Position Stability of Surface Laid Submarine Optical Fiber Cables

Position Stability of Surface Laid Submarine Optical Fiber Cables
Abstract
Buried installation for submarine cable and optical fiber submarine
cable is always a first choice, but when considering some other
factors surface laid method is sometimes selected to install
submarine cable. In such case, it is of great importance to consider
the position stability of a submarine cable under water current. In
this paper, a seabed touched submarine cable in marine current is
analyzed by method of mechanics of fluids. The position stability of
surface laid submarine cable was analyzed. It is pointed out that the
position stability of surface laid submarine cable depends on a cable
structure parameter—a cable weight related parameter called
position stability factor rather than cable weight. According to this
consideration optical fiber submarine cable with higher position
stability was designed and manufactured.
Keywords: Submarine cable; optical fiber submarine cable;
surface laid; position stability factor of submarine cable.
1. Introduction
Generally buried installation for submarine cable and optical fiber
submarine cable is always a first choice since it could protect cables
from various kinds of damage and ensure cable lifetime.
But in practice, considering equipments, seabed topography or
installation cost, surface laid method is selected to install submarine
cable. For example, submarine power cables are often installed by
surface laid method. Even for optical fiber submarine cables,
trenching operation becomes much difficult in rocky seabed and
deep sea, sometimes buried installation is not adopted, and cables
are laid by cable ship, and then sink onto seabed.
In order to repair the cable when fault is found, people need to know
the exact position of submarine cable, so as to recover it. Therefore
the study on position stability of surface laid submarine cable when
exposed to water current is very important in practice. In this paper
mechanics analysis is made on a horizontal cable surface laid on a
flat horizontal seabed under the action of current.
2. Mechanics Analysis
The forces acting on a submarine cable laid on seabed under water
current could be considered the forces acting on a horizontal laid
cylinder laid on a flat horizontal bottom in a steady flow of viscous
liquid.
There are three forces acting on the cylinder with diameter of d in
viscosity liquid current in vertical direction: gravity of cylinder,
flotage, lift force; and two forces acting on the cylinder in horizontal
direction: push force of liquid current and friction between lower
surface of cylinder and bottom as shown in Figure 1, where the
weight in water means gravity minus flotage.
Chen Xihao, Huang Junhua, Xu Jun
Tongguang Group Co., Ltd.
Shanghai, China
+86-21-50588702 · chenxihao1945@yahoo.com.cn
+86-21-50588703 · pdhjhat@vip.163.com
+86-21-50588700 · xujun@tgjt.cn
2.1 Force Analysis in Vertical Direction
There are three forces acting on the horizontal laid cylinder in
vertical direction: gravity of cylinder, flotage and lift force. The
resultant force is in vertical direction and equals to gravity minus
flotage and lift force.
Figure 1. The forces a submarine cable subjected
in water current
(a) Cable Weight in Sea Water. Gravity minus flotage is the
cylinder weight in the liquid. Thus the resultant force in vertical
direction equals to cylinder weight in the liquid minus lift force. For
submarine cable gravity minus flotage means the cable weight in sea
water.
(b) Lift Force. For a horizontal laid cylinder suspending in
liquid current, suppose current is in horizontal direction and
perpendicular to cylinder central axis, the liquid will flow equally
above and beneath the cylinder, and zero lift force will exert on the
cylinder. For a horizontal laid sunken cylinder things are different:
the liquid flows transversely above the topside of cylinder with a
velocity component perpendicular to cylinder v; no liquid flows
beneath the underside of cylinder since cylinder touched with
bottom and stream is blocked. According to the Bernoulli’s
Equation in fluid mechanics, it is known that an increase in speed of
the fluid occurs simultaneously with a decrease in pressure [1]. That
means an upward lift force will exert on the cylinder due to flow of
liquid current.
