Journal of
Marine Science 
and Engineering
Article
AnAnalysis Tool for the Installation of Submarine
Cables in an S-Lay Configuration Including “In and
Out of Water” Cable Segments
Vasileios A. Mamatsopoulos 1,2, Constantine Michailides 1,* and Efstathios E. Theotokoglou 3
1
2
3
*
Department of Civil Engineering and Geomatics, Cyprus University of Technology, Limassol 3036, Cyprus;
va.mamatsopoulos@edu.cut.ac.cy
C.D.C. Construction Company, Athens TX 75752, Greece
Department of Mechanics, National Technical University of Athens, Athens GR 15773, Greece;
stathis@central.ntua.gr
Correspondence: c.michailides@cut.ac.cy; Tel.: +357-2500-2396
Received: 30 November 2019; Accepted: 14 January 2020; Published: 16 January 2020
Abstract: Today, the offshore oil and gas and wind power industry is a heavily regulated segment,
and current standards have established restrictions which yield a very limited weather window for
submarine cable installations due to experience with cable failure in bad weather. There are two main
limiting factors in current practice during cable installation of an S-lay configuration: the design
criterion for the minimum allowable radius of curvature in the touch down point and the avoidance of
axial compression in the touch down zone. Accurate assessment of the cable integrity during offshore
installation has drawn great attention and is related to the existing available analysis and design
tools. The main purpose of this paper is to develop and propose a quick and easy custom-made
analysis tool, which is able to export similar results as sophisticated finite element analysis software.
The developed tool utilizes analytical equations of a catenary-type submarine structure extended to
account for varying cross-sections with different weights and/or stiffnesses, as is the real practice. A
comparative study is presented in this paper to evaluate the significance for the modeling of the “out
of water” cable segment required for accurate safety factor quantification during a laying operation.
The efficiency and accuracy of the proposed tool are proven through a validation study comparing
the results and the computational effort and time with commercial finite element analysis software.
The analysis error in the case of not modeling the “out of water” cable part is significant, especially in
shallow water areas, which proves the importance of using the proposed analysis tool.
Keywords: submarine cable; S-lay cable installation analysis; touch down point (TDP); minimum
bending radius (MBR); bottom tension; catenary theory
1. Introduction
A submarine cable is a crucial connection between onshore/offshore topside facilities and/or
equipment located on the seabed. The cable normally consists of both a dynamic and a static part
during the installation period. The static part is laid by the cable lay vessel (CLV) and is located on the
seabed under stable environmental conditions, while the dynamic part hangs freely from the onboard
vessel’s equipment (tensioner and overboard chutes). The dynamic part is subjected to loading due to
vessel motions and environmental loads. The touch down zone (TDZ), which is the zone where the
cable first hits the seabed, is critical with respect to failure of the cable during installation. This region
maybeexposed to severe curvature and axial compression, which may result in local buckling inside
the cross-section that causes the cross-section to be unstable in torsion, global loop formation, or a
combination of those that may finally result in capacity failure [1]. The current practice is to avoid
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the occurrence of compression at the TDZ to eliminate any possibility of cable failure. Although it is
not always clear how much submarine composite cables can be compressed before their integrity is
compromised, cable manufacturers are often reluctant to allow significant cable compression. However,
in local buckling inside the cross-section that causes the cross-section to be unstable in torsion, global 
loop formation, or a combination of those that may finally result in capacity failure [1]. The current 
practice is to avoid the occurrence of compression at the TDZ to eliminate any possibility of cable 
failure. Although it is not always clear how much submarine composite cables can be compressed 
before their integrity is compromised, cable manufacturers are often reluctant to allow significant 
cable compression. However, this restricts the weather window for the laying operation since the 
dynamic responses of the CLV, especially the motions along the cable axis (surging of the CLV), 
significantly affect the axial force applied to the cable during installation. The limited weather 
window results in high installation costs. It is therefore of great interest to investigate various 
installation scenarios and propose an efficient analysis tool for cable installers in order to accurately 
analyze/monitor the cable laying operation with the aim of eliminating the CLV idle time. 
this restricts the weather window for the laying operation since the dynamic responses of the CLV,
especially the motions along the cable axis (surging of the CLV), significantly affect the axial force
applied to the cable during installation. The limited weather window results in high installation costs.
It is therefore of great interest to investigate various installation scenarios and propose an efficient
analysis tool for cable installers in order to accurately analyze/monitor the cable laying operation with
the aim of eliminating the CLV idle time.
Offshore cable installation is a complex task [2]. In the planning phase, an installation analysis
needs to be performed, which considers factors such as the cable properties, route characteristics,
available installation equipment, and capacities of the cable installer [3]. Figure 1 shows some of the
most influential parameters in an installation operation [4]. The departure angle is the complimentary
angle of the cable exit angle at the overboard chute of the CLV (departure angle = 90 deg-exit angle).
Offshore cable installation is a complex task [2]. In the planning phase, an installation analysis 
needs to be performed, which considers factors such as the cable properties, route characteristics, 
available installation equipment, and capacities of the cable installer [3]. Figure 1 shows some of the 
most influential parameters in an installation operation [4]. The departure angle is the complimentary 
angle of the cable exit angle at the overboard chute of the CLV (departure angle = 90 deg-exit angle). 
Top tension is the tension applied to the cable using the onboard caterpillar or wheel tensioner 
machine. Layback is the horizontal distance between the cable exit point from the CLV and the touch 
down point (TDP) on the seabed. The bend radius at the TDP is the actual cable radius of curvature, 
which is one of the most critical design parameters for cable integrity. Bottom tension is the residual 
tension at the TDP, representing another critical parameter for the cable lifetime. 
Top tension is the tension applied to the cable using the onboard caterpillar or wheel tensioner machine.
Layback is the horizontal distance between the cable exit point from the CLV and the touch down point
(TDP) on the seabed. The bend radius at the TDP is the actual cable radius of curvature, which is one
of the most critical design parameters for cable integrity. Bottom tension is the residual tension at the
TDP, representing another critical parameter for the cable lifetime.
Figure 1. Demonstration of the most influential parameters during a cable laying process.
Figure 1. Demonstration of the most influential parameters during a cable laying process. 
In some cases, local conditions will require the vessel to ground near the landfall location.
The limited water depth requires careful management of the cable catenary as a short catenary leaves
little room for error and can easily compromise the cable integrity. Furthermore, the limited water
depth requires a better accuracy for the cable catenary profile analysis since the part of the cable in
the air is a significant proportion of the whole suspended length of the cable and cannot be omitted
In some cases, local conditions will require the vessel to ground near the landfall location. The 
limited water depth requires careful management of the cable catenary as a short catenary leaves 
little room for error and can easily compromise the cable integrity. Furthermore, the limited water 
depth requires a better accuracy for the cable catenary profile analysis since the part of the cable in 
the air is a significant proportion of the whole suspended length of the cable and cannot be omitted 
from the installation analysis. In shallow-water areas, modeling of the “out of water” cable segment 
is significant for accurate safety factor quantification during a laying operation. In the present paper, 
the proposed analysis tool is able to provide an accurate assessment of the cable integrity, even in 
shallow-water areas, using an iterative procedure for modeling of the “out of water” cable segment. 
from the installation analysis. In shallow-water areas, modeling of the “out of water” cable segment is
significant for accurate safety factor quantification during a laying operation. In the present paper,
the proposed analysis tool is able to provide an accurate assessment of the cable integrity, even in
shallow-water areas, using an iterative procedure for modeling of the “out of water” cable segment.
