REV.
DATE
ORIGINATOR
REVIEWED
APPROVED
DESCRIPTION
THIS DOCUMENT IS INTENDED FOR USE BY ADCO AND ITS NOMINATED CONSULTANTS, CONTRACTORS, MANUFACTURERS AND SUPPLIERS
TABLE OF CONTENTS
1.
GENERAL .................................................................................................................... 3
1.1
Introduction ....................................................................................................... 3
1.2
Purpose ............................................................................................................. 3
1.3
Definitions/ Abbreviations .................................................................................. 3
2.
CODES AND STANDARDS ......................................................................................... 4
3.
REFERENCES ............................................................................................................. 4
4.
3.1
Project Documents ............................................................................................ 4
3.2
Drawings ........................................................................................................... 4
INPUT DATA ................................................................................................................ 4
4.1
5.
6.
7.
Pipeline Data ..................................................................................................... 4
CODES & STANDARDS SUMMARY ........................................................................... 5
5.1
General ............................................................................................................. 5
5.2
Shell DEP Manual ............................................................................................. 5
5.3
K Peters Approach ............................................................................................ 6
5.4
Calculation Methodology ................................................................................... 6
RESULTS ..................................................................................................................... 9
6.1
Stability Check................................................................................................... 9
6.2
Maximum Allowable Bend Angle ....................................................................... 9
6.3
Direction Changes Summary ........................................................................... 10
6.4
Summary of Critical Bend Angles .................................................................... 10
CONCLUSION AND RECOMMENDATIONS ............................................................. 10
APPENDIX-1: BUCKLING CALCULATION REPORT ............................................................. 12
APPENDIX-2: DIRECTION CHANGES SUMMARY ................................................................. 13
APPENDIX-3: CALCULATIONS FOR CRITICAL BEND ANGLES .......................................... 14
1.
GENERAL
1.1
Introduction
Global buckling is a response to compressive effective axial force and it reduces the axial carrying
capacity. Buckling may appear downward, lateral or vertically upward. In case of buried pipelines,
the high axial compressive forces induced due to extreme operating conditions, cause the pipeline
to buckle upwards.
The scope of this document is to evaluate the critical segments of RDS-7 to BCDS pipeline which
are prone to upheaval buckling. In case any such pipeline segments exist, suitable mitigation
measures have been recommended to prevent buckling.
The calculation has been carried out using Mathcad V 15.0. Shell DEP manual and K Peters
methodology have been used for buckling evaluation.
1.2
Purpose
The pipeline system supplies crude oil (sour service) from RDS-7 to BCDS. Buckling analysis of
the pipeline system is carried out due to following reasons:
1.3
-
To ensure that soil resistance force at various pipeline segments is sufficient to withstand the
induced axial compressive force.
-
To evaluate the affect of buckling phenomenon on pipeline
-
To identify various critical locations which are prone to buckling
-
To provide recommendations to prevent buckling of pipeline.
Definitions/ Abbreviations
Company
:
Abu Dhabi Company for Onshore Oil Operations (ADCO)
Contractor
:
National Petroleum Construction Company (NPCC)
Project
:
EPC FOR BAB THAMAMA G & HABSHAN 2 1.8 MMBOPD PHASE-1
DEVELOPMENT PROJECT
RDS
:
Remote Degassing Station
BCDS
:
Bab Central Degassing Station
2.
3.
CODES AND STANDARDS
Shell DEP – 31.40.10.16
-
Upheaval Buckling Pipelines
K Peters Research
Paper
-
About upheaval and lateral buckling of embedded
pipelines
OTC 6365
-
Design of submarine pipelines against upheaval buckling
REFERENCES
The following references documents have been used for the preparation of this Report.
3.1
3.2
Project Documents
11-99-91-1654
-
Pipeline Mechanical Design Basis
11-78-91-1715
-
Pipeline Mechanical Design Report
11-78-12-1737
-
Specification for Pipeline Flexibility Analysis
11-78-23-1911
-
Stress analysis report for RDS-7 oil transfer line
Drawings
11-78-22-3802
4.
INPUT DATA
4.1
Pipeline Data
-
Pipeline Alignment Sheets 01 to 05
The following parameters are used in the analysis:
Pipeline Outside Diameter, D
16’’ (406.4 mm)
Pipeline Wall Thickness, tn
9.5 mm
Corrosion Allowance, A1
6 mm
Design/ Internal Pressure, P
46.6 bar (4.66 MPa)
Maximum Design Temperature, Td
100 °C
Installation/ Ambient Temperature, Ti
21°C
Pipe Material
API 5L X60
SMYS
415 MPa
Coating (3LPP) Thickness, tcorr
2.7 mm
Coating (3LPP) Density, ρcorr
930 kg/m³
Steel Density, ρsteel
7850 kg/m³
Content Density, ρcont
850 kg/m³
Poisson ratio, ν
0.3
Young’s Modulus, E
207000 MPa
Coefficient of thermal expansion, α
