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This paper explores the performance of distributed optical fiber sensors based on Rayleigh backscattering for the monitoring of strains in reinforced concrete elements subjected to different types of long-term external loading. In particular, the reliability and accuracy of robust fiber optic cables with an inner steel tube and an external protective polymeric cladding were investigated through a series of laboratory experiments involving large-scale reinforced concrete beams subjected to either sustained deflection or cyclic loading for 96 days. The unmatched spatial resolution of the strain measurements provided by the sensors allows for a level of detail that leads to new insights in the understanding of the structural behavior of reinforced concrete specimens. Moreover , the accuracy and stability of the sensors enabled the monitoring of subtle strain variations, both in the short-term due to changes of the external load and in the long-term due to time-dependent effects such as creep. Moreover, a comparison with Digital Image Correlation measurements revealed that the strain measurements and the calculation of deflection and crack widths derived thereof remain accurate over time. Therefore, the study concluded that this type of fiber optic has great potential to be used in real long-term monitoring applications in reinforced concrete structures .
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Sensors 2021, 21, 6338. https://doi.org/10.3390/s21196338 www.mdpi.com/journal/sensors
Article
Long-Term Performance of Distributed Optical Fiber Sensors
Embedded in Reinforced Concrete Beams under Sustained
Deflection and Cyclic Loading
Ignasi Fernandez 1,*, Carlos G. Berrocal 1,2 and Rasmus Rempling 1,3
1 Division of Structural Engineering, Chalmers University of Technology, 41296 Göteborg, Sweden;
carlos.gil@chalmers.se (C.G.B.); rasmus.rempling@chalmers.se (R.R.)
2 Thomas Concrete Group AB, Södra Vägen 28, 41254 Göteborg, Sweden
3 NCC Sverige AB, 205 47 Gotheburg, Sweden
* Correspondence: ignasi.fernandez@chalmers.se
Abstract: This paper explores the performance of distributed optical fiber sensors based on Rayleigh
backscattering for the monitoring of strains in reinforced concrete elements subjected to different
types of long-term external loading. In particular, the reliability and accuracy of robust fiber optic
cables with an inner steel tube and an external protective polymeric cladding were investigated
through a series of laboratory experiments involving large-scale reinforced concrete beams sub-
jected to either sustained deflection or cyclic loading for 96 days. The unmatched spatial resolution
of the strain measurements provided by the sensors allows for a level of detail that leads to new
insights in the understanding of the structural behavior of reinforced concrete specimens. Moreo-
ver, the accuracy and stability of the sensors enabled the monitoring of subtle strain variations, both
in the short-term due to changes of the external load and in the long-term due to time-dependent
effects such as creep. Moreover, a comparison with Digital Image Correlation measurements re-
vealed that the strain measurements and the calculation of deflection and crack widths derived
thereof remain accurate over time. Therefore, the study concluded that this type of fiber optic has
great potential to be used in real long-term monitoring applications in reinforced concrete struc-
tures.
Keywords: reinforced concrete; distributed optical fiber sensing; Rayleigh backscattering; cyclic
loading; performance indicators
1. Introduction
According to a recent report [1], only about 25% of the infrastructure required to meet
the needs of the projected world’s population growth and the increasing migration to ur-
ban areas is currently built. This huge demand for new infrastructure is shaped by con-
temporary social and environmental challenges that require the development of more sus-
tainable construction: safer, climate resilient and energy efficient. To that end, the integra-
tion of Structural Health Monitoring (SHM) systems in newly built structures would en-
able the early detection of structural faults, hence the planning of timely repair/strength-
ening measures, while preventing the occurrence of potentially catastrophic accidents due
to improper maintenance, thus leading to tremendous economical savings while mini-
mizing the social impact of ageing infrastructure. Unfortunately, the use of SHM systems
in civil engineering structures is still reserved to very specific cases due to the lack of
reliable, scalable and affordable monitoring solutions [2].
Optical fiber sensors have gained considerable traction in the past decade due to hav-
ing numerous advantages over other traditional sensors, such as their small size, light
weight, corrosion resistance and immunity to electromagnetic fields [3]. Even though
Citation:
Fernandez, I.; Berrocal,
C.G.; Rempling, R.
Long-Term
Performance of Distributed Optical
Fiber Sensors Embedded in
Reinforced Concrete Beams under
Sustained Deflection and Cyclic
Loading.
Sensors 2021, 21, 6338.
https://doi.org/10.3390/s21196338
Academic Editor
s: Nicola Giaquinto,
Francesco Adamo
and Maurizio
Spadave
cchia
Received:
06 September 2021
Accepted:
20 September 2021
Published:
22 September 2021
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opyright: © 2021 by the authors. Li-
censee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and con-
ditions of the Creative Commons At-
tribution (CC BY) license (http
://crea-
tivecommons.org/licenses/by/4.0/).
