Experimental and numerical research on the behavior of offshore tubular member under lateral indentation

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1 INTRODUCTION
Tubular members which have a relatively large radi-
us to thickness ratio are widely used in the offshore
structures such as fixed jacket platforms and wind
turbine supporters (Yu & Amdahl 2018). Tubular
structures are exposed to risks of collision with sup-
ply vessels and impact of dropped heavy objects.
These impacts are mostly in a lateral direction to the
tubular member structures. In extreme conditions,
failure of several tubular members in collision acci-
dent may cause collapsing of the whole platform,
which will lead to catastrophic consequences, in-
cluding great economic loss, environmental pollu-
tion and human lives loss. Therefore, it is of great
importance to consider the dynamic performances of
the tubular members subjected to lateral impact dur-
ing the structural design stage.
For the methods on estimating the dynamic perfor-
mance of tubular member during lateral impact sce-
nario, there are normally four typical analyzing
methods including empirical method, experimental
method, numerical simulation and simplified analyt-
ical method. Currently, empirical method is seldom
used in the engineering practice. Experimental
methods, including full-scaled experiment and mod-
el-scale test are the most straightforward method
with the best accuracy. However, due to the high
economic cost, impact experiment of full-scale off-
shore structures can hardly be undertaken, but mod-
el-scaled tubular member impact experiments have
been conducted to investigate the dynamic perfor-
mances. Jones et al (1992) conducted an experi-
mental study on the lateral impact of fully clamped
mild steel pipe; Jones & Birch (2010) presented an
experimental research on pressurized pipelines, and
discussed the influence of the pressure load on the
response of the pipes; Guo et al (2013) presented an
experimental research on the response of pipelines
under two-point lateral indentation, and investigated
the local buckling failure of the pipe; Cho et al
(2013) present dynamic impact tests of the tubular
members under low temperature; Hu et al (2016) &
Liu et al (2016) proposed impact of fully clamped
tubular member and clamped offshore T-joint struc-
ture. Rong et al (2018) proposed systematic experi-
mental study on the response of the pipes under im-
pact of conical, hemispherical, and cylindrical
indenter.
Besides, numerical simulation method has been
popularly used in the past decade. For a specific giv-
en structural details, the numerical simulation meth-
od has shown powerful capability to acquire struc-
tural performance of offshore structures in the
impact scenarios. Travanca & Hao (2014) presented
numerical simulation of response of a tubular mem-
ber; Sourne et al (2015) & Bela et al (2017) present-
ed numerical simulation of responses of the total
offshore platform under impact; Travanca & Hao
(2015), Yu & Amdahl (2018) presented numerical
simulation of ship-platform interaction.
In the present research, a quasi-static experiment of
clamped tubular structures subjected to lateral inden-
Experimental and numerical research on the behavior of offshore tubular
member under lateral indentation
Yu Rong, Hua Yuan, Jingxi Liu & Weiguang Liu
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology,
Wuhan 430074, China
Wei Luo
China Ship Development and Design Centre, Wuhan 430064, China
Zhiqiang Hu
School of Engineering, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK
ABSTRACT: A combined experimental and numerical research is performed in this paper to identify the me-
chanical performances of the clamped offshore tubular structure subjected to lateral indentation. Quasi-static
lateral indentation experiments of the tubular structural members are performed, load carrying capability, de-
formation mode and failure mode are discussed. A numerical simulation method has been performed by
ABAQUS analysis package, and good agreements have been achieved between the numerical results and the
experimental results. Serial numerical simulations have been carried out, with consideration of the span of the
tubular members, width of the indenter and indenting location. Numerical results show that centric indenta-
tion with a wedge indenter would cause the largest permanent lateral displacement. The present method pro-
vide thorough insight into the global performance of the tubular structures subjected to lateral indentation,
and would be used in rapid prediction during the design stage of the offshore structures.