The magnitude of lift force is related to density of fluid, velocity of
flow and size of cylinder, and could be expressed as below:
F1 = k1 ρ d v 2 (1)
Where, F1 is the magnitude of lift force, k1 is a coefficient, ρ is the
density of fluid, d is the diameter of cylinder, and v is the velocity of
flow.
International Wire & Cable Symposium 436 Proceedings of the 57th IWCS

Thus, the resultant force exerted on cylinder in vertical direction
becomes:
W-F1 = W-k1 ρdv 2 (2)
In equation (2), W represents the weight of cylinder in liquid.
Normally, lift force is smaller than the weight of cylinder in the
liquid, the direction of resultant force is in downward direction.
Once lift force is larger than the weight of cylinder in the liquid, the
cylinder will be lifted up, then the stream will flow beneath the
cylinder, results lift force to zero.
2.2 Force Analysis in Horizontal Direction
For low velocity and laminar flow, the current push force acting on
cylinder equals to viscous resistance, and could be expressed as:
F2=k2 μ d v (3)
Where F2 represents push force, k2 is a coefficient, μ is viscosity
coefficient of fluid.
For high velocity, when Reynolds Numbers beyond 4000, the flow
is completely turbulent, and the push force acting on cylinder could
be expressed as:
F 3=k 3 ρ d v 2 (4)
Where F3 represents push force, k3 is a coefficient.
The maximum static friction force f between lower surface of
cylinder and bottom equals to:
f = k (W- F1)= k (W-k1 ρ d v 2 ) (5)
Where k is static friction coefficient and the meanings of other
symbols are same as before.
2.3 Position Stability Analysis
The cylinder will remain at rest in condition that weight in water is
large than lift force and the push force is less than friction, i. e:
W-k1 ρdv 2 >0 and
(6)
F2 < f (for low velocity and laminar flow) (7)
Substituting (3) and (5) to (7), we get:
k2 μ v+ k k1 ρ v 2 < k W/d (8)
Or
W-k1 ρdv 2 >0 and
(6)
F3 < f (for high velocity and turbulent flow) (9)
Substituting (4) and (5) to (9), we get:
(k3 + k k1) ρ v 2 < k W/d (10)
When push force equals to friction, inequalities (8) and (10) could
be expressed as equations:
k k1 ρ v 2 + k2 μ v - k W/d=0 (11)
And (k3 + k k1) ρ v 2 - k W/d =0 (12)
Mark vcl and vct as the solutions of equation (11) or equation (12),
which represent critical velocity.
The solution of equation (11) for laminar flow could be solved as:
v cl
=
( k μ)
2
2
2 ⎛W
⎞
+ 4k
k1ρ
⎜ ⎟ − k 2μ
⎝ d ⎠
2kk
ρ
The solution of equation (12) for turbulent flow could be solved as:
v ct
=
k
( k + kk )
3
1
1
⎛W
⎜
ρ ⎝ d
⎞
⎟
⎠
(13)
(14)
From equations (13) and (14) we know: if the velocity component
of horizontal flow in perpendicular to cylinder axis direction is less
than critical velocity, the cylinder will remain at rest, no movement
will happen.
In equation (13) and (14), density ρ of fluid and viscosity coefficient
μ are parameters depend on the nature of fluid itself; W/d is ratio
of weight of cylinder in liquid to diameter of cylinder; k1, k2 and
k3 are parameters related to fluid and surface property of cylinder;
static friction coefficient k is a parameter related to materials and
surface roughness of contacting.
Equation (13) and (14) could be rewritten as:
vc = F(k, k1 ,k2, k3, μ, ρ, W/d) (15)
From equation (15) we know that position stability of submarine
cable is a function of fluid property, outer cover materials of
submarine cable and its surface property, density ρ and viscosity
coefficient μ of seawater, and ratio of weight of cable in seawater
to cable diameter.
For submarine cables with same outer layer materials, to be
placed onto same seabed, the parameter of k, k1 , k2, k3, μ and ρ
are same, thus the position stability of cables only depend on their
W/d, the ratio of weight of cable in seawater to cable diameter
involved. W/d could be defined as position stability factor of
submarine cable. A submarine cable with bigger ratio of W/d could
keep stationary at larger flow velocity.