0.0000117 /°C
Pipeline cover, Hc
1.0 m
Soil density, soil
1686 kg/m³
Soil friction angle, φ
30°
Imperfection prop height, δ
0.5m
5.
CODES & STANDARDS SUMMARY
5.1
General
Shell DEP manual (31.40.10.16) UPHEAVAL BUCKLING OF PIPELINES has been adapted to
perform stability check of the under ground pipeline. A shell DEP guideline has been incorporated
wherever applicable.
K Peters methodology has been adapted to evaluate the maximum allowable bend angle to avoid
buckling. The change in material properties of steel subjected to external factors is not considered
for the calculation.
The calculations for the analysis have been carried out using Mathcad V 15.0.
5.2
Shell DEP Manual
Stabilization against upheaval buckling has been evaluated as per Shell DEP manual
(31.40.10.16). Required downward force for stability along with specified safety factor has been
evaluated.
The stability check (local equilibrium forces acting on pipeline) has been considered as explained
below.
The vertical force per unit length available to hold the pipe in position is w + r, where w is the
submerged weight and r the uplift resistance.
The external vertical force per unit length required to hold the pipeline in position is q and SF is the
safety factor.
If w + r > (SFxq), pipeline is stable.
5.3
K Peters Approach
Most of the classical buckling theories rely on the local equilibrium of the forces perpendicular to
the pipe axis. This approach is not practical if narrow bends or even mitre bends are involved.
Wherever directional changes (lateral and vertical) are present, axial resistance due to pipe
bending should be considered.
K Peters method considers the rough profiles which are quite common in onshore pipelines. A
simplified heuristic model has been developed based on the equilibrium for deformed structures.
This theory allows for a local lack of soil resistance leading to a controlled elastic deformation.
Buckling can be evaluated for the given soil resistance by deriving allowable deflection angles on a
(Euler) buckling length. Similarly, required soil resistance can be evaluated for a given deflection
angles on a buckling length.
For any small bending radii, the local equilibrium violates in any case. Therefore a pipeline
deflection is provoked on a certain length. This length is defined by the global equilibrium between
soil resistance and upheaval (or lateral) force induced due to axial compressive force.
Allowable deflection angle over a buckling length (λ) can be calculated for the given ultimate soil
resistance and the allowable bending stress. Accordingly, pipeline profile can be refined and
redesigned to prevent buckling phenomenon.
5.4
Calculation Methodology
All input parameters are considered as per project data.
The input parameters are used in successive calculations for uplift resistance and buckling driving
forces of the pipeline.
Uplift resistance force Ru, is calculated as per the section 2.4 of Shell DEP
Uplift resistance Ru = H. Dcorr . ρsoil (1+f Hc / Dcorr)
Where
Hc = Soil cover height
f = Uplift resistance factor
Dcorr = Diameter of pipe including corrosion coating
Uplift resistance factor, f is as per the section 2.4 of Shell DEP 31.40.10.16
Shell DEP manual recommends a methodology to calculate driving force to cause buckling. As per
section 2.2.1 of Shell DEP, for fully constrained pipelines “The driving force that creates the
upheaval buckling is the longitudinal compressive force”. One component of this is due to
temperature increase. Another component of the driving force is due to pressure.
The longitudinal compressive force is given by equation
2
(
)
( 1 − 2) Rm  P + 2    Rm teff  E  Td − Ti − TR
Ne
(Section 2.2.1 of Shell DEP)
Where
Ne = longitudinal driving force
Rm = Mean radius of the pipe (corroded condition)
P = design pressure
Teff = Effective thickness
TR = Residual tension
Required downward force to hold the pipeline in position is calculated as per Section 2.3.3 of Shell
DEP
The span of pipe ‘L’ subjected to maximum downward force is verified with the criteria
L < 4.44 √(EI/Ne)
The calculated ‘L’ value is 18.7m. Since the unsupported span subjected to max downward force
shall be less than 18.7m in buried pipeline, the below equation is used for calculating the required
downward force.
q = Ne² δ/ (4 EI g)
( Section 2.3.3 of Shell DEP 31.40.10.16 )
Where
q = external downward force required
δ = imperfection prop height of a continuous supported sinusoidal profile
I = Section modulus of the pipe
As per section 2.5 of Shell DEP, stability check can be performed using below equation. If the
pipeline is stable no further action is required.
W + Ru > SF.q
Where
W = submerged weight of the pipe
Ru = upward soil resistance
q = required external downward force
SF = safety factor = 1.5 (as per section 2.3.8 of shell DEP)
In case pipeline is not stable, suitable counter measures to avoid buckling are specified.
After stability check, for the given lateral compressive force, the buckle length is calculated as per
the K Peters method.
The area of pipe cross section is considered in un-corroded condition.
The compressive restraining force for pipeline is calculated for the above condition using equation
given below.
Fcr
(
)
 E A cs  Td − Ti + ( 1 − 2  )  P A int
Where
Fcr = Compressive restraining force
Acs = Area of cross section of line pipe
Aint = internal area of line pipe
The buckling length of pipeline is calculated as per K Peter’s method
Buckle length λ = √4.π.EI/Fcr
The allowable bending stress σall is evaluated from max allowable stress Sa, Tensile hoop stress
Sh and Compressive longitudinal stress.
all
Sa − Sh − Sl
The ultimate soil resistance is calculated as per K Peter’s method
Rult




