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An experimental study on loading rate effect on acoustic emission based b-values related to reinforced concrete fracture
Construction and Building Materials 70 (2014) 460–472
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
An experimental study on loading rate effect on acoustic emission based b-values related to reinforced concrete fracture R. Vidya Sagar a,⇑, M.V.M.S. Rao b a b
Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India 4-1-107, Street#2, Bhavani Nagar, Nacharam, Hyderabad 500 076, India
h i g h l i g h t s b-Values analysis was performed to study fracture process in reinforced concrete T-beams. AE based b-values are compared with strain in steel reinforcement in T-beams. Concrete relatively more brittle at higher loading rates. b-Values are lower in average as a few and strong cracking AE events occured at higher loading rates.
a r t i c l e
i n f o
Article history: Received 19 June 2014 Received in revised form 21 July 2014 Accepted 24 July 2014
Keywords: Acoustic emission Fracture Reinforced concrete structures b-Value GBR relationship
a b s t r a c t This article reports on analysis of fracture processes in reinforced concrete (RC) beams with acoustic emission (AE) technique. An emphasis was given to study the effect of loading rate on variation in AE based b-values with the development of cracks in RC structures. RC beams of length 3.2 m were tested under load control at a rate of 4 kN/s, 5 kN/s and 6 kN/s and the b-value analysis available in seismology was used to study the fracture process in RC structures. Moreover, the b-value is related to the strain in steel to assess the damage state. It is observed that when the loading rate is higher, quick cracking development lead to rapid fluctuations and drops in the b-values. Also it is observed that concrete behaves relatively more brittle at higher loading rates (or at higher strain rates). The average b-values are lower as a few but larger amplitudes of AE events occur in contrast to more number of low amplitude AE events occur at low loading rates (or at low strain rates). Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The issue of monitoring fracture process in concrete structures is always open, since many points need clarification. The fracture characteristics of RC structural members are affected by loading rates [1]. AE released during fracture process in real scale components still needs refinement. It is known that both concrete and steel are loading rate dependent materials. Strength, stiffness, brittleness, ductility of concrete and steel are affected by loading rates. A survey on response of RC structures subjected to different loading rate has been presented [2]. The physical mechanism involved in the behavior of concrete in tension at different loading rates was summarized and the study concluded that at smaller strain rates the physical mechanism is a viscous mechanism known as Stefan effect which counter both microcracking and macrocrack propagation. At high strain rates the forces of inertia ⇑ Corresponding author. Tel.: +91 80 22933120; fax: +91 80 23600404. E-mail address: [email protected] (R. Vidya Sagar). http://dx.doi.org/10.1016/j.conbuildmat.2014.07.076 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.
counter the microcracking localization and propagation. The viscous effects, together with the forces of inertia results in increasing the Young’s modulus and tensile strength of the concrete [3]. Zhang et al. studied fracture behavior of high-strength concrete at various loading rates. The fracture energy and the peak load were measured. The study concluded that the fracture energy and the peak load increase as the loading rate increases. Under high loading rates the increase in the fracture energy and peak load are influenced due to the effect of inertia [4]. The strength and the elastic modulus of concrete increased with the increasing loading rate. Also the yield strength and the corresponding strain of steel increased with the increasing loading rate. Muller reviewed the experimental data available on fracture properties of high strength concrete subjected different loading rates [5]. Su et al. studied the loading rate effect on mechanical properties of concrete used for hydraulic structures using AE technique and concluded that as the strain rate increases, the cumulative AE events, hits, hit rate around peak stress decrease correspondingly for the same size of specimens [6].
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Fig. 1. (a) Bridge deck plan (b) cross section of the bridge deck, [kerb 600 mm 300 mm, deckslab thickness 0.2 m, breadth of cross girder is 0.3 m, wearing coat is 0.08 m, carriage ways is 7.5 m] (c) application of load on bridge.
Table 1 Design moments and shear forces. Bending moment (kN-m)
Outer girders Inner girder
Shear force (kN)
Dead load
Live load
Total
Dead load
Live load
Total
1218 1218
1513 912
2731 2130
292 292
280.1 402.6
572.1 694.6
Table 2 Geometric details of the RC test beams (X and Y are the sensor location/coordinates in XY-plane; The name LC2M37 stands L for large specimen, c for concrete, 2 for second specimen, M37 stands for concrete mix having 28th day strength of 37 MPa). T-beam Web(rib) Rate of Sensor location (mm) loading (kN/s) Depth Width Wf Depth Width 1 2 3 (mm) (mm) (mm) Wrib (mm) X Y X Y X
Specimen £ n As S L Total depth T-beam Flange (mm) (mm2) (mm) (mm) D (mm)
LC2M37 LLR3 LLR1
20 20 20
4 1256 4 1256 4 1256
2600 3210 560 2600 3210 560 2600 3210 560
180 180 180
500 500 500
380 380 380
180 180 180
4 5 6
5 Y
X
6 Y
X
8 Y
X
Y
460 300 900 240 1600 175 2000 160 2400 210 2800 190 460 300 900 240 1600 200 2000 160 2420 230 2800 200 460 300 900 240 1600 200 2000 160 2400 230 2800 200
£ is the diameter of reinforcing bar; n is number of main reinforcing bars; S is span of the test beam; L is the total length of the test beam.
The issues such as monitoring fracture process in concrete structures using AE technique concern mainly the interpretation of AE parameters which in many cases is subject to assumptions that although reasonable they are still assumptions. Loading rate effect on AE based b-values related to fracture process in RC structures may help to clear the trends and useful in order to build the
experience of the AE and concrete community working in structural health monitoring research area. Only few design codes take into account the effect of loading rates on the RC structures. There is a need to do structural health monitoring tests and confirm old RC structures performance and safety. Because in India there are many RC structures constructed
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Spreader beam Test specimen
AE amplifier
LVDT
AE sensors
Fig. 2. RC beam specimen in the test rig, structures lab, department of civil engineering, Indian institute of science, Bangalore, India.
Fig. 3. Reinforcement details of the RC beam [ LLR3 specimen].
several years ago. AE based b-value analysis can be a useful method to assess the microcracking which is related to the level of damage in a RC structure. Relatively there is still lack of sufficient experimental data concerning the loading rate effect on variation in b-values for damage assessment in RC structures [7–12]. 1.1. b-Value analysis In seismology, an empirical formula proposed by Guttenberg– Richter given in Eq. (1) is used for b-value analysis [13].
NðP mÞ ¼ 10abm
ð1Þ
where N is the cumulative number of earthquakes of magnitude Pm in a particular area over a specified time span, a and b are constants which vary with the region [14–17]. In context of AE technique, the Gutenberg–Richter formula is given in Eq. (2) [18–21].
log10 N ¼ a b
AdB 20
identical features at different scales for micro-seismicity during fracture process in RC structures. Therefore, during fracture process in RC structures a decreasing b-value could be indicative of increasing stress (or load) levels, i.e. indicative of an impending fracture. Thus, the b-value is a useful tool for assessing damage status. In fact, recording of all released AE waves during monitoring of fracture process in RC structures is a difficult task. Therefore, a statistical approaches such as b-value analysis is needed. Aim is to study the application of b-value to assess damage in RC structures by considering different loading rates.
ð2Þ
where N is the number of AE hits with an amplitude higher than AdB. a is a constant determined largely by the background noise present in the surroundings of testing and b is the negative slope of the curve plotted between log10(N) and AE signal amplitude (AdB). The b-value is defined as the ‘log-linear slope of the frequency–magnitude distribution’ of AE. In fact b-value represents the ‘scaling of amplitude distribution’ of AE, and is a measure of the relative numbers of small and large AE which are finger-prints of cracks developed [22]. Several researchers working in the area of civil engineering studied the application AE frequency–amplitude distribution analysis to concrete structures [23–32]. The hypothesis to be tested is that according to researchers working in the area of seismology and rock mechanics the b-value decreases before the occurrence of an earthquake. It was observed that the b-value is inversely related to the accumulation of stress in a given region. Analogous to AE technique, the b-value represents the scaling of AE amplitude distribution and is an appearance of
2. Experimental procedure 2.1. Determination of test specimen dimensions A RC T-beam girder bridge of span 16 m as shown in Fig. 1 has been studied. The effective span of the Tee beam is 16 m and width of the carriage way is 7.5 m. The bridge has wearing coat of thickness 80 mm. Width of main girders is 300 mm. Kerbs 600 mm wide by 300 mm deep are provided. Cross girders are provided at every 4 m intervals. Breadth of cross girders is 300 mm. The geometric details of the RC Tee beam girder bridge are shown in Fig. 1. The live load was applied by following IRC code class-AA tracked vehicle load on the bridge and obtained bending moment and shear forces are shown in Table 1 [33]. In order to study the fracture process in the RC beams in laboratory it was assumed that the scaling of the beams has been done, and the scaled geometry details of RC T-beams are shown in Table 2. Three RC T-beams are cast with same concrete and reinforcement to study the effect of rate of loading.
