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Performance characterization of plain and CFRP-bonded concrete subjected to sulfuric acid


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This paper presents the durability performance of concrete subjected to sulfuric acid. Accelerated conditioning is conducted at a 5% concentration employing concrete blocks bonded with carbon fiber reinforced polymer (CFRP) sheets, which are used for rehabilitating impaired structural members, and plain concrete blocks. After deteriorating the specimens for up to 9 weeks, various physical and mechanical tests are carried out such as digital microscopy, resonance frequency, porosity, thermogravimetry, and flexural loading. The initial uptake of sulfuric acid raises the mass of the concrete by 5.9%, on average; however, with the increased exposure period, the mass decreases by 19.8% because of the dissolved cement paste and enlarged pores. The presence of a CFRP layer partially hinders the ingress of sulfuric acid and improves the integrity of the concrete. Irreversible damage in the conditioned specimens reduces their resonant frequency and dynamic modulus as low as 20.3% and 49.0%, respectively. According to thermogravimetric results, the acid conditioning changes the microstructure of the concrete. While the flexural capacity of the blocks rises over 409% after CFRP-bonding, the level of uncertainty increases owing to the irregular deterioration of the CFRP-concrete interface. Furthermore, the capacity reduction and flexural stiffness of the specimens, as well as the debonding characteristics of CFRP, are dependent upon exposure period. A probability-based analytical model is formulated to complement the experimental findings, including the quantification of hazard and reliability. By comprehending the unexplored degradation mechanisms of concrete with and without CFRP-bonding under the sulfuric acid environment, a link is established between material-level damage and sustainable rehabilitation systems.
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Performance characterization of plain and CFRP-bonded concrete
subjected to sulfuric acid
Yongcheng Ji
, Yanmin Jia
College of Civil Engineering, Northeast Forestry University, Harbin 150040, China
Department of Civil Engineering, University of Colorado Denver, Denver, CO 80217, United States
The presence of a composite layer par-
tially hinders the ingress of sulfuric
acid and improves the integrity of con-
Irregular deterioration raises uncer-
tainty in the composite-concrete inter-
The hazard function of the conditioned
specimens increases, while the compos-
ite enhances the reliability of the
abstractarticle info
Article history:
Received 12 April 2020
Received in revised form 18 September 2020
Accepted 21 September 2020
Available online 23 September 2020
Carbon ber reinforced polymer (CFRP)
Performance characterization
Sulfuric acid
This paper presents the durability performanceof concrete subjected to sulfuric acid. Accelerated conditioning is
conductedat a 5% concentration employing concrete blocks bondedwith carbon ber reinforced polymer (CFRP)
sheets, which are used for rehabilitating impaired structural members, and plain concrete blocks. After deterio-
rating the specimens for up to 9 weeks, various physical and mechanical tests are carried out such as digital mi-
croscopy, resonance frequency, porosity, thermogravimetry, and exural loading. The initial uptake of sulfuric
acid raises the mass of the concrete by 5.9%, on average; however, with the increased exposure period, the
mass decreases by 19.8% because of the dissolved cement paste and enlarged pores. The presence of a CFRP
layer partially hinders the ingress of sulfuric acid and improves the integrity of the concrete. Irreversible damage
in the conditioned specimens reducestheir resonant frequency and dynamic modulus as low as 20.3% and 49.0%,
respectively. According to thermogravimetric results, the acid conditioning changes the microstructure of the
concrete. While the exural capacity of the blocks rises over 409% after CFRP-bonding, the level of uncertainty
increasesowing to the irregulardeterioration of theCFRP-concrete interface. Furthermore, the capacity reduction
and exural stiffness of the specimens, as well as the debonding characteristics of CFRP, are dependent upon ex-
posure period. A probability-based analytical model is formulated to complement the experimental ndings, in-
cluding the quantication of hazard and reliability. By comprehending the unexplored degradation mechanisms
of concrete with and without CFRP-bonding under the sulfuric acid environment, a link is established between
material-level damage and sustainable rehabilitation systems.
© 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://
1. Introduction
The demand for durable and cost-effective materials has been of
long-time interest because the service life of a structure is dominated
Materials and Design 197 (2021) 109176
Corresponding author.
E-mail address: (Y. Jia).
0264-1275/© 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (
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by the functionality of its constituents. From an economic perspective,
the durability of constructed structures is of concern and owners have
been spending a considerable amount of dollars. For instance, more
than 60% of the total spending in the United States' civil infrastructure
is for operation and maintenance expenses [1]. Among various envi-
ronments impinging upon the behavior of construction materials
(e.g., freeze-thaw, wet-dry, temperature, ultraviolet rays, carbonation,
and deleterious chemicals), sulfuric acid is a representative source
degrading the performance of structural materials in industrial and ag-
ricultural regions [2,3]. When concrete is exposed to sulfuric acid, sub-
stantial changes take place in mechanical and physical properties,
thereby decreasing compressive strength by more than 20% [4,5].
