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Evaluating the effect of corrosion on shear-critical RC beams by
integrated NDT
Citation for published version:
Gao, Y, Suryanto, B, Chai, HK & Forde, MC 2021, 'Evaluating the effect of corrosion on shear-critical RC
beams by integrated NDT', Developments in the Built Environment, vol. 7, 100050.
https://doi.org/10.1016/j.dibe.2021.100050
Digital Object Identifier (DOI):
10.1016/j.dibe.2021.100050
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Developments in the Built Environment
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Download date: 17. Jun. 2025
1
Evaluating the effect of corrosion on shear-critical RC beams by
2
integrated NDT
3
Y. Gao1, B. Suryanto2, H. K. Chai1* and M. C. Forde1
1
4
5
2
School of Engineering, The University of Edinburgh, Edinburgh, United Kingdom
Institute for Infrastructure and Environment, Heriot-Watt University, Edinburgh, United Kingdom
6
Highlights:
7
1) Changes in ductility and failure mechanism of shear-critical reinforced concrete (RC) beam
8
specimens were observed when steel reinforcement corrosion level increased from 0% to 5.09%.
9
2) Multi-faceted information relating to the effect of corrosion on the structural behaviour and failure
10
mechanism of RC beam was revealed by the data of mechanical loading test, acoustic emission
11
monitoring and digital image correlation technique.
12
3) Grid search method utilizing finite difference modelling of RC beam was successfully carried out in
13
locating the sources of acoustic emission signals.
14
1. Abstract
15
Integrated non-destructive testing (NDT) method consisting of acoustic emission (AE) and
16
digital image correlation (DIC) was used to monitor and evaluate the load behaviour of shear-
17
critical reinforced concrete beams subjected to corrosion. Measurement data in the forms of
18
mechanical load, deflection, surface strain and AE signals were processed and collectively
19
analysed to facilitate interpretation of damage development and change of structural behaviour
20
in a more comprehensive manner. Results show that when corrosion level increases, the failure
21
mode of the beams changes from shear to flexure, leading to an increase in beam ductility. The
22
steel-concrete bond deterioration caused the change of internal force transfer mechanism when
23
beams were loaded, as indicated by DIC strain maps and AE b-value analysis. Integrated NDT
24
method demonstrates the potential to intuitively and quantitatively indicate damage
25
development of the RC specimen.
26
Key words: Reinforced concrete; Shear-critical beams; Corrosion; Digital image correlation;
27
Acoustic emission; Integrated NDT.
28
29
30
2. Introduction
31
Corrosion of steel reinforcement has been one of the common issues that affect durability of
32
reinforced concrete (RC) structures. Owing to either concrete carbonation or chloride attack,
33
de-passivation of steel occurs inside the concrete and leads to irreversible corrosion process
34
(Böhni, 2005; Kim et al., 2021). In the past decades, considerable research has been dedicated
35
to investigating the effect of corrosion on RC members by either experimental testing or
36
numerical simulation. Previous findings suggest that the structural behaviour of corroded RC
37
members is affected by a variety of factors including the type of corrosion and the level of
38
corrosion.
39
The initiation of a corrosion process is normally marked by the formation of corrosion cells.
40
The corrosion cells consist of metallically and electrolytically connected anodes and cathodes.
41
The cells can work as micro-cells or macro-cells leading to different types of corrosion,
42
namely, general corrosion or pitting corrosion (Raupach, 1996). General corrosion is usually
43
triggered in the circumstance of concrete carbonation or uniformly distributed chloride
44
contents in the vicinity of steel. General corrosion is characterized by the uniform removal of
45
steel and the formation of rust layer along with the steel (Böhni, 2005). With the accumulation
46
of corrosion products, the rust expands and leads to concrete cover cracking and spalling,
47
meaning that general corrosion tends to affect the steel-concrete bond behaviour, the internal
48
force transfer mechanism, and the durability of the RC member (Val et al., 2009). Another type
49
of corrosion is pitting corrosion and it is normally initiated by localized chloride concentration.
50
As a result of pitting corrosion, steel sectional loss occurs locally and causes an abrupt
51
reduction of steel yielding strength and ultimate elongation (Dang & François, 2013). Pitting
52
corrosion is likely to make the RC member to behave in an unanticipated brittle manner when
53
loaded. Particularly, the bond deterioration or sectional loss of steel reinforcement, or the
54
combination of both can trigger diversified consequences to RC beams when loaded. The
55
common observations of load-behaviour for RC beams with corrosion are categorized based
56
on the failure mode and beam type, as shown in Table 1.
57
Table 1. Observations for the effect of corrosion on the load-behaviour of RC beams when
58
corrosion level is increasing.
Dominant mode
of failure
Beam type
Observations
References
Flexure
Slender beam
a/d > 5.5
•
•
•
Shear
Torsion
Reduction of ductility
Degradation of flexural
stiffness
Decrease of ultimate strength
Dekoster et al., 2003; Dang
& François, 2013; Zhu &
François, 2014; Liu et al.,
2016; Li & Zheng, 2005; Ye
et al., 2018; Castel et al.,
2000; Maaddawy et al., 2005
Slender beam
2.5 < a/d <
5.5
•
•
•
Increase of ultimate load
Increase of ductility
Shift of failure mode from
shear to flexure
Azam & Soudki, 2013; Ye et
al., 2018
Deep beam
a/d < 2.5
•
No significant effect on
ultimate load
Change of failure mode from
shear compression to concrete
splitting
Azam & Soudki, 2012
Slender beam
•
Reduction of torsional moment
capacity
Degradation of bearing
capacity
Yalciner et al., 2019; Gomaa
et al., 2019
•
•
Note: Span to effective depth ratio a/d is used as a general reference of the beam slenderness (Nawy, 2000).