2.2. Materials and test specimens A specimen in the test rig and reinforcement details are shown in Fig. 2 and Fig. 3 respectively. During testing a RC specimen was loaded at mid-span and simply supported over a span S. The loading was conducted by means of a fourpoint bending configuration. The 28-day compressive strength of concrete mix (maximum coarse aggregate size is 20 mm) was 37 MPa. Two-point loading span was 1 m with 2.6 m supporting-span as shown in Fig. 1c. The geometry and reinforcement details are given in Table 1 and in the same table £ is nominal diameter of reinforcement; n is number of reinforcement bars; L is beam length; S is span of the beam; b is beam width; D is beam depth; As is% of cross-section of steel reinforcement.
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Fig. 4. (a) Loading protocol for the specimen LLR3 (b) recorded plot of mid-span displacement and load (c) variation in strain in steel at mid-span with load.
2.3. Testing arrangement The experimental setup consisted of a servo hydraulic loading frame (1200 kN) with a data acquisition system and a 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 four point bending) in incremental cycles till failure of the specimen. The data acquisition records load, displacement at center of the beam, strain in the steel at the centre of the RC beam and time. The mid-span displacement was measured using a linearly varying displacement transformer (LVDT), placed at the center on the underside of the RC beam. The strain in steel at mid section of the test
specimen is recorded using electrical strain gauge which was fixed to main steel reinforcing bar (tensile reinforcement) before casting.
2.4. AE monitoring system The AE monitoring system (PAC make) had eight channels one for each of the eight resonant type sensors (R6D resonant type AE differential sensor), pre-amplifiers, data acquisition system, processing instrumentation and AEwin SAMOS software and the sensor’s location (X and Y coordinates) are shown in Table 1.
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Table 3 AE parameters and b-value and Ib-value at different loading stages. Test specimen
LC2M37
LLR3
LLR1
Number of loading phases Rate of loading (kN/s) Number of cycles Total AE energy (V2-s) Total AE hits Total AE events Load at which first crack appeared (kN) Failure load (kN) Time of final failure (min) Cumulative hits (sum of all phases) Number of hits in last phase Cumulative energy counts (sum of all phases) Energy counts in last phase Average amplitude (dB) (average of all phases) amplitude in last phase Average b-value (average of all phases) b-value of last phase Average energy per hit (average of all phases) energy per hit in last phase Average Ib-value (average of all phases) Ib-value in last phase
7 4 69 40,387,185 1,249,061 44,586 290 811 105 318,655 123,109 9,952,427 3,958,379 49.07 49.75 0.995 0.91 23.56 32.15 1.220 1.126
6 5 57 84,507,360 958,564 28,215 137 797 58 174,688 59,963 11,804,404 5,569,472 49.76 50.67 0.961 0.878 58.75 92.88 1.161 1.084
6 6 56 38,694,379 727,681 21,874 124 801 49 266,389 89,711 24,987,722 13,000,000 49.51 50.75 0.983 0.848 81.93 145.47 1.243 1.093
Table 4 Recorded AE parameters during testing of LC2M37 specimen (rate of loading 4 kN/s).
Peak-load (kN) Strain in steel (est) AE hits Minimum b-value (Ch-6) AE energy (volt2-sec) Displacement – LVDT (mm) Max b-value (channel-6) Appearance of cracks
Phase-I Phase-II Phase-III
Phase-IV
Phase-V
Phase-VI
Phase -VII
180 0.0005 3979 0.6690 39,186 0.531 1.4794 No cracks
450 0.0027 35,527 0.0485 1,216,748 1.978 1.5639 the cracks appeared in third phase grew from hair line to visible cracks
500 0.0033 33,965 0.2958 826,504 2.794 1.5626 Multiple shear cracks near the supports. These are symmetric at left and right supports
570 0.0040 88,475 0.1910 2,115,675 3.942 1.6738 At 550 kN, tensile cracks near the mid zone reached the flange. At 662 kN, Shear cracks opened up
800 0.00511 123,109 0.0241 5,110,990 5.895 1.8634 the tensile cracks opened up to 1 mm and the cracks appeared in flange at 715 kN. The cracks branched at 780 kN and several tensile cracks developed. concrete spalling was seen at the right hand support. The beam was bent at 800 kN. It failed at 810 kN
200 0.0016 5400 0.6319 65,784 0.885 1.5525 No cracks
300 0.00244 28,200 0.1040 853,780 1.747 1.6744 Tensile cracks at 290 kN in moment zone
The AE transducer has peak sensitivity at 75 dB with reference 1 V/(m/s) [1 V/mbar]. The operating frequency of the sensor was 35–100 kHz. The response was almost same for all PAC R6D sensors used in this study. The AE signals were amplified with a gain of 40 dB in a preamplifier. Vacuum grease LR (high vacuum silicon grease) was used as couplant. The threshold value of 40 dB was selected to ensure a high signal to noise ratio. The total AE energy released was calculated by summing up the AE energy recorded by the used 6 channels. 2.5. Loading procedure adopted The loading pattern applied on the RC beam (assumed as a beam in a bridge) is shown in Fig. 4a. The idea of loading protocol was to simulate traffic on a bridge beam. In a real-situation, it is required to collect moving vehicles data for designing the various structural members in a bridge. A real bridge would have experienced many smaller service-level loads as well as due to unknown higher overloads. In this present study a series of service-level load cycles are applied in between test trucks (TTs). These test trucks were chosen to represent the case of structural load testing in the field. TTs were variable in loading magnitude. The smaller load repetitions indicative of service level loads. From Fig. 4a one can observe that a series of TTs was repeated. The reason for this is to study the effect of repetitions on the AE response. It is known that AE signals are unique and thus theoretically not repeatable. The RC beam specimen is subjected to loading protocol which has two types of pattern as shown in Fig. 4a. The first pattern has load intensity with relatively less peak and constitutes transport vehicle effect. The second pattern has higher peak load which constitutes elevated simulated test truck. The two patterns together give single loading phase. Each phase has varying load peaks. The loading phase details are given in Fig. 4a. The loading rates used for the RC specimens are different as shown in Table 2 and this was intentional.
3. Results and discussion The rate of loading, number of loading phases and total number of recorded AE hits, events, energy, counts are shown in Table 3. In case of low rate of loading, there is ample time for the damage to grow. Hence, there is less scope of microcracks to develop and there is also less chances of spreading the micorcracks fast. It was observed the recorded AE events and AE hits are less when the rate of loading is high as shown in Table 3. The first crack appeared at higher load when the rate of loading is less. Tables 4–6 shows the AE parameters recorded and b-value for each phase of loading. Fig 4b shows a recorded plot of midspan displacement versus load which is similar to the plot obtained by previous researchers for cyclic load test [1,31]. Fig. 4c shows the strain in tensile steel at mid section of the RC beam. 3.1. Computation of AE based b-values In the present study AE b-value was computed for each 125 hit amplitudes forward in time. Fig. 5 shows the variation of AE based b-value with load. It is observed from Fig. 5 that a sudden drop in b-values occur at the peak load in each load cycle. The damage growth is characterized by the progressive coalescence of
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R. Vidya Sagar, M.V.M.S. Rao / Construction and Building Materials 70 (2014) 460–472 Table 5 Recorded AE parameters during testing of LLR3 specimen (rate of loading 5 kN/s).
Peak-load (kN) Strain in steel (est) AE hits Minimum b-value (Ch-6) P AE energy E (volt2-sec) Displacement – LVDT (mm) Max b-value (channel-6) Appearance of cracks
Phase-I
Phase-II
Phase-III
Phase-IV
Phase-V
Phase-VI
180 0.000688 6758 0.315055 475,935 0.621 1.8577 No cracks
200 0.0011 9164 0.215849 425,430 0.828 1.78981 tensile crack appeared at 187 kN in moment zone
300 0.00189 34,559 0.011054 2,633,958 1.425 1.71693 The propagation of tensile crack was seen in third phase at 247 kN. The diagonal cracks appeared in shear zone at 288 kN of third phase. Hair line tensile cracks were seen near moment zone at 288 kN
450 0.001385 54,525 0.053745 7,422,092 0.856 1.88728 The crack propagation was seen during IV phase at 267 kN. The diagonal cracks in shear zone propagated at 382 kN and multiple cracks were observed in that zone in phase-IV
360 0.0029 71,672 0.0054 2,244,323 3.254 1.6319 The crack opening was seen in moment zone at 539 kN
800 0.01099 89,711 0.0015 21,884,016 5.726 1.6548 The cracks appeared at flange at 512 kN. At 600 kN of phase five, the cracks were vigorous and opened up to l mm width. The beam failed at 752 kN
Table 6 Recorded AE parameters during testing of LLR1 specimen (rate of loading 6 kN/s).