Sensors 2021, 21, 6338 2 of 20
Fiber Bragg Grating and FabryPerot are currently the most commonly used type of opti-
cal fiber sensors in practice [4,5], they have restrictions regarding the number and spacing
of measuring gauges, which limits their applicability. One possible solution to overcome
the limitations of this type of sensors is the use of multiplexing, which can deliver quasi-
distributed fiber optic sensors, see, e.g., [6]. However, recent advancements in optical fiber
sensing have led to the development of Distributed Optical Fiber Sensors (DOFS), featur-
ing unprecedented spatial resolutions that open up a broad range of new applications. For
strain sensing, the two main available technologies are Brillouin and Rayleigh backscat-
tering based sensors. Brillouin backscattering allows for a measuring range of up to sev-
eral hundreds of km, yet its spatial resolution is limited to a few tens of centimeters [7].
Conversely, the range of Rayleigh backscattering sensors is currently limited to about 70
m but, in exchange, they offer a spatial resolution in the sub-millimetric scale [8].
Considerable work has been carried out using both technologies in order to investi-
gate the suitability of using DOFS for the monitoring of the civil infrastructure. In partic-
ular, the viability of applying Rayleigh-based DOFS for crack detection and crack width
monitoring in reinforced concrete structures has been already studied through laboratory
experiments by several teams of researchers, see, e.g., [914]. Regarding crack detection
in concrete structures, it is of special relevance the pioneering work led by Casas and col-
leagues, which focused on the use of thin polyimide-coated fibers bonded to either the
concrete surface [15,16], or the reinforcement [17] as well as on different bonding tech-
niques and their impact on the quality of the strain measurements [18,19]. Similarly, Hoult
and coworkers have made important contributions to the topic of crack detection and
monitoring in reinforced concrete structures, where they have developed strategies to lo-
cate and quantify the individual crack width of multiple cracks in a same element using
both embedded and surface-bonded thin nylon-coated fiber sensors [2022]. In a more
recent study by Bassil et al. [23,24], a shear lag model was calibrated to establish an ana-
lytical relationship between the crack width of a single crack and the strain measurement
of robust sensing cables, which was verified on several types of cable, both embedded and
bonded inside a notch in the concrete surface.
In a previous study by the authors [25], it was shown that when using robust fiber
optic sensors embedded in concrete, most cracks could be clearly identified in the strain
profiles as regions of strain localization and that the integration of the strain curve, within
a neighboring region of the crack, provided a good approximation of the individual crack
width without the need of additional analytical models. In the same study, it was demon-
strated that when bending is dominant, performing a double integration of the curvature
distribution, calculated from the strain distribution at two different heights of the beam,
provides an accurate estimation of the deflections, given the right boundary conditions
are applied. Brault and Hoult had previously demonstrated the validity of this approach
for thin fibers bonded to the surface of RC beams [26] and later, Poldon et al. [27] investi-
gated the error introduced by this approach when shear behavior is dominant, through
large-scale beam tests.
The study and application of DOFS has not been limited to laboratory experiments
and several cases exist where this sensing technology has been successfully deployed and
applied on-site for the monitoring of real structures. Some examples of real-world appli-
cations are the Sarajevo bridge [28], the precast tunnel lining of the L9 subway line in
Barcelona [29], the shotcrete lining in the Sammering Base tunnel [30] or the monitoring
of driven ductile piles [31], to mention just a few. Despite the successful implementation
of DOFS systems in real structures, the existing applications are often either limited to the
measurement of strains or unable to be validated against complementary systems or car-
ried out in a discontinuous way and/or for a short period of time. Therefore, one of the
aspects that needs to be further investigated is the long-term performance of DOFS sen-
sors for the accurate and reliable assessment of crack widths and deflections based on
strain measurements and, particularly, under cyclic loading, as highlighted in a recent
review paper by Bado et al. [32].
Sensors 2021, 21, 6338 3 of 20
Indeed, the number of available studies reporting experimental evidence of the per-
formance of DOFS under repeated load cycles is scarce. In Barrias et al. [33], two short
reinforced concrete beams with dimensions 150 × 150 × 600 mm and outfitted with thin
polyimide-coated fiber sensors attached to the bottom surface of the beams using different
types of adhesive, were subjected to fatigue testing using 2 million load cycles at a fre-
quency of 4 Hz and a constant load range between 11.75 and 13.73 kN. Their results
showed that the DOFS had good stability with no signs of performance loss even after the
2 million cycles. However, the type of adhesive used played a key role in the accuracy of
the results, especially when cracks were present. In Cantone et al. [34], thin polyimide-
coated fibers were either inserted into a notch carved along a reinforcement bar or glued
to the surface of a rebar using cyanoacrylate adhesive, in order to revisit the theory behind
steelconcrete interaction through a series of cyclic loading tests in both tensile and bend-
ing members. In the tensile tests, 100 load cycles between the maximum and minimum
nominal stresses of 275 and 27.5 MPa, respectively, were applied to tie-rod elements with
dimensions 100 × 100 × 1150 mm at a frequency of approximately 1 cycle every 2 min. In
the bending tests, three beams with dimensions 300 × 320 × 3000 mm were subjected to 50
quasi-static load cycles at a different maximum force each, prior to unloading and reload-
ing them to failure. Even though the aim of the work was not to assess the performance
of the DOFS, no issues with the strain measurements were reported regardless of the load-
ing configuration, the presence of cracks or the maximum load of the cycles. A recent
study by Broth and Hoult [35], looked into the potential of using dynamic DOFS for mon-
itoring of reinforced concrete elements under repeated loading. To that end, two groups
of four reinforced concrete beams with dimensions 350 × 230 × 2850 mm and 550 × 250 ×
2850 mm were subjected to 3600 load cycles at 1 Hz under three and four-point bending
configuration reaching a maximum strain in the tensile reinforcement of 1500 µm. Thin
nylon-coated fiber optic cables were bonded to the top and bottom reinforcement using
cyanoacrylate adhesive and further protected with a layer of silicone. In that study, the
authors reported that the type of fiber and installation method used was able to withstand
the dynamic cyclic loading.