2. Scope of this Study
2. Scope of this Study  
Cable handling and monitoring are important during the cable laying process as the cable can
be damaged if the minimum bending radius, actual strain, or other limits are not respected during
installation. Typically, during laying from the landfall site towards offshore, the water depth will
Cable handling and monitoring are important during the cable laying process as the cable can 
be damaged if the minimum bending radius, actual strain, or other limits are not respected during 
installation. Typically, during laying from the landfall site towards offshore, the water depth will 
increase along the route and whilst the cable catenary becomes easier to manage, tension in the cable 
becomes more important. Due to the fact that conventional installers of power cables do not have the 
increase along the route and whilst the cable catenary becomes easier to manage, tension in the cable
becomes more important. Due to the fact that conventional installers of power cables do not have
the means to accurately estimate the cable tension on the seabed, they operate with very high safety
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factors. Consequently, power cables are usually installed with tensions that are much higher than the
required values. Cable suspensions occur more often than desired as a result due to the restrained
tension created by the friction between the seabed and cable. Between high spots on the seabed, the soil
friction acts as a support, both horizontally and vertically, and the segment of the cable maintains
a residual tension, creating a catenary suspension. As shown in Figure 2, at these seafloor contact
means to accurately estimate the cable tension on the seabed, they operate with very high safety 
factors. Consequently, power cables are usually installed with tensions that are much higher than the 
required values. Cable suspensions occur more often than desired as a result due to the restrained 
tension created by the friction between the seabed and cable. Between high spots on the seabed, the 
soil friction acts as a support, both horizontally and vertically, and the segment of the cable maintains 
a residual tension, creating a catenary suspension. As shown in Figure 2, at these seafloor contact 
points, large reaction forces (local supports) and small bending radii are common, thereby reducing 
the lifetime of the cable due to increased wearing and chafing. In order to maximize the lifetime of 
the cable, the power cable installers must be equipped with an analysis tool to accurately predict the 
bottom tension in order to lay the cable with low values of bottom tension to avoid cable suspensions, 
but at the same time, they must maintain a small amount of tension at the touchdown to prevent 
cable damage. 
points, large reaction forces (local supports) and small bending radii are common, thereby reducing
the lifetime of the cable due to increased wearing and chafing. In order to maximize the lifetime of
the cable, the power cable installers must be equipped with an analysis tool to accurately predict the
bottom tension in order to lay the cable with low values of bottom tension to avoid cable suspensions,
but at the same time, they must maintain a small amount of tension at the touchdown to prevent
cable damage.
Figure 2. High or reduced bottom tension during a cable laying operation.
Figure 2. High or reduced bottom tension during a cable laying operation. 
As it can be realized, accurate prediction of the bottom tension during the S-lay installation of a
submarine cable is of great interest to marine civil engineering research since this parameter is very
crucial for both the installation and operation of the cable lifetime. Based on different assumptions,
numerous theories have been developed for the static and dynamic response of a submarine cable
during a laying operation. Among these, Zajac [5] first developed a steady-state theory, in which
the cable was modeled as a straight line and excluded the effect of transient motions. Later on,
Yoshizawa and Yabuta [6] presented an analytical method for the tension analysis of cables, without
considering the tangential drag forces. Wang et al. [7] presented linear and nonlinear methods
separately to build up a dynamic model. Vaz and Patel [8] developed a model for prediction of the
As it can be realized, accurate prediction of the bottom tension during the S-lay installation of a 
submarine cable is of great interest to marine civil engineering research since this parameter is very 
crucial for both the installation and operation of the cable lifetime. Based on different assumptions, 
numerous theories have been developed for the static and dynamic response of a submarine cable 
during a laying operation. Among these, Zajac [5] first developed a steady-state theory, in which the 
cable was modeled as a straight line and excluded the effect of transient motions. Later on, Yoshizawa 
and Yabuta [6] presented an analytical method for the tension analysis of cables, without considering 
the tangential drag forces. Wang et al. [7] presented linear and nonlinear methods separately to build 
up a dynamic model. Vaz and Patel [8] developed a model for prediction of the transient behavior of 
a cable when the cable ship changes speed during towing operations. Following their previous work, 
Vaz et al. [9] presented a formulation and numerical solution for the 3D transient behavior of a cable 
during laying operations. Extending from [9], Vaz and Patel [10] developed the formulation and 
solution of governing equations used to analyze the 3D behavior of cables subjected to arbitrary 
sheared currents. Similarly, Wang et al. [11] presented an efficient numerical schemes-boundary 
condition transformed into a set of nonlinear governing equations with initial values. The vertical 
movement of the cable ship caused by wave-induced vessel motion adds a non-ignorable tension 
force at the laying cable. Prpic J. and Nabergoj R. [12,13] presented a two-dimensional model of cable 
dynamics accounting for the effects of head sea conditions. Yang N. et al. [14] presented a semi
transient behavior of a cable when the cable ship changes speed during towing operations. Following
their previous work, Vaz et al. [9] presented a formulation and numerical solution for the 3D transient
behavior of a cable during laying operations. Extending from [9], Vaz and Patel [10] developed
the formulation and solution of governing equations used to analyze the 3D behavior of cables
subjected to arbitrary sheared currents. Similarly, Wang et al. [11] presented an efficient numerical
schemes-boundaryconditiontransformedintoasetofnonlineargoverningequationswithinitialvalues.
The vertical movement of the cable ship caused by wave-induced vessel motion adds a non-ignorable
tension force at the laying cable. Prpic J. and Nabergoj R. [12,13] presented a two-dimensional model
of cable dynamics accounting for the effects of head sea conditions. Yang N. et al. [14] presented a
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semi-analytical approximation for a two-dimensional tension analysis of a submarine cable during
laying operations, obtaining a set of differential equations to simulate the problem. In summary,
all the aforementioned models have completely ignored the influence of the “out of water” cable
segment, which significantly affects the cable configuration during laying operations, especially in
shallow-water areas. The catenary theory model, both in static [15] and dynamic [16] conditions, was
adopted and extended in [17] to support the analytical equations of the proposed analysis method
using an additional iterative procedure to combine the submerged catenary configuration and the
catenary curve created by the ‘out of water” cable part at the sea surface. In [17], the results of the
method for laying a composite submarine cable at an intermediate water depth were compared with
relevant results exported by the commercial Finite Element Analysis (FEA) software RSTAB [18] and
were found to be in very good agreement.
In thepresentpaper, aninnovativeandefficientanalysismethodisvalidatedinvariousinstallation
scenarios and an analysis tool (developed from scratch) is proposed for cable installers for the accurate
prediction of crucial installation parameters (minimum bending radius and bottom tension at the TDP)
and the cable configuration during laying operations, including the “out of water” cable part. Reliable
andcommercial FEAsoftwareisutilized to validate the accuracy and efficiency of the new analysis tool.
Furthermore, the importance of modeling the “out of water” part of the cable between the overboard
vessel’s chute and the sea surface is investigated. The analysis error in the case of not modeling the
“out of water” cable part is significant, especially in shallow-water areas, due to the fact that the part
of the cable in air is a non-ignorable proportion of the whole suspended length of the cable. It is
proven that when ignoring the modeling of the “out of water” cable segment, the cable integrity can
be jeopardized during laying activities. The proposed analysis tool is an innovation for cable laying
operations because it can provide quick and accurate results as sophisticated and time-consuming FEA
software. The tool allows cable installers to conduct real-time monitoring and re-adjustment of the
constant tension activator onboard the CLV to avoid laying the cable with an excess of residual tension
on the sea-bottom. In addition, the tool is able to accurately quantify the actual safety factor and
predict the correct S-lay configuration during laying, even in shallow-water areas, using an iterative
procedure for the combination of two catenary profiles with different properties (in and out of water
cable segments).