A beam is slender if its a/d ratio is greater than 2 according to BS 8110, or greater than 3 as per Eurocode
2.
59
For RC beams that fail in a flexural manner, it is commonly observed that corrosion of steel
60
reinforcement imposes negative effects on the load-behaviour of beams, resulting generally in
61
a reduction in ductility, bending stiffness and flexural strength. However, for beams that fail in
62
shear, it is interesting to see that steel corrosion was observed to be beneficial for the structural
63
behaviour of slender beams. In some cases, an improvement in the ultimate load is observed,
64
and a changing in the failure mode from brittle shear failure to be more ductile failure (see
65
Table 1). Direct evidence that could explain this effect of corrosion on shear-critical RC beams
66
is still lacking. Besides, the concrete fracture mechanism of shear-critical beams under the
67
influence of corrosion in a loading process should also be understood. In this study, the testing
68
of beam specimens is implemented in parallel with non-destructive testing (NDT) to reveal the
69
characteristics of concrete fracture in the process of beam deformation.
70
Among the common NDT techniques used for structural assessment purposes, digital image
71
correlation (DIC) has been a popular method used for studying surface fracture of RC members
72
in the laboratory environment. DIC is capable of detecting full-field displacement of the region
73
of interest (ROI) by capturing and correlating speckle images. DIC technique has the advantage
74
of definitive accuracy for surface deformation description, allowing discontinuities such as
75
concrete cracks to be disclosed effectively from the full-field displacement map. For example,
76
DIC technique has been used in the monitoring of fatigue damage of shear-critical RC beams
77
under customized moving load (Suryanto et al., 2017 & 2019). It was also used to estimate the
78
load-carrying capacity of RC members with the help of machine learning technique (Davoudi
79
et al., 2018).
80
Another widely used NDT method is the acoustic emission (AE) technique. AE utilises a multi-
81
sensor system that can record elastic stress waves triggered by micro-fracture or friction events.
82
With the appropriate instrumentation, AE is capable of sensitively capturing the development
83
of sub-microscopic and macro cracking in cementitious materials (Aggelis et al., 2012; Xu et
84
al., 2018 & 2019; Han et al., 2019). Successful application of AE technique for concrete
85
damage monitoring has been reported in a number of studies. For instants, Zaki et al. (2017)
86
applied AE monitoring to study concrete fracture mechanisms of corroded RC beam, and
87
established the relationship between damage in the beam and mechanical loading process based
88
on cumulative AE energy. Ohtsu and co-workers (2010) demonstrated that cumulative AE
89
signals acquired from monitoring a three-phase accelerated corrosion process of RC beams
90
were useful in predicting the level of corrosion in steel reinforcements and the resulting damage
91
to concrete. In another study, a moment-tensor based method, namely simplified Green’s
92
functions for moment tensor analysis (SiGMA), was developed on the basis of inversion
93
analysis of AE waveform. SiGMA was then utilized to study shear failure mechanism and
94
corrosion mechanism of RC beams (Ohno et al., 2008; Kawasaki et al., 2013).
95
Furthermore, researchers have also been exploring the feasibility of combining AE and DIC
96
techniques to enhance damage detection and assessment from both the internal fracture process
97
and surface cracking pattern of RC members. Aggelis et al. carried out AE and DIC combined
98
monitoring to study the mechanical behaviour of FRP reinforced beams (Aggelis et al., 2013).
99
Omondi et al. (2016) suggested an improved method for concrete crack detection using the
100
integrated AE and DIC monitoring system, in which the quantitative measurement of concrete
101
cracks based on discontinuities in displacement has been verified to be feasible. Alam et al.
102
(2015) used the integrated techniques to measure crack opening and spacing in evaluating the
103
effects of size of RC members. Additionally, the integrated NDT techniques were also
104
implemented to monitor crack movements in self-healing concrete (Feiteira et al., 2017).
105
This research aims to investigate the load-behaviour and fracture mechanism of shear-critical
106
RC beams under the influence of steel corrosion. Five RC beam specimens were cast, cured
107
and tested. Corrosion of steel reinforcements was simulated by immersing the RC beams into
108
3% sodium chloride solution with electricity connected to the steel. Beams were loaded
109
monotonically by three-point bending until failure. AE and DIC were deployed in parallel with
110
the loading test to monitor the progressive failure of beams and indicate the effect of corrosion.
111
3. Methodologies
112
3.1 Beam specimen and accelerated corrosion
113
The design of steel reinforcement used Eurocode 2 as the guidance to achieve the design load.
114
The dimensions of the beams are 2200×200×350 mm in length, width and depth, respectively.
115
The beams were reinforced with four ribbed bars, two 20 mm tension bars and two 10 mm
116
compression bars, equaling to a tensile reinforcement ratio 𝜌! of 1.02%. The stirrups were
117
provided at a 200 mm interval along the whole length, corresponding to a shear reinforcement
118
ratio 𝜌" of 0.25%, as illustrated in Fig. 1. The shear span 𝑎 and the effective depth of the beam
119
𝑑 are 900 and 305 mm respectively. Thus, the shear span to effective depth ratio 𝑎/𝑑 is around
120
3.0. In this case, the control specimen is expected to fail in a diagonal shear manner according
121
to theoretical prediction (Kani, 1966). Besides, the flexural and shear capacities were made
122
comparable while the flexural capacity was made slightly higher. The shear capacity was
123
estimated to be 70% of flexural capacity as per (Cucchiara et al., 2004; Bazant & Kim, 1984).
124
As such, the control specimen is critical in shear when loaded, and any changes to either
125
flexural or shear capacity of the specimen can be suggested from its failure behaviour.
126
127
Fig. 1. Schematic representation of the three-point bending setup (unit: mm).
