Content uploaded by Yi Min Xie
Author content
All content in this area was uploaded by Yi Min Xie on Sep 24, 2023
Content may be subject to copyright.
Engineering Structures 296 (2023) 116907
0141-0296/© 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Impact behaviour of tunnel lining assembled from non-planar interlocking
steel bre reinforced concrete bricks
Wenzheng Xu
a
,
b
, Xiaoshan Lin
b
,
*
, Pengda Li
a
, Yu-Fei Wu
a
,
c
, Yi Min Xie
b
a
Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, Shenzhen University, Shenzhen 518060, China
b
Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne 3000, Australia
c
School of Engineering, RMIT University, Melbourne 3000, Australia
ARTICLE INFO
Keywords:
Non-planar interlocking element
Tunnel
Fibre reinforced concrete
Impact test
ABSTRACT
In this study, a new design of tunnel lining assembled from non-planar interlocking segments was developed and
tested. The new tunnel segment is made of steel bre reinforced concrete (SFRC), and it has six symmetrical side
surfaces with a concave-convex topology, which can prevent the movement of each element in the interlocked
tunnel. A series of lab-scale drop weight tests were conducted to investigate the performance of the interlocking
SFRC tunnel specimen under impact. A special aluminium mould was designed to cast the developed tunnel
segments, and a novel testing frame was developed to allow the drop hammer to hit on the inner surface of the
tunnel specimen. The peak impact force, the displacement of the drop hammer and the failure pattern of the
interlocking SFRC brick were measured and analysed, considering the inuences of hammer dropping height and
conning load on the dynamic behaviour of the interlocking SFRC tunnel specimen.
1. Introduction
Underground tunnels are the key to the growth of transport system in
modern society. With the development of technology, precast tunnel
segments have been widely used in recent tunnelling projects, as it can
provide a cost effective and environmentally friendly solution [1,2].
Precast concrete tunnel linings usually have a design life of 100 years
[3]. During their operation, tunnel structures may be exposed to a va-
riety of hazardous environments that may affect their service life. For
instance, segmental joint opening during tunnel operation is one of the
major concerns, which would affect the functionality and serviceability
of tunnel lining. Also, concrete cracking and the corrosion of steel
reinforcement due to de-icing salt and chlorides in underground water
are common hazards encountered, which can signicantly affect the
durability and structural integrity of tunnel linings [4].
In recent years, bre reinforced concrete (FRC) has been increasingly
applied in the fabrication of tunnel segments. With the addition of
reinforcing bres, concrete cracks and steel corrosion can be effectively
mitigated [5–9]. Extensive research has been conducted to investigate
the structural performance of FRC segments [10–14]. For example, to
assess the load-bearing capacity of FRC segments under possible bending
during demoulding and transport phases, Caratelli et al. [15] conducted
full-scale exural test on FRC segments reinforced with steel bres.
Caratelli et al. [16] also carried out a series of point load tests on FRC
segments to imitate the high compression stress from the actuator of
tunnel boring machine (TBM) during construction phase, and they found
that the FRC segments behaved similarly to those reinforced with con-
ventional steel reinforcement. Besides, the structural performance of
FRC segments subjected to a combination of bending and axial forces
was tested by Meng et al. [17], and they found that the cracking resis-
tance and toughness of precast tunnel segments could be improved by
introducing steel bres in concrete. During the service life of tunnel
linings, they may experience accidental loading scenarios, such as the
impacts from moving vehicles and derailed trains, which may result in
signicant damage to tunnel segments and joints, leading to water
leakage, lining failure and structural instability [18]. However, no study
has been reported in literature on the dynamic response of FRC tunnel
linings under impact load. For precast tunnel segment with conventional
steel reinforcement, the dynamic response of shield tunnel under the
impact of derailed train was investigated by Yan et al. [19]. A 3D nite
element model was created in their study with the consideration of the
effects of the number of carriages, impact velocity and impact angle. Yan
et al. [20] conducted an extended nite element analysis to determine
the cracking and failure characteristics of conventional steel reinforced
* Corresponding author.
E-mail address: susanna.lin@rmit.edu.au (X. Lin).
Contents lists available at ScienceDirect
Engineering Structures
journal homepage: www.elsevier.com/locate/engstruct
https://doi.org/10.1016/j.engstruct.2023.116907
Received 21 March 2023; Received in revised form 6 September 2023; Accepted 17 September 2023
Engineering Structures 296 (2023) 116907
2
concrete tunnel linings under the impact of a derailed high-speed train.
More recently, a train-lining-rock model was proposed by Yan et al. [21]
for concrete tunnel lining with conventional steel reinforcement. It was
found that the train absorbed most of the impact energy through plastic
deformation, and the tensile damage was much worse than the
compressive damage in the tunnel segments. At present, the studies on
the dynamic behaviour of tunnel linings are very few. In particular, the
experimental investigation, which is complex and time and effort
consuming, is lacking. Furthermore, to the best of the authors’ knowl-
edge, the study on the dynamic performance of FRC tunnel lining is
currently not available. Therefore, it is imperative to investigate the
impact behaviour of FRC tunnel lining and optimise the FRC segment
design to enhance the impact resistance of tunnel structure.