3. Description of the Proposed Analysis Tool
TheproposedanalysistoolforthelayingofasubmarinecableinanS-layconfigurationisdescribed
here. Details about the mathematical model, analysis assumptions, loads, boundaries, and cable
properties are presented.
The composite submarine cable that is used in the present study consists of the following:
1.
2.
3.
4.
5.
6.
7.
8.
3 nos 18/30(36) kV Power Cores, 500 mm2 Tinned Copper (Class 2) conductors;
2 nos Fiber Optic Cables, 48 nos Single Mode Fibers;
Extruded Shaped Fillers;
Binder tape;
Anti-Teredo copper tape;
Polypropylene bedding yarns;
One-layer galvanized steel wire armor;
Polypropylene yarns serving (2 nos layers with bitumen).
The submarine cable is simulated using the mechanical parameters provided by the cable
manufacturer Prysmian Group [19], which are presented in Table 1 and are used and must be respected
at all times during cable handling in any possible operation.
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Table 1. Cable mechanical properties.
Parameter
Unit of Measure
Value
Outer diameter
Approximate weight (in air)
Approximate weight (in water)
Maxstraight pulling tension
Maxsidewall pressure
Flexural stiffness [19]
Minimumallowable bending radius
mm
kg/m
kg/m
kN
kN/m
Nm2
m
144
37
23
176
40
10,000
2.2
Thedevelopedcustom-madetoolforthecableanalysisduringinstallationinanS-layconfiguration
consists of one main component, which is (a) the cable, and three boundaries: (a) the seabed, (b) the sea
surface, and (c) the CLV. The developed tool utilizes analytical equations of a catenary-type structure.
The catenary method is probably the most successful attempt to find an approximate solution to the
shape of aslender beamlifted at oneendfromahorizontalplane. Themethodwasoriginallysuggested
to find the configuration and stresses in a pipeline with negligible stiffness suspended between the
sea floor and an inclined ramp that is free to rotate and hence give a moment-free upper end of the
pipeline. These boundary conditions are identical to the ideal conditions for a catenary composite
submarine cable with an S-lay configuration, which means that the method should be well-suited to
analyze this type of structure. The method is limited to analyzing a uniform beam loaded by its own
weight only. Varying cross-sections, buoys, or current forces can therefore not be considered. However,
the proposed tool has extended the original method to account for varying cross-sections with different
weights, as is the real practice when a non-ignorable length of cable is out of the water between the
overboard chute and the sea level during a laying operation in a shallow water area.
The stiffened catenary method was originally suggested by Plunkett [20] and later applied by
Dixon andRutledge[21] to findtheconfiguration andstresses in a pipeline with non-ignorable stiffness
suspended between the sea floor and an inclined ramp, as frequently applied for pipe laying. The idea
of the stiffened catenary solution is that the bending stiffness causes secondary effects in boundary
regions only, and that the deviation from the simple catenary solution can be found as a rapidly
converging series expansion. For a cable laying analysis problem, it has been proven that the stiffness
of the cable can be ignored in order to minimize the computational effort, without losing the accuracy
of the results.
Therefore, in this paper, the extended catenary method is developed and proposed in order to
build up the cable catenary configuration. As described above, the catenary theory model [15,16] has
been adopted and extended to support the proposed tool analytical equations using an additional
iterative procedure to combine the submerged catenary configuration and the catenary curve created
by the “out of water” cable part at the sea surface. The reference configuration is assumed to be a
straight linear elastic beam with a length equal to the cable’s initial length (elongation due to tension is
ignored). In this analysis, the cable self-weight load (different weight in and out of water, see Table 1) is
imposed and the tension load “T_tensioner” is applied in a horizontal direction through the caterpillar
tensioner (just before the overboard chute of the CLV) to induce necessary tension in the cable, as
illustrated in Figure 3. By inducing prescribed translation at the connection node, the cable, along
with the vessel, is pulled up above the sea surface. This yields the establishment of the catenary
configuration. In this analysis, there is no axial stiffness of the cable present and no sliding along the
seabed can occur. Therefore, there is a fixed support on the seabed and a sliding horizontal support on
the CLV. The sea surface is the boundary of the different cross-section properties.
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Figure 3. Symbols and notations used for the description of the proposed analysis tool.
Figure 3. Symbols and notations used for the description of the proposed analysis tool. 
Figure 3. Symbols and notations used for the description of the proposed analysis tool. 
The input parameters required by the proposed analysis tool are listed below and presented in
Figure 4:
The input parameters required by the proposed analysis tool are listed below and presented in 
Figure 4: 
The input parameters required by the proposed analysis tool are listed below and presented in 
Figure 4: 
• Waterdepth,D;
• Water depth, D; 
• Water depth, D; 
• Distancebetween the sea level and the overboard chute at the CLV, c;
• Distance between the sea level and the overboard chute at the CLV, c; 
• Distance between the sea level and the overboard chute at the CLV, c; 
• Bottomtensionat the TDP, H;
• Bottom tension at the TDP, H; 
• Bottom tension at the TDP, H; 
• Cable weight in water, q1 (Table 1); 
• Cableweightinwater, q1 (Table 1);
• Cable weight in water, q1 (Table 1); 
• Cable weight in air, q2 (Table 1). 
• Cableweightinair, q2 (Table 1).
• Cable weight in air, q2 (Table 1). 
Figure 4. Symbols used for the mathematical formulation.
Figure 4. Symbols used for the mathematical formulation. 
Figure 4. Symbols used for the mathematical formulation. 
The basic theory underlying the behavior of catenary lines is utilized. However, an extension of
the basic theory is proposed through an iterative procedure to combine the two catenary-type curves
consisting of the two different cross-section properties for each cable segment, which are (a) submerged
and (b) out of water. This procedure can be further developed to combine three or more segments of
different cross-sections in order to analyze various cases studies of the oil and gas and wind power
industry, like the installation of umbilicals, pipelines, anchor lines, etc. Connection between the two or
The basic theory underlying the behavior of catenary lines is utilized. However, an extension of 
the basic theory is proposed through an iterative procedure to combine the two catenary-type curves 
consisting of the two different cross-section properties for each cable segment, which are (a) 
submerged and (b) out of water. This procedure can be further developed to combine three or more 
segments of different cross-sections in order to analyze various cases studies of the oil and gas and 
wind power industry, like the installation of umbilicals, pipelines, anchor lines, etc. Connection 
between the two or more different curves is achieved through the determination of a dummy 
equilibrium node where the vertical component of the internal force V’ is equal at both curves. The 
position of this dummy node for our study is at the sea surface elevation, as illustrated in Figure 4. 
The horizontal component of the internal force H along the cable configuration is constant and equal 
to the bottom tension at the TDP, as governed by the equilibrium equation on the X axis. Therefore, 
equilibrium on the Y axis using the vertical component V’ accurately determines the dummy 
equilibrium node. 
more different curves is achieved through the determination of a dummy equilibrium node where the
The basic theory underlying the behavior of catenary lines is utilized. However, an extension of 
the basic theory is proposed through an iterative procedure to combine the two catenary-type curves 
consisting of the two different cross-section properties for each cable segment, which are (a) 
submerged and (b) out of water. This procedure can be further developed to combine three or more 
segments of different cross-sections in order to analyze various cases studies of the oil and gas and 
wind power industry, like the installation of umbilicals, pipelines, anchor lines, etc. Connection 
between the two or more different curves is achieved through the determination of a dummy 
equilibrium node where the vertical component of the internal force V’ is equal at both curves. The 
position of this dummy node for our study is at the sea surface elevation, as illustrated in Figure 4. 