Despite the successful application of thin polyimide-coated fibers in the mentioned
studies, this type of fiber still presents critical challenges with respect to its deployment
in real RC structures. Indeed, in addition to their fragile nature, which requires extreme
care during handling, a number of studies have reported that Strain Reading Anomalies
(SRAs) are commonly observed at points where the DOFS cross a crack, both when
bonded to the concrete surface and to the embedded reinforcement [17,21,36,37], high-
lighting the importance of choosing the correct combination of adhesive and protective
coatings. The use of robust fiber optic cables with one or more protective layers around
the glass core (cladding, coating, buffer, etc.), which are better suited for the demands of
on-site operations, arises as a natural step in order to bring the manifold advantages of
distributed fiber optics identified and verified through numerous laboratory experiments
to real structures. However, there is currently a lack of experiments looking at the perfor-
mance of robust cables for strain monitoring in RC structures, particularly under long-
term cyclic loading.
The aim of this paper is to investigate the long-term performance in terms of strain
monitoring of robust optic fiber cables when embedded in RC elements. To achieve that
aim, an experimental program was devised where large-scale RC beams were outfitted
with robust DOFS and strains were continuously monitored while the beams were sub-
jected to either sustained deflection or cyclic loading for an extended period. The strain
measurements of the DOFS were complemented by surface measurements from Digital
Image Correlation. The following sections of this paper provide a description of the ex-
perimental program, a discussion of the test results and the main findings of the study.
Sensors 2021, 21, 6338 4 of 20
2. Experimental Program
An experimental program was devised to investigate the long-term performance of
DOFS as well as to assess their ability to provide accurate information about a structure’s
serviceability condition under sustained and cyclic loading. The program comprised four
identical RC beams, all of them outfitted with DOFS deployed in a multilayer configura-
tion. All four beams were initially pre-cracked and later divided into two groups: (i) two
beams subjected to a sustained deflection and (ii) two beams subjected cyclic loading. The
tests were conducted over a period of 96 days, for which DOFS measurements were rec-
orded periodically under the test duration. The most relevant aspects of the experimental
program are described in the following.
2.1. Geometry and Reinforcement Layout
The specimens used in this work were RC beams with a total length of 3 m and a
rectangular cross-section of 200 × 250 mm. Each beam was reinforced with three 16 mm
rebar at the bottom and two 10 mm at the top. Moreover, six 8 mm closed-loop stirrups
equally spaced at 200 mm were placed on either side of the beams. All reinforcement was
made of normal ductility carbon-steel (B500B) with a nominal yield strength of 500 MPa.
Plastic spacers were placed between the stirrups and the bottom and lateral sides of the
form to ensure a clear concrete cover of 20 mm. The ends of the bottom bars were bent
upwards to improve the anchorage. The geometry and reinforcement layout of the beams
is presented in Figure 1. Note that at one of the beam ends, the bars protruded from the
concrete surface, which was required for a later stage of the experiments in which accel-
erated corrosion was planned.
Figure 1. Geometry of the beam specimens, reinforcement layout and DOFS configuration (all measurements in mm).
A self-compacting concrete mix with a water-to-cement ratio (w/c) of 0.45 was used
to cast all the beams. The mix included a sulphate resistant Portland cement with low C3A
content and moderate heat development. Following the casting, the beams were covered
with a polyethylene sheet to reduce moisture evaporation and stored in an indoor climate
(20 ± 2 °C and 60 ± 10% RH) for 15 days until they were pre-cracked. Thereafter, the beams
remained in the same indoor climate for 6 months until the long-term experiments were
initiated. The concrete compressive strength at 28 days was 68.2 MPa (CoV = 5.6%) based
on tests performed in accordance with EN 12390-3:2009 [38] on three 150 mm cubes.
Sensors 2021, 21, 6338 5 of 20
2.2. Instrumentation
In this study, the robust fiber optic cable BRUsens V9 from Solifos, featuring an inner
steel tube and an external rugged polyamide cladding, was used. The V9 cable has a 3.2
mm diameter and its minimum bending radius, when tensioned, is about 64 mm, which
makes it stiffer and less suitable for surface applications than other cables without a pro-
tective cladding, such as the 125 µm-thick polyimide-coated fibers commonly used in sev-
eral research studies, see, e.g., [16,19,39]. Conversely, the V9 cable can be easily handled
and deployed without risk of rupture, making it especially suitable for embedding in con-
crete. Furthermore, a recent study by the authors showed that the V9 cable is less sensitive
to local disturbances, thus less prone to yield strain reading anomalies [25]. More im-
portantly, in the same study it was shown that measurements obtained with the V9 cable
provided very satisfactory results without performing any correction to account for the
shear deformation of the cladding as described by Tan et al. [40].