Peak-load (kN) Strain in steel (est) AE hits Minimum b-value (Ch-2) P AE energy ( E) (volt2-sec) Displacement – LVDT (mm) Max b-value (channel-2) Appearance of cracks
Phase-I
Phase-II
Phase-III
Phase-IV
Phase-V
Phase-VI
180 0.000533 6189 0.299280 190,283 0.58681 1.66220 first tensile crack appeared at 124 kN. At 176 kN, the multiple tensile cracks appeared in moment zone of the beam
200 0.000831 7142 0.38802 131,680 0.950712 1.510309 No changes
300 0.001119 28,640 0.032896 1,694,134 1.393842 1.56369 At 284 kN, growth of the tensile crack were seen. The diagonal cracks appeared simultaneously on shear span at 284 kN. Multiple cracks appeared in midspan of beam at 300 kN
450 0.00069 39,992 0.00174201 1,848,267 1.9752797 1.539284 At 418 kN shear cracks were observed prominently
560 0.00094 32,762 0.507649 533,175 2.9447917 1.55345 At fifth phase, during loading around 360 kN crack propagation of tensile cracks were seen. During loading, at 532 kN, diagonal crack which appeared at phase-III widened and were clearly visible. The hair line cracks widened at 532 kN
670 0.00264 59,963 0.054056 7,445,499 3.9921869 1.755492 crack appeared on the flange at 615 kN. As the load increased, the cracks were vigorously opened up. The beam failed around 800 kN
Fig. 5. The variation of AE based b-value with load [ channel 8 and LLR1 specimen].
microcracks to form fracture surfaces. In the geometry and spatial sense, the fractal dimension D = 2b of the damaged domain is expected to decrease from an initial value comprised between 2 and 3 (that means as damage is initially diffused in the specimen volume and a surface), toward a final value nearly equal to 2, forming the final fracture surface [27]. D is fractal dimension of the damage domain and ‘b’ is the b-value. It was observed from
Fig. 5 that b-values started from values very close to 1.5, representing a fractal dimension (D) of the initial damage D = 2b = 3. During a loading process, the damage growth is characterized by the progressive coalescence of microcracks to form fracture surfaces. Because cracks at the beginning of the loading process are mainly distributed in the bulk of the material [27]. In the initial stages of fracture process, the b-value varied from 1.5 to 1.8 and later it
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Fig. 6. Variation of b-value with strain in steel recorded at (a) ch-3 tensile cracking zone (at centre), (b) ch-1 (shear cracking zone (near left support)) and (c) ch-8 (shear cracking zone (near right support)).
decreases with increase in load (or stress) equal to 1.0 and less, showing temporal fluctuations as the impending failure approaches in the RC beam specimen. A high b-value arises due to low amplitude hits in large number representing new crack formation and slow crack growth, whereas
a low b-value indicates faster or unstable crack growth accompanied by relatively high amplitude AE in small numbers. Therefore the low b-value trend indicates macrocracks have formed, whilst the high b-value trend represents microcrack growth. During the first loading cycle, high b-values were observed with the opening
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Fig. 7. Variation of b-value recorded at ch-3 (at centre) with displacement.
of micro-cracks. Later b-values, showed a decrease as the load increased. The second loading phase was characterized by a large scatter of b-values. During fracture process in RC structures there are three distinct stages of micro-cracking activity, namely (a) initiation, (b) stable growth and (c) nucleation prior to the final failure takes place [1,21]. The AE statistical behavior of each individual stage is dependent on the number and size distribution of micro-cracks. Growth and coalescence of micro-cracks formed during the crack propagation are sources of AE. As most AE signals were generated during formation of microcracks, and therefore this is likely source for occurrence of the lowest b-values. Another source of AE is the bond failure between steel reinforcement and concrete, also between coarse aggregate and cement mortar and this may be responsible for fluctuations in AE generation and hence rapid changes in b-values. The RC test specimen (LLR3) is relatively of large length (more than 3 m). Therefore, several fracturing events may occur simultaneously. It is known that the shear cracks follow tensile cracks. The recorded AE data is grouped according to the position of AE sensors. AE sensors S1 (or ch-1) and S8 (or ch-8) are in the shearing area away from the center and therefore, S1 and S8 reasonably receive AE hits at the moments of development of shear cracks [34]. On the other hand AE sensor S3 is in the center so it recorded information from the tensile cracks from bottom to top. As an example at the moments when the shear cracks develop, the near by sensors (S1 and S8) receive high intensity AE signals. However, possibly the central or other far away sensors may not get similar activity. This is why it was attempted to check the b-value for different sensors separately, and compared with strain in steel at mid section of the specimen LLR3 as shown in Fig. 6. Earlier researchers confirmed that a b-value less than 1.0 represents macro-damage (visible cracks). It was observed that there are several drops (or fluctuations) in b-value computed based on ch-3 when compared to ch-1 and ch-8. This may be due to several tensile cracking occurred before occurrence of shear cracks. The b-value dropped below 1.0 at the end of the loading phase-I. The load magnitude associated with appearance of first tensile crack appeared is 137 kN in moment zone. At around 30 min, the b-value showed a significant drop indicating that more damage occurred, and it is noted that noticeable cracking occurred. The lowest b-value was recorded during last loading cycles because of shear cracking. The increase in the b-value in the last cycles is attributed to attenuation of AE signals due to damage in the specimen. The computed
AE based b-value can be correlated to physical measurements such as strain in tensile reinforcement and mid-span displacement as shown in Fig. 6. Fig. 7 shows the variation of b-value with displacement. It was observed that when the b-value reached 1.0 the midspan displacement was around 3.2 mm. AE released during cycling loading of RC structures could be due to different sources such as crack opening and crack propagation or friction of existing crack surfaces which could occur during opening or closure of cracks. It means that in such structures damage accumulation could be related to a variation of the AE patterns. 3.2. loading rate effect on b-value Fig. 8a shows variation of strain in steel. The specimen yielded relatively quickly when the rate of loading is high. It was observed that the steel yielded more quickly with a higher loading rate, in terms of time, as the load is applied over a shorter time frame. When there is an increase in the rate of loading the slope of the strain versus time plot increases as shown in Fig. 8b. Also the recorded hits are less for the specimen tested with high rate of loading as shown in Fig. 8b. From Fig. 8b, one can observe that the rate of occurrence of AE hits are more in case of LLR1 (tested with 6 kN/s loading rate) when compared with LC2M37 (tested with 4 kN/s loading rate) specimen. Relatively the loading rate applied on LC2M37 specimen is small. The AE b-values are less for the specimen tested with high rate of loading. This may be due to release of high amplitude AE events. For three loading rates of 4 kN/s, 5 kN/s and 6 kN/s on RC beam specimens, the times of occurrence of the lowest b-values vary as shown in Fig. 8c. Higher AE activity such as large number of AE events per time and higher intensity events are also observed around the last loading phases. These observations further prove that the instance of damage initiation is predicted by the lowest b-value. Low b-value may be due to initiation of micro-cracks and cracks opening. The increase in b-value during the unloading in a cycle could be related to shear cracks development and crack sliding. However, the test specimen which is subjected to a lower loading rate of 4 kN/s has shown some characteristic AE signatures while the sample LLR1 which was subjected to a loading rate of 6 kN/s seem to have undergone more damage in a short time relatively as inferred from the average amplitude, b-value, energy/hit and cumulative energy counts as shown in Fig. 9. In case of LC2M37 test specimen, damage is less because of lower loading rate. And incase of LLR3 damage is intermediate since the rate of
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Fig. 8. (a). Variation of strain in steel with time (b) Variation of cumulative AE hits with time. (c) Distinction in b-value with time due to change in rate of loading.
loading is also intermediate. Damage is more in LLR1 because of higher loading rate. Rate of loading can accelerate the micro crack damage which is accompanied by the release of AE. If the rate of loading is too fast (more than what is suggested by the ASTM), there can be a surge or heavy rush of AE that the data logging equipment cannot cope up. In such a case the number of AE events or hits recorded would be less giving rise to higher b-values. The fluctuations in the b-value variation is more when the rate of loading is high. One can observe that the specimen LC2M37 underwent less damage at smaller rate of loading in terms of the data of b-value, AE energy per hit. From Fig. 9b one can observe that there is a distinction in b-value with time due to change in rate of loading. It was observed that when the loading rate is high, then the quick cracking development takes place because high energy events released, which leads to rapid fluctuations and also there was drops in the b-values. Also it was observed that the material
behaves relatively more brittle at higher loading rates (or in higher strain rates), the b-values are lower in average as a few and strong cracking AE events with higher energy are created. But when the loading rate is low more AE and with less AE energy are released. It was observed that significant fluctuations in b-value were occurred in the last phases of loading. AE signals experience attenuation during fracture process in concrete structures, and for that matter in any other imperfect or quasi-brittle materials. Attenuation of AE may be due to heterogeneity of the material as well as microcracking. A change in the volume of the specimen causes a change in the propagation path length from the crack to the AE sensor, which may affect the recorded AE amplitude. Both the AE amplitude and AE energy as well as the number of AE would be affected uniformly be it weak or strong. In this present study authors invariably use the number as well as AE amplitude (or energy data) for computing the b-value and the normalized values of energy for the evaluation of damage. So it should not matter
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160 4 kN/sec
Energy/AE hit
140
5 kN/sec
120
(a)
6 kN/sec
100 80 60 40 20 0 0
1
2
3
4
5
6
7
8
loading phase 1.2 4 kN/sec 5 kN/sec 6 kN/sec
1.15
mean b-value
1.1 1.05
(b)
1 0.95 0.9 0.85 0.8 0
1
2
3
4
5
6
7
8
loading phase 14000000
4 kN/sec 5 kN/sec 6 kN/sec
culmulative energy
12000000 10000000
(c)
8000000 6000000 4000000 2000000 0 0
1
2
3
4
5
6
7
8
loading phase
mean amplitude (dB)
51
(d)
50 49
4 kN/sec 5 kN/sec 6 kN/sec
48 47 0
1
2
3
4
5
6
7
8
loading phase Fig. 9. (a) Variation of energy per hit (b) mean b-value (c) cumulative energy (d) mean amplitude with loading phase.
