Cyclic Bond-Slip Behavior of Partially Debonded Tendons for Sustainable Design of Non-Emulative Precast Segmental Bridge Columns

Abstract

The precast segmental bridge columns incorporating resettable sliding joints have been proposed to extend the accelerated bridge construction techniques to regions of moderate to high seismicity while fulfilling the sustainability-based resilient seismic design concept. Following a rethink of the design strategy in the light of inspirations from hybrid sliding-rocking joints, the design of resettable sliding joints can accommodate a certain amount of horizontal sliding displacement and adopt partially debonded tendons in a vertical manner, probably resulting in complicated tensile-flexural loading scenarios in these tendons during earthquakes, which is rarely considered in practice. In this paper, the sustainable design of resettable sliding joints is introduced. A tailor-made setup was established and simplified cyclic bond-slip tests were conducted to validate the practicality of the proposed partially debonded tendon system. Twelve specimens were fabricated using different strands and grouting techniques, and a two-stage numerical model was proposed to interpret the experimental results of seven typical specimens. The results suggest that the deterioration of reloading stiffnesses can be captured by an additional effective length caused by bond failure, and the strands perform mostly elastically under relatively large transverse displacements. The loading stiffness of the anchorage is 26.3 kN/mm, and it has significant effects and the proposed two-stage model can satisfactorily capture the envelope of the response of the partially debonded tendons, providing practical design for the proposed partially debonded tendons used in sustainable non-emulative precast segmental bridge columns.

Full text

Citation: Xia, L.; Hu, H.; Guan, S.;
Shah, Y.I.; Liu, Y. Cyclic Bond-Slip
Behavior of Partially Debonded
Tendons for Sustainable Design of
Non-Emulative Precast Segmental
Bridge Columns. Sustainability 2023,
15, 8128. https://doi.org/10.3390/
su15108128
Academic Editor: Jurgita
Antucheviˇcien˙
e
Received: 8 April 2023
Revised: 11 May 2023
Accepted: 12 May 2023
Published: 17 May 2023
Copyright: © 2023 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/).
sustainability
Article
Cyclic Bond-Slip Behavior of Partially Debonded Tendons for
Sustainable Design of Non-Emulative Precast Segmental
Bridge Columns
Leilei Xia 1, Hongcheng Hu 2, Shiyu Guan 2, Yasir Ibrahim Shah 1and Yingqi Liu 1,3 ,*
1
School of Transportation and Logistics Engineering, Wuhan University of Technology, Wuhan 430072, China;
xialeilei@whut.edu.cn (L.X.); yasiribrahimshah@whut.edu.cn (Y.I.S.)
2China Construction Third Bureau First Engineering Co., Ltd., Wuhan 430040, China;
huhongcheng2023@163.com (H.H.); guansy91@outlook.com (S.G.)
3Department of Civil Engineering, The University of Hong Kong, Hong Kong, China
*Correspondence: selbyliu@whut.edu.cn
Abstract:
The precast segmental bridge columns incorporating resettable sliding joints have been
proposed to extend the accelerated bridge construction techniques to regions of moderate to high
seismicity while fulfilling the sustainability-based resilient seismic design concept. Following a
rethink of the design strategy in the light of inspirations from hybrid sliding-rocking joints, the design
of resettable sliding joints can accommodate a certain amount of horizontal sliding displacement and
adopt partially debonded tendons in a vertical manner, probably resulting in complicated tensile-
flexural loading scenarios in these tendons during earthquakes, which is rarely considered in practice.
In this paper, the sustainable design of resettable sliding joints is introduced. A tailor-made setup
was established and simplified cyclic bond-slip tests were conducted to validate the practicality of
the proposed partially debonded tendon system. Twelve specimens were fabricated using different
strands and grouting techniques, and a two-stage numerical model was proposed to interpret the
experimental results of seven typical specimens. The results suggest that the deterioration of reloading
stiffnesses can be captured by an additional effective length caused by bond failure, and the strands
perform mostly elastically under relatively large transverse displacements. The loading stiffness
of the anchorage is 26.3 kN/mm, and it has significant effects and the proposed two-stage model
can satisfactorily capture the envelope of the response of the partially debonded tendons, providing
practical design for the proposed partially debonded tendons used in sustainable non-emulative
precast segmental bridge columns.
Keywords:
bond-slip tests; partially debonded tendons; resettable sliding joints; precast segmental
bridge columns
1. Introduction
Prefabrication of bridge columns is often preferred because of better efficiency, econ-
omy, and quality, as well as less disruption to the site. As shown in Figure 1, 17 pairs
of emulative prefabricated bridge columns have been constructed in a local highway
renovation project.
However, the application of precast segmental bridge columns (PSBC) is still limited
mostly to low-seismicity regions due to the uncertainty over their seismic performance [
1
].
On the other hand, increasing knowledge of material science and structural dynamics
provides all kinds of possibilities for achieving high ductility with minor damage and
high energy dissipation capacity. To achieve better sustainability in structural engineering,
resilience—i.e., the ability of systems to recover from external disturbance—has there-
fore been proposed for structural seismic design and has quickly become popular. The
Sustainability 2023,15, 8128. https://doi.org/10.3390/su15108128 https://www.mdpi.com/journal/sustainability

Sustainability 2023,15, 8128 2 of 24
successful application of emulative PSBC in the low-seismicity regions has promoted re-
search on seismic-resistant PSBC with the non-emulative joints, basically, non-grouted
dry connections between precast column segments that allow gap opening or relative
sliding behavior.
Sustainability 2023, 15, x FOR PEER REVIEW 2 of 26
Figure 1. Cross section of a city bypass using prefabricated bridge columns.
However, the application of precast segmental bridge columns (PSBC) is still limited
mostly to low-seismicity regions due to the uncertainty over their seismic performance
[1]. On the other hand, increasing knowledge of material science and structural dynamics
provides all kinds of possibilities for achieving high ductility with minor damage and
high energy dissipation capacity. To achieve beer sustainability in structural engineer-
ing, resilience—i.e., the ability of systems to recover from external disturbance—has there-
fore been proposed for structural seismic design and has quickly become popular. The
successful application of emulative PSBC in the low-seismicity regions has promoted re-
search on seismic-resistant PSBC with the non-emulative joints, basically, non-grouted
dry connections between precast column segments that allow gap opening or relative slid-
ing behavior.
Earlier non-emulative PSBC were inspired by the discovery of the rocking seismic
isolation mechanism. Rocking joints can result in large localized deformation in the vicin-
ity of the opening gaps. Therefore, conventional fully bonded tendons are most likely to
rupture before rocking columns reach target drift ratios [2,3]. A debonded region near the
rocking joint interface could provide longer effective tendon lengths to distribute the lo-
calized deformation, thereby preserving the necessary tendon force for clamping the col-
umn segments together and, more importantly, providing some self-centering force for
pulling column segments back to their original relative position. A partially debonded
tendon system [4,5] and a fully unbonded tendon system [6–10] have been put forward
for precast beam-column joints, or PSBC. The subsequent research on non-emulative
PSBC with rocking joints has then focused more on the effective use of passive energy
dissipation devices at the rocking joints, either in the form of energy dissipation steel bars
[6–8,11–16] or as externally replaceable yielding devices [17–21].
With a beer understanding of the seismic behavior of PSBC with non-emulative
joints, hybrid sliding-rocking (HSR) joints have been proposed using fully unbonded ten-
dons. The drift capacity of the proposed segmental column system with HSR joints in
quasi-static pushover tests reaches 15%, and its superior low-damage seismic perfor-
mance has been observed by shaking table tests [22,23]. Following the similar seismic iso-
lation concept, reseable sliding joints (RSJ) have been proposed [24,25] to further enhance
the seismic resilience of PSBC with regard to higher energy dissipation capacity and lower
residual drift, where the adopted partially debonded tendon system is new to the indus-
try.
In this paper, the features of the sustainable design of RSJ are introduced. A tailor-
made setup was established and simplified cyclic bond-slip tests were conducted to vali-
date the practicality of the proposed partially debonded tendon system. Twelve different
specimens were fabricated and a two-stage numerical model was proposed to interpret
experimental results. The results suggest that the 7-wire strand performs essentially elas-
tically under orthogonal curvature at 12°, and the anchorage slip helps to dissipate energy.
Figure 1. Cross section of a city bypass using prefabricated bridge columns.
Earlier non-emulative PSBC were inspired by the discovery of the rocking seismic
isolation mechanism. Rocking joints can result in large localized deformation in the vicinity
of the opening gaps. Therefore, conventional fully bonded tendons are most likely to
rupture before rocking columns reach target drift ratios [
2
,
3
]. A debonded region near
the rocking joint interface could provide longer effective tendon lengths to distribute the
localized deformation, thereby preserving the necessary tendon force for clamping the
column segments together and, more importantly, providing some self-centering force for
pulling column segments back to their original relative position. A partially debonded
tendon system [
4
,
5
] and a fully unbonded tendon system [
6
–
10
] have been put forward for
precast beam-column joints, or PSBC. The subsequent research on non-emulative PSBC
with rocking joints has then focused more on the effective use of passive energy dissipation
devices at the rocking joints, either in the form of energy dissipation steel bars [
6
–
8
,
11
–
16
]
or as externally replaceable yielding devices [17–21].
With a better understanding of the seismic behavior of PSBC with non-emulative joints,
hybrid sliding-rocking (HSR) joints have been proposed using fully unbonded tendons.
The drift capacity of the proposed segmental column system with HSR joints in quasi-static
pushover tests reaches 15%, and its superior low-damage seismic performance has been
observed by shaking table tests [
22
,
23
]. Following the similar seismic isolation concept,
resettable sliding joints (RSJ) have been proposed [
24
,
25
] to further enhance the seismic
resilience of PSBC with regard to higher energy dissipation capacity and lower residual
drift, where the adopted partially debonded tendon system is new to the industry.
In this paper, the features of the sustainable design of RSJ are introduced. A tailor-made
setup was established and simplified cyclic bond-slip tests were conducted to validate the
practicality of the proposed partially debonded tendon system. Twelve different specimens
were fabricated and a two-stage numerical model was proposed to interpret experimental
results. The results suggest that the 7-wire strand performs essentially elastically under
orthogonal curvature at 12
◦
, and the anchorage slip helps to dissipate energy. This study
indicates that the proposed partially debonded tendon system can be a suitable option
for precast segmental bridge columns with RSJs, and proper methods are provided to
design the proposed partially debonded tendons used in sustainable non-emulative precast
segmental bridge columns.