tation has been conducted firstly. Then a numerical
simulation has been conducted, and the correctness
is verified in terms of force-displacement relation-
ship, deformation mode and failure mode. The next
step is to analyze the influential parameters by nu-
merical simulation, influence of the tubular span, the
indenter width and indenting location on the me-
chanical behavior of tubular structure are presented.
2 EXPERIMENTAL METHODOLOGY
2.1 Specimens
The tubular specimen with a diameter of 159mm and
a shell thickness of 5mm, was fabricated by hot-
rolled seamless mild steel tube, and two square
plates with a width of 230mm and a thickness of
20mm are welded at the end, as shown in Fig. 1.
Material properties of mild steel were obtained by
quasi-static tensile test with a loading velocity of
2mm/min. The nominal and true stress-strain curves
are shown in Fig. 2. In the true curve, until necking,
the true stress
σ
t and strain
ε
t were expressed by
nominal stress
σ
e and nominal strain
ε
e:
(1 )
ln(1 )
te e
te








 (1)
The true stress-strain curve beyond necking was rep-
resented by (Villavicencio & Soares, 2004):
ln(1 )
(/)
1 / (0.24 0.01395 )
n
tt
g
n
m
m
C
nA
CRen
Ag R








(2)
Where Rm is the maximum nominal stress, e is the
natural constant; C, Ag and n are all intermediate
variables.
2.2 Experimental set-up
The experimental set-up consists of clamps, hydrau-
lic jack, draw-wire position sensor, piezoelectric
force transducer and the indenter, as shown in Fig. 3.
The tubular specimen was fixed by circumferentially
arranged M26 (diameter 26mm) bolts at each clamp,
as shown in Fig. 3b. The two clamps were bolted to
the rigid base.
A flat indenter with a width of 80mm, and a wedge
indenter with an angle of 60o were designed to simu-
late shapes of different striking objects, as shown in
Fig. 4. The indenter located at mid-span of the tubu-
lar specimen is driven by the hydraulic jack, and
moves upward with a velocity of 1.25 mm/s.
The indentation force and displacement were meas-
ured during the test process. A piezoelectric force
transducer was mounted between the indenter and
the hydraulic jack to measure the indentation force,
a draw-wire position sensor was connected to the in-
denter to measure total lateral displacement of the
indenter. Both the force transducer and the position
sensor are working with a sampling frequency of
50Hz.
Φ159
230
8×Φ26
A
A
A-A
5
20
2301200
(a)
(b)
Fig. 1 The tubular specimen: (a) geometric configurations; (b)
photograph (unit: mm)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
0
100
200
300
400
500
600
E=205 GPa
σ
s
=305 MPa
Stress (MPa)
Strain
Nominal stress-strain
True stress-strain until necking
True stress-strain beyond necking
Fig. 2 Mechanical properties of the mild steel
3 NUMERICAL ANALYSIS
3.1 FEM modeling
The lateral indentation is simulated in the ABAQUS
package to further investigate the response of the
tubular members. The FEM model is consists of the
indenter and the specimen, as shown in Fig. 5. Geo-
metric configurations of the numerical models are
the same as these in the experimental tests.
The tubular specimen, both the tube and the plates at
the support were modelled by S4R elements (4-
node, doubly curved shell, reduced integration ele-
ments). During the analysis process, an automatic
surface-to-surface contact is employed between the
potential contact surfaces. Friction coefficient value
is set to 0.3. The specimen is constrained in all di-
rections at the support. The indenter is modeled as a
rigid body by using a rigid constraint. The move-
ment of the indenter is restrained in all directions
except the translational degree of freedom in the ver-
tical direction, and the indentation would be defined
by specifying a forced displacement.

