ISO 16134:2006
(Main)Earthquake- and subsidence-resistant design of ductile iron pipelines
Earthquake- and subsidence-resistant design of ductile iron pipelines
ISO 16134:2006 specifies the design of earthquake- and subsidence-resistant ductile iron pipelines suitable for use in areas where seismic activity and land subsidence can be expected. It provides a means of determining and checking the resistance of buried pipelines and also gives example calculations. It is applicable to ductile iron pipes and fittings with joints that have expansion/contraction and deflection capabilities, used in pipelines buried underground.
Conceptions de canalisations en fonte ductile résistant aux tremblements de terre et aux affaissements
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Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 16134
First edition
2006-02-01
Earthquake- and subsidence-resistant
design of ductile iron pipelines
Conception de canalisations en fonte ductile résistant aux tremblements
de terre et aux affaissements
Reference number
ISO 16134:2006(E)
©
ISO 2006
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ISO 16134:2006(E)
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ISO 16134:2006(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Terms and definitions. 1
3 Earthquake-resistant design . 1
3.1 Seismic hazards to buried pipelines. 1
3.2 Qualitative design considerations . 2
3.3 Design procedure . 2
3.4 Earthquake resistance calculations and safety checking. 3
3.5 Calculation of earthquake resistance — Response displacement method. 3
4 Design for ground deformation by earthquake . 6
4.1 General. 6
4.2 Evaluation of possibility of liquefaction. 6
4.3 Checking basic resistance. 7
5 Design for ground subsidence in soft ground (e.g. reclaimed ground) . 7
5.1 Calculating ground subsidence . 7
5.2 Basic safety checking . 7
6 Pipeline system design . 8
6.1 Pipeline components. 8
6.2 Earthquake-resistant joints . 8
Annex A (informative) Example of earthquake resistance calculation. 9
Annex B (informative) Relationship between seismic intensity scales and ground surface
acceleration . 17
Annex C (informative) Example of calculation of liquefaction resistance coefficient value . 18
Annex D (informative) Checking pipeline resistance to ground deformation. 23
Annex E (informative) Example of ground subsidence calculation. 26
Bibliography . 32
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ISO 16134:2006(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 16134 was prepared by Technical Committee ISO/TC 5, Ferrous metal pipes and metallic fittings,
Subcommittee SC 2, Cast iron pipes, fittings and their joints.
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ISO 16134:2006(E)
Introduction
Buried pipelines are often subjected to damage by earthquakes. It is therefore necessary to take earthquake
resistance into consideration, where applicable, in the design of the pipelines. In reclaimed ground and other
areas where ground subsidence is expected, the pipeline design must also take the subsidence into
consideration.
Even though ductile iron pipelines are generally considered to be earthquake-resistant, since their joints are
flexible and expand/contract according to the seismic motion to minimize the stress on the pipe body,
nevertheless there have been reports of the joints becoming disconnected by either a large quake motion or
major ground deformation such as liquefaction.
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INTERNATIONAL STANDARD ISO 16134:2006(E)
Earthquake- and subsidence-resistant design of ductile iron
pipelines
1 Scope
This International Standard specifies the design of earthquake- and subsidence-resistant ductile iron pipelines
suitable for use in areas where seismic activity and land subsidence can be expected. It provides a means of
determining and checking the resistance of buried pipelines and also gives example calculations. It is
applicable to ductile iron pipes and fittings with joints that have expansion/contraction and deflection
capabilities, used in pipelines buried underground.
2 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
2.1
burying
placing of pipes underground in a condition where they touch the soil directly
2.2
response displacement method
earthquake-resistant calculation method in which the underground pipeline structure is affected by the ground
displacement in its axial direction during an earthquake
2.3
liquefaction
phenomenon in which sandy ground rapidly loses its strength and rigidity due to repeated stress during an
earthquake, and where the whole ground behaves just like a liquid
2.4
earthquake-resistant joint
joint having slip-out resistance as well as expansion/contraction and deflection capabilities
3 Earthquake-resistant design
3.1 Seismic hazards to buried pipelines
In general, there are several main causes of seismic hazards to buried pipelines:
a) ground displacement and ground strain caused by seismic ground shaking;
b) ground deformation such as a ground surface crack, ground subsidence and lateral spread induced by
liquefaction;
c) relative displacement at the connecting part with the structure, etc.;
d) ground displacement and rupture along a fault zone.