Sustainability 2023,15, 8128 3 of 24
2. PSBC with Resettable Sliding Joints
2.1. Overall Design
A conceptual design of PSBC with resettable sliding joints (RSJ) is developed using non-
emulative hybrid sliding-rocking (HSR) joints for applications in regions with moderate
and high seismicity. In this design, the segments are able to oscillate about the original
relative position by sliding and/or rocking for satisfactory seismic isolation during the
stage of strong shaking. Moreover, the segments also have the tendency to slide back to the
original relative position under the subsequent excitations of smaller magnitudes to achieve
satisfactory self-centering performance as if the dislodged segments are reset at the joints
upon cessation of an earthquake, thus achieving high resilience and great sustainability
toward seismic hazards. In particular, the resettable sliding joint [
24
] consists of three major
components as shown in Figure 2: (i) durable low-friction concrete-to-concrete contact
surfaces [
26
]; (ii) non-planar contact surfaces with gentle guide keys [
27
]; and (iii) partially
debonded tendons with low initial prestress.
Sustainability 2023, 15, x FOR PEER REVIEW 3 of 26
This study indicates that the proposed partially debonded tendon system can be a suitable
option for precast segmental bridge columns with RSJs, and proper methods are provided
to design the proposed partially debonded tendons used in sustainable non-emulative
precast segmental bridge columns.
2. PSBC with Reseable Sliding Joints
2.1. Overall Design
A conceptual design of PSBC with reseable sliding joints (RSJ) is developed using
non-emulative hybrid sliding-rocking (HSR) joints for applications in regions with mod-
erate and high seismicity. In this design, the segments are able to oscillate about the orig-
inal relative position by sliding and/or rocking for satisfactory seismic isolation during the
stage of strong shaking. Moreover, the segments also have the tendency to slide back to
the original relative position under the subsequent excitations of smaller magnitudes to
achieve satisfactory self-centering performance as if the dislodged segments are reset at
the joints upon cessation of an earthquake, thus achieving high resilience and great sus-
tainability toward seismic hazards. In particular, the reseable sliding joint [24] consists
of three major components as shown in Figure 2: (i) durable low-friction concrete-to-con-
crete contact surfaces [26]; (ii) non-planar contact surfaces with gentle guide keys [27]; and
(iii) partially debonded tendons with low initial prestress.
Figure 2. Major components of a reseable sliding joint.
2.2. Partially Debonded Tendons
Figures 2 and 3 show that the partially debonded tendon comprises a grouted tendon
inside a regular duct with a certain length of the duct adjacent to each joint at the contact
surface wrapped by an annulus of soft resilient material to allow a certain amount of rel-
ative sliding movement at the contact surface during an earthquake. This design not only
creates room for relative sliding at the contact surface but also provides some restoring
force to assist in reseing. It is, however, necessary to provide sufficient operational pre-
stressing force in the tendons considering the inclination of the gentle guide keys in order
to avoid any sliding at joints during conditions of horizontal loading other than earth-
quakes.
Figure 2. Major components of a resettable sliding joint.
2.2. Partially Debonded Tendons
Figures 2and 3show that the partially debonded tendon comprises a grouted tendon
inside a regular duct with a certain length of the duct adjacent to each joint at the contact
surface wrapped by an annulus of soft resilient material to allow a certain amount of relative
sliding movement at the contact surface during an earthquake. This design not only creates
room for relative sliding at the contact surface but also provides some restoring force to
assist in resetting. It is, however, necessary to provide sufficient operational prestressing
force in the tendons considering the inclination of the gentle guide keys in order to avoid
any sliding at joints during conditions of horizontal loading other than earthquakes.
Moreover, unlike the fully unbonded tendons, the presence of grout not only boosts
the durability of tendons but also enhances the interaction between adjacent segments.
Flexural cracking or crushing of the grout under excessive sliding oscillation during an
earthquake is inevitable, but the damage to the grout is considered acceptable during
an earthquake.

Sustainability 2023,15, 8128 4 of 24
Sustainability 2023, 15, x FOR PEER REVIEW 4 of 26
Figure 3. Schematic view of precast segmental bridge column with reseable sliding joints.
Moreover, unlike the fully unbonded tendons, the presence of grout not only boosts
the durability of tendons but also enhances the interaction between adjacent segments.
Flexural cracking or crushing of the grout under excessive sliding oscillation during an
earthquake is inevitable, but the damage to the grout is considered acceptable during an
earthquake.
3. Cyclic Bond-Slip Behavior of Partially Debonded Tendons
3.1. Bond Behavior of Tendons
According to classical research [28], adhesion, Hoyer’s effect, and mechanical inter-
lock are the three controlling mechanisms of the bond between the prestressing strand
and concrete. Experiments for investigating the bond performance between the strand and
the surrounding materials are usually conducted through pull-out tests [29]. Tests of
strands embedded in grout showed that the bond strength increased with a growing pos-
itive lateral pressure, embedded length, and grout strength [30]. Other pull-out tests were
conducted on strands bonded in the mortar, and the bond strength was higher in speci-
mens with larger strand diameters. Apart from the above obvious factors, the bond force
was also reported [31] to be affected by different designs with regard to the concrete cover
or spacing between bars and transverse confining steel. Improved bond behavior can be
aributed to improved confinement conditions, such as the provision of metal ducts and
additional reinforcement. The surface condition of the tendon would also dramatically
affect the ultimate bond performance [32].
The primary function of the partially debonded tendon system for the RSJs is to keep
the integrity of the assembled column while accommodating some relative joint sliding
without causing too much damage. Conventional pull-out tests cannot cater to the com-
plicated tensile-flexural loading scenarios expected during severe sliding conditions.
Figure 3. Schematic view of precast segmental bridge column with resettable sliding joints.
3. Cyclic Bond-Slip Behavior of Partially Debonded Tendons
3.1. Bond Behavior of Tendons
According to classical research [
28
], adhesion, Hoyer’s effect, and mechanical interlock
are the three controlling mechanisms of the bond between the prestressing strand and
concrete. Experiments for investigating the bond performance between the strand and the
surrounding materials are usually conducted through pull-out tests [
29
]. Tests of strands
embedded in grout showed that the bond strength increased with a growing positive lateral
pressure, embedded length, and grout strength [
30
]. Other pull-out tests were conducted
on strands bonded in the mortar, and the bond strength was higher in specimens with
larger strand diameters. Apart from the above obvious factors, the bond force was also
reported [
31
] to be affected by different designs with regard to the concrete cover or spacing
between bars and transverse confining steel. Improved bond behavior can be attributed
to improved confinement conditions, such as the provision of metal ducts and additional
reinforcement. The surface condition of the tendon would also dramatically affect the
ultimate bond performance [32].
The primary function of the partially debonded tendon system for the RSJs is to
keep the integrity of the assembled column while accommodating some relative joint
sliding without causing too much damage. Conventional pull-out tests cannot cater to the
complicated tensile-flexural loading scenarios expected during severe sliding conditions.
Thus, a simplified cyclic bond test is proposed to investigate cyclic bond performance and
energy dissipation of a partially debonded tendon across a sliding joint under vertical
sliding displacements.