The migration of sulfuric acid through concrete is driven by effective
porosity and capillary sorptivity [6]. Since the size of capillary pores
plays an important role in transporting liquids and chemicals [7], acid-
damaged pores can expedite the degradation process of the concrete.
Furthermore, chemical reactions (H
+ Ca(OH)
plus C
A) create
gypsum (CaSO
O) and ettringite (3Cao
which lead to the disruptive expansion and cracking of concrete [8,9].
Sulfate-resistant cement possessing limited C
A may be mixed with
concrete if sulfuric-acid problems are expected at the design stage;
however, deviationsfrom intended service environments for a structure
that has been constructed with ordinary cementcan incur durability is-
sues. The ramications of sulfuric acid on durability of concrete are still
under debate, particularly for time-dependent responses, serviceable
life, maintenance, and post-damage rehabilitation [2,9]. Current design
approaches aligning with prescriptive provisions [10], which dene
three exposure classes at a water-cement ratio of 0.45 to 0.50, are insuf-
cient to address technical requirements for the longevity of concrete
members subjected to sulfuric acid; therefore, performance-based de-
sign should be implemented based on an adequate understanding of
the concrete behavior.
Carbon ber reinforced polymer (CFRP) composites are becoming a
major material for rehabilitating deteriorated concrete structures, in-
cluding a number of advantages such as favorable long-term durability,
ease of application, high strength, light weight, and reduced mainte-
nance costs [11]. For the enhancement of load-carrying capacity, CFRP
sheets may be bonded to a soft of concrete members using an epoxy ad-
hesive. Notwithstanding the availability of published specications
[11,12] and the knowledge on progressive interfacial damage [13], the
degradation of CFRP-strengthened concrete subjected to sulfuric acid is
not documented due to a dearth of research [5] and the rehabilitation in-
dustry is reluctant to adopt this promising technology. The failure char-
acteristics of CFRP bonded to a concrete substrate (i.e., disintegration of
the interface caused by either adhesion or cohesion), thus need to be in-
vestigated when exposed to sulfuric acid that can inuence the integrity
of such a bimaterial interface.
Elucidating the degradation mechanism of materials under a harsh
service condition is a prerequisite to accomplishing sustainable infra-
structure. To restore the load-carrying capacity of an impaired concrete
member, CFRP-strengthening is frequently conducted. One of the criti-
cal problems in subjecting CFRP application toaggressive environments
is premature interfacial failure resulting from weakened bond. In spite
of extensive investigations into the durability of a CFRP-concrete inter-
face, the implications of sulfuric acid are not well understood and test
data are scarce. Without knowing specicdamagemechanismsassoci-
ated with sulfuric acid, the design of concrete members bonded with
CFRP can be arbitrary and overly conservative.
This paper deals with an experimental program concerning the du-
rability of concrete with and without CFRP-bonding under an acceler-
ated sulfuric acid environment. Material characterization is carried out
using a variety of physical and mechanical tests, namely, digital micros-
copy, resonance frequency, porosity, thermogravitimetry, and exural
loading. Based on probability theory, analytical modeling is conducted
to quantify the performance of the concrete.
2. Experimental program
2.1. Materials
Table 1 summarizes the material and geometric properties of constit-
uents. Because the application of CFRP was wet-layup, the equivalent
ber thickness of 0.165 mm was adopted and used for obtaining the
properties of the composite sheets. The mixture proportion of concrete
,ne aggregate = 535 kg/m
aggregate = 1223 kg/m
. After 28 days of curing
under a temperature of 23 °C and a relative humidity of 50%, concrete
cylinders (Φ100 mm and 200 mm deep) were monotonically loaded
per ASTM C39 [14] and an average strength of 21 MPa was obtained.
CFRP composite sheets consisted of unidirectional carbon bers and an
epoxy resin.
2.2. Specimens
A total of 32 concrete blocks were prepared at a dimension of
100 mm by 100 mm by 300 mm (Fig. 1(a)) and moisture-cured for
28 days. As specied by a test protocol in ACI 440.9R-15 [15], all speci-
mens were notch-cut by 50 mm at midspan; afterward, the blocks
were cleansed and unnecessary residues were eliminated. Two catego-
ries were tested: plain and CFRP-bonded cases (16 blocks, each). The
surface of the blocks was sanded to enhance the bond between the sub-
strate and CFRP, and a premixed epoxy was pasted. A single layer of car-
bon fabric(75 mm by 200 mm) was then completely impregnated onto
the matrix and the epoxy residues were squeezed out using a spatula to
maintaina uniform interface thickness of 1 mm for the CFRP composite.