Since ductile iron pipe has high tensile strength as well as the capacity for expansion/contraction and
deflection from its joint part, giving it the ability to follow the ground movement during the earthquake, the
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ISO 16134:2006(E)
stress generated on the pipe body is relatively small. Few ruptures of pipe body have occurred during
earthquakes in the past. It is therefore important to consider whether the pipeline can follow the ground
displacement and ground strain without slipping out of joint when considering its earthquake resistance. The
internal hydrodynamic surge pressures induced by seismic shaking are normally small enough not to be
considered.
3.2 Qualitative design considerations
3.2.1 General
To increase the resistance of ductile iron pipelines to seismic hazards, the following qualitative design
measures should be taken into consideration.
a) Provide pipelines with expansion/contraction and deflection capability.
EXAMPLE Use of shorter pipe segments, special joints or sleeves and anti-slip-out mechanisms according to
the anticipated intensity or nature of the earthquake.
b) Lay pipelines in a firm foundation.
c) Use smooth back fill materials.
NOTE Polyethylene sleeves and special coating are also effective in special cases.
d) Install more valves.
3.2.2 Where high earthquake resistance is needed
It is desirable to enhance the earthquake resistance of parts connecting the pipelines to structures and when
burying the pipes in
a) soft ground such as alluvium,
b) reclaimed ground,
c) filled ground,
d) suddenly changing soil types (geology) or topography,
e) sloping ground,
f) near revetments,
g) liquefied ground, and/or
h) near an active fault.
3.3 Design procedure
To ensure earthquake-resistant design for ductile iron pipelines:
a) select the piping route;
b) investigate the potential for earthquakes and ground movement;
c) assume probable earthquake motion (seismic intensity);
d) undertake earthquake-resistant calculation and safety checking;
e) select joints.
Solid/firm foundations should be chosen for the pipeline route.
When investigating earthquakes and ground conditions, take into account any previous earthquakes in the
area where the pipeline is to be laid.
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ISO 16134:2006(E)
3.4 Earthquake resistance calculations and safety checking
When checking the resistance of pipelines to the effects of earthquakes, the calculation shall be carried out for
the condition in which the normal load (dead load and normal live load) is combined with the influence of the
earthquake.
The pipe body stress, expansion/contraction value of joint, and deflection angle of joint are calculated by the
response displacement method. Earthquake resistance is checked by comparing these values with their
respective allowable values. The basic criteria are given in Table 1.
A flowchart of earthquake resistance determination and safety checking is shown in Figure 1. The basic
equations only for earthquake resistance calculation are given in 3.5. A detailed example of calculation is
given in Annex A.
Table 1 — Basic earthquake resistance check criteria
Load condition Criterion
Pipe body stress u Allowable stress (proof stress) of ductile iron pipe
u Allowable expansion/contraction value of ductile
Load in earthquake motion
Expansion/contraction value of joint
iron pipe joint
and normal load
u Allowable deflection angle of ductile iron pipe
Deflection angle of joint
joint
3.5 Calculation of earthquake resistance — Response displacement method
3.5.1 General
This method shall be used except when the manufacturer and the customer agree on an alternative
recognized method.
3.5.2 Design earthquake motion
The design acceleration for different seismic intensity scales can be determined according to the relationship
between the several kinds of seismic intensity scales and the acceleration of ground surface, as given in
Annex B.
3.5.3 Horizontal displacement amplitude of ground
The horizontal displacement amplitude of the ground is calculated using Equation (1) (see Annex A):
2
⎛⎞T
π⋅ x
G
Ux=⋅a⋅cos (1)
()
⎜⎟
h
22π H
⎝⎠
where
Ux( ) is the horizontal displacement amplitude of the ground x m deep from the ground surface to the
h
centre line of the pipe, in metres (m);
x is the depth from the ground surface, in metres (m);
T is the predominant period of the subsurface layer, in seconds (s);
G
2
a is the acceleration on the ground surface for design, in metres per second squared (m/s );
H is the thickness of the subsurface layer, in metres (m).