The horizontal component of the internal force H along the cable configuration is constant and equal 
to the bottom tension at the TDP, as governed by the equilibrium equation on the X axis. Therefore, 
equilibrium on the Y axis using the vertical component V’ accurately determines the dummy 
equilibrium node. 
vertical component of the internal force V’ is equal at both curves. The position of this dummy node
for our study is at the sea surface elevation, as illustrated in Figure 4. The horizontal component of the
internal force H along the cable configuration is constant and equal to the bottom tension at the TDP,
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as governed by the equilibrium equation on the X axis. Therefore, equilibrium on the Y axis using the
vertical component V’ accurately determines the dummy equilibrium node.
The following equations present the parameters defining the catenary shape, while Figure 4
illustrates how the parameters relate to the cable configuration. The step-by-step iterative procedure is
presented hereafter.
3.1. STEP 1: Determination of the Submerged Catenary Curve
For y =y1=Dandq=q1,x1isdetermined using Equation (1):
x = H
q arccosh y∗q
H +1 .
For x =x1, S1 and V’ are determined using Equations (2) and (3):
S = H
q sinh q∗x
H ,
V =H∗sinh q∗x
H ,
(1)
(2)
(3)
where S is the length along the curved cable configuration and V is the vertical component of the
internal force.
Therefore, at the end of this step, the V’ of the dummy equilibrium node has been calculated and
this is followed by the next step with multiple iterations.
3.2. STEP 2: Iterative Procedure to Define the “Correct” Catenary Curve in Air Which Can Be Combined with
the Submerged One
For the first iteration, we set y = y2 = D and q = q2, and then x2 is determined using Equation (1)
andV2usingEquation(3). TheiterativeprocedurewillcontinueuntilV2isequaltoV’.Theconvergence
threshold for the termination of the iterative procedure is set at 0.001 kN. Therefore, at the end of this
step, the x2 value is determined.
3.3. STEP 3: Determination of Various Parameters for the Catenary Curve in Air
For y2=y2+c,x2 isdetermined using Equation (1).
For x =x2,Visdetermined using Equation (3’).
V
H =sinh q∗x
tanθ = V
H ,
H =sinh q∗x
H ,
where θ is the exit angle of the cable from the overboard chute on the CLV (Figure 3).
The exit angle θ is equal to [90 deg-departure angle] (Figure 1).
3.4. STEP 4: Determination of the Combined Catenary Curve Configuration (In and out of Water)
For x =x2andq=q2,S2,1 is determined using Equation (2).
For x =x2 andq=q2,S2isdetermined using Equation (2).
S2,2 = S2−S2,1,
S =S1+S2,2,
a/2 = x1+(x2−x2),
(3’)
(4)
(5)
(6)
(7)
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whereα/2representsthelayback,whichishorizontaldistancebetweentheTDPontheseabedandthe
exitpointontheoverboardchuteontheCLV.
Inordertoplotthecombinedcatenarycurve,thefollowingequationsareusedindependentlyfor
eachdifferentpart(a)submergedand(b)inairofthecombinedcatenarycurve.
y=H
q coshq∗x
H −1 . (8)
Foreachpoint,thefollowingequationsarevalidanddeterminethetangentialinternalforceT:
T= H2+V2, (9.1)
T=H+q∗y. (9.2)
ThehorizontaltensionloadT_tensioner(Figure3)ispracticallyappliedtothecablethrough
theconstanttensionactivator(usuallyawheelorcaterpillartensioner).Thecableispassedthrough
thetensionerandafterthat,itfollowsinarollerwaybeforereachingtheoverboardchute.Contact
betweenthecableandoverboardchutecreatesafrictionforcewhichiscalculatedusingthefollowing
formula(Capstanequation[22]):
Tout=Tin∗eβ∗µ, (10)
whereβistheβ=θangle(equaltotheexitangleinradians)betweenthevectorsofTinandToutandµ
isthefrictioncoefficientbetweenthecableandoverboardchute.
Forourcase,wesetthefollowingnotations:
Tinisthetensionappliedbytheconstanttensionactivatorand
Tout isthetangentialinternalforceattheexitpointofthecableattheoverboardchuteontheCLV.
y=sinh q∗x
H , (11.1)
y=tan(ϕ), (11.2)
ϕ=arctan(y), (11.3)
whereϕisthetangentanglebetweentwoconsecutivenodes.
Theproposedanalysistoolhastheabilitytosplitthetotallengthofthecableandgenerateasmany
nodesastheuserdesires.Thedeterminationoftheminimumradiusofcurvatureismoreaccurate
astherearesomanynodesthatthetotal lengthofthecableissplit. Theuserisabletoperforma
sensitivityanalysisinordertodeterminethelimitwhenthecomputationaltimevs.Theaccuracyis
thedesiredone.
y = q
H∗cosh q∗x
H , (12)
R=
1+y2 3
2
y , (13.1)
R=
1+sinh q∗x
H
2 3
2
q
H∗cosh q∗x
H
, (13.2)
whereRistheradiusofcurvaturebetweentwoconsecutivenodes.
Theactualsafetyfactor(SF)duringasubmarinecablelayingoperationisgivenbythefollowing
Equation(14).Thesafetyfactoristheratiooftheminimumactualradiusofcurvaturebetweentwo
consecutivenodesalongtheS-curveconfiguration,asperEquation(13.2),totheminimumallowable
J. Mar. Sci. Eng. 2020, 8, 48
9 of 18
bending radius recommended bythecable manufacturer (Table 1). Usually, the actual minimum radius
of curvature is located at the TDZ area, where the cable touches the seabed.
SF =
minR (Equation (13.2))
minimumallowable bending radius (Table 1) .
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 
(14)
The basic assumptions regarding the components and the boundary conditions of the proposed
model are as follows:
9 of 18 
• Noflexuralandaxialstiffness is taken into consideration for the composite cable modeling;
• TheCLVis modeled as a fixed vertical support using the overboard chute. It also applies a
• The CLV is modeled as a fixed vertical support using the overboard chute. It also applies a 
horizontal tensile force to the cable through the constant tension activator. Friction between 
the overboard chute and cable is numerically modeled using Equation (10); 
horizontal tensile force to the cable through the constant tension activator. Friction between the
overboard chute and cable is numerically modeled using Equation (10);
• The sea surface is taken into consideration through the different weight of the cable (in and 
out of the water); 
• Theseasurface is taken into consideration through the different weight of the cable (in and out of
the water);
• The seabed is analyzed as a fixed support in all translational degrees of freedom. Seabed
• The seabed is analyzed as a fixed support in all translational degrees of freedom. Seabed 
support is implemented at the TDP (X = 0, Y = 0, in Figure 4). No cable–soil interaction is 
taken into consideration. 
support is implemented at the TDP (X = 0, Y = 0, in Figure 4). No cable–soil interaction is taken
into consideration.
4. Validation of the Proposed Analysis Tool 
4. Validation of the Proposed Analysis Tool
Validation of the proposed analysis and design tool is presented in this section. For this reason,
Validation of the proposed analysis and design tool is presented in this section. For this reason, 
the case of an installation of a composite submarine cable using a CLV at a 93 m water depth has been 
selected for analysis using two different numerical methods: 
the case of an installation of a composite submarine cable using a CLV at a 93 m water depth has been
selected for analysis using two different numerical methods:
• The custom-made analysis and design tool that utilizes analytical equations of a catenary
type structure (presented above in Section 3), and 
• Thecustom-madeanalysis and design tool that utilizes analytical equations of a catenary-type
structure (presented above in Section 3), and
• An FEA model utilizing the structural analysis commercially available software RSTAB [18]. 
