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Damage limit states of reinforced concrete beams subjected to incremental

cyclic loading using relaxation ratio analysis of AE parameters

R. Vidya Sagar ⇑, B.K. Raghu Prasad

Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India

a r t i c l e i n f o

 Article history:

Received 10 October 2011

Received in revised form 10 January 2012

Accepted 25 February 2012

Available online 13 April 2012

Keywords:

Reinforced concrete beams

Acoustic emission testing

Damage assessment

Incremental cyclic loading

Digital image correlation technique

a b s t r a c t

This paper presents an experimental study on damage assessment of reinforced concrete (RC) beams sub-

 jected to incremental cyclic loading. During testing acoustic emissions (AEs) were recorded. The analysis

of the AE released was carried out by using parameters relaxation ratio, load ratio and calm ratio. Digital

image correlation (DIC) technique and tracking with available MATLAB program were used to measure

the displacement and surface strains in concrete. Earlier researchers classified the damage in RC beams

using Kaiser effect, crack mouth opening displacement and proposed a standard. In general (or in

practical situations), multiple cracks occur in reinforced concrete beams. In the present study damage

assessment in RC beams was studied according to different limit states specified by the code of practice

IS-456:2000 and AE technique. Based on the two ratios namely load ratio and calm ratio and when the

deflection reached approximately 85% of the maximum allowable deflection it was observed that the

RC beams were heavily damaged. The combination of AE and DIC techniques has the potential to provide

the state of damage in RC structures.

 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Maintenance of reinforced concrete (RC) structures is important

to ensure long term conservation of concrete structures to serve its

intended purpose. The vulnerability of these RC structures to

aggressive environment during their service life is a cause of major

concern for structural engineers. In general, the structural damage

inspection comprises the monitoring and the evaluation of the per-

formance of each component of concrete structure throughout its

service life. Any deficiency in performance could be detected and

corrected early. The inspection could be routine inspection, in-

depth inspection or special inspection. The routine inspection in-

volves a general examination of the structure to look for obvious

outward physical evidence of distress that might require repair

or maintenance. An in-depth inspection requires a detailed visual

examination of all superstructures and substructure elements

and this kind of inspection is necessary for old RC structures

[1–3]. Among the many available technologies, nowadays AE mon-

itoring, one of the non-destructive techniques (NDTs) is used to

evaluate the damage in RC structures[4–19]. In general, AE tech-

nique is a passive monitoring technique which can be appropri-

ately used for damage assessment of RC structures   [4,20–24].

Usually AE monitoring is used to obtain qualitative results by

observing the trends of AE parameters recorded during the exper-

iment and the extent of damage is then determined  [4,11–15,17].

Over the past few years, researchers attempted to state the

damage in RC beams using parametric based AE techniques   [4–

19]. By defining two ratios namely calm ratio and load ratio based

on AE energy and Kaiser effect, researchers assessed the state of 

damage in RC beams [4,11,17]. Ohtsu et al. made a damage assess-

ment chart on the basis of load ratio and calm ratio and related

them with crack mouth opening displacement (CMOD)  [11]. Co-

lombo et al. studied AE based   b-value which is based on Guten-

berg–Richter formula to study the fracture process in concrete

beams and concluded that the variation of  b-value during fracture

process in RC beams showed a significant relationship with micro

and macro cracking [12]. Researchers used AE energy parameter to

evaluate damage of concrete beams [13–15]. By defining a param-

eter ‘‘relaxation ratio’’ Colombo et al. concluded that there is a sig-

nificant change in relaxation ratio at 45% of the ultimate failure

load [13,14]. Ridge and Ziehl used cumulative AE signal strength

parameter to evaluate damage in concrete specimens  [15]. Nair

and Cai used intensity analysis technique to assess damage in con-

crete bridges   [16]. Nowadays most of the researchers are using

parametric based AE techniques because of the availability of high

speed multi channel AE recording and source location systems. In

the present study the limit state of serviceability conditions are

used  [25–34,37–39].

Research in application of AE technique to RC structures has pro-

gressed quite sufficiently. Most of the RC structures built a few dec-

ades ago are sufficiently exposed to aggressive environment and

0950-0618/$ - see front matter   2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.conbuildmat.2012.02.057

⇑ Corresponding author. Tel.: +91 80 2293 3120; fax: +91 80 2360 0404.

