Review of the Development of an Unbonded Flexible Riser: New Material, Types of Layers, and Cross-Sectional Mechanical Properties

Abstract

Unbonded flexible risers consist of several helical and cylindrical layers, which can undergo large bending deformation and can be installed in different configurations to adapt to harsh marine environments; thus, they can be applied to transport oil and gas resources from ultra-deep waters (UDW). Due to their special geometric characteristics, they can ensure sufficient axial tensile stiffness while having small bending stiffness, which can undergo large deflection bending deformation. In recent years, the development of unbonded flexible risers has been moving in an intelligent, integrated direction. This paper presents a review of unbonded flexible risers. Firstly, the form and properties of each interlayer of an unbonded flexible riser are introduced, as well as the corresponding performance and configuration characteristics. In recent years, the development of unbonded flexible risers has been evolving, and the development of machine learning on unbonded flexible risers is discussed. Finally, with emphasis on exploring the design characteristics and working principles, three new types of unbonded flexible risers, an integrated production bundle, an unbonded flexible riser with an anti-H2S layer, and an unbonded flexible riser with a composite armor layer, are presented. The research results show that: (1) the analytical methods of cross-sectional properties of unbonded flexible risers are solved based on ideal assumptions, and the computational accuracy needs to be improved. (2) Numerical methods have evolved from equivalent simplified models to models that account for detailed geometric properties. (3) Compared with ordinary steel risers, the unbonded flexible riser is more suitable for deep-sea resource development, and the structure of each layer can be designed according to the requirements of the actual environment.

Full text

Citation: Liu, Q.; Qu, Z.; Chen, F.; Liu,
X.; Wang, G. Review of the
Development of an Unbonded
Flexible Riser: New Material, Types of
Layers, and Cross-Sectional
Mechanical Properties. Materials 2024,
17, 2560. https://doi.org/10.3390/
ma17112560
Academic Editor: Enrique Casarejos
Received: 7 April 2024
Revised: 22 May 2024
Accepted: 23 May 2024
Published: 26 May 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
materials
Review
Review of the Development of an Unbonded Flexible Riser:
New Material, Types of Layers, and Cross-Sectional
Mechanical Properties
Qingsheng Liu †, Zhongyuan Qu †, Feng Chen *, Xiaoya Liu and Gang Wang
School of Mechanical and Electric Engineering, Soochow University, Suzhou 215131, China;
qsliu@suda.edu.cn (Q.L.)
*Correspondence: chenfeng508@suda.edu.cn; Tel.: +86-512-65790196
†These authors contributed equally to this work.
Abstract: Unbonded flexible risers consist of several helical and cylindrical layers, which can undergo
large bending deformation and can be installed in different configurations to adapt to harsh marine
environments; thus, they can be applied to transport oil and gas resources from ultra-deep waters
(UDW). Due to their special geometric characteristics, they can ensure sufficient axial tensile stiffness
while having small bending stiffness, which can undergo large deflection bending deformation. In
recent years, the development of unbonded flexible risers has been moving in an intelligent, integrated
direction. This paper presents a review of unbonded flexible risers. Firstly, the form and properties of
each interlayer of an unbonded flexible riser are introduced, as well as the corresponding performance
and configuration characteristics. In recent years, the development of unbonded flexible risers has
been evolving, and the development of machine learning on unbonded flexible risers is discussed.
Finally, with emphasis on exploring the design characteristics and working principles, three new
types of unbonded flexible risers, an integrated production bundle, an unbonded flexible riser with
an anti-H
2
S layer, and an unbonded flexible riser with a composite armor layer, are presented. The
research results show that: (1) the analytical methods of cross-sectional properties of unbonded
flexible risers are solved based on ideal assumptions, and the computational accuracy needs to be
improved. (2) Numerical methods have evolved from equivalent simplified models to models that
account for detailed geometric properties. (3) Compared with ordinary steel risers, the unbonded
flexible riser is more suitable for deep-sea resource development, and the structure of each layer can
be designed according to the requirements of the actual environment.
Keywords: unbonded flexible riser; deep-sea development; mechanical properties; composite armor
layer; configuration
1. Introduction
Riser systems (see Figure 1) are the key components of the offshore oil and gas extraction
process, essentially referring to the conduit system that connects the surface floating unit to
subsea equipment, which is required for the extraction of any offshore oil and gas resources.
Offshore risers can be categorized in a variety of ways, and functionally, they can be simply
divided into production riser systems and drilling risers. Among them, production risers
have many structural forms, such as flexible risers, top tensioned risers (TTRs), steel catenary
risers (SCRs), hybrid tower risers, and so on. With the advancement of science and technology,
the operating water depth is increasing, and new riser structures come into being, such as
compliant vertical access risers (CVARs), hybrid risers with multiple holes, etc. [
1
]. Since
flexible risers have advantages, such as low bending stiffness, resistance to large deformation,
corrosion resistance, ease of installation, and recyclability, they are prioritized or must be used
for the extraction of offshore oil and gas resources in many cases [
2
–
5
]. In practical industrial
applications, approximately 85% of dynamic risers are flexible risers [6].
Materials 2024,17, 2560. https://doi.org/10.3390/ma17112560 https://www.mdpi.com/journal/materials

Materials 2024,17, 2560 2 of 34
Flexible risers can be subdivided into bonded flexible risers and unbonded flexible
risers (see Figure 2), both of which are multilayered composite structures containing an
indefinite number of laying layers with different geometries, material properties, and
functions (e.g., compressive armoring, tensile armoring, protective armoring, etc.) to
ensure the safety of the riser during installation and operation. Flexible risers have flexible
arrangement and configuration and can, therefore, be used in a wide range of applications,
not only for the transmission of liquefied natural gas in close proximity (thermal insulation
structure) but also as a long-distance oil pipeline. At the same time, they can be used
as a transmission medium for cables (an integrated production bundle, IPB), which is a
key piece of equipment in the field of offshore engineering. The difference between the
two types of risers is that bonded flexible risers are laid by physical extrusion or chemical
methods (e.g., vulcanization of rubber), in which interlayers cannot be separated or slip
due to external forces. Bonded risers are commonly used as jumper hoses to transport
resources between short distances [
7
,
8
]. An unbonded flexible riser, on the other hand,
directly sets the layers in sequence. The following assembly may even generate interlayer
gaps, and slipping between adjacent layers can occur under external forces. This type of
riser is commonly used for long-distance oil and gas transportation [
9
,
10
]. The special
structural form leads to the complex cross-sectional mechanical properties of unbonded
flexible risers, especially when subjected to bending loads due to the relative slip of the
internal spiral layers (mainly the tensile armored layers), which can lead to a sharp decrease
in bending stiffness and the hysteresis phenomenon.
Materials 2024, 17, x FOR PEER REVIEW 2 of 36
resistance to large deformation, corrosion resistance, ease of installation, and recyclability,
they are prioritized or must be used for the extraction of offshore oil and gas resources in
many cases [2–5]. In practical industrial applications, approximately 85% of dynamic ris-
ers are flexible risers [6].
Flexible risers can be subdivided into bonded flexible risers and unbonded flexible
risers (see Figure 2), both of which are multilayered composite structures containing an
indefinite number of laying layers with different geometries, material properties, and
functions (e.g., compressive armoring, tensile armoring, protective armoring, etc.) to en-
sure the safety of the riser during installation and operation. Flexible risers have flexible
arrangement and configuration and can, therefore, be used in a wide range of applica-
tions, not only for the transmission of liquefied natural gas in close proximity (thermal
insulation structure) but also as a long-distance oil pipeline. At the same time, they can be
used as a transmission medium for cables (an integrated production bundle, IPB), which
is a key piece of equipment in the field of offshore engineering. The difference between
the two types of risers is that bonded flexible risers are laid by physical extrusion or chem-
ical methods (e.g., vulcanization of rubber), in which interlayers cannot be separated or
slip due to external forces. Bonded risers are commonly used as jumper hoses to transport
resources between short distances [7,8]. An unbonded flexible riser, on the other hand,
directly sets the layers in sequence. The following assembly may even generate interlayer
gaps, and slipping between adjacent layers can occur under external forces. This type of
riser is commonly used for long-distance oil and gas transportation [9,10]. The special
structural form leads to the complex cross-sectional mechanical properties of unbonded
flexible risers, especially when subjected to bending loads due to the relative slip of the
internal spiral layers (mainly the tensile armored layers), which can lead to a sharp de-
crease in bending stiffness and the hysteresis phenomenon.
Figure 1. Sketch of riser system.
Figure 1. Sketch of riser system.
Materials 2024, 17, x FOR PEER REVIEW 3 of 36
Figure 2. Sketch of unbonded flexible riser [11].
In recent years, the marine oil and gas industry has experienced a significant shift
towards deep-water operations, which has led to increased demand for robust and so-
phisticated technology and equipment. The design of unbonded flexible risers has become
particularly critical due to the challenges posed by deeper waters, such as higher pressures
and the need for precise buoyancy control. A key factor in this design process is the sus-
pended weight of the riser, which has prompted the exploration of novel materials to meet
these stringent requirements.
One such innovation is the introduction of high-strength composite materials, includ-
ing carbon fiber composites, which are now being utilized in the tensile armor layer of
unbonded flexible risers. These materials not only ensure that unbonded flexible risers
possess the necessary strength but also significantly reduce the weight of the tensile armor
layer and the overall riser system. Additionally, composite cylindrical layer structures,
such as Kevlar 49, are being employed to prevent radial failure, commonly referred to as
birdcage failure, and to serve other functions like thermal insulation, which, in turn, in-
fluences the cross-sectional mechanical properties of unbonded flexible risers [12,13].
The integration of composites in unbonded flexible riser manufacturing is seen as a
promising development within the industry, offering enhanced performance and reliabil-
ity in deep-water environments. However, the material properties of these composites and
the geometrical properties of unbonded flexible riser layers are complex and present a
significant area of focus for future research and development. As the industry continues
to push the boundaries of deep-water exploration, understanding and optimizing these
properties will be pivotal in shaping future trends and advancements in marine oil and
gas extraction technology.
2. Form, Performance Characteristics, and Configuration Characteristics of
an Unbonded Flexible Riser
2.1. Form of Interlayers of an Unbonded Flexible Riser
Unbonded flexible risers have been widely used in the offshore oil and gas industry
since their inception in the 1970s. The internal layers of unbonded flexible risers can be
assembled in a certain order; typically, the innermost layer is the carcass layer that bears
the external compressive load and prevents damage during the manufacturing process.
This type of unbonded flexible risers are also known as rough bore-type unbonded flexi-
ble risers (shown in Figure 3a), whereas unbonded flexible risers used in shallow waters
do not generally contain this layer of structure, and are known as smooth bore-type un-
bonded flexible risers (as shown in Figure 3b). The interlayers of unbonded flexible risers
can be divided into cylindrical and helical layers. Helical layers typically include a carcass
layer, a pressure armor layer, and a tensile armor layer, and cylindrical layers include an
internal and external sheath. Conventional unbonded flexible risers typically contain only
metal layers and polymer layers. Based on the structure shown in Figure 3a, together with
the development of an unbonded flexible riser, the geometric and material properties of
Figure 2. Sketch of unbonded flexible riser [11].
In recent years, the marine oil and gas industry has experienced a significant shift
towards deep-water operations, which has led to increased demand for robust and sophis-

Materials 2024,17, 2560 3 of 34
ticated technology and equipment. The design of unbonded flexible risers has become
particularly critical due to the challenges posed by deeper waters, such as higher pressures
and the need for precise buoyancy control. A key factor in this design process is the sus-
pended weight of the riser, which has prompted the exploration of novel materials to meet
these stringent requirements.
One such innovation is the introduction of high-strength composite materials, includ-
ing carbon fiber composites, which are now being utilized in the tensile armor layer of
unbonded flexible risers. These materials not only ensure that unbonded flexible risers
possess the necessary strength but also significantly reduce the weight of the tensile armor
layer and the overall riser system. Additionally, composite cylindrical layer structures,
such as Kevlar 49, are being employed to prevent radial failure, commonly referred to
as birdcage failure, and to serve other functions like thermal insulation, which, in turn,
influences the cross-sectional mechanical properties of unbonded flexible risers [12,13].
The integration of composites in unbonded flexible riser manufacturing is seen as a
promising development within the industry, offering enhanced performance and reliability
in deep-water environments. However, the material properties of these composites and the
geometrical properties of unbonded flexible riser layers are complex and present a significant
area of focus for future research and development. As the industry continues to push the
boundaries of deep-water exploration, understanding and optimizing these properties will be
pivotal in shaping future trends and advancements in marine oil and gas extraction technology.
2. Form, Performance Characteristics, and Configuration Characteristics of an Unbonded
Flexible Riser
2.1. Form of Interlayers of an Unbonded Flexible Riser
Unbonded flexible risers have been widely used in the offshore oil and gas industry
since their inception in the 1970s. The internal layers of unbonded flexible risers can be
assembled in a certain order; typically, the innermost layer is the carcass layer that bears
the external compressive load and prevents damage during the manufacturing process.
This type of unbonded flexible risers are also known as rough bore-type unbonded flexible
risers (shown in Figure 3a), whereas unbonded flexible risers used in shallow waters do
not generally contain this layer of structure, and are known as smooth bore-type unbonded
flexible risers (as shown in Figure 3b). The interlayers of unbonded flexible risers can be
divided into cylindrical and helical layers. Helical layers typically include a carcass layer, a
pressure armor layer, and a tensile armor layer, and cylindrical layers include an internal
and external sheath. Conventional unbonded flexible risers typically contain only metal
layers and polymer layers. Based on the structure shown in Figure 3a, together with the
development of an unbonded flexible riser, the geometric and material properties of each
layer, as well as some functional layer and newly proposed layers, are presented from the
inner to the outer layers:
Materials 2024, 17, x FOR PEER REVIEW 4 of 36
each layer, as well as some functional layer and newly proposed layers, are presented from
the inner to the outer layers:
Carcass layer
Inner sheath
Pressure armor layer
Anti-friction layer
Inner tensile armor layer
Outer tensile armor layer
Outer sheath
Anti-friction layer
Inner sheath
Outer sheath
Outer tensile armor
layer
Inner tensile armor
layer
Anti
-friction layer
Pressure armor layer
(a) Unbonded flexible riser of rough bore type
(b) Unbonded flexible riser of smooth bore type
Figure 3. Different types of unbonded flexible risers [14].
1. Carcass layer (Figure 4). The carcass layer is typically composed of carbon steel, stain-
less steel (austenitic stainless steel AISl304, 304L, 316, 316L, or duplex stainless steel,
etc.), corrosion-resistant alloys (resistant to the corrosive effects of H2S, CO2, CL ions,
etc.), and other metal materials. The self-locking, non-watertight structure consists of
steel material wound at a laying angle of close to 90°, and the cross-section is usually
S-shaped, as shown in Figure 4. The special geometric form makes the axial tensile
stiffness and torsional stiffness of the skeleton layer very small while ensuring suffi-
cient bending performance but also preventing compression failure caused by exter-
nal compressive loads. In general, as shown in Ta b l e 1, the skeleton layer of un-
bonded flexible risers features specific dimensional specifications tailored to risers of
varying sizes. The typical failure modes of the carcass layer, as well as the pressure
armor layer, are presented in Figure 5 [15].
Figure 4. Sketch of the cross-section of the carcass layer.
Figure 3. Different types of unbonded flexible risers [14].