Topological interlocking is a powerful technique for developing
materials and structures [22]. The concept of topological interlocking is
to replace traditional monolithic structures with assemblies of a number
of interlocking elements without any binder or connector [23,24]. These
elements, by virtue of their special shape and arrangement, are kept in
place by kinematic constraints. To date, experimental and numerical
studies have been conducted to investigate the structural behaviour of
assemblies with interlocking features, and they have been found to have
many benecial characteristics, including high energy absorption ca-
pacity, high impact resistance, good tolerance to the absence of failure
blocks, and excellent resistance to fracture propagation [25–28]. For
example, the interlocking ceramic panels assembled by platonic bricks
with 14 different designs and one monolithic panel were tested by
Mirkhalaf et al. [29] under both quasi-static and impact loads, and the
interlocking octahedral panel was found to be much tougher and
stronger than the other designs. The structural behaviour of an assembly
of osteomorphic blocks developed by Dyskin et al. [30] was investigated
through indentation tests by Autruffe et al. [31]. A different interlocking
block was proposed by Rezaee Javan et al. [32], in which all side sur-
faces were curved, and the patterns on top and bottom surfaces of the
assembly plate were the same. Later, they performed numerical study
and found that the plate assembled by this kind of bricks showed less
deection while absorbed more energy than the ostemorphic assembly
plate under impact [33].
So far, most of the reported studies have been focused on the as-
sembly of planar elements, and very limited research has been con-
ducted on the design of non-planar elements [34]. Recently, the authors
proposed a novel design of non-planar interlocking element for tubular
structures, and the dynamic response of a tunnel structure assembled by
the new elements was numerically investigated [35]. Compared to
monolithic tunnel and the tunnel consisted of normal segments, the
interlocking assembly tunnel showed higher energy absorption capacity
and smaller damage area and joint opening. Therefore, it is promising to
apply interlocking design in tunnel linings, and more comprehensive
and in-depth studies are required to provide reliable references for
structural design.
In this paper, the impact behaviour of a new tunnel structure
assembled from non-planar interlocking elements is investigated
through impact test. Steel bre reinforced concrete (SFRC) has been
employed to fabricate the interlocking bricks, which could not only
provide excellent strength, toughness and crack control ability, but also
strengthen the edges of the non-planar interlocking bricks. Also, the
fabrication process has been simplied without the use of traditional
steel reinforcing cage. In addition, a customised aluminium mould was
designed in this study to cast the non-planar interlocking bricks. To
simulate the impacts from train derailment and car collision, the non-
planar interlocking SFRC bricks were assembled and tted into a
specially designed steel frame to allow drop hammer to hit the inner
surface of the tunnel specimen. The impact force, the displacement of
the drop hammer and the failure patterns of the interlocking SFRC bricks
have been obtained and analysed to highlight the potential benet of the
developed interlocking tunnel segment in improving the impact resis-
tance of tunnel lining structure.
2. Design and fabrication of tunnel specimen assembled with
non-planar interlocking elements
2.1. SFRC mix design
The SFRC mix design and the characteristics of steel bres used in
this study are shown in Tables 1 and 2, respectively. Six SFRC cylinders
(100 mm diameter ×200 mm height) were fabricated, and the
compressive strength and splitting tensile strength were tested accord-
ing to AS 1012.9 [36] and AS 1012.10 [37], respectively. The average
compressive strength and splitting tensile strength obtained from the
experimental tests were 100.4 MPa and 9.5 MPa respectively.
2.2. Tunnel specimen design
In the authors’ previous study [35], a non-planar interlocking
element was proposed for tubular shape structures. As shown in Fig. 1
(a), the new element had a symmetrical geometry with six curved side
surfaces that could be interlocked with adjacent elements. By assem-
bling a number of elements, a tubular structure could be formed with
identical patterns on both internal and external surfaces [Fig. 1 (b)]. The
curved side surfaces created a unique interlocking mechanism that re-
stricts movement in all directions. This feature stood in contrast to the
at side surfaces commonly seen in traditional tunnel segment designs,
which often failed to effectively control the displacement of the hex-
agonal segment in the radial direction of the tunnel. The proposed
design of the interlocking segments ensured that the assembly remains
stable and functional, even in the event of segment damage or absence.
Additionally, the interlocking interface in the proposed design could
potentially enhance the sealing of tunnel structure, addressing the
prevalent problem of gap opening over successive rings. In the present
study, a lab-scale tunnel specimen was designed to have a length of 675
mm, an external diameter of 744 mm and a thickness of 50 mm [Fig. 1
(b)]. The tunnel specimen consisted of ve rings, including three rings of
full bricks (in the middle) and two rings of half bricks (at both ends).
Each ring was assembled by 12 bricks. Therefore, 48 interlocking bricks
with an arc length of 194.78 mm and a thickness of 50 mm were
fabricated to form one specimen, of which 12 full bricks were cut into a
half.
It was found from previous study [35] that the interlocking elements
were susceptible to damage at the edges near the concave and convex
curved surfaces. In this study, SFRC was employed to improve the shear
resistance of the edges of the interlocking bricks. Moreover, as the
interlocking bricks have irregular geometry, it is difcult to apply con-
ventional steel reinforcement. By using SFRC, the construction process
can be signicantly simplied. In addition, an enhanced impact resis-
tance is expected to be obtained for the interlocking tunnel specimen
made of SFRC due to its featured bre bridging effect, excellent energy
absorption capacity and high strength and toughness [38–41].
2.3. Fabrication of novel non-planar interlocking bricks
To fabricate the non-planar interlocking bricks for assembling the
tunnel specimen, aluminium casting moulds were specially designed in
this study, as shown in Fig. 2 (a). The main body of the mould consisted
of two side bafes whose inner surfaces matched the side surfaces of the
non-planar interlocking element. The two side bafes were supported by
an aluminium block with a curved top surface and covered by a lid
connected by bolts to form the bottom and top surfaces of the designed
Table 1
SFRC mix design.