Position stability factor W/d is the measure of position stability for
surface laid submarine cable.
Position stability of submarine cable depends on W/d, the ratio of
cable weight in seawater to cable diameter rather than cable weight
or cable weight in seawater.
Cables with same position stability factor will have same position
stability; a lighter cable with small diameter maybe has same even
better position stability with a heavy cable with big diameter; among
cables with same diameter the heavy one will have better position
stability.
3. Design Application
In one area in East China Sea, an optical fibers submarine cable was
planned to be laid on rocky seabed with maximum water depth of
100m and maximum current velocity of 1.81m/s. In this area many
other submarine cables or pipes have been installed before and new
submarine cable would cross with some of them The CBL (cable
breaking load) requirement of cable is 450kN, and the fiber count is
36. Because of such seabed situation, surface laid method is selected;
the new cable will ask better position stability.
To meet such application, an optical fiber submarine cable with
three armoring layers was designed. The structure of this cable is
shown in Figure 2 and could be further described as below:
International Wire & Cable Symposium 437 Proceedings of the 57th IWCS

• Cable core: Stainless steel loose tube with 36 fibers. Inside of
tube water blocking compound is filled to prevent water ingress
into the tube. HDPE is extruded over the stainless steel tube to
insulate the tube. The nominal diameter of the insulation is
10mm.
• The first layer of armoring: The first layer of armoring consists
of 12 high-tensile galvanized steel wires of 3.2mm nominal
diameter. These wires are flooded with special bitumen
compound and helically applied over the cable core with left
hand lay direction.
• Buffering layer: Buffering layer consists of polypropylene yarn
applied over the first armoring layer.
Figure 2. Cross-section structure of triple armored
submarine cable
• The second layer of armoring: The second layer of armoring
consists of 12 high-tensile galvanized steel wires of 5.0mm
nominal diameter. The wires are flooded with special bitumen
compound and helically applied over the cable core with same
lay direction as the first armoring.
• The third layer of armoring: The third layer of armoring consists
of 16 low-tensile galvanized steel wires of 6.0mm nominal
diameter. The wires are flooded with special bitumen compound
and helically applied over the cable core with same lay direction
as the first armoring.
• Outer serving: Outer serving consists of two layers of
polypropylene yarn helically applied over the armoring wires
with opposite lay direction. Bitumen compound is flooded to the
first layer of PP yarn. The finished cable is coated with talcum
powder. The nominal cable diameter is 45mm.
• Calculated position stability factor of the cable is 138kg/mm·km.
Main characteristics of the optical fiber submarine cable are shown
in Table 1, also listed in Table 1 are parameters of one double
armored submarine cable and one single armored submarine cable
for comparing. The double armored cable has similar structure as
triple armored cable but without the third armoring, as shown in
Figure 3. The single armored cable has similar structure as triple
armored cable but without the second and the third armoring, as
shown in Figure 4.
According to calculating results listed in Table 1, we know the
position stability factor of special designed triple armored
submarine cable is double than that of the double armored cable and
more than 4 times than that of the single armored cable.
In structure of the triple armored cable, the main function of the
first layer of armoring and the second layer of armoring is to
provide cable mechanical strength, steel wires with high-tensile
strength( better than 1200MPa) are used; and the main function of
the third layer of armoring is to provide cable position stability,
increase W/d of the cable, steel wires with low-tensile strength
( about 340MPa) are fit for such purpose, they provide lower cost
and are easy to be armored compare with high-tensile steel wires
while meet total CBL requirement of the cable.