For each beam, a single DOFS was installed in a multilayer configuration to monitor
the variation of strain along the beam in the region between the supports at five different
locations of the beam’s cross-section: above the two outer tensile rebars (bar 1 and bar 3);
under one of the compressive rebars (top); at mid-height (middle); and at the bottom sur-
face of the beam (bottom). The DOFS were either supported along the longitudinal rein-
forcement (bar1, bar3 and top), fixed to the stirrups (middle) or resting on the formwork
(bottom), using electric tape to fix the sensors in place.
The Optical Distributed Sensor Interrogator (ODiSI) 6000 series from Luna Inc. was
used as data acquisition unit. This instrument offers a strain resolution of 0.1 µε, a maxi-
mum strain range of ±15,000 µε and a sample rate that can go up to 250 Hz depending on
the gauge pitch, cable and length and number of active channels. In all tests, the largest
available spatial resolution between the measuring points provided by the interrogator
was chosen, namely 2.6 mm. This configuration provided a combined accuracy (instru-
ment + interrogator) of ±30 µε, whereas the sample rate was set at 1 Hz. It is worth noting
a cubic Hermite polynomial interpolation with a spatial resolution of 10 mm was per-
formed on the measured raw data before proceeding to the analysis of the results in order
to reduce the data volume without compromising the accuracy.
Digital Image Correlation (DIC) was also performed on one of the lateral sides of the
beams to measure the deformation and strain fields as well as to measure the evolution of
crack widths. For that purpose, images were taken periodically using two Fujifilm X-T30
digital cameras. The obtained images had a resolution of 26 megapixels, 6240 × 4160 pixels,
and each individual image covered a region of the central part of the beams of approxi-
mately 1.2 × 0.8 m, providing a coverage of 0.19 mm/pixel. Images were taken every 15
min for the beams subjected to cyclic loading, whereas only one image every 2 h was taken
for the beams subjected to sustained deflection. Subsequently, the images were processed
and analyzed in the free software GOM Correlate.
2.3. Test Setup and Loading Procedure
The beam specimens were tested under four-point bending. Prior to the long-term
loading procedure, all beams were subjected to two load cycles reaching a maximum total
load of 60 kN (corresponding to about 30% of the estimated capacity), to induce cracking
and validate the performance of the V9 cables under short-term loading. It should be
noted that the results of the pre-cracking stage are reported elsewhere [25], and they are
only briefly described in the present work for completeness.
For the long-term loading, the beams were divided into two groups and the beams
in each group were clamped together according to the setup illustrated in Figure 2. In that
setup, the bottom beam was turned upside down so that the tension reinforcement was
facing upwards. Then, the top beam was positioned onto two sets of support plates resting
on the bottom beam, the centers of which were 2700 mm apart. Thereafter, the load was
Sensors 2021, 21, 6338 6 of 20
introduced at two loading points, where the clamping devices were mounted, which di-
vided the total span into three equal spans of 900 mm.
For the group of beams subjected to cyclic loading, a hydraulic cylinder was placed
between the clamping device and the loading plate of the top beam, cf. Detail A in Figure
2; the imposed deformation on the group of beams subjected to sustained deflection was
achieved by tightening a threaded bolt screwed into the clamping device, cf. Detail B in
Figure 2. Two load cells were provisioned at the loading points over the top beam and
one more between the support plates at one of the ends in order to ensure a symmetric
load distribution. The load of the Enerpac hydraulic cylinder was automatically controlled
using a close-loop feedback control system retrofitted with the measurement of the load-
cells.
Figure 2. Loading setup for the long-term loading experiments (all measurements in mm).
The definition of the loading procedure for the cyclically loaded beams in the time
domain was performed according to a squared wave signal where both the amplitude and
the duration of the pulses were randomly varied within a given interval, as illustrated in
Figure 3. A closed-loop feedback system was used to control the load applied by the hy-
draulic cylinders. The maximum load applied for each cycle varied between 10 and 36 kN
(per cylinder) whereas the pulse duration varied between 1 and 6 h. Conversely, both the
load and the interval between pulses were kept constant at 6 kN and 1 h, respectively. The
beams subjected to sustained deflection were initially loaded to approximately 30 kN (per
loading point) and then reloaded after 44 days to compensate the part of the load lost due
to creep effects.
Sensors 2021, 21, 6338 7 of 20
Figure 3. Definition of the loading procedure for the cyclically loaded beams.
3. Results and Discussion
3.1. DOFS Measurements and Beam Behavior under Sustained Deflection
3.1.1. Load Evolution under Sustained Deflection
The variation of the load in the beams subjected to a sustained deflection as measured
by a load cell located over one of the loading plates is presented in Figure 4a. A gradual
load decay due to relaxation effects caused by the creep of the concrete can be observed
up to the point where the load was manually increased to restore the initial load level.
Thereafter, the load continued decreasing following a trend similar to before the reload-
ing. Accordingly, the total monitoring time is divided into two periods, where the begin-
ning of the second period is marked by the reloading of the beams. Four different times
in period one, depicted in Figure 4a as circular markers, were selected to investigate var-
iations over time of the spatial distribution of the beam parameters. Note that in period
two, a certain region is shaded in grey indicating a period of missing data due to unavail-
ability of the optical fiber interrogator.
