance
Incidental Pressure containment check
ANALISIS FREE SPAN PIPA BAWAH LAUT
Pb 2
2.352 × 103 psi
γ sc1⋅γ m Plio = Pinc + ρcont3 .g.d = Pd .γ inc + ρcont3.g.d
Pb 2
γ sc1⋅γ m
≥ Plio
1.199 ×103 psi
Ok!
4-10
TUGAS AKHIR
BAB 4 STUDI KASUS
System collapse criteria Tabel 4.11 Perhitungan System Collapse Criteria.
No. Keterangan 1
Rumus
Nilai
Construction and system pressure test
Ellastic collapse pressure
t 2⋅ E ⋅ 2 OD Pel = 1 −υ 2
Plastic collapse pressure
Pp = 2 ⋅ f y ⋅ α fab ⋅
3
733.29 psi
t2 OD
2.368 × 103 psi
b = −Pel
− 733.29 psi
2 OD c = − Pp + Pp ⋅ Pel ⋅ f o t 2
− 6.433 × 10 6 psi 2
d dd = Pel ⋅ Pp
2
4.111× 109 psi 3
u=
1 −1 ⋅ ⋅b + c 3 3
− 2.204 × 10 6 psi 2
v=
1 2 3 1 ⋅ ⋅ b − ⋅ b ⋅ c + d dd 2 27 3
1.255 × 109 psi 3
The Charactristic Resistance for External Pressure Solution
−v Σ = 3 −u
− 0.383
φ = a cos(Σ )
1.964rad
φ 60 ⋅ π φ = −2 ⋅ − u ⋅ cos + 3
ANALISIS FREE SPAN PIPA BAWAH LAUT
180
388.405 psi
4-11
TUGAS AKHIR
BAB 4 STUDI KASUS
1 Pc1 = y − ⋅ b 3 Pc1
Resistance
System collapse check
Pe max 2 = ρ sw .g.d max 2 Pc1
γ sc1⋅γ m
177 .63 psi
≥ Pe max 2
Ok!
Operational Condition Pc 2
Resistance
482.711 psi
γ sc 2⋅γ m
External pressure design
System collapse check
•
482.711 psi
γ sc1⋅γ m
External pressure design
2
632.835 psi
Pe max = ρ sw .g.d max Pc 2
γ sc 2⋅γ m
178.213 psi
≥ Pe max
Ok!
Combined loading-load controlled condition
Tabel 4.12 Perhitungan Combined Loading-Load Controlled Condition.
No Keterangan 1
Rumus
Nilai
Installation condition Effective axial forces
γ SC 2 ⋅ γ m M d α ⋅M p c
and external
Sd + γ SC 2 ⋅ γ m ⋅ α ⋅S c p
2
2
P + γ SC 2 ⋅ γ m e max 2 P c1
2
0.243
overpressure
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-12
TUGAS AKHIR
BAB 4 STUDI KASUS
Effective axial forces and external overpressure
2
2 2 γ SC 2 ⋅ γ m M d + γ SC 2 ⋅ γ m ⋅ Sd + γ SC 2 ⋅ γ m Pe max 2 ≤ 1 P α ⋅M α ⋅ S p c1 c c p
Ok!
check
2
Operational Condition Effective axial forces and external
2
2 2 γ SC 2 ⋅ γ m M d + γ SC 2 ⋅ γ m ⋅ S d + γ SC 2 ⋅ γ m Pe max P α ⋅M α ⋅ S p c 2 c c p
0.369
overpressure Effective axial forces and external overpressure
γ SC 2 ⋅ γ m M d αc ⋅ M p
+ γ SC 2 ⋅ γ m ⋅ S d αc ⋅ S p
2
2
P + γ SC 2 ⋅ γ m e max P c2
2
≤ 1
Ok!
check Effective axial forces and internal
2
2 2 γ SC 2 ⋅ γ m M d + γ SC 2 ⋅ γ m ⋅ S d + γ SC 2 ⋅ γ m Pe max P α ⋅M α ⋅ S p c2 c c p
0.136
overpressure Effective axial forces and internal overpressure
γ SC 2 ⋅ γ m M d α ⋅M p c
2 + γ SC 2 ⋅ γ m ⋅ S d α ⋅S c p
2
2
P + γ SC 2 ⋅ γ m e max P c2
≤ 1
Ok!
check
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-13
TUGAS AKHIR
•
BAB 4 STUDI KASUS
Propagation buckling check
Tabel 4.13 Perhitungan Propagation Buckling Check.