• AnFEAmodelutilizingthe structural analysis commercially available software RSTAB [18].
The installation model developed with the 3D FEA structural software RSTAB [18] consists of the
same components and boundaries as the relevant proposed analysis tool. A non-linear static analysis
is initially conducted to build up the catenary configuration. The most general way to find the static
condition for a flexible composite submarine cable during S-lay configuration is to define a stress-free
The installation model developed with the 3D FEA structural software RSTAB [18] consists of 
the same components and boundaries as the relevant proposed analysis tool. A non-linear static 
analysis is initially conducted to build up the catenary configuration. The most general way to find 
the static condition for a flexible composite submarine cable during S-lay configuration is to define a 
stress-free condition and introduce load contributions. Load types will normally consist of volume 
forces (weight and buoyancy), prescribed displacements at nodes with given boundary conditions, 
friction forces between the cable and sea bottom, etc. The initial (stress-free) condition cannot have 
any curvature and will hence be significantly different from the static shape. Figure 5 illustrates how 
one end of the cable must be moved down to the sea bottom, while the other must be moved to the 
overboard chute of the CLV. 
condition and introduce load contributions. Load types will normally consist of volume forces (weight
and buoyancy), prescribed displacements at nodes with given boundary conditions, friction forces
between the cable and sea bottom, etc. The initial (stress-free) condition cannot have any curvature
and will hence be significantly different from the static shape. Figure 5 illustrates how one end of the
cable must be moved down to the sea bottom, while the other must be moved to the overboard chute
of the CLV.
Figure 5. Initial (stress-free) and static condition of a submarine cable in S-lay configuration.
Figure 5. Initial (stress-free) and static condition of a submarine cable in S-lay configuration. 
The number of load increments within a load group might be high—often in the order of 100.
This is particularly the case for the prescribed displacements. Note that equilibrium must be obtained
The number of load increments within a load group might be high—often in the order of 100. 
This is particularly the case for the prescribed displacements. Note that equilibrium must be obtained 
for each load increment, which might be difficult at some intermediate end positions between initial 
and final positions, especially when the number of load increments is low. The reference 
configuration of the cable in the stress-free condition (Figure 5) is assumed to be a straight linear 
elastic beam with a length equal to the cable’s initial length (part of the cable under the analysis 
process that the user is able to define). All the supports of the cable beam elements in the stress-free 
J. Mar. Sci. Eng. 2020, 8, 48
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for each load increment, which might be difficult at some intermediate end positions between initial
and final positions, especially when the number of load increments is low. The reference configuration
of the cable in the stress-free condition (Figure 5) is assumed to be a straight linear elastic beam with a
length equal to the cable’s initial length (part of the cable under the analysis process that the user is
able to define). All the supports of the cable beam elements in the stress-free condition are modeled
as diagram-type non-linear springs, active in tension and compression loads, which can accurately
apply the actual boundaries of the model. In the non-linear static analysis, the cable self-weight load,
different for the segments of cable in and out of the water, is imposed and a tension load T is applied in
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 
the horizontal direction through the caterpillar tensioner just before the overboard chute at the CLV.
10 of 18 
This yields the establishment of a catenary configuration. Non-linear spring supports are utilized to
model the cable–soil interaction at the TDZ on the seabed and any possible free-span scenario in the
case of an uneven bottom profile that can be inserted using the relevant diagrams for non-linear spring
supports. Non-linear spring supports are utilized for the modeling of the overboard chute and the
spring supports are utilized to model the cable–soil interaction at the TDZ on the seabed and any 
possible free-span scenario in the case of an uneven bottom profile that can be inserted using the 
relevant diagrams for non-linear spring supports. Non-linear spring supports are utilized for the 
modeling of the overboard chute and the roller supports right after the tensioner onboard the CLV 
(Figure 3), in order to apply friction between the cable and the handling accessories, as done in the 
proposed analysis tool using Equation (10).  
roller supports right after the tensioner onboard the CLV (Figure 3), in order to apply friction between
the cable and the handling accessories, as done in the proposed analysis tool using Equation (10).
The input parameters required by the FEA software RSTAB are as follows:
The input parameters required by the FEA software RSTAB are as follows: 
• Thewaterdepth,D(Figure 3);
• The water depth, D (Figure 3); 
• Distancefromthe sea level of the overboard chute at the CLV, c;
• Distance from the sea level of the overboard chute at the CLV, c; 
• Geometryoftheoverboard chute onboard the CLV (Figures 6 and 7);
• Geometry of the overboard chute onboard the CLV (Figures 6 and 7); 
• Bottomtensionat the TDP, H;
• Bottom tension at the TDP, H; 
• Cableweightinwater, q1;
• Cable weight in water, q1; 
• Cableweightinair, q2;
• Cable weight in air, q2; 
• Non-linear diagrams (reaction force N/deflection mm) for the cable–soil interaction in two
directions (X, Y);
• Non-linear diagrams (reaction force N/deflection mm) for the cable–soil interaction in two 
directions (X, Y); 
• Compositecableflexural stiffness, EI (Table 1);
• Composite cable flexural stiffness, EI (Table 1); 
• Compositecableaxial stiffness, EA (Table 1).
• Composite cable axial stiffness, EA (Table 1). 
Figure 6. Geometry of the overboard chute dimensions in mm.
Figure 6. Geometry of the overboard chute dimensions in mm. 
Each cable element has been modeled as a beam element which is an elastic 3D element with
constant axial strain and torsion consisting of two nodes. Each element includes six degrees of freedom
per node. The element has a circular cross-section with a constant radius along its length. A linear
material model is used with properties for elastic cable elements since the target of all the analysis
steps is to keep the cable in an elastic safe limit (not a failure analysis problem). The software uses the
full Newton-Raphson large deformation analysis procedure, in which the stiffness matrix is updated at
every equilibrium iteration. The maximum number of iterations per load increment is set at 600 and the
Each cable element has been modeled as a beam element which is an elastic 3D element with 
constant axial strain and torsion consisting of two nodes. Each element includes six degrees of 
freedom per node. The element has a circular cross-section with a constant radius along its length. A 
linear material model is used with properties for elastic cable elements since the target of all the 
analysis steps is to keep the cable in an elastic safe limit (not a failure analysis problem). The software 
uses the full Newton-Raphson large deformation analysis procedure, in which the stiffness matrix is 
updated at every equilibrium iteration. The maximum number of iterations per load increment is set 
at 600 and the number of load increments at 700. Many attempts have been conducted with less load 
increments and a lower maximum number of iterations; however, due to the large deformations 
required to achieve the static condition starting from the initial stress-free condition (Figure 5), all of 
them terminated due to convergence inability at intermediate steps. Shear deformations are also 
taken into consideration. Cross-section and material properties are modified accordingly to 
correspond to an equivalent section with mechanical parameters provided by the cable manufacturer 
(Table 1).  
number of load increments at 700. Many attempts have been conducted with less load increments and
a lower maximumnumberof iterations; however, due to the large deformations required to achieve
the static condition starting from the initial stress-free condition (Figure 5), all of them terminated due
to convergence inability at intermediate steps. Shear deformations are also taken into consideration.
Cross-section and material properties are modified accordingly to correspond to an equivalent section
with mechanical parameters provided by the cable manufacturer (Table 1).