Figure 4b shows the initial distribution of strains at the tensile reinforcement in beam
5, where the position of identified cracks, clearly discernible in the strain profile as strain
peaks, have been indicated by triangular markers. Two sections of interest were selected
to investigate the variation over time of the DOFS measurements, as well as derived mag-
nitudes, for specific locations. The sections corresponded to the position of two different
cracks, one located in the shear span (Section 1) and one in the constant moment region
(Section 2), as shown in Figure 4b.
Sensors 2021, 21, 6338 8 of 20
Figure 4. (a) Time evolution of the load for the beams subjected to sustained deflection where four selected times of interest
(t1, t3, t3, t4) are indicated by markers. (b) Strain profile at one of the tensile reinforcement bars of beam 5 at the beginning
of the test. Triangular markers indicate the positions of identified cracks and dashed lines highlight the position of two
sections of interest, a crack in the shear span (Section 1) and a crack in the constant moment region (Section 2).
3.1.2. Evolution of Strain, Curvature and Crack width in Cracked Sections
The increments of strain at the top and bottom reinforcement, the increments of cur-
vature and the increments of crack width during period 1 is presented for Section 1 and
Section 2 in Figure 5a,c,e and Figure 5b,d,f), respectively. Furthermore, Figure 5g shows
the measured ambient temperature and the variation of strain in the concrete attributable
to temperature changes. The temperature strain, which is used for temperature compen-
sation, was obtained by analyzing the strain in a section of the fiber optic cable embedded
beyond the beam support, hence in a section without mechanically induced strains.
Looking at the results of Section 2, Figure 5b reveals that the strains at the bottom
reinforcement suffer a negative increment, i.e., they decrease in magnitude, which can be
explained by the progressive loss of load observed, although to a lesser extent, the strains
at the top reinforcement also become more negative, i.e., they increase in magnitude,
which can be attributed to the concrete creep in the compressive zone of the beam. Note
that the increase in magnitude of the compressive strains is not incompatible with the
decrease in load since creep-induced strains are not mechanical strains. However, they do
contribute to the curvature and deflection of the beam. Accordingly, using the strain at
the bottom and top reinforcement, the curvature at a certain coordinate x along the beam,
χ(x), can be calculated according to Equation (1) as:
()=()()
(1
)
Sensors 2021, 21, 6338 9 of 20
where () and () are the measured strains at the bottom and top reinforcement,
respectively, and z is the vertical distance between the position of the DOFS. Figure 5d
illustrates how the curvature of the beam at Section 2 tends to decrease over time. How-
ever, since the deflection of the beam must remain constant due to the boundary condi-
tions of the test setup, the loss of curvature in Section 2 needs to be compensated by an
increase in curvature elsewhere in the beam.
Interestingly, the curvature at Section 1, located in the shear span of the beam, follows
an opposite trend to that of the curvature at Section 2. In Section 1, the strain at the top
reinforcement decreases similar to what was observed for Section 2, which can also be
attributed to the effect of concrete creep. Conversely, the strain at the bottom reinforce-
ment does not display any significant change. This seems to indicate that a redistribution
of curvature in the beam occurs under conditions of sustained deflection, where the cur-
vature decreases in the most loaded region, where the curvature is initially larger, and it
increases in regions where the curvature is lower from the start.
As reported in [25], for the current combination of loading setup, sensor deployment
and fiber optic cable used, the crack width of individual bending cracks can be calculated
with an accuracy of ±20 µm based on the strain measured by the DOFS at the tensile rein-
forcement according to Equation (2):
,=  () 
,
,
 () ()
,
, (2
)
where εDOFS(x) is the measured strain (at the bottom reinforcement), () is the strain var-
ying linearly between cracks, =/, and =/ are the reinforcement ratio
and the modular ratio, respectively, and 
 and ,
are the ends of transmission length
along which slips occurs, assumed as the valleys in the strain profile to the left and right
sides of the i-th crack, wcr,i. For further details of the calculation procedure, the reader is
referred to [14,25]. Due to the tight dependency between the calculated crack width and
the measured strain at the tensile reinforcement, it can be observed in Figure 5e,f that the
variation of crack width over time displays an obvious correlation with the variation of
strain in the bottom reinforcement, thus the crack width at Section 1 remains almost un-
altered whereas a decrease in the crack width is observed at Section 2. It is worth high-
lighting that despite the accuracy of the method (±20 µm), the high resolution of the fiber
optic system enabled us to detect changes in crack width with a higher precision (in the
order of ±1 µm), which was not possible with the DIC system due to insufficient resolu-
tion.
Sensors 2021, 21, 6338 10 of 20
Figure 5. Incremental variation of measured and calculated magnitudes in the beam over time for Section 1 and Section 2:
(a,b) strain; (c,d) curvature; (e,f) crack width. (g) Variation of ambient temperature and the corresponding temperature-
induced strain.