The prepared specimens were cured for 7 days in thelaboratory, as sug-
gested by the manufacturer.
2.3. Accelerated conditioning in sulfuric acid solution
An accelerated conditioning scheme was adopted to deteriorate the
plain and CFRP-bonded concrete specimens (Table 2). A 5%-concentra-
tion sulfuric acid solution, diluted by distilled water, was poured in plas-
tic containers where the specimens were placed. The initial pH value
was 0.33 andspontaneous reactions were allowed between the acid so-
lution andconcrete over time without adding the solutions. This test ap-
proach was referenced from published papers [2,16]sincenostandard
test method was available. The total conditioning period was 9 weeks,
which was sufcient to deteriorate concrete in sulfuric acid [16] and
this fact would be conrmed by load testing, and 8 specimens (4 plain
and 4 CFRP-bonded blocks) were taken out of the containers every
3 weeks (plus the rst week for ancillary testing described in Sec. 2.4)
to examine the effects of the acid exposure.
2.4. Test methods
2.4.1. Microscopy
The intact and deteriorated concrete surfaces of the concrete were
appraised by an optical microscope (Fig. 2(a)). The digital microscope
Table 1
Material and geometric properties.
Material Property Value
Concrete Compressive strength 20 MPa
CFRP Equivalent ber thickness 0.165 mm
Tensile strength 3800 MPa
Elastic modulus 227 GPa
Rupture strain 0.0167
Epoxy Tensile strength 52 MPa
Elastic modulus 2.6 GPa
Y. Ji, Y.J. Kim and Y. Jia Materials and Design 197 (2021) 109176
is capable of generating 1280-by-1024 pixel images at 30 FPS (frames
per second).
2.4.2. Fundamental frequency
Pursuant to ASTM C215 [17], a resonant test was performed to non-
destructively evaluate the conditioned concrete with and without CFRP.
Each specimen was placed on two roller supports spanningat a distance
of 180 mm and was excited using an impact hammer, as shown in Fig. 2
(b). A receiver detected signals passing through the specimen so that
fundamental resonance frequencies were identied. Five repetitions
were conducted per specimen in order to provide reliable test data.
Upon attaining the frequencies, the dynamic elastic modulus of the indi-
vidual concrete (E
) was calculated by [17].
Edyn ¼0:9464 L3T
where L,b,andtare the length, width, and thickness of the block in me-
ters, respectively; Tis a correction factor (T=6.15);Mis the mass in kg;
and Fis the frequency in Hz.
2.4.3. Porosity
The apparent porosity (P) and liquid absorption (A) of the concrete
were determined as per ASTM C20 [18].
WS100 ð2Þ
D100 ð3Þ
where W,D,andSare the saturated, dried, and suspended masses, re-
spectively, as given in Fig. 2(c). The dimension of the blocks was greater
than the size required by ASTM C20 [18]. When measuring the
suspended mass using a digital scale, the specimen was submerged in
water. The specimen wasthen taken out and blotted with a paper towel
for quantifying a saturated mass.
2.4.4. Thermogravimetry
ASTM E1131 [19] was employed to characterize th e thermal stability
of the conditioned concrete and CFRP (Fig. 2(d)), which represents the
degree of deterioration. Samples were acquired from the blocks and
powdered (50 mg to 100 mg per test), while pieces of the CFRP sheets
were taken after predened exposure periods. Elevated temperatures
were applied up to 1000 °C and the loss of mass was recorded by a
data acquisition computer.
2.4.5. Three-point bending
Following ACI 440.9R-15 [15], a three-point bending test was per-
formed with all intact and conditioned blocks at a loading rate of
2.5 mm/min (Fig. 2(e)). For a simply-supported condition, two steel
rods were placed underneath the block with a loading span of
250 mm. The CFRP-bondedspecimens were clamped on one side to ob-
serve consistent bond failure on the other side. At the bottom of the in-
dividual blocks, a displacementtransducer was installed for logging the
opening of the notch. A load cell and a linear potentiometer were used
to measure the load applied and the displacement at midspan,
3. Test results and discussion
3.1. Mass change
Fig. 3(a) shows a change in mass of the plain concrete blocks sub-
jected to sulfuric acid. There was an average increase of 5.9% at an expo-
sure period of 1 week, whereas a consistent decrease was logged
thereafter. Such a transition is explained by the fact that the concrete
initially absorbed the acid solution and, then, physical deterioration
took place assulfuric acid dissolved the cement paste, including gypsum
O) formed by chemical reactions [20]. The increased poros-
ity of the conditioned concrete also lowered the mass (to be detailed in
Sec. 3.2). It should be noted that sulfuric acid reduces the potential hy-
drogen (pH) of concrete; consequently, the concrete undergoes disinte-
gration with enlarged pores [4,7]. Regarding the CFRP-bonded concrete,
a similar trend was observed with less amounts(Fig. 3(b)). F or example,
the gain and loss of the mass at1 week and 9 weeks were 2.1% and 7.3%,
respectively, relative to the initial mass. Although the CFRP sheet par-
tially covered the concrete block, its integrity was noticeably improved
since the sheet raised the volume-to-surface ratio of the specimen ex-
posed to the acid solution. The average mass-variation rates of the
plain and CFRP-bonded specimens were 6.28%/week and 2.13%/week
up to 3 weeks, respectively, which were appreciably higher than the
Fig. 1. Specimens: (a) dimensions and strengthening scheme (unit in mm); (b) conditioning in sulfuric acid (H
) solution.