11 of 18
J. Mar. Sci. Eng. 2020, 8, 48
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 
Figure 7. 3D model of the cable lay vessel (CLV) that is used as a reference for the analysis.
Figure 7. 3D model of the cable lay vessel (CLV) that is used as a reference for the analysis. 
11 of 18 
The soil properties are defined by the cable–soil non-linear interaction spring supports model.
This model allows for user-defined friction coefficients in different directions. The soil resistance is
The soil properties are defined by the cable–soil non-linear interaction spring supports model. 
This model allows for user-defined friction coefficients in different directions. The soil resistance is 
defined in three directions: vertically, laterally, and axially. 
defined in three directions: vertically, laterally, and axially.
The Coulomb friction coefficients presented in Table 2 are used to represent the soil conditions. 
The Coulomb friction coefficients presented in Table 2 are used to represent the soil conditions,
whereµx =0.4(conservativevalueofthefrictioncoefficientalongthecableaxis)andµy =0.8(thelateral
degree of freedom will be ignored).
Table 2. Typical soil stiffness and friction coefficient. 
Seabed Type Direction Stiffness (kN/m2) Friction Coefficient 
Table 2. Typical soil stiffness and friction coefficient.
Sand
 Axial 
100 to 250 
0.4–0.6 
Seabed Type
Sand 
Direction
Lateral 
Stiffness (kN/m2)
50 to 100 
Friction Coefficient
0.8 
Sand
Sand
Axial
 Vertical 
200 to 10,000 
100 to 250- 
0.4–0.6
Sand
Sand
Lateral
Vertical
50 to 100
200 to 10,000
0.8
where μx = 0.4 (conservative value of the friction coefficient along the cable axis) and μy = 0.8 (the 
lateral degree of freedom will be ignored). 
The vertical resistance of all model nodes (except the ones onboard the CLV) is expressed as a
non-linear spring, which starts to be active at Y = −D (depth) and afterwards follows soil vertical
The vertical resistance of all model nodes (except the ones onboard the CLV) is expressed as a 
non-linear spring, which starts to be active at Y = −D (depth) and afterwards follows soil vertical 
resistance behavior, as indicated in Table 2. 
resistance behavior, as indicated in Table 2.
The basic assumptions regarding the components and the boundary conditions of the FEA model
in RSTAB software are as follows:
The basic assumptions regarding the components and the boundary conditions of the FEA 
model in RSTAB software are as follows: 
• Flexural stiffness is taken into consideration for the composite cable modeling (Table 1); 
• Flexuralstiffness is taken into consideration for the composite cable modeling (Table 1);
• TheCLVismodeledasanon-linearvertical support. A vertical reaction is applied when the cable
touches the configuration of the overboard chute (Figure 6). The CLV also applies a horizontal
• The CLV is modeled as a non-linear vertical support. A vertical reaction is applied when the 
cable touches the configuration of the overboard chute (Figure 6). The CLV also applies a 
horizontal tensile force to the cable through the constant tension activator. Friction between 
the overboard chute and cable is modeled using non-linear spring supports, as per Equation 
(10);  
tensile force to the cable through the constant tension activator. Friction between the overboard
chute and cable is modeled using non-linear spring supports, as per Equation (10);
• Theseasurfaceis taken into consideration through the different weights of the cable segments in
and out of the water;
• The sea surface is taken into consideration through the different weights of the cable 
segments in and out of the water; 
• Theseabedisanalyzed as non-linear vertical and horizontal support. A full cable–soil interaction
is taken into consideration.
• The seabed is analyzed as non-linear vertical and horizontal support. A full cable–soil 
interaction is taken into consideration. 
A comparative study of the two methods (proposed analysis tool vs. FEA model in RSTAB) has 
been conducted and is presented below to allow for an effective validation of the innovative analysis 
tool for the submarine cable laying installation. Three different cases are analyzed using the two 
models, as described above in Sections 3 and 4, respectively. Each case corresponds to a different 
bottom tension at the TDP. The bottom tension is a very crucial parameter for the safe installation of 
a submarine cable, both in shallow and deep waters. A different bottom tension at the TDP means 
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Acomparative study of the two methods (proposed analysis tool vs. FEA model in RSTAB) has
been conducted and is presented below to allow for an effective validation of the innovative analysis
tool for the submarine cable laying installation. Three different cases are analyzed using the two
models, as described above in Sections 3 and 4, respectively. Each case corresponds to a different
bottom tension at the TDP. The bottom tension is a very crucial parameter for the safe installation of
a submarine cable, both in shallow and deep waters. A different bottom tension at the TDP means
that the whole configuration of the S-curve has been changed and thus the following parameters are
affected:
• Minimumbendingradius(MBR);
• Exitanglefromthe overboard chute (θ, angles);
• Catenarylength;
• Layback,whichisthe position of the TDP;
• Horizontal,vertical,andtangentialresultantforceattheoverboardchute(H,V,andT,respectively).
Different values of bottom tension mean different equipment onboard the CLV (capacity-wise) for
the cable installer, a different configuration of the submarine cable during laying, a different minimum
bending radius at the TDP, and thus a different safety factor during the laying process.
MBR is the minimum radius of curvature along the S-curve configuration. In most cases, in
typical S-lay operations, the MBR is spotted at the TDZ, just before the cable touches the sea bottom.
The MBRisacrucial parameter for the integrity of the cable because it is an alternative way to measure
the bending stresses and easily compare those with the recommended limits provided by the cable
manufacturer (Table 1).
Three cases with bottom tension values of H1 = 1200 kg, H2 = 2000 kg, and H3 = 4000 kg and a
water depth of 93 m were analyzed using the analytical proposed analysis tool. The most important
parameters for the installation process were exported by the analysis tool and are presented in Table 3.
Table 3. Results obtained using the proposed analysis tool.
Water Depth = 93 m
Bottom
Tension H (kg)
Layback
Distance (m)
Catenary
Length (m)
Exit Angle
θ(degs)
Min. Bending
Radius (m)
TTensioner
Constant Tension
Adjustment (kg)
1200
2000
4000
89.029
119.717
175.462
139.002
161.306
206.797
69.714
62.008
50.293
52.173
86.956
173.914
895
1664
3429
It is easily understandable that as the bottom tension value increases, adjustment on the constant
tension activator onboard the CLV should be increased in order to achieve the desired bottom tension.
Furthermore, as the bottom tension value increases, the layback distance (Figure 3, presented as “a/2”)
and the catenary length (Figure 3, presented as “S”) increase as well, since the TDP is drawn away
from the CLV. The exit angle (Figure 3) is decreased and the cable exit from the overboard chute
becomes smoother at each step of bottom tension increase. Last but not least, as the bottom tension
increases, the actual minimum bending radius is increased as well, which means that the safety margin
for the integrity of the cable during the laying process is increased. It should be remembered that a
high bottom tension (higher than the required one) may create free spans along an uneven sea floor.
Exported S-lay configurations for different bottom tension values using the proposed analysis tool are
illustrated in Figure 8.
J.Mar.Sci.Eng.2020,8,48 13of18
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 13 of 18 
 
 
Figure 8. Exported S-lay configurations for different bottom tension values obtained using the 
proposed analysis tool. 
The same cases were inserted in the 3D FEA structural software RSTAB using the parameters as 
described above in Section 4. The most important parameters for the installation process were 
exported by the software and tabulated below (Table 4), in order to compare them with those 
exported by the proposed analysis tool. Exported S-lay configurations for different bottom tension 
values using the FEA structural software RSTAB are illustrated in Figure 9. 