E-mail address: rvsagar@civil.iisc.ernet.in (R. Vidya Sagar).

Construction and Building Materials 35 (2012) 139–148

Contents lists available at SciVerse ScienceDirect

Construction and Building Materials

j o u r n a l h o m e p a g e :   w w w . e l s e v i e r . c o m / l o c a t e / c o n b u i l d m a t

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thereforeboth steel andconcretecould haveundergonedamage.It is

needed to conduct investigationregardingthe stateof the structures

like existence of invisible cracks, and level of corrosion in steel. It is

possible to know the existence of cracks by AE technique. AE tech-

nique is a non-invasive one and thus very conversant for structures

under use. AE technique can easily quantify the extent of damage

[4,11–15,17,20–24].

2. Research importance

By following Ohtsu et al. (2002) and Colombo et al. (2005) the

aim of the present experimental study is to assess the damage of 

RC beams subjected to incremental cyclic loading and the present

study is an extension of earlier work by theauthors [11–14,40]. Ear-

lier researchers proposed a standard (NDIS-2421: The Japanese

Society for Non-Destructive Inspection (JSNDI)) to classify the dam-

age in RC beams [11]. In general, multiple cracks take place in RC

beams under bending as shown in  Fig. 1, therefore utilization of 

CMOD of a singlecrackmay not be appropriate. In the present study

the damage in RC beams is classified on the basis of AE released,

deflection, strainin steel andconcrete, specified by thecode of prac-

tice IS-456:2000 for different limit states[25]. According to Indian

code of practice IS:456-2000, The limit state of serviceability corre-

sponds to development of excessive deformation and is used for

checking structural members in which magnitude of deformation

may limit the use of the structure or its components. This limit

may correspond to (a) deflection (b) cracking and (c) vibration. In

general a reinforced concrete structure should satisfy the service-

ability limit state, that is, if a section is of sufficient strength to sup-

port the design loads, there should not be excessive deformation

and cracks which may affect the appearance. The strain in concrete

is measuredusingDIC technique andstrain in steel at midsection of 

the test specimen is recorded using electrical strain gauge which

was embedded before casting of the RC beam specimens. The valid-

ity of the present experimental study results were compared with

the assessment criterion suggested by the JSNDI [11,18–19].

3. Methods adopted to assess damage in beams

 3.1. Relaxation ratio

Researchers in the past used relaxation ratio as a parameter to assess damage

qualitatively in concrete beams  [13,14]. The RC beams are loaded cyclically and

each load cycle consists of loading and unloading phase. Earlier researchers

observed that AE activity during the unloading is generally an indication of struc-

tural deterioration. An analogous representation was drawn with earthquake se-

quences present in seismology and with AE released during fracture process in

RC beams  [13,14,26,27]. It is known that earthquake ground motion consists of 

three phases, viz., main shock followed by after shocks[13,14,26,27]. After shocks

follow main shock. After shocks typically begin immediately after the main shock.

Foreshock are smaller earthquakes that preceded the main shock. These foreshock

generally occur in the vicinity of main-shock hypocenter and also part of the nucle-

ation process. In fact, after-shocks relax the stress concentration caused by the main

shock [13,14,26,27]. By using the principles of the seismology, the fracture processin a concrete test specimen at the end of a load cycle, can be considered analogously

as the AE generated respectively during the loading and unloading phases  [14]. In

the present study authors used a parameter relaxation ratio defined by Colombo

et al. [13,14]

Relaxation ratio ¼ Average energy during unloading phase

Average energy during loading phase  ð1Þ

Average energy ¼ Cumulative energy recorded for each phase

Total number of recorded hits  ð2Þ

The average energy is the cumulative energy recorded by all the sensors divided

by number of recorded hits for each phase. A relaxation ratio greater than one im-

plies that the average energy recorded during the unloading cycle is higher than the

average energy recorded during the corresponding loading cycle and therefore the

relaxation is dominant [13,14].