Materials 2024,17, 2560 4 of 34
1.
Carcass layer (Figure 4). The carcass layer is typically composed of carbon steel,
stainless steel (austenitic stainless steel AISl304, 304L, 316, 316L, or duplex stainless
steel, etc.), corrosion-resistant alloys (resistant to the corrosive effects of H
2
S, CO
2
,
CL ions, etc.), and other metal materials. The self-locking, non-watertight structure
consists of steel material wound at a laying angle of close to 90
◦
, and the cross-section
is usually S-shaped, as shown in Figure 4. The special geometric form makes the axial
tensile stiffness and torsional stiffness of the skeleton layer very small while ensuring
sufficient bending performance but also preventing compression failure caused by
external compressive loads. In general, as shown in Table 1, the skeleton layer of
unbonded flexible risers features specific dimensional specifications tailored to risers
of varying sizes. The typical failure modes of the carcass layer, as well as the pressure
armor layer, are presented in Figure 5[15].
Materials 2024, 17, x FOR PEER REVIEW 4 of 36
each layer, as well as some functional layer and newly proposed layers, are presented from
the inner to the outer layers:
Carcass layer
Inner sheath
Pressure armor layer
Anti-friction layer
Inner tensile armor layer
Outer tensile armor layer
Outer sheath
Anti-friction layer
Inner sheath
Outer sheath
Outer tensile armor
layer
Inner tensile armor
layer
Anti
-friction layer
Pressure armor layer
(a) Unbonded flexible riser of rough bore type
(b) Unbonded flexible riser of smooth bore type
Figure 3. Different types of unbonded flexible risers [14].
1. Carcass layer (Figure 4). The carcass layer is typically composed of carbon steel, stain-
less steel (austenitic stainless steel AISl304, 304L, 316, 316L, or duplex stainless steel,
etc.), corrosion-resistant alloys (resistant to the corrosive effects of H2S, CO2, CL ions,
etc.), and other metal materials. The self-locking, non-watertight structure consists of
steel material wound at a laying angle of close to 90°, and the cross-section is usually
S-shaped, as shown in Figure 4. The special geometric form makes the axial tensile
stiffness and torsional stiffness of the skeleton layer very small while ensuring suffi-
cient bending performance but also preventing compression failure caused by exter-
nal compressive loads. In general, as shown in Table 1, the skeleton layer of un-
bonded flexible risers features specific dimensional specifications tailored to risers of
varying sizes. The typical failure modes of the carcass layer, as well as the pressure
armor layer, are presented in Figure 5 [15].
Figure 4. Sketch of the cross-section of the carcass layer.
Figure 4. Sketch of the cross-section of the carcass layer.
Materials 2024, 17, x FOR PEER REVIEW 5 of 36
(a) Elliptical collapse failure
(b) Heart-shape collapse failure
Figure 5. Collapse modes of the carcass layer [15].
Table 1. Geometry, specification parameters, and scope of the application of a carcass layer [13].
Cross-Sectional Area/mm
2
Thickness/mm
Scope of Application (Riser I.D. Size)/mm
0.62 × 28
3.25
50.8~76.2
1.00 × 36
5.00
76.2~127.0
1.20 × 40
6.00
152.4~203.2
1.40 × 55
7.00
203.2~304.8
1.60 × 55
8.00
203.2~304.8
2.00 × 72
10.00
304.8~421.6
2. Inner sheath. The internal sheath layer is a closed cylindrical shell structure extruded
from polymers, usually nylon 11 (PA-11), nylon 12 (PA-12), cross-linked polyethylene
(XLPE), high-density polyethylene (HDPE), etc. The thickness of this layer is usually
5.5 to 18 mm and is used for conveying medium (oil and gas resources). During the
design process, the inner sheath layer is mainly considered with the compatibility of
the fluid medium, fluid permeability, mechanical and thermal properties, and other
factors. It should be noted that there may be gaps between the internal carcass layer
and the inner sheath layer, which can lead to an infiltration phenomenon where gas-
eous substances accumulate in the annular region between these two layers [16].
3. Pressure armor layer [17–21]. The geometric properties of the pressure armor layer
are similar to that of the carcass layer, which is a steel self-locking structure with a
high laying angle, where the axial tensile and torsional stiffness can be basically ig-
nored. The thickness of the layer is 4 to 12 mm, and the section geometry is mainly of
the Z-type, C-type, or T-type (such as Figure 6a–d). The pressure armor layer mainly
provides the radial stiffness of the unbonded flexible riser and carries the riser’s in-
ternal and external pressure (mainly carrying the internal pressure load caused by
the internal medium). In cases where the riser is subjected to less internal pressure,
the riser design can similarly eliminate that layer of the structure. The “Z-type” pres-
sure armor layer is the main cross-section in the unbonded flexible riser industry. The
specification parameters and scope of application of the pressure armor layer are pre-
sented in Table 2. In addition, there are some special cross-section shapes of the pres-
sure armor layer, as shown in Figure 6e,f. These two structural forms of fatigue per-
formance assessment are complex and do not promote application. Unlocking is the
most common failure mode of tensile armor layers due to the fact that they are not
completely self-locking like the skeleton layer structure and the asymmetry of the
structural cross-section profile. The bearing ability of internal pressure is one of the
Figure 5. Collapse modes of the carcass layer [15].
Table 1. Geometry, specification parameters, and scope of the application of a carcass layer [13].
Cross-Sectional Area/mm2Thickness/mm Scope of Application
(Riser I.D. Size)/mm
0.62 ×28 3.25 50.8~76.2
1.00 ×36 5.00 76.2~127.0
1.20 ×40 6.00 152.4~203.2
1.40 ×55 7.00 203.2~304.8
1.60 ×55 8.00 203.2~304.8
2.00 ×72 10.00 304.8~421.6

Materials 2024,17, 2560 5 of 34
2.
Inner sheath. The internal sheath layer is a closed cylindrical shell structure extruded
from polymers, usually nylon 11 (PA-11), nylon 12 (PA-12), cross-linked polyethylene
(XLPE), high-density polyethylene (HDPE), etc. The thickness of this layer is usually
5.5 to 18 mm and is used for conveying medium (oil and gas resources). During the
design process, the inner sheath layer is mainly considered with the compatibility
of the fluid medium, fluid permeability, mechanical and thermal properties, and
other factors. It should be noted that there may be gaps between the internal carcass
layer and the inner sheath layer, which can lead to an infiltration phenomenon where
gaseous substances accumulate in the annular region between these two layers [16].
3.
Pressure armor layer [
17
–
21
]. The geometric properties of the pressure armor layer are
similar to that of the carcass layer, which is a steel self-locking structure with a high
laying angle, where the axial tensile and torsional stiffness can be basically ignored.
The thickness of the layer is 4 to 12 mm, and the section geometry is mainly of the
Z-type, C-type, or T-type (such as Figure 6a–d). The pressure armor layer mainly
provides the radial stiffness of the unbonded flexible riser and carries the riser’s
internal and external pressure (mainly carrying the internal pressure load caused by
the internal medium). In cases where the riser is subjected to less internal pressure, the
riser design can similarly eliminate that layer of the structure. The “Z-type” pressure
armor layer is the main cross-section in the unbonded flexible riser industry. The
specification parameters and scope of application of the pressure armor layer are
presented in Table 2. In addition, there are some special cross-section shapes of the
pressure armor layer, as shown in Figure 6e,f. These two structural forms of fatigue
performance assessment are complex and do not promote application. Unlocking is
the most common failure mode of tensile armor layers due to the fact that they are
not completely self-locking like the skeleton layer structure and the asymmetry of
the structural cross-section profile. The bearing ability of internal pressure is one of
the most important properties of unbonded flexible risers. The burst failure of the
pressure armor layer is illustrated in Figure 7.
Table 2. Specification parameters and scope of the application of a ‘Z’-type pressure armor layer [
13
].
Cross-Sectional Area/mm2Scope of Application (Riser I.D. Size)/mm
10.6 ×4.8 50.8~76.2
14.4 ×6.4 76.2~127.0
18.0 ×8.0 152.4~203.2
22.4 ×10.0 203.2~304.8
27.0 ×12.0 203.2~304.8
4.
Anti-friction layer: The anti-friction layer is made of polymer winding or directly
formed by a non-metallic thermoplastic sheath cylindrical shell layer, usually PA11/6,
PVDF, PP, etc. The anti-friction layer is located between the metal layers, mainly
used to reduce and prevent friction between the metal layers, which can enhance the
fatigue life of the pipeline and prolong its use.
5.
Tensile armor layer. The tensile armor layer is the most important component layer of
an unbonded flexible riser. A traditional unbonded flexible riser tensile armor layer
consists of double or four layers of steel tendon with rectangular cross-sections, which
are relatively wound. Additionally, the tensile armor layer is mainly used to provide
axial stiffness, bearing the role of axial tension and torque, which can ensure the safe
operation of the riser when it is subjected to self-weight and other external loads. In
order to balance the role of tensile force and circumferential stress, the laying angle
of the tensile armor layer can generally vary from 20
◦
to 55
◦
, and the gap between
tendons generally accounts for 7~11% of the annular area of the tensile armor layer.
The ability of the tensile armor layer directly determines the structural safety of the
unbonded flexible riser. Additionally, structural failure is mainly caused by axial force,
which mainly contains three failure modes: fracture failure, radial failure (birdcage

Materials 2024,17, 2560 6 of 34
failure, caused by axial compression, see Figure 8a), and lateral failure (caused by
axial compression and wet environment, see Figure 8b).
6.
Other intermediate layer structures (cylindrical layer). The intermediate layer of the
unbonded flexible riser can be flexibly designed according to the needs of the actual
situation. Additionally, according to the function of these cylindrical layers, they can
be divided into an auxiliary layer, a bending-resistant layer, a thermal insulation layer,
etc. Most of the intermediate layer structure is composed of a composite material
cylindrical layer, such as a H
2
S gas corrosion-resistant layer and a thermal insulation
layer. Some unbonded flexible risers add a layer of higher-strength composite material
(typically Kevlar 49) as an anti-birdcage tape on the outside of the tensile armor layer
to prevent radial failures from occurring [12].
Materials 2024, 17, x FOR PEER REVIEW 6 of 36
most important properties of unbonded flexible risers. The burst failure of the pres-
sure armor layer is illustrated in Figure 7.
(a) Z-type
(b) C-type
(c) T-type—1
(d) T-type—2
(e) K-type
(f) X-type
Figure 6. Profiles of the pressure armor layer.
4. Anti-friction layer: The anti-friction layer is made of polymer winding or directly
formed by a non-metallic thermoplastic sheath cylindrical shell layer, usually PA11/6,
PVDF, PP, etc. The anti-friction layer is located between the metal layers, mainly used
to reduce and prevent friction between the metal layers, which can enhance the fa-
tigue life of the pipeline and prolong its use.
Table 2. Specification parameters and scope of the application of a ‘Z’-type pressure armor layer
[13].
Cross-Sectional Area/mm
2
Scope of Application (Riser I.D. Size)/mm
10.6 4.8
×
50.8~76.2
14.4 6.4
×
76.2~127.0
18.0 8.0×
152.4~203.2
22.4 10.0
×
203.2~304.8
27.0 12.0×
203.2~304.8
Figure 7. Burst of the pressure armor layer.
Figure 6. Profiles of the pressure armor layer.
Materials 2024, 17, x FOR PEER REVIEW 6 of 36
most important properties of unbonded flexible risers. The burst failure of the pres-
sure armor layer is illustrated in Figure 7.
(a) Z-type
(b) C-type
(c) T-type—1
(d) T-type—2
(e) K-type
(f) X-type
Figure 6. Profiles of the pressure armor layer.
4. Anti-friction layer: The anti-friction layer is made of polymer winding or directly
formed by a non-metallic thermoplastic sheath cylindrical shell layer, usually PA11/6,
PVDF, PP, etc. The anti-friction layer is located between the metal layers, mainly used
to reduce and prevent friction between the metal layers, which can enhance the fa-
tigue life of the pipeline and prolong its use.
Table 2. Specification parameters and scope of the application of a ‘Z’-type pressure armor layer
[13].
Cross-Sectional Area/mm
2
Scope of Application (Riser I.D. Size)/mm
10.6 4.8
×
50.8~76.2
14.4 6.4
×
76.2~127.0
18.0 8.0×
152.4~203.2
22.4 10.0
×
203.2~304.8
27.0 12.0×
203.2~304.8
Figure 7. Burst of the pressure armor layer.
Figure 7. Burst of the pressure armor layer.