Sustainability 2023,15, 8128 5 of 24
3.2. Overview of Test Setup
3.2.1. Setup and Experiment Design
The Universal Test Machine in the structural lab of the University of Hong Kong is
utilized to accommodate specimens with long strands. Figure 4a shows that the machine
consists of two major components: a fixed crosshead at the top and a movable loading
platform at the bottom. The top crosshead can be adjusted and locked at different levels of
the steel-resisting frame. The bottom loading platform can move vertically and is controlled
by the hydraulically actuated system. The force capacity is 1000 kN and the vertical stroke
of the machine is 273 mm. Displacement-based loading can be applied only in compression
(with the bottom platform moving upward). The machine can only be operated manually
while providing displacement-controlled axial loading at a slow rate of 1 mm/min to
30 mm/min.
Sustainability 2023, 15, x FOR PEER REVIEW 5 of 26
Thus, a simplified cyclic bond test is proposed to investigate cyclic bond performance and
energy dissipation of a partially debonded tendon across a sliding joint under vertical
sliding displacements.
3.2. Overview of Test Setup
3.2.1. Setup and Experiment Design
The Universal Test Machine in the structural lab of the University of Hong Kong is
utilized to accommodate specimens with long strands. Figure 4a shows that the machine
consists of two major components: a fixed crosshead at the top and a movable loading
platform at the boom. The top crosshead can be adjusted and locked at different levels
of the steel-resisting frame. The boom loading platform can move vertically and is con-
trolled by the hydraulically actuated system. The force capacity is 1000 kN and the vertical
stroke of the machine is 273 mm. Displacement-based loading can be applied only in com-
pression (with the boom platform moving upward). The machine can only be operated
manually while providing displacement-controlled axial loading at a slow rate of
1mm/min to 30 mm/min.
In Figure 4, the specimen, consisting of a concrete prism with a long grouted strand,
is mounted horizontally onto the loading platform to simulate a typical partially bonded
strand. The unbonded length of the tendon with soft wrapping is simulated by a free
length of the strand in the experiment. As shown in Figure 4b, two sets of wedge and
barrel anchors were mounted at the two ends of the strand to provide horizontal con-
straint, while linear variable differential transformers (LVDTs) with 50 mm stoke and load
cells with maximum compressive force capacity of 300 kN were installed near these an-
chors to keep a record of the horizontal movements and forces induced from the imposed
vertical midspan displacement. To impose vertical midspan loading displacement onto
the specimen, a steel loading head was fixed to the underside of the crosshead and kept
stationary throughout the test. The contact surface of the loading head with the strand
had a curved shape and its position was adjusted with the help of laser positioning. Dur-
ing testing, the imposed vertical displacement would cause deformation of the strand as
depicted by a doed line in Figure 4b.
(a)
Sustainability 2023, 15, x FOR PEER REVIEW 6 of 26
(b)
Figure 4. Simplified cyclic bond test: (a) test setup and (b) measurements.
At the steel end support, a roller resting on a concave surface was provided. Two
LVDTs (with 25 mm stroke) were mounted near the bracket and end support to monitor
any incidental horizontal displacements. No prestress was applied to the strand during
the fabrication of the specimen. The anchorages were installed manually by hammering
the steel wedges into the conical cavity. A hydraulic jack was used to tension the strand
before testing. A one-way cyclic testing protocol was adopted as the strand should always
be taut during testing.
3.2.2. Design of Specimens
Altogether, 12 specimens were cast with grouted strands in two separate batches, and
the same C45 concrete mix design was adopted for all the specimens as presented in Table
1. In view of the various factors that may affect the bond performance between the strand
and grout, different types of the tendon, grout mix designs, and confining reinforcement
are considered.
Table 1. Concrete mix design and material properties.
Batch Grade
Cement Water
kg/m
3
)
Fine
Aggregate
(kg/m
3
)
10 mm
Aggregate
(kg/m
3
)
28-Day
Cylinder
Strength
(MPa)
28-Day
Cube
Strength
(Mpa)
(kg/m
3
)
First C45 501 256 857 701 45.0 50.1
Second C45 501 256 857 701 44.6 51.0
Figure 5 shows the concrete prism with a rectangular cross section adopted for the
test specimen. Two types of grout were used in the two batches of specimens. Grade 52.5R
ordinary Portland cement [33] with a water/cement ratio of 0.4 (which falls in the recom-
mended range of 0.35–0.45 from CEN) was adopted as one option. The other was a com-
mercial product with the brand name of SikaGrout
TM
(Sika, Baar, Swierland), where a
water/Sika-powder ratio of 0.2 was adopted according to the data sheet [34]. Despite the
different mix designs, the strength testing results (with 40 mm cube specimens for both
grout mixes) indicated that they had similar 7-day compressive strength above 40 MPa,
Figure 4. Simplified cyclic bond test: (a) test setup and (b) measurements.

Sustainability 2023,15, 8128 6 of 24
In Figure 4, the specimen, consisting of a concrete prism with a long grouted strand,
is mounted horizontally onto the loading platform to simulate a typical partially bonded
strand. The unbonded length of the tendon with soft wrapping is simulated by a free
length of the strand in the experiment. As shown in Figure 4b, two sets of wedge and barrel
anchors were mounted at the two ends of the strand to provide horizontal constraint, while
linear variable differential transformers (LVDTs) with 50 mm stoke and load cells with
maximum compressive force capacity of 300 kN were installed near these anchors to keep a
record of the horizontal movements and forces induced from the imposed vertical midspan
displacement. To impose vertical midspan loading displacement onto the specimen, a steel
loading head was fixed to the underside of the crosshead and kept stationary throughout
the test. The contact surface of the loading head with the strand had a curved shape and
its position was adjusted with the help of laser positioning. During testing, the imposed
vertical displacement would cause deformation of the strand as depicted by a dotted line
in Figure 4b.
At the steel end support, a roller resting on a concave surface was provided. Two
LVDTs (with 25 mm stroke) were mounted near the bracket and end support to monitor
any incidental horizontal displacements. No prestress was applied to the strand during the
fabrication of the specimen. The anchorages were installed manually by hammering the
steel wedges into the conical cavity. A hydraulic jack was used to tension the strand before
testing. A one-way cyclic testing protocol was adopted as the strand should always be taut
during testing.
3.2.2. Design of Specimens
Altogether, 12 specimens were cast with grouted strands in two separate batches, and
the same C45 concrete mix design was adopted for all the specimens as presented in Table 1.
In view of the various factors that may affect the bond performance between the strand
and grout, different types of the tendon, grout mix designs, and confining reinforcement
are considered.
Table 1. Concrete mix design and material properties.
Batch Grade Cement Water
(kg/m3)
Fine Aggregate
(kg/m3)
10 mm Aggregate
(kg/m3)
28-Day Cylinder
Strength (MPa)
28-Day Cube
Strength (Mpa)
(kg/m3)
First C45 501 256 857 701 45.0 50.1
Second
C45 501 256 857 701 44.6 51.0
Figure 5shows the concrete prism with a rectangular cross section adopted for the
test specimen. Two types of grout were used in the two batches of specimens. Grade
52.5R ordinary Portland cement [
33
] with a water/cement ratio of 0.4 (which falls in the
recommended range of 0.35–0.45 from CEN) was adopted as one option. The other was a
commercial product with the brand name of SikaGrout
TM
(Sika, Baar, Switzerland), where
a water/Sika-powder ratio of 0.2 was adopted according to the data sheet [
34
]. Despite the
different mix designs, the strength testing results (with 40 mm cube specimens for both
grout mixes) indicated that they had similar 7-day compressive strength above 40 MPa,
and the ultimate 28-day compressive strength was 60.5 MPa and 65.2 MPa, respectively, for
cement grout and Sika grout.
Low-relaxation 7-wire strands of 15.2 mm nominal diameter conforming to BS 5896 [
35
]
were used, and Young’s modulus and ultimate tensile strength of these strands at ambient
temperature were 200 GPa and 1860 MPa, respectively [
36
]. The strands used in the first
batch were newly bought, and they were coated with oil. In the second batch, strands with
dry and clean surfaces were used. The detailed descriptions and labels for different cases
are shown in Table 2.

Sustainability 2023,15, 8128 7 of 24
Sustainability 2023, 15, x FOR PEER REVIEW 7 of 26
and the ultimate 28-day compressive strength was 60.5 MPa and 65.2MPa, respectively,
for cement grout and Sika grout.
(a)
(b)
Figure 5. Concrete prism in the specimen for simplified cyclic bond test: (a) transverse cross section;
and (b) longitudinal cross section.
Low-relaxation 7-wire strands of 15.2 mm nominal diameter conforming to BS 5896
[35] were used, and Young’s modulus and ultimate tensile strength of these strands at
ambient temperature were 200 GPa and 1860 MPa, respectively [36]. The strands used in
the first batch were newly bought, and they were coated with oil. In the second batch,
strands with dry and clean surfaces were used. The detailed descriptions and labels for
different cases are shown in Table 2.
Table 2. Summary of specimens for cyclic bond tests.
No. Batch Label
Strand
Surface
Condition
Stirrup Grout Length
(mm) Notes
1
First
batch
I-60-270P1
coated with
oil
60 w/c = 0.4 270 axial only
2 I-60-270P2 60 w/c = 0.4 270 axial only
3 I-60-270P3 60 w/c = 0.4 270 axial only
4 I-60-510P 60 w/c = 0.4 510 axial only
5 I-60-270 60 w/c = 0.4 270 vertical cyclic
6 I-60-750 60 w/c = 0.4 750 vertical cyclic
Figure 5.
Concrete prism in the specimen for simplified cyclic bond test: (
a
) transverse cross section;
and (b) longitudinal cross section.
Some of the specimens were tested in axial tension only to provide information about
the maximum bond resistance as well as to fine-tune the setup and loading protocol for the
one-way cyclic bond tests.
3.2.3. Fabrication of Specimens
The reinforcement cage was fabricated according to the design and then positioned
in the mold. Plastic spacers were used to position the reinforcement cage with cable ties
and instant glue to ensure the provision of proper concrete cover. As illustrated in Figure 6,
four larger horizontal plastic spacers were used to restrain the reinforcement cage while
leaving space for the compaction of concrete.
Care should be exercised during casting to ensure that the fresh concrete could fill
the mold completely, including the corners. The four plastic horizontal spacers at the top
should be kept until the compaction of the concrete is completed. After 7-day air curing
of the freshly cast specimens, 15.2 mm diameter strands were then threaded through the
concrete prisms. Any protruding grout lengths of tubes were cut off flush with the surface
of the prism. Holes were drilled through the grout tubes and plastic ducts right into the
corrugated duct. To avoid leakage of grouting materials, a rubber sheet was attached to the
jigs to seal off any gaps. The gaps between the jig and the strand were sealed by plasticine.

Sustainability 2023,15, 8128 8 of 24
Table 2. Summary of specimens for cyclic bond tests.
No. Batch Label
Strand
Surface
Condition
Stirrup Grout Length (mm) Notes
1
First batch
I-60-270P1
coated
with oil
60 w/c = 0.4 270 axial only
2 I-60-270P2 60 w/c = 0.4 270 axial only
3 I-60-270P3 60 w/c = 0.4 270 axial only
4 I-60-510P 60 w/c = 0.4 510 axial only
5 I-60-270 60 w/c = 0.4 270
vertical cyclic
6 I-60-750 60 w/c = 0.4 750
vertical cyclic
7
Second batch
II-60-270P
dry and clean
60 w/sika = 0.2 270 axial only
8 II-48-270 48 w/sika = 0.2 270
vertical cyclic
9 II-80-270 80 w/sika = 0.2 270
vertical cyclic
10 II-60-270 60 w/sika = 0.2 270
vertical cyclic
11 II-60-510 60 w/sika = 0.2 510
vertical cyclic
12 II-60-750 60 w/sika = 0.2 750
vertical cyclic
Sustainability 2023, 15, x FOR PEER REVIEW 8 of 26
7
Second
batch
II-60-270P
dry and clean
60 w/sika = 0.2 270 axial only
8 II-48-270 48 w/sika = 0.2 270 vertical cyclic
9 II-80-270 80 w/sika = 0.2 270 vertical cyclic
10 II-60-270 60 w/sika = 0.2 270 vertical cyclic
11 II-60-510 60 w/sika = 0.2 510 vertical cyclic
12 II-60-750 60 w/sika = 0.2 750 vertical cyclic
Some of the specimens were tested in axial tension only to provide information about
the maximum bond resistance as well as to fine-tune the setup and loading protocol for
the one-way cyclic bond tests.
3.2.3. Fabrication of Specimens
The reinforcement cage was fabricated according to the design and then positioned
in the mold. Plastic spacers were used to position the reinforcement cage with cable ties
and instant glue to ensure the provision of proper concrete cover. As illustrated in Figure
6, four larger horizontal plastic spacers were used to restrain the reinforcement cage while
leaving space for the compaction of concrete.
(a)
(b)
Figure 6. Fabrication of the specimen: (a) reinforcement positioning; and (b) strand threading and
fixing at the active side.
Figure 6.
Fabrication of the specimen: (
a
) reinforcement positioning; and (
b
) strand threading and
fixing at the active side.