 3.2. NDIS-2421. specifications for damage assessment 

Under the proposed standard NDIS-2421 by the JSNDI, the Kaiser effect was

evaluated as part of the criterion for damage assessment of concrete structures

[4,11,17–19]. The damage assessment criterion proposed by NDIS-2421 is based

on two parameters namely load ratio and calm ratio  [11]. They are

Load ratio ¼ Load at the onset of AE activity in the subsequent loading

The previous maximum load  ð3Þ

Calm ratio ¼ The number of cumulative AE activities during unloading process

Total AE activity during the last loading cycle up to maximum

ð4Þ

The load at onset of AE activity and previous load in the subsequent loading

were selected based on the plot between cumulative AE hits and load. The number

of cumulative AE activities (viz., AE hits) and total AE activity (viz., total AE hits)during the last loading can be obtained by the AE recording system. However, in

the present experimental study, the serviceability limits namely deflections, strains

in steel and concrete were used to assess damage in RC beams.

4. DIC technique to measure the strain in concrete

DIC technique for measuring strain in concrete has been exten-

sively described in the literature [28–31]. But for the sake of com-

pleteness a brief review of the relevant material will be given here.

DIC technique is a field image analysis method, based on gray value

of the digital images and this DIC analysis is useful to determine

displacements and strains developed in a structure under load

[28–32]. Earlier researchers used DIC technique for measurement

of strain in concrete from the digital images recorded during

experiments [28,30]. DIC is based on the maximization of a corre-

lation coefficient that is determined by examining pixel intensity

array subsets on two or more corresponding images and extracting

the deformation mapping function that relates the images re-

corded during the experiments. An iterative approach is used to

minimize the 2D correlation coefficient by using nonlinear optimi-

zation techniques  [29,31,32]. The cross correlation coefficient  r ij  is

defined as

r ij   u; v ; @ u

@  x ; @ u

@  y; @ v 

@  x ; @ v 

@  y

¼

  RiR j½F ð xi; yiÞ  F ½Gð xi ; y

i Þ  G ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

RiR j½F ð xi; y jÞ  F 2RiR j½Gð x

i y

i Þ  G2

q ð5Þ

F ( xi, y j) is the pixel intensity or the gray scale value at a point ( xi, y j)in the undeformed image,   Gð x

i  ; y j Þ   is gray scale value at a point

Multiple cracks

Fig. 1.  Multiple cracks developed in RC beam under bending failure  [40].

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ð xi  ; y

 j Þ   in the deformed image,   F   is mean values of the intensity

matrix F , and G  is the mean values of the intensity matrix  G.

The grid points ( xi, y j) and ð xi  ; y

 j Þ are related by the deformation

that occurs between the two images.

If the motion is perpendicular to the optical axis of the camera,

then the relation between ( xi,  y j) and  ð xi  ; y

 j Þ  can be approximated

by a 2D affine transformation such as:

 x ¼ x þ u þ @ u@  x

D x þ @ u@  y

D y   ð6Þ

 y ¼ y þ v  þ @ v 

@  xD x þ

 @ v 

@  yD y   ð7Þ

Here u  and  v  are translations of the center of the sub-image in the  x

and y  directions, respectively. The distances from the center of the

sub-image to the point ( x,  y) are denoted by  D x  and  D y. Thus, the

correlation coefficient r ij  is a function of displacement components

(u,   v ) and displacement gradients which can be determined

[29,31,32].

5. Experimental program

5.1. Materials and test specimens

The 28-day compressive strength of concrete mix was 58 MPa

and the strength was determined by testing concrete cubes of 

dimension 150 mm  150 mm  150 mm made in laboratory and

tensile strength of concrete mix was 3.56 MPa and the same was

determined by conducting split cylinder (300 mm  150 mm)

tests. The maximum size of coarse aggregate was 20 mm. A total

of 9 RC beams were tested and the geometric details of these spec-

imens are given in Table 1. In the test specimen naming designa-

tions LL1, first letter L indicates long, second letter L indicate

‘‘large’’ and the number ‘‘1’’ indicates first test specimen

(depth = 450 mm). In the naming designations LM2, first letter L 

indicates long, second letter M represent ‘‘medium’’ and the num-ber ‘‘2’’ indicates second test specimen (depth = 300 mm). In the

naming designations LS3, first letter L indicates long, second letter

S indicates ‘‘small’’ and the number ‘‘3’’ indicates third test speci-

men (depth = 150 mm). The specimens were tested in structures

lab, department of civil engineering, Indian Institute of Science,

Bangalore, India. An electrical strain gauge was affixed to the main

reinforcing bar before casting to measure the strain in steel at mid

section of the specimen and during the test DIC technique was

performed to measure the surface strain in concrete.