128
Ready-mix concrete from a local supplier was used in this casting. The concrete design was
129
according to BS 206 for a concrete grade of C25/30 and the free water to cement ratio was
130
0.62. The properties of concrete were tested according to ASTM standards (ASTM C496;
131
ASTM C39) at different curing times. After casting, the beams were immediately covered with
132
polyethene sheeting for 24 hours and then de-moulded. In the curing process, all beams were
133
wrapped with plastic sheets and kept in humid ambient condition for 28 days. Compressive
134
and splitting strength of concrete were tested at 28-day and the day of testing. The 28-day mean
135
cubic compressive strength was found to be 27.2 MPa, while the 28-day mean tensile splitting
136
strength of concrete was 2.6 MPa. On the day of testing, the mean cubic compressive strength
137
was found to increase to 38.2 MPa, while the mean tensile splitting strength to 3.3 MPa. The
138
nominal characteristic strength of steel was 500 MPa according to BS 4449, and the estimated
139
actual yield strength of steel was around 630 MPa.
140
After curing, accelerated corrosion (AC) procedure was applied to three beams. The beams
141
were immersed into a water tank with 3% sodium chloride (NaCl) solution to accelerate the
142
electrochemical process of steel corrosion, as conceptualized in Fig. 2. Direct current unit with
143
the output capacity of 15.5V 2A was connected to the steel reinforcement (anode) with copper
144
tube (cathode). Due to the conductivity of steel through the whole reinforcement, signs of
145
corrosion products were noticed at both sides of the beam during AC process.
146
147
Fig. 2. Schematic diagram of accelerated corrosion setup.
148
After AC procedure, the mass loss of steel was estimated using theoretical calculation. It has
149
been found that the commonly used Faraday’s law in estimating steel mass loss tends to
150
overestimate corrosion levels inside RC beam (Al-Saidy et al., 2016; Al-Hammoud et al.,
151
2011). In this research, the corrosion level of the beam specimens was determined using
152
modified Faraday’s law (Auyeung et al., 2000), which considers two major reduction factors,
153
as described in Eq. (1-3). The first factor (0.4651) is to consider the resistance provided by the
154
concrete when bars are placed inside concrete, which reduces the actual mass loss rate. The
155
second factor is the energy needed to de-passivate the steel protection film. The actual
156
corrosion begins only when the theoretical prediction exceeded 0.5624% (Auyeung et al.,
157
2000). Thus, modified Faraday’s law is expected to produce a more accurate estimation of the
158
corrosion levels for this test.
Mass loss (g) =
MIT
zF
(1)
Corrosion level (%) =
(intial mass − final mass)
× 100
initial mass
Actual corrosion level (%) = 0.4651 × theoretical corrosion level (%) − 0.5624
(2)
(3)
159
where M is the atomic mass of steel (56 g/mol); I is the current density (A); T is the accelerated
160
corrosion time (s); z is the ionic charge (2); and F is the Faraday’s constant (96487 C/mol).
161
The beams were simply supported over a clear span of 1800 mm and subjected to a
162
concentrated load at the mid-span (see Fig. 1). The loading process was controlled using
163
displacement through a servo-hydraulic universal testing machine Losenhausen-2000. The
164
load was transferred through a thick steel plate to avoid concrete crushing at the vicinity of the
165
loading point. Linear variable displacement transducer (LVDT) was placed underneath the
166
beam to measure the beam deflection at mid-span. The loading rate was set to be 0.3 mm/min
167
in the up-loading phase and then increased to 1 mm/min after steel yielding. The readings
168
from LVDT and loading machine were recorded using a data acquisition system. Besides, the
169
loading process was paused for hand marking of cracks at the backside of the beam when the
170
load reached 50, 100, 150, 200 and 250 kN.
171
3.2 Assessment scheme
172
The DIC image capture system consists of Canon Rebel T3i camera with a resolution of 5184
173
× 3456 pixels and an image capture software. The camera was positioned at a distance of 1200
174
mm targeting the front side of the beam, as shown in Fig. 3. The region of interest (ROI) was
175
an axisymmetric area with a cover length of 1500 mm, which covered around 70% of the front
176
surface of the beam.
177
178
Fig. 3. Dimensions of ROI on the beam (Front side, unit: mm).
179
Lighting was provided during the test to ensure adequate and uniform illumination. Both the
180
front and back surfaces of the beam were white-painted before testing. Beams were speckled
181
on the front surface with black and white granite effect spray paint (Montana EG7000). During
182
the tests, speckle images were captured with a time interval of 30 seconds. 2D image correlation
183
analysis was delivered by using software Ncorr (Blaber et al., 2015). Ncorr is an open-source
184
MATLAB code that computes and produces full-field displacement and strain maps using on
185
speckled images. Strain radius was set to be 30 pixels on the image to filter noisy displacement
186
results. Table 2 shows the details of parameter selection. Displacement jump method (Omondi
187
et al., 2016) was also used to quantitatively measure the width of concrete surface cracks. It is
188
worthwhile mentioning that due to the limitation of camera resolution, the spatial resolution
189
for this DIC setup was around 0.4 mm/pixel. Meaning that if a crack width is smaller than
190
0.02 mm , such as a hairline crack, then the crack cannot be effectively identified from
191
displacement discontinuities.
Table 2. Parameters used for DIC processing.
192
Subset radius
(Pixels)
Subset spacing
(Pixels)
Norm of difference
vector cutoff
Iteration number
Strain radius
(Pixels)
30
8
1e-08
50
5
193
A six-channel Soundwel SAEU2S system was utilised in AE monitoring. AE waveforms were
194
recorded and stored by the acquisition software. Six sensors were with the resonance of 150
195
kHz (R15) and the sensitivity range of 60 – 400 kHz. Coupling between sensor and concrete
196
was ensured by vacuum glue that hardens at room temperature after 12 hours, as shown in Fig.