since both low amplitude (energy) and high amplitude (energy) as well as number (small or large) of AE are considered for the evaluation of damage or to study the fracture process. 3.3. Trends of b-value with the appearance of cracks In case of specimen tested with loading rate 4 kN/s [LC2M37] no cracks appeared till 200 kN. During loading phase-III, tensile cracks at 290 kN in moment zone appeared and the maximum AE b-value [for channel 6] was 1.67 and minimum was 0.1. The cracks appeared in third loading phase grew from micro cracks to macro cracks at 450 kN. During loading phase-IV, the b-value maximum
was 1.56 and minimum was 0.04. In loading phase-V, multiple shear cracks near the supports are formed. These cracks are symmetric at left and right supports. The b-value maximum was 1.56 and minimum was 0.29. During loading phase-VI, at 550 kN, tensile cracks near the moment zone reached the RC beam flange. At 662 kN, shear cracks opened further. The b-value maximum was 1.67 and minimum was 0.004. During loading phase-VII, the tensile cracks opened up to 1 mm and the cracks appeared in flange at 715 kN. The cracks branched at 780 kN and several tensile cracks developed also concrete spalling was observed at the right side support. The beam was bent at 800 kN and it was collapsed at 810 kN. The b-value maximum was 1.86 and minimum was 0.0051.
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Fig. 10. Variation of average frequency with load (LLR3 specimen).
Fig. 11. Variation of b-value with RA (LLR3 specimen).
Because of increase in rate of loading to 5 kN/s, tensile crack appeared at 187 kN in moment zone in LLR3 specimen. However, no crack appeared in loading phase-I. The b-value [for channel 6] maximum was 1.78 and minimum was 0.21 in loading phase-II. The propagation of tensile crack was observed in third loading phase at 247 kN. Also the diagonal cracks appeared in shear zone at 288 kN. Hair line tensile cracks were observed near moment zone at 288 kN. The b-value maximum was 1.71 and minimum was 0.01 in loading phase-III. The crack propagation was observed during loading phase-IV at 267 kN. The diagonal cracks in shear zone starts propagated at 382 kN and multiple cracks were observed in that zone in phase-IV. The crack opening was seen in moment zone at 539 kN. The b-value maximum was 1.71 and minimum was 0.01 in loading phase-III. The cracks propagated till to flange at 512 kN. At 600 kN of loading phase-V, the cracks were vigorous and opened further to l mm width. The beam failed at 752 kN. The maximum b-value was 1.65 and minimum was 0.001. In case of LLR1 specimen tested at 6 kN/s loading rate, first tensile crack appeared at 124 kN in loading phase-I. At 176 kN, the multiple tensile cracks appeared in moment zone of the beam during loading phase-II. The maximum b-value [ for channel 2] was 1.66 and minimum was 0.29. When compared with the previous RC beam specimens tested (at 4 kN/s and 5 kN/s), cracks appeared
quickly in first loading phase. However there are no new cracks appeared during loading phase-II. At 284 kN, growth of the tensile crack were seen. The diagonal cracks appeared simultaneously on shear span at 284 kN. Multiple cracks appeared in midspan of beam at 300 kN. The maximum b-value was 1.56 and minimum was 0.03. During loading phase-IV, at 418 kN shear cracks were observed significantly. The maximum b-value was 1.53 and minimum was 0.001. At fifth loading phase, propagation of tensile cracks were observed at 360 kN. During loading, at 532 kN, diagonal crack which appeared at phase-III widened and were clearly visible. The hair line cracks widened at 532 kN. The maximum bvalue was 1.55 and minimum was 0.50. cracks propagated to flange at 615 kN. As the load increased further, the cracks were opened up. The RC beam failed around 800 kN. The maximum bvalue was 1.75 and minimum was 0.05. 3.4. Fluctuations of average frequency (AF) and rise angle (RA) The tensile mode of cracking which includes opposing movement of the crack sides, results in AE waveforms with short rise time (RT) and high frequency. On the contrary shear type of cracks result in longer AE waveforms, with low frequency and longer rise time. AF value for each load cycle decreases gradually as the
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Fig. 12. Schematic diagram of the development of cracks in RC beam specimens (crack number and the load are indicated in parenthesis).
loading progresses as shown in Fig. 10. When the AF of a signal is higher the crack can be classified as of tensile mode. The gradual decrease in AF shows the formation of the shear cracks at the final stage of the loading. Fig. 11 shows the fluctuations of RA (rise time/amplitude) that could be temporary shift between small and large scale events and coincide with the drops of b-value. Rise time is observed to increase for the last loading cycles compared to the initial ones. This could be due to the formation of shear cracks. Shear cracks is relatively brittle in nature. Therefore fracture takes place suddenly and the rise time is relatively small. During the initial
loading cycles the AE hits were of shorter rise time compared to the final loading cycles which had AE hits with longer rise time. Hence for the final cycles shear cracks are observed as the rise time is longer. From Fig. 11, one can observe that a sudden bvalue drops when there is a rise in RA value. This could be due to formation of new crack or propagation of existing crack. Fig. 12 shows the schematic diagram of cracks developed in the test specimen. From Fig. 12, one can observe that first cracks appeared in the midspan of the specimen and later cracks appeared near to supports. RT is high when shear cracks are formed and b-value decreases.
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4. Practical significance The practical importance of this work is AE based b-value analysis is useful to assess the level of damage in a RC structure in situ. It may be possible to correlate the computed b-value with the physical measurements such as strain in tensile reinforcement and midspan displacement. By using the allowable limits given by codes of practice, one can compare the present b-value and assess the state of damage as minor, intermediate, heavy. 5. Conclusions Based on the above results the given below major conclusions are drawn 1. It was observed that when the loading rate is faster, then the quick cracking development lead to quick fluctuations and drops in the b-value. 2. Since the material behaves relatively more brittle at higher loading rates (or in higher strain rates), the b-values are lower in average as a few and strong cracking AE events are created, in contrast to more and weaker for low rate of loading (or low strain rate). 3. b-Value analysis is useful in evaluating the damage level in RC structures in-situ, the instance of damage initiation can be predicted by the lowest b-value. And also when the rate of loading is high, the b-value is minimum. b-Value analysis may be useful to estimate the present operating load conditions. 4. A sudden drop in b-value occurred when there is a rise in RA value. This could be due to formation of new crack or propagation of existing crack.