Sustainability 2023,15, 8128 9 of 24
Grouting was the last step for specimen fabrication upon completion of strand thread-
ing. A tailor-made grout injection tube with a fitted nozzle was used for grouting operations.
The specimen was slightly tilted before grouting so that the grout outlet was slightly higher
than the grout inlet to allow for the expulsion of air.
3.2.4. Testing Procedures
In accordance with the design described in Section 3.2.1, the specimen was mounted
onto the testing frame and a very small force was applied by the hydraulic jack to keep
the strand taut. Several displacement cycles were imposed while monitoring the force
by the active load cell. Upon reaching the target displacement amplitude in a cycle, the
specimen would go through force-based unloading to the minimum force (close to 0 kN).
The yielding of the stand was not the major concern of the simplified cyclic bond tests
because the strand should remain elastic. In the loading or reloading phase of a typical
cycle, additional displacement was imposed in accordance with Table 3by displacement
control. Then in the subsequent unloading phase, force control was adopted until the force
applied was reduced to zero, possibly resulting in an increase in residual displacement.
Table 3. Proposed one-way cyclic loading protocol.
Stage Cycles Loading Rate
(mm/min)
Loading and Reloading Unloading
Displacement
Control (mm)
Force
Control (kN)
1
2
10
5 to zero
2 10 to zero
3 15 to zero
4 20 to zero
5 25 to zero
6
15
30 to zero
7 40 to zero
8 50 to zero
9 60 to zero
10 70 to zero
11 80 to zero
12 90 to zero
Sustainability 2023, 15, x FOR PEER REVIEW 9 of 26
Care should be exercised during casting to ensure that the fresh concrete could fill
the mold completely, including the corners. The four plastic horizontal spacers at the top
should be kept until the compaction of the concrete is completed. After 7-day air curing
of the freshly cast specimens, 15.2 mm diameter strands were then threaded through the
concrete prisms. Any protruding grout lengths of tubes were cut off flush with the surface
of the prism. Holes were drilled through the grout tubes and plastic ducts right into the
corrugated duct. To avoid leakage of grouting materials, a rubber sheet was aached to
the jigs to seal off any gaps. The gaps between the jig and the strand were sealed by plas-
ticine.
Grouting was the last step for specimen fabrication upon completion of strand
threading. A tailor-made grout injection tube with a fied nozzle was used for grouting
operations. The specimen was slightly tilted before grouting so that the grout outlet was
slightly higher than the grout inlet to allow for the expulsion of air.
3.2.4. Testing Procedures
In accordance with the design described in Section 3.2.1, the specimen was mounted
onto the testing frame and a very small force was applied by the hydraulic jack to keep
the strand taut. Several displacement cycles were imposed while monitoring the force by
the active load cell. Upon reaching the target displacement amplitude in a cycle, the spec-
imen would go through force-based unloading to the minimum force (close to 0 kN). The
yielding of the stand was not the major concern of the simplified cyclic bond tests because
the strand should remain elastic. In the loading or reloading phase of a typical cycle, ad-
ditional displacement was imposed in accordance with Table 3 by displacement control.
Then in the subsequent unloading phase, force control was adopted until the force applied
was reduced to zero, possibly resulting in an increase in residual displacement.
Table 3. Proposed one-way cyclic loading protocol.
Stage Cycles
Loading Rate
(mm/min)
Loading and Reloading Unloading
Displacement Control (mm) Force Control (kN)
1
2
10
5 to zero
2 10 to zero
3 15 to zero
4 20 to zero
5 25 to zero
6
15
30 to zero
7 40 to zero
8 50 to zero
9 60 to zero
10 70 to zero
11 80 to zero
12 90 to zero
Typical time history for one-way cyclic loading
Typical time history for one-way cyclic loading
4. Evaluation of Testing Results
4.1. Specimens
During the cyclic testing, concentrated vertical loading was applied to the strand
by the loading head, causing the strand to deform as indicated in Figure 7. The original
roughly round cross section of the 7-wire strand was flattened due to the large vertical force
applied from the loading head of the setup, resulting in a permanent curvature. Similar
strand damage with smaller permanent curvature was also observed at the roller support
and the active side of the concrete prism. As shown in Figure 8, the bonding region located
at the passive side of the concrete prism was intact, while the damage observed at the

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bonding region on the active side was largely limited to the corrugated duct. No cracking
was observed in the concrete prism, and the failure observed was the slipping of the strand.
Sustainability 2023, 15, x FOR PEER REVIEW 10 of 26
4. Evaluation of Testing Results
4.1. Specimens
During the cyclic testing, concentrated vertical loading was applied to the strand by
the loading head, causing the strand to deform as indicated in Figure 7. The original
roughly round cross section of the 7-wire strand was flaened due to the large vertical
force applied from the loading head of the setup, resulting in a permanent curvature. Sim-
ilar strand damage with smaller permanent curvature was also observed at the roller sup-
port and the active side of the concrete prism. As shown in Figure 8, the bonding region
located at the passive side of the concrete prism was intact, while the damage observed at
the bonding region on the active side was largely limited to the corrugated duct. No crack-
ing was observed in the concrete prism, and the failure observed was the slipping of the
strand.
Figure 7. Specimen II-60-750 after testing.
Figure 7. Specimen II-60-750 after testing.
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Figure 8. Concrete prism of Specimen II-60-750 after testing.
4.2. Bond Performance
4.2.1. Bond Parameters
During the axial tensile testing, or the cyclic bond testing, the grout in the vicinity of
the strand gradually became detached as the cable force increased. The equivalent bond
stress 𝜏 assuming uniform distribution along the embedded length can be calculated
from the cable force 𝑃 acting over the bonded area as shown in Equation (1),
𝜏𝑃/𝑙∙𝑙 (1)
where 𝑙 is the envelope perimeter as shown in Figure 5, which is equal to 󰇛𝜋∙𝑑󰇜 for a
mono-strand tendon, and 𝑙 is the bonded length as shown in Figure 9.
Figure 9. Envelope perimeter of the tendon.
As the bond stress may not be evenly distributed, especially for long bonded lengths,
the equivalent bond stress 𝜏 obtained is indicative only.
4.2.2. Cyclic Bond-Slip Performance
During testing, the load cell readings could be used to estimate the bond force in the
concrete prism. Similarly, the LVDTs at the prism ends were used to estimate the relative
slip of the strand in the concrete prism. The data obtained from the load cells and LVDTs
Figure 8. Concrete prism of Specimen II-60-750 after testing.
4.2. Bond Performance
4.2.1. Bond Parameters
During the axial tensile testing, or the cyclic bond testing, the grout in the vicinity of
the strand gradually became detached as the cable force increased. The equivalent bond

Sustainability 2023,15, 8128 11 of 24
stress
τb
assuming uniform distribution along the embedded length can be calculated from
the cable force Pacting over the bonded area as shown in Equation (1),
τb=P/le·lspecimen(1)
where
le
is the envelope perimeter as shown in Figure 5, which is equal to
(π·db)
for a
mono-strand tendon, and lspecimen is the bonded length as shown in Figure 9.
Sustainability 2023, 15, x FOR PEER REVIEW 11 of 26
Figure 8. Concrete prism of Specimen II-60-750 after testing.
4.2. Bond Performance
4.2.1. Bond Parameters
During the axial tensile testing, or the cyclic bond testing, the grout in the vicinity of
the strand gradually became detached as the cable force increased. The equivalent bond
stress 𝜏 assuming uniform distribution along the embedded length can be calculated
from the cable force 𝑃 acting over the bonded area as shown in Equation (1),
𝜏𝑃/𝑙∙𝑙 (1)
where 𝑙 is the envelope perimeter as shown in Figure 5, which is equal to 󰇛𝜋∙𝑑󰇜 for a
mono-strand tendon, and 𝑙 is the bonded length as shown in Figure 9.
Figure 9. Envelope perimeter of the tendon.
As the bond stress may not be evenly distributed, especially for long bonded lengths,
the equivalent bond stress 𝜏 obtained is indicative only.
4.2.2. Cyclic Bond-Slip Performance
During testing, the load cell readings could be used to estimate the bond force in the
concrete prism. Similarly, the LVDTs at the prism ends were used to estimate the relative
slip of the strand in the concrete prism. The data obtained from the load cells and LVDTs
Figure 9. Envelope perimeter of the tendon.
As the bond stress may not be evenly distributed, especially for long bonded lengths,
the equivalent bond stress τbobtained is indicative only.
4.2.2. Cyclic Bond-Slip Performance
During testing, the load cell readings could be used to estimate the bond force in the
concrete prism. Similarly, the LVDTs at the prism ends were used to estimate the relative
slip of the strand in the concrete prism. The data obtained from the load cells and LVDTs
were adopted to investigate the bond-slip performance of the specimens. The typical
bond-slip curve for the specimens tested under vertical cyclic imposed displacement is
presented in Figure 10.
Sustainability 2023, 15, x FOR PEER REVIEW 12 of 26
were adopted to investigate the bond-slip performance of the specimens. The typical
bond-slip curve for the specimens tested under vertical cyclic imposed displacement is
presented in Figure 10.
Figure 10. The bond-slip curve for Specimen I-60-270.
As the tensile strand force kept increasing, the bond force in the concrete prism
would gradually reach its maximum strength and the passive anchorage would start to
provide additional resistance together with a positive strand slip toward the active end of
the concrete prism. The accumulated resisting force at the passive end of the prism would
not be released during the initial stage of unloading, thus leading to a reversed bond force
as the active tensile strand force decreased. A drop in this passive resisting force was only
observed with a reversed strand slip.
Owing to the high bond forces in some specimens of the second batch with larger
bonded lengths, reversed slip was not observed in Specimen II-60-510 and Specimen II-
60-750. For the rest of the cases, the maximum mean bond stresses associated with posi-
tive-strand slips were approximately twice the values of the corresponding maximum
mean bond stresses obtained during reversed strand slips. The cyclic nature of the im-
posed displacement might have impaired the residual bond between the grout and the
strand. A slight reduction in bond stress was always observed upon unloading and re-
loading the specimen to the same magnitude of imposed vertical displacement.
4.2.3. Mean Bond Stress and Bond Force
Apart from the seven specimens for vertical cyclic tests (Table 3), the other five spec-
imens tested by direct axial tension also provided experimental results on the mean bond
stress and the bond force.
The other five specimens in the second batch, as shown in Figure 11, share a fairly
stable mean bond stress of about 5.3 MPa. However, the mean bond stresses in all the
specimens of the first batch are below 1.2 MPa as shown in Figure 12, indicating that the
grouting techniques adopted in the second batch might be capable of providing a higher
bond strength between the grout and strand. The oil on the surface of the strands in the
specimens of the first batch might have adversely affected the bond performance of grout
in the prestressing strand, which was consistent with the findings reported by Borzovič
and Laco [32]. From the results of the group of 270 mm long specimens, the adoption of
direct axial tension or cyclic testing procedure hardly affected the mean bond stress re-
sults.
Figure 10. The bond-slip curve for Specimen I-60-270.
As the tensile strand force kept increasing, the bond force in the concrete prism would
gradually reach its maximum strength and the passive anchorage would start to provide
additional resistance together with a positive strand slip toward the active end of the
concrete prism. The accumulated resisting force at the passive end of the prism would not
be released during the initial stage of unloading, thus leading to a reversed bond force as