197
4. In addition, a three-dimensional sensor layout was adopted in monitoring, as shown in Fig.
198
5. Four sensors were placed at the front and back surface of the beam, near to the concrete
199
fracture zone, and labelled as the “Side” group. The rest two sensors were arranged at the
200
bottom of the beam to indicate activities near the tensile reinforcement, namely the “Bottom”
201
group. 3D source localization was achieved using the data collected by four sensors from the
202
“Side” group.
203
Fig. 4. The front side of the beam during the loading test.
204
The sensitivity of the AE sensor and channel was checked prior to each test by the pencil lead
205
test. The sampling rate was set to be 10 MHz to ensure proper sampling quality. Sample length
206
was set to be 5000 points (500 us) to record complete AE waveforms. Peak definition time, hit
207
definition time, and hit lock time was chosen to be 200, 400, and 800 us respectively to reduce
208
boundary reflection signals. The amplitude threshold level was 45 dB with the amplifier of 40
209
dB to eliminate electric and mechanical noise. Besides, duration-amplitude filter was applied
210
during data post-processing to reduce the possible reflection signals from the beam boundaries
211
(ElBatanouny et al., 2012).
212
213
Fig. 5. Layout of AE sensors on the beam (unit: mm).
214
b-value is the statistical estimation of the slope between the logarithm of frequency and
215
magnitude, and it can be calculated using the Gutenberg-Richter relationship 𝑙𝑜𝑔#$ 𝑁 = 𝑎 −
216
𝑏𝑀 (Leet et al. 1950). Based on the principle that different fracture modes tend to generate
217
different types of AE signals, micro-cracks usually generate a large number of low amplitude
218
AE signals, while macro-cracks tend to emit fewer events but with higher amplitude. Thus, b-
219
value decrease when the fracture process moves from micro- to macro-cracking, which usually
220
companied by internal stress redistribution (Kurz et al., 2006). Besides, b-value analysis was
221
proven to be feasible for monitoring the fracture process inside RC beams (Colombo et al.,
222
2005). The typical approach to calculate the b-value is the maximum-likelihood method (Aki,
223
1965):
𝑏=
𝑙𝑜𝑔 (𝑒)
⟨𝑀⟩ − 𝑀!"#
(4)
224
where 𝑒 is Eulerian number; ⟨𝑀⟩ is the mean amplitude of AE (dB); 𝑀%&' is the cut-off
225
amplitude of AE (dB).
226
In this test, the sliding window length of AE data was selected to be 500 events while 𝑀%&'
227
was set to be 53 dB. Besides, the type of concrete fracture type was depicted by AE parameters,
228
namely AF and RA, as expressed in Eq. (5-6).
AF (kHz) = Counts / Duration
(5)
RA (us/V) = Rise time / Amplitude
(6)
229
The classification method for concrete cracking was established based on moment tensor
230
analysis (Ohtsu, 1991), and further verified by Aggelis (2011) for its suitability for the
231
evaluation of RC beams. b-value and AF vs. RA analysis have been widely used in the
232
monitoring and evaluation of concrete structures (Ohtsu et al. 2016).
233
In this study, 3D source localization was realized for RC specimen using the grid search method
234
provided by the ‘FaATSO’ software (Brantut, 2018). By means of grid search, the most likely
235
AE location can be estimated by minimising the least-absolute value between theoretical and
236
observed arrival times. Particularly, the theoretical travel times (the forward problem) are
237
computed using the fast marching method (Sethian, 1999), which solves discretized version of
238
Eikonal equation (Rouy & Tourin, 1992) on a regular Cartesian grid using an upwind finite-
239
difference scheme. Based on this scheme, the advancing of wave-front can be approximated,
240
and the theoretical travel times can be found throughout the grid. In this current study, a refined
241
finite-difference model of the RC specimen was built with a grid spacing of 2.5 mm, and the
242
steel and concrete were regarded as constant isotropic materials with different primary wave
243
(P-wave) velocities. P-wave is a component of the bulk waves with particle movements in the
244
direction of its propagation path. P-waves travels the fastest among all seismic waves, hence it
245
is relatively easy to identify its onset from time series data to determine its arrival time. The
246
average P-wave velocity in sound concrete was determined to be 4010 m/s by the semi-direct
247
transmission method as per BS 1881-203. In addition, ray tracing inside the RC was also
248
considered to eliminate the error caused by the waveguide effect of steel reinforcement when
249
the P-wave velocity of steel in higher than concrete. In the isotropic medium, the orientation
250
of rays at every point is always perpendicular to the wave-front. Accordingly, the rays are
251
traced from the receivers to the source by successively following the gradient of the arrival
252
time (Brantut, 2018).
253
Fig. 6. shows the finite-difference model of the RC beam and the forward simulation results of
254
a representative AE event that was triggered at the centre of the RC beam to demonstrate the
255
waveguide effect of steel and the necessity of ray tracing. The contours of AE wave-front inside
256
the beam are marked with different colours depending on the value of travel time, as shown in
257
Fig. 6 (c). It is clear that the propagation of AE wave-front inside RC is partially accelerated
258
along the steel bars, changing the form of wave-front to “cone” shapes. This is reasonable
259
because steel reinforcement allows for faster propagation of AE signals than concrete, hence
260
the former often acts as waveguide which directs and influences the propagation of AE signal
261
to result in the shortest travel time. The shortest travel path of this simulated AE event is traced
262
from a receiver to the source as highlighted with a red dotted line in Fig. 6 (d). It is shown that
263
the shortest travel path is not in a straight line, and part of the path is covered by the longitudinal
264
steel bar.
(a)
(b)
(c)
(d)
265
Fig. 6. (a) Finite-difference model of RC beam with a total node number of 10,061,901; (b)
266
forward simulation of AE wave-front using the fast marching method; (c) contours of the
267
computed travel times of AE wave-front; (d) the shortest travel path of AE signal between the
268
source and a receiver.