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[10] RILEM TC 212-ACD. Acoustic emission and related NDE techniques for crack detection and damage evaluation in concrete. Test Method for damage qualification of reinforced concrete beams by AE. Mater Struct 2010;43:1183–6. [11] RILEM TC 212-ACD. Acoustic emission and related NDE techniques for crack detection and damage evaluation in concrete. Test method for classification of active cracks in concrete structures by acoustic emission. Mater Struct 2010;43:1187–9. [12] NDIS-2421. Recommended practice for in-situ monitoring of concrete structures by acoustic emission. Jpn Soc Non-Destruct Inspection 2000. [13] Richter Charles F. Elementary seismology. San Francisco and London: W.H. Freeman and Company; 1958. [14] Smith W. Evidence for precursory changes in the frequency–magnitude bvalue. Geophys J R Astron Soc 1986;86:815–38. [15] Scholz CH. The frequency–magnitude relation of microfracturing in rock and its relation to earthquakes. Bull Seismol Soc Am 1968;58:399–415. [16] Wyss M. Towards a physical understanding of the earthquake frequency distribution. Geophys J R Astr Soc 1973;31:341–59. [17] Fielder G. Local b-values related to seismicity. Tectonophysics 1974;23:277–82. [18] Cox SJD, Meridith PG. Microcracking formation and material softening in rock measured by monitoring acoustic emissions. Int J Rock Mech Min Sci Geomech Abs 1983;30:11–24. [19] Turcotte DL, Newman WL, Shcherbakov R. Micro and macroscopic models of rock fracture. Geophys Int J 2003;152:712–28. [20] Hatton CG, Main IG, Meredith PG. A comparison of seismic and structural measurements of scaling exponents during tensile sub-critical crack growth. J Struct Geo 1993;15:1485–95. [21] Rao MVMS, Lakshmi KJP. Analysis of b-value and improved b-value of acoustic emissions accompanying rock fracture. Curr Sci 2005;89:1577–82. [22] Carpinteri A. Critical behavior in concrete structures and damage localization by acoustic emission. Key Eng Mater 2006;312:305–10. [23] Farhidzadeh Alireza, Salamore Salvatore, Luna Bismark, Whittaket Andrew. Acoustic emission monitoring of a reinforced concrete shear wall by b-value based outlier analysis. Struct Health Monit 2013;12:3–13. [24] Farhidzadeh Alireza, Dehghan-Niri Ehsan, Salamone Salvatore, Luna Bismark, Whittaker Andrew. Monitoring crack propagation in reinforced concrete shear walls by acoustic emission. J Mater Civil Eng 2013;139(12):040130-1–04013010. [25] Kurz JH, Finck F, Grosse CU, Reinhardt HW. Stress drop and stress redistribution in concrete quantified over time by the b-value analysis’’. Struct Heal Monit 2006;5:69–81. [26] Schumacher T, Higgins C, Lovejoy S. Estimating operating load conditions on reinforced concrete highway bridges with b-value analysis from acoustic emission monitoring. Struct Health Monit 2011;10:17–32. [27] Carpinteri A, Lacidogna G, Puzzi S. From criticality to final collapse: evolution of b-value 1.5 to 1.0. Chaos Solit Fract 2009;41:843–53. [28] Shiotani T, Aggelis DG, Makishima O. Global monitoring of large concrete structures using acoustic emission and ultrasonic techniques: case study. J Brid Eng 2009;14:188–92. [29] Colombo S, Main IG, Forde MC. Assessing damage of reinforced concrete beam using b-value analysis of acoustic emission signals. J Mater Civil Eng 2003;15:280–6. [30] Main IG. A modified Griffith criterion for the evolution of damage with a fractal distribution of crack lengths: application to seismic event rates and b-values. Geophys J Int 1991;107:353–62. [31] ElBatanouny M, Ziehl P, Larosche A, Mangual J, Nanni A, Matta F. Condition assessment of prestressed concrete beams via acoustic emission monitoring. Cons Build Mater 2014;58:46–53. [32] Aggelis DG, Shiotani T, Momoki S, Hirama A. Acoustic emission and ultrasound for damage characterization of concrete elements. ACI Mater J 2009;106:509–14. [33] IRC:6. Standard specifications and code of practice for road bridges II: loads and stresses. Indian road congress, New Delhi; 2000. [34] Aggelis DG. Classification of cracking in concrete by acoustic emission parameters. Mech Res Comm 2011;38:153–7.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
An experimental study on loading rate effect on acoustic emission based b-values related to reinforced concrete fracture R. Vidya Sagar a,⇑, M.V.M.S. Rao b a b
Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India 4-1-107, Street#2, Bhavani Nagar, Nacharam, Hyderabad 500 076, India
h i g h l i g h t s b-Values analysis was performed to study fracture process in reinforced concrete T-beams. AE based b-values are compared with strain in steel reinforcement in T-beams. Concrete relatively more brittle at higher loading rates. b-Values are lower in average as a few and strong cracking AE events occured at higher loading rates.
a r t i c l e
i n f o
Article history: Received 19 June 2014 Received in revised form 21 July 2014 Accepted 24 July 2014
Keywords: Acoustic emission Fracture Reinforced concrete structures b-Value GBR relationship
a b s t r a c t This article reports on analysis of fracture processes in reinforced concrete (RC) beams with acoustic emission (AE) technique. An emphasis was given to study the effect of loading rate on variation in AE based b-values with the development of cracks in RC structures. RC beams of length 3.2 m were tested under load control at a rate of 4 kN/s, 5 kN/s and 6 kN/s and the b-value analysis available in seismology was used to study the fracture process in RC structures. Moreover, the b-value is related to the strain in steel to assess the damage state. It is observed that when the loading rate is higher, quick cracking development lead to rapid fluctuations and drops in the b-values. Also it is observed that concrete behaves relatively more brittle at higher loading rates (or at higher strain rates). The average b-values are lower as a few but larger amplitudes of AE events occur in contrast to more number of low amplitude AE events occur at low loading rates (or at low strain rates). Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The issue of monitoring fracture process in concrete structures is always open, since many points need clarification. The fracture characteristics of RC structural members are affected by loading rates [1]. AE released during fracture process in real scale components still needs refinement. It is known that both concrete and steel are loading rate dependent materials. Strength, stiffness, brittleness, ductility of concrete and steel are affected by loading rates. A survey on response of RC structures subjected to different loading rate has been presented [2]. The physical mechanism involved in the behavior of concrete in tension at different loading rates was summarized and the study concluded that at smaller strain rates the physical mechanism is a viscous mechanism known as Stefan effect which counter both microcracking and macrocrack propagation. At high strain rates the forces of inertia ⇑ Corresponding author. Tel.: +91 80 22933120; fax: +91 80 23600404. E-mail address: [email protected] (R. Vidya Sagar). http://dx.doi.org/10.1016/j.conbuildmat.2014.07.076 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.
counter the microcracking localization and propagation. The viscous effects, together with the forces of inertia results in increasing the Young’s modulus and tensile strength of the concrete [3]. Zhang et al. studied fracture behavior of high-strength concrete at various loading rates. The fracture energy and the peak load were measured. The study concluded that the fracture energy and the peak load increase as the loading rate increases. Under high loading rates the increase in the fracture energy and peak load are influenced due to the effect of inertia [4]. The strength and the elastic modulus of concrete increased with the increasing loading rate. Also the yield strength and the corresponding strain of steel increased with the increasing loading rate. Muller reviewed the experimental data available on fracture properties of high strength concrete subjected different loading rates [5]. Su et al. studied the loading rate effect on mechanical properties of concrete used for hydraulic structures using AE technique and concluded that as the strain rate increases, the cumulative AE events, hits, hit rate around peak stress decrease correspondingly for the same size of specimens [6].
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Fig. 1. (a) Bridge deck plan (b) cross section of the bridge deck, [kerb 600 mm 300 mm, deckslab thickness 0.2 m, breadth of cross girder is 0.3 m, wearing coat is 0.08 m, carriage ways is 7.5 m] (c) application of load on bridge.
Table 1 Design moments and shear forces. Bending moment (kN-m)
Outer girders Inner girder
Shear force (kN)
Dead load
Live load
Total
Dead load
Live load
Total
1218 1218
1513 912
2731 2130
292 292
280.1 402.6
572.1 694.6
Table 2 Geometric details of the RC test beams (X and Y are the sensor location/coordinates in XY-plane; The name LC2M37 stands L for large specimen, c for concrete, 2 for second specimen, M37 stands for concrete mix having 28th day strength of 37 MPa). T-beam Web(rib) Rate of Sensor location (mm) loading (kN/s) Depth Width Wf Depth Width 1 2 3 (mm) (mm) (mm) Wrib (mm) X Y X Y X
Specimen £ n As S L Total depth T-beam Flange (mm) (mm2) (mm) (mm) D (mm)
LC2M37 LLR3 LLR1
20 20 20
4 1256 4 1256 4 1256
2600 3210 560 2600 3210 560 2600 3210 560
180 180 180
500 500 500
380 380 380
180 180 180
4 5 6
5 Y
X
6 Y
X
8 Y
X
Y
460 300 900 240 1600 175 2000 160 2400 210 2800 190 460 300 900 240 1600 200 2000 160 2420 230 2800 200 460 300 900 240 1600 200 2000 160 2400 230 2800 200
£ is the diameter of reinforcing bar; n is number of main reinforcing bars; S is span of the test beam; L is the total length of the test beam.
The issues such as monitoring fracture process in concrete structures using AE technique concern mainly the interpretation of AE parameters which in many cases is subject to assumptions that although reasonable they are still assumptions. Loading rate effect on AE based b-values related to fracture process in RC structures may help to clear the trends and useful in order to build the
experience of the AE and concrete community working in structural health monitoring research area. Only few design codes take into account the effect of loading rates on the RC structures. There is a need to do structural health monitoring tests and confirm old RC structures performance and safety. Because in India there are many RC structures constructed
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Spreader beam Test specimen
AE amplifier
LVDT
AE sensors
Fig. 2. RC beam specimen in the test rig, structures lab, department of civil engineering, Indian institute of science, Bangalore, India.
Fig. 3. Reinforcement details of the RC beam [ LLR3 specimen].
several years ago. AE based b-value analysis can be a useful method to assess the microcracking which is related to the level of damage in a RC structure. Relatively there is still lack of sufficient experimental data concerning the loading rate effect on variation in b-values for damage assessment in RC structures [7–12]. 1.1. b-Value analysis In seismology, an empirical formula proposed by Guttenberg– Richter given in Eq. (1) is used for b-value analysis [13].
NðP mÞ ¼ 10abm
ð1Þ
where N is the cumulative number of earthquakes of magnitude Pm in a particular area over a specified time span, a and b are constants which vary with the region [14–17]. In context of AE technique, the Gutenberg–Richter formula is given in Eq. (2) [18–21].
log10 N ¼ a b
AdB 20
identical features at different scales for micro-seismicity during fracture process in RC structures. Therefore, during fracture process in RC structures a decreasing b-value could be indicative of increasing stress (or load) levels, i.e. indicative of an impending fracture. Thus, the b-value is a useful tool for assessing damage status. In fact, recording of all released AE waves during monitoring of fracture process in RC structures is a difficult task. Therefore, a statistical approaches such as b-value analysis is needed. Aim is to study the application of b-value to assess damage in RC structures by considering different loading rates.