1
2
342
5
78
6
(a)
(b)
5
7
8
6
Fig. 3 Experimental set-up: (a) Photograph of the experimental
set-up; (b) Setting of the lateral indentation and data acquisi-
tion system. (1- rigid ground; 2- clamp; 3- bolt; 4- tubular
specimen; 5-hydraulic jack; 6- draw-wire position sensor; 7-
piezoelectric force transducer; 8-indenter)
70mm
60°
(a)
70mm
(b)
Fig. 4 Geometric configurations of the two indenters: (a)
wedge indenter; (b) flat indenter
Fig. 5 FE model of the indentation
3.2 Validation of numerical analysis
The permanent deformation of the tubular specimens
conducted by experiment and numerical simulation
are presented in Fig. 6 and Fig. 7, which clearly
show that the deformation mode of the specimens
are combination of local denting and global beam
deformation. The tubular specimens dented obvious-
ly in the indentation area, while cross section of the
tubular specimens remained circular in the area far
away from the indentation area. Typical lateral glob-
al beam deformation occurred, the tubular specimen
presented a permanent V-shaped deformation. Due
to large lateral deformation at the mid-span, the tub-
ular specimen trend to axial membrane stretching,
and ductile rupture occurred at the front side of the
specimen at the support, while the remains intact.
Lateral force- displacement curves are shown in Fig.
8. In the beginning, the tubular shells in the indenta-
tion area dented, the indentation force grew up rap-
idly with the raising of the displacement. As soon as
the indentation raised to a threshold value, the tubu-
lar specimen began to form global beam defor-
mation, and the indentation force grew up continu-
ously with a smaller slope. At the last stage, the
indentation force dropped down rapidly as soon as
failure occurred at the support.
Fig. 6 comparison of the permanent deformation mode and
failure subjected to wedge indenter
Fig. 7 comparison of the permanent deformation mode and
failure subjected to flat indenter
It is obviously shown in Fig. 8 that the indenter
shape has a significant influence on the mechanical
behavior of the tubular specimen under lateral in-
dentation. Indentation force generated by the flat in-
denter is about 10%-15% larger than the indentation
force generated by the wedge indenter at the same
lateral indentation depth. The main reason is that the
flat indenter lead to a larger denting area, and ab-
sorbed more energy during the indentation process.

Whether the deformation/failure mode or the force-
displacement curves, the numerical simulation re-
sults match well with the experimental results,
which obviously show the correctness of the numer-
ical method.
0 50 100 150
0
50
100
150
200
250
300
Force (kN)
Displacement (mm)
FEM
Experimental
Wedge indenter
0 50 100 150
0
50
100
150
200
250
300
Flat indenter
Force (kN)
Displacement (mm)
FEM
Experimental
Fig. 8 comparison of the force-displacement curves with dif-
ferent indenter shapes
4 ANALYSIS OF INFLUENTIAL
PARAMETERS
In order to understand the influence of different pa-
rameters on the responses of the tubular structures
subjected to lateral indentation, three configurations
of the indentation are compared that are given by:
Case 1, mechanical behaviors of tubular members
with different spans under lateral indentation of
wedge indenter; Case 2, mechanical behaviors of
tubular members with a span of 1800mm indented
by indenters with different width; Case 3, mechani-
cal behaviors of eccentric lateral indentation of the
tubular specimen with a span of 1800mm.
4.1 Influence of the span
To investigate influence of the spans on the mechan-
ical responses, responses four tubular members with
spans of 1200mm, 1500mm, 18000 and 2500mm are
simulated, respectively. The final deformations are
presented in Fig. 9, the four tubular members pre-
sented combination of V-shaped global deformation
and local denting, and suffered ductile fracture on
the front-side of the cross section at the support.
The force- displacement curve raises slower with the
increase of the span, threshold value of force and
displacement until fracture raised with the increase
of the span, as shown in Fig. 10. As the span in-
creases from 1200mm to 2500mm, the threshold
force increases from 280kN to 350kN, and threshold
lateral displacement increases rapidly from 150mm
to 360mm. The main reason is that the global beam
deformation stiffness increased with decreasing of
the span. For the tubular members with a lower span,
lateral force raised faster and the tubular member
suffered a premature fracture at the support.
Recently, Cerik et al (2016) suggested an indicator
P0/Pc to classify the impact responses of tubular
members:








00
22
2
0
4/
(3 6 4 )
3( )
s
s
PML
DDttDt
MDt
Dt
(3)






0
2
0
/
/4
c
s
PmDt
mt
(4)
Where P0 represents the load of a slender beam un-
der lateral indentation once the three-hinge bending
begins to form, Pc represents characteristic load for
local denting of the tubular member; M0 is the ulti-
mate plastic bending moment of cross section of the
tube, m0 is the fully plastic bending moment of the
shell of the tube at a unit width, L is the half length
of the span, D is the diameter of the tube, t is the
thickness of the shell of the tube, and
σ
s is the yield
stress of the material. Tubular member with the indi-
cator 10<P0/Pc<23 presents a perfect deformation
with combination of local denting and global beam
deformation. In the present numerical research, a
tubular with a span of 1800mm has an indicator
P0/Pc of 15.94 is an ideal model, hence the tubular
member with a span of 1800mm has been adopted in
Case 2 and Case 3.
(a) Span- 1200mm
(b) Span- 1500mm
(c) Span- 1800mm
(d) Span- 2500mm
Fig. 9 Permanent deformation of the tubular members with dif-
ferent spans