Materials 2024,17, 2560 7 of 34
Materials 2024, 17, x FOR PEER REVIEW 7 of 36
5. Tensile armor layer. The tensile armor layer is the most important component layer
of an unbonded flexible riser. A traditional unbonded flexible riser tensile armor
layer consists of double or four layers of steel tendon with rectangular cross-sections,
which are relatively wound. Additionally, the tensile armor layer is mainly used to
provide axial stiffness, bearing the role of axial tension and torque, which can ensure
the safe operation of the riser when it is subjected to self-weight and other external
loads. In order to balance the role of tensile force and circumferential stress, the lay-
ing angle of the tensile armor layer can generally vary from 20° to 55°, and the gap
between tendons generally accounts for 7~11% of the annular area of the tensile ar-
mor layer. The ability of the tensile armor layer directly determines the structural
safety of the unbonded flexible riser. Additionally, structural failure is mainly caused
by axial force, which mainly contains three failure modes: fracture failure, radial fail-
ure (birdcage failure, caused by axial compression, see Figure 8a), and lateral failure
(caused by axial compression and wet environment, see Figure 8b).
6. Other intermediate layer structures (cylindrical layer). The intermediate layer of the
unbonded flexible riser can be flexibly designed according to the needs of the actual
situation. Additionally, according to the function of these cylindrical layers, they can
be divided into an auxiliary layer, a bending-resistant layer, a thermal insulation
layer, etc. Most of the intermediate layer structure is composed of a composite mate-
rial cylindrical layer, such as a H2S gas corrosion-resistant layer and a thermal insu-
lation layer. Some unbonded flexible risers add a layer of higher-strength composite
material (typically Kevlar 49) as an anti-birdcage tape on the outside of the tensile
armor layer to prevent radial failures from occurring [12].
(a) Radial failure
(b) Lateral failure
Figure 8. Burst of the pressure armor layer [22].
7. Composite tensile armor layer [23–28]. The composite tensile armor layer is the ap-
plication of composite materials to manufacture the tensile armor layer structure; its
geometry is consistent with the traditional steel tensile armor layer. A schematic dia-
gram containing a composite tensile armor layer of an unbonded flexible riser pro-
vided by Technip is presented in Figure 9. Offshore engineering towards ultra-deep
waters is the reason that composite armor layers are generated. Beyond 2000 m of
water depth, the weight of conventional flexible pipe becomes critical not only for the
pipelay equipment and vessel but for the production floater as well. Substituting ten-
sile steel armor with composite armor made from fiber-reinforced polymer has the
potential to significantly reduce the weight of the pipe. Due to the high strength/mass
ratio of carbon fiber, it can greatly reduce the overall quality of the unbonded flexible
riser and improve the fatigue performance of the riser while meeting the strength; at
the same time, compared with the steel structure, the composite material has beer
corrosion resistance, which can reduce the corrosive effect of chemicals and seawater
on the risers in oil and gas fields, and it is the future direction of the development of
unbonded flexible risers.
Figure 8. Burst of the pressure armor layer [22].
7.
Composite tensile armor layer [
23
–
28
]. The composite tensile armor layer is the
application of composite materials to manufacture the tensile armor layer structure;
its geometry is consistent with the traditional steel tensile armor layer. A schematic
diagram containing a composite tensile armor layer of an unbonded flexible riser
provided by Technip is presented in Figure 9. Offshore engineering towards ultra-
deep waters is the reason that composite armor layers are generated. Beyond 2000 m
of water depth, the weight of conventional flexible pipe becomes critical not only for
the pipelay equipment and vessel but for the production floater as well. Substituting
tensile steel armor with composite armor made from fiber-reinforced polymer has the
potential to significantly reduce the weight of the pipe. Due to the high strength/mass
ratio of carbon fiber, it can greatly reduce the overall quality of the unbonded flexible
riser and improve the fatigue performance of the riser while meeting the strength; at
the same time, compared with the steel structure, the composite material has better
corrosion resistance, which can reduce the corrosive effect of chemicals and seawater
on the risers in oil and gas fields, and it is the future direction of the development of
unbonded flexible risers.
Materials 2024, 17, x FOR PEER REVIEW 8 of 36
Composite armor layer
Figure 9. Unbonded flexible riser with a composite armor layer [24,25].
2.2. Performance Characteristics
Compared to traditional steel risers, unbonded flexible risers containing multilayer
composite structures have the advantages of corrosion resistance, fast installation, good
flexibility for large deflection deformation, resistance to large internal and external pres-
sures, high reliability, modular design, low maintenance cost, recyclability, etc. Depend-
ing on different needs, the number of interlayers of unbonded flexible risers can vary from
the simplest of 4 layers to the most complex of 19 layers. Some performance characteristics
can be drawn as follows:
1. Flexible. The interlayers of an unbonded flexible riser are relatively independent of
each other, and the layers can slip relative to each other; thus, flexibility is the most
prominent characteristic of the riser. For example, a typical unbonded flexible hose
with an inner diameter of 203.2 mm has a safe bending radius of 2 m. It can fit the
seabed terrain well without a large overhang and can be used in floating systems or
on an uneven seabed. It is also easily wound, transported, and installed [13,29].
2. Convenient installation. Despite the high costs of unbonded flexible risers, installa-
tion costs are relatively low. Since conventional steel pipe laying costs are high, the
sea welding inspection workload is large, and the laying cycle is long. An unbonded
flexible riser has laying safety, convenience, and fast features, meaning the risers can
be laid using an ordinary power positioning vessel, and the laying cost of construc-
tion compared to conventional steel pipe is reduced by more than 50%. The pipe is
continuously wound on a winch, and the entire length of the pipe can be several
thousand meters long (see Figure 10). The laying cycle is short, the offshore connec-
tion workload is small, and the laying speed is generally 500 m/h on average, which
is more than five times the speed of steel pipe laying. Separate sections can be placed
on the deck, and connections can be synchronized during installation without the
need for other riser-based structures or underwater connection aids.
Figure 9. Unbonded flexible riser with a composite armor layer [24,25].
2.2. Performance Characteristics
Compared to traditional steel risers, unbonded flexible risers containing multilayer
composite structures have the advantages of corrosion resistance, fast installation, good
flexibility for large deflection deformation, resistance to large internal and external pres-
sures, high reliability, modular design, low maintenance cost, recyclability, etc. Depending
on different needs, the number of interlayers of unbonded flexible risers can vary from the
simplest of 4 layers to the most complex of 19 layers. Some performance characteristics can
be drawn as follows:

Materials 2024,17, 2560 8 of 34
1.
Flexible. The interlayers of an unbonded flexible riser are relatively independent of
each other, and the layers can slip relative to each other; thus, flexibility is the most
prominent characteristic of the riser. For example, a typical unbonded flexible hose
with an inner diameter of 203.2 mm has a safe bending radius of 2 m. It can fit the
seabed terrain well without a large overhang and can be used in floating systems or
on an uneven seabed. It is also easily wound, transported, and installed [13,29].
2.
Convenient installation. Despite the high costs of unbonded flexible risers, installation
costs are relatively low. Since conventional steel pipe laying costs are high, the sea
welding inspection workload is large, and the laying cycle is long. An unbonded
flexible riser has laying safety, convenience, and fast features, meaning the risers can
be laid using an ordinary power positioning vessel, and the laying cost of construction
compared to conventional steel pipe is reduced by more than 50%. The pipe is
continuously wound on a winch, and the entire length of the pipe can be several
thousand meters long (see Figure 10). The laying cycle is short, the offshore connection
workload is small, and the laying speed is generally 500 m/h on average, which is
more than five times the speed of steel pipe laying. Separate sections can be placed on
the deck, and connections can be synchronized during installation without the need
for other riser-based structures or underwater connection aids.
Materials 2024, 17, x FOR PEER REVIEW 9 of 36
Figure 10. Sketch of a flexible pipe on the winch.
3. Modularization. The interlayers of unbonded flexible riser construction are inde-
pendent of each other, making it possible to realize the exact requirements of a spe-
cific development. A simple riser for medium pressure resistance requires only 4 lay-
ers, while the most complex riser can have up to 19 layers. In addition to basic liquid
leakage and anti-pressure layers, other layers can be sandwiched between the helical
steel layers for abrasion resistance or thermal insulation. The modularity of the riser
production process facilitates the adjustment of the thickness, cross-sectional shape,
and number of layers to meet the different requirements of the customer.
4. Low corrosion-resistance requirement for steel helical tendons. Since the steel tensile
armor of an unbonded flexible riser does not come into direct contact with the con-
veyed liquid, it does not need to have the same corrosion resistance as a conventional
steel pipe. However, the innermost carcass layer of the hose must be in contact with
the conveyed liquid and must be corrosion-resistant.
5. High pressure resistance. Unbonded flexible hose can have both internal and external
pressure due to the specific configuration of the carcass layer, anti-pressure armor
layer, and tensile armor layer.
6. Long production cycle life and low maintenance. Conventional steel pipe requires a
large number of welded connections, while a sperate unbonded flexible riser is very
long with fewer connecting joints in the whole riser, which is not needed for mainte-
nance and repair of welds after being put into production and would not affect the
production operation under adverse sea conditions. Additionally, the unbonded flex-
ible riser would meet the requirements of continuous production, which has a longer
fatigue life than that of steel pipe.
7. Recyclable. An unbonded flexible riser is easy to recycle and reuse, thus increasing
the deep-sea oil field investment overall and is conductive to the environment.
2.3. Configuration Characteristics
Marine dynamic risers require careful design to prevent excessive bending. This de-
sign process involves line configuration, which takes into account the riser’s own gravity,
buoyancy, and the constraint forces as presented by its overall shape. As depicted in Fig-
ure 11, there are various configurations, ranging from relatively simple to more complex.
The simplest form is the free-hanging catenary configuration. This basic design is then
adapted into more intricate shapes to meet specific design and operational needs. The
configurations evolve from the catenary to include the following: the lazy wave
Figure 10. Sketch of a flexible pipe on the winch.
3.
Modularization. The interlayers of unbonded flexible riser construction are indepen-
dent of each other, making it possible to realize the exact requirements of a specific
development. A simple riser for medium pressure resistance requires only 4 layers,
while the most complex riser can have up to 19 layers. In addition to basic liquid
leakage and anti-pressure layers, other layers can be sandwiched between the helical
steel layers for abrasion resistance or thermal insulation. The modularity of the riser
production process facilitates the adjustment of the thickness, cross-sectional shape,
and number of layers to meet the different requirements of the customer.
4.
Low corrosion-resistance requirement for steel helical tendons. Since the steel tensile
armor of an unbonded flexible riser does not come into direct contact with the con-
veyed liquid, it does not need to have the same corrosion resistance as a conventional
steel pipe. However, the innermost carcass layer of the hose must be in contact with
the conveyed liquid and must be corrosion-resistant.

Materials 2024,17, 2560 9 of 34
5.
High pressure resistance. Unbonded flexible hose can have both internal and external
pressure due to the specific configuration of the carcass layer, anti-pressure armor
layer, and tensile armor layer.
6.
Long production cycle life and low maintenance. Conventional steel pipe requires
a large number of welded connections, while a sperate unbonded flexible riser is
very long with fewer connecting joints in the whole riser, which is not needed for
maintenance and repair of welds after being put into production and would not affect
the production operation under adverse sea conditions. Additionally, the unbonded
flexible riser would meet the requirements of continuous production, which has a
longer fatigue life than that of steel pipe.
7.
Recyclable. An unbonded flexible riser is easy to recycle and reuse, thus increasing
the deep-sea oil field investment overall and is conductive to the environment.
2.3. Configuration Characteristics
Marine dynamic risers require careful design to prevent excessive bending. This
design process involves line configuration, which takes into account the riser’s own gravity,
buoyancy, and the constraint forces as presented by its overall shape. As depicted in
Figure 11, there are various configurations, ranging from relatively simple to more complex.
The simplest form is the free-hanging catenary configuration. This basic design is then
adapted into more intricate shapes to meet specific design and operational needs. The
configurations evolve from the catenary to include the following: the lazy wave configura-
tion, which offers a more relaxed curvature; the steep wave configuration, characterized
by sharper bends; the lazy-S configuration, which introduces an S-shaped pattern with a
gradual transition; the steep-S configuration, featuring a more pronounced S-shape with
abrupt changes in direction; the pliant wave configuration, which provides flexibility to
adapt to various marine conditions. Each of these configuration designs is tailored to
different requirements, ensuring that dynamic risers can function effectively in diverse
marine environments [30].
Materials 2024, 17, x FOR PEER REVIEW 10 of 36
configuration, which offers a more relaxed curvature; the steep wave configuration, char-
acterized by sharper bends; the lazy-S configuration, which introduces an S-shaped pat-
tern with a gradual transition; the steep-S configuration, featuring a more pronounced S-
shape with abrupt changes in direction; the pliant wave configuration, which provides
flexibility to adapt to various marine conditions. Each of these configuration designs is
tailored to different requirements, ensuring that dynamic risers can function effectively in
diverse marine environments [30].
Figure 11. Configurations of an unbonded flexible riser.
A typical configuration of an unbonded flexible riser with composite tensile armor
layers is shown in Figure 12, wherein the top riser is the unbonded flexible riser containing
the composite material tensile armor layer, and the boom riser is the conventional un-
bonded flexible riser containing steel tensile armor layers. In deep water situations, un-
bonded flexible risers arranged in this way can significantly reduce the tensile forces on
the top floating platform.
Figure 11. Configurations of an unbonded flexible riser.
A typical configuration of an unbonded flexible riser with composite tensile armor lay-
ers is shown in Figure 12, wherein the top riser is the unbonded flexible riser containing the
composite material tensile armor layer, and the bottom riser is the conventional unbonded
flexible riser containing steel tensile armor layers. In deep water situations, unbonded
flexible risers arranged in this way can significantly reduce the tensile forces on the top
floating platform.

Materials 2024,17, 2560 10 of 34
Materials 2024, 17, x FOR PEER REVIEW 11 of 36
Figure 12. Sketch of a flexible pipe on the winch.
Risers and pipelines can be designed with reference to a variety of codes and stand-
ards from organizations such as classification societies and petroleum associations [31–
37]. For unbonded flexible risers, the widely used codes are API 17B and API 17J, proposed
by the American Petroleum Institute (API) [9,10], of which API 17B (Recommended Prac-
tice for Flexible Pipe) provides guidance on the design, analysis, fabrication, testing, in-
stallation, and operation of risers; API 17J (Specification for Unbonded Flexible Pipe) is
the relevant standard specifically for unbonded flexible risers and includes guidance on
safety, functionality, and dimensional definition. In addition, reference can also be made
to standards such as DNV-OS-F201 (Dynamic Risers) from Det Norske Veritas [37].
3. Development of Cross-Sectional Properties of an Unbonded Flexible Riser
An unbonded flexible riser is a composite structure containing multiple layers, and
there is also complex contact and friction between different layers. Under the action of
external complex loads, the interlayers would be in contact or detachment with each other,
and the tendons within the tensile armor layers would also undergo relative slippage,
which makes solving the cross-section mechanical properties of unbonded flexible risers
particularly complex. Additionally, the nonlinear cross-sectional properties of unbonded
flexible risers have always been a hotspot and a difficulty in the research of the offshore
oil and gas industry [6]. Structures such as umbilical cables and submarine cables also
have similar structures to unbonded flexible risers, and even some unbonded flexible ris-
ers may contain a cable layer inside due to some special applications [38].
Figure 12. Sketch of a flexible pipe on the winch.
Risers and pipelines can be designed with reference to a variety of codes and standards
from organizations such as classification societies and petroleum associations [
31
–
37
]. For
unbonded flexible risers, the widely used codes are API 17B and API 17J, proposed by the
American Petroleum Institute (API) [
9
,
10
], of which API 17B (Recommended Practice for
Flexible Pipe) provides guidance on the design, analysis, fabrication, testing, installation,
and operation of risers; API 17J (Specification for Unbonded Flexible Pipe) is the relevant
standard specifically for unbonded flexible risers and includes guidance on safety, func-
tionality, and dimensional definition. In addition, reference can also be made to standards
such as DNV-OS-F201 (Dynamic Risers) from Det Norske Veritas [37].
3. Development of Cross-Sectional Properties of an Unbonded Flexible Riser
An unbonded flexible riser is a composite structure containing multiple layers, and
there is also complex contact and friction between different layers. Under the action of
external complex loads, the interlayers would be in contact or detachment with each other,
and the tendons within the tensile armor layers would also undergo relative slippage,
which makes solving the cross-section mechanical properties of unbonded flexible risers
particularly complex. Additionally, the nonlinear cross-sectional properties of unbonded
flexible risers have always been a hotspot and a difficulty in the research of the offshore oil
and gas industry [
6
]. Structures such as umbilical cables and submarine cables also have
similar structures to unbonded flexible risers, and even some unbonded flexible risers may
contain a cable layer inside due to some special applications [38].
In terms of the research type, the mechanical properties of unbonded flexible risers can
be mainly divided into the mechanical properties under axisymmetric load (axial tension,