269
4. Results and discussion
270
4.1 Results of corrosion and loading test
271
As a result of the AC process, rust formed on steel was evident at the ends of longitudinal bars
272
which were exposed. Stains and traces of rust could also be found on the surface of the bottom
273
concrete cover, as shown in Fig. 7–(a). Concrete cover cracking was also noticed for specimens
274
B4 and B5 by visual inspection. The locations of cracks generally coincided with the positions
275
of the tensile bars and stirrups, as exemplified in Fig. 7–(b).
(a)
(b)
276
277
Fig. 7. (a) Typical signs of corrosion at the side of the beam, and (b) distribution of concrete
cover cracks on the side face of specimen B5.
278
Table 3 shows the summary of AC and loading test results. Theoretical estimations of corrosion
279
levels for specimens B3 – B5 are 0.37%, 1.30% and 5.09% respectively. A slight (5%) increase
280
of ultimate strength was noticed for specimen B3 compared with the control beams. No
281
cracking of concrete cover was found on specimen B3 at the end of AC process. The small
282
increase in strength of this specimen could be attributed to the slight improvement of its steel-
283
concrete bond capacity, a result of the formation of expansive corrosion products and
284
reactionary confinement. The increased bond capacity allows a higher bearing capacity of RC
285
members as it has been also observed in previous tests of RC members (Almusallam et al.,
286
1996; Al-Sulaimani et al. 1990; Jin & Zhao, 2001). Hence, within the context of this study, a
287
small amount of reinforcement corrosion was found to be beneficial in increasing the flexural
288
capacity of RC beam, as evidenced by specimen B3 with 0.37% corrosion in its rebars.
Table 3. Summary of AC and load test results.
289
Specimen
Corrosion
Experiment
Dominant
mode of
failure
𝑇(h)
𝜂(%)
𝑃$ (kN)
𝛥$ (mm)
𝑃" (kN)
𝛥" (mm)
𝑉" (kN)
∆" /∆$
B1
0
0
240.0
7.5
256.0
18.5
128.0
2.46
FS
B2
0
0
240.0
8.0
257.8
24.2
128.9
3.03
FS
B3
168
0.37
240.0
8.0
270.6
38.6
135.3
4.83
FS
B4
336
1.30
240.0
7.0
251.9
41.8
125.9
6.00
FC
B5
1008
5.09
230.0
7.5
265.6
66.8
132.8
8.90
FC
𝑇 : Duration of AC
𝛥$ : Yielding deflection
FS: Flexure-shear failure
𝜂 : Estimated corrosion level
𝛥" : Maximum deflection
FC: Flexure-compression failure
𝑃$ : Yielding load
∆" /∆$ : Ductility factor
𝑃" : Ultimate load
𝑉" : Ultimate shear strength
290
Fig. 8 depicts the load-deflection results of the beam specimens. All the specimens exhibited
291
generally similar behaviour before yielding. The load-deflection response was almost linear-
292
elastic up to 50 kN for all the specimens, implying that reinforcement corrosion (up to 5.09%
293
in this study) was not significant enough to have changed the beam elastic stiffness. As shown
294
by the results, stiffness of the corroded specimens did not seem to have changed markedly in
295
comparison to the control specimens up to approximately 210 kN. When the specimens started
296
to yield under loading, the ductility of beam was found to increase with the level of corrosion,
297
due to the change in the mode failure from shear to flexure. In fact, all the specimens exceeded
298
250 kN after yielding, without showing significant strength reduction as the result of corrosion.
299
The ultimate deflection increased from 18.5 mm and 24.2 mm for the control specimens (B1
300
and B2 respectively) to 66.8 mm for specimen B5. Consequently, the ductility factor ∆( /∆) of
301
beams shows a nearly three-fold rise, from 2.46 and 3.0 for the control specimens (B1 and B2
302
respectively) to 8.90 for specimen B5. It is evident from this test that steel corrosion has
303
facilitated higher ductility of shear-critical RC beams under bending, the finding of which
304
agrees with some previous studies (Azam & Soudki, 2013; Ye et al., 2018).
305
306
Fig. 8. Load-deflection relationship of the beams.
307
At the end of the test, the control beams (B1 and B2) failed in shear with a critical macro crack
308
developed from one of the support locations to the loading point. This is one of the typical
309
modes of shear failure, and it indicates the strength of beam in shear is lower than its strength
310
in flexural (Nawy, 2000). Specimen B3 experienced shear failure, with horizontal tensile
311
splitting cracks developed in the concrete cover. This was an indication of debonding along
312
rebar caused by the operative hoop stress in the tension zone of concrete (Almusallam et al.,
313
1996). When the corrosion level reached 1.30%, the failure mode changed from shear to flexure.
314
Both the specimens B4 and B5 failed in flexure-compression, represented by crushing of
315
concrete in the compression zone as shown in Fig. 9. Evidently, the failure mode of beam
316
specimens tested in this study was found to have shifted from shear to flexure due to the
317
induced corrosion. The shift of failure mode is further examined by analyzing the data for AE
318
monitoring and DIC measurement, which findings are discussed next.
319
320
Fig. 9. Cracking pattern of the beam specimens at the end of loading test (Front side).
321
4.2 Results of AE monitoring and DIC measurement
322
4.2.1 Evaluation of load-behaviour
323
To facilitate AE data analysis, the loading process of the specimens before final failure is
324
generally classified into five distinct stages, each associated with typical one or two mechanical
325
behaviours, as given in Table 4. Cracks that developed in all the specimens in each of the five
326
load stages were recorded as illustrated in Fig. 10.
327
Table 4. Classification of loading stages and the associated mechanical behaviour.