Figure 3. Cross-section structure of double armored
submarine cable
Figure 4. Cross-section structure of single armored
submarine cable
Table 1. Main structure parameters and characteristics of
three optical fiber submarine cables
Item Unit
Triple
armored
cable
Double
armored
cable
Single
armored
cable
Core size mm 10 10 10
1st layer
armoring wires
(1200MPa)
2nd layer
armoring wires
(1200MPa)
3rd layer
armoring wires
(340MPa)
12 x
3.2mm
12 x
5.0mm
16 x
6.0mm
12 x
3.2mm
12 x
5.0mm
12 x
3.2mm
N/A
N/A N/A
Overall diameter mm 45 33 23
CBL** kN 520 400 120
NTTS** kN 310 240 72
NOTS** kN 160 150 45
Weight in air kg/m 7.85 3.1 1.1
Weight in sea
water*
Position stability
factor
kg/m 6.23 2.23 0.67
kg/mm·k
m
138 67 29
* Density of sea water =1.023.
** Definitions used are according to ITU-T G.972.
International Wire & Cable Symposium 438 Proceedings of the 57th IWCS

The above designed three armored optical fiber submarine cable
was manufactured by Tongguang Group and surface laid in sea
area for already more than one year and has worked well.
4. Conclusions
In this paper the position stability of a surface laid submarine cable
was analyzed by fluid mechanics method. It is shown that position
stability of surface laid submarine cable depends on one cable
structure parameter W/d, ratio of cable weight in water to cable
diameter. It is suggested to call this parameter as position stability
factor.
According to such analysis, an optical fiber submarine cable with
better position stability was designed, fabricated and surface laid in
East China Sea for more than 1 year and has worked well. The main
function of the 3 rd layer of armoring in the cable structure is to
increase W/d of the cable. The position stability factor of the cable
was calculated and compared with that of corresponding double
armored cable and single armored cable.
All the coefficients appeared in the formula could be obtained by
further experiments, and it is believed that more detail engineering
calculation will be possible.
5. Acknowledgments
Special thanks to Mr. Zhang Qiang of Tongguang Group for his
support to this work and Mr. Li Wanmeng of Tongguang Group for
helpful discussion.
6. References
[1] M C Potter, D C Wiggert and & M Hondzo, “ Mechanics of
Fluids” , 2 nd edition, Prentice Hall, 1997
7. About the Authors
Mr. Chen Xihao was
born in Apr 1945 in
Shanghai. He is
senior engineer now.
Mr. Chen graduated
from the University
of Science and
Technology of China
in 1967, and has been
engaged in the field
of optical fiber and
optical fiber cable
since 1976. He
studied in Tohoku
University ( Japan ) from 1984 to 1986. He worked for
Shanghai Transmission Lines Research Institute from 1968 to
1998, worked for Alcatel Shanghai Optical Fiber Cable Co., Ltd
from 1998 to 2005. At present he works for Tongguang Group
Company. His E-mail address is: chenxihao1945 @yahoo.com.cn
Mr. Huang Junhua was
born in Apr 1949 in
Shanghai, he is senior
engineer now. Mr.
Huang graduated from
Shanghai Construction
Engineering School in
1969 and studied in
Shanghai University of
Science and
Technology from 1982
to 1985, and he has
been engaged in the
field of optical fiber
and optical fiber cable since1976. He worked for Shanghai Quartz
Glass Works from 1969 to 1985, worked for Shanghai Optical
Fiber Communication Company from 1986 to 1995, worked for
Alcatel Shanghai Optical Fiber Cable Co., Ltd from 1995 to 2001.
He has worked for Tongguang Group Company since 2002; he is
Deputy General Manager of Tongguang Group Company now.
His E-mail address is: pdhjhat@vip.163.com
Mr. Xu Jun was born
in 1977 in Haimen
City, Jiangsu
Province. He
graduated from
Nanjing University
of Science and
Technology in 1997.
He has worked for
Tongguang Group
Company since 1999,
and has been
engaged in the field
of optical fiber cable
technology since
then. Mr. Xu is Vise Chief Engineer of Tongguang Group
Company now. His E-mail address is: xujun@tgjt.cn.
International Wire & Cable Symposium 439 Proceedings of the 57th IWCS