Materials 2024,17, 2560 11 of 34
pressure, internal and external pressure, torque, and other loads alone or jointly) and the
mechanical properties under bending load. When the material of the unbonded flexible
riser changes only in the elastic range, the strain–load curve changes linearly when it is
only subjected to axisymmetric loading [
6
,
7
]. Under a bending moment, the tendons within
helical layers (mainly referring to the tensile armor layer) undergo relative slipping when
the bending moment increases, which makes the bending stiffness of the unbonded flexible
riser decrease sharply and then the hysteresis phenomenon occurs [39–43].
The mechanical properties of unbonded flexible risers are mainly studied by theo-
retical, numerical, and experimental methods. Although the test method can truly reflect
the mechanical properties of unbonded flexible risers, the structure of unbonded flexible
risers is relatively complex, the costs of unbonded flexible riser specimens are high and
rare, and sometimes special test equipment is also needed to simulate external pressure
or carry out the test. Thus, it is difficult to determine the detailed geometric and material
properties of the specimen of unbonded flexible risers in published papers, and there
are fewer corresponding data; so, at present, theoretical and numerical methods are the
most important research methods used to study the mechanical properties of unbonded
flexible risers.
Each of the three research methods has its own characteristics: the theoretical method
is based on relatively strict assumptions and can be quickly calculated to obtain the approxi-
mate mechanical properties of unbonded flexible risers. In recent years, numerical methods,
due to the advancement of computer technology, have been developed from equivalent
simplified models to detailed geometrical models, and some new computational models
have been proposed based on some assumptions for calculating the failure characteristics of
unbonded flexible risers. The test methods also develop from initial indoor tests to the real
sea dynamic test to verify the feasibility of full-size unbonded flexible risers [
6
,
7
,
44
]. The
research progress on the cross-section mechanics of unbonded flexible risers is described in
detail below.
3.1. Development of Unbonded Flexible Riser under Axisymmetric Loads
3.1.1. Theoretical Method
The theoretical approach is generally based on some strict assumptions for the solution.
Firstly, it is assumed that axisymmetric loads and the bending moment acting on the unbonded
flexible riser can be decoupled [
45
,
46
], which is the basis of the solution. Secondly, the influence
of the end boundary conditions is generally ignored in the theoretical model It is considered
that the layers still comply with the assumption of flat cross-section under the action of the
axisymmetric load [
38
] and show the same axial strains and torsion angles [
47
–
49
]. In contrast,
factors such as initial defects of the layers of unbonded flexible risers [
50
,
51
] are neglected.
Finally, the solution is based on the functional principle or the force balance differential
equation [40,47,48,52,53].
Early theoretical models of unbonded flexible risers under axisymmetric loading were
often specific to a particular mechanical property of the unbonded flexible riser. Féret and
Bournazel [
54
] presented an analytical method to quickly assess the stress of the helical
tendon, ignoring the effects of internal and external pressures and interlayer gaps in the
unbonded flexible riser model. It was concluded that the non-metallic cylindrical shell layer
only transmits interlayer pressures and ignores the role of its axial stiffness. Goto et al. [
55
]
provided a theoretical model for evaluating the ultimate strength of unbonded flexible
risers under axisymmetric loading and presented the corresponding simple formulae.
Berge et al. [
36
] proposed a fast method for calculating the overall response of an unbonded
flexible riser and presented expressions for the stress–load relationship under separate
actions of axial force, internal pressure, and torque, respectively; however, the theoretical
method is only applicable to separate load actions, and the response characteristics of each
layer cannot be decoupled.
Subsequent studies have begun synthesizing theoretical models for unbonded flexible
risers under multiple load conditions. McNamara and Harte [
56
] proposed a theoretical

Materials 2024,17, 2560 12 of 34
model that takes into account the effects of axial tension, torque, bending moment around
the axis, and internal and external pressures, deriving stiffness, load, and displacement
matrices for each layer based on the principle of fictitious work, and then assembling
them to form an overall matrix, but ignoring variations in tube thickness. Later, Harte
and McNamara [
57
] improved the accuracy of the analytical model by accounting for
variations in tube thickness in their subsequent work. Witz and Tan [
58
] investigated the
structural response of structures such as flexible risers, umbilical cables, and marine cables
under axial and torsional loads based on the theory of nonlinear equations for classical
spiral belts. Claydon et al. [
59
] divided the layers of unbonded flexible risers into helical
layers and isotropic cylindrical shell layers and established a stiffness model including the
relationship between the axial force–displacement and the internal pressure differential–
radial displacement in the layers. Still, they ignored the effect of the interlayers’ contact
within the unbonded flexible riser and considered that the axial force of unbonded flexible
risers was the sum of the axial forces acting on each layer.
At present, the theoretical model of unbonded flexible risers under axisymmetric
loading mainly considers the force and deformation relationship of each layer of the struc-
ture separately and, at the same time, considers the mutual contact effect between layers.
Kebadze et al. [
60
,
61
] made a great contribution to the theoretical modeling of unbonded
flexible risers under axisymmetric loading, and they summarized the theoretical models
of their predecessors by dividing all the layers of unbonded flexible risers into cylindrical
shell layers and helical layers, in which the cylindrical shell layer was analyzed using a
thin-walled cylinder model, and the helical layer was divided into a helical layer with
a regular cross-section (the tensile armored layer) and a helical layer with a non-regular
cross-section. Assuming that each layer has the same axial elongation and torsion angle,
considering the axial elongation and torsion angle of the overall unbonded flexible riser,
as well as the thickness and radial strain of each layer, combined with the geometric rela-
tionship between the layers, the overall stiffness matrix is deduced through the functional
principle, which can be used to arbitrarily solve the unknowns of each layer according to
the force condition, determine the contact condition of neighboring layers, and calculate
the effect of the interlayer contact pressure. Most of the subsequent research adopted
Kebadze’s theoretical model. The subsequent work of Dong et al. [
7
,
62
] fully considered
the tendon geometrical relationship of the helical layer accordingly. In addition, Bahtui [
44
],
based on Kebadze’s theoretical model, simplified the helical layer structure with complex
cross-sectional geometrical properties, such as the carcass layer and pressure armor layer,
to an orthotropic anisotropic cylindrical shell. Ramos Jr. et al. [
63
,
64
] derived equilibrium
equations for unbonded flexible risers under axisymmetric loading by a method similar
to that of Kebadze, and presented in detail the assumptions of the theoretical approach:
(1) the axial elongation and torsion angle are the same for all interlayers; (2) the interstitial
gaps between the adjacent layers are not considered at the initial stage; (3) the inter contact
between helical tendons in the tensile armor layer is not considered; (4) all materials are ho-
mogeneous, isotropic, and vary within the linear elastic range; (5) all strains are sufficiently
small compared to the unit (small strain assumption, geometrically linear assumption);
(6) initial defects arising from fabrication are ignored; (7) thickness varies uniformly in each
layer; (8) for the helical tendons in the tensile armor layers, only the tangential and normal
stresses to the direction of the interstitial axes are accounted for; (9) the frictional internal
energy due to the relative displacement between the layers is neglected.
In addition, some other studies have provided equilibrium equations for unbonded
flexible risers under axisymmetric loading through the simplified mathematical models.
Among them, Custódio and Vaz [
65
] used the Laméand Clebsch-Kirchhoff equations
to describe the equilibrium equations for cylindrical shell and helical layers, taking into
account the nonlinearity of the material and the relative contact between neighboring layers
and provided an explanation for the occurrence of interlayer gaps through the contact
between the layers. However, their theoretical model was not able to take into account the
effects of the local bending and torsion of the helical layers. Sævik et al. [
66
] established the

Materials 2024,17, 2560 13 of 34
static equilibrium equations of helical belts from a microscopic point of view and presented
a theoretical model of a helical belt layer under axisymmetric loading by means of the
relationship between displacement and strain. Li et al. [
67
] analyzed the ultimate bearing
capacity of unbonded flexible riser layers under axial force and radial pressure based on
the theoretical model of Claydon et al. [
59
]. Knapp [
68
] derived the structural response
of aluminum and steel helical tendons under axisymmetric loading based on the cable
structure. Sævik and Bruaseth [
69
] used the umbilical cable as a research object and derived
a theoretical model of the umbilical cable under axisymmetric loading through the principle
of virtual work. Liu et al. [
70
,
71
] considered the viscoelasticity and structural damping of
the nonmetallic layer in the unbonded flexible riser and established its theoretical model
under axisymmetric loading. Liu et al. [
24
] extended the theoretical model of the steel
tensile armor layer to the model of the composite tensile armor layer, which can be used
for the structural response calculation of unbonded flexible risers containing both steel and
composite tensile armored layers under the action of axisymmetric loading. The accuracy
was verified through an eight-layer unbonded flexible riser model.
3.1.2. Numerical Method
Although the theoretical method can be used to facilitate rapid calculations of the
cross-sectional mechanical properties of unbonded flexible risers, it does not truly reflect
the stress–strain level of the internal layer structure of unbonded flexible risers due to
various assumptions. Meanwhile, it is expensive to carry out the tests of unbonded flexible
risers, and some tests require specialized test equipment; therefore, the numerical method
is an effective alternative method of research.
Numerical methods generally use either specialized finite element software (Bflex,
version 3.10, https://www.sintef.no/en/software/bflex-for-flexible-risers/) to simulate
the tendon of tensile armor layers and calculate their stress levels or general-purpose finite
element software (ANSYS, version 24 R1, https://www.ansys.com/, ABAQUS, version
2024, Abaqus Finite Element Analysis|SIMULIA-Dassault Systèmes (3ds.com), and MARC,
version 2024.1, https://hexagon.com/products/marc, etc.) to build a complete three-
dimensional numerical model to simulate the mutual contact effects between layers. The
former is based on the bending beam model [
70
] to simulate the helical tendon, which
is computationally efficient, while the latter method meshes the whole numerical model
and takes into account the effects of nonlinear contact between and within layers, which
is computationally relatively inefficient. Among them, computational analysis based on
general-purpose finite element software is commonly used as a numerical method, and
the numerical analysis model has gradually evolved from an equivalent simplified model
to a three-dimensional model, taking into account detailed cross-section geometry. The
progress of the numerical method under axisymmetric loading will be introduced in the
following section.
Numerical methods need to simulate the action of the layers of an unbonded flexible
riser as much as possible, as well as the mutual contact between the layers; most of the early
numerical models of unbonded flexible risers simplified the internal complex structure to
some extent. Sousa et al. [
72
–
80
] carried out many studies on the mechanical properties of
unbonded flexible risers based on numerical methods. They established a finite element
model of unbonded flexible risers with a multilayered structure using ANSYS finite element
software based on the study of Cruz [
81
], and investigated the structural responses under
individual and combined axisymmetric loads, respectively. They divided the layers of
the unbonded flexible riser into three types (Figure 13), in which the carcass layer and
the pressure armor layer are simplified into an orthotropic anisotropic shell element, the
nonmetallic cylindrical shell layer is simulated by an isotropic cylindrical shell element,
and the tensile armor layer is simulated by an isotropic three-dimensional Euler beam
element. This numerical model can be used to analyze the mechanical properties of the
cross-section under axisymmetric loads, such as axial force and external pressure.

Materials 2024,17, 2560 14 of 34
Materials 2024, 17, x FOR PEER REVIEW 15 of 36
beam element. This numerical model can be used to analyze the mechanical properties of
the cross-section under axisymmetric loads, such as axial force and external pressure.
Figure 13. Simplified numerical model of an eight-layer unbonded flexible riser.
The tensile armor layer structure is the most important load-bearing structure in un-
bonded flexible risers, and different studies have proposed different treatments for this
layer structure. Bahtui et al. [3,44,50,52,82,83] established the actual shape of the tensile
armor layer based on ABAQUS software (version 2024) using an eight-node linear, re-
duced integrator element for simulation, with the multilayer modeling scheme taking into
account the contact effect between the layers, which provides the possibility to analyze
the hysteresis effect of unbonded flexible risers under bending moments. Vaz and Rizzo
[29] simplified the tensile armor layer as an equivalent helical tendon, establishing a nu-
merical model of a nine-layer unbonded flexible riser with high computational efficiency,
which was modeled based using ABAQUS software (version 2024) with a lot of simplifi-
cations and assumptions. The spring element was used to simulate the supporting role of
the internal and external structures of the two tensile armor layers, a cylindrical surface
without thickness was established between two equivalent spiral steel strips to simulate
the interlayer friction, and the friction coefficient was reduced to simulate the role of the
anti-friction layer between the two layers. At the same time, a beam was established at the
axisymmetric center of the unbonded flexible riser to simulate the axial and torsional stiff-
nesses of the skeleton layer, the internal sheath layer, the compressive armor layer, and
the internal anti-friction layer. The authors also investigated the failure characteristics of
the tensile armor layer under external pressure and axial compression based on the pro-
posed numerical model.
The type of solution algorithm is crucial for solving the structural response of the
numerical model of an unbonded flexible riser under external loading. Leroy and Perdri-
zet et al. [84,85] focused on explicit and implicit solution algorithms, and they developed
a class of unbonded flexible riser numerical models containing five layers and equated the
internal carcass layer, the inter sheath layer, and the pressure armor layer as a layer of
cylindrical shell layer structure, the outer sheath structure of the tensile armor layer as a
cylindrical layer, and the two tensile armor layers were simulated using body elements.
Furthermore, the anti-friction layer structure between the two tensile armor layers was
simulated using shell elements. The numerical model geometry is relatively simple and
can be solved using both the explicit and standard algorithms of ABAQUS. In addition,
Perdrizet et al. [84] conducted a more in-depth study on the algorithmic issues applied in
the structural response calculations of unbonded flexible risers based on ABAQUS
Figure 13. Simplified numerical model of an eight-layer unbonded flexible riser.
The tensile armor layer structure is the most important load-bearing structure in
unbonded flexible risers, and different studies have proposed different treatments for this
layer structure. Bahtui et al. [
3
,
44
,
50
,
52
,
82
,
83
] established the actual shape of the tensile
armor layer based on ABAQUS software (version 2024) using an eight-node linear, reduced
integrator element for simulation, with the multilayer modeling scheme taking into account
the contact effect between the layers, which provides the possibility to analyze the hysteresis
effect of unbonded flexible risers under bending moments. Vaz and Rizzo [
29
] simplified
the tensile armor layer as an equivalent helical tendon, establishing a numerical model of a
nine-layer unbonded flexible riser with high computational efficiency, which was modeled
based using ABAQUS software (version 2024) with a lot of simplifications and assumptions.
The spring element was used to simulate the supporting role of the internal and external
structures of the two tensile armor layers, a cylindrical surface without thickness was
established between two equivalent spiral steel strips to simulate the interlayer friction, and
the friction coefficient was reduced to simulate the role of the anti-friction layer between
the two layers. At the same time, a beam was established at the axisymmetric center of the
unbonded flexible riser to simulate the axial and torsional stiffnesses of the skeleton layer,
the internal sheath layer, the compressive armor layer, and the internal anti-friction layer.
The authors also investigated the failure characteristics of the tensile armor layer under
external pressure and axial compression based on the proposed numerical model.
The type of solution algorithm is crucial for solving the structural response of the
numerical model of an unbonded flexible riser under external loading. Leroy and Perdrizet
et al. [
84
,
85
] focused on explicit and implicit solution algorithms, and they developed a
class of unbonded flexible riser numerical models containing five layers and equated the
internal carcass layer, the inter sheath layer, and the pressure armor layer as a layer of
cylindrical shell layer structure, the outer sheath structure of the tensile armor layer as a
cylindrical layer, and the two tensile armor layers were simulated using body elements.
Furthermore, the anti-friction layer structure between the two tensile armor layers was
simulated using shell elements. The numerical model geometry is relatively simple and
can be solved using both the explicit and standard algorithms of ABAQUS. In addition,
Perdrizet et al. [
84
] conducted a more in-depth study on the algorithmic issues applied in
the structural response calculations of unbonded flexible risers based on ABAQUS software
(version 2024). The results showed that the use of the explicit algorithm needs to take into
account the influence of inertial effects on the results of the calculations, and accordingly,
the computation time is long. On the contrary, the standard algorithm has a higher solving
efficiency, while the calculation is not easy to converge considering the geometric and
material nonlinearities as well as the nonlinearities of interlayer and intralayer mutual
contact. Thus, Perdrizet et al. [
84
] recommended using the explicit solving algorithm while
taking into account computational time and computational efficiency. In recent years,
some researchers have used the numerical method of taking into account the geometric