No. Keterangan 1
Nilai
Construction and system pressure test
Resistance
External pressure design
Propagation buckling check
2
Rumus
Ppr
105.408 psi
γ sc 2⋅γ m Pe max 2 = ρ sw .g.d max 2 Ppr
γ sc 2⋅γ m
≥ Pe max 2
177 .63 psi
Not Ok!
Operational Condition
Resistance
External pressure design
Propagation buckling check
Ppr
105.408 psi
γ sc 2⋅γ m Pe max = ρ sw .g.d max Ppr
γ sc 2⋅γ m
≥ Pe max
178.213 psi
Not Ok!
Melalui hasil perhitungan yang telah dilakukan dapat dilihat bahwa ketebalan yang digunakan belum memenuhi syarat propagation buckling check. Agar memenuhi syarat ketebalan pipa harus ditambah hingga mencapai 0.78 in. Namun pada kasus ini, pipa telah terpasang sehingga ketebalan pipa tidak mungkin untuk ditambah solusi untuk kasus ini yaitu dengan memasangkan buckle arrestor. Buckle arrestor digunakan sebagai pengaman pipa dari buckling. Buckle arrestor merupakan cincin yang menyelimuti pipa, yang berfungsi untuk menambah ketebalan dinding (wall thickness) agar propagation buckling tidak terjadi. Perhitungan buckle arrestor tidak dibahas dalam Tugas Akhir ini.
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-14
TUGAS AKHIR
4.4.2
BAB 4 STUDI KASUS
Analisis Stabilitas Pipa
Perhitungan On-Bottom Stability menggunakan standar DNV-RP-E305 (On-Botom Stability Design of submarine pipelines). Tabel 4.14 adalah tabel hasil perhitungan on-bottom stability. Input yang digunakan untuk perhitungan stabilitas pipa adalah: Diameter luar pipa baja
: Ds
= 28 in
Tebal pipa
: ts
= 0.625 in
Diameter dalam pipa
: ID
= 26.75 in
Tebal lapisan anti karat
: tcorr
= 3 mm
Densitas lapisan anti karat
: ρcorr
= 915 kg/m
3
3
Densitas lapisan thermal insulation : ρins
= 72.083 kg/m
Densitas lapisan beton
: ρcc
= 3040 kg/m
Densitas air laut
: ρsw
= 1025 kg/m
Densitas Baja
: ρs
= 7849 kg/m
Densitas asphalt
: ρas
= 1300 kg/m
Tebal lapisan beton
: tcc
= 1.75 in
Tinggi gelombang signifikan
: Hs1
= 2 m (kondisi instalasi dan hydrotest)
: Hs100
= 3.6 m (kondisi operasional)
: Tp1
= 5.9 s (kondisi instalasi dan hydrotest)
: Tp100
= 7.9 s (kondisi operasional)
Viskositas kinematik air laut
: v
= 1.076 x 10-5 ft2/sec
Current 3 m above seabed
: Ur
= 0.7 m/sec
Periode puncak
ANALISIS FREE SPAN PIPA BAWAH LAUT
3
3
3
3
4-15
TUGAS AKHIR
BAB 4 STUDI KASUS
Tabel 4.14 Hasil Perhitungan On-bottom Stability.