ð2Þ
where N is the number of AE hits with an amplitude higher than AdB. a is a constant determined largely by the background noise present in the surroundings of testing and b is the negative slope of the curve plotted between log10(N) and AE signal amplitude (AdB). The b-value is defined as the ‘log-linear slope of the frequency–magnitude distribution’ of AE. In fact b-value represents the ‘scaling of amplitude distribution’ of AE, and is a measure of the relative numbers of small and large AE which are finger-prints of cracks developed [22]. Several researchers working in the area of civil engineering studied the application AE frequency–amplitude distribution analysis to concrete structures [23–32]. The hypothesis to be tested is that according to researchers working in the area of seismology and rock mechanics the b-value decreases before the occurrence of an earthquake. It was observed that the b-value is inversely related to the accumulation of stress in a given region. Analogous to AE technique, the b-value represents the scaling of AE amplitude distribution and is an appearance of
2. Experimental procedure 2.1. Determination of test specimen dimensions A RC T-beam girder bridge of span 16 m as shown in Fig. 1 has been studied. The effective span of the Tee beam is 16 m and width of the carriage way is 7.5 m. The bridge has wearing coat of thickness 80 mm. Width of main girders is 300 mm. Kerbs 600 mm wide by 300 mm deep are provided. Cross girders are provided at every 4 m intervals. Breadth of cross girders is 300 mm. The geometric details of the RC Tee beam girder bridge are shown in Fig. 1. The live load was applied by following IRC code class-AA tracked vehicle load on the bridge and obtained bending moment and shear forces are shown in Table 1 [33]. In order to study the fracture process in the RC beams in laboratory it was assumed that the scaling of the beams has been done, and the scaled geometry details of RC T-beams are shown in Table 2. Three RC T-beams are cast with same concrete and reinforcement to study the effect of rate of loading.
2.2. Materials and test specimens A specimen in the test rig and reinforcement details are shown in Fig. 2 and Fig. 3 respectively. During testing a RC specimen was loaded at mid-span and simply supported over a span S. The loading was conducted by means of a fourpoint bending configuration. The 28-day compressive strength of concrete mix (maximum coarse aggregate size is 20 mm) was 37 MPa. Two-point loading span was 1 m with 2.6 m supporting-span as shown in Fig. 1c. The geometry and reinforcement details are given in Table 1 and in the same table £ is nominal diameter of reinforcement; n is number of reinforcement bars; L is beam length; S is span of the beam; b is beam width; D is beam depth; As is% of cross-section of steel reinforcement.
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Fig. 4. (a) Loading protocol for the specimen LLR3 (b) recorded plot of mid-span displacement and load (c) variation in strain in steel at mid-span with load.
2.3. Testing arrangement The experimental setup consisted of a servo hydraulic loading frame (1200 kN) with a data acquisition system and a 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 four point bending) in incremental cycles till failure of the specimen. The data acquisition records load, displacement at center of the beam, strain in the steel at the centre of the RC beam and time. The mid-span displacement was measured using a linearly varying displacement transformer (LVDT), placed at the center on the underside of the RC beam. The strain in steel at mid section of the test
specimen is recorded using electrical strain gauge which was fixed to main steel reinforcing bar (tensile reinforcement) before casting.
2.4. AE monitoring system The AE monitoring system (PAC make) had eight channels one for each of the eight resonant type sensors (R6D resonant type AE differential sensor), pre-amplifiers, data acquisition system, processing instrumentation and AEwin SAMOS software and the sensor’s location (X and Y coordinates) are shown in Table 1.
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Table 3 AE parameters and b-value and Ib-value at different loading stages. Test specimen
LC2M37
LLR3
LLR1
Number of loading phases Rate of loading (kN/s) Number of cycles Total AE energy (V2-s) Total AE hits Total AE events Load at which first crack appeared (kN) Failure load (kN) Time of final failure (min) Cumulative hits (sum of all phases) Number of hits in last phase Cumulative energy counts (sum of all phases) Energy counts in last phase Average amplitude (dB) (average of all phases) amplitude in last phase Average b-value (average of all phases) b-value of last phase Average energy per hit (average of all phases) energy per hit in last phase Average Ib-value (average of all phases) Ib-value in last phase
7 4 69 40,387,185 1,249,061 44,586 290 811 105 318,655 123,109 9,952,427 3,958,379 49.07 49.75 0.995 0.91 23.56 32.15 1.220 1.126
6 5 57 84,507,360 958,564 28,215 137 797 58 174,688 59,963 11,804,404 5,569,472 49.76 50.67 0.961 0.878 58.75 92.88 1.161 1.084
6 6 56 38,694,379 727,681 21,874 124 801 49 266,389 89,711 24,987,722 13,000,000 49.51 50.75 0.983 0.848 81.93 145.47 1.243 1.093
Table 4 Recorded AE parameters during testing of LC2M37 specimen (rate of loading 4 kN/s).
Peak-load (kN) Strain in steel (est) AE hits Minimum b-value (Ch-6) AE energy (volt2-sec) Displacement – LVDT (mm) Max b-value (channel-6) Appearance of cracks
Phase-I Phase-II Phase-III
Phase-IV
Phase-V
Phase-VI
Phase -VII
180 0.0005 3979 0.6690 39,186 0.531 1.4794 No cracks
450 0.0027 35,527 0.0485 1,216,748 1.978 1.5639 the cracks appeared in third phase grew from hair line to visible cracks
500 0.0033 33,965 0.2958 826,504 2.794 1.5626 Multiple shear cracks near the supports. These are symmetric at left and right supports
570 0.0040 88,475 0.1910 2,115,675 3.942 1.6738 At 550 kN, tensile cracks near the mid zone reached the flange. At 662 kN, Shear cracks opened up
800 0.00511 123,109 0.0241 5,110,990 5.895 1.8634 the tensile cracks opened up to 1 mm and the cracks appeared in flange at 715 kN. The cracks branched at 780 kN and several tensile cracks developed. concrete spalling was seen at the right hand support. The beam was bent at 800 kN. It failed at 810 kN
200 0.0016 5400 0.6319 65,784 0.885 1.5525 No cracks
300 0.00244 28,200 0.1040 853,780 1.747 1.6744 Tensile cracks at 290 kN in moment zone
The AE transducer has peak sensitivity at 75 dB with reference 1 V/(m/s) [1 V/mbar]. The operating frequency of the sensor was 35–100 kHz. The response was almost same for all PAC R6D sensors used in this study. The AE signals were amplified with a gain of 40 dB in a preamplifier. Vacuum grease LR (high vacuum silicon grease) was used as couplant. The threshold value of 40 dB was selected to ensure a high signal to noise ratio. The total AE energy released was calculated by summing up the AE energy recorded by the used 6 channels. 2.5. Loading procedure adopted The loading pattern applied on the RC beam (assumed as a beam in a bridge) is shown in Fig. 4a. The idea of loading protocol was to simulate traffic on a bridge beam. In a real-situation, it is required to collect moving vehicles data for designing the various structural members in a bridge. A real bridge would have experienced many smaller service-level loads as well as due to unknown higher overloads. In this present study a series of service-level load cycles are applied in between test trucks (TTs). These test trucks were chosen to represent the case of structural load testing in the field. TTs were variable in loading magnitude. The smaller load repetitions indicative of service level loads. From Fig. 4a one can observe that a series of TTs was repeated. The reason for this is to study the effect of repetitions on the AE response. It is known that AE signals are unique and thus theoretically not repeatable. The RC beam specimen is subjected to loading protocol which has two types of pattern as shown in Fig. 4a. The first pattern has load intensity with relatively less peak and constitutes transport vehicle effect. The second pattern has higher peak load which constitutes elevated simulated test truck. The two patterns together give single loading phase. Each phase has varying load peaks. The loading phase details are given in Fig. 4a. The loading rates used for the RC specimens are different as shown in Table 2 and this was intentional.