SFRC mixture composition (kg/m
3
)
Cement Slag Silica fume Sand Water Superplasticizer Steel bre
457 315 262 1049 224 21 80
W. Xu et al.
Engineering Structures 296 (2023) 116907
3
interlocking element. During the casting process, the concrete mixture
was poured into the mould through the centre hole on the lid [Fig. 2 (b)].
Demoulding was performed 48 h after casting. The obtained non-planar
interlocking brick is shown in Fig. 2 (c).
3. Impact test program
3.1. Impact test setup and instrumentation
To investigate the impact behaviour of the interlocking SFRC tunnel,
a lab-scale drop weight test was performed. A special specimen frame
and a supporting frame were designed in this study for the impact test, as
shown in Fig. 3. The specimen frame was employed to hold the tunnel
specimen in place and restrict its movement along the longitudinal axis.
The specimen frame consisted of a bottom frame, a middle frame and a
top frame. A 6 mm thick steel tube with an inner diameter of 974 mm
was welded to a circular steel piece with an inner diameter of 664 mm to
form the bottom frame. A 115 mm gap was created between the tunnel
specimen and its frame so that customised rubber blocks could be placed
in the gap to support the interlocking assembly tunnel. The top frame
consisted of the same steel tube and circular steel piece, but they were
separated. By doing so, the distance between the top and the bottom
could be adjusted through the steel threaded rod to match the length of
the tunnel specimen. The middle part of the specimen frame was
partially strengthened by ribs, and it was connected to the supporting
frame through pin connections, which held the specimen frame at a 45-
degree angle to the horizontal plane (Fig. 3). The supporting frame was
xed on the platform, thereby eliminating any possibility of rigid
movement for the frames. Besides, in this test, the drop hammer was
designed to have a length of 750 mm and a hemispherical hammerhead
with 100 mm diameter, and it was set to freely fall along the guide
columns. The horizontal displacement of the hammer was not
completely restrained, as there was a small gap of approximately 3 mm
between the guide columns and the hammer. With this unique test setup
and hammer design, the inner surface of the tunnel specimen could be
impacted by the hammerhead to mimic the impact from uncontrolled
car or derailed train in a tunnel.
To construct the tunnel specimen, the half bricks on the bottom layer
were rstly assembled and preloaded with steel strip hoop by fastening
the bolt connection (Fig. 4). Different levels of conning load could be
generated by applying various torques on the bolts, so that an almost
uniform pressure could be exerted on the surface of the tunnel specimen.
The gap between the specimen and the steel frame was lled with cus-
tomised rubber blocks to support the specimen and maintain the
conning load on its outer surface. After that, the tunnel specimen was
assembled layer by layer following the same procedure.
In addition, for the area subjected to direct impact, two types of
centre brick (centre brick-A and centre brick-B) were tested to examine
the effect of contact angle on the impact process. Centre brick-A repre-
sented the original interlocking brick as shown in Fig. 2 (c) and Fig. 5
(a). As the tunnel specimen was inclined at 45◦, the hammerhead might
have slipped along the inclined surface when it hit the specimen and
damage the impact machine. To avoid the slippage of hammerhead and
ensure the accuracy of the tests, centre brick-B was designed, as shown
in Fig. 5 (b). As can be seen, in centre brick-B, a shallow groove (10 mm)
was created. A steel block was then attached to the brick so that the
contact area was perpendicular to the impact angle and the slippage of
the hammerhead could be prevented. In real-world scenarios, a tunnel
may be subjected to various types of impact, for instance, from a
derailed train or an errant vehicle. They are often applied as a distrib-
uted load over a certain contact area. The design of centre brick-B better
represented the surface impact.
In this experiment, the interlocking assembly tunnel specimen was
conned by eight equally spaced steel strip hoops (Fig. 4). The same
torque was applied to all strip hoops using a torque wrench to generate
conning load. Two strain gauges (Fig. 4), with a length of 20 mm, were
installed on each steel strip hoop at 180-degree apart to measure the
hoop strains and monitor the applied conning load.
During the test, the drop hammer freely fell from different heights to
impact the specimen. The impact force signals were measured by a load
Table 2
Steel bre characteristics.
Length
(mm)
Diameter
(mm)
Tensile strength
(MPa)
Modulus of elasticity
(MPa)
15 0.3 800 206,000
Fig. 1. Non-planar interlocking element and tunnel specimen: (a) a new non-planar interlocking element, and (b) design of tunnel specimen.
W. Xu et al.
Engineering Structures 296 (2023) 116907
4
cell mounted at the neck of the hammer and were collected by a data
acquisition system (Fig. 3). A high-speed camera was used to record the
impact process with a frame rate of 960 fps, including the deformation
and failure mode of the specimen. The high-speed camera was placed in
front of the specimen at 1 m distance (Fig. 3), focusing on the central
area of the specimen at an angle of 45-degree to the horizontal plane.
The displacement of the hammerhead could be obtained by processing
the images taken by the high-speed camera.