Sensors 2021, 21, 6338 11 of 20
3.1.3. Evolution of Curvature Distribution and Maximum Deflection
In order to confirm whether the hypothesis that a redistribution of curvatures exist
in the beam under sustained deflection, the distribution of curvature increments along the
beam calculated at t2, t3 and t4 with respect to the initial instant t1 is presented in Figure
6a. As observed, a decrease in curvature occurs for all the cracked sections located in the
constant moment region, and even for those that are outside the region but close to it,
whereas for the sections between cracks the curvature generally increased. In the region
of the shear spans closer to the support, on the other hand, a consistent but non-uniform
increase in the curvature is observed within a distance of between 600 and 700 mm from
the support. From Figure 6a it can be also appreciated that the rate of change is faster in
the beginning, which indicates that the redistribution of curvature is driven by creep and
is likely caused by the differential rate of creep deformation occurring between the most
loaded sections (cracked section in the constant moment regions) and the rest of sections.
Figure 6. (a) Distribution of curvature increment along the beam for the instants t2, t3 and t4 with respect to the initial
instant t1; (b) evolution of the maximum deflection in beam 5 calculated from the DOFS strain measurements together
with the corresponding evolution of applied load.
Last, in Figure 6b, the maximum deflection calculated through the double integration
of the curvature distributions defined in Equation (1) is presented. As observed, the max-
imum deflection remains constant within each of the two periods, and it only increased at
the instant when the beams were reloaded to restore the initial load level. These results
demonstrate that the DOFS were able to measure correctly during the entire monitoring
period and that the variation of strains and the consequent redistribution of curvatures
Sensors 2021, 21, 6338 12 of 20
observed in Figure 6a were measured accurately despite their magnitude being very
small.
3.2. DOFS Measurements and Beam Behavior under Cyclic Loading
3.2.1. Load History
The load history of the beams subjected to cyclic loading is presented in Figure 7
where the more than 400 load cycles applied during the monitoring period are displayed.
The additional period of missing data between the days 49 and 56 of the test was caused
by a malfunctioning of the hydraulic system used to apply the loads.
Figure 7. Load history of the beams subjected to cyclic loading. A zoomed-in region is presented to show the variability
of the load cycles both in load magnitude and pulse duration and how the corresponding measurements of the DOFS and
DIC correlate with the applied load. A further zoomed-in region is presented for the load, DOFS deflection and DIC dis-
placement to illustrate the noise of the load-control system and the averaged values used for the analysis of results.
Sensors 2021, 21, 6338 13 of 20
A zoom-in of the load history between days 10 and 16 of the test is also presented in
Figure 7 to better appreciate the variability of the load cycles, together with the maximum
deflection calculated from the DOFS measurements and the midspan displacement meas-
ured from the DIC system for the same period. As observed, a good agreement exists be-
tween the overall shape of the deflection/displacement measured by both monitoring sys-
tems and the shape of the applied load. However, a closer look at the acquired data re-
vealed that the values measured by the load cells differed significantly from the aimed
load values due to the inability of the system to accurately stabilize the oil pressure, hence
the load, resulting in discrepancies of up to ±5%. More importantly, due to the slight time
shift in the acquisition of data between the different systems (load cells, DOFS and DIC),
the comparison of results for a specific load cycle is no longer straightforward. Therefore,
in order to minimize the impact of the load signal noise on the comparison of results, an
averaging procedure was carried out to obtain mean values of the load as well as deflec-
tions and displacements (see Figure 7).
3.2.2. Evolution of Strains and Crack Widths
To study how repeated load cycles affect the strain distribution at the tensile rein-
forcement, the strain profiles measured by the DOFS during the application of a load cycle
of similar magnitude (28.5 kN), but occurring at different times during the test, are pre-
sented in Figure 8. As observed, the strain remains virtually unaltered in the central 900
mm of the beam with no apparent difference between the strain profile at day 1 and at
day 90. This seems to indicate that despite the cyclic loading, no bond degradation oc-
curred between the reinforcement and the concrete at that load level. Conversely, an in-
creasing trend is observed for the strain in the shear span regions, which is more evident
near the supports. This effect can be explained by the formation of new cracks and the
development of existing incipient cracks in the shear span caused by the higher load levels
reached in the cyclic loading compared to the pre-cracking procedure.
Figure 8. Strain profiles at the tensile reinforcement of beam 4 at different times for a loading cycle of ca. 28.5 kN.
In Figure 9, the evolution of strain at the bottom and top reinforcement of beam 4 is
presented for both Section 1 and Section 2 (cf. Figure 8) together with the evolution of the
crack width for each section. Note, however, that to attain comparable strain results, the
impact of the loading cycle and the influence of the section position were removed by
normalizing the values of the strain by the corresponding sectional bending moment. An
observation common to both sections is the fact that the magnitude of the top reinforce-
ment strain under the low-cycle load increases, proportionally, much faster than the strain
at higher loads which in most cases displayed a very limited variation. This can be ex-
plained by the development of greater creep strains under the continuously applied low-
Sensors 2021, 21, 6338 14 of 20
cycle load compared to the relatively instantaneous loading-unloading of each individual
cycle.