3. Results and discussion The rate of loading, number of loading phases and total number of recorded AE hits, events, energy, counts are shown in Table 3. In case of low rate of loading, there is ample time for the damage to grow. Hence, there is less scope of microcracks to develop and there is also less chances of spreading the micorcracks fast. It was observed the recorded AE events and AE hits are less when the rate of loading is high as shown in Table 3. The first crack appeared at higher load when the rate of loading is less. Tables 4–6 shows the AE parameters recorded and b-value for each phase of loading. Fig 4b shows a recorded plot of midspan displacement versus load which is similar to the plot obtained by previous researchers for cyclic load test [1,31]. Fig. 4c shows the strain in tensile steel at mid section of the RC beam. 3.1. Computation of AE based b-values In the present study AE b-value was computed for each 125 hit amplitudes forward in time. Fig. 5 shows the variation of AE based b-value with load. It is observed from Fig. 5 that a sudden drop in b-values occur at the peak load in each load cycle. The damage growth is characterized by the progressive coalescence of
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Peak-load (kN) Strain in steel (est) AE hits Minimum b-value (Ch-6) P AE energy E (volt2-sec) Displacement – LVDT (mm) Max b-value (channel-6) Appearance of cracks
Phase-I
Phase-II
Phase-III
Phase-IV
Phase-V
Phase-VI
180 0.000688 6758 0.315055 475,935 0.621 1.8577 No cracks
200 0.0011 9164 0.215849 425,430 0.828 1.78981 tensile crack appeared at 187 kN in moment zone
300 0.00189 34,559 0.011054 2,633,958 1.425 1.71693 The propagation of tensile crack was seen in third phase at 247 kN. The diagonal cracks appeared in shear zone at 288 kN of third phase. Hair line tensile cracks were seen near moment zone at 288 kN
450 0.001385 54,525 0.053745 7,422,092 0.856 1.88728 The crack propagation was seen during IV phase at 267 kN. The diagonal cracks in shear zone propagated at 382 kN and multiple cracks were observed in that zone in phase-IV
360 0.0029 71,672 0.0054 2,244,323 3.254 1.6319 The crack opening was seen in moment zone at 539 kN
800 0.01099 89,711 0.0015 21,884,016 5.726 1.6548 The cracks appeared at flange at 512 kN. At 600 kN of phase five, the cracks were vigorous and opened up to l mm width. The beam failed at 752 kN
Table 6 Recorded AE parameters during testing of LLR1 specimen (rate of loading 6 kN/s).
Peak-load (kN) Strain in steel (est) AE hits Minimum b-value (Ch-2) P AE energy ( E) (volt2-sec) Displacement – LVDT (mm) Max b-value (channel-2) Appearance of cracks
Phase-I
Phase-II
Phase-III
Phase-IV
Phase-V
Phase-VI
180 0.000533 6189 0.299280 190,283 0.58681 1.66220 first tensile crack appeared at 124 kN. At 176 kN, the multiple tensile cracks appeared in moment zone of the beam
200 0.000831 7142 0.38802 131,680 0.950712 1.510309 No changes
300 0.001119 28,640 0.032896 1,694,134 1.393842 1.56369 At 284 kN, growth of the tensile crack were seen. The diagonal cracks appeared simultaneously on shear span at 284 kN. Multiple cracks appeared in midspan of beam at 300 kN
450 0.00069 39,992 0.00174201 1,848,267 1.9752797 1.539284 At 418 kN shear cracks were observed prominently
560 0.00094 32,762 0.507649 533,175 2.9447917 1.55345 At fifth phase, during loading around 360 kN crack propagation of tensile cracks were seen. During loading, at 532 kN, diagonal crack which appeared at phase-III widened and were clearly visible. The hair line cracks widened at 532 kN
670 0.00264 59,963 0.054056 7,445,499 3.9921869 1.755492 crack appeared on the flange at 615 kN. As the load increased, the cracks were vigorously opened up. The beam failed around 800 kN
Fig. 5. The variation of AE based b-value with load [ channel 8 and LLR1 specimen].
microcracks to form fracture surfaces. In the geometry and spatial sense, the fractal dimension D = 2b of the damaged domain is expected to decrease from an initial value comprised between 2 and 3 (that means as damage is initially diffused in the specimen volume and a surface), toward a final value nearly equal to 2, forming the final fracture surface [27]. D is fractal dimension of the damage domain and ‘b’ is the b-value. It was observed from
Fig. 5 that b-values started from values very close to 1.5, representing a fractal dimension (D) of the initial damage D = 2b = 3. During a loading process, the damage growth is characterized by the progressive coalescence of microcracks to form fracture surfaces. Because cracks at the beginning of the loading process are mainly distributed in the bulk of the material [27]. In the initial stages of fracture process, the b-value varied from 1.5 to 1.8 and later it
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Fig. 6. Variation of b-value with strain in steel recorded at (a) ch-3 tensile cracking zone (at centre), (b) ch-1 (shear cracking zone (near left support)) and (c) ch-8 (shear cracking zone (near right support)).
decreases with increase in load (or stress) equal to 1.0 and less, showing temporal fluctuations as the impending failure approaches in the RC beam specimen. A high b-value arises due to low amplitude hits in large number representing new crack formation and slow crack growth, whereas
a low b-value indicates faster or unstable crack growth accompanied by relatively high amplitude AE in small numbers. Therefore the low b-value trend indicates macrocracks have formed, whilst the high b-value trend represents microcrack growth. During the first loading cycle, high b-values were observed with the opening
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Fig. 7. Variation of b-value recorded at ch-3 (at centre) with displacement.
of micro-cracks. Later b-values, showed a decrease as the load increased. The second loading phase was characterized by a large scatter of b-values. During fracture process in RC structures there are three distinct stages of micro-cracking activity, namely (a) initiation, (b) stable growth and (c) nucleation prior to the final failure takes place [1,21]. The AE statistical behavior of each individual stage is dependent on the number and size distribution of micro-cracks. Growth and coalescence of micro-cracks formed during the crack propagation are sources of AE. As most AE signals were generated during formation of microcracks, and therefore this is likely source for occurrence of the lowest b-values. Another source of AE is the bond failure between steel reinforcement and concrete, also between coarse aggregate and cement mortar and this may be responsible for fluctuations in AE generation and hence rapid changes in b-values. The RC test specimen (LLR3) is relatively of large length (more than 3 m). Therefore, several fracturing events may occur simultaneously. It is known that the shear cracks follow tensile cracks. The recorded AE data is grouped according to the position of AE sensors. AE sensors S1 (or ch-1) and S8 (or ch-8) are in the shearing area away from the center and therefore, S1 and S8 reasonably receive AE hits at the moments of development of shear cracks [34]. On the other hand AE sensor S3 is in the center so it recorded information from the tensile cracks from bottom to top. As an example at the moments when the shear cracks develop, the near by sensors (S1 and S8) receive high intensity AE signals. However, possibly the central or other far away sensors may not get similar activity. This is why it was attempted to check the b-value for different sensors separately, and compared with strain in steel at mid section of the specimen LLR3 as shown in Fig. 6. Earlier researchers confirmed that a b-value less than 1.0 represents macro-damage (visible cracks). It was observed that there are several drops (or fluctuations) in b-value computed based on ch-3 when compared to ch-1 and ch-8. This may be due to several tensile cracking occurred before occurrence of shear cracks. The b-value dropped below 1.0 at the end of the loading phase-I. The load magnitude associated with appearance of first tensile crack appeared is 137 kN in moment zone. At around 30 min, the b-value showed a significant drop indicating that more damage occurred, and it is noted that noticeable cracking occurred. The lowest b-value was recorded during last loading cycles because of shear cracking. The increase in the b-value in the last cycles is attributed to attenuation of AE signals due to damage in the specimen. The computed
AE based b-value can be correlated to physical measurements such as strain in tensile reinforcement and mid-span displacement as shown in Fig. 6. Fig. 7 shows the variation of b-value with displacement. It was observed that when the b-value reached 1.0 the midspan displacement was around 3.2 mm. AE released during cycling loading of RC structures could be due to different sources such as crack opening and crack propagation or friction of existing crack surfaces which could occur during opening or closure of cracks. It means that in such structures damage accumulation could be related to a variation of the AE patterns. 3.2. loading rate effect on b-value Fig. 8a shows variation of strain in steel. The specimen yielded relatively quickly when the rate of loading is high. It was observed that the steel yielded more quickly with a higher loading rate, in terms of time, as the load is applied over a shorter time frame. When there is an increase in the rate of loading the slope of the strain versus time plot increases as shown in Fig. 8b. Also the recorded hits are less for the specimen tested with high rate of loading as shown in Fig. 8b. From Fig. 8b, one can observe that the rate of occurrence of AE hits are more in case of LLR1 (tested with 6 kN/s loading rate) when compared with LC2M37 (tested with 4 kN/s loading rate) specimen. Relatively the loading rate applied on LC2M37 specimen is small. The AE b-values are less for the specimen tested with high rate of loading. This may be due to release of high amplitude AE events. For three loading rates of 4 kN/s, 5 kN/s and 6 kN/s on RC beam specimens, the times of occurrence of the lowest b-values vary as shown in Fig. 8c. Higher AE activity such as large number of AE events per time and higher intensity events are also observed around the last loading phases. These observations further prove that the instance of damage initiation is predicted by the lowest b-value. Low b-value may be due to initiation of micro-cracks and cracks opening. The increase in b-value during the unloading in a cycle could be related to shear cracks development and crack sliding. However, the test specimen which is subjected to a lower loading rate of 4 kN/s has shown some characteristic AE signatures while the sample LLR1 which was subjected to a loading rate of 6 kN/s seem to have undergone more damage in a short time relatively as inferred from the average amplitude, b-value, energy/hit and cumulative energy counts as shown in Fig. 9. In case of LC2M37 test specimen, damage is less because of lower loading rate. And incase of LLR3 damage is intermediate since the rate of
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Fig. 8. (a). Variation of strain in steel with time (b) Variation of cumulative AE hits with time. (c) Distinction in b-value with time due to change in rate of loading.