3.2. Impact test
To study the impact response of the developed interlocking SFRC
tunnel, the specimen was tested under combined conning load and
impact load. The effects of initial impact velocity and the level of
connement on the impact performance of the interlocking SFRC tunnel
were investigated. To generate different levels of connement, two
different torques, i.e., 2.5 Nm and 5 Nm, were applied to pre-tighten the
steel strip hoops. The hammer was dropped from 0.15 m and 0.25 m
Fig. 2. Fabrication of non-planar interlocking SFRC brick: (a) specially designed casting mould, (b) casting interlocking SFRC brick and (c) nal non-planar
interlocking brick.
Fig. 3. Impact test setup.
W. Xu et al.
Engineering Structures 296 (2023) 116907
5
Fig. 4. Fabrication of interlocking tunnel specimen.
Fig. 5. Tunnel specimen with (a) centre brick-A and (b) centre brick-B.
W. Xu et al.
Engineering Structures 296 (2023) 116907
6
heights, resulting in initial impact velocities of 1.72 m/s and 2.21 m/s,
respectively. Table 3 summarises the loading cases employed in this
study. The interlocking tunnel specimens with centre brick-A and centre
brick-B under different loading conditions were named IAT-A-Number
and IAT-B-Number, respectively. The peak impact force and the dam-
age distribution of the interlocking SFRC tunnel were investigated. In
addition, the displacement of the drop hammer was recorded to evaluate
the deformation at the contact area of the tunnel specimen.
4. Results and discussion
4.1. Displacement history of drop hammer
Fig. 6 (a) shows the displacement histories of the drop hammer ob-
tained for IAT-A-1 and IAT-A-2, which were recorded from the moment
when the hammerhead came into contact with the specimen. As can be
seen, the hammer moved rapidly when the impact took place, and then it
rebounded at about 10 ms after impact. After that, the hammer moved
downwards again to its maximum displacement. It should be noted that
the rise in displacement over a short period (10 ms−25 ms) during
impact was not caused by the bouncing up of the hammerhead but the
slippage of the hammerhead along the inclined surface of the specimen.
For example, when the hammer was dropped from 0.25 m (IAT-A-2), the
initial position of the hammerhead in contact with the specimen was
marked by a yellow dot as shown in Fig. 6 (a). However, the hammer-
head slipped along the inclined surface and moved away from the yellow
dot as shown in the gure at 25 ms. Thus, the projected displacement of
the hammerhead in vertical direction appeared to be increased. When
the dropping height of the hammer was 0.15 m (IAT-A-1), the slippage of
the hammerhead was relatively small, thus the inuence on the
displacement values was reduced. The slippage of the hammerhead
during impact highlighted the signicance of the impact angle in the
performance of interlocking assembly tunnels. These ndings offer
valuable insights for optimising the design and enhancing the perfor-
mance of such structures. Besides, by comparing the displacement
curves for IAT-A-1 and IAT-A-2, the maximum displacement of the
hammer increased from 17.4 mm to 20.3 mm when the dropping height
was increased from 0.15 m to 0.25 m. With the increase of the dropping
height, the initial impact velocity increased, which resulted in higher
incident impact energy, larger maximum hammer displacement and
more signicant hammerhead slippage.
Fig. 6 (b) describes the hammerhead displacements obtained for the
specimens with centre brick-B (IAT-B-1, IAT-B-2 and IAT-B-3) subjected
to different initial impact velocities and conning loads. Since a steel
block was introduced in centre brick-B, the impact angle was vertical,
thus no slippage was observed in the experiment. Compared to the
hammer displacement obtained for IAT-A-1, although both conning
load and dropping height were the same, a signicant bounce of the
hammerhead could be observed for IAT-B-1, and a greater maximum
displacement of 19.9 mm was recorded. Similarly, when the hammer
height was lifted from 0.15 m to 0.25 m, the maximum displacement
obtained for specimen IAT-B-2 was 36.2 mm, which was approximately
78% larger than that of IAT-A-2. The test results suggested that the at
surface of the steel block promoted a more direct and efcient trans-
mission of impact energy, thereby resulting in larger displacement.
Slippage could be avoided through the vertical impact angle, max-
imising the amount of energy transferred to the tunnel specimen. In
addition, it can be seen that when the conning load changed from 2.5
Nm (IAT-B-2) to 5 Nm (IAT-B-3), the maximum displacement was
reduced to 33.1 mm, and it was attained at a later time (43.7 ms for IAT-
B-2, and 61.4 ms for IAT-B-3). This was because the increased conning
load brought the interlocking bricks closer, leading to improved friction
and interlocking effect. The decrease in displacement and delay in
obtaining the maximum displacement under increased conning load
suggest that the stability and impact resistance of the assembly may be
modulated by adjusting this parameter.
Based on the above comparison, it can be concluded that a more
signicant hammer displacement will be obtained for the tunnel spec-
imen with centre brick-B when the working conditions are the same, as
the impact force could be better transferred to the specimen without
slippage. Also, the conning load has a noticeable inuence on the
interlocking effect and the impact response of the SFRC tunnel
specimen.