Materials 2024,17, 2560 15 of 34
properties of the detailed cross-sectional properties of unbonded flexible risers in multilayer
composite structures, and due to the existence of complex contacts and strong geometric
nonlinearities in the numerical model, the explicit algorithm is applied for the solution.
With the improvement of computer computational performance, more and more re-
searchers began to consider the establishment of numerical models containing the detailed
geometric characteristics of unbonded flexible risers. Among them, Li et al. [
86
,
87
] estab-
lished a ten-layer unbonded flexible riser numerical model based on ABAQUS software
(version 2024) containing detailed the geometric properties of the carcass layer and pressure
armor layer, in which the carcass layer was simulated using a four-node reduced integral
shell element. All other layers were simulated using an 8-node linear reduced integral body
element. The structural response of this numerical model of unbonded flexible risers under
axial tension and internal and external pressures was also investigated to evaluate the stress
levels in each layer. Ren et al. [
88
] established a numerical model of a class of unbonded
flexible risers with a 2.5-inch eight-layer structure based on ABAQUS software (version
2024), including the establishment of the S-type skeleton layer and the Z-type pressure-
resistant armored layer containing all the geometric characteristics (e.g., Figures 4and 6).
All the layer structures were simulated with the eight-node linearly reduced integration of
the body element, and the amplification of the computation time was adopted to solve the
problem of long calculation time. The step method is used to solve the problem of long
calculation time, and the structural response of the unbonded flexible riser under axisym-
metric load is verified by theoretical and experimental methods. The numerical model can
effectively simulate the mutual contact and friction effects between and within the layers;
therefore, it can be used to calculate the mechanical properties of the cross-section under
axisymmetric and bending loads. Ren et al. [
88
–
90
] established a numerical model of a class
of unbonded flexible risers with a 2.5-inch eight-layer structure based on ABAQUS soft-
ware (version 2024), including the establishment of the S-type carcass layer and the Z-type
pressure armor layer containing all the geometric characteristics (see Figure 14). All the
layers were simulated linearly by the eight-node reduced integration of the body element.
Meanwhile, the method of enlarging the calculation time step was adopted to solve the
problem of long calculation time, and the structural response of unbonded flexible risers
under axisymmetric loading was verified by theoretical and experimental methods. The
numerical model can effectively simulate the mutual contact and friction effects between
and within layers; therefore, it can be used to calculate the mechanical properties of the
cross-section under axisymmetric and bending moments. Yoo et al. [
91
,
92
] established a
carcass layer with detailed geometrical characteristics using ANSYS software (version 24
R1) and simplified it to an equivalent cylindrical shell layer by analyzing the mechanical
failure characteristics of the carcass layer under axial force. Taking a class of eight-layer 2.5-
inch unbonded flexible risers as an example, an equivalent simplified eight-layer numerical
model and a five-layer numerical model (the internal four-layer structure was equivalent
to one layer) were established, and the effect of simulating the cylindrical shell layer using
a shell element or a body element was taken into account to study the axial load carrying
capacity of the unbonded flexible risers. Zhang et al. [
11
] also developed a numerical model
containing detailed geometries, and all the layer structures were also simulated using body
elements and analyzed the structural response under external loads such as axial tension,
torque, and internal and external pressures.
In summary, the establishment of a three-dimensional numerical model of an un-
bonded flexible riser under axisymmetric loading has roughly gone through development
from simplifying part of the layer structure to taking into account the detailed geometrical
properties of each layer, and due to the existence of a large number of geometrical nonlin-
earities and contact nonlinearities within the numerical model, it is generally solved by
explicit algorithms.

Materials 2024,17, 2560 16 of 34
Materials 2024, 17, x FOR PEER REVIEW 17 of 36
Figure 14. Numerical model of an eight-layer unbonded flexible riser with detailed carcass layer
and pressure armor layer.
In summary, the establishment of a three-dimensional numerical model of an un-
bonded flexible riser under axisymmetric loading has roughly gone through development
from simplifying part of the layer structure to taking into account the detailed geometrical
properties of each layer, and due to the existence of a large number of geometrical nonlin-
earities and contact nonlinearities within the numerical model, it is generally solved by
explicit algorithms.
3.1.3. Test Method
There is a relative lack of research on the cross-section mechanical properties of un-
bonded flexible risers based on the experimental research method, partly due to the high
cost of unbonded flexible risers and partly because some special test equipment is needed
to carry out the tests. The load–strain relationship is basically linear, and the related ex-
perimental studies are relatively few compared to the mechanical properties under bend-
ing load, which is a strong nonlinear phenomenon.
Most of the model tests under axisymmetric loading are based on modeling a suffi-
ciently long section of the unbonded flexible riser. Among them, Wi [14] carried out a
class of eight-layer 2.5-inch unbonded flexible riser tests, which is the most representative
test in the published literature so far, and he not only provided the geometrical and ma-
terial properties of each layer of the unbonded flexible riser, but also elaborated the pro-
cess of carrying out the test and the imposed boundary conditions. Furthermore, the test
results were compared to the predictions provided by several research organizations;
therefore, most of the subsequent theoretical and numerical method studies are based on
this test as reference and validation, and the test results show that the experimental data
of the structural response under axial tension and torque loading are in good agreement
with the theoretical predictions. Ramos Jr. et al. [11,93] investigated the relationship be-
tween axial force and axial elongation of unbonded flexible risers by loading cyclic axial
force, and the results showed that unbonded flexible risers also suffer from some nonlin-
ear hysteresis under cyclic axial force. Vargas-Londoño et al. [94] found a similar phenom-
enon in a subsequent experimental study and found that the different spiral steel strips in
the tensile armored layer did not have the same load-carrying capacity. Zhou et al. [95]
investigated the effect of anti-friction layers in unbonded flexible risers based on experi-
mental methods and also obtained a nonlinear relationship of load–strain under axisym-
metric loading. Sousa et al. [96] investigated the structural response of a class of 4-inch,
seven-layer unbonded flexible risers under axial pressure by experimental methods. The
test results showed that the axial force–strain curve of the unbonded flexible riser varied
approximately linearly before radial failure occurred, followed by the destruction of the
outer sheath layer (shown in Figure 15) and radial failure of the riser.
Figure 14. Numerical model of an eight-layer unbonded flexible riser with detailed carcass layer and
pressure armor layer.
3.1.3. Test Method
There is a relative lack of research on the cross-section mechanical properties of
unbonded flexible risers based on the experimental research method, partly due to the
high cost of unbonded flexible risers and partly because some special test equipment is
needed to carry out the tests. The load–strain relationship is basically linear, and the
related experimental studies are relatively few compared to the mechanical properties
under bending load, which is a strong nonlinear phenomenon.
Most of the model tests under axisymmetric loading are based on modeling a suffi-
ciently long section of the unbonded flexible riser. Among them, Witz [
14
] carried out a
class of eight-layer 2.5-inch unbonded flexible riser tests, which is the most representative
test in the published literature so far, and he not only provided the geometrical and material
properties of each layer of the unbonded flexible riser, but also elaborated the process of car-
rying out the test and the imposed boundary conditions. Furthermore, the test results were
compared to the predictions provided by several research organizations; therefore, most of
the subsequent theoretical and numerical method studies are based on this test as reference
and validation, and the test results show that the experimental data of the structural re-
sponse under axial tension and torque loading are in good agreement with the theoretical
predictions. Ramos Jr. et al. [
11
,
93
] investigated the relationship between axial force and
axial elongation of unbonded flexible risers by loading cyclic axial force, and the results
showed that unbonded flexible risers also suffer from some nonlinear hysteresis under
cyclic axial force. Vargas-Londoño et al. [
94
] found a similar phenomenon in a subsequent
experimental study and found that the different spiral steel strips in the tensile armored
layer did not have the same load-carrying capacity. Zhou et al. [95] investigated the effect
of anti-friction layers in unbonded flexible risers based on experimental methods and
also obtained a nonlinear relationship of load–strain under axisymmetric loading. Sousa
et al. [
96
] investigated the structural response of a class of 4-inch, seven-layer unbonded
flexible risers under axial pressure by experimental methods. The test results showed that
the axial force–strain curve of the unbonded flexible riser varied approximately linearly
before radial failure occurred, followed by the destruction of the outer sheath layer (shown
in Figure 15) and radial failure of the riser.
In addition, Yue et al. [
97
] verified the mechanical properties of unbonded flexible risers
in shallow water under axial tension through full-scale modeling tests. Sævik et al. [
98
]
and Vaz et al. [
99
] carried out studies based on experimental methods for umbilical cable
structures with similar properties to unbonded flexible risers and also found that the
structures have certain axisymmetric loading with nonlinear properties.

Materials 2024,17, 2560 17 of 34
Materials 2024, 17, x FOR PEER REVIEW 18 of 36
Figure 15. Radial failure of a seven-layer, 4-inch unbonded flexible riser.
In addition, Yue et al. [97] verified the mechanical properties of unbonded flexible
risers in shallow water under axial tension through full-scale modeling tests. Sævik et al.
[98] and Vaz et al. [99] carried out studies based on experimental methods for umbilical
cable structures with similar properties to unbonded flexible risers and also found that
the structures have certain axisymmetric loading with nonlinear properties.
3.2. Development of an Unbonded Flexible Riser under a Bending Moment
Under the action of a bending moment, the increasing curvature of the helical layer
would gradually overcome the interlayer friction, and then relative slip would occur.
Thus, the bending stiffness of the unbonded flexible riser decreases sharply, and the phe-
nomenon of nonlinear hysteresis occurs, which has always been the hotspot and difficult
point of academic research.
3.2.1. Theoretical Method
The understanding of the slippage of spiral layer structures in unbonded flexible ris-
ers has gone through a process from simple to complex. Among them, Lanteigne [100]
proposed the flat cross-section assumption in the bending model and argued that the
bending stiffness of the helical layers is not fixed but depends on the radial forces and
tensions in each layer by gradually overcoming the effect of friction and going through a
transitional phase until the layers were free to slide between each other. At the same time,
the tendons in different layers are subjected to different forces, and the slip starts from the
outermost layer of the helical layer with different critical curvatures. Féret and Bournazel
[54] derived formulas for the displacement and offset angle of a spiral belt along its own
axial and lateral directions based on spatial geometric relationships, and they pointed out
that the frictional moment between layers needs to be overcome before bending an un-
bonded flexible riser, providing a moment–curvature hysteresis curve. Mciver [101] intro-
duced a theoretical modeling method for the structure of each layer separately, where the
homogeneous layer is considered as a thick-walled continuum, and the helical layer is
considered a bending beam with axial, bending, and torsional stiffness. The bending hys-
teresis characteristics of the riser were analyzed by considering the loads, including ten-
sion, torque, shear, and bending moment, as well as the effects of wall pressures, temper-
ature differences, and friction. Ramos Jr. et al. [102] introduced the process of solving the
bending stiffness of unbonded flexible risers, i.e., first assuming that the riser was in an
unstressed state, after which axisymmetric loads (axial force, internal and external pres-
sures, and torsion) were applied, and finally, bending moments are applied. As a result,
the structural response characteristics of the un-slip and full-slip phases were solved. They
Figure 15. Radial failure of a seven-layer, 4-inch unbonded flexible riser.
3.2. Development of an Unbonded Flexible Riser under a Bending Moment
Under the action of a bending moment, the increasing curvature of the helical layer
would gradually overcome the interlayer friction, and then relative slip would occur. Thus,
the bending stiffness of the unbonded flexible riser decreases sharply, and the phenomenon
of nonlinear hysteresis occurs, which has always been the hotspot and difficult point of
academic research.
3.2.1. Theoretical Method
The understanding of the slippage of spiral layer structures in unbonded flexible
risers has gone through a process from simple to complex. Among them, Lanteigne [
100
]
proposed the flat cross-section assumption in the bending model and argued that the
bending stiffness of the helical layers is not fixed but depends on the radial forces and
tensions in each layer by gradually overcoming the effect of friction and going through
a transitional phase until the layers were free to slide between each other. At the same
time, the tendons in different layers are subjected to different forces, and the slip starts
from the outermost layer of the helical layer with different critical curvatures. Féret and
Bournazel [
54
] derived formulas for the displacement and offset angle of a spiral belt along
its own axial and lateral directions based on spatial geometric relationships, and they
pointed out that the frictional moment between layers needs to be overcome before bending
an unbonded flexible riser, providing a moment–curvature hysteresis curve. Mciver [
101
]
introduced a theoretical modeling method for the structure of each layer separately, where
the homogeneous layer is considered as a thick-walled continuum, and the helical layer
is considered a bending beam with axial, bending, and torsional stiffness. The bending
hysteresis characteristics of the riser were analyzed by considering the loads, including
tension, torque, shear, and bending moment, as well as the effects of wall pressures,
temperature differences, and friction. Ramos Jr. et al. [
102
] introduced the process of
solving the bending stiffness of unbonded flexible risers, i.e., first assuming that the riser
was in an unstressed state, after which axisymmetric loads (axial force, internal and external
pressures, and torsion) were applied, and finally, bending moments are applied. As a result,
the structural response characteristics of the un-slip and full-slip phases were solved. They
ignored the bending stiffness of the partially slipped phase, which can be used to quickly
calculate the bending stiffness in the full slip phase.
Subsequent studies assumed that the helical strip varies only along its own axis
under the bending moment to give a slip model of the helical tendon, and the nonlinear
moment–curvature relationship for some of the phases was given. Among them, Kebadze
et al. [
60
,
61
] considered that the tensile armor layer, after overcoming the friction between