Table 2
Specimen details.
Plain concrete CFRP-bonded concrete
Ultimate load (kN) Time
Ultimate load (kN)
Individual Average COV Individual Average COV
0 5.28 5.24 0.113 0 21.45 21.35 0.071
5.29 21.65
5.91 23.00
4.47 19.33
3 3.03 3.55 0.112 3 18.06 16.17 0.160
3.49 14.00
3.96 13.88
3.73 18.73
6 3.02 2.85 0.123 6 17.88 13.64 0.220
2.41 10.99
2.75 12.20
3.22 13.48
9 2.80 2.45 0.246 9 14.71 12.42 0.250
3.09 12.43
2.17 8.02
1.75 14.51
COV = coefcient of variation.
Y. Ji, Y.J. Kim and Y. Jia Materials and Design 197 (2021) 109176
corresponding rates of 2.04%/week and 0.87%/week between 6 and
9 weeks, respectively.
3.2. Physical properties
The dry bulk density of the plain and CFRP-bonded specimens is pro-
vided in Fig. 4(a). The ratio between the dry mass and the exterior vol-
ume is an indicator that the concrete functions properly as a structural
material. Despite the marginal difference, the CFRP-bonded blocks
maintained higher bulk densities than the plain blocks during the entire
exposure periods by an average of 2.7% (Fig. 4(a), inset). Fig. 4
(b) reveals a ratio between the dry and wet bulk densities of theblocks.
The ratios steadily decreased with the conditioning time because of the
physical degradation: from 0.974 to 0.939 for the plain concrete and
from 0.978 to 0.949 for the CFRP-bonded concrete. The percentage of
liquid absorption is graphed in Fig. 4(c). It is apparent to state that the
CFRP sheet inhibited the ingress of the solution and reduced the amount
of sulfuric acid inside the concrete. The average porosity of the plain
concrete was 15.7% higher than that of the CFRP-bonded concrete, on
average, as shown in Fig. 4(d). These observations explain the reason
Fig. 2. Test methods for material characteriza tion and mechanical response: (a) optical microscopy ; (b) dynamic frequ ency; (c) apparent porosity and water abs orption:
(d) thermogravimetry; (e) three-point bending.
Y. Ji, Y.J. Kim and Y. Jia Materials and Design 197 (2021) 109176
why the deterioration of the CFRP-bonded concrete was not as signi-
cant as that of its plain counterpart (Fig. 3).
3.3. Image analysis
Pictured in Fig. 5 is the surface of the concrete at a magnication of
20 times, depending upon exposure period. Unlike the intact concrete
at 0 weeks, the conditioned concrete revealed aggregates owing to the
dissolved cement alongside the decomposition of the cement hydrate
(e.g., calcium hydroxide, Ca(OH)
): after dissolution of Ca(OH)
in a
hardened cement layer, the acid solution migrated to the next layer
[7]. Once the aggregates were exposed, the progression of sulfuric acid
retarded since the reactive plane of the cement paste decreased.
For those subjected to sulfuric acid during 6 and 9 weeks, micro-
cracks were noticed near the aggregates. This fact points out that
stress concentrations occurred in the interfacial transition zone
(ITZ), which would eventually lead to a reduction in the concrete
strength (to be articulated in Sec. 3.6). Literature reports that envi-
ronmentally damaged concrete demonstrates micro-cracks at the
ITZ level where pores accelerated the uptake of capillary water and
the leaching of portlandite [21]. Besides, the degree of hydration in
the ITZ differs from that of the cement paste, resulting in a change
in their microstructures associated with calcium hydroxide
) and calcium-silicate-hydrate (C-S-H) [22].