Table 4. Results obtained using the 3D FEA structural software RSTAB. 
Water Depth = 93 m 
Bottom 
Tension H 
(kg) 
Layback 
Distance 
(m) 
Catenary 
Length (m) 
Exit 
Angle θ 
(degs) 
Min. 
Bending 
Radius (m) 
T_Tensioner Constant 
Tension Adjustment 
(kg) 
1200 92.70 141.62 67.815 56.10 895 
2000 125.20 165.90 60.10 93.00 1664 
4000 183.90 214.60 48.40 185.30 3429 -100-90-80-70-60-50-40-30-20-10
0
10
0 20 40 60 80 100 120 140 160 180 200
Water Depth (m)
Layback length(m)
S-Lay configuration, H1=1200kg S-Lay configuration, H2=2000kg
S-Lay configuration, H3=4000kg
Figure8.ExportedS-layconfigurationsfordifferentbottomtensionvaluesobtainedusingtheproposed
analysistool.
Thesamecaseswereinsertedinthe3DFEAstructuralsoftwareRSTABusingtheparametersas
describedaboveinSection4.Themostimportantparametersfortheinstallationprocesswereexported
bythesoftwareandtabulatedbelow(Table4),inordertocomparethemwiththoseexportedbythe
proposedanalysistool.ExportedS-layconfigurationsfordifferentbottomtensionvaluesusingthe
FEAstructuralsoftwareRSTABareillustratedinFigure9.
Table4.Resultsobtainedusingthe3DFEAstructuralsoftwareRSTAB.
WaterDepth=93m
Bottom
TensionH(kg)
Layback
Distance(m)
Catenary
Length(m)
ExitAngle
θ(degs)
Min.Bending
Radius(m)
T_Tensioner
ConstantTension
Adjustment(kg)
1200 92.70 141.62 67.815 56.10 895
2000 125.20 165.90 60.10 93.00 1664
4000 183.90 214.60 48.40 185.30 3429
Asitcanberealized,comparingtherelevantresults(Tables3and4)betweenthetwodifferent
numericalmethods,thedifferenceforallthecriticalparametersislessthan6.5%. Ingeneral,theflexural
stiffnessofthecablecanbeignored,significantlyimprovingthecomputationaleffortwithoutsensibly
demotingtheaccuracyoftheresults.Theplottedcableconfigurationsexportedbybothnumerical
methodsareillustratedforvisualcomparisoninFigure10.
Thecomparativestudypresentedaboveprovesthattheproposedanalyticaltoolforthecable
layinganalysisprovidesreliableandsaferesults,similartothoseobtainedwithsophisticatedand
time-consuming3DFEAcommerciallyavailablesoftware.Thedivergencebetweentheresultsofthe
twomethodsislogicalsincetheflexuralstiffnessofthecompositecablewasconsiderednegligiblefor
theproposedanalyticaltool.Therefore,moreS-curvesareexportedbytheFEAsoftware,evenwitha
biggerMBR.Insummary,theproposedtoolcanbeconsideredfullyreliableforcablelayinganalysis
anddesignactivitiesusingmuchlesscomputationaleffortandallowingthecableinstallerstoconduct
areal-timeanalysisandmonitoringofthelayingprocess.
14 of 18
J. Mar. Sci. Eng. 2020, 8, 48
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 
14 of 18 
S-Lay configuration FEA model, H1=1200 kg S-Lay configuration FEA model, H2=2000 kg
S-Lay configuration FEA model, H3=4000 kg
10
0-20
Water Depth (m)-10-20-30-40-50-60-70-80-90
0
20
40
60
80
100
120
140
160
180-100
Layback length(m)
200
Figure 9. Exported S-lay configurations for different bottom tension values obtained using the FEA
structural software RSTAB.
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 
Figure 9. Exported S-lay configurations for different bottom tension values obtained using the FEA 
structural software RSTAB. 
S-Lay configuration, H1=1200kg S-Lay configuration, H2=2000kg
15 of 18 
S-Lay configuration, H3=4000kg S-Lay configuration FEA model, H1=1200kg-20
S-Lay configuration FEA model, H2=2000kg S-Lay configuration FEA model, H3=4000kg
10
0-10-20-30
0
20
40
60
As it can be realized, comparing the relevant results (Tables 3 and 4) between the two different 
numerical methods, the difference for all the critical parameters is less than 6.5%. In general, the 
flexural stiffness of the cable can be ignored, significantly improving the computational effort without 
sensibly demoting the accuracy of the results. The plotted cable configurations exported by both 
numerical methods are illustrated for visual comparison in Figure 10. 
The comparative study presented above proves that the proposed analytical tool for the cable 
laying analysis provides reliable and safe results, similar to those obtained with sophisticated and 
time-consuming 3D FEA commercially available software. The divergence between the results of the 
two methods is logical since the flexural stiffness of the composite cable was considered negligible 
for the proposed analytical tool. Therefore, more S-curves are exported by the FEA software, even 
with a bigger MBR. In summary, the proposed tool can be considered fully reliable for cable laying 
analysis and design activities using much less computational effort and allowing the cable installers 
to conduct a real-time analysis and monitoring of the laying process. 
80
Water Depth (m)-40-50-60-70-80-90
100
120
140
160
180-100
Layback length(m)
Figure 10. Exported S-lay configurations for different bottom tension values using both the proposed 
analysis tool and the FEA software. 
Figure 10. Exported S-lay configurations for different bottom tension values using both the proposed
analysis tool and the FEA software.
5. Significance of the Modeling of the “Out of Water” Cable Segment 
200
The influence of the inclusion of the “out of water” cable segment in the mathematical modeling 
has been investigated, especially for shallow-water applications, and the results are presented below. 
Two different scenarios have been analyzed and the relevant results have been compared to 
J.Mar.Sci.Eng.2020,8,48 15of18
5.SignificanceoftheModelingofthe“OutofWater”CableSegment
Theinfluenceoftheinclusionofthe“outofwater”cablesegmentinthemathematicalmodeling
hasbeeninvestigated,especiallyforshallow-waterapplications,andtheresultsarepresentedbelow.
Twodifferentscenarioshavebeenanalyzedandtherelevantresultshavebeencomparedto
evaluatetheinfluenceformodelingofthe“outofwater”cablesegment:
• ScenarioNo1:Modelingofbothcablesegments,assuming“submerged”representsthepart
betweenthetouchdownpointandtheseasurfaceand“inair”representsthepartbetweenthe
seasurfaceandthelastpointtouchingtheoverboardchuteonthecablelayvessel,and
• ScenarioNo2:Modelingofbothcablesegmentswiththesameweight.Commonweightsforboth
segmentshavebeenchosenfortheweightinwater.
Bothoftheabovedescribedscenarioshavebeenanalyzedassumingdifferentwaterdepthvalues
startingfroma3mwaterdepthandendingata15mwaterdepth. Furthermore,asthebottom
tensioninput,asetofthreedifferentrunswereconducted,assumingthevaluesof1200/2000/4000kg
(Tables5–7). Specificbottomtensionvalueswerechosenforthecomparativestudybecausethese
arethecommonconstanttensionactivator(tensioner)availablecapacitiesinthecableindustryfora
submarinecableinstallationuptoa200mwaterdepth.
Table5.Comparativestudyofvariousinstallationscenariosusingtheproposedanalysistool:Scenario
No1vs.ScenarioNo2assumingbottomtension=1200kg.