Materials 2024,17, 2560 18 of 34
the adjacent layers, transitions from the beginning of partial slip to full slip and summarized
the bending process into three stages: no slip, partial slip, and full slip (see Figure 16).
They ignored the mutual contact between the helical steel tendon of the tensile armor
layer and provided an expression for the strain of the helical layer by means of a spatial
geometric relation. Then, the expression between the bending moment–curvature was
given by the functional principle in three stages, and the expression of the bending stiffness
in each stage was presented, as in Figure 17. Firstly, the model under axisymmetric loading
was used to solve the interlayer contact pressure, and the static friction was calculated
by assuming that the pressure is constant. Then, the critical curvature was given as the
calculation method: in the OA segment shown in Figure 16
K≤Kmin
cr
, the tensile armor
layers have not been able to overcome the static friction between the layers, and there is
no change in bending stiffness (segment OA of Figure 17). In the AB segment shown in
Figure 16
Kmin
cr <K<π·Kmin
cr /
2, the unit at the neutral axis of the tendon reaches the
critical curvature and starts to slip, while the other parts of the tendon are still subject to
static friction, and gradually transition to the unit farthest from the neutral axis reaching
the critical curvature, where the bending stiffness decreases nonlinearly (segment AB of
Figure 17). In the BC segment shown in Figure 16
K≥π·Kmin
cr /
2, the whole helical tendon
has overcome the role of static friction. At this time, the strain of the tendon is completely
determined by the static friction and, in the absence of consideration of the local bending
and torsion of the spiral belt, the tensile armor layer completely loses bending stiffness, as
seen in the BC section shown in Figure 17, and the corresponding bending stiffness is zero.
Kebadze and Kraincanic [
61
] also provided formulas for calculating the bending stiffness
induced by the effects of local bending and torsion of the helical tendon. Then, Dong
et al. [
7
,
62
,
103
], on the basis of the theoretical model of Kebadze, accurately calculated the
curvature and deflection changes of the helical tendon and regained the bending stiffness
induced by the effects of local bending and torsion of the helical tendon. At the same time,
they provided the explicit expression of bending stiffness in the partially slipping phase,
which greatly simplified the calculation process. In addition, Wang et al. [
104
,
105
] analyzed
the variation of stresses in helical belts under the action of irregularly varying bending
moments and curvatures based on the theoretical models of Kebadze et al. [
61
] and Dong
et al. [103].
Materials 2024, 17, x FOR PEER REVIEW 19 of 36
ignored the bending stiffness of the partially slipped phase, which can be used to quickly
calculate the bending stiffness in the full slip phase.
Subsequent studies assumed that the helical strip varies only along its own axis un-
der the bending moment to give a slip model of the helical tendon, and the nonlinear
moment–curvature relationship for some of the phases was given. Among them, Kebadze
et al. [60,61] considered that the tensile armor layer, after overcoming the friction between
the adjacent layers, transitions from the beginning of partial slip to full slip and summa-
rized the bending process into three stages: no slip, partial slip, and full slip (see Figure
16). They ignored the mutual contact between the helical steel tendon of the tensile armor
layer and provided an expression for the strain of the helical layer by means of a spatial
geometric relation. Then, the expression between the bending moment–curvature was
given by the functional principle in three stages, and the expression of the bending stiff-
ness in each stage was presented, as in Figure 17. Firstly, the model under axisymmetric
loading was used to solve the interlayer contact pressure, and the static friction was cal-
culated by assuming that the pressure is constant. Then, the critical curvature was given
as the calculation method: in the OA segment shown in Figure 16
min
cr
KK≤
, the tensile
armor layers have not been able to overcome the static friction between the layers, and
there is no change in bending stiffness (segment OA of Figure 17). In the AB segment
shown in Figure 16
min min
/2
cr cr
KKK
π
< <⋅
, the unit at the neutral axis of the tendon reaches
the critical curvature and starts to slip, while the other parts of the tendon are still subject
to static friction, and gradually transition to the unit farthest from the neutral axis reaching
the critical curvature, where the bending stiffness decreases nonlinearly (segment AB of
Figure 17). In the BC segment shown in Figure 16
min
/2
cr
KK
π
≥⋅
, the whole helical ten-
don has overcome the role of static friction. At this time, the strain of the tendon is com-
pletely determined by the static friction and, in the absence of consideration of the local
bending and torsion of the spiral belt, the tensile armor layer completely loses bending
stiffness, as seen in the BC section shown in Figure 17, and the corresponding bending
stiffness is zero. Kebadze and Kraincanic [61] also provided formulas for calculating the
bending stiffness induced by the effects of local bending and torsion of the helical tendon.
Then, Dong et al. [7,62,103], on the basis of the theoretical model of Kebadze, accurately
calculated the curvature and deflection changes of the helical tendon and regained the
bending stiffness induced by the effects of local bending and torsion of the helical tendon.
At the same time, they provided the explicit expression of bending stiffness in the partially
slipping phase, which greatly simplified the calculation process. In addition, Wang et al.
[104,105] analyzed the variation of stresses in helical belts under the action of irregularly
varying bending moments and curvatures based on the theoretical models of Kebadze et
al. [61] and Dong et al. [103].
Bending curvature
Bending moment
Figure 16. Hysteresis curve of the bending moment versus bending curvature.
Figure 16. Hysteresis curve of the bending moment versus bending curvature.
In addition, some other research has developed equivalent mathematical and ana-
lytical models based on the nonlinear bending characteristics of unbonded flexible risers.
Østergaard et al. [
106
] provided a mathematical expression for the free sliding of a heli-
cal belt in a frictionless cylindrical shell layer. Approximate expressions for the bending
stiffness have also been presented by some riser manufacturers, e.g., Péronne et al. [
107
]
and Zhang et al. [
108
]. Meanwhile, Witz and Tan [
109
,
110
] investigated the bending char-

Materials 2024,17, 2560 19 of 34
acteristics of marine and umbilical cable structures and proposed the theory that friction
affects bending characteristics. They pointed out that slip is caused by an inhomogeneous
axial deformation of the helices prior to the occurrence of the slip and that homogeneous
axial deformation is expected along the deflected helices after the slip occurs. The effect of
boundary conditions was also investigated, and it was proposed that when the ends are not
subjected to any physical constraints, the helix would experience minimum uniform axial
strain, and the helix at the ends would no longer be retained in the planar cross-section.
Materials 2024, 17, x FOR PEER REVIEW 20 of 36
Bending stifness
Bending curvature
Present
Formor
Figure 17. Bending stiffness versus bending curvature curve.
In addition, some other research has developed equivalent mathematical and analyt-
ical models based on the nonlinear bending characteristics of unbonded flexible risers.
Østergaard et al. [106] provided a mathematical expression for the free sliding of a helical
belt in a frictionless cylindrical shell layer. Approximate expressions for the bending stiff-
ness have also been presented by some riser manufacturers, e.g., Péronne et al. [107] and
Zhang et al. [108]. Meanwhile, Wi and Tan [109,110] investigated the bending character-
istics of marine and umbilical cable structures and proposed the theory that friction affects
bending characteristics. They pointed out that slip is caused by an inhomogeneous axial
deformation of the helices prior to the occurrence of the slip and that homogeneous axial
deformation is expected along the deflected helices after the slip occurs. The effect of
boundary conditions was also investigated, and it was proposed that when the ends are
not subjected to any physical constraints, the helix would experience minimum uniform
axial strain, and the helix at the ends would no longer be retained in the planar cross-
section.
Bending hysteresis characteristics remain a hot topic for unbonded flexible risers
[111–116]. For the tensile armor layer structure, current research mainly focuses on how
to accurately describe the slip characteristics of the helical tendon using the following
models: the tensile armor layer bending hysteresis model established by considering dif-
ferent friction models and based on the theory of bending beams [117,118]; the analytical
analysis model considering the deformation characteristics of the tensile armor layer un-
der the action of riser torque and bending around the axis [62]; the bending hysteresis
model established by considering the effect of shear deformation of the cylindrical shell
layer structure in the riser [119].
3.2.2. Numerical Method
The numerical method used under the bending moment is analogous to the one used
under axisymmetric load, which is also based on special finite element software or based
on general-purpose finite element software using a layered modeling method for analysis.
Additionally, the importance of interlayer contact and friction is mentioned in the above
theoretical approach, which must be focused on in the numerical simulation.
Numerical methods for the bending characteristics of unbonded flexible risers have
also evolved from equivalent simplified models to models that account for detailed geo-
metric properties. Based on finite element software, different studies have established
multi-layer numerical models of unbonded flexible risers to study their nonlinear bending
characteristics. Most of them have simplified the numerical model [82,83]. Yun et al. [119]
simplified the structure of the carcass layer and pressure armor layer and studied the
bending characteristics of unbonded flexible risers by applying the axisymmetric load and
then the bending moment (Figure 18). They investigated the effect of different axisymmet-
ric loads on the bending characteristics, and the results of the calculations showed obvious
Figure 17. Bending stiffness versus bending curvature curve.
Bending hysteresis characteristics remain a hot topic for unbonded flexible risers [
111
–
116
].
For the tensile armor layer structure, current research mainly focuses on how to accurately
describe the slip characteristics of the helical tendon using the following models: the
tensile armor layer bending hysteresis model established by considering different friction
models and based on the theory of bending beams [
117
,
118
]; the analytical analysis model
considering the deformation characteristics of the tensile armor layer under the action of
riser torque and bending around the axis [
62
]; the bending hysteresis model established by
considering the effect of shear deformation of the cylindrical shell layer structure in the
riser [119].
3.2.2. Numerical Method
The numerical method used under the bending moment is analogous to the one used
under axisymmetric load, which is also based on special finite element software or based
on general-purpose finite element software using a layered modeling method for analysis.
Additionally, the importance of interlayer contact and friction is mentioned in the above
theoretical approach, which must be focused on in the numerical simulation.
Numerical methods for the bending characteristics of unbonded flexible risers have
also evolved from equivalent simplified models to models that account for detailed ge-
ometric properties. Based on finite element software, different studies have established
multi-layer numerical models of unbonded flexible risers to study their nonlinear bending
characteristics. Most of them have simplified the numerical model [
82
,
83
]. Yun et al. [
119
]
simplified the structure of the carcass layer and pressure armor layer and studied the
bending characteristics of unbonded flexible risers by applying the axisymmetric load and
then the bending moment (Figure 18). They investigated the effect of different axisymmetric
loads on the bending characteristics, and the results of the calculations showed obvious
hysteresis. The authors suggested that the bending characteristics of risers need to be
taken into account segmentally when analyzing the dynamic response of unbonded flexible
risers [120].

Materials 2024,17, 2560 20 of 34
Materials 2024, 17, x FOR PEER REVIEW 21 of 36
hysteresis. The authors suggested that the bending characteristics of risers need to be
taken into account segmentally when analyzing the dynamic response of unbonded flex-
ible risers [120].
Figure 18. Loading sequence for combined loads [119].
The multi-layer modeling method considering detailed geometry can effectively sim-
ulate the complex contact between and within the helical layer (mainly the carcass layer
and pressure armor layer); in contrast, the corresponding numerical method is difficult to
model with more elements, the calculation time is too long, and it is easy to cause the
results to be non-convergent. Few studies have carried out research on the cross-sectional
mechanical properties of unbonded flexible risers under bending loads using this method.
Among them, Zhang et al. [121] took a class of eight-layer 2.5-inch unbonded flexible ris-
ers as the object of study, and simplified the cross-sectional mechanical structure of the
carcass layer and the pressure armor layer to some extent (shown in Figure 19). The mesh
of the regular cylindrical shell layers was divided into large elements. The initial prestress-
ing effect between the adjacent layers was given by applying a large external pressure (1.8
MPa) to the outermost sheath layer, after which the applied bending moment load showed
significant hysteresis characteristics.
The development of numerical models of unbonded flexible risers containing de-
tailed geometric properties to simulate the nonlinear hysteresis characteristics of the struc-
ture is the current direction of development [122–125]. The advantages of this include sim-
ulating the nonlinear contact and friction characteristics between adjacent layers and cal-
culating the structural response characteristics of the unbonded flexible risers under the
action of complex coupling loads. The disadvantages include strong geometric nonlinear-
ity, the fact that numerical process calculations are not easy to converge, and the nonlinear
contact within and between the layers in the model may lead to unacceptable computa-
tional time.
Figure 18. Loading sequence for combined loads [119].
The multi-layer modeling method considering detailed geometry can effectively sim-
ulate the complex contact between and within the helical layer (mainly the carcass layer
and pressure armor layer); in contrast, the corresponding numerical method is difficult
to model with more elements, the calculation time is too long, and it is easy to cause the
results to be non-convergent. Few studies have carried out research on the cross-sectional
mechanical properties of unbonded flexible risers under bending loads using this method.
Among them, Zhang et al. [
121
] took a class of eight-layer 2.5-inch unbonded flexible risers
as the object of study, and simplified the cross-sectional mechanical structure of the carcass
layer and the pressure armor layer to some extent (shown in Figure 19). The mesh of the
regular cylindrical shell layers was divided into large elements. The initial prestressing
effect between the adjacent layers was given by applying a large external pressure (1.8 MPa)
to the outermost sheath layer, after which the applied bending moment load showed
significant hysteresis characteristics.
Materials 2024, 17, x FOR PEER REVIEW 22 of 36
Figure 19. Finite-element model of Zhang et al. for an unbonded flexible riser [121].
3.2.3. Test Method
The structural response of unbonded flexible risers under the bending moment is
complex, and the corresponding experimental studies are relatively few. Most of the open
literature is characterized by some experimental data given by the riser manufacturers,
and the detailed geometrical parameters and material properties of the risers are generally
not given.
Among the tests, the most classical test of a class of eight-layer 2.5-inch unbonded
flexible risers was carried out by Wi [14], who provided the structural response of un-
bonded flexible risers under cyclic bending loads and observed significant hysteresis char-
acteristics. Meanwhile, Wi [14] also investigated the effect of internal pressure on bend-
ing, providing moment–curvature curves at an internal pressure of 30 MPa. They found
that the bending stiffness of the complete slip phase decreased after the application of
internal pressure, but this result is highly controversial. Magluta et al. [126], in a subse-
quent experimental study, found that bending stiffness was not affected by internal pres-
sure, while Bech and Skallerud [127] and Troina et al. [128] also found that bending stiff-
ness increased after the application of an internal pressure load by means of experimental
methods. No recognized solution has yet been formulated to address this problem. With
the exception of Wi [14], most of tests were conducted by riser manufacturers. For ex-
ample, Zhang et al. [108] carried out an experimental study based on three different sizes
of 4-inch, 10-inch, and 15-inch pipes, simplified the bending hysteresis model to a bifold
model, and developed an approximate calculation method of equivalent non-slip stiffness
and full slip stiffness considering parameters such as internal and external pressure, axial
force, and interlayer friction coefficient. However, some parameters in this calculation
method are obtained by experiments, and the parameter data are not given in the paper.
Overall, there are relatively few experimental studies on the bending hysteresis char-
acteristics of unbonded flexible risers, but the test results all show the obvious hysteresis
characteristics of unbonded flexible risers under bending loads.
3.3. Development of the Study of Typical Failure Characteristics of Unbonded Flexible Risers
Unbonded flexible risers transport marine oil and gas, and once they fail, they not
only bring economic losses but they might even threaten the marine environment and
cause serious consequences. The main failure modes of unbonded flexible risers are as
follows: collapse failure of the carcass layer and pressure armor layer; burst failure of the
pressure armor layer; fracture, lateral, and birdcage (radial) failure of the tensile armor
layer, etc. The following is a brief introduction to these failure modes from the perspec-
tives of the theoretical method, numerical method, and test method.
Figure 19. Finite-element model of Zhang et al. for an unbonded flexible riser [121].
The development of numerical models of unbonded flexible risers containing detailed
geometric properties to simulate the nonlinear hysteresis characteristics of the structure is
the current direction of development [
122
–
125
]. The advantages of this include simulating
the nonlinear contact and friction characteristics between adjacent layers and calculating
the structural response characteristics of the unbonded flexible risers under the action of
complex coupling loads. The disadvantages include strong geometric nonlinearity, the fact
that numerical process calculations are not easy to converge, and the nonlinear contact
within and between the layers in the model may lead to unacceptable computational time.