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ISO 16134:2006(E)
Figure 1 — Flowchart for calculation of earthquake resistance of buried pipelines
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ISO 16134:2006(E)
3.5.4 Pipe body stress
Pipe body stress is calculated using Equations (2), (3) and (4).
Axial stress:
π⋅Ux( )
h
σξ=⋅α⋅ ⋅ E (2)
L1 1
L
Bending stress:
2
2π⋅DU⋅ x
()
h
σξ=⋅α⋅ ⋅ E (3)
B2 2
2
L
Combined stress:
22
σσ=⋅3,12 +σ (4)
x LB
where
σ , σ are the axial stress and the bending stress, respectively, in pascals (Pa);
L B
σ is the combination of the axial and bending stresses, in pascals (Pa);
x
ξ is the correction factor of axial stress in the case of expansion flexible joints;
1
ξ is the correction factor of the bending stress in the case of expansion flexible joints;
2
α , α are the transfer coefficient of ground displacement in the pipe axis and pipe perpendicular
1 2
directions, respectively;
Ux is the horizontal displacement amplitude of ground x m deep from the ground surface, in
( )
h
metres (m);
L is the wavelength, in metres (m);
D is the outside diameter of the buried pipeline, in metres (m);
E is the elastic modulus of the buried pipeline, in pascals (Pa).
3.5.5 Expansion/contraction of joint in pipe axis direction
The amount of expansion/contraction of the joint in the pipe axis direction is calculated using Equation (5)
(see Annex A):
ul=±ε ⋅ (5)
G
where
u is the amount of expansion/contraction of the joint in the pipe axis direction, in metres (m);
π⋅U
h
ε is the ground strain =
G
L
L is the wavelength, in metres (m);
U is the horizontal displacement amplitude of ground x m deep from the ground surface, in metres (m);
h
l is the pipe length, in metres (m).
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ISO 16134:2006(E)
3.5.6 Joint deflection angle
The joint deflection angle is calculated using Equation (6) (see Annex A):
2
4⋅π ⋅lU⋅
h
θ=± (6)
2
L
where
θ is the joint deflection angle, in radians (rad);
l is the pipe length, in metres (m);
U is the horizontal displacement amplitude of ground x m deep from the ground surface, in metres (m);
h
L is the wavelength, in metres (m).
The above calculations, such as the amount of expansion/contraction of joint by the response displacement
method, are based on the assumption that the ground will deform uniformly. However, since strain can be
concentrated locally during an earthquake (due to the heterogeneity of the ground) and there is a possibility
that the value can be greater than the calculation result, a certain value of safety margin — for instance, twice
as much — is recommended.
4 Design for ground deformation by earthquake
4.1 General
Large-scale ground deformation such as ground cracks, ground subsidence and lateral displacement near
revetments and inclined ground can be generated by liquefaction during an earthquake. Since such ground
deformations can affect the buried pipeline, it is necessary to consider this possibility and to take it into
account in the pipeline design.
4.2 Evaluation of possibility of liquefaction
The possibility of liquefaction shall be evaluated for soil layers when the following conditions are present:
a) saturated soil layer u 25 m from the ground surface;
b) average grain diameter, D , u 10 mm;
50
c) content by weight of small grain particles (with grain diameter u 0,075 mm) u 30 %.
The possibility of liquefaction can be evaluated by calculating the liquefaction resistance coefficient, F , using
L
Equation (7):
F = RL (7)
L
where
R is the dynamic shear strength ratio indicating the resistance to liquefaction;
L is the ground shear stress ratio during an earthquake, which indicates the generated shear stress in
ground due to the earthquake.
When F< 1,0, the layer is considered to be liquefied.
L
A detailed example of the evaluation of liquefaction assessment is given in Annex C.
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ISO 16134:2006(E)
4.3 Checking basic resistance
For ground deformation such as lateral displacement and ground subsidence induced by liquefaction, the
basic resistance of the pipeline shall be checked by observing whether it can absorb the ground movement by
the expansion/contraction and deflection of joints.
A detailed example of safety checking is given in Annex D.