loading is also intermediate. Damage is more in LLR1 because of higher loading rate. Rate of loading can accelerate the micro crack damage which is accompanied by the release of AE. If the rate of loading is too fast (more than what is suggested by the ASTM), there can be a surge or heavy rush of AE that the data logging equipment cannot cope up. In such a case the number of AE events or hits recorded would be less giving rise to higher b-values. The fluctuations in the b-value variation is more when the rate of loading is high. One can observe that the specimen LC2M37 underwent less damage at smaller rate of loading in terms of the data of b-value, AE energy per hit. From Fig. 9b one can observe that there is a distinction in b-value with time due to change in rate of loading. It was observed that when the loading rate is high, then the quick cracking development takes place because high energy events released, which leads to rapid fluctuations and also there was drops in the b-values. Also it was observed that the material
behaves relatively more brittle at higher loading rates (or in higher strain rates), the b-values are lower in average as a few and strong cracking AE events with higher energy are created. But when the loading rate is low more AE and with less AE energy are released. It was observed that significant fluctuations in b-value were occurred in the last phases of loading. AE signals experience attenuation during fracture process in concrete structures, and for that matter in any other imperfect or quasi-brittle materials. Attenuation of AE may be due to heterogeneity of the material as well as microcracking. A change in the volume of the specimen causes a change in the propagation path length from the crack to the AE sensor, which may affect the recorded AE amplitude. Both the AE amplitude and AE energy as well as the number of AE would be affected uniformly be it weak or strong. In this present study authors invariably use the number as well as AE amplitude (or energy data) for computing the b-value and the normalized values of energy for the evaluation of damage. So it should not matter
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160 4 kN/sec
Energy/AE hit
140
5 kN/sec
120
(a)
6 kN/sec
100 80 60 40 20 0 0
1
2
3
4
5
6
7
8
loading phase 1.2 4 kN/sec 5 kN/sec 6 kN/sec
1.15
mean b-value
1.1 1.05
(b)
1 0.95 0.9 0.85 0.8 0
1
2
3
4
5
6
7
8
loading phase 14000000
4 kN/sec 5 kN/sec 6 kN/sec
culmulative energy
12000000 10000000
(c)
8000000 6000000 4000000 2000000 0 0
1
2
3
4
5
6
7
8
loading phase
mean amplitude (dB)
51
(d)
50 49
4 kN/sec 5 kN/sec 6 kN/sec
48 47 0
1
2
3
4
5
6
7
8
loading phase Fig. 9. (a) Variation of energy per hit (b) mean b-value (c) cumulative energy (d) mean amplitude with loading phase.
since both low amplitude (energy) and high amplitude (energy) as well as number (small or large) of AE are considered for the evaluation of damage or to study the fracture process. 3.3. Trends of b-value with the appearance of cracks In case of specimen tested with loading rate 4 kN/s [LC2M37] no cracks appeared till 200 kN. During loading phase-III, tensile cracks at 290 kN in moment zone appeared and the maximum AE b-value [for channel 6] was 1.67 and minimum was 0.1. The cracks appeared in third loading phase grew from micro cracks to macro cracks at 450 kN. During loading phase-IV, the b-value maximum
was 1.56 and minimum was 0.04. In loading phase-V, multiple shear cracks near the supports are formed. These cracks are symmetric at left and right supports. The b-value maximum was 1.56 and minimum was 0.29. During loading phase-VI, at 550 kN, tensile cracks near the moment zone reached the RC beam flange. At 662 kN, shear cracks opened further. The b-value maximum was 1.67 and minimum was 0.004. During loading phase-VII, the tensile cracks opened up to 1 mm and the cracks appeared in flange at 715 kN. The cracks branched at 780 kN and several tensile cracks developed also concrete spalling was observed at the right side support. The beam was bent at 800 kN and it was collapsed at 810 kN. The b-value maximum was 1.86 and minimum was 0.0051.
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Fig. 10. Variation of average frequency with load (LLR3 specimen).
Fig. 11. Variation of b-value with RA (LLR3 specimen).
Because of increase in rate of loading to 5 kN/s, tensile crack appeared at 187 kN in moment zone in LLR3 specimen. However, no crack appeared in loading phase-I. The b-value [for channel 6] maximum was 1.78 and minimum was 0.21 in loading phase-II. The propagation of tensile crack was observed in third loading phase at 247 kN. Also the diagonal cracks appeared in shear zone at 288 kN. Hair line tensile cracks were observed near moment zone at 288 kN. The b-value maximum was 1.71 and minimum was 0.01 in loading phase-III. The crack propagation was observed during loading phase-IV at 267 kN. The diagonal cracks in shear zone starts propagated at 382 kN and multiple cracks were observed in that zone in phase-IV. The crack opening was seen in moment zone at 539 kN. The b-value maximum was 1.71 and minimum was 0.01 in loading phase-III. The cracks propagated till to flange at 512 kN. At 600 kN of loading phase-V, the cracks were vigorous and opened further to l mm width. The beam failed at 752 kN. The maximum b-value was 1.65 and minimum was 0.001. In case of LLR1 specimen tested at 6 kN/s loading rate, first tensile crack appeared at 124 kN in loading phase-I. At 176 kN, the multiple tensile cracks appeared in moment zone of the beam during loading phase-II. The maximum b-value [ for channel 2] was 1.66 and minimum was 0.29. When compared with the previous RC beam specimens tested (at 4 kN/s and 5 kN/s), cracks appeared
quickly in first loading phase. However there are no new cracks appeared during loading phase-II. At 284 kN, growth of the tensile crack were seen. The diagonal cracks appeared simultaneously on shear span at 284 kN. Multiple cracks appeared in midspan of beam at 300 kN. The maximum b-value was 1.56 and minimum was 0.03. During loading phase-IV, at 418 kN shear cracks were observed significantly. The maximum b-value was 1.53 and minimum was 0.001. At fifth loading phase, propagation of tensile cracks were observed at 360 kN. During loading, at 532 kN, diagonal crack which appeared at phase-III widened and were clearly visible. The hair line cracks widened at 532 kN. The maximum bvalue was 1.55 and minimum was 0.50. cracks propagated to flange at 615 kN. As the load increased further, the cracks were opened up. The RC beam failed around 800 kN. The maximum bvalue was 1.75 and minimum was 0.05. 3.4. Fluctuations of average frequency (AF) and rise angle (RA) The tensile mode of cracking which includes opposing movement of the crack sides, results in AE waveforms with short rise time (RT) and high frequency. On the contrary shear type of cracks result in longer AE waveforms, with low frequency and longer rise time. AF value for each load cycle decreases gradually as the
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Fig. 12. Schematic diagram of the development of cracks in RC beam specimens (crack number and the load are indicated in parenthesis).
loading progresses as shown in Fig. 10. When the AF of a signal is higher the crack can be classified as of tensile mode. The gradual decrease in AF shows the formation of the shear cracks at the final stage of the loading. Fig. 11 shows the fluctuations of RA (rise time/amplitude) that could be temporary shift between small and large scale events and coincide with the drops of b-value. Rise time is observed to increase for the last loading cycles compared to the initial ones. This could be due to the formation of shear cracks. Shear cracks is relatively brittle in nature. Therefore fracture takes place suddenly and the rise time is relatively small. During the initial
loading cycles the AE hits were of shorter rise time compared to the final loading cycles which had AE hits with longer rise time. Hence for the final cycles shear cracks are observed as the rise time is longer. From Fig. 11, one can observe that a sudden bvalue drops when there is a rise in RA value. This could be due to formation of new crack or propagation of existing crack. Fig. 12 shows the schematic diagram of cracks developed in the test specimen. From Fig. 12, one can observe that first cracks appeared in the midspan of the specimen and later cracks appeared near to supports. RT is high when shear cracks are formed and b-value decreases.
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4. Practical significance The practical importance of this work is AE based b-value analysis is useful to assess the level of damage in a RC structure in situ. It may be possible to correlate the computed b-value with the physical measurements such as strain in tensile reinforcement and midspan displacement. By using the allowable limits given by codes of practice, one can compare the present b-value and assess the state of damage as minor, intermediate, heavy. 5. Conclusions Based on the above results the given below major conclusions are drawn 1. It was observed that when the loading rate is faster, then the quick cracking development lead to quick fluctuations and drops in the b-value. 2. Since the material behaves relatively more brittle at higher loading rates (or in higher strain rates), the b-values are lower in average as a few and strong cracking AE events are created, in contrast to more and weaker for low rate of loading (or low strain rate). 3. b-Value analysis is useful in evaluating the damage level in RC structures in-situ, the instance of damage initiation can be predicted by the lowest b-value. And also when the rate of loading is high, the b-value is minimum. b-Value analysis may be useful to estimate the present operating load conditions. 4. A sudden drop in b-value occurred when there is a rise in RA value