Fig. 3. Mass changes: (a) plain concrete; (b) CFRP-bonded concrete.
Fig. 4. Physical properties: (a) dry bulk density; (b) average ratio between dry and wet bulk densities; (c) liquid absorption; (d) apparent porosity.
Y. Ji, Y.J. Kim and Y. Jia Materials and Design 197 (2021) 109176
3.4. Impact resonance
3.4.1. Fundamental frequency
The resonant frequency of the blocks is plotted in Fig. 6(a). Without
the acid conditioning, the CFRP-bondedconcrete showed a 59.5% higher
frequency than the plain concrete, on average. The increased frequency
due to CFRP-bonding implies that the concrete blocks became stifffrom
a holistic standpoint [23]. As the exposure period progressed, the fre-
quencies dwindled, reafrming the acid-induced deterioration of the
concrete. The gap between the plain and CFRP-bonded blocks enlarged
up to 77.1% at an exposure period of 9 weeks on account of a difference
in the frequency reduction (Fig. 6(b)). The frequency, passing through
the cement and aggregates, should not be directly engaged with the
concrete strength.
3.4.2. Dynamic elastic modulus
Fig. 6(c) exhibits the dynamic elastic modulus of the specimens cal-
culated from the aforementioned resonant frequency together with
curve-tting equations. Considering the rapid passing of wave signals,
micro-cracks in the concrete are generally not crucial to determining
the dynamic modulus that is greater than a corresponding static modu-
lus [24,25]. The descending modulus with the conditioning timecorrob-
orates thepresence of irreversible damage inside theconcrete structure.
The reduction rates with time were highest when the specimens were
initially exposed to the acid (1.69 GPa/week and 2.26 GPa/week for
the plain and CFRP-strengthened cases, respectively, from 0 to
1 week); then, the rates gradually decreased to 1.04 GPa/week and
1.78 GPa/week for the plain and CFRP-strengthened cases, respectively,
from 6 to 9 weeks. It is postulated that the micro-voids lled with the
solution became saturated and retarded the ingress of the sulfuric
acid; as such, the variation of the dynamic elastic modulus was less sus-
ceptible tothe exposure period. As shown in Fig. 6(d), where reductions
in the dynamic elastic modulus are calculated, the extent of deteriora-
tion was better identied by the dynamic modulus compared with the
resonant frequency (Fig. 6(b)). Given that the failure of a material
may be dened when its dynamic elastic modulus drops by 50% [26],
the plain concrete conditioned for 9 weeks approached the failure
state unlike the case of the CFRP-bonded concrete showing a reduction
ratio of 27.3%.
3.5. Thermogravimetric analysis
The results of the thermogravimetry are provided in Fig. 7(a) with
an emphasis on the thermal stability of the individual constituents
(i.e., concrete and CFRP). For the unconditioned concrete (0 weeks),
the loss of mass was 4.6% at 1000 °C. The loss of the conditioned con-
crete was insignicant as well up to 100 °C before the internal moisture
evaporated. However, precipitous drops were observed between 100 °C
and 200 °C, which were dependent upon the exposure period (that is,
damage level). When all moisture disappeared, the mass losses were
almost constant since the solid ingredients were insusceptible to ele-
vated temperatures, and the calcium hydroxide (CH) decomposed
into calcium oxide (CaO) and water (H
O) [27]. The inset of Fig. 7
(a) illustrates changes in the mass of CFRP (for clarity, test data belong-
ing to 0 and 9 weeks are given). The control CFRP at 0 weeks steadily
lost its mass until 300 °C,followed by a rapid decrease because of the de-
composition of the epoxy resin. Similar to the case of the concrete, a
plateau-like response was noted after 500 °C with carbon bers that
Fig. 5. Qualitative image analysis of concrete surface exposed to sulfuric acid (20 times magnication).
Y. Ji, Y.J. Kim and Y. Jia Materials and Design 197 (2021) 109176
generally possess thermal stability over 1000 °C [28]. Within a temper-
ature range from 500 °C to 600 °C, the pyrolysis of the resin formed py-
rolytic carbon [29]. The recorded mass at 1000 °C manifests that the
bers accounted for 40% of the composite mass. The degraded resin al-
tered the thermal behavior of CFRP at an exposure period of 9 weeks,
and the residual mass of 29.2% at 500°C signies that the bers were de -
teriorated by sulfuric acid. The preserved mass of the concrete and CFRP
at 1000 °C is charted in Fig. 7(b). The inorganic components in the con-
crete contributed to maintaining the mass, while the organic CFRP ma-
terial experienced a considerable mass loss that was accelerated by the
acid exposure and ber oxidation [30].