The strain measured at the bottom reinforcement, on the other hand, displays a dif-
ferent behavior for the two investigated sections. For instance, in Section 1, the measured
strain clearly increases with the number of cycles. This is attributed to the imperfect clo-
sure of cracks during the unloading phase of the cycle, which leads to compressive stresses
in the cracks and a residual crack opening causing the appearance of steel stresses, hence
strains, larger than what would be expected. This effect, which was suggested by Hordijk
[41] and later verified experimentally using DOFS by Cantone et al. [34], is supported by
the increasing crack width observed in Section 1, see Figure 9b. Conversely, in Section 2,
the bottom reinforcement strains decrease with the number of cycles applied, yet the var-
iation of the crack width is almost negligible. This could be explained by a weaker bond
between concrete and steel in the unloading phase, which enables the concrete between
cracks to recover a greater fraction of its elastic strain. It should be noted that the effect of
imperfect crack closure is more pronounced for inclined cracks and stress levels close to
zero, which explains why is not observed for the cracks in the region with constant bend-
ing moment. Last, it is interesting to note that whereas the residual crack width for Section
1 and Section 2 varies over time, the difference between the crack width at minimum and
maximum loads seems to remain constant.
Figure 9. Evolution of strains over time represented as the ratio between the DOFS strain measurement and the section
bending moment and evolution of crack width for Section 1 (a,b) and Section 2 (c,d).
Sensors 2021, 21, 6338 15 of 20
3.2.3. Evolution and Validation of Beam Deflections
The deflection of an element subjected primarily to bending action is a good indicator
of the performance of the element while in service and, in many cases, it can be directly
compared to reference threshold values specified in current design codes to ensure the
functionality of the structure. Therefore, obtaining the long-term deflection of a structural
element subjected to external loading can be of interest to verify the condition of the ele-
ment. In Section 3.1.3, it was shown that the deflections calculated from the DOFS strain
measurements agreed well with the actual imposed deflection on the monitored beam for
a period of more than three months. In this section, the aim is to assess whether the DOFS
measurements can be used to obtain an accurate calculation of the beam deflection over
the same period when subjected to repeated cyclic loading.
One of the main advantages of the procedure described in this work to calculate the
deflections is that as long as the element is statically determined, the boundary conditions
are well defined and the measurements are independent of any kind of rigid body motion
of the system, such as supports settlements. Unfortunately, the same is not always true
for the DIC system. In this study, only the central region of the beam was captured in the
pictures taken with the digital camera, which means that any support settlement occur-
ring outside the field of vision of the camera cannot be accounted for in the calculation of
the beam deflection. In addition, in the analysis of the DIC results, a progressive drifting
in the fixture of the camera was detected, which compromised the accuracy of the DIC
results for the calculation of long-term deflections. Therefore, Figure 10 presents the long-
term deflection of beam 3 and beam 4 only for the values calculated based on the DOFS
strains measurements. As observed, the flexural behavior of both beams is almost identi-
cal, describing a slight increasing tendency of the residual midspan deflection over time,
which can be attributed to creep effects. The results show only slight differences between
the two beams, indicating a minor variation of the stiffness. More importantly, the simi-
larity between the results obtained by two individual DOFS on two separate specimens
with the same geometry and subjected to the same load denotes a good repeatability of
the presented methodology, hence a robust solution to monitor deflections.
Figure 10. Evolution of the midspan deflection calculated from DOFS strain measurements for (a) beam 3 and (b) beam
4.
However, even though the absolute deflection of the beams could not be obtained
from the DIC, the long-term performance of the DOFS could still be validated by analyz-
ing the deflection increments of each individual load cycle over time. To achieve that, the
Sensors 2021, 21, 6338 16 of 20
deflection increment measured by the DIC for the j-th load cycle, 
, was calculated
according to Equation (3) as:

=/(,) /() (3
)
where /(,) and /() are the vertical displacements measured by the DIC
at the midspan section for the peak load of the j-th load cycle and the low cycle load,
respectively. However, it should be noted that since the camera is fixed on the floor, the
displacements measured by the DIC, hence the deflections given by Equation (3), are rel-
ative to the supports of the whole system and not to the support plates placed between
the two beams. Therefore, to enable a comparison of results, the deflection increment
measured by the DOFS for the the j-th load cycle, Δj, was calculated according to Equa-
tion (4) as: =(,) () (4
)
where =+  is the midspan deflection, , corrected by the relative displacement
between the support plates and the system supports, , the contribution of which is
positive for beam 3 and negative for beam 4. The comparison of the deflection increments
for each individual cycle is presented in Figure 11a,b in the form of deflection ratios be-
tween the DOFS and the DIC for beam 3 and beam 4, respectively. As observed, in both
cases the mean error is below 5%, which agrees with previous results by the authors [25].
Furthermore, it is worth highlighting that the results show very little scatter and that no
apparent influence of the applied load level nor the number of cycles can be observed.
These results reveal that the calculation of deflections based on DOFS is reliable over time,
even under repeated load cycles, and potentially more robust than non-contact image-
based systems since it does not require a fixed external reference for the computation of
deflections.
Figure 11. Ratio of the deflection increment calculated from the DOFS and measured by the DIC for (a) beam 3 and (b)
beam 4.