Materials 2024,17, 2560 21 of 34
3.2.3. Test Method
The structural response of unbonded flexible risers under the bending moment is
complex, and the corresponding experimental studies are relatively few. Most of the open
literature is characterized by some experimental data given by the riser manufacturers,
and the detailed geometrical parameters and material properties of the risers are generally
not given.
Among the tests, the most classical test of a class of eight-layer 2.5-inch unbonded
flexible risers was carried out by Witz [
14
], who provided the structural response of
unbonded flexible risers under cyclic bending loads and observed significant hysteresis
characteristics. Meanwhile, Witz [
14
] also investigated the effect of internal pressure on
bending, providing moment–curvature curves at an internal pressure of 30 MPa. They
found that the bending stiffness of the complete slip phase decreased after the application of
internal pressure, but this result is highly controversial. Magluta et al. [
126
], in a subsequent
experimental study, found that bending stiffness was not affected by internal pressure,
while Bech and Skallerud [
127
] and Troina et al. [
128
] also found that bending stiffness
increased after the application of an internal pressure load by means of experimental
methods. No recognized solution has yet been formulated to address this problem. With
the exception of Witz [
14
], most of tests were conducted by riser manufacturers. For
example, Zhang et al. [
108
] carried out an experimental study based on three different sizes
of 4-inch, 10-inch, and 15-inch pipes, simplified the bending hysteresis model to a bifold
model, and developed an approximate calculation method of equivalent non-slip stiffness
and full slip stiffness considering parameters such as internal and external pressure, axial
force, and interlayer friction coefficient. However, some parameters in this calculation
method are obtained by experiments, and the parameter data are not given in the paper.
Overall, there are relatively few experimental studies on the bending hysteresis char-
acteristics of unbonded flexible risers, but the test results all show the obvious hysteresis
characteristics of unbonded flexible risers under bending loads.
3.3. Development of the Study of Typical Failure Characteristics of Unbonded Flexible Risers
Unbonded flexible risers transport marine oil and gas, and once they fail, they not only
bring economic losses but they might even threaten the marine environment and cause
serious consequences. The main failure modes of unbonded flexible risers are as follows:
collapse failure of the carcass layer and pressure armor layer; burst failure of the pressure
armor layer; fracture, lateral, and birdcage (radial) failure of the tensile armor layer, etc.
The following is a brief introduction to these failure modes from the perspectives of the
theoretical method, numerical method, and test method.
3.3.1. Collapse Failure of the Carcass Layer and Pressure Armor Layer
The structure of the carcass layer is similar to that of the pressure armor layer, and
the collapse failure mode is also relatively similar, as shown in Figure 5. The reasons for
failure mainly include excessive axial tension or external pressure, excessive load during
installation, breakage of the outer sheath layer, and initial defects in manufacturing [129].
Uniform external pressure or radial compression might lead to collapse failure. For
uniform external pressure, the theoretical approach is mainly used to equate the carcass
layer and the pressure armor layer as a circular structure with a rectangular cross-section,
after which the differential equations of the deflection curves of the circular ring are
established by solving the elastic stability theory to calculate the critical compression failure
value [
130
]. Numerical methods are used to investigate the structural properties under
uniform external or radial compressive loads by building numerical models taking into
account the detailed geometry. Due to the symmetry of the structure, 1/4 or 1/2 circular
numerical models or full-size models can be used for the solution [131–135].

Materials 2024,17, 2560 22 of 34
3.3.2. Burst Failure of the Pressure Armor Layer
Burst failure (see Figure 7) of compressive armor layers is caused by excessive internal
pressure, which might also cause the failure of tensile armor layers.
There are relatively few studies on the burst failure of unbonded flexible risers. Theo-
retical models are mostly based on single-layer pipes, which are categorized into elastic
failure, plastic failure, and ultimate failure according to the distribution state of cross-section
stress and solved by yield conditions such as Mises’ criterion and Tresca’s criterion [
1
]. In
addition, Yuan [
136
] investigated the limit state of unbonded flexible risers under internal
compressive loading by a numerical method of multilayer modeling.
3.3.3. Failure of the Tensile Armor Layer
The tensile armor layer bears the main axial force and torque of unbonded flexible
risers, which is the most important layer in risers, and the failure modes can be classified
into fracture failure, birdcage failure (radial failure), and lateral failure.
The tensile armor layer of unbonded flexible risers may suffer fracture failure when
subjected to excessive tensile forces. The principle of failure is relatively simple, i.e., failure
occurs when the tensile armor layer reaches its axial load-carrying capacity. Theoretical
solution methods are based on the theoretical model of an unbonded flexible riser under
axisymmetric loading, considering the elasticity and plasticity of the material of the tensile
armor layer and calculating the stress, which is considered to lose its axial load carrying
capacity by reaching plasticity [
91
]. Numerical methods often rely on simplified models or
approximations to make complex calculations more tractable. Yoo et al. [
91
] investigated
the ultimate carrying capacity under axial tension based on a class of eight-layer 2.5-inch
unbonded flexible risers and simplified it to equivalent eight- or five-layer structures.
The failure modes of the tensile armor layer under axial compression are complicated
since the special structural form of the unbonded flexible riser leads to its axial compressive
stiffness being much smaller than the axial tensile stiffness, so it might fail when subjected
to compression during the installation or life cycle. There are two failure modes under axial
compression: radial failure and lateral failure, as shown in Figure 8[
24
,
137
]. The cause of
both failure modes starts from damage to the outer sheath layer. After damage to the outer
jacket layer occurs, radial failure occurs in the tensile armor layer, which loses the radial
constraints [138], and lateral failure might occur when there is sufficient radial support or
when the friction between the layers is very small [
139
]. Lateral failure is more difficult to
observe and is more hazardous compared to radial failure modes.
For theoretical methods, Sævik and Thorsen [
140
] presented a quick calculation of
radial and lateral failure of tensile armor layers based on the bending beam theory and
compared it to the test results, which showed that the theoretical predictions were relatively
conservative. Østergaard et al. [
141
,
142
] provided a method for calculating lateral failure,
and the theoretical results are also lower than those obtained through tests.
Numerical methods facilitated some simplifications of unbonded flexible risers, gener-
ally by simplifying the internal structure (carcass layer, pressure armor layer, internal sheath
layer, etc.) into a rigid core layer [
143
–
145
], and the radial and lateral failure characteristics
were investigated, taking into account the effects of material nonlinearity and other factors.
The test methods for tensile armor layers under the axial compression can be di-
vided into three forms: deepwater immersion tests (DIP), pressure tank tests (as shown in
Figure 20 [
146
,
147
]), and mechanical performance experiments (as shown in Figure 21 [
22
]).
The DIP test uses a real-size unbonded flexible riser to carry out the test and requires
the cooperation of specialized equipment such as underwater robots and pipe-laying
vessels. Although detailed riser failure characteristics can be observed, the DIP test is
extremely costly, has a long cycle time, and only very few riser manufacturers have the
strength to carry out the DIP test at present.
Pressure tank tests can simulate the wet environment of the ocean, and the cost is
only 1/5 to 1/10 of that of carrying out DIP tests. Secher et al. [
145
] simulated the lateral
failure characteristics of three different sizes of unbonded flexible risers, 7-inch, 9-inch, and

Materials 2024,17, 2560 23 of 34
11-inch, respectively, by DIP and pressure tank tests. The results obtained from the two
different test methods were found to be basically the same, and it was found that the larger
the size of the unbonded flexible riser, the more prone it was to lateral failure.
Mechanical tests require relatively low levels of test equipment and can use X-rays to
detect the occurrence of failure in the internal structure of unbonded flexible risers.
Materials 2024, 17, x FOR PEER REVIEW 24 of 36
relatively conservative. Østergaard et al. [141,142] provided a method for calculating lat-
eral failure, and the theoretical results are also lower than those obtained through tests.
Numerical methods facilitated some simplifications of unbonded flexible risers, gen-
erally by simplifying the internal structure (carcass layer, pressure armor layer, internal
sheath layer, etc.) into a rigid core layer [143–145], and the radial and lateral failure char-
acteristics were investigated, taking into account the effects of material nonlinearity and
other factors.
The test methods for tensile armor layers under the axial compression can be divided
into three forms: deepwater immersion tests (DIP), pressure tank tests (as shown in Figure
20 [146,147]), and mechanical performance experiments (as shown in Figure 21 [22]).
Figure 20. Profile of the pressure tank test [146,147].
Figure 21. Compression test arrangement for an unbonded flexible riser [22].
The DIP test uses a real-size unbonded flexible riser to carry out the test and requires
the cooperation of specialized equipment such as underwater robots and pipe-laying ves-
sels. Although detailed riser failure characteristics can be observed, the DIP test is ex-
tremely costly, has a long cycle time, and only very few riser manufacturers have the
strength to carry out the DIP test at present.
Pressure tank tests can simulate the wet environment of the ocean, and the cost is
only 1/5 to 1/10 of that of carrying out DIP tests. Secher et al. [145] simulated the lateral
failure characteristics of three different sizes of unbonded flexible risers, 7-inch, 9-inch,
Figure 20. Profile of the pressure tank test [146,147].
Materials 2024, 17, x FOR PEER REVIEW 24 of 36
relatively conservative. Østergaard et al. [141,142] provided a method for calculating lat-
eral failure, and the theoretical results are also lower than those obtained through tests.
Numerical methods facilitated some simplifications of unbonded flexible risers, gen-
erally by simplifying the internal structure (carcass layer, pressure armor layer, internal
sheath layer, etc.) into a rigid core layer [143–145], and the radial and lateral failure char-
acteristics were investigated, taking into account the effects of material nonlinearity and
other factors.
The test methods for tensile armor layers under the axial compression can be divided
into three forms: deepwater immersion tests (DIP), pressure tank tests (as shown in Figure
20 [146,147]), and mechanical performance experiments (as shown in Figure 21 [22]).
Figure 20. Profile of the pressure tank test [146,147].
Figure 21. Compression test arrangement for an unbonded flexible riser [22].
The DIP test uses a real-size unbonded flexible riser to carry out the test and requires
the cooperation of specialized equipment such as underwater robots and pipe-laying ves-
sels. Although detailed riser failure characteristics can be observed, the DIP test is ex-
tremely costly, has a long cycle time, and only very few riser manufacturers have the
strength to carry out the DIP test at present.
Pressure tank tests can simulate the wet environment of the ocean, and the cost is
only 1/5 to 1/10 of that of carrying out DIP tests. Secher et al. [145] simulated the lateral
failure characteristics of three different sizes of unbonded flexible risers, 7-inch, 9-inch,
Figure 21. Compression test arrangement for an unbonded flexible riser [22].
There is a rising trend of research on the failure of the tensile armor layer of unbonded
flexible risers, and many researchers have also investigated the failure characteristics of the
structure through different methods in recent years [148–152].
3.4. Development of Machine Learning Methods on Unbonded Flexible Risers
With the rapid development of information technology, the field of artificial intel-
ligence has achieved impressive results, and the cross-study between machine learning
methods (ML) and the traditional engineering industry has opened up a new way for solv-
ing complex engineering problems. Furthermore, a variety of data-driven algorithms, such
as neural networks and support vector machines, etc., have been proven to have strong
practical applications in marine and offshore engineering [
153
]. In the field of marine
risers, the models established by machine learning methods have been able to realize the

Materials 2024,17, 2560 24 of 34
calculation of some structural response characteristics and the prediction of riser design
parameters quickly, efficiently, and with high accuracy [
154
,
155
]. Currently, in the field
of unbonded flexible risers, researchers have used data-driven kriging-based methods
to predict the collapse pressure of spiral self-locking skeleton layer structures [
156
]. In
addition, a Bayesian inversion framework using phase field modes for type estimation
of material parameters during ductile fracture may also have future applications in the
study of unbonded flexible risers for composites. The use of machine learning methods
to solve complex engineering problems related to riser structures is a popular research
direction of common concern at home and abroad at present. However, the possibility of
using machine learning and deep learning methods to help solve marine engineering prob-
lems is still being continuously explored, and the study of the mechanical properties and
failure characteristics of the cross-section of unbonded flexible risers based on the machine
learning method will help the design of the future structure of unbonded flexible risers.
4. New Types of Unbonded Flexible Risers and Research Hotspots
The development of unbonded flexible risers in recent years has focused more on the
functionality of the structure and the need for expansion into the deep sea. Three newer
types of unbonded flexible risers are briefly described below.
4.1. Integrated Production Bundle, IPB
Technip has developed the integrated production bundle (IPB, as shown in Figure 22)
as a deep-sea dynamic riser. The IPB is a combination of a typical riser and an umbilical riser,
where the primary role of the IPB is to transfer chemicals or electricity. The IPB combines
efficient heating and temperature monitoring for safer and more flexible operation. At the
same time, the IPB, for the first time, puts gas lift and electric heating in the same riser, with
cables and isolators assembled in the form of S and Z around the core of a standard riser
with an inner diameter of 50.8 to 304.8 mm.
Materials 2024, 17, x FOR PEER REVIEW 26 of 36
Figure 22. Sketch of an IPB [14].
4.2. An Unbonded Flexible Riser with an Anti-H2S Layer
When transporting oil or gas with H2S, it can diffuse through the polymer liner, and
the diffusion mechanism is affected by temperature, H2S content, the thickness of the H2S-
resistant layer, and the permeability of the material. Affected by H2S diffusion, the selec-
tion of the pressure armor layer and tensile armor layer should consider the compatibility
of alloy steel, so it is advisable to choose the steel with high anti-H2S performance, but
possibly at the expense of its mechanical properties. To achieve the performance require-
ments of the unbonded flexible riser, it is necessary to increase the wall thickness of steel
materials to match the mechanical load, axial pressure, and water depth pressure of the
riser. The inner sheath layer is the sealing layer for the transported fluid, and over time,
water, CO2, and H2S will permeate through the inner sheath layer. An H2S-resistant layer
between the polymer liner layer and the pressure armor layer effectively blocks the diffu-
sion of H2S [23].
PEZnO is a thermoplastic polyethylene (PE) matrix composite containing a blend of
ZnO and Fe2O3. ZnO would chemically react with H2S penetrating through the inner
sheath layer, greatly reducing the penetration rate of H2S, thus improving the H2S re-
sistance of unbonded flexible risers. Fe2O3 is the initial purple material and would act as a
visual tracer for the reaction with H2S. The main reaction of the anti-H2S process is as
follows:
ZnO + H2S → ZnS + H2O. (1
)
The chemical reaction occurs within a very thin area, known as the reaction zone, and
is irreversible. The mechanism of H2S resistance in an unbonded flexible riser that incor-
porates an H2S-resistant layer is as follows: the reaction initiates on the inner surface of
the H2S-resistant layer. Over time, as H2S penetrates and diffuses, the thin reaction zone
progressively advances. ZnO on the inner surface of the H2S-resistant layer reacts with
H2S to form ZnS, marking the formation of the PEZnS region. In areas where H2S has not
yet penetrated, the ZnO remains unreacted, preserving the integrity of the H2S-resistant
layer. [12].
The advantages of using an H2S-resistant layer are as follows: (1) mass reduction: the
unbonded flexible riser has 30% less mass with the same structural dimensions, and the
H2S-resistant steel can be replaced with non-H2S-resistant steel, which improves the anti-
H2S performance of the riser, reduces the cross-sectional area of the riser, and reduces the
tensile load on the top, which is even more advantageous in ultra-deep water applications;
Figure 22. Sketch of an IPB [14].
Technip installed an IPB dynamic riser with a total length of 13,200 m and an internal
diameter of 273.05 mm, electrically heated and gas-lifted, for a total of 1350 m offshore
Angola. They also installed 2400 m of IPB dynamic risers with an internal diameter of
254 mm, electrically heated and airlifted, in the same sea area. Meanwhile, a 110 km long
riser, with an internal diameter of 152.4 mm and heated IPB, was installed at the Papa-Terra
project in Brazil. The project uses innovative distributed temperature sensors to monitor
and control the heating of the riser, which heats up the thick oil as it is being transported,
reducing the viscosity of the oil and increasing the flow rate and oil production rate.