Stage
Load (kN)
General behaviour
Ι
0 - 50
Elastic deformation
ΙΙ
51 - 100
Flexural cracking
ΙΙΙ
101 - 150
Flexural & shear cracking
ΙV
151 - 200
Shear cracking
V
201 - 250
Shear cracking &
Yielding of steel
328
329
330
Fig. 10. Crack development of beam specimens by hand marking (Back side).
331
Fig. 11 depicts the cumulative AE hit and energy data recorded for the five loading stages. It
332
is sensible to find that both the amounts AE hit and energy increase as loading stage changes
333
from stage I to IV due to cumulative effect. The rates of accumulation from one loading stage
334
to the other are different between the two AE parameters. The release rate of AE energy and
335
hits accelerates with the progression of loading for all specimens. This is due to the appearance
336
of flexural and shear cracks when the load exceeded 150 kN. As loading progressed, shear
337
cracks appeared with further opening of flexural cracks. As a result, the release of AE hits and
338
energy was accelerated. It is also noticed from Fig. 11 that the corroded beam specimens
339
generally produced higher number of AE energy during loading. This is probably due to the
340
additional friction activities between steel and concrete caused by the corrosion rust layer.
(a)
(b)
341
Fig. 11. (a) Cumulative hits and (b) cumulative energy of AE received during loading.
342
Fig. 12. shows the plots of AF versus RA values for all specimens to characterize the cracking
343
type in different stages based on AE data collected by all six channels. The average values of
344
the control and corroded specimens are also plotted in the same figure. It can be seen that the
345
control specimens have collectively higher RA values with an average of 2800 𝑢𝑠/𝑉 in
346
comparison to the corroded specimens, which have an average of approximately 2000 𝑢𝑠/𝑉
347
for the said parameter. Meanwhile, the AF values obtained from the corroded specimens were
348
slightly higher, with an average of 65 kHz in comparison to that from the control specimens
349
(61 kHz). No clear separation could be identified between the data of corroded specimens and
350
those of the control specimen. However, majority of the data obtained from the corroded
351
specimens seem to have higher AF but lower RA values than those from the control specimens,
352
implying that the former group of specimens have a higher tendency to develop tensile mode
353
failure than the latter group that failed in shear. Ohno and Ohtsu (2010) suggested that, for RC
354
beam failed in shear, the failure process of specimen could generate a higher ratio of shear-
355
type cracks. The AF-RA analysis results are thus in general agreement with the findings from
356
loading tests, in justifying the change in failure mode of beam specimens as a result of
357
reinforcement corrosion.
358
359
Fig. 12. AF versus RA obtained from different loading stages.
360
4.2.2 Evaluation of fracture process
361
DIC strain mapping results are shown in Fig. 13, representing the development and
362
distributions of surface cracks at different loading levels. The distribution patterns of cracks
363
for the five specimens are generally in good agreement with hand marking results, which were
364
obtained from the back side of specimens (Fig. 10). Detailed information such as crack width,
365
height and spacing in different stages was measured from the full-field displacement results.
366
In the first loading stage (0-50 kN), no obvious cracking could be identified from the strain
367
maps. With the increase of load, differences in the cracking pattern between the control and
368
the corroded specimens became noticeable, as early as in stage II of loading, which is up to
369
100 kN. The number of flexural cracks in specimens B4 and B5 decreased with increasing
370
average crack width. Further evaluation was carried out at 100 kN on the distributed cracks
371
and results are quantified in Table 5. It is confirmed that the number of cracks developed at
372
this loading level decreased with the increase of corrosion level. The average crack spacing has
373
significantly increased in specimens B4 and B5 (up to 225 mm) in comparison to the control
374
specimens (100 mm). This decrease of crack number and increase of crack spacing in specimen
375
B4 and B5 suggest the slight loss of uniformity in stress distribution at the concrete-steel
376
interface. This occurred as a result of steel reinforcement corrosion, which has caused
377
deterioration of steel-concrete bond in such way that stresses transfer seemed to have become
378
more localised, i.e. concentrated at specific locations where steel-concrete bond was still intact.
50 kN
100 kN
379
150 kN
200 kN
250 kN
380
Fig. 13. Cracking patterns indicated by DIC strain maps along the longitudinal and vertical
381
axes at different load levels.
382
Table 5. Quantitative measurements of cracks at 100 kN level.
Specimen
Crack properties
Number
Average
spacing
(mm)
Maximum
spacing
(mm)
Average
width
(mm)
Maximum
width
(mm)
Maximum
height
(mm)
B1
7
100
140
0.09
0.13
230
B2
8
90
115
0.08
0.13
230
B3
7
120
185
0.10
0.16
200
B4
6
145
230
0.10
0.13
230
B5
3
225
235
0.16
0.22
245
Note: The width of the cracks was measured in the horizontal direction at beam
bottom, while the height of the cracks was measured starting from the bottom of the
beam. The measurements of average and maximum spacing were rounded off to the
nearest 5 mm.
383
The crack distribution results, as visually inspected on the back side of the specimens (Fig. 10)
384
also show that there have been some splitting cracks in the concrete cover zone of specimen
385
B5. The splitting cracks initiated from the load level of 100-150 kN around mid-span of the
386
beam and developed with the increase of load. When the load reached 250 kN, the several
387
splitting cracks coalesced in the concrete cover along the path of tensile reinforcement. The
388
propagation of these cracks was mainly due to the result of the hoop stresses around the tension
389
bars caused by edging effect of the bar rib when loaded (Almusallam et al., 1996). As a result,
390
the confinement provided by concrete was further reduced, and this has facilitated slipping of
391
tensile reinforcement and larger deflection of the beam specimen.