3.6. Flexural capacity
The average exural capacities (load-carrying limits) of the plain
and CFRP-bonded blocks are shown in Fig. 8(a). The acid-conditioning
impinged upon the exural capacity of the concrete, resulting from
the increased porosity along with micro-cracking in the cement binder.
The volume of voids and pore distributions were crucial in determining
the exural capacity. The coefcient of variation of the CFRP-bonded
specimens(COV = 0.175) was 17.4% higher than that of the plain spec-
imens (COV = 0.149). This is ascribed to the irregular deterioration of
the CFRP-concrete interface, specically at the level of the epoxy
Fig. 6. Impact resonance: (a) frequency variation; (b) average frequency reduction; (c) dynamic modulus; (d) average modulus reduction.
Fig. 7. Thermogravimetry results: (a) temperature-dependent mass loss of concrete; (b) comparison between concrete and CFRP at 1000 °C.
Y. Ji, Y.J. Kim and Y. Jia Materials and Design 197 (2021) 109176
adhesive. In general, the permeation of a liquid through a multimaterial
interfaceabates surface energy and prompts the plasticization of the ad-
hesive [31]. The molecular-level acid diffusion through the resin led to
the hydrolysis and micro-cracking of the composite; moreover, the
chain scission of the polymer interrupted proper interactions between
the embedded bers [32,33]. From a mechanics point of view, the
acid-affected concrete strength lowered the modulus of rupture and ac-
celerated cracking at the notch tip of the specimens under three-point
bending [34]. The exural capacity ratio between the CFRP-bonded
and plain blocks tended to rise with the exposure period (Fig. 8(b)),
albeit scattered, which means that the effectiveness of CFRP in-
creased as the base concrete deteriorated further. Fig. 8(c) details
the exural capacity decrease with and without CFRP. The discrep-
ancy between these categories went up from 7.9% (3 weeks) to
11.3% (9 weeks), on average. The decrease rate in Fig. 8(d) claries
that the exural capacity variation was conspicuous when the con-
crete was initially exposed to sulfuric acid (0 to 3 weeks); thence-
forth, the rate slowed down because the cement pores were lled
with the acid solution and the ingress of sulfuric acid was impeded
by the formation of colloidal silicouoric gel [7].
3.7. Flexural behavior
The load-displacement curves of the specimens are given in Fig. 9.
Regardless of exposure time, all blocks failed in a brittle manner. The
slopes of the plain and CFRP-bonded cases declined from 0 weeks to
3weeks(Fig. 9(a)) owing to the deterioration of the concrete, and
their similarity was maintained (that is, the slopes of those cases were
alike at 0 and 3 weeks since the contribution of the thin CFRP sheet
was negligible to the global stiffness of the block system). The increased
displacements over time denote that the acid exposure abated the cohe-
sion of the cement binder, which facilitated the dislocation ofthe micro-
structural particles (i.e., the topochemical reactions between calcium
sulfate and tricalcium aluminate [7]). Contrary to the specimens sub-
jected to the 0- and 3-week exposure periods, the slopes of the speci-
mens under the 6- and 9-week periods were analogous (Fig. 9(b)),
indicating that the exural stiffness of the CFRP-bonded specimens con-
verged with the progression of damage in the concrete.
Fig. 10(a) is concerned with notch-opening displacements at failure
of the specimens. The elevating trend of notch-opening with the expo-
sure time is attributed to the reduced exural capacity of the blocks
alongside strain-softening (increased deformation of the concrete
with a reduction in post-peak stress) associated with the formation of
O[8]. Due to the partial-constraining effect by the CFRP
sheet, also known as pseudo-conning, the opening of the CFRP-
bonded specimens was consistently higher than that of the plain speci-
mens, which is benecial in terms of crack control for CFRP-
strengthened concrete members [35]. The notch-opening rate of the
plain and CFRP-bonded specimens varies linearly (Fig. 10(b)). The
opening rate in mm/kN is equivalent to the exural compliance of a
cracked member in fracture mechanics [34]; accordingly, this linear
propensity suggests a hypothesis that the stress intensity factor of the
test specimens, whether bonded with CFRP or not, is proportional to
the acid exposure time.
3.8. Failure characteristics
The failure modes of the three-point-loaded blocks are available in
Fig. 11(a) to (d). It is worth noting that the interface failure (primary) oc-
Fig. 8. Flexural capacity: (a) comparison between plain and CFRP-bonded concrete specimens; (b) capacity ratio; (c) capacity decrease; (d) capacity decrease rate.