Sustainability 2023,15, 8128 12 of 24
the active tensile strand force decreased. A drop in this passive resisting force was only
observed with a reversed strand slip.
Owing to the high bond forces in some specimens of the second batch with larger
bonded lengths, reversed slip was not observed in Specimen II-60-510 and Specimen
II-60-750. For the rest of the cases, the maximum mean bond stresses associated with
positive-strand slips were approximately twice the values of the corresponding maximum
mean bond stresses obtained during reversed strand slips. The cyclic nature of the imposed
displacement might have impaired the residual bond between the grout and the strand. A
slight reduction in bond stress was always observed upon unloading and reloading the
specimen to the same magnitude of imposed vertical displacement.
4.2.3. Mean Bond Stress and Bond Force
Apart from the seven specimens for vertical cyclic tests (Table 3), the other five speci-
mens tested by direct axial tension also provided experimental results on the mean bond
stress and the bond force.
The other five specimens in the second batch, as shown in Figure 11, share a fairly
stable mean bond stress of about 5.3 MPa. However, the mean bond stresses in all the
specimens of the first batch are below 1.2 MPa as shown in Figure 12, indicating that the
grouting techniques adopted in the second batch might be capable of providing a higher
bond strength between the grout and strand. The oil on the surface of the strands in the
specimens of the first batch might have adversely affected the bond performance of grout
in the prestressing strand, which was consistent with the findings reported by Borzoviˇc
and Laco [
32
]. From the results of the group of 270 mm long specimens, the adoption of
direct axial tension or cyclic testing procedure hardly affected the mean bond stress results.
Sustainability 2023, 15, x FOR PEER REVIEW 13 of 26
Figure 11. Bond performance of specimens in the second batch.
Figure 12. Bond performance of specimens in the first batch.
Apparently higher mean bond stresses were observed in specimens with relatively
shorter bonded lengths [37
–
39] as the evenly distributed bond stress assumption was most
likely valid. To beer understand the relative low bond stresses in first batch specimens,
specimen I-60-270P1 was cut through for detailed inspection of the bonding interface be-
tween the strand and grout, as shown in Figure 13. Grooves were observed as the strand
slid across the bonding interface, indicating that the cement grout failed to keep a tight
grip on the strand. This observation could be aributed to the insufficient interlocking
effect due to the helical configuration of the strand, the shrinkage of cement grout, and
the lubrication effects caused by the oil on the surface of strands in the specimens in the
first batch.
Figure 11. Bond performance of specimens in the second batch.
Apparently higher mean bond stresses were observed in specimens with relatively
shorter bonded lengths [
37
–
39
] as the evenly distributed bond stress assumption was most
likely valid. To better understand the relative low bond stresses in first batch specimens,
specimen I-60-270P1 was cut through for detailed inspection of the bonding interface
between the strand and grout, as shown in Figure 13. Grooves were observed as the strand
slid across the bonding interface, indicating that the cement grout failed to keep a tight
grip on the strand. This observation could be attributed to the insufficient interlocking
effect due to the helical configuration of the strand, the shrinkage of cement grout, and
the lubrication effects caused by the oil on the surface of strands in the specimens in the
first batch.

Sustainability 2023,15, 8128 13 of 24
Sustainability 2023, 15, x FOR PEER REVIEW 13 of 26
Figure 11. Bond performance of specimens in the second batch.
Figure 12. Bond performance of specimens in the first batch.
Apparently higher mean bond stresses were observed in specimens with relatively
shorter bonded lengths [37
–
39] as the evenly distributed bond stress assumption was most
likely valid. To beer understand the relative low bond stresses in first batch specimens,
specimen I-60-270P1 was cut through for detailed inspection of the bonding interface be-
tween the strand and grout, as shown in Figure 13. Grooves were observed as the strand
slid across the bonding interface, indicating that the cement grout failed to keep a tight
grip on the strand. This observation could be aributed to the insufficient interlocking
effect due to the helical configuration of the strand, the shrinkage of cement grout, and
the lubrication effects caused by the oil on the surface of strands in the specimens in the
first batch.
Figure 12. Bond performance of specimens in the first batch.
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Figure 13. Bonding interface between strand and grout in Specimen I-60-270P1.
4.3. Cyclic Bond Behaviors
4.3.1. Vertical Forces
The vertical load cell can record the vertical force associated with the V-shaped de-
formation of the strand. As shown in Figure 14, the relationship between the applied ver-
tical force and the measured horizontal force due to the deformation of the strand during
the cyclic testing of Specimen II-60-750 is presented as a representative example. The color
of the curve presented gradually changes from black to light gray with the progression of
cyclic testing. In each cycle of the imposed vertical displacement, the curve consists of a
loading or reloading segment and an unloading segment.
Figure 14. Relationship between vertical force and horizontal force during cyclic testing of Specimen
II-60-750.
Figure 15 shows that both the vertical force and the horizontal force increase with the
progression of testing. A pin-connected truss with simplified geometry, as shown in Fig-
ure 15, is used to calculate the vertical force ignoring any bending and shearing effects for
comparison.
Figure 13. Bonding interface between strand and grout in Specimen I-60-270P1.
4.3. Cyclic Bond Behaviors
4.3.1. Vertical Forces
The vertical load cell can record the vertical force associated with the V-shaped defor-
mation of the strand. As shown in Figure 14, the relationship between the applied vertical
force and the measured horizontal force due to the deformation of the strand during the
cyclic testing of Specimen II-60-750 is presented as a representative example. The color of
the curve presented gradually changes from black to light gray with the progression of
cyclic testing. In each cycle of the imposed vertical displacement, the curve consists of a
loading or reloading segment and an unloading segment.
Figure 15 shows that both the vertical force and the horizontal force increase with
the progression of testing. A pin-connected truss with simplified geometry, as shown in
Figure 15, is used to calculate the vertical force ignoring any bending and shearing effects
for comparison.