392
Additionally, Fig. 14. shows the b-value and load synchronized in time for evaluating the AE
393
activities in different fracture zones during the test. The b-value data were divided into two
394
groups to enable comparison of the characteristic of AE activities received from the side and
395
bottom surface of the beam respectively. Owing to the low amount of AE activities that
396
occurred within the period corresponding to the initial loading stage (0-50 kN), no much b-
397
value could be generated in this period of time due to the settings of this study. A dataset of at
398
least 500 AE events is required for calculating b-value. It was found that in many instances for
399
all the specimens, the b-value generally experienced sharp drops and fluctuations in magnitude
400
whenever there is an increase in load. The b-value of the “Side” datasets as recorded for
401
specimens B1-B3 were found to have more drops and fluctuations compared those of the
402
respective “Side” datasets, as indicated in Fig. 14. This infers that the fracture from the surface
403
where flexural and critical shear cracking occurred of specimens was more intense than in the
404
bottom areas of the three specimens dominated by flexure-shear. On the contrary, the b-value
405
data collected from the “Bottom” datasets have lower magnitudes and higher fluctuations for
406
specimens B4 and B5. This signifies that the AE activities were more dynamic and intensified
407
from the bottom of the specimen, where tensile reinforcements have been placed. In
408
conjunction with the evaluation outcome based on DIC results on steel-concrete bond
409
deterioration in specimens B4 and B5, the shift of active AE signal release zone from the beam
410
mid-section to its bottom may be attributed to the change in the bond-slip behaviour of tensile
411
reinforcements. It is considered that during the bond-slip process, widening of concrete cover
412
cracks has occurred, as justified by the appearance of splitting crack in specimen B5. The bond-
413
slip process is usually accompanied by transverse secondary cracks, shearing of concrete
414
matrix between steel ribs and steel-concrete interfacial friction (Malvar 1991; Goto & Otsuka
415
1980). These mechanical activities can generate a large amount of AE signals. In addition,
416
multiple drops in the magnitude of b-value found in the “Side” dataset are observed in
417
specimens B4 and B5 in the phase of yielding before failure (> 6000 s) took place. Based on
418
visual observations, the drops in b-values were considered to have been caused by concrete
419
crushing in the compression zone and the opening of flexural cracks in the midsection as load
420
increased in the tests.
421
422
423
424
425
426
427
Fig. 14. AE b–value response during the loading tests.
4.3. Effect of corrosion
428
Consolidating the findings from analysing and evaluating the results of visual inspections, AE
429
monitoring and DIC measurement, it is known that the internal stress transfer mechanism has
430
significantly changed for specimens B4 and B5 due to steel-concrete bond degradation, which
431
also contributed to bond-slipping at the tension side. In this context, it is reasonable to reckon
432
that the beam specimens B4 and B5 have behaved in a more ductile manner compared to the
433
other specimens which were not corroded or less corroded. The failure mode of these two
434
specimens was considered to have been dominated by flexure-compression rather than flexure-
435
shear. According to the principles of force equilibrium and deformation compatibility, which
436
must be satisfied regardless of the condition of steel-concrete bond, the change of strain
437
distribution along a beam subjected to bending can be conceptualized in Fig 15, for the two
438
typical scenarios with perfect and deteriorated bond conditions.
(a)
(b)
439
Fig. 15. Conditions of equilibrium for RC beams with (a) perfect bond and (b) deteriorated
440
bond (Wang & Liu, 2008).
441
When the steel and concrete are perfectly bonded, the depth of neutral axis is constant
442
throughout the span of the beam once load is applied. The level arm length z*+,- between the
443
line of action of the compression force C*+,- in concrete and tensile force T*+,- in
444
reinforcement is also constant at this moment. Tensile stress in steel and compressive stress in
445
concrete ε.# vary proportionally to the applied moment (Cairns & Zhao, 1993). In the case of
446
bond deterioration, the depth of neutral axis varied throughout the span to satisfy equilibrium
447
of forces. Followed by the raise of level arm length z(,*+,- at the midsection, the maximum
448
concrete compressive stress ε./ is increased in proportion with the reduction of neutral axis
449
depth. Meanwhile, the strain in concrete at the level of tensile steel ε.- was significantly
450
increased in the midsection of the beam. Due to the simultaneous increase of concrete strain at
451
both tension and compression zone, wider flexural cracks would appear in the midsection of
452
the specimen with bond degradation during loading, and the associated crushing at concrete
453
compression zone constitutes failure of the specimens. This explains the wider flexural cracks
454
observed in B4 and B5. The transition of failure mode from flexure-shear to flexure was caused
455
by to the lack of sufficient bond and anchorage of tensile reinforcement, and it was also partly
456
due to the slight reduction in bar cross-section area at crack locations. The combined effects
457
reduced the flexural capacity and hence causing the beams to fail in flexure, rather than a mixed
458
of flexure-shear as in the control beams.
459
4.4 Integration of NDT
460
Further post-processing was attempted to relate the results of AE monitoring and DIC, as
461
exemplified in Fig. 16. The surface strain mapping results by DIC analysis are incorporated
462
with AE source location results in the three-dimensional domain to assess the state of internal
463
damage of the beam specimens. Particularly, the distribution of strain in the horizontal
464
direction 𝑒00 provides information on the flexural cracking pattern as well as shear and
465
compression zone. Flexural cracks are indicated by 𝑒00 that is greater than zero while shear
466
cracks and concrete crushing zone shows 𝑒00 values below zero. The distributions of AE events
467
presented in the forms of AE energy and AF are given in the figures. The distribution of AE
468
events generally agrees with the trajectory of crack propagation and damage zone. This implies
469
that the grid search method was effective in performing three-dimensional AE source
470
localisation in RC medium, utilizing arrival time data collected by a limited number of AE
471
sensors. It can be seen that most of the AE events were located inside the beam instead of on
472
the surfaces. The evaluation of internal fracture of RC beam is considered more challenging
473
because cracks were scattered in the three-dimensional domain, but the estimated AE locations
474
were helpful in confirming the trend of development of damage zones within the beam.