3.2.4. Validation of the Crack Width Calculation
In Section 3.2.2, the evolution of the calculated crack widths was presented for two
cracks located at the shear span and in the constant moment region, respectively. In the
present section, the accuracy of the DOFS to monitor the crack width of individual cracks
over time in beams subjected to cyclic loading is investigated. Figure 12 shows an image
with an overlay of the results of the DIC analysis displaying the main principal strains on
Sensors 2021, 21, 6338 17 of 20
the concrete surface. In that image, nine cracks (numbered from 5 to 13) in beam 4 are
clearly discernible as regions of high strain concentration. Out of the nine visible cracks,
cracks 5, 6 and 9 are partially hidden by elements of the test setup. Crack 7 and 10 were
secondary cracks with a limited crack opening. The remaining four cracks, namely crack
8, 11, 12 and 13, were selected to investigate the evolution of crack widths by comparing
the measurements of the DIC to the calculated values from the DOFS strains. It should be
noted that due to the identified issue with the long-term drift of the camera fixture, the
same approach as for the deflections was adopted, i.e., comparing the increment of crack
width between the low and peak loads of each cycle.
Figure 12. Results of the DIC showing the field of principal strains to highlight the position of cracks on the surface of
beam 4 along the region of constant bending moment (top). Relationship between increment of crack width and applied
load for selected cracks (middle). Crack width error between the DIC and DOFS measurements (bottom).
Sensors 2021, 21, 6338 18 of 20
The results of the comparison are presented in Figure 12 as a function of the cycle
load, where each marker corresponds to one cycle and the color of the marker indicates
the time, in days, for which the cycle occurred Additionally, the crack width error calcu-
lated as the difference between the increment of crack width measured by the DIC and
the DOFS is also presented in Figure 12 for each crack. In terms of accuracy, it can be
observed that the agreement between the DOFS and the DIC varies from crack to crack
but, overall, the maximum error is generally below 0.02 mm, except for one crack where
it reaches 0.04 mm at higher loads, which is in accordance with previous results [25].
Moreover, in all cases the relationship between the increment of crack width and the ap-
plied load remains linear for both the DIC and the DOFS. This agrees with the results
shown in Figure 9b,d, in which despite a certain variation of the total crack width over
time, the variation of crack width between the peak and low cycle loads remained nearly
constant. The fact that increment of crack width stayed proportional to the applied load
over time suggests that the cyclic loading did not cause any significant bond degradation,
which otherwise would be translated into an increased crack width over time. Further-
more, it is worth noting that despite the linearity observed in the results from both sys-
tems, the DOFS results exhibit a much lower scatter than the DIC. These results further
highlight the potential of DOFS for monitoring of RC structures.
4. Conclusions
This article investigated the long-term performance of robust DOFS based on Ray-
leigh backscattering for the monitoring of strains in RC structures. A set of beams were
cast with embedded robust fiber optic cables deployed in a multilayer configuration and
the beams were subjected to different loading conditions for a period of 96 days while
being continuously monitored. The main conclusions drawn from this study are the fol-
lowing:
The high precision, accuracy, and stability of the DOFS enabled the detection of sub-
tle changes in strain and deflections due to both short-time variations of the applied
load regardless of the load magnitude and the cycle pulse duration, as well as long-
term time-dependent effects such as creep. In particular, a curvature redistribution
due to differential creep between the constant moment region and the shear spans
was detected in beams subjected to sustain deflection.
It has been shown that methods developed and tested in previous studies for the
monitoring of deflections and crack widths under short-term loading can be also ap-
plied under long-term sustained and cyclic loading to measure the structural perfor-
mance of RC elements over time.
Using DIC as a reference, it was demonstrated that the values of deflection and crack
widths calculated based on the measured DOFS strains remain accurate over time,
regardless of the type of loading.
None of the results seem to indicate a loss of performance of the fiber optic cable over
time, either under sustained deflection (no relaxation due to high sustain load) or
under cyclic loading (no bond degradation due to repeated loading). Therefore, the
combination of Rayleigh scattering and the tested robust fiber optic cable have the
potential to be used in real long-term applications without losing accuracy.
Author Contributions: Conceptualization, C.G.B. and I.F.; methodology, C.G.B. and I.F.; validation,
C.G.B. and I.F.; formal analysis C.G.B. and I.F.; investigation, C.G.B., I.F. and R.R; writingoriginal
draft preparation, C.G.B., I.F. and R.R; writingreview and editing, C.G.B., I.F. and R.R; visualiza-
tion, R.R; project administration, R.R.; funding acquisition, R.R. All authors have read and agreed
to the published version of the manuscript.
Funding: This research has been performed as part of the project: ‘Sensor-driven cloud-based strat-
egies for infrastructure ManagementSensIT’ funded by the Swedish Transport Administration
(Trafikverket) under the grant TRV/BBT 2017-028.
Sensors 2021, 21, 6338 19 of 20
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declared no potential conflicts of interest with respect to the re-
search, authorship and/or publication of this article.
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This study develops a method to measure crack width using a distributed fiber optic sensor. To this end, a customized specimen was designed to manipulate cracks under precise displacement control. An optical fiber was attached on the specimen and served as a distributed sensor which measured strain distributions along the fiber based on optical frequency domain reflectometry. An algorithm was presented to analyze crack width based on the measured strain distribution. Compared with the crack width measured by an extensometer, the crack width measured by the distributed sensor had an accuracy of 5.6 µm. Parametric studies were conducted and revealed that the coating thickness of optical fiber, the spatial resolution of strain distribution, and the spacing of cracks had significant effects on the measurement of cracks using the distributed sensor. This study is expected to enhance the capability of detecting, locating, and quantifying cracks by using distributed fiber optic sensors.
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