5.2. Test setup and procedures

Fig. 2a shows the complete experimental setup. The experimen-

tal setup consisted of a servo hydraulic loading frame with a data

acquisition system and the AE monitoring system. A steel I-beam

was placed beneath the actuator to transfer the load as two point

loads. The load was applied in incremental cycles till failure of 

the specimen. The total number of cycles varied for different spec-

imens. The specimen was simply supported and the generated AE

signals were recorded using the physical acoustic corporation

(PAC) AE system. Fig. 2b shows schematic diagram of the test spec-

imen, linear variable differential transformer (LVDT) which wasplaced on the underside of the specimen to measure displacement

of the beam at three locations and reinforcement details. The data

acquisition records load, displacement at center and 1/3 span from

the ends of the beam, strain in the steel and time. The locations of 

each LVDT were 1 m from the right and left end of the specimen

and at mid span of the specimen.

5.3. DIC set up

DIC technique was employed to measure strains by non-contact

method in order to reduce the effect from cracking and other dis-

turbances on the surface.  Fig. 2a also shows the test setup for

DIC which includes a servo-controlled loading device, image grab-

bing equipment and focusing lights. A digital camera (6.1 effective

megapixels) was used to acquire digital images from RC test spec-

imen surfaces. Before experiment, specimens were prepared by

applying a fine spray paint pattern to the surface and generated

the speckle random pattern for the image correlation. The images

of the specimens were captured continuously at various instances

during loading and unloading regimes up to complete failure. The

images have been taken for all the cycles using a digital camera

and a remote control to avoid any vibration and also to keep the

distance between camera lens and the specimen unchanged. A

speckle pattern 30  30 is taken in x-direction and y-direction for

image correlation on the surface specimen.

5.4. AE system

The AE monitoring system had eight channels one for each of the eight resonant type sensors and sensor’s location are shown

in   Table 2. The transducers (sensors) used in the experimental

study are R6D resonant type AE differential transducers. The AE

sensor had peak sensitivity at  75 dB with reference 1 V/mbars.

The operating frequency of the sensor was 35 kHz–100 kHz. The

AE signals were amplified with a gain of 40 dB in a preamplifier.

The AE monitoring system had eight channels one for each of the

eight resonant type sensors, pre-amplifiers and data acquisition

system, processing instrumentation and AEwin software. AE acqui-

sition system records AE parameters. The AE system used in this

present experimental study was a eight channel AEwin for SAMOS

E2.0 (Sensor based Acoustic Multi channel Operating System)

developed by Physical Acoustics Corporation (PAC). It is well

known that AE sensor converts a stress (sound) wave to an

 Table 1

Specimen types and loading conditions.

Specimen Ø (mm)   n As (mm2)   L (mm)   S  (mm)   b (mm)   D (mm)   P  (%) a/d   P u   (kN)

LL1 Large 20 3 943 3200 3000 150 450 1.396 2.0 367.4

LL2 Large 20 3 943 3200 3000 150 450 1.396 2.0 330.0

LL3 Large 20 3 943 3200 3000 150 450 1.396 2.0 382.9

LM1 Medium 20 2 628 3200 3000 150 300 1.395 3.34 130.9

LM2 Medium 20 2 628 3200 3000 150 300 1.395 3.34 132.8

LM3 Medium 20 2 628 3200 3000 150 300 1.395 3.0 135.3

LS1 Small 12 3 339 3200 3000 150 150 1.506 6.0 25.5

LS2 Small 12 3 339 3200 3000 150 150 1.506 6.0 25.9

LS3 Small 12 3 339 3200 3000 150 150 1.506 6.0 27.8

Ø = nominal diameter of reinforcement;  n  = number of reinforcement bars;  As = area of reinforcement;  L  = beam length;  S  = span of the beam; b  = beam width;  D  = beamdepth;  p  = % of reinforcement; a/d = ratio of shear span to depth;  P u = final failure load.