g  Hc D soil  1 + f 
Hc 

 + W to
D 

Where
Wto = Weight of pipe
For the calculated value of ultimate soil resistance, allowable deflection angle has been identified
for nominal 1 m depth as per K Peter’s method.
Allowable bend angle in radians
AR
  
Rult
Fcr
The factor η is calculated from the K Peter’s equation below.
 1 −   guess  cos (  guess ) 


sin (  guess ) 

2
all
Fcr
D E Rult
All the direction changes as per alignment sheets have been noted. The bend angles have been
verified against obtained allowable angle as per K Peters method. Refer Appendix-2 of this
document. For all the direction changes, minimum cover depth required to avoid buckling has been
evaluated in Appendix-3 of this document. Suitable recommendations have been provided to avoid
upheaval buckling wherever required.
Few recommendations include – change in direction/ angle, change in depth, addition of weight by
extra coating, redesign of pipeline profile, recommendation of suitable backfill material or backfill
process etc.
6.
RESULTS
6.1
Stability Check
The vertical downward force per unit length available from the uplift resistivity of the 1.0m soil
cover and the submerged weight of the line pipe is greater than the required vertical downward
force to hold the pipeline in position. Hence, Pipeline is stable.
6.2
Maximum Allowable Bend Angle
Maximum allowable bend angle for 1.0 m cover depth to hold the pipeline stable against upheaval
buckling is 3.54° as per K Peter’s method.
6.3
Direction Changes Summary
All the direction changes as per alignment sheets have been tabulated in Appendix-2 of this
document. For all the direction changes above allowable angle of 3.54°, minimum cover depth
required to avoid buckling has been evaluated in Appendix-3 of this document.
6.4
Summary of Critical Bend Angles
Below is the list of direction changes (as per alignment sheets) which exceeds allowable limit.
Recommendations have been mentioned for each case. For node numbers/ location of bends,
refer Appendix-4 of this document.
Sl. No
Node
Number
Chainage
Bend
Recommendation
Angle
1
1460
0+920.48
7.0°
Additional cover height of 0.5m required at this location
2
1470
0+970.85
6.0o
The present cover depth of 2.0m is safe.
3
1560
1+230.72
5.8°
The present cover depth of 2.0m is safe.
4
2440
4+194
4.0°
Additional cover height of 0.2 m required at this location
5
2560
4+453.50
4.0°
Additional cover height of 0.2 m required at this location
Note: Please refer highlighted node number in the APPENDIX-2 of this document
7.
CONCLUSION AND RECOMMENDATIONS
The following are the conclusions drawn based on the buckling calculation results:
• The upheaval buckling calculation results for the buried pipelines are summarized in
Appendix 2 and detailed calculation is in Appendix 1 & 3.
• Based on the calculation in Appendix 1 pipeline system from RDS-7 to BCDS is stable to
withstand induced axial compressive force.
• Maximum allowable bend angle over the buckling length based on the calculation in