0 50 100 150 200 250 300 350
0
50
100
150
200
250
300
350
Force (kN)
Displacement (mm)
Span: 1200mm
Span: 1500mm
Span: 1800mm
Span: 2500mm
Fig. 10 Force- displacement curves of the tubular members
with different spans
4.2 Influence of the indenter width
Four types of indenter, including wedge indenter,
flat indenters with width of 80mm, 160mm, and
240mm are considered.
The permanent deformation of the tubular members
subjected to different indenters are listed in Fig. 11.
Deformation mode of the tubular members are com-
bination of local denting and global beam defor-
mation, and ductile fracture occurred on the front
side of the cross section at the support. The tube
shell dented at the indentation area, and ductile frac-
ture occurred at the support.
As the width of the indenter increases from 0 mm to
240 mm, the slope of the force- displacement curve
gradually increases, as shown in Fig. 12. Threshold
force decreases from 340kN to 290kN, threshold
displacement decreases from 240mm to 165mm.
The denting area increases with the width increases,
hence the reaction force increases due to larger en-
ergy absorption of local denting. The increase in the
width of the indenter is equivalent to the reduction
of the span of the tubular member, so the threshold
force and displacement till fracture are correspond-
ingly reduced.
4.3 Influence of the impacting location
Tubular member with a span of 1800mm under ec-
centric indentation of a wedge indenter have been
conducted. The indenter collide the tube at the mid-
span, 3/8 span, quart span and 1/8 span, respectively,
permanent deformation are shown in Fig. 13. For
eccentric indentation, ductile fracture occurs at the
support which get closer to the indenter.
The force displacement curves are presented in Fig.
14. The four curves tend to be consistent when the
displacement is less than 30mm, due to local dent-
ing. For the specimen under indentation at 1/8 span,
a global beam deformation does not formed. As the
indenter approaches the support, the threshold force
and displacement drop sharply.
(a) Wedge indenter
(b) Indenter width- 80mm
(c) Indenter width- 160mm
(d) Indenter width- 240mm
Fig. 11 Permanent deformation of the tubular members sub-
jected to indentation of different indenters
0 50 100 150 200 250
0
50
100
150
200
250
300
350
Force (kN)
Displacement (mm)
0 mm
80mm
160mm
240mm
indenter width
Fig. 12 Force- displacement curves of the tubular members
subjected to indentation of different indenters
1/2 span
3/8 span
1/4 span
1/8 span
Fig. 13 Permanent deformation for eccentric indentation

0 50 100 150 200 250
0
50
100
150
200
250
300
350
Force (kN)
Displacement (mm)
1/8 span
1/4 span
3/8 span
1/2 span
Fig. 14 Force- displacement curves for eccentric indentation
4.4 Discussion
A fully clamped tubular structure with a longer span
is more likely to get a larger permanent lateral dis-
placement under the same lateral impact load or the
same impact energy.
A tubular structure has the lowest load carrying ca-
pability and energy absorption capability subjected
to a concentrated load.
The closer the indentation area to the mid span of
the tubular structure, the easier it is to cause damage
and deformation.
5 CONCLUSION
Experimental investigations of fully clamped tubular
specimens under quasi-static indentation of wedge
indenter and flat indenter are conducted, the defor-
mation mode is a combination of local shell denting
and global beam deformation. FE method is estab-
lished and the numerical results are verified by ex-
periment results.
Serial numerical simulations of the collision scenar-
ios between the tubular structures and the indenters,
which are of different tubular spans, different in-
denter width, and eccentric indentation. Numerical
results show that centric indentation with a wedge
indenter would cause the largest permanent lateral
displacement.
The present method provide thorough insight into
the global performance of the tubular structures sub-
jected to lateral indentation, and would be used in
rapid prediction during the design stage of the off-
shore structures.
ACKNOWLEDGEMENTS
Authors acknowledge financial support from the Na-
tional Natural Science Foundation of China (Grant
No. 51579110), and the Natural Science Foundation
of Hubei Province (Grant No. 2018CFB569).
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