BottomTension=1200kg
Water
Depth
(m)
LaybackDistance(m) CatenaryLength(m) ExitAngle(deg) MBR(m)
Scen
1
Scen
2
Differ
(%)
Scen
1
Scen
2
Differ
(%)
Scen
1 Scen Differ
(%)
Scen
1
Scen
2
Differ
(%)
3 24.73 25.39 2.66 25.81 26.40 2.30 30.39 26.84 11.67 36.27 52.17 43.85
5 28.64 29.05 1.44 30.22 30.58 1.19 33.39 30.37 9.02 38.95 52.17 33.95
7 31.98 32.27 0.91 34.12 34.36 0.72 35.99 33.37 7.28 41.72 52.17 25.06
9 34.94 35.16 0.63 37.70 37.88 0.48 38.30 35.98 6.06 44.59 52.17 17.01
11 37.62 37.80 0.46 41.05 41.19 0.34 40.37 38.29 5.16 47.55 52.17 9.71
13 40.09 40.24 0.36 44.24 44.35 0.25 42.25 40.36 4.46 50.61 52.17 3.10
15 42.39 42.51 0.28 47.29 47.38 0.19 43.96 42.24 3.90 52.17 52.17 0.00
Table6.Comparativestudyofvariousinstallationscenariosusingtheproposedanalysistool:Scenario
No1vs.ScenarioNo2assumingbottomtension=2000kg.
BottomTension=2000kg
Water
Depth
(m)
LaybackDistance(m) CatenaryLength(m) ExitAngle(deg) MBR(m)
Scen
1
Scen
2
Differ
(%)
Scen
1
Scen
2
Differ
(%)
Scen
1
Scen
2
Differ
(%)
Scen
1
Scen
2
Differ
(%)
3 32.06 32.90 2.62 32.90 33.69 2.40 24.11 21.18 12.14 57.85 86.96 50.32
5 37.17 37.70 1.42 38.41 38.89 1.26 24.62 24.10 9.49 60.45 86.96 43.84
7 41.55 41.92 0.89 43.23 43.56 0.77 28.84 26.61 7.73 63.11 86.96 37.79
9 45.44 45.72 0.62 47.61 47.86 0.52 30.83 28.83 6.49 65.82 86.96 32.11
11 48.99 49.21 0.45 51.69 51.88 0.37 32.64 30.82 5.58 68.60 86.96 26.76
13 52.26 52.44 0.35 55.53 55.68 0.28 34.30 32.63 4.86 71.42 86.96 21.75
15 55.32 55.47 0.27 59.18 59.31 0.21 35.83 34.30 4.29 74.30 86.96 17.03
J.Mar.Sci.Eng.2020,8,48 16of18
Table7.Comparativestudyofvariousinstallationscenariosusingtheproposedanalysistool:Scenario
No1vs.ScenarioNo2assumingbottomtension=4000kg.
BottomTension=4000kg
Water
Depth
(m)
LaybackDistance(m) CatenaryLength(m) ExitAngle(deg) MBR(m)
Scen
1
Scen
2
Differ
(%)
Scen
1
Scen
2
Differ
(%)
Scen
1
Scen
2
Differ
(%)
Scen
1
Scen
2
Differ
(%)
3 45.49 46.67 2.60 46.09 47.23 2.48 17.37 15.19 12.52 111.87 173.91 55.46
5 52.78 53.52 1.40 53.66 54.37 1.32 19.26 17.36 9.87 114.42 173.91 52.00
7 59.05 59.56 0.88 60.25 60.74 0.81 20.95 19.25 8.10 116.99 173.91 48.66
9 64.64 65.03 0.60 66.19 66.56 0.55 22.49 20.94 6.87 119.59 173.91 45.43
11 69.74 70.05 0.44 71.67 71.96 0.40 23.90 22.48 5.95 122.22 173.91 42.29
13 74.47 74.72 0.34 76.81 77.04 0.30 25.21 23.89 5.22 124.87 173.91 39.27
15 78.89 79.10 0.26 81.67 81.85 0.23 26.43 25.21 4.65 127.55 173.91 36.35
Summarizingthecomparativestudyabove,thelaybackdistanceandthecatenarylengtharenot
significantlyinfluencedbythemodelingofthe“outofwater”cablesegment.Contrarytothis,thecable
exitangleandMBRaredrasticallyaffectedbythemodelingofthe“outofwater”cablesegment,
especiallyinshallowwaters. Regardingthecableexitangleparameter, themaximumcalculated
variationbetweenthetwoscenariosis12.52%andispresentinshallowwaters(waterdepth=3m).
RegardingtheMBRparameter,themaximumcalculatedvariationbetweenthetwoscenariosis55.46%
andissimilarlypresentinshallowwaters(waterdepth=3m).
6.Conclusions
Themainpurposeofthisstudywastoproposeaneffectiveanalysisanddesigntoolforcablelaying
operations.Thevalidationstudypresentedaboveprovesthattheproposedcustom-madetoolprovides
reliableandsaferesults,eveninshallow-waterareas,similartosophisticatedandtime-consuming
commerciallyavailableFEAsoftware. Thedifferencesbetweentheresultsofthetwomethodsare
reasonable.Therefore,moreS-curvesareexportedbytheFEAsoftware,evenwithabiggerminimum
bendingradius.
Inaddition,asperthestudyconductedregardingtheinfluenceofthemodelingofthe“outof
water”cablesegment,guidanceforallcableinstallersshouldbeprovidedtotakeintoconsiderationthe
segmentofcablebetweentheseasurfaceandoverboardchuteassumingthecorrectweight.According
totheresultspresented,theanalysiserrorinthecaseofnotmodelingthe“outofwater”cablepart
withthecorrectweightforthecalculationoftheminimumbendingradius,especiallyinshallow-water
areas,isnotacceptableandmayjeopardizetheintegrityofthesubmarinecable.Thecablesegment
“outofwater”shouldbemodeledforanaccuratepredictionoftheminimumbendingradius(actual
bendingradiusofcurvature)inshallow-waterareas,wherethecablelayingoperationisriskierand
moreelegant. Theanalysiserrorforthecalculationoftheminimumbendingradius,aspresented
above,isnotacceptable(55.46%difference)andthemodelingofthe“outofwater”partisamustfora
safecablelayingoperationsinswallow-waterareas.
TheanalysisofvariousinstallationscenariosforasubmarinecablelayingoperationinanS-lay
configurationunderdifferentbottomtensionvaluesandvaryingwaterdepthsusingtheproposed
analysistoolisunderimplementationandtheresultswillbepresentedinfutureworkasguidance
forallcableinstallers. Thedynamicmovementofthecableandtheinfluenceofthecabletension
duethemovementofthecablelayingvesselaretwokeyproblemstobesolvedduringthecable
layingoperationsimulation.Bothofthemareunderimplementationtobeaddedfortheextension
ofbothnumericaltoolspresentedinthisstudyandtoevaluatewhetheritisimportantthattheyare
modeledandwhichcasescanbeignored,withoutlosingtheresults’accuracy,inordertominimizethe
computationaleffort.
J. Mar. Sci. Eng. 2020, 8, 48
17 of 18
Author Contributions: Conceptualization, V.A.M., C.M. and E.E.T.; methodology, V.A.M., C.M. and E.E.T.;
software, V.A.M., C.M. and E.E.T.; validation and formal analysis, V.A.M., C.M. and E.E.T.; investigation, V.A.M.,
C.M. andE.E.T.; writing—original draft preparation, V.A.M., C.M. and E.E.T.; writing—review and editing, V.A.M.,
C.M. and E.E.T. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Acknowledgments: The authors declare no administrative and technical support or donation in king.
Conflicts of Interest: The authors declare no conflict of interest.
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