5 Design for ground subsidence in soft ground (e.g. reclaimed ground)
5.1 Calculating ground subsidence
When burying pipes in soft ground, the amount of ground subsidence is estimated by calculating the
increased earth pressure at the bottom of the trench in considering the weight of pipes, the weight of water in
the pipes and the earth pressure of back-fill, using Equations (8), (9) and (10):
ee−
0
δ=⋅ H (8)
cc
1+ e
0
δ=⋅mP∆⋅H (9)
cv c
C
PP+∆
c
δ=⋅ H⋅ log (10)
cc
1+ep
0
where
δ is the consolidation settlement, in metres (m);
c
e is the initial void ratio of the undisturbed ground;
0
e is the void ratio after loading;
H is the thickness of consolidated layers, in metres (m);
c
m is the volume change ratio of the soil (coefficient of volume compressibility), in square metres per
v
2
newton (m /N);
C is the compression index of the soil;
c
2
P is the pre-load of the undisturbed ground, in newtons per square metre (N/m );
2
∆P is the increased load, in newtons per square metre (N/m ), where
∆=P IW⋅∆ (11)
σ
I is the influence by depth value;
σ
2
∆W is the increased load, in newtons per square metre (N/m ).
A detailed example of calculation of the amount of ground subsidence is shown in Annex E.
5.2 Basic safety checking
For ground subsidence in soft ground such as reclaimed ground, safety shall be checked by observing if the
pipeline can absorb the ground movement by expansion/contraction and deflection of the joints. This way of
safety checking is the same as for the ground deformation in the pipe perpendicular direction induced by
liquefaction, which is given in Annex D.
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ISO 16134:2006(E)
6 Pipeline system design
6.1 Pipeline components
According to the results of calculations for expansion/contraction, slip-out resistance, and joint deflection, the
pipeline system may be designed using the same joint for all pipes, or, alternatively, using a
range/combination of pipeline components. If necessary, pipeline system components may be classified
according to Table 2.
Table 2 — Classification of pipeline components
Parameter Class Component performance
S-1 ± 1 % of L or more
Expansion/contraction
S-2 ± 0,5 % to less than ± 1 % of L
performance
S-3 Less than ± 0,5 % of L
A 3 d kN or more
B 1,5 kN to less than 3 kN
Slip-out resistance
C 0,75 kN to less than 1,5 kN
less than 0,75 d kN
D
M-1 ± 15° or more
Joint deflection angle
M-2 ± 7,5° to < 15°
M-3 Less than ± 7,5°
L is the component length, in millimetres (mm)
d is the nominal diameter of pipe, in millimetres (mm)
6.2 Earthquake-resistant joints
In cases where pipelines are to be laid in locations where ground deformation could be induced by liquefaction
during an earthquake, and where ground subsidence is anticipated in soft soil such as reclaimed ground, a
pipeline having earthquake-resistant joints with slip-out resistance, as well as an expansion/contraction and
deflection capability, should be used.
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ISO 16134:2006(E)
Annex A
(informative)
Example of earthquake resistance calculation
A.1 General
This annex presents an example of the calculation of the earthquake resistance of a pipeline, specified in A.2.
A.2 Specifications and conditions
The example pipeline and conditions are the following.
a) Type of pipe: 500 mm nominal diameter ductile iron pipe (K-9 class)
b) Outside diameter of pipe: D = 0,532 m
c) Standard thickness of pipe: t = 0,009 m
1)
d) Calculated thickness of pipe : t = 0,007 2 m(= t − 0,001 8)
1
e) Pipe length: l = 6 m
f) Soil covering above pipes: h = 1,20 m
3
g) Unit weight of soil: γ = 17 kN/m
t
2
h) Elastic modulus of ductile cast iron: E = 1,6 × 108 kN/m
2
i) Design acceleration on the ground surface: a = 0,94 m/s (corresponding to Modified Mercalli scale
intensity of VII).
A.3 Ground model
See Figure A.1.
A.4 Various values of pipe profiles
A.4.1 Cross-sectional area, A
r
This is calculated using Equation (A.1):
ππ
22
⎡⎤⎡22⎤ −
2
2
AD=⋅ −D− 2⋅t = × 0,532− 0,532− 2× 0,007 2 = 1,187×10 m (A.1)
() ()
r1
⎢⎥⎢ ⎥
44⎣⎦⎣ ⎦
where
D is the outside diameter of pipe = 0,532 m;
t is the calculated thickness of pipe = 0,007 2 m.