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electrical signal and the use of the amplifier is to raise the signal to

a usable level. AE sensor is a device which generates an electrical

signal when it stimulated by AE waves. Most transducers used in

conventional AE systems are piezoelectric crystals. The most

important factor of an AE measurement is the selection of the

appropriate AE transducer. The transducers used in the experimen-

tal study were R6D resonant type differential AE transducers. In

general differential sensors are used in environments where verylow level AE signals need to be processed and is also very applica-

ble in high noise environments. The output of a differential sensor

is processed by a differential amplifier. By using a differential pre-

amplifier, common mode noise is eliminated, resulting in a lower

noise output from the preamplifier, and a higher electrical noise

rejection in difficult and noisy environments. The AE sensor diam-

eter is 19 mm and its height is 22.0 mm and works in the temper-

ature range of –65 C to 177 C. The AE transducers has peak

sensitivity at 75 dB with reference 1 V/(m/s) [1 V/mbar]. The oper-

ating frequency is 35 kHz–100 kHz. Sensors are coupled to the test

specimen by means of a couplant and are secured with a tape. An

essential requirement in mounting a sensor is enough coupling be-

tween the sensor face and the concrete test specimen surface. Vac-

uum grease LR (high vacuum silicon grease) was used as couplantin the present experimental study. Application of a couplant layer

was thin, so that the couplant fill gaps caused by surface roughness

and eliminate air gaps to ensure good acoustic transmission. And

all sensors were held firmly to the testing surface. The AE signals

were amplified with a gain of 40 dB in a preamplifier. The thresh-

old value 40 dB was selected to ensure a high signal to noise ratio.

6. Results and discussion

6.1. AE results

There are three different depths of beams tested viz., 150, 300

and 450 mm. From   Table 3   it is obvious that specimens withdepth 450 mm, 300 mm and 150 mm failed at different loads.

It is observed that number of cycles has influenced the AE activ-

ity recorded. Another observation here is that AE energy also

varies with beam depth as shown in  Table 3   and it increases

with beam depth. In high grade concrete like the one used here

the cement matrix is much stronger and the bond between

aggregate and cement mortar is also very strong. During the

fracture process AE events with high energy content will be re-

leased. The same trend is noted in other specimens with depth300 mm and 150 mm. Therefore may be loading rate influences

the AE activity proportionately.   Fig. 3   shows typical recorded

plots of load versus time, load versus deflection and load versus

axial strain in steel at mid section of the specimen with depth

450 mm respectively. It is interesting to see that the steel

yielded at strain of 0.002 [34,35].

6.2. Results based on relaxation ratio

Figs. 4–6  show the relaxation ratio plots for most active chan-

nel 3 for specimens with depth 450 mm, 300 mm and 150 mm

respectively. Plots of relaxation ratio versus loading cycle number

are divided into two phases with a dotted horizontal line at relax-ation ratio equal to one. The ratio generally increases with the cy-

cle number or in other words as damage increases. The trend

changes when the load reaches about 70.7%, 75.75% and 45.9%

of maximum failure load respectively as shown in  Fig. 4. From

these plots it is observed that initially, the loading phase is dom-

inant and the values of the relaxation ratio remain less than one

or below the horizontal dotted line. Besides during initial stages

of the loading, the AE energy recorded during the unloading of 

the test specimens is very limited. It can be expected only in

the post peak region.

An attempt is made to relate the level of damage to the relax-

ation ratio. The relaxation ratio remains in the loading phase or

the relaxation phase depending on the level of damage. When

the level of damage is small, like in the initial stages of loading, the ratio remains in the loading phase and when the

MAIN REIFORCEMENT

R.C.C BEAM

Ø8mm @ 200mm LVDT 2 LVDT 3LVDT 1

I - SECTIONP

2 - Ø20mm

2 - Ø8mmSTIRRUPS

AE monitoringsystem

Focusinglight

Testspecimen

Camera

SpreaderBeam,I-section

(a)

(b)

Fig. 2.  (a) Test set-up at structures lab, Civil engineering department, Indian Institute of Science, Bangalore, India, (b) schematic diagram of RC beam LM1  [40].