Materials 2024,17, 2560 25 of 34
4.2. An Unbonded Flexible Riser with an Anti-H2S Layer
When transporting oil or gas with H
2
S, it can diffuse through the polymer liner, and
the diffusion mechanism is affected by temperature, H
2
S content, the thickness of the H
2
S-
resistant layer, and the permeability of the material. Affected by H
2
S diffusion, the selection
of the pressure armor layer and tensile armor layer should consider the compatibility of
alloy steel, so it is advisable to choose the steel with high anti-H
2
S performance, but possibly
at the expense of its mechanical properties. To achieve the performance requirements of
the unbonded flexible riser, it is necessary to increase the wall thickness of steel materials
to match the mechanical load, axial pressure, and water depth pressure of the riser. The
inner sheath layer is the sealing layer for the transported fluid, and over time, water, CO
2
,
and H
2
S will permeate through the inner sheath layer. An H
2
S-resistant layer between
the polymer liner layer and the pressure armor layer effectively blocks the diffusion of
H2S [23].
PEZnO is a thermoplastic polyethylene (PE) matrix composite containing a blend of
ZnO and Fe
2
O
3
. ZnO would chemically react with H
2
S penetrating through the inner
sheath layer, greatly reducing the penetration rate of H
2
S, thus improving the H
2
S resistance
of unbonded flexible risers. Fe
2
O
3
is the initial purple material and would act as a visual
tracer for the reaction with H2S. The main reaction of the anti-H2S process is as follows:
ZnO + H2S→ZnS + H2O. (1)
The chemical reaction occurs within a very thin area, known as the reaction zone,
and is irreversible. The mechanism of H
2
S resistance in an unbonded flexible riser that
incorporates an H
2
S-resistant layer is as follows: the reaction initiates on the inner surface
of the H
2
S-resistant layer. Over time, as H
2
S penetrates and diffuses, the thin reaction zone
progressively advances. ZnO on the inner surface of the H
2
S-resistant layer reacts with
H
2
S to form ZnS, marking the formation of the PEZnS region. In areas where H
2
S has not
yet penetrated, the ZnO remains unreacted, preserving the integrity of the H
2
S-resistant
layer [12].
The advantages of using an H
2
S-resistant layer are as follows: (1) mass reduction: the
unbonded flexible riser has 30% less mass with the same structural dimensions, and the
H
2
S-resistant steel can be replaced with non-H
2
S-resistant steel, which improves the anti-
H
2
S performance of the riser, reduces the cross-sectional area of the riser, and reduces the
tensile load on the top, which is even more advantageous in ultra-deep water applications;
(2) extended service life: the H
2
S-resistant riser can transport H
2
S-containing liquids with a
partial pressure of 0.1 MPa for 20 years.
The average temperature of the H
2
S-resistant layer in conventional static risers is 70
◦
C.
The focus of current research is to extend the application temperature of the H
2
S-resistant
layer (100
◦
C, 130
◦
C); thus, it can be adapted to dynamic high-temperature environments.
Direct and indirect monitoring techniques for evaluating the consumption of H
2
S-resistant
materials are also a focus of the research. The large amount of technical information
obtained by actually monitoring and collecting the results of the use of the H
2
S-resistant
layer allows for a more precise design of the H
2
S-resistant layer, thus extending the service
life of the riser.
4.3. Unbonded Flexible Risers with Composite Armor Layers
Composites usually consist of matrix material and reinforcing material (usually fibers)
and have been used for many years in the field of offshore engineering. They are usually
structured in the form of a regular cylindrical shell structure and are commonly used in
structures such as reinforced thermoplastic pipes and marine hoses [
157
,
158
]. The structural
properties of composites are more complex than those of isotropic materials and are usually
simplified to anisotropic materials for treatment and analysis.
With the development of the operating water depth of the offshore oil and gas industry
to ultra-deep water, the suspended weight and fatigue performance of risers have gradually

Materials 2024,17, 2560 26 of 34
become the dominant factors in their design [
24
,
25
]. Additionally, when the operating
water depth exceeds 2000 m, the supporting equipment, such as pipe-laying vessels and
buoyant counterweights, would be difficult to satisfy the laying demands of the traditional
steel pipelines of the traditional unbonded flexible risers. The use of composites with less
mass can be a good solution to this challenge.
Composites cannot only reduce the overall mass of unbonded flexible risers [
26
–
28
]
but they have good fatigue and corrosion resistance as well and can reduce the cost by
approximately 15% compared to conventional steel tensile armor layers under the same
conditions. Riser manufacturers such as Technip have carried out real-scale dynamic tests
in ultra-deep waters in West Africa, as well as in Brazil and the Gulf of Mexico, to verify
the feasibility of containing composite tensile armor layers.
The excellent fatigue resistance of carbon fiber composites under external loading
makes them very suitable for deep-water dynamic risers. In acidic environments containing
H
2
S, the structural layers of normal flexible risers have to be made of hydrogen sulphone-
resistant steel with lower mechanical properties. In typical acidic service conditions and
ultra-deep-water conditions, flexible risers with a steel tensile armor layer with an inner
diameter of 228.6 mm require a mass of 265 kg per meter and a top tension of 3110 kN.
The advantages of using carbon fiber as the tensile armor layer include the following:
higher strength versus the mass ratio of the carbon fibre tensile armor layer, which allows a
significant reduction of the riser mass under the same structural performance conditions,
up to 139 kg per meter of riser; improving the fatigue performance of the riser, in particular,
high strength versus the mass ratio reduces the buoyant counterweight on the top riser,
thus, only a small vessel is required for its installation and transportation, which can
reduce the costs of installing the riser system by reducing the size of the vessel. The latter
advantage that is even more evident in the installation of riser systems in ultra-deep water.
Meanwhile, the carbon fiber tensile armor layer is insensitive to H
2
S, which can reduce the
corrosion of the riser by oilfield chemicals and seawater.
Selection of the optimum fibers, resins, and manufacturing processes is the key to
creating carbon fiber tensile armor layers. Superior carbon fiber materials can have tensile
strengths in excess of 3000 MPa. The strength of carbon fiber tensile armor layers is more
than twice as strong as that of high-strength steel tensile armor layers, but only 1/5 the
mass. The corresponding comparison is presented in Table 3.
Table 3. Comparison of different tensile armor layers [16].
Material Tensile Strength/MPa Elongation/% Young’s Modulus/GPa Densities/g·cm−3
High strength steel 3.25 ≥5 210 7.8
Corrosion-resistant steel 5.00 ≥10 210 7.8
Composite 10.00 ≥1.8 160 1.7
The most significant advantage of carbon fiber tensile armor layers is the reduction in
tensile loads at the top of the riser, which offers the possibility of reducing the buoyancy
module, making it cost-effective for applications in ultra-deep water.
The material properties of composites are more complex than those of isotropic homo-
geneous materials, and the mechanical properties of the tensile armor layer of composites,
taking into account the complex spatial geometry of the tensile armor layer, are even more
complex. As a result, few corresponding studies have been carried out so far. Based on the
theoretical model of Kebadze [
60
], Liu et al. [
24
,
25
] extended the theoretical model of the
traditional homogeneous tensile armor layer to a theoretical model that can simultaneously
take into account the tensile armor layer of composites and the steel tensile armor layer
and carried out the calculation of the mechanical properties of the composite tensile armor
layer in different working conditions by establishing a numerical model with detailed
geometric properties. Consequently, the accuracy of the theoretical and numerical methods
was mutually verified.

Materials 2024,17, 2560 27 of 34
5. Research Prospect
Unbonded flexible risers are structurally complex. In recent years, industrial and
academic research interest in unbonded flexible risers has increased, and with the devel-
opment of the offshore oil and gas industry, some new technologies and materials have
been gradually introduced into the design and manufacture of unbonded flexible risers.
Expanding the application range of unbonded flexible risers is accompanied by some new
problems that need to be solved. Combining the limitations of this paper and the future
development trend of unbonded flexible risers, it is believed that in-depth research can be
carried out on the following aspects in the future:
1.
Experimental research on the cross-sectional mechanical properties of unbonded
flexible risers with composite tensile armor layers: Carrying out model tests of un-
bonded flexible risers with composite tensile armor layers is of great significance for
understanding the structural characteristics of composite tensile armor layers and
carrying out the design of unbonded flexible risers. In addition, the influence of
axisymmetric loads, such as internal and external pressures, on the bending hysteresis
effect of unbonded flexible risers is inconclusive; thus, carrying out research on the
bending characteristics of unbonded flexible risers with the action of internal and ex-
ternal pressure loads can lead to a better understanding and mastery of the hysteresis
characteristics of unbonded flexible risers.
2.
Failure characteristics of composite tensile armor layers: The failure characteristics
of composites and isotropic materials are different. Due to their special structural
form, the destructive stress in the axial and radial directions of composites differ
greatly. While focusing on the axial tensile destruction of the tensile armor layer of
the composite material, it is also necessary to be alert to their destruction under the
action of internal and external pressure loads. At the same time, the tensile armor
layer might undergo complex radial and lateral failure under axial compression. The
replacement of the original steel tensile armor layer with a composite tensile armor
layer might also have a certain impact on the failure characteristics. It is recommended
that the failure characteristics of composite tensile armor layers under axial force and
internal and external pressure loads should be studied by experimental methods and
simulated by reasonable numerical methods.
3.
Theoretical modeling of radial and lateral failure of tensile armor layers: The failure
mode of the tensile armor layer structure under axial compression is relatively com-
plex. The current theoretical model is based on the straight and curved beam theory
to solve the equilibrium equation of the helical tendon under axial compression. The
present theoretical method has made many assumptions, and the relative deviation
from the test and numerical calculation results is relatively large. It is suggested to
consider the failure path of the helical tendon reasonably under axial compression,
thus predicting the ultimate bearing capacity of the tensile armor layer under axial
compression more accurately.
4. Dynamic response of unbonded flexible risers: Due to the nonlinear bending charac-
teristics of unbonded flexible risers, their dynamic response analysis is very complex
and is mostly calculated using Orcaflex commercial software, version 11.4 (OrcaFlex—
dynamic analysis software for offshore marine systems (orcina.com)). However, the
treatment of unbonded flexible risers using Orcaflex software (version 11.4) is rela-
tively simple and cannot take into account the elongation conditions of risers, which
might have a great impact on the results of the dynamic calculations under high
tension. It is proposed to carry out the dynamic response study of unbonded flexible
risers based on the slender theory, establishing the force balance equation of un-
bonded flexible risers and the control equation considering the elongation condition.
Meanwhile, the bending nonlinearity is taken into account, and the bending stiffness
matrix of the unbonded flexible riser element is updated in real-time to carry out the
analysis of the overall dynamic response characteristics of unbonded flexible risers in
the marine environment.

Materials 2024,17, 2560 28 of 34
5.
Effect of temperature on the mechanical properties of unbonded flexible riser sections:
The material properties of the layer structure in unbonded flexible risers, especially
the polymer structure, are strongly influenced by temperature, and the effect of
temperature on the material should be taken into account to affect the cross-section
mechanical properties of unbonded flexible risers.
6.
Application of artificial intelligence and machine learning: The rise of artificial intelli-
gence (AI) and machine learning (ML) opens up a range of new avenues for solving
engineering problems, with rising applications in the field of offshore industry. AI
and ML would aid in the structural design of future unbonded flexible risers.
6. Conclusions
This paper presents the development of unbonded flexible risers on new material,
types of layers, and mechanical properties. The following conclusions have been drawn:
1.
The theoretical models of unbonded flexible risers are all established based on a large
number of strict assumptions. Considering the geometric relationship and based
on the functional principle, the load–strain relationship of unbonded flexible risers
under axisymmetric loading is basically linear. The theoretical model of unbonded
flexible risers under the bending moment is more complicated compared to that under
axisymmetric load; the helical tendons of the tensile armor layers are free to slide after
overcoming interlayer friction, resulting in a decrease in bending stiffness.
2.
The establishment of a three-dimensional numerical model of an unbonded flexible
riser under axisymmetric loading has roughly gone through development, simplifying
part of the layer structure and taking into account the detailed geometrical properties
of each layer. Additionally, due to the existence of a large number of geometrical
nonlinearities and contact nonlinearities within the numerical model, it is generally
solved by explicit algorithms. Applying axisymmetric loads to the numerical model
of the unbonded flexible riser is required before applying the bending moment to
determine the initial prestressing effect between adjacent layers.
3.
The introduction of composite materials into the manufacturing of unbonded flexible
risers is the current development trend of marine unbonded flexible risers. The
mechanical properties of unbonded flexible risers containing composites are extremely
complex, although some riser manufacturers have given verification tests of unbonded
flexible risers containing composite tensile armor layers. However, the relevant
research on the mechanical properties of the cross-section of the composite tensile
armor layer is still lacking, and carrying out the relevant research is conducive to
the breakthrough of the key technologies for the development of marine oil and
gas resources.
4.
Unbonded flexible risers technology is poised to become even more integral to the
marine industry. As deepwater exploration continues to expand, the demand for
high-performance, unbonded flexible risers will grow. The long-term vision includes
the development of unbonded flexible risers that are not only more robust and reliable
but also adaptable to various marine environments and operational demands.
In conclusion, the development of unbonded flexible risers is a dynamic field with on-
going advancements in materials science and computational modeling. The insights gained
from this study provide a solid foundation for future research and development efforts,
ultimately contributing to the advancement of marine oil and gas extraction technologies.
Author Contributions: Conceptualization, Q.L.; investigation, Q.L. and F.C.; validation, X.L. and
Z.Q.; resources, F.C. and G.W.; writing—original draft preparation, Q.L.; writing—review and editing,
Z.Q.; supervision, F.C.; project administration, F.C. and G.W.; funding acquisition, F.C. and G.W. All
authors have read and agreed to the published version of the manuscript.
Funding: This paper was funded by the National Natural Science Foundation of China (Grant No.
52102425), the Natural Science Foundation of Jiangsu Province (Grant No. BK20220500), and the
Jiangsu Funding Program for Excellent Postdoctoral Talent (Grant No. 2022ZB560).

Materials 2024,17, 2560 29 of 34
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Data are contained within the article.
Conflicts of Interest: The authors declare no conflicts of interest.
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