1
1) The casting tolerance is subtracted from t.
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ISO 16134:2006(E)
Dimensions in metres
Key
1 first layer (alluvium sandy soil) 6 thickness of subsurface layer
2 second layer (alluvium sandy soil) 7 ground surface
3 thickness of layer 8 bedrock surface
4 thickness of layer 9 diluvium sandy soil
5 soil covering
Figure A.1 — Ground model
A.4.2 Moment of inertia of area, I
This is calculated using Equation (A.2):
ππ44
⎡⎤44⎡ ⎤ −4
4
I=⋅DDt− − 2⋅ = × 0,532− 0,532− 2× 0,007 2 = 4,087×10 m (A.2)
() ()
1
⎢⎥⎢ ⎥
⎣⎦⎣ ⎦
64 64
A.5 Pipe body stress, expansion/contraction and deflection angle of joint due to
earthquake motions
A.5.1 Calculation of seismic properties
A.5.1.1 Shear elastic wave velocity by layer
See Table A.1 for the shear elastic wave velocity and Table A.2 for the shear elastic wave velocity for different
types of soil with respect to the shearing strain of the ground.
A.5.1.2 Average shear elastic wave velocity of surface layer, V
DS
This is calculated using Equation (A.3):
H
20,0
∑ i
V== = 81,23m/s (A.3)
DS
⎛⎞ 0,154 0+ 0,092 2
H
i
⎜⎟
∑
V
⎝⎠si
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ISO 16134:2006(E)
Table A.1 — Shear elastic wave velocity
a b
Layer Thickness of layer H Soil type N value Average shear elastic wave velocity H /V
i i si
V
si
m m/s s
0,211 0,211
12 0,154 0
61,8⋅=N 61,8× 3
First Alluvium sandy soil 3
(= H ) (= H /V )
= 77,92 V
()
1 s1 1 s1
0,211 0,211
8 0,092 2
61,8⋅=N 61,8× 5
Second Alluvium sandy soil 5
(= H ) = 86,79 V (= H /V )
()
2 2 s2
s2
0,125 0,125
205⋅=N 205×50
Bedrock — Diluvium sandy soil 50 —
= 334,29 V
()
BS
a
The N value is derived from the standard penetration test defined in JIS A-1219, ASTM D-1586 and BS 1377 test 19, etc.
b
Japan Water Works Association, Seismic Design and Construction Guidelines for Water Supply Facilities (1997).
Table A.2 — Velocity of ground shearing elastic wave
V
s
m/s
Soil type
−3 −4 −6
10 10 10
0,183 0,183 0,183
Clay 129 N 156 N 172 N
Diluvium
0,125 0,125 0,125
Sand 123 N 200 N 205 N
0,077 7 0,077 7 0,077 7
Clay 122 N 142 N 143 N
Alluvium
0,211 0,211 0,211
Sand 61,8 N 90 N 103 N
−3 −4 −6
NOTE 1 10 , 10 and 10 show the shearing strain of ground.
NOTE 2 Classified by composition ratio of sand and clay type soils.
−3 −6
NOTE 3 For the surface ground, use shearing strain of 10 level, and 10 for the bed rock.
NOTE 4 Table taken from Seismic Design and Construction Guidelines for Water Supply Facilities (1997), Japan Water Works
Association.
A.5.1.3 Predominant period of subsurface layer, T
G
This is calculated using Equation (A.4):
TH=⋅4/V =4×()0,1540+0,0922=0,98s (A.4)
()
Gsii
∑
A.5.1.4 Wavelength, L
This is calculated using Equation A.5:
LV=⋅T= 81,23× 0,98= 79,61m
1DS G
LV=⋅T= 334,29× 0,98= 327,60 m
2BS G
2LL⋅ 2××79,61 327,60
12
L== = 128,09 m (A.5)
LL++79,61 327,60
12
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ISO 16134:2006(E)
where
V is the average shear elastic wave velocity of subsurface layer = 81,23 m/s [Equation (A.3)];
DS
V is the shear elastic wave velocity of bedrock = 334,29 m/s (see Table A.1);
BS
T is the predominant period of subsurface layer = 0,98 s [Equation (A.4)].