4.2. Peak impact force
Fig. 7 compares the peak impact forces obtained for all ve speci-
mens with different dropping heights and conning loads. It should be
noted that the impact force data collected from the tests differ from the
contact force between the hammerhead and the centre brick of the
interlocking tunnel, as the load cell was placed at the neck of the
hammer with a distance of about 800 mm. As shown in this gure, the
peak impact forces for the tunnel specimens with centre brick-A and
centre brick-B increased with the hammer dropping height from 0.15 m
to 0.25 m. For example, compared to IAT-A-1 (65.1 kN), there was a 15.1
% rise in the maximum impact force of IAT-A-2 (74.9 kN). In addition,
under the same loading condition, the test specimens with centre brick-B
exhibited a higher peak impact forces than those with centre brick-A, as
the forces could be fully transferred to the specimens with centre brick-B
when the hammerhead slippage was prevented. Specically, the peak
impact forces of IAT-B-1 and IAT-B-2 were 87.8 kN and 109.8 kN, which
were 34.8% and 46.6% higher than those of IAT-A-1 and IAT-A-2,
respectively. The introduction of the steel block altered the impact
angle, and hence increased the peak impact forces. In addition,
compared to IAT-B-2, the peak impact force of IAT-B-3 climbed to 112
kN when the conning load (applied torque) doubled from 2.5 Nm to 5
Nm. The reason for the higher maximum impact force may be due to the
fact that the growing conning load would cause increased stiffness,
thereby generating a larger impact force. This nding demonstrates the
signicance of optimising conning load to achieve desired impact
resistance of interlocking tunnel structures.
In general, the interlocking tunnel specimens with centre brick-B
showed higher peak impact forces than those subjected to direct
impact on the concrete surface when the loading conditions were
identical. In addition, the increase in dropping height and conning load
could lead to a larger impact force. Since the number of lab-scale
specimens was limited in this study, the inuence of the conning
load on the impact force shall be examined further through more
experimental tests and numerical simulations.
4.3. Damage pattern
In this section, the damage distributions obtained for the interlocking
tunnel specimens are discussed. Fig. 8 (a) shows the failure patterns on
the bricks in the impact area of the specimen IAT-A-1, including the
centre brick and its adjacent bricks. When the hammer dropped from
0.15 m height, the damage on the top surface of the centre brick was
minor, while severe shear cracks were observed on one of its side sur-
faces. Besides, several small cracks could be found on the side of the
adjacent brick, which was caused by the impact load transferred from
the centre brick through the interlocked contact surfaces. With the
Table 3
Summary of impact tests.
Specimen Torque (Nm) Drop height
(m)
Maximum deection
(mm)
Peak force
(kN)
IAT-A-1 2.5 0.15 17.4 65.1
IAT-A-2 2.5 0.25 20.3 74.9
IAT-B-1 2.5 0.15 19.9 87.8
IAT-B-2 2.5 0.25 36.2 109.8
IAT-B-3 5 0.25 33.1 112.0
W. Xu et al.
Engineering Structures 296 (2023) 116907
7
increase of the dropping height to 0.25 m (IAT-A-2), more severe
damage could be found on the top surface as well as sides of the centre
brick, and visible cracks could be found on its adjacent brick [Fig. 8 (b)].
As can be seen in Fig. 8 (a) and 8 (b), both specimens had scratch-like
damage on the top surfaces of the centre bricks, which was caused by
the slippage of the hammerhead. Compared to IAT-A-1, where two
major shear cracks were observed on its centre brick, more obvious
shear cracks were found in IAT-A-2, and the crack widths also increased
signicantly. Also, for both cases, it could be seen that the steel bres in
concrete efciently bridged the cracks and prevented brittle fracture.
The experimental observation demonstrates that the SFRC has a clear
advantage in terms of crack control and can be used as an ideal material
for reinforcing interlocking tunnel segments.
Fig. 9 shows the damage patterns of the specimens with centre brick-
B. The damage of IAT-B-1 specimen (0.15 m drop height and 2.5 Nm
applied torque) was mainly located in the centre brick. During impact,
the steel block produced compression on the shallow groove of the
centre brick, which consequently caused severe cracks on its side sur-
faces. Besides, several obvious cracks appeared on the top surface of the
brick, while no visible cracks were identied on its rear surface. In
addition to the damage caused by direct impact, clear cracks could also
be found on the top surface in the load transferring path, highlighted by
red circle in Fig. 9 (a). When the torque was maintained at 2.5 Nm, but
the dropping height was increased to 0.25 m (IAT-B-2), both the number
and the width of the cracks on the top surface and sides of the centre
brick increased, as shown in Fig. 9 (b). Also, one nearly completely
penetrated crack emerged on the lower edge of the bottom surface of the
centre brick. However, because of the strong bond between steel bres
Fig. 6. Displacement histories of drop hammer for (a) specimens with centre brick-A, and (b) specimens with centre brick-B.
W. Xu et al.
Engineering Structures 296 (2023) 116907
8
and concrete, the complete breakage of the brick edge was prevented by
the bre bridging effect. Additionally, as the impact load was transferred
to the neighbouring bricks through the curved interfaces, cracks were
observed on the edges and corners of the contact surfaces of the adjacent
interlocking SFRC brick. Fig. 9 (c) shows the damage pattern of spec-
imen IAT-B-3 which had the same dropping height as IAT-B-2 (0.25 m)
but increased torque of 5 Nm. It can clearly be seen from Fig. 9 (c) that
the sides of the centre interlocking brick were full of severe cracks, and
the crack width on the bottom surface was also signicantly increased.
The more severe damage in the centre brick could have been caused by
the improved overall stiffness but reduced exibility of the interlocking
tunnel due to the increased applied torque. Although the centre brick
was almost damaged completely, the interlocking interface inhibited the
development and propagation of cracks across the assembly, allowing
the remaining test blocks that were not in the direct impact area to keep
functioning and preventing the overall failure of the structure.