Appendix 1 is 3.54°. These values shall not be exceeded during construction of the
underground pipelines.
• Calculations are done for total effective cover depth of 1.0m. The berm height is not
considered at any point of calculation.
• The pipeline (buried) shall be laid in trench in such a way that the pipeline profile is
smooth without steep (vertical) direction changes. Construction methods like, cutting
and filling & other suitable methods shall be followed to achieve the smooth profile of the
pipeline.
• For buried pipeline laid in trenches, calculation for lateral buckling is not required due to
the high lateral soil resistance within the trench.
• Recommendations for all the direction changes with cumulative bend angle more than
3.54o have been tabulated in section 6.4 of this document and Appendix 2.
• The cover height needs to be increased at three (3) locations (chainages: 0+920.48,
4+194.0, 4+453.50 ) as mentioned in section 6.4 & Appendix 2 of this document.
•
The alignment sheets shall be updated based on the above recommendations.
• The minimum cover heights and related recommendations specified in section 6.4 shall
be considered during stress analysis.
• Construction shall also refer to the corresponding stress analysis report.
APPENDIX-1: BUCKLING CALCULATION REPORT
APPENDIX -1
INPUT PARAMETERS
Pipe outside diameter,
D  16in  406.4  mm
Nominal wall thickness,
tn  10.3 mm
Pipe material X60,
Corrosion allowance,
SMYS  415MPa
( 60200psi )
A1  6mm
Corrosion coating (3LPP) thickness,
tcorr  2.7mm
Design pressure, P  4.66MPa
(46.6 barg)
kg
Steel density, ρsteel  7850
3
m
Soil density,
kg
ρsoil  1686
3
m
Corrosion coating (3LPP) density,
kg
ρcorr  930 
3
m
Content (fluid) density, ρcont  850
kg
3
m
Installation (Backfill) Temperature, Ti  21 °C
Design temperature,
Td  100 °C
Nominal Pipeline cover depth,
Hc  1.0m
Imperfection prop height, δ  0.50m
Friction angle,
Poissons ratio
φ  30°  0.5236 rad
ν  0.3
Report no: 1931002 Appendix-1
Young's Modulus ,
E  207000MPa
Thermal expansion coefficient,
α  0.0000117
Corroded condition
Effective thickness,
teff  tn  A1  4.3 mm
TOTAL WEIGHT OF PIPELINE PER UNIT LENGTH
Mean Radius,
Rm 
D  teff 
2
(corroded condition)
 201.05 mm
Inner diameter of pipe, Di  D  2  teff  397.8  mm
Corrosion coating (3LPP) diameter,
Dcorr  D  2  tcorr  411.8  mm
π  D  Di

2
Steel cross sectional area,
Ap 
2
4
  5.432  103 mm2
 D 2  D2
corr
  3.47  103 mm2
Corrosion coating (3LPP) area, Acorr  π 
4
Pipe content sectional area, Acont 
Pipe flexural rigidity,
I 
64
2
5
4
  1.098  108 mm4
3
7 m  kg
EI  E I  2.273  10
2
s
Weight of steel pipe,
Report no: 1931002 Appendix-1
2
 1.243  10  mm
4
π  D  Di

4
Pipe section modulus,
π Di
kg
Wpipe  Ap  ρsteel  42.64
m
kg
Weight of Corrosion coating (3LPP), Wcorr  Acorr ρcorr  3.227
m
Weight of pipe contents,
kg
Wcont  Acont ρcont  105.642
m
kg
Total weight of pipeline, W  Wpipe  Wcorr  Wcont  151.51
m
(As per section 2.4 of Shell DEP)
UPLIFT RESISTANCE FORCE
For pipeline in Medium dense sand
Uplift Resistance factor,
f  0.50
Hc 