G
A.5.1.5 Apparent wavelength, L′
This is calculated using Equation (A.6):
′
LL=⋅2 = 2×128,09= 181,15 m (A.6)
where
L is the wavelength = 128,09 m [Equation (A.5)].
A.5.2 Calculation
A.5.2.1 Horizontal displacement amplitude of ground, Ux
( )
h
This is calculated using Equation (A.7):
2 2
⎛⎞Tππx⎛⎞0,98 ×1,47
G −2
Ux=⋅a⋅ cos= ⋅0,94⋅cos = 2,27× 10 m (A.7)
()
h ⎜⎟ ⎜⎟
22ππH2 2×20
⎝⎠ ⎝⎠
where
T is the predominant period of subsurface layer = 0,98 s [Equation (A.4)];
G
2
a is the design acceleration on the ground surface = 0,94 m/s (corresponding to a Modified Mercalli
scale intensity of VII);
H is the thickness of the subsurface layer = 20 m;
x is the depth of pipe centre =+hD / 2= 1,20+ 0,532 2= 1,47 m.
A.5.2.2 Ground strain in pipe axis direction, ε
G
This is calculated using Equation (A.8):
−2
π⋅Ux()
π× 2,27×10
h
ε== = 0,000 56 (A.8)
G
L 128,09
where
−2
Ux is the horizontal displacement amplitude of ground = 2,27 × 10 m [Equation (A.7)];
( )
h
L is the wavelength = 128,09 m [Equation (A.5)].
A.5.2.3 Rigidity coefficient of ground, K , K
g1 g2
This is calculated using Equations (A.9) and (A.10):
γ 17
22 42
t
KC=⋅⋅V = 1,5× × 77,92= 1,58×10 kN/m (A.9)
g1 g1 s1
g 9,8
γ
17
t22 42
KC=⋅⋅V = 3× × 77,92= 3,16×10 kN/m (A.10)
g2 g2 s1
g 9,8
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ISO 16134:2006(E)
where
3
γ is the unit weight of soil = 17 kN/m ;
t
2
g is the gravitational acceleration = 9,8 m/s ;
V is the shear elastic wave velocity of subsurface layer (first layer) in pipeline
s1
position = 77,92 m/s (see Table A.1);
C , C are the constants corresponding to the rigidity coefficient of layer per unit length in the pipe
g1 g2
axis and pipe perpendicular directions of buried pipelines, where C = 1,5 and C = 3.
g1 g2
A.5.2.4 Transfer coefficient of ground displacement, α , α
1 2
This is calculated using Equations (A.11) and (A.12):
11
α== = 0,873 (A.11)
1
28 −2 2
1,6××10 1,187×10
EA⋅
⎛⎞2π 2π
⎛⎞
r
1+
1+
⎜⎟
⎜⎟
4
′
KL 181,15
⎝⎠
g1 1,58×10 ⎝⎠
11
α== = 1, 000 (A.12)
2
48 −4 4
1,6××10 4,087×10
EI⋅π⎛⎞2 2π
⎛⎞
1+ 1+
⎜⎟ ⎜⎟
4
KL 128,09
⎝⎠
g2 3,16×10 ⎝⎠
where
4 2
K is the rigidity coefficient of ground in pipe axis direction = 1,58 × 10 kN/m [Equation (A.9)];
g1
4 2
K is the rigidity coefficient of ground in pipe perpendicular direction = 3,16 × 10 kN/m
g2
[Equation (A.10)];
8 2
E is the elastic modulus of ductile cast iron = 1,6 × 10 kN/m ;
−2 2
A is the cross-sectional area of pipe = 1,187 × 10 m [Equation (A.1)];
r
−4 4
I is the moment of inertia of area = 4,087 × 10 m [Equation (A.2)];
L' is the apparent wavelength = 181,15 m [Equation (A.6)];
L is the wavelength = 128,09 m [Equation (A.5)].
A.5.2.5 Stress correction factor for pipelines with expansion-flexible joints, ξ , ξ
1 2
This is calculated as follows, with the results expressed by Equations (A.13) and (A.14):
22
...
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