It can be concluded that the structural responses and damage dis-
tributions of interlocking SFRC tunnel specimens can be signicantly
affected by the impact angle, applied torque and hammer dropping
height. The tunnel specimens assembled by the developed non-planar
interlocking bricks demonstrated the advantage of maintaining struc-
tural integrity under impact, even when one or more bricks were
severely damaged. Moreover, the contact surfaces of the interlocking
structure aided in distributing impact load to neighbouring segments,
which helped reduce localised stress concentrations and enhance the
overall impact resistance of the structure. This intricate interaction be-
tween joint conguration and local performance could be further un-
derstood by delving into the mechanics underlying the load distribution
process. The interlocking nature of the design fostered a cooperative
load-sharing mechanism among adjacent elements, promoting a more
uniform stress distribution across the structure. When subjected to
external forces, the contact surfaces engaged, creating a network of load
paths that diverted stress away from potential stress concentration
points. This strategic stress distribution diminished the likelihood of
localised failure and preserved the structural integrity of the assembly.
Besides, the interlocking conguration imparted a unique exibility to
the tunnel structure. This was crucial during an impact event as it
allowed for some degree of deformation without causing catastrophic
failure of the structure. Thus, the structure could more effectively absorb
and dissipate the energy from impact, thereby reducing the risk of severe
structural damage. The interplay between joint conguration, load
redistribution, and controlled exibility contributed to the overall
resilience of the interlocking tunnel structure.
It is worth noting that the number of the side surfaces and the
thickness of the element are key parameters that could be adjusted to
tune the interlocking behaviour and the impact performance. This al-
lows for optimising the design of the interlocking elements to deal with
specic conditions or requirements. To further investigate and optimise
the design of the interlocking SFRC tunnel, a comprehensive study is
required in the future considering different geometrical parameters and
material designs.
5. Conclusions
In this study, a novel non-planar interlocking element previously
proposed by the authors has been further developed and employed as
tunnel segment. The behaviour of tunnel specimen assembled by the
new segments under impact was investigated experimentally. The
developed interlocking segment is made of SFRC and has six symmet-
rical side surfaces with a concave-convex topology, which can prevent
the movement of each element in the interlocking SFRC tunnel struc-
ture. To cast the non-planar interlocking bricks, an aluminium mould
was designed for easy fabrication. Also, to simulate the impact from
moving vehicle, a unique steel testing frame, including a specimen frame
and a supporting frame, was designed to allow the drop hammer to hit
the inner surface of the tunnel specimen. The impact force, the
displacement of the drop hammer and the failure pattern of the inter-
locking SFRC brick were investigated with the consideration of the in-
uences of dropping height and conning load on the impact response of
the interlocking SFRC tunnel. The following conclusions can be drawn
from this research.
1. The developed non-planar interlocking SFRC tunnel segments could
be successfully assembled to form a tunnel specimen, and the
movement of each element was restricted in all directions through
the interlocking feature.
2. The maximum axial displacement of the hammer increased with the
dropping height, but it reduced with the increase in the conning
load. The increased dropping height and conning load could lead to
a larger impact force.
3. The interlocking SFRC tunnel specimens with centre brick-B showed
a higher peak impact force than those with centre brick-A under the
Fig. 7. Comparison of peak impact forces obtained for different interlocking tunnel specimens.
W. Xu et al.
Engineering Structures 296 (2023) 116907
9
Fig. 8. Damage patterns of interlocking SFRC tunnel specimens: (a) IAT-A-1, and (b) IAT-A-2.
W. Xu et al.
Engineering Structures 296 (2023) 116907
10
same loading condition, which is because the slippage of the
hammerhead was prevented in the specimens with centre brick-B
and the impact force could be fully transferred to the specimens.
4. With the addition of steel bres, the development of cracks could be
limited, and the complete breakage of the edges of the interlocking
bricks could be prevented by the bre bridging effect.
5. The interlocking interface could limit the development and propa-
gation of cracks across the assembly, allowing the remaining test
blocks to keep functioning and preventing the overall failure of the
structure.
In future research, it is recommended to conduct a comprehensive
nite element analysis to understand the stress, strain, and deformation
of interlocking tunnel assemblies. This analysis will incorporate complex
loading and boundary conditions that simulate real tunnel environ-
ments, including factors like water pressure, longitudinal forces, and soil
characteristics. An effective and accurate numerical model will be
established in the future study to further investigate the performances of
RC specimen and SFRC specimen, and a comprehensive comparison will
be conducted. Moreover, the comparison of normal SFRC segments and
interlocking SFRC segments will be conducted as a part of our ongoing
Fig. 9. Damage patterns of interlocking SFRC tunnel specimens: (a) IAT-B-1, (b) IAT-B-2, and (c) IAT-B-3.
W. Xu et al.
Engineering Structures 296 (2023) 116907
11
research.
CRediT authorship contribution statement
Wenzheng Xu: Conceptualization, Formal analysis, Methodology,
Investigation, Writing – original draft, Writing – review & editing.
Xiaoshan Lin: Supervision, Conceptualization, Methodology, Project
administration, Resources, Writing – review & editing. Pengda Li:
Funding acquisition, Resources, Project administration. Yu-Fei Wu:
Supervision, Funding acquisition, Project administration. Yi Min Xie:
Supervision, Conceptualization, Writing – review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgements
This work was supported by the Guangdong Provincial Key Labora-
tory of Durability for Marine Civil Engineering with nancial support
from Shenzhen University, China. The technical and equipment support
from Dr Zhenyu Huang and his team in the Key Laboratory of Coastal
Urban Resilient Infrastructures is highly appreciated. In addition, the
authors acknowledge all the technicians, engineers and students at
Shenzhen University and RMIT University who have rendered this work
their generous help.