Sustainability 2023,15, 8128 14 of 24
Sustainability 2023, 15, x FOR PEER REVIEW 14 of 26
Figure 13. Bonding interface between strand and grout in Specimen I-60-270P1.
4.3. Cyclic Bond Behaviors
4.3.1. Vertical Forces
The vertical load cell can record the vertical force associated with the V-shaped de-
formation of the strand. As shown in Figure 14, the relationship between the applied ver-
tical force and the measured horizontal force due to the deformation of the strand during
the cyclic testing of Specimen II-60-750 is presented as a representative example. The color
of the curve presented gradually changes from black to light gray with the progression of
cyclic testing. In each cycle of the imposed vertical displacement, the curve consists of a
loading or reloading segment and an unloading segment.
Figure 14. Relationship between vertical force and horizontal force during cyclic testing of Specimen
II-60-750.
Figure 15 shows that both the vertical force and the horizontal force increase with the
progression of testing. A pin-connected truss with simplified geometry, as shown in Fig-
ure 15, is used to calculate the vertical force ignoring any bending and shearing effects for
comparison.
Figure 14.
Relationship between vertical force and horizontal force during cyclic testing of Specimen
II-60-750.
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Figure 15. Relationship between applied and calculated vertical forces of seven specimens.
4.3.2. Horizontal Forces at Different Vertical Loading Conditions
Figure 16 shows the relationship between the horizontal force measured by the active
load cell and the cyclic vertical displacement of Specimen II-60-510 as an example. Similar
to Figure 14, each cycle consists of a loading segment and an unloading or reloading seg-
ment.
Figure 16. Relationship between horizontal force and imposed vertical displacement of Specimen
II-60-510.
Figure 16 shows that the horizontal force increases rapidly with the progression of
testing. In the envelope of loading curve segments, the reduction of the rate of increase is
associated with the bond slip. Residual vertical displacement is observed as the measured
horizontal force approaches zero upon unloading. This phenomenon is associated with
multiple factors, including permanent slip at the anchorage.
The trends of force-displacement histories in other cases and their maximum hori-
zontal forces recorded in the loading curve segments at each vertical displacement are
illustrated in Figure 17. Since the results are similar among specimens with different stir-
rup spacings, Specimens II-48-270, and II-80-270 are excluded. Among the five cases pre-
sented, three specimens in the second batch (i.e., II-60-270, II-60-510, and II-60-750) share
a similar trend of maximum horizontal force before reaching a vertical displacement of 60
mm. Normally the softening observed is associated with bond-slip failures. Two
Figure 15. Relationship between applied and calculated vertical forces of seven specimens.
4.3.2. Horizontal Forces at Different Vertical Loading Conditions
Figure 16 shows the relationship between the horizontal force measured by the active
load cell and the cyclic vertical displacement of Specimen II-60-510 as an example. Similar to
Figure 14, each cycle consists of a loading segment and an unloading or
reloading segment
.
Figure 16 shows that the horizontal force increases rapidly with the progression of
testing. In the envelope of loading curve segments, the reduction of the rate of increase is
associated with the bond slip. Residual vertical displacement is observed as the measured
horizontal force approaches zero upon unloading. This phenomenon is associated with
multiple factors, including permanent slip at the anchorage.
The trends of force-displacement histories in other cases and their maximum horizontal
forces recorded in the loading curve segments at each vertical displacement are illustrated
in Figure 17. Since the results are similar among specimens with different stirrup spacings,
Specimens II-48-270, and II-80-270 are excluded. Among the five cases presented, three
specimens in the second batch (i.e., II-60-270, II-60-510, and II-60-750) share a similar trend
of maximum horizontal force before reaching a vertical displacement of 60 mm. Normally
the softening observed is associated with bond-slip failures. Two specimens in the first
batch quickly reached bond failures, and their maximum horizontal forces under higher
vertical displacements were lower than those obtained in the second batch specimens.

Sustainability 2023,15, 8128 15 of 24
Owing to a longer bonded length and lower bond strength, the lowest maximum horizontal
forces were obtained in Specimen I-60-750.
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Figure 15. Relationship between applied and calculated vertical forces of seven specimens.
4.3.2. Horizontal Forces at Different Vertical Loading Conditions
Figure 16 shows the relationship between the horizontal force measured by the active
load cell and the cyclic vertical displacement of Specimen II-60-510 as an example. Similar
to Figure 14, each cycle consists of a loading segment and an unloading or reloading seg-
ment.
Figure 16. Relationship between horizontal force and imposed vertical displacement of Specimen
II-60-510.
Figure 16 shows that the horizontal force increases rapidly with the progression of
testing. In the envelope of loading curve segments, the reduction of the rate of increase is
associated with the bond slip. Residual vertical displacement is observed as the measured
horizontal force approaches zero upon unloading. This phenomenon is associated with
multiple factors, including permanent slip at the anchorage.
The trends of force-displacement histories in other cases and their maximum hori-
zontal forces recorded in the loading curve segments at each vertical displacement are
illustrated in Figure 17. Since the results are similar among specimens with different stir-
rup spacings, Specimens II-48-270, and II-80-270 are excluded. Among the five cases pre-
sented, three specimens in the second batch (i.e., II-60-270, II-60-510, and II-60-750) share
a similar trend of maximum horizontal force before reaching a vertical displacement of 60
mm. Normally the softening observed is associated with bond-slip failures. Two
Figure 16.
Relationship between horizontal force and imposed vertical displacement of Specimen
II-60-510.
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specimens in the first batch quickly reached bond failures, and their maximum horizontal
forces under higher vertical displacements were lower than those obtained in the second
batch specimens. Owing to a longer bonded length and lower bond strength, the lowest
maximum horizontal forces were obtained in Specimen I-60-750.
Figure 17. Relationship between maximum horizontal force and vertical displacement for selective
specimens.
5. Further Evaluation of Testing Results
The experimental data in the previous analysis and the observations of cyclic testing
suggest that the responses of the specimens are considerably affected by a bond failure in
the concrete prism and possible slip at the anchorage(s) at the two ends. To beer under-
stand the performance of the proposed partially debonded tendon system, the testing re-
sults are further evaluated based on the calculated force-elongation responses of the spec-
imens. A two-stage numerical model is developed and calibrated to describe the envelope
of the observed force-elongation responses.
5.1. Calculated Axial Elongation
Figure 18 relates the imposed vertical displacement to the simplified triangular ge-
ometry, as shown in the doed line in Figure 18, to derive the axial elongation of the
strand. Considering the movements measured by the active and passive LVDTs, the axial
elongation induced by the imposed vertical displacement can be calculated as
Figure 17.
Relationship between maximum horizontal force and vertical displacement for
selective specimens.
5. Further Evaluation of Testing Results
The experimental data in the previous analysis and the observations of cyclic testing
suggest that the responses of the specimens are considerably affected by a bond failure
in the concrete prism and possible slip at the anchorage(s) at the two ends. To better
understand the performance of the proposed partially debonded tendon system, the testing
results are further evaluated based on the calculated force-elongation responses of the
specimens. A two-stage numerical model is developed and calibrated to describe the
envelope of the observed force-elongation responses.
5.1. Calculated Axial Elongation
Figure 18 relates the imposed vertical displacement to the simplified triangular ge-
ometry, as shown in the dotted line in Figure 18, to derive the axial elongation of the

Sustainability 2023,15, 8128 16 of 24
strand. Considering the movements measured by the active and passive LVDTs, the axial
elongation induced by the imposed vertical displacement can be calculated as
the lelongation =q4·∆2
vertical +l2
span −lspan −∆active −∆passive (2)
where
∆vertical
,
∆active
and
∆passive
are the readings recorded in the vertical, active, and
passive LVDTs, respectively, and the longer edge of the simplified triangular geometry is
lspan =405 ×2=810 mm.
Sustainability 2023, 15, x FOR PEER REVIEW 16 of 26
specimens in the first batch quickly reached bond failures, and their maximum horizontal
forces under higher vertical displacements were lower than those obtained in the second
batch specimens. Owing to a longer bonded length and lower bond strength, the lowest
maximum horizontal forces were obtained in Specimen I-60-750.
Figure 17. Relationship between maximum horizontal force and vertical displacement for selective
specimens.
5. Further Evaluation of Testing Results
The experimental data in the previous analysis and the observations of cyclic testing
suggest that the responses of the specimens are considerably affected by a bond failure in
the concrete prism and possible slip at the anchorage(s) at the two ends. To beer under-
stand the performance of the proposed partially debonded tendon system, the testing re-
sults are further evaluated based on the calculated force-elongation responses of the spec-
imens. A two-stage numerical model is developed and calibrated to describe the envelope
of the observed force-elongation responses.
5.1. Calculated Axial Elongation
Figure 18 relates the imposed vertical displacement to the simplified triangular ge-
ometry, as shown in the doed line in Figure 18, to derive the axial elongation of the
strand. Considering the movements measured by the active and passive LVDTs, the axial
elongation induced by the imposed vertical displacement can be calculated as
Figure 18. Simplified assumptions for calculation of axial elongation.
The experimental results of the two extreme cases are replotted in Figure 19 with the
corresponding axial elongation calculated based on the vertical loading conditions. Com-
pared with Specimen I-60-750 with early bond failure, the stiffnesses associated with the
loading curve segment of Specimen II-60-750 are much higher, which could be explained by
the additional participation of the anchorage at the passive side of the specimen. The early
bond failure certainly affected the fixity of the strand in the concrete prism as evidenced by
the readings of the passive load cell for Specimen I-60-750.
Sustainability 2023, 15, x FOR PEER REVIEW 17 of 26
Figure 18. Simplified assumptions for calculation of axial elongation.
𝑡ℎ𝑒 𝑙 4∙∆
𝑙
𝑙 ∆ ∆ (2)
where ∆, ∆ and ∆ are the readings recorded in the vertical, active, and
passive LVDTs, respectively, and the longer edge of the simplified triangular geometry is
𝑙  405  2  810 mm.
The experimental results of the two extreme cases are reploed in Figure 19 with the
corresponding axial elongation calculated based on the vertical loading conditions. Com-
pared with Specimen I-60-750 with early bond failure, the stiffnesses associated with the
loading curve segment of Specimen II-60-750 are much higher, which could be explained
by the additional participation of the anchorage at the passive side of the specimen. The
early bond failure certainly affected the fixity of the strand in the concrete prism as evi-
denced by the readings of the passive load cell for Specimen I-60-750.
Figure 19. Relationship between horizontal force and elongation for two specimens.
5.2. Deterioration of Fixity Due to Bond Failure
From the analysis of pull-out testing of strand-anchor systems of Sideris (2012), the
wedges slide on the tapered interior surface of the barrel chucks to provide larger radial
compression to the strand as the axial load in the strand increases. Owing to the high
friction at the wedge-to-barrel chuck interface, the wedges cannot slide back in the oppo-
site direction as the axial strand force reduces as if the wedges remain “locked” at their
ever-reached maximum sliding amplitude. The stiffnesses of the reloading curve seg-
ments at different vertical displacements are relevant characteristics. The effective length
of the strand can be estimated accordingly.
Figure 20 shows that the original effective length 𝑙, of the strand before testing is
1260 mm. The effective elastic stiffness is then calculated based on strand material prop-
erties as 𝑘  200 𝐺𝑃𝑎 140 mm 1260 mm  22.2 kN/mm . According to experi-
mental results presented in Figure 20a, the reloading stiffnesses of specimens II-60-510
and II-60-750 agree well with the effective stiffness, and no deterioration is observed, in-
dicating that the original effective length of the strand is maintained under high loading
scenarios. In the other three specimens, as shown in Figure 20b, the reloading stiffnesses
deteriorate upon the bond failure. The largest stiffness reduction is observed in Specimen
I-60-750, which can be aributed to the lower bond strength and larger bonded length
Figure 19. Relationship between horizontal force and elongation for two specimens.
5.2. Deterioration of Fixity Due to Bond Failure
From the analysis of pull-out testing of strand-anchor systems of Sideris (2012), the
wedges slide on the tapered interior surface of the barrel chucks to provide larger radial
compression to the strand as the axial load in the strand increases. Owing to the high