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 Table 2

AE sensor locations in test specimens.

Specimen D = 450 (mm) Sensor no. Sensor

location

Specimen D  = 300 (mm) Sensor no. Sensor

location

Specimen D  = 150 (mm) Sensor no. Sensor

location

 x y x y x y

LL1 1 1200 397 LM1 1 2395 245 LS1 1 735 50

3 1200 100 2 2395 25 3 1200 75

5 2000 100 4 2600 145 5 1800 110

7 2000 397 5 800 272 7 2500 40

LL2 1 1200 397 7 795 25 LS2 1 480 120

3 1200 100 8 440 140 3 1200 75

5 2000 100 LM2 4 1900 250 5 1800 110

7 2000 397 5 1900 50 7 2500 40

LL3 1 1200 397 7 1100 250 LS3 1 480 120

3 1200 100 8 1100 50 3 1200 75

5 2000 100 LM3 1 1200 100 5 1800 110

7 2000 397 3 2000 100 7 2500 40

5 1200 273

7 2000 273

 Table 3

Number of load cycles, rate of loading and recorded AE parameters for all the RC specimens.

RC beam test specimens

LL1 LL2 LL3 LM1 LM2 LM3 LS1 LS2 LS3

Number of load cycles 18 15 16 9 10 10 4 7 11

Total AE energy (relative units) 3771,38,096 338,89,816 719,63,270 310,80,064 244,59,407 1425,23,579 248,67,776 170,80,860 225,56,584

AE hits 81,63,394 15,94,772 26,64,268 16,72,298 11,65,591 28,60,636 172,098 294,339 410,877

AE events 34,110 7644 15,691 1428 1171 235 488 868 858

Rate of loading (kN/s) 0.216 0.5 0.5 0.5 0.1 0.216 0.25 0.1 0.1

Counts 4837,05,637 600,41,363 874,58,149 448,93,818 401,90,092 2142,00,091 211,44,868 185,55,644 208,21,034

Fig. 3.  Typical recorded plots (a) load-time, (b) load–deflection, (c) load–axial strain in steel at mid section of the RC beam, (d) axial strain in Steel versus time.

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level of damage is large, it enters the relaxation phase. The load

level at which the transition from loading phase to relaxation

phase occurs is expressed as a percentage of the peak load and

the same are mentioned in the plots. For example they are70.7%, 75.75% and 45.9% for beam LL1, LL2 and LL3 respectively.

The level of damage obviously increases with the number of cy-

cles depending on the grade of concrete and the size of the

beams. It is hoped that the plots when standardized can be con-

veniently used to assess damage of the existing structures in

health monitoring. However, some more work with more number

of beams with different grades and sizes have to be tested to fix

the transition loads. Figs. 4–6   shows the level of damage based

on limit state of serviceability  [25]. But unlike earlier studies

by previous researcher, here the level of damage is based on

deflection limits, which we call as serviceability limits. The re-

lease of AE energy increases in the unloading phase with the ap-

proach of failure. A change of trend occurs when the load reaches

near collapse when the deflection becomes approximately greaterthan 85% of the maximum deflection. The percentage value indi-

cated in the figure referring to percentage of the load at which it

shifts from the loading phase to the relaxation phase to the ulti-

mate failure load [13,14]. Concrete structures contain flaws such

as pores, air voids, and shrinkage cracks even before they are

loaded. The flaws, especially the small cracks, grow stably under

Specimen-LL1

70.7%

Specimen - LL2

Relaxation Dominant75.75%

Fig. 4.  Relaxation ratio results for LL1, LL2, LL3 specimens with depth 450 mm. The

dotted line corresponds to a relaxation ratio equal to one. [] Serviceable state, [j]

non-serviceable, and [N] near-collapse respectively (channel 3).

Specimen LM2

84.2%

Fig. 5.  Relaxation ratio results for specimen LM1, LM2, LM3 specimens with depth

300 mm. The dotted line corresponds to a relaxation ratio equal to one. []

Serviceable, [j] non-Serviceable, and [N] near collapse (channel 3).

Specimen LS1

Fig. 6.   Relaxation ratio results for specimen LS1 with depth 150 mm. The dotted

line corresponds to a relaxation ratio equal to one. [] Serviceable, [j] non-serviceable, and [N] near-collapse (channel 3).