3 kg
Ru  Hc Dcorr ρsoil  1  f 
  1.537  10
Dcorr
m


Uplift Resistance, R.u
DRIVING FORCE FOR UPHEAVAL BUCKLING (FULLY CONSTRAINED PIPELINE)
"The driving force that creates the upheaval buckling is the longitudinal compressive force
in the restrained pipeline and its contents"
As per section 2.2.1 of Shell DEP
Residual Tension,
Driving Force,
TR  0kg

2

Ne  ( 1  2ν)π Rm  P  2  π Rm teff  E α Td  Ti  TR
Hence, Driving Force
6
Ne  1.276  10 N
EXTERNAL FORCE PER UNIT LENGTH
"It is recommended to perform proper infilling under the pipe and it is geotechnically
competent to provide resistance to downward movement."
Report no: 1931002 Appendix-1
As per section 2.3.3 of Shell DEP 31.40.10.16
L < 4.44
EI
Ne
 18.738 m
Assuming the unsupported span (L ) subjected to max buckling force shall be less than
19 m in burried pipeline
Required Downward Force,
kg
δ
2
q  Ne 
 913.132
m
4EI g
STABILITY CHECK AGANIST UPLIFT (AS PER SECTION 2.5 OF SHELL DEP
31.40.10.16)
Force per unit length required to hold the pipe in position,
Force per unit length available to hold the pipe in
position,
Considering safety factor,
Stability Condition
SF  1.5
q  913.132
kg
m
kg
W  Ru  1688.8
m
(As per section 2.3.8 OF Shell DEP)
W  Ru  SF  q  1
( '1' stands for PASS)
Hence, Pipeline is Stable against uplift
Calculation of Buckling length ( as per K Peters method )
For the K Peter's method the change in material properties of steel subjected to
external factors is not considered for the calculation.
Report no: 1931002 Appendix-1
Modulus of elasticity, E
E  207000MPa
Coefficient of thermal expansion , α
α  0.0000117 /°C
Non corroded condition
D2   D  2t  2
n 
2

Acs  π
 0.013 m
4
Area of pipe cross section, Acs
Internal Area of pipe, Aint
Pipe section modulus,
Pipe flexural rigidity,
I 
Aint  π
D  2tn2
π D  D  2tn


4
4
4
2
 0.117 m
8
4
 2.515  10  mm
64
3
7 m  kg
EI  E I  5.207  10
2
s
Compressive restraining force , F.crest


6
Fcr  α E Acs Td  Ti  ( 1  2  ν)  P Aint  2.67  10 N
Buckling length = λ
λ 
2 EI
4 π 
Fcr
 27.746 m
Calculation of allowable bending angle as per K Peters method
Max allowable stress = Sa
8
Sa  0.9 SMYS  3.735  10 Pa
Tensile Hoop stress = Sh
Sh  P
D
2 tn
7
 9.193  10 Pa


8
Compressive longitudinal stress = Sl
Sl  E α Td  Ti  ( 0.3 Sh)  1.638  10 Pa
Allowable bending stress =
σall
σall  Sa  Sh  Sl  1.178  10 Pa
Report no: 1931002 Appendix-1
8
Weight of pipe, Wto
kg
Wto  ρsteel Acs  Wcorr  ρcont Aint  203.207
m
Calculation of Ultimate soil resistance
With out considering berm height (worst case scenario)
Height of soil cover , Hb
Hb  1.0m
Ultimate Soil resistance = Rult
Guess:




Rult  g  Hb  D ρsoil  1  f 
Hb 

kg
  Wto  1.698  104
2
D 

s
ηguess  0.01
Given
 1  π ηguess cos( π ηguess) 


sin( π ηguess ) 