References
[1] Ding W, Gong C, Mosalam KM, Soga K. Development and application of the
integrated sealant test apparatus for sealing gaskets in tunnel segmental joints.
Tunn Undergr Space Technol 2017;63:54–68. https://doi.org/10.1016/j.
tust.2016.12.008.
[2] Arnau O, Molins C, Blom CBM, Walraven JC. Longitudinal time-dependent
response of segmental tunnel linings. Tunn Undergr Space Technol 2012;28:
98–108. https://doi.org/10.1016/j.tust.2011.10.002.
[3] Kasper T, Edvardsen C, Wittneben G, Neumann D. Lining design for the district
heating tunnel in Copenhagen with steel bre reinforced concrete segments. Tunn
Undergr Space Technol 2008;23(5):574–87. https://doi.org/10.1016/j.
tust.2007.11.001.
[4] Abbas S, Soliman AM, Nehdi ML. Mechanical performance of RC and SFRC precast
tunnel lining segments: a case study. ACI Mater J 2014;111(5). https://doi.org/
10.14359/51687101.
[5] Tang K, Wilkinson S. Corrosion resistance of electried railway tunnels made of
steel bre reinforced concrete. Constr Build Mater 2020;230:117006. https://doi.
org/10.1016/j.conbuildmat.2019.117006.
[6] Liu X, Sun Q, Yuan Y, Taerwe L. Comparison of the structural behavior of
reinforced concrete tunnel segments with steel ber and synthetic ber addition.
Tunn Undergr Space Technol 2020;103:103506. https://doi.org/10.1016/j.
tust.2020.103506.
[7] Wang X, Fan F, Lai J, Xie Y. Steel ber reinforced concrete: a review of its material
properties and usage in tunnel lining. Structures 2021;34:1080–98. https://doi.
org/10.1016/j.istruc.2021.07.086.
[8] Chilvers J, Yang L, Lin X, Zhang YX. Experimental and numerical investigations of
hybrid-bre engineered cementitious composite panels under contact explosions.
Eng Struct 2022;266:114582. https://doi.org/10.1016/j.engstruct.2022.114582.
[9] Wu H, Lin X, Zhou A, Zhang YX. A temperature-dependent material model for
numerical simulation of steel bre reinforced concrete. Constr Build Mater 2022;
320:126329. https://doi.org/10.1016/j.conbuildmat.2022.126329.
[10] Ding Y, Liu H, Pacheco-Torgal F, Jalali S. Experimental investigation on the
mechanical behaviour of the ber reinforced high-performance concrete tunnel
segment. Compos Struct 2011;93(4):1284–9.
[11] Liao L, de la Fuente A, Cavalaro S, Aguado A. Design of FRC tunnel segments
considering the ductility requirements of the Model Code 2010. Tunn Undergr
Space Technol 2015;47:200–10. https://doi.org/10.1016/j.tust.2015.01.006.
[12] Buratti N, Ferracuti B, Savoia M. Concrete crack reduction in tunnel linings by steel
bre-reinforced concretes. Constr Build Mater 2013/07/01/ 2013,;44:249–59.
https://doi.org/10.1016/j.conbuildmat.2013.02.063.
[13] Abbas S, Soliman AM, Nehdi ML. Experimental study on settlement and punching
behavior of full-scale RC and SFRC precast tunnel lining segments. Eng Struct
2014;72:1–10. https://doi.org/10.1016/j.engstruct.2014.04.024.
[14] Molins C, Arnau O. Experimental and analytical study of the structural response of
segmental tunnel linings based on an in situ loading test. Tunn Undergr Space
Technol 2011;26(6):764–77. https://doi.org/10.1016/j.tust.2011.05.002.
[15] Caratelli A, Meda A, Rinaldi Z. Design according to MC2010 of a bre-reinforced
concrete tunnel in Monte Lirio, Panama. Struct Concr 2012;13(3):166–73. https://
doi.org/10.1002/suco.201100034.
[16] Caratelli A, Meda A, Rinaldi Z, Romualdi P. Structural behaviour of precast tunnel
segments in ber reinforced concrete. Tunn Undergr Space Technol 2011;26(2):
284–91. https://doi.org/10.1016/j.tust.2010.10.003.
[17] Meng G, Gao B, Zhou J, Cao G, Zhang Q. Experimental investigation of the
mechanical behavior of the steel ber reinforced concrete tunnel segment. Constr
Build Mater 2016;126:98–107. https://doi.org/10.1016/j.
conbuildmat.2016.09.028.
[18] Yan Q, Deng Z, Zhang Y, Yang W. Failure characteristics of joint bolts in shield
tunnels subjected to impact loads from a derailed train. Shock Vib 2017;2017:
1–17. https://doi.org/10.1155/2017/2829783.
[19] Yan Q, Li B, Geng P, Chen C, He C, Yang W. Dynamic response of a double-lined
shield tunnel to train impact loads. Tunn Undergr Space Technol 2016;53:33–45.
https://doi.org/10.1016/j.tust.2015.12.004.
[20] Yan Q, Xu Y, Zhang W, Geng P, Yang W. Numerical analysis of the cracking and
failure behaviors of segmental lining structure of an underwater shield tunnel
subjected to a derailed high-speed train impact. Tunn Undergr Space Technol
2018;72:41–54. https://doi.org/10.1016/j.tust.2017.11.002.