475
Majority of the AE events were obtained after approximately 83 minutes (>5000 s) into the
476
loading test. This indicated that most of the major fracture events happened in the second half
477
of the loading process, i.e. after yielding has started. A distinct difference in AE event
478
distributions can be observed for specimens that failed in different modes. Most of the AE
479
events obtained from specimen B2 are clustered in the vicinity of the critical shear crack, as
480
indicated by the contour of negative strain values. Meanwhile, the AE events in specimen B5
481
have separate clusters covering the zones of flexural cracks and concrete crushing. There are
482
also scattered AE events in the proximity of the cracks, which justified the development of
483
internal fracture which could not be detected by DIC on the surface of the specimen.
484
The distribution of events with high AE energy (>1000 relative unit) is used to indicate
485
incidents that released relatively high fracture energy when the specimen was loaded, since the
486
AE energy and fracture energy was suggested to have a linear relationship (Prasad and Sagar,
487
2008; Han et al., 2018). No clear clustering of high AE energy points could be identified in
488
specimen B2, suggesting that the fracture energy of cracks was possibly released from
489
relatively sparse positions across the specimen. However, clusters of high AE energy events
490
could be observed in specimen B5, as shown in Fig.16–(b). These clusters are located not only
491
inside the main flexural cracking zones but also in the areas adjacent to the concrete crushing
492
zone. Besides, most (>85%) of the AE events recorded in both specimens have AF values of
493
less than 90 kHz. The AE events with high AF values (>90 kHz) could be associated with
494
micro cracking, which occurred before the formation of major cracks (Aggelis, 2011). After
495
that, the widening and coalescence of cracks generated AE events with relatively low acoustic
496
frequency and higher energy compared to micro cracking. It is also worth noting that the high
497
frequency components of AE signal attenuate when propagating through concrete and cracking
498
zones (Aggelis et al., 2005), meaning that the frequency of AE events became lower with
499
damage development, as loading progressed.
500
The integration of AE and DIC results in data post-processing suggests a doable way of
501
visualizing and evaluating damage in a three-dimensional domain, which has good potential to
502
facilitate a better evaluation and interpretation of the evolution of damage inside RC elements
503
subjected to loading.
(a)
Specimen: B2 (𝜂 = 0%); Number of AE events: 6266
(b)
Specimen: B5 (𝜂 = 5.09%); Number of AE events: 7396
504
Fig. 16. Integration of strain map and AE source locations in 3D view and parallel projection
505
view of (a) control specimen B2 and (b) corroded specimen B5 (unit: mm).
506
5. Conclusions
507
This study investigates the effect of reinforcement corrosion on the load-behaviour of shear-
508
critical RC beams through combined assessment by mechanical loading tests, AE monitoring
509
and DIC measurement. All the beam specimens were statically loaded in three-point bending,
510
during which AE monitoring and continuous digital image capturing of specimen movements
511
were performed. Main conclusions are summarized as follows:
512
(1) All the beam specimens exhibited similar load-deflection behaviour before yielding
513
occurred. The failure of the control specimens was dominated by the formation of shear
514
cracks that extended from the proximity of support to loading point at the specimen top.
515
The ductility of specimens was found to have a nearly three-fold rise when the corrosion
516
level increased from 0% to 5.09%. The ultimate load of specimens did not show a
517
significant decrease due to corrosion. On the contrary, the ultimate load of specimen B3
518
increased approximately 5% suggesting a beneficial effect of a small amount of
519
corrosion. Furthermore, the dominating mode that failed the specimens has shifted by
520
corrosion from flexure-shear to flexure-compression, the latter of which is represented
521
by the formation of macro flexural cracks followed by crushing of concrete at the
522
compression zone.
523
(2) DIC strain maps obtained at different load levels suggest the change in the uniformity
524
of load transfer from concrete to tensile reinforcements in specimens B4 and B5. This
525
also signifies the reduction in load transfer efficiency, attributed to steel-concrete bond
526
deterioration caused by corrosion damage. Additionally, the AE b-value results of these
527
two specimens indicated that there were more active and prominent AE signals obtained
528
from the bottom area of the beam than the sides, which were attributed to mechanical
529
movements related to slipping of tension steel-concrete bond during loading.
530
(3) Based on the principles of force equilibrium and deformation compatibility, the
531
neutral axis of the corroded beam specimens varied along their shear span when loaded
532
because of steel-concrete bond deterioration. The reduced neutral axis depth at the beam
533
midsection resulted in an increase of maximum concrete compressive stress in the
534
compression zone, and higher concrete strain at the level of tensile reinforcement.
535
Consequently, flexural cracks in the midsection of the beam with bond deterioration
536
continued to widen and propagate upward with the increase of load, until the compression
537
strength of concrete has been reached to result in crushing at the top face of specimens.
538
Thus, the failure of specimens with bond deterioration was dominated by flexure-
539
compression rather than flexure-shear.
540
(4) The grid search method was successfully applied to estimate AE source locations,
541
with the consideration of the ray paths of AE signals inside the specimens. AE source
542
locations were found with distribution patterns that generally indicate the trajectory of
543
crack propagation and major damage zones. Successful integration of AE and DIC
544
analysis results in data post-processing stage demonstrates the potential of intuitive
545
damage visualization in the three-dimensional domain for RC members.
546
Acknowledgement
547
The financial supports from The University of Edinburgh and Daiwa Foundation Award (Ref:
548
12116/12917) for this research project are much appreciated. The authors are also very grateful
549
to the technician team at Heriot-Watt University: Paul Miller, Graham Sorley and Martin
550
Aitken for the help rendered in specimen preparation and testing.
551
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552
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