= σall
2
Fcr
D E Rult
η  Find( ηguess )
η  0.35
Allowable bend angle in radians = A.R
Rult
AR  η λ
 0.062
Fcr
Allowable bend angle in degree = A.D
180
AD  AR
 3.54 °
π
For all the directional changes less than 3.54°, no additional backfill is required.
All bend angle greater than 3.54° ( as per the alignment sheets ) will be
evaluated separately in APPENDIX-3.
Report no: 1931002 Appendix-1
APPENDIX-2: DIRECTION CHANGES SUMMARY
APPENDIX-2
Vertical direction changes as per Alignment sheets
Slno.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
Node
630
700
850
1160
1320
1400
1440
1460
1470
1490
1520
1550
1560
1630
1760
1780
1830
1850
1920
1940
1970
1990
2020
2100
2130
2170
2250
2290
2310
2330
2410
2440
2470
2480
2510
2520
2560
2580
2620
2660
2680
2690
Chainage
0+100
0+139
0+267.5
0+521.9
0+682.3
0+803.92
0+869.75
0+920.48
0+970.85
1+030.01
1+119.03
1+156.68
1+230.72
1+507.08
1+950
2+047.05
2+232.90
2+299
2+561.77
2+632.94
2+719.54
2+776.74
2+884.58
3+200
3+327.37
3+378.25
3+639.59
3+772.33
3+831.91
3+888.10
4+119.31
4+194
4+266.91
4+300
4+360.81
4+385.21
4+453.50
4+545.15
4+653.27
4+706.45
4+754.25
4+784.63
Report # 1931002 Appendix -2
Vertical angle change in
12m span
anti clock
clock wise
wise
0
1.3
1.3
0
0
0.8
0
3
3.5
0
0
2.4
3.5
0
7
0
0
6
0
0.44
2.5
0
3.5
0
0
5.8
0
0.57
0
0.24
0.24
0
0
1.08
0.95
0
0
0.25
0
0.66
0
0.38
3.5
0
0
1.85
0
1.8
3.5
0
0
1.86
0
0.98
0
1
3.5
0
0
1.52
0.4
0
0
4
3.5
0
0
3.5
3.5
0
2.5
0
0
4
1.47
0
0
3.5
3.5
0
3.5
0
0
3.5
Total included
angle
1.3
1.3
0.8
3.0
3.5
2.4
3.5
7.0
6.0
0.4
2.5
3.5
5.8
0.6
0.2
0.2
1.1
1.0
0.3
0.7
0.4
3.5
1.9
1.8
3.5
1.9
1.0
1.0
3.5
1.5
0.4
4.0
3.5
3.5
3.5
2.5
4.0
1.5
3.5
3.5
3.5
3.5
Remarks
Change of angle is within allowable limit
,,
,,
,,
,,
,,
,,
Change of angle exceeds allowable limit
Change of angle exceeds allowable limit
Change of angle is within allowable limit
,,
,,
Change of angle exceeds allowable limit
Change of angle is within allowable limit
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
Change of angle exceeds allowable limit
Change of angle is within allowable limit
,,
,,
,,
Change of angle exceeds allowable limit
Change of angle is within allowable limit
,,
,,
,,
,,
Min back fill height
required (m)
0.154
0.154
0
0.79
0.98
0.57
0.98
2.325
1.94
0
0.6
0.98
1.86
0
0
0
0.076
0.036
0
0
0
0.98
0.38
0.34
0.98
0.38
0.036
0.036
0.98
0.231
0
1.17
0.98
0.98
0.98
0.6
1.17
0.23
0.98
0.98
0.98
0.98
Present
Depth(m)
2
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
Reccomendation
Present design is safe
,,
,,
,,
,,
,,
,,
Additional 0.5 m backfill required
Present design is safe
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
,,
Additional 0.2m backfill required
Present design is safe
,,
,,
,,
Additional 0.2m backfill required
Present design is safe
,,
,,
,,
,,
Page 1 of 2
APPENDIX-2
Vertical direction changes as per Alignment sheets
Slno.
43
44
45
46
47
48
49
Node
2730
2750
2810
2870
2930
2950
2980
Chainage
4+867.35
4+916.34
5+070.52
5+211.70
5+382.47
5+432.28
5+509.94
Vertical angle change in
12m span
anti clock
clock wise
wise
0
3.5
3.5
0
0
0.63
0
1.8
2.4
0
0
1.58
1.58
0
Total included
angle
3.5
3.5
0.6
1.8
2.4
1.6
1.6
Remarks
,,
,,
,,
,,
,,
,,
,,
Min back fill height
required (m)
0.98
0.98
0
0.344
0.57
0.27
0.27
Present
Depth(m)
1
1
1
1
1
1
1
Reccomendation
,,
,,
,,
,,
,,
,,
,,
NOTES:
1
Node numbers are considered as per stress analyis models.
Marked up alignment sheets for all critical bend angles have ben provided in APPENDIX -4
2
Maximum allowable bend angle for 1.0m cover depth as per bukling calculation is 3.54°
3
The maximum allowable angle for 2.0m cover depth as per buckling calculation is 6.1°
Report # 1931002 Appendix -2
Page 2 of 2
APPENDIX-3: CALCULATIONS FOR CRITICAL BEND ANGLES
APPENDIX-3
Calculation of minimum cover depth for pipeline vertical bend angles
above 3.54° as per the alignment sheets
For 7.0° bend
( Node :1460)
Bend angle in degree = BD
BD  7.0
Bend angle in radian = B.R
π
BR  BD
 0.122
180
Guess:
η2guess  0.01
Given
 1  π η2guess  cos( π η2guess ) 