[21] Yan Q, Sun M, Qing S, Deng Z, Dong W. Numerical investigation on the damage
and cracking characteristics of the shield tunnel caused by derailed high-speed
train. Eng Fail Anal 2020;108:104205. https://doi.org/10.1016/j.
engfailanal.2019.104205.
[22] Feng Y, Siegmund T, Habtour E, Riddick J. Impact mechanics of topologically
interlocked material assemblies. Int J Impact Eng 2015;75:140–9. https://doi.org/
10.1016/j.ijimpeng.2014.08.003.
[23] Estrin Y, Dyskin AV, Pasternak E. Topological interlocking as a material design
concept. Mater Sci Eng C 2011;31(6):1189–94. https://doi.org/10.1016/j.
msec.2010.11.011.
[24] Dyskin AV, Estrin Y, Kanel-Belov AJ, Pasternak E. A new concept in design of
materials and structures: assemblies of interlocked tetrahedron-shaped elements.
Scr Mater 2001;44(12):2689–94. https://doi.org/10.1016/s1359-6462(01)00968-
x.
[25] Dugu´
e M, Fivel M, Br´
echet Y, Dendievel R. Indentation of interlocked assemblies:
3D discrete simulations and experiments. Comput Mater Sci 2013;79:591–8.
https://doi.org/10.1016/j.commatsci.2013.07.014.
[26] Brugger C, Br´
echet Y, Fivel M. Experiments and numerical simulations of
interlocked materials. Adv Mat Res 2008;47–50:125–8. https://doi.org/10.4028/
www.scientic.net/AMR.47-50.125.
[27] Khandelwal S, Siegmund T, Cipra RJ, Bolton JS. Transverse loading of cellular
topologically interlocked materials. Int J Solids Struct 2012;49(18):2394–403.
https://doi.org/10.1016/j.ijsolstr.2012.04.035.
[28] Rezaee Javan A, Sei H, Lin X, Xie YM. Mechanical behaviour of composite
structures made of topologically interlocking concrete bricks with soft interfaces.
Mater Des 2020;186:108347. https://doi.org/10.1016/j.matdes.2019.108347.
[29] Mirkhalaf M, Zhou T, Barthelat F. Simultaneous improvements of strength and
toughness in topologically interlocked ceramics. PNAS 2018;115(37):9128–33.
https://doi.org/10.1073/pnas.1807272115.
[30] Dyskin AV, Estrin Y, Pasternak E, Khor HC, Kanel-Belov AJ. Fracture resistant
structures based on topological interlocking with non-planar contacts. Adv Eng
Mater 2003;5(3):116–9. https://doi.org/10.1002/adem.200390016.
[31] Autruffe A, Pelloux F, Brugger C, Duval P, Br´
echet Y, Fivel M. Indentation
behaviour of interlocked structures made of ice: inuence of the friction
coefcient. Adv Eng Mater 2007;9(8):664–6. https://doi.org/10.1002/
adem.200700111.
[32] Rezaee Javan A, Sei H, Xu S, Ruan D, Xie YM. The impact behaviour of plate-like
assemblies made of new interlocking bricks: an experimental study. Mater. Des.
2017;134:361–73. https://doi.org/10.1016/j.matdes.2017.08.056.
[33] Rezaee Javan A, Sei H, Xu S, Lin X, Xie YM. Impact behaviour of plate-like
assemblies made of new and existing interlocking bricks: a comparative study. Int J
Impact Eng 2018;116:79–93. https://doi.org/10.1016/j.ijimpeng.2018.02.008.
[34] Fallacara G, Barberio M, Colella M. Topological interlocking blocks for
architecture: from at to curved morphologies. In: Architectured materials in
nature and engineering, springer series in materials Science; 2019. p. 423–445
[Chapter 14].
[35] Xu W, Lin X, Xie YM. A novel non-planar interlocking element for tubular
structures. Tunn Undergr Space Technol 2020;103:103503. https://doi.org/
10.1016/j.tust.2020.103503.
[36] Method 9: Compressive strength tests— concrete, mortar and grout specimens, AS,
Australia; 2014.
[37] Method 10: Determination of indirect tensile strength of concrete cylinders
(‘Brazil’ or splitting test), AS, Australia; 2014.
[38] Khan MI, Abbas YM, Fares G. Review of high and ultrahigh performance
cementitious composites incorporating various combinations of bers and
ultranes. J King Saud Univ - Eng Sci 2017;29(4):339–47. https://doi.org/
10.1016/j.jksues.2017.03.006.
W. Xu et al.
Engineering Structures 296 (2023) 116907
12
[39] Balendran R, Zhou F, Nadeem A, Leung A. Inuence of steel bres on strength and
ductility of normal and lightweight high strength concrete. Build Environ 2002;37
(12):1361–7.
[40] Buratti N, Mazzotti C, Savoia M. Post-cracking behaviour of steel and macro-
synthetic bre-reinforced concretes. Constr Build Mater 2011;25(5):2713–22.
https://doi.org/10.1016/j.conbuildmat.2010.12.022.
[41] Farnam Y, Mohammadi S, Shekarchi M. Experimental and numerical investigations
of low velocity impact behavior of high-performance ber-reinforced cement based
composite. Int J Impact Eng 2010;37(2):220–9. https://doi.org/10.1016/j.
ijimpeng.2009.08.006.
W. Xu et al.