Y. Ji, Y.J. Kim and Y. Jia Materials and Design 197 (2021) 109176
blocks. The 0-week specimens with and without CFRP failed at midspan
(Fig. 11(a) and (b)). By contrast, the failure plane of the CFRP-bonded
block at 9 weeks (Fig. 11(d)) deviated from the plane of the correspond-
ing plain block (Fig. 11(c)) for which random deterioration in the cement
binder is responsible, especially around the ITZ as discussed earlier. The
failed surfaces of the debonded CFRP sheets at exposure periods of 0
and 9 weeks are visible in Fig. 11(e) and (f), respectively. As far as the con-
trol interface is concerned at 0 weeks (Fig. 11(e)), cohesion and adhesion
failure characteristics were mixed (cohesion = integrity of the concrete;
adhesion = bond between thesubstrate and epoxy). The abatedconcrete,
however, caused the cohesion failure of the 9-week interface (Fig. 11(f))
in tandem with multistage damage propagation mechanisms [13]:
i) insignicant shear deformation along the bond-line, ii) interface degra-
dation due to the acid exposure and mechanical distress, iii) initiation of
physical cracking in the concrete layer, iv) widening of the cracks, and
v) complete delamination at the substrate level.
4. Performance modeling
4.1. Formulation
A probability distribution on the exural capacity of the plain and
CFRP-bonded blocks, f(P), may be expressed using the format of a
two-parameter Weibull function, which is frequently employed to de-
scribe the time-dependent damage progression and failure characteris-
tics of materials and structures [36]:
βαexp P
 ð4Þ
 ð6Þ
where αand βare Weibull constants; and COV
and μ
are the coef-
cient of variation and the mean of the capacity at a certain exposure
condition, respectively. It should be mentioned that Weibull functions
are frequently employed for modeling the progressivedamage of struc-
tural materials [37]. The cumulative distribution, F(P), of Eq. (4) is
¼1exp P
 ð7Þ
A hazard function, h(P), representing the failure rate of the blocks, is
dened as
RPðÞ ð8Þ
RPðÞ¼1FPðÞ ð9Þ
where R(P) is the reliability function of the specimen. The expected fail-
ure load of the blocks, E(P), is then
Fig. 9. Load-displacement behavior: (a) 0 and 3 weeks; (b) 6 and 9 weeks.
Fig. 10. Load-notch opening displacement: (a) average maximum notch opening; (b) notch opening rate.
Y. Ji, Y.J. Kim and Y. Jia Materials and Design 197 (2021) 109176
Fig. 11. Failure mode: (a) plainconcrete at 0 weeks; (b) CFRP-bonded concrete at 0 weeks; (c) plain concrete at 9 weeks; (d)CFRP-bonded concrete at 9 weeks; (e) failed CFRP-concrete
interface at 0 weeks; (f) failed CFRP-concrete interface at 9 weeks.
Fig. 12. Weibull distribution (wk = weak): (a) characteristic constants; (b) sensitivity analysis of plain concrete at 0 weeks; (c) probability density function of plain concrete;
(d) cumulative distribution function of plain concrete.
Y. Ji, Y.J. Kim and Y. Jia Materials and Design 197 (2021) 109176
Pf PðÞdP ¼Z
RPðÞdP ð10Þ
4.2. Implementation
4.2.1. Weibull characteristics
Fig. 12 summarizes the Weibull constants (Table 3)andprobability
distributions of the plain and CFRP-bonded blocks. For modeling conve-
nience, the coefcients of variation of the individual exposure periods
were averaged (COV = 0.149 and 0.175 for the plain and CFRP-
bonded blocks, respectively). The dependency of the Weibull constants
on the exposure period is shown in Fig. 12(a). The invariable αconstant
of the plain concrete was 16.3% higher than that of the CFRP-bonded
case, because of a difference in COV; in contrast, the latter revealed sub-
stantially higher βconstants than theformer. Fig. 12(b) exhibits the im-
pact of these constants on the variation of probability density functions
concerning the plain concrete without sulfuric acid exposure (0 weeks).
When the βconstant was a single valueof 5.8, the αconstant altered the
magnitude of peak probabilities with a marginal change in the breadth
of the curves (α4). The inuence of the βconstant was noticeable in
shifting the value of the most probable failure load (Fig. 12(b), inset),
meaning that the capacity of the CFRP-bonded blocks would be more
susceptible to the sulfuric-acid exposure compared with the capacity
of the plain blocks (Fig. 12(a)). The probability density functions of
the conditioned concrete are presented in Fig. 12(c). As the exposure
period increased, the mode of the function (most probable values)
repositioned toward the left with an elevated probability density (nar-
row curve width). This observation implies that a weak link in the con-
crete (i.e., deteriorated cement binder with micro-cracks) governed the
failure of the blocks and that the presence of such a link became appar-
ent with the conditioning. The cumulative distribution function of the
plain concrete in Fig. 12(d) demonstrates relative sensitivity to the ulti-
mate load of the blocks, contingent upon exposure time, at a specicoc-
currence probability.