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external loading. The small cracks join together with existing or

newly-formed micro cracks to form a macro crack which cause

the collapse of the structure  [36]. The primary AE activity may

be considered as the AE released during early stages of the frac-

ture process when the micro cracks are forming and the damage

is still controlled. The secondary AE activity may be considered asthe AE activity due to friction between the existing cracks starts,

which may be visible during relaxation phase   [13]. When the

cracks are developing there is a dominance of primary AE activity

and once the damage has progressed further the secondary AE

activity is prevailed in the relaxation phase. It is interesting to

see that relaxation plot constructed from the recorded AE energy

follows a similar trend that was obtained by Colombo et al.

[13,14]. It is observed that there is a change in trend near loading

cycle 2 and 3 in almost 4 specimens (LL1, LL3, LM1, and LM2).

In serviceability limit state a structure remains functional for its

intended use subject to routine loading, and as such the structure

must not cause users discomfort under routine conditions. In fact a

concrete structure is deemed to satisfy the serviceability limit state

when the constituent structural elements do not deflect by morethan the limits laid down in the codes of practice IS:456:2000

[25,33]. In the present study authors assumed that the damage in

concrete is considered to be in serviceable state when the deflec-

tion limit is in the range of (0–50)%. No cracks were noticed on

the specimen in the serviceable state and the concrete is consid-

ered to be safe. When the deflection value is in the range of (50–

85)% of the maximum allowable the damage is considered to bein non-serviceable state. Micro cracks were observed on the sur-

face of the specimen in this state of damage. The third state of 

damage is collapse when the deflection value is greater than 85%

of the maximum allowable. The specimen is considered to be in

a state of collapse when the micro cracks coalesce to form macro

cracks on the surface of the specimen and the beam is considered

to be collapsed. It is also noted in beams of depth 450 mm the load-

ing cycle number 10 the damage is in the serviceable state and

from load cycle 10 to load cycle 15 it is in non-serviceable state

and in the last two cycles, it is near collapse 450 mm. In case of 

specimens with depth 300 mm the first 5 cycles are in serviceable

state and next three are in non-serviceable state and last 2 are near

collapse. However in specimens of depth 150 mm four load cycles

were applied and the specimen shows a trend as observed by ear-lier researchers [13,14].

Fig. 7.  (a) Variation of load with mid span vertical deflection, (b) Variation of  x-strain in concrete and load versus image number. The strain in concrete is obtained using DIC

technique.

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6.3. DIC results

An optical technique (DIC technique) has been used to measurethe 2D surface displacements and strain in concrete at mid section

of the RC beam (1.5 m from left support) along with the available

mathematical program MATLAB [36]. Some selective images were

taken during the experiment at different load levels and was pro-

cessed with the mathematical tool (MATLAB program) developed

by the Eberl et al.  [36]. The displacement obtained from DIC and

displacement recorded by LVDT follows approximately the same

trend as shown in Fig. 7a. Finally, the x-direction strain in concrete

versus image number has been plotted corresponding to the load

to see the variation of strain in concrete in a cyclic loading. In

the same plot (Fig. 7b) it is observed that after 8th cycle the strain

in concrete becomes positive. The variation of strain in concrete

measured using DIC technique increases with the increase in load-

ing. The strains in concrete measured by DIC technique is used toassess the damage in concrete beams.

7. Comparison with the NDIS procedure

The analysis described in Sections   5 and 6  is compared withNDIS-2421 quantitative assessment criterion proposed by the

committee JSNDI  [4,11,13,14,18,19]. The limits of the classification

are fixed on the basis of the maximum deflection recommended

by code of practice IS:456–2000  [25]. The data recorded from

the most active channel number 3 is used for the calculations of 

load ratio and calm ratio. The results are shown in Figs. 8–10 for

specimens with depth 450 mm, 300 mm and 150 mm respectively.