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friction at the wedge-to-barrel chuck interface, the wedges cannot slide back in the opposite
direction as the axial strand force reduces as if the wedges remain “locked” at their ever-
reached maximum sliding amplitude. The stiffnesses of the reloading curve segments at
different vertical displacements are relevant characteristics. The effective length of the
strand can be estimated accordingly.
Figure 20 shows that the original effective length
le f f ,O
of the strand before testing
is 1260 mm. The effective elastic stiffness is then calculated based on strand material
properties as
ke f f =
200
GPa ×
140
mm2÷
1260
mm =
22.2
kN/mm
. According to
experimental results presented in Figure 20a, the reloading stiffnesses of specimens II-60-
510 and II-60-750 agree well with the effective stiffness, and no deterioration is observed,
indicating that the original effective length of the strand is maintained under high loading
scenarios. In the other three specimens, as shown in Figure 20b, the reloading stiffnesses
deteriorate upon the bond failure. The largest stiffness reduction is observed in Specimen
I-60-750, which can be attributed to the lower bond strength and larger bonded length
when compared with the other cases as shown in Figure 21. To estimate the additional
effective length le f f ,add caused by bond failure, one may use
le f f ,add =ke f f
ktrans
−1le f f ,O(3)
where the ktrans denotes the transient reloading stiffness.
Sustainability 2023, 15, x FOR PEER REVIEW 18 of 26
when compared with the other cases as shown in Figure 21. To estimate the additional
effective length 𝑙, caused by bond failure, one may use
𝑙, 󰇧𝑘
𝑘 1󰇨𝑙, (3)
where the 𝑘 denotes the transient reloading stiffness.
(a)
(b)
Figure 20. Reloading stiffnesses at different vertical displacement conditions for selected specimens
(a) without deterioration; and (b) with deterioration.
Figure 20.
Reloading stiffnesses at different vertical displacement conditions for selected specimens
(a) without deterioration; and (b) with deterioration.

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Figure 21. Estimation of additional effective lengths at 80 mm imposed vertical displacement.
5.3. Two-Stage Numerical Model for Partially Debonded Tendon System
The unloading and reloading curve segments of the horizontal force and elongation
histories can be characterized by the effective elastic stiffness 𝑘 and the additional ef-
fective length 𝑙, calculated by Equation (3) with the transient reloading stiffness
𝑘. However, the loading curve segments of the experimental results in the horizontal
force and elongation histories are affected by several factors, including the loading stiff-
ness 𝑘 of the anchorage(s) and the stiffness 𝑘 of the strand.
5.3.1. Establishment of the Model
Referring to the previous model for the direct pull-out strand-anchor system [40] and
the observations in the proposed cyclic bond testing, a simplified two-stage numerical
model, as shown in Figure 22, is established to describe the envelope of the responses of
the partially debonded tendon system.
Figure 22. A two-stage numerical model for partially debonded tendon system.
Specifically, at the initial stage, an anchorage spring and a strand spring are con-
nected in series to describe the loading curve segment of the partially debonded tendon
system. Upon observation of bond failure, the subsequent loading curve segment is de-
scribed by three springs in series, where another anchorage spring with identical loading
Figure 21. Estimation of additional effective lengths at 80 mm imposed vertical displacement.
5.3. Two-Stage Numerical Model for Partially Debonded Tendon System
The unloading and reloading curve segments of the horizontal force and elongation
histories can be characterized by the effective elastic stiffness
ke f f
and the additional
effective length
le f f ,add
calculated by Equation (3) with the transient reloading stiffness
ktrans
. However, the loading curve segments of the experimental results in the horizontal
force and elongation histories are affected by several factors, including the loading stiffness
kaof the anchorage(s) and the stiffness ksof the strand.
5.3.1. Establishment of the Model
Referring to the previous model for the direct pull-out strand-anchor system [
40
] and
the observations in the proposed cyclic bond testing, a simplified two-stage numerical
model, as shown in Figure 22, is established to describe the envelope of the responses of
the partially debonded tendon system.
Sustainability 2023, 15, x FOR PEER REVIEW 19 of 26
Figure 21. Estimation of additional effective lengths at 80 mm imposed vertical displacement.
5.3. Two-Stage Numerical Model for Partially Debonded Tendon System
The unloading and reloading curve segments of the horizontal force and elongation
histories can be characterized by the effective elastic stiffness 𝑘 and the additional ef-
fective length 𝑙, calculated by Equation (3) with the transient reloading stiffness
𝑘. However, the loading curve segments of the experimental results in the horizontal
force and elongation histories are affected by several factors, including the loading stiff-
ness 𝑘 of the anchorage(s) and the stiffness 𝑘 of the strand.
5.3.1. Establishment of the Model
Referring to the previous model for the direct pull-out strand-anchor system [40] and
the observations in the proposed cyclic bond testing, a simplified two-stage numerical
model, as shown in Figure 22, is established to describe the envelope of the responses of
the partially debonded tendon system.
Figure 22. A two-stage numerical model for partially debonded tendon system.
Specifically, at the initial stage, an anchorage spring and a strand spring are con-
nected in series to describe the loading curve segment of the partially debonded tendon
system. Upon observation of bond failure, the subsequent loading curve segment is de-
scribed by three springs in series, where another anchorage spring with identical loading
Figure 22. A two-stage numerical model for partially debonded tendon system.
Specifically, at the initial stage, an anchorage spring and a strand spring are connected
in series to describe the loading curve segment of the partially debonded tendon system.
Upon observation of bond failure, the subsequent loading curve segment is described by

Sustainability 2023,15, 8128 19 of 24
three springs in series, where another anchorage spring with identical loading stiffness
would be added and the strand spring at the initial stage would be softened by a factor
γ
calculated based on the additional fixity length as
γ=le f f ,O/le f f ,add +le f f ,O(4)
The force-elongation models adopted for these springs are shown in Figure 23.
Sustainability 2023, 15, x FOR PEER REVIEW 20 of 26
stiffness would be added and the strand spring at the initial stage would be softened by a
factor 𝛾 calculated based on the additional fixity length as
𝛾𝑙, / 𝑙, 𝑙, (4)
The force‒elongation models adopted for these springs are shown in Figure 23.
(a) (b) (c)
Figure 23. Force‒elongation models: (a) anchorage springs; (b) strand spring; and (c) softened strand
spring.
5.3.2. Calibration of the Models
The stiffness of anchorage 𝑘, the stiffness of strand 𝑘,and the additional effective
length are calibrated with the representative experimental results of Specimens II-60-270
and II-60-750; the calibrated 𝑘 and 𝑘 are identical while the calibrated additional effec-
tive lengths are different in these two cases. The additional effective length is first deter-
mined based on the angent value of the unloading and reloading curve segments. Negli-
gible bond damage was observed in Specimen II-60-750, so the additional effective length
is zero and there is only one stage in Specimen II-60-750, and the sum of 𝑘 and 𝑘 can
be calculated according to the tangent value of the loading curve segment. Considering
the additional results in Specimen II-60-270, the 𝑘 and 𝑘 can be determined.
Since 𝑘𝑘 and the calibrated 𝑘 is larger than 𝑘 , therefore, 𝑘𝑘 
22.2 𝑘𝑁/𝑚𝑚 is adopted, and 𝑘 26.3 𝑘𝑁/𝑚𝑚 is determined accordingly. The relevant
values are determined from the experimental results to describe the transition between
various stages and various loading/unloading curve segments. The corresponding param-
eters are listed in Table 4, and the related envelopes provided by the calibrated two-stage
models are presented in Figures 24 and 25.
Table 4. Parameters used for two-stage model calibration.
Unit II-60-270 II-60-750
maximum bond force kN 63 154
maximum horizontal force kN 130 154
anchorage stiffness 𝑘 kN/mm 26.3 26.3
strand stiffness 𝑘 kN/mm 22.2 22.2
additional effective length mm 180 0
softening factor 𝛾 - 0.875 1
Figure 23.
Force-elongation models: (
a
) anchorage springs; (
b
) strand spring; and (
c
) softened
strand spring.
5.3.2. Calibration of the Models
The stiffness of anchorage
ka
, the stiffness of strand
ks
, and the additional effective
length are calibrated with the representative experimental results of Specimens II-60-270
and II-60-750; the calibrated
ka
and
ks
are identical while the calibrated additional effective
lengths are different in these two cases. The additional effective length is first determined
based on the angent value of the unloading and reloading curve segments. Negligible bond
damage was observed in Specimen II-60-750, so the additional effective length is zero and
there is only one stage in Specimen II-60-750, and the sum of
ka
and
ks
can be calculated
according to the tangent value of the loading curve segment. Considering the additional
results in Specimen II-60-270, the kaand kscan be determined.
Since
ks≤ke f f
and the calibrated
ks
is larger than
ke f f
, therefore,
ks=ke f f =
22.2
kN/mm
is adopted, and
ka=
26.3
kN/mm
is determined accordingly. The relevant
values are determined from the experimental results to describe the transition between
various stages and various loading/unloading curve segments. The corresponding param-
eters are listed in Table 4, and the related envelopes provided by the calibrated two-stage
models are presented in Figures 24 and 25.
Table 4. Parameters used for two-stage model calibration.
Unit II-60-270 II-60-750
maximum bond force kN 63 154
maximum horizontal force kN 130 154
anchorage stiffness kakN/mm 26.3 26.3
strand stiffness kskN/mm 22.2 22.2
additional effective length mm 180 0
softening factor γ- 0.875 1

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Figure 24. Envelope for force‒elongation history for Specimen II-60-270.
Figure 25. Envelope for force‒elongation history for Specimen II-60-750.
5.3.3. Comparison of Calibrated Model with Other Results
By similar procedures, a comparison between the numerical and experimental results
is provided for each of the other three cases and presented in Figures 26 and 27 with the
parameters listed in Table 5.
Figure 24. Envelope for force-elongation history for Specimen II-60-270.
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Figure 24. Envelope for force‒elongation history for Specimen II-60-270.
Figure 25. Envelope for force‒elongation history for Specimen II-60-750.
5.3.3. Comparison of Calibrated Model with Other Results
By similar procedures, a comparison between the numerical and experimental results
is provided for each of the other three cases and presented in Figures 26 and 27 with the
parameters listed in Table 5.
Figure 25. Envelope for force-elongation history for Specimen II-60-750.
5.3.3. Comparison of Calibrated Model with Other Results
By similar procedures, a comparison between the numerical and experimental results
is provided for each of the other three cases and presented in Figures 26 and 27 with the
parameters listed in Table 5.
In general, the envelopes provided by the calibrated numerical models are in good
agreement with the experimental force and elongation histories in the other three cases,
particularly with regard to the value of stiffness at the bond failure stage. For the force
and elongation history of Specimen I-60-750, as shown in Figure 28, the stiffness transition
between the initial and bond failure stages is unclear, and the additional effective length
obtained as 970 mm is much larger than the length of the concrete prism, which can be
attributed to the overestimated vertical displacement during the cyclic testing.