Safety
Safety
Factor arah
Factor arah
vertikal
lateral
536.263
1.481
1.157
33.258
536.263
13.715
1.851
87.88
536.263
1.225
1.201
Submerged
Requirement
Weight
Weight
(kg/m)
(kg/m)
Installation
84.41
56.995
Hydrotest
456.122
Operating
107.642
Case
Bouyancy (kg/m)
Analisis dari perhitungan on-bottom stability sangat penting untuk dilakukan. Karena analisis perhitungan ini dilakukan untuk mengetahui kestabilan pipa di bawah laut, apakah pipa sudah cukup berat dan stabil untuk diletakkan pada seabed atau pipa justru akan mengapung karena submerged weight tidak cukup berat terhadap buoyancy dan gaya luar. Apabila requirement weight lebih berat daripada submerged weight maka salah satu alternatif yang dapat dilakukan adalah menambah ketebalan concrete coating (pelindung beton). Berdasarkan hasil perhitungan yang dilakukan diketahui bahwa kestabilan pipa telah memenuhi kriteria dari on-bottom stability dalam berbagai kondisi.
4.4.3
Analisis Free Span
Perhitungan panjang span maksimum dilakukan dengan menggunakan standar DNV RPF105 dan OS-F101. Tabel 4.15 menyajikan data-data mengenai free span yang diperoleh dari hasil perhitungan screening FLS free span. Input yang digunakan untuk perhitungan free span adalah: Modulus elastisitas baja
: Esteel
= 2.068 x 1011 Pa
Modulus elastisitas beton
: Econc
= 2.999 x 1011 Pa
Design pressure
: Pd1
= 0 psi (kondisi instalasi)
: Pd2
= 1650 psi (kondisi hydrotest)
: Pd3
= 1100 psi (kondisi operasional)
: SMYS
= 65000 psi
Specified minimum tensile strength : SMTS
= 77000 psi
Specified minimum yield strength
Design temperature
: Td
= 100° C
Laying temperature
: Tsw
= 20° C
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-16
TUGAS AKHIR
BAB 4 STUDI KASUS
Temperature expansion coefficient
: αe
= 1.17 x 10-5 1/K
Kecepatan arus
: Uc1
= 0.7m/s (kondisi instalasi dan hydrotest)
: Uc10
= 0.8m/s (kondisi operasional)
Wave spreading coefficient
: Rd
=1
Boundary Condition Coefficient
: C1
= 1.57
C2
= 1.00
C3
= 0.8
C4
= 4.39
C5
= 1/8
C6
= 5/384
Tabel 4.15 Perhitungan Free Span Berdasarkan Screening FLS.
Case
Maximum Allowable Span
Installation
28.529 m
Hydrotest
27.626 m
Operation
8.132 m
Setelah screening FLS dilakukan analisis free span selanjutnya adalah melakukan screening ULS. Tabel 4.16 sampai Tabel 4.18 menyajikan hasil dari perhitungan screening ULS. •
Kondisi Instalasi
Tabel 4.16 Perhitungan Free Span Berdasarkan Screening ULS pada Kondisi Instalasi.
No. Keterangan 1
Rumus
Nilai
Stress range In-line unit stress amplitude
ANALISIS FREE SPAN PIPA BAWAH LAUT
AIL = ACD = C 4 ⋅ (1 + CSF ) ⋅
D ⋅ (D s − t s ) ⋅ E steel Leff
2
1.076 × 105 psi
4-17
TUGAS AKHIR
In-line stress range Cross flow stress range In-line stress dynamic Cross flow stress dynamic
2
BAB 4 STUDI KASUS
S IL = 2 ⋅ AIL ⋅ A yo .ψ αIL .γ s
2.046 × 10 4 psi
S IL = 2 ⋅ ACF ⋅ Azo .Rk .γ s
0 psi
1 2
σ dynIL = max S IL ,0.4 ⋅ S CF ⋅
σ dynCF =
AIL ACF
1 (S CF ) 2
1.023 × 10 4 psi
0 psi
Bending moment Effective axial force
S eff = H eff − [ ( ∆pi ). Ai .(1 − 2υ ) ] − [ As .E .( ∆T ).α e ]
Inertia of concrete
I conc =
Inertia of steel
I steel =
π 64
π 64
[
4
⋅ D 4 − (Ds + 2 ⋅ t corr )
[
⋅ D 4 − ID 4
]
]
− 6.893 × 10 6 N
8.787 × 10 −3 m 4
2.097 × 10 −3 m 4
Dynamic bending moment due to viv
M dyn = max(σ dynIL , σ dynCF ) ⋅
2 ⋅ I steel Ds − t s
500 .244 kJ
or direct wave act.
Static bending
M static = C5 ⋅
moment
Design bending moment
2
Wsub ⋅ Leff
2
S eff 1 + PE
⋅g
M d = max (M dyn , M static )
1.102 × 10 3 kJ
1.102 × 10 3 kJ
Design pressure differential Design pressure differential
ANALISIS FREE SPAN PIPA BAWAH LAUT
∆Pd = γ p ⋅ [Pd + ρ content ⋅ g ⋅ h − ρ sw ⋅ g ⋅ h ]
180.665 psi
4-18
TUGAS AKHIR
3
4
5
BAB 4 STUDI KASUS
Moment and axial plastic limit Axial plastic limit
S p = f y ⋅ π ⋅ (D s − t s ) ⋅ t s
Moment plastic limit
M p = f y ⋅ π ⋅ (D s − t s ) ⋅ t s
Bursting pressure
Pb =
1.492 × 10 7 N
2
1.037 × 10 7 J
f 2 ⋅ ts ⋅ min f y , u 3 Ds − t s 1.15
2
3.22 × 10 3 psi
⋅
Requirement for pipe member subject to bending moment, effective axial force, and internal overpressure 2 2 2 Seff M ∆ P ∆ P d d d + γ SC ⋅ γ m ⋅ + γ SC ⋅ γ m ⋅ 1 − α ⋅ S α ⋅ M α ⋅ P α ⋅ P c p c p c b c b
0.408
2 2 2 Seff ∆Pd ∆Pd Md ≤1 + + γ SC ⋅ γ m ⋅ ⋅ 1 − γ SC ⋅ γ m α ⋅ S α c ⋅ M p α c ⋅ Pb α c ⋅ Pb c p
Ok!
Requirement for pipe member subject to bending moment, effective axial force, and external overpressure
Md γ SC ⋅ γ m α ⋅ M p c
S + γ SC ⋅ γ m eff α ⋅ S c p
2
2
P + γ SC ⋅ γ m ⋅ e P c
2
0.262
2
2 2 Md Seff Pe + γ SC ⋅ γ m + γ SC ⋅ γ m ⋅ ≤ 1 γ SC ⋅ γ m P αc ⋅ M p α c ⋅ S p c
ANALISIS FREE SPAN PIPA BAWAH LAUT
Ok!
4-19
TUGAS AKHIR
•
BAB 4 STUDI KASUS
Kondisi Hydrotest
Tabel 4.17 Perhitungan Free Span Berdasarkan Screening ULS pada Kondisi Hydrotest.
No. Keterangan 1
Rumus
Nilai
Stress range In-line unit stress
AIL = ACD = C 4 ⋅ (1 + CSF ) ⋅
D ⋅ (D s − t s ) ⋅ E steel Leff
amplitude In-line stress range Cross flow stress range In-line stress dynamic Cross flow stress dynamic
2
2
1.155 × 10 5 psi
S IL = 2 ⋅ AIL ⋅ A yo .ψ αIL .γ s
2.042 × 10 4 psi
S IL = 2 ⋅ ACF ⋅ Azo .Rk .γ s
0 psi
1 2
σ dynIL = max S IL ,0.4 ⋅ S CF ⋅
σ dynCF =
AIL ACF
1 (S CF ) 2
1.021× 10 4 psi
0 psi
Bending moment Effective axial force
S eff = H eff − [ ( ∆pi ). Ai .(1 − 2υ ) ] − [ As .E .( ∆T ).α e ]
Inertia of concrete
I conc =
Inertia of steel
I steel =
π 64
π 64
[
4
⋅ D 4 − (Ds + 2 ⋅ t corr )
[
⋅ D 4 − ID 4
]
− 8.444 × 10 6 N
8.787 × 10 −3 m 4 2.097 × 10 −3 m 4
]
Dynamic bending moment due to viv
M dyn = max(σ dynIL , σ dynCF ) ⋅
2 ⋅ I steel Ds − t s
424 .563kJ
or direct wave act.
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-20
TUGAS AKHIR
BAB 4 STUDI KASUS
Static bending
M static = C5 ⋅
moment
Design bending
⋅g
1.651 × 10 3 kJ
1.651 × 10 3 kJ
∆Pd = γ p ⋅ [Pd + ρ content ⋅ g ⋅ h − ρ sw ⋅ g ⋅ h ]
differential
Moment plastic
S p = f y ⋅ π ⋅ (D s − t s ) ⋅ t s
1.492 × 10 7 N
2
M p = f y ⋅ π ⋅ (D s − t s ) ⋅ t s
limit
Bursting pressure
Pb =
1.037 × 10 7 J
f 2 ⋅ ts ⋅ min f y , u 3 Ds − t s 1.15
2
3.22 × 10 3 psi
⋅
Requirement for pipe member subject to bending moment, effective axial force, and internal overpressure
γ SC
S eff ⋅γ m α ⋅ S c p
2
+ γ SC ⋅ γ m
∆Pd Md ⋅ ⋅ 1 − α c ⋅ M p α c ⋅ Pb
2
+ ∆Pd α c ⋅ Pb
2 2 2 Seff ∆Pd ∆Pd Md + ≤1 + γ SC ⋅ γ m ⋅ ⋅ 1 − γ SC ⋅ γ m α ⋅ S α c ⋅ M p α c ⋅ Pb α c ⋅ Pb c p
5
1.731× 10 3 psi
Moment and axial plastic limit Axial plastic limit
4
S eff 1 + PE
Design pressure differential Design pressure
3
2
M d = max (M dyn , M static )
moment
2
Wsub ⋅ Leff
2
0.74
Ok!
Requirement for pipe member subject to bending moment, effective axial force, and external overpressure
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-21
TUGAS AKHIR
Md γ SC ⋅ γ m α ⋅ M p c
BAB 4 STUDI KASUS
S + γ SC ⋅ γ m eff α ⋅ S c p
2
2
P + γ SC ⋅ γ m ⋅ e P c
2
0.59
2
2 2 Md Seff Pe + γ ⋅γ + γ ⋅γ ⋅ ≤ 1 γ SC ⋅ γ m α ⋅ M SC m α ⋅ S SC m P p c c c p
•
Ok!
Kondisi Operation
Tabel 4.18 Perhitungan Free Span Berdasarkan Screening ULS pada Kondisi Operation.
No. Keterangan 1
Rumus
Nilai
Stress range In-line unit stress
AIL = ACD = C 4 ⋅ (1 + CSF ) ⋅
D ⋅ (D s − t s ) ⋅ E steel Leff
amplitude In-line stress range Cross flow stress range In-line stress dynamic Cross flow stress dynamic
2
2
2.703 × 10 4 psi
S IL = 2 ⋅ AIL ⋅ A yo .ψ αIL .γ s
S IL = 2 ⋅ ACF ⋅ Azo .Rk .γ s
1 2
σ dynIL = max S IL ,0.4 ⋅ S CF ⋅
σ dynCF =
1.155 × 10 5 psi
0 psi
AIL ACF
1 (S CF ) 2
1.351× 10 4 psi
0 psi
Bending moment Effective axial force
S eff = H eff − [ ( ∆pi ). Ai .(1 − 2υ ) ] − [ As .E .( ∆T ).α e ]
ANALISIS FREE SPAN PIPA BAWAH LAUT
− 7.698 × 10 6 N
4-22
TUGAS AKHIR
Inertia of concrete
Inertia of steel
BAB 4 STUDI KASUS
I conc =
I steel =
π 64
π 64
[
4
⋅ D 4 − (Ds + 2 ⋅ t corr )
[
⋅ D 4 − ID 4
]
8.787 × 10 −3 m 4
2.097 × 10 −3 m 4
]
Dynamic bending moment due to viv or direct wave
M dyn = max(σ dynIL , σ dynCF ) ⋅
2 ⋅ I steel Ds − t s
561 .921kJ
act.
Static bending
M static = C5 ⋅
moment
Design bending moment
3
differential
S eff 1 + PE
⋅g
M d = max (M dyn , M static )
809 . 638 kJ
809 .638 kJ
∆Pd = γ p ⋅ [Pd + ρ content ⋅ g ⋅ h − ρ sw ⋅ g ⋅ h ]
985 .559 psi
Moment and axial plastic limit Axial plastic limit Moment plastic limit
Bursting pressure
5
2
Design pressure differential Design pressure
4
Wsub ⋅ Leff
S p = f y ⋅ π ⋅ (D s − t s ) ⋅ t s
2
M p = f y ⋅ π ⋅ (D s − t s ) ⋅ t s
Pb =
2 ⋅ ts f ⋅ min f y , u 3 Ds − t s 1.15
2
⋅
1.492 × 10 7 N
1.037 × 10 7 J
3.22 × 10 3 psi
Requirement for pipe member subject to bending moment, effective axial force, and internal overpressure
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-23
TUGAS AKHIR
γ SC
BAB 4 STUDI KASUS
S eff ⋅γ m α ⋅ S c p
2
+ γ SC ⋅ γ m
∆Pd Md ⋅ ⋅ 1 − α c ⋅ M p α c ⋅ Pb
2
+ ∆Pd α c ⋅ Pb
2 2 2 Seff ∆Pd ∆Pd Md + ≤1 γ SC ⋅ γ m + γ SC ⋅ γ m ⋅ ⋅ 1 − α ⋅S α c ⋅ M p α c ⋅ Pb α c ⋅ Pb c p
6
2
0.441
Ok!
Requirement for pipe member subject to bending moment, effective axial force, and external overpressure
Md γ SC ⋅ γ m α ⋅ M p c
S + γ SC ⋅ γ m eff α ⋅ S c p
2
2
P + γ SC ⋅ γ m ⋅ e P c
2
0.421
2
2 2 Md Seff Pe + γ ⋅γ + γ ⋅γ ⋅ ≤ 1 γ SC ⋅ γ m α ⋅ M SC m α ⋅ S SC m P c p c p c
Ok!
Kesimpulan yang didapatkan dari seluruh hasil perhitungan free span adalah bahwa span yang boleh terjadi tidak boleh melebihi nilai maximum allowable span, jika terdapat span yang melebihi batas maximum allowale span maka pipa akan mengalami vibrasi yang kemudian nantinya pipa akan mengalami kelelahan (fatigue) dan dapat menyebabkan kegagalan pada pipa tersebut.
4.4.4
Analisis Umur Fatigue
Perhitungan fatigue ini dilakukan untuk setiap data gelombang dan arus pada setiap sea-state, dengan menggunakan data gelombang 1 tahun dengan perioda ulang 1 tahunan di stasiun Kangean (dapat dilihat pada Tabel 4.19), karena keterbatasan data maka pengolahan data fatigue hanya berlaku untuk kepentingan studi ini saja. Perhitungan fatigue hanya dilakukan pada span yang melebihi batas allowable span maximum, dari 20 data span yang terdapat 13 span yang melebihi nilai allowable span maximum. Tabel 4.20 menyajikan hasil perhitungan akumulasi kerusakan fatigue.
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-24
TUGAS AKHIR
BAB 4 STUDI KASUS
Tabel 4.19 Data gelombang selama 1 tahun dengan perioda ulang 1 tahunan. Wave Height (m)
Hs (m)
Kejadian
0.000
-
0.490
0.245
10043613
0.500
-
0.990
0.745
7417485
1.000
-
1.490
1.245
1640910
1.500
-
1.990
1.745
217635
2.000
-
2.490
2.245
20994
2.500
-
2.990
2.745
1266
3.000
-
3.490
3.245
0
Input yang digunakan untuk perhitungan umur fatigue adalah: Nilai eksponen fatigue
: m
= 3
Nilai karakteristik strength
: C
= 4.3 x 1011
Safety factor untuk fekuensi natural : γf
= 1.20
Safety factor for damping
: γk
= 1.15
Safety factor for stress range
: γs
= 1.30
Tabel 4.20 Summary Perhitungan Fatigue. Span Properties #
Start KP (km)
End KP (km)
Water Depth (m)
Span Length (m)
Maximum Span Height (m)
Frekuensi Natural fn_IL
fn_CF
0.766
0.58
Dfat-IL Lifetime Total (thn) 0.045 22.344
0.084
11.942
Dfat-CF Lifetime Total (thn) 0.006 161.715
0.013
77.230
805
150.636
150.67
100.6
34
0.42
806
150.677
150.71
100.3
23
2.01
808
151.17
151.192
99.8
22
0.96
809
151.41
151.448
100.2
38
0.48
0.736
0.574
811
151.829
151.865
99.3
36
0.83
0.752
0.578
0.064
15.694
0.008
120.607
826
152.911
152.961
99.4
50
1.18
0.633
0.52
0.138
7.246
0.098
10.168
828
153.08
153.17
99.2
90
1.06
0.403
0.39
0.285
3.509
0.219
4.568
838
154.041
154.079
99.8
26
1.54
841
154.563
154.586
101.3
23
1.49
846
155.973
156.003
103.6
20
0.46
852
157.436
157.455
102.5
19
0.97
855
158.015
158.033
100.6
18
1.38
862
159.415
159.463
100.3
48
1.92
0.65
0.527
0.129
7.752
0.090
11.089
869
160.186
160.224
95.9
58
1.29
0.572
0.503
0.149
6.702
0.121
8.243
870
160.249
160.282
95.2
33
1.18
0.772
0.583
0.030
33.474
0.005
187.165
871
160.288
160.335
93.7
47
0.93
0.658
0.556
0.123
8.163
0.082
12.250
872
160.474
160.517
91.4
43
0.46
0.693
0.571
0.109
9.174
0.047
21.114
873
160.736
160.953
90.2
45
0.53
0.676
0.564
0.118
8.475
0.063
15.939
874
160.809
160.953
90.2
144
0.78
0.263
0.26
0.548
1.825
0.350
2.857
875
160.96
160.99
89.8
39
0.64
0.728
0.573
0.099
10.130
0.019
51.980
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-25
TUGAS AKHIR
BAB 4 STUDI KASUS
Span pipa #828 (90m) dan #874 (144m) memiliki remaining life time akibat fatigue in line yang sangat kecil, yaitu 3 tahun 6 bulan dan 1 tahun 10 bulan, oleh karena itu pada kasus ini harus segera dilakukan remidiasi (ditangani), penanganan ini dapat berupa pemberian support agar span yang terjadi pada pipa menjadi semakin kecil. Pemberian support dapat dilakukan dengan berbagai macam cara diantaranya: •
grout bag support : penyangga yang berupa karung semen yang diinjeksi.
•
rock dumping : memberikan batu-batuan pada span dalam jumlah yang banyak sehingga span yang terjadi bisa diperkecil.
Selain itu cara lain untuk memperkecil span adalah melakukan: •
jet trenching : meratakan seabed didasar laut dengan menggunakan alat jet trenching.
•
chain cutter : meratakan seabed didasar laut dengan menngunakan alat chain cutter.
ANALISIS FREE SPAN PIPA BAWAH LAUT
4-26