The load ratio and the calm ratio are indicated on the horizontal

and vertical axes. From these plots it can be seen that specimens

with depth 450 mm, the limits for load ratio and calm ratio is

0.9 and 1.2 respectively. The assessment chart for all specimens

(LM1, LM2 and LM3) with depth 300 mm is superimposed and

the limits for load ratio and calm ratio are 1.1 and 0.8. In case of 

specimens with depth 150 mm the limits for load ratio is 0.6and for calm ratio is 0.6. The minor damage has been taken place

Fig. 8.  Damage assessment plots for specimens with depth 450 mm based on mid span deflection.

Fig. 9.  Damage assessment plots for beams LM1, LM2 and LM3 [filled (LM1), partial fill (LM2) and hallow (LM3)] based on central deflection of specimen.

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in the range of 0–50% of the mid span deflection and intermediate

damage falls in the range of 50–85% and the heavy damage occurs

above 85% of the mid span deflection. A similar assessment crite-

rion is prepared for LL1 specimen on the basis of strain in steel and

strain in concrete shown in Fig. 11. Serviceable state is considered

when the strain in concrete is 0–20% and strain in steel is 0–30% of 

the yield strain. Non-serviceable state is defined when the strain

in concrete is between 20% and 80% and strain steel in 30–80%

of yield strain. Near–Collapse state is defined when the strain in

concrete exceeds 80% of the maximum strain and strain in steelalso exceeds above 80% of the yield strain. Here it is important

to mentioned that the damage classes are considered arbitrary

and it was assumed based on IS:456:2000. It is interesting to see

that when the strain in steel and concrete increases the damage

shifts from minor damage to heavy damage.

It was observed that beam depth has influenced the damage ta-

ken place in the specimens. The limiting values fixed in NDIS

assessment chart is decreased with the decrease in beam depth.

The relaxation ratio plots and NDIS assessment charts obtained

for specimens with depth 450 mm has shown more variations than

the results obtained in case of specimens with depth 300 mm and

150 mm.

It has to be pointed out that the loading rates used for different

specimens are different as shown in Table 3 and it was intentional.Change in the loading rate may have influenced the change in the

trend recorded in relaxation ratio plots as shown in Figs. 4–6. The

percentage of failure load to which the change of dominant phases

occurs is 70.7%, 75.75%, 45.90% for specimens LL1, LL2 and LL3

respectively. In specimens LM1, LM2 and LM3 the percentages

are 60.10%, 84.2% and 67.8%. Specimen with beam depth 150 mm

shows a regular trend and changes from loading phase to relaxa-

tion phase at 81.2%. The variation in the percentage could be due

to change in the loading rate.

8. Practical applications of the work 

It may be possible to assess the damage in concrete beams

in situ by monitoring AE and using DIC techniques. Earlier

researchers classified the damage in the beams using Kaiser effect

of AE, CMOD and proposed a standard NDIS-2421 by JSNDI. In gen-

eral, multiple cracks take place in reinforced concrete beams under

bending. The damage in RC beams may be classified on the basis of 

limit state of serviceability specified by the code of practice and AE

monitoring is appropriate.

9. Concluding remarks

Based on the above experimental results the following threemajor conclusions can be drawn

Fig. 10.  Damage assessment results for beams LS1 based on deflection of specimen under loading.

80 %<εcc< 100 %

80 %<εst< 100 %

εcc = strain in concrete   εst = strain in steel

Servicable Non Servicable Near Collapse

Maximum Strains

0 %<εcc< 20 % 45 %<εcc< 80 %

0 %<εst< 30 % 30 %<εst< 80 %

Fig. 11.  Damage assessment chart for specimen LL1 based on limit state of serviceability.

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1. The relaxation ratio could be a good parameter to identify the

level of damage.

2. The damage levels estimated from the maximum deflection

were in approximately agreement with the damage qualified

by load ratio and calm ratio.

3. During the fracture process of RC beams the damage levels

qualified by AE data shifts from minor to major levels as the

strain in steel and concrete increases.4. DIC technique is useful to record strain in concrete structures

remotely without hindering the usage.

5. The combination of AE and DIC techniques has the potential to

provide the state of damage in RC structures effectively.

Further work is needed to establish the applicability of this

method to assess damage in RC structures.

 Acknowledgements

This work was financially supported by Centre for infrastruc-

ture, Sustainable Transportation and Urban Planning (CiSTUP), In-

dian institute of science, Bangalore India via the research Project

CIST/MCV/RV/008.

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