4.2.2. Performance assessment
The hazard function of each exposure case is provided in Fig. 13(a).
The failure rate of the plain concrete at 0 weeks began to rise at a load
of 4.7 kN and the rate of other conditioned plain blocks ascended at
lower loads. An analogous tendency was noticed in the CFRP-bonded
concrete (Fig. 13(a), inset), whereas the intensity of the failure rates
was less than that of the 0-week plain concrete. Fig. 13(b) further sup-
ports the efcacy of CFRP-bonding based on the quantied resistance
against the probability of the failure rates. The reliability of the plain
concrete plummeted in a load range between 1.5 kN and 3 kN, while a
remarkable improvement was made with CFRP. At a typical reliability
Table 3
Weibull constants.
Specimen Constant Exposure time (weeks)
Plain concrete α7.84 7.84 7.84 7.84
β5.57 3.77 3.03 2.60
CFRP-bonded concrete α6.57 6.57 6.57 6.57
β22.90 17.34 14.63 13.32
Fig. 13. Performance characterization(wk = weak): (a) hazard function; (b) reliability function: (c)time-dependent ultimate load; (d) comparison between expected and tested failure
Y. Ji, Y.J. Kim and Y. Jia Materials and Design 197 (2021) 109176
of 75%, the failure loads of the blocks conditioned for 9 weeks were 2.2
kN and 11.0 kN for the plain and CFRP-bonded blocks, respectively. The
expected failure loads of the blocks (Eq. (10)) are evaluated against the
test data in Fig. 13(c) and (d). The model prediction showed anaverage
absolute margin of 11.8% and 13.8% for the plain and CFRP-bonded
blocks, respectively.
5. Summary and conclusions
This paper has discussed the characteristics of concrete with and
without CFRP sheets subjected to sulfuric acid. An accelerated test pro-
tocol was employed to deteriorate specimens, categorized into plain
and CFRP-bonded concrete blocks. The physical and mechanical re-
sponses of the conditioned blocks were investigated. The analytical
model developed in accordance with probability theory complemented
experimental ndings. The following conclusions are drawn:
The mass of the concrete blocks initially rose by 5.9%, on average, due
to the absorbed acid solution and, then, decreased by 19.8% as the ce-
ment paste dissolved and the porosity increased with the formation of
micro-cracks. The amount of aggregate exposure diminished when
the reactive plane of the cement narrowed down, accompanied by
the retarded migration of the solution. CFRP-bonding reduced the de-
gree of change in mass up to 76.4% by improving the integrity of the
blocks through inhibiting the ingress of sulfuric acid.
The resonant frequency of the CFRP-bonded concrete was 59.5%
higher than that of the plain concrete, whereas irreversible damage
in the base concrete lowered the frequency and associated dynamic
elastic modulus. The exposure period altered the microstructure of
the concrete and CFRP, substantiated by the thermogravimetric re-
sponses of the conditioned specimens (e.g., decomposition of calcium
As a result of irregular deterioration in the CFRP-concrete interface,
the level of uncertainty coupled with the exural capacity of the
CFRP-bonded concrete was higher than its plain counterpart. For the
rst 3 weeks, the capacity degradation over time was rapid but then
became slow owing to the progressive lling of the pores, which im-
peded the ow of sulfuric acid through the concrete. Likewise, the
exural stiffness of the specimens converged with an increase in the
exposure period.
The CFRP sheet partially constrained the opening of the notch until
debonding failure occurred, after which the fracture of the concrete
advanced across midspan. The interfacial failure of the CFRP-bonded
specimens shifted from the mixture of cohesion and adhesion (intact
blocks) to cohesion (conditioned blocks).
The probability density of the specimens' ultimate loads tended to
concentrate as the extent of deterioration went up, conrming the
presence of a weak link that controlled the failure of the concrete. Sul-
furic acid raised the hazard function of the blocks, while the CFRP
sheet enhanced the reliability of the concrete capacity.
Declaration of Competing Interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inu-
ence the work reported in this paper.
The authors declare the following nancial interests/personal rela-
tionships which may be considered as potential competing interests:
The authors would like to acknowledge support from the Funda-
mental Research Funds from the Heilongjiang Province Postdoctoral Re-
search Program in China (No. LBH-Z19105), the Fundamental Research
Funds for the Central Universities in China (No. 2572019BJ05), and the
US Department of Transportation through the Mountain-Plains Consor-
tium. Proprietary information such as product names and manufac-
turers was not included to avoid commercialism. Technical contents
presented in this paper are based on the opinion of the authors, and
do not necessarily represent that of others.
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