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Figure 26. Envelope for force‒elongation history for Specimen I-60-270.
Figure 27. Envelope for force‒elongation history for Specimen I-60-750.
Table 5. Parameters used for comparison.
Unit I-60-270 I-60-750 II-60-510
maximum bond force kN 14 63 126
maximum horizontal force kN 73 130 145
anchorage stiffness 𝑘 kN/mm 26.3 26.3 26.3
strand stiffness 𝑘 kN/mm 22.2 22.2 22.2
additional effective length mm 270 970 70
softening factor 𝛾 - 0.824 0.565 0.947
In general, the envelopes provided by the calibrated numerical models are in good
agreement with the experimental force and elongation histories in the other three cases,
particularly with regard to the value of stiffness at the bond failure stage. For the force
and elongation history of Specimen I-60-750, as shown in Figure 28, the stiffness transition
between the initial and bond failure stages is unclear, and the additional effective length
obtained as 970 mm is much larger than the length of the concrete prism, which can be
aributed to the overestimated vertical displacement during the cyclic testing.
Figure 26. Envelope for force-elongation history for Specimen I-60-270.
Sustainability 2023, 15, x FOR PEER REVIEW 22 of 26
Figure 26. Envelope for force‒elongation history for Specimen I-60-270.
Figure 27. Envelope for force‒elongation history for Specimen I-60-750.
Table 5. Parameters used for comparison.
Unit I-60-270 I-60-750 II-60-510
maximum bond force kN 14 63 126
maximum horizontal force kN 73 130 145
anchorage stiffness 𝑘 kN/mm 26.3 26.3 26.3
strand stiffness 𝑘 kN/mm 22.2 22.2 22.2
additional effective length mm 270 970 70
softening factor 𝛾 - 0.824 0.565 0.947
In general, the envelopes provided by the calibrated numerical models are in good
agreement with the experimental force and elongation histories in the other three cases,
particularly with regard to the value of stiffness at the bond failure stage. For the force
and elongation history of Specimen I-60-750, as shown in Figure 28, the stiffness transition
between the initial and bond failure stages is unclear, and the additional effective length
obtained as 970 mm is much larger than the length of the concrete prism, which can be
aributed to the overestimated vertical displacement during the cyclic testing.
Figure 27. Envelope for force-elongation history for Specimen I-60-750.
Table 5. Parameters used for comparison.
Unit I-60-270 I-60-750 II-60-510
maximum bond force kN 14 63 126
maximum horizontal force kN 73 130 145
anchorage stiffness kakN/mm 26.3 26.3 26.3
strand stiffness kskN/mm 22.2 22.2 22.2
additional effective length mm 270 970 70
softening factor γ- 0.824 0.565 0.947
From the analysis of the response provided by the proposed two-stage numerical
model, the contribution of the anchorages to the response of the partially debonded tendon
system is significant as the stiffness of the anchorages
ka
is comparable to that of the
strand. The stiffness of the strand
ks
is taken to be equal to the effective elastic stiffness
ke f f
,
indicating that the strand is performing within its elastic stage.
The anchorage used in this study consists of three steel wedges and a barrel chuck. The
calibrated stiffness of the anchorage
ka
is equal to 26.3 kN/mm and its unloading/reloading
stiffness is taken to be infinite due to the high friction locking effect. However, the choice of
such values should be subject to the shape of the anchorage.

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Figure 28. Envelope for force‒elongation history for Specimen II-60-510.
From the analysis of the response provided by the proposed two-stage numerical
model, the contribution of the anchorages to the response of the partially debonded ten-
don system is significant as the stiffness of the anchorages 𝑘 is comparable to that of the
strand. The stiffness of the strand 𝑘 is taken to be equal to the effective elastic stiffness
𝑘, indicating that the strand is performing within its elastic stage.
The anchorage used in this study consists of three steel wedges and a barrel chuck.
The calibrated stiffness of the anchorage 𝑘 is equal to 26.3 kN/mm and its unloading/re-
loading stiffness is taken to be infinite due to the high friction locking effect. However, the
choice of such values should be subject to the shape of the anchorage.
6. Conclusions
In this paper, the sustainable design of PSBC with RSJ is introduced, specimens with
grouted strands are prepared to conduct the quasi-static cyclic bond testing, and the re-
sponse of a typical partially debonded tendon system under orthogonal cyclic displace-
ment is presented and analyzed. A two-stage numerical model is developed to capture
the envelope of the observed responses as well as to simulate the contributions from the
key components of the partially debonded tendon system. Based on the experimental and
simulation results, the following conclusions can be drawn:
• The established setup of the simplified bond testing is suitable to study the cyclic
bond behavior of partially debonded tendons. For tendons with relatively low bond
stresses, the stirrups in the specimens hardly affect the debonding between the ten-
don and grout. The direct axial tension and cyclic orthogonal displacement provide
comparable values of bond strength.
• The deterioration of reloading stiffnesses can be represented by an additional effec-
tive debonded length caused by a bond failure in specimens. For partially debonded
tendons with low initial prestress, the gradual fastening of the end anchorages must
be considered as the loading stiffness during analysis.
• With proper calibration, a two-stage numerical model with a series of anchorage and
strand springs can satisfactorily capture the envelope of the responses of the partially
debonded tendon system.
• Despite the observation of permanent transverse deformation after testing, the 7-wire
strand performs essentially elastically under large imposed vertical displacement
(maximum orthogonal curvature at 12°) in the simplified cyclic bond testing, and
Figure 28. Envelope for force-elongation history for Specimen II-60-510.
6. Conclusions
In this paper, the sustainable design of PSBC with RSJ is introduced, specimens with
grouted strands are prepared to conduct the quasi-static cyclic bond testing, and the re-
sponse of a typical partially debonded tendon system under orthogonal cyclic displacement
is presented and analyzed. A two-stage numerical model is developed to capture the en-
velope of the observed responses as well as to simulate the contributions from the key
components of the partially debonded tendon system. Based on the experimental and
simulation results, the following conclusions can be drawn:
•
The established setup of the simplified bond testing is suitable to study the cyclic bond
behavior of partially debonded tendons. For tendons with relatively low bond stresses,
the stirrups in the specimens hardly affect the debonding between the tendon and
grout. The direct axial tension and cyclic orthogonal displacement provide comparable
values of bond strength.
•
The deterioration of reloading stiffnesses can be represented by an additional effective
debonded length caused by a bond failure in specimens. For partially debonded
tendons with low initial prestress, the gradual fastening of the end anchorages must
be considered as the loading stiffness during analysis.
•
With proper calibration, a two-stage numerical model with a series of anchorage and
strand springs can satisfactorily capture the envelope of the responses of the partially
debonded tendon system.
•
Despite the observation of permanent transverse deformation after testing, the 7-wire
strand performs essentially elastically under large imposed vertical displacement
(maximum orthogonal curvature at 12
◦
) in the simplified cyclic bond testing, and the
anchorage slip helps to dissipate energy. The proposed partially debonded tendon
system can be a suitable option for precast segmental bridge columns with RSJs.
Author Contributions:
Conceptualization, Y.L.; methodology, Y.L.; software, L.X. and Y.L.; validation,
L.X. and Y.L.; formal analysis, L.X. and Y.L.; investigation, L.X. and Y.L.; resources, H.H. and S.G.;
data curation, Y.I.S.; writing—original draft preparation, L.X. and Y.L.; writing—review and editing,
Y.I.S. and Y.L.; visualization, L.X.; supervision, Y.L.; project administration, Y.L.; funding acquisition,
Y.L. All authors have read and agreed to the published version of the manuscript.
Funding:
This research was partially funded by [the Ministry of Science and Technology, China]
grant number [2019YFB1600702].
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: https://figshare.com/s/f3d763899cd580d5577c.

Sustainability 2023,15, 8128 23 of 24
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
cconcrete cover to reinforcement in concrete prism
ka,ksstiffness of anchorage and strand, respectively
ke f f effective stiffness of steel mono-strand
ktrans transient stiffness of steel mono-strand
le f f,add additional fixity length induced by strand bond failure
le f f,Ooriginal fixity length determined by the setup
lelongation axial elongation of strand induced by vertical loading
ldb debonded length of partially debonded tendons
lspan free length of the strand in cyclic bond testing
lspecimen total length of concrete prism
∆active measurement recorded in active LVDT
∆passive measurement recorded in passive LVDT
∆vertical measurement recorded in vertical LVDT
γstiffness softening factor of strand due to bond failures
ABC accelerated bridge construction
LVDT linear variable differential transformer
PSBC precast segmental bridge columns
RSJ resettable sliding joint
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