sin( π η2guess ) 

= σall
2  η2guess
λ
D E BR
η2  Find( η2guess )
η2  0.189
BR
4 kg
Rreq  Fcr
 6.228  10
( η2 )  λ
2
s
Hreq1 
D 
Rreq
f
  1  1
 
 Wto  
f   g
  ρ  D2  4 2

 soil 


Berm Height required for 7.0° bend, Ha
Buried depth = Bh
Bh  2.0 m
Ha  Hreq1  Bh  0.325 m
Report no: 1931002 Appendix-3
;
Hreq1  2.325 m
For 6.0° bend
( Node :1470)
Bend angle in degree = BD1
BD1  6.0
Bend angle in radian = B.R1
BR1  BD1
Guess:
π
180
 0.105
η3guess  0.01
Given
 1  π η3guess  cos( π η3guess ) 


sin( π η3guess ) 

= σall
2  η3guess
λ
D E BR1
η3  Find( η3guess )
η3  0.218
BR1
4 kg
Rreq1  Fcr
 4.614  10
( η3 )  λ
2
s
Hreq2 
D 
Rreq1
f
  1  1
 
 Wto  
f   g
  ρ  D2  4 2

 soil 


;
C
Berm Height required for 6.0° bend, Ha
Buried depth = Bh
Bh  2.0 m
Ha  Hreq2  Bh  0.06 m
Report no: 1931002 Appendix-3
( no additional backfill required )
Hreq2  1.94 m
For 5.8° bend
( Node :1560)
Bend angle in degree = BD2
BD2  5.8
Bend angle in radian = B.R2
π
BR2  BD2
 0.101
180
Guess:
η4guess  0.01
Given
 1  π η4guess  cos( π η4guess ) 


sin( π η4guess ) 

= σall
2  η4guess
λ
D E BR2
η4  Find( η4guess )
η4  0.225
BR2
4 kg
Rreq2  Fcr
 4.321  10
( η4 )  λ
2
s
Hreq3 
D 
Rreq2
f
  1  1
 
 Wto  
f   g
  ρ  D2  4 2

 soil 


;
Berm Height required for 5.8° bend, Ha
Buried depth = Bh
Bh.  2.0 m
Ha.  Hreq3  Bh.  0.137 m
Report no: 1931002 Appendix-3
( no additional backfill required )
Hreq3  1.863 m
For 4.0° bend
( Node :2440,2560)
Bend angle in degree = BD3
BD3  4.0
Bend angle in radian = B.R3
π
BR3  BD3
 0.07
180
Guess:
η5guess  0.01
Given
 1  π η5guess  cos( π η5guess ) 


sin( π η5guess ) 

= σall
2  η5guess
λ
D E BR3
η5  Find( η5guess )
η5  0.316
BR3
4 kg
Rreq3  Fcr
 2.129  10
( η5 )  λ
2
s
Hreq4 
D 
Rreq3
f
  1  1
 
 Wto  
f   g
  ρ  D2  4 2

 soil 


Berm Height required for 4.0° bend, Ha
Buried depth = Bh
Bh..  1  m
Ha..  Hreq4  Bh..  0.175 m
Report no: 1931002 Appendix-3
;
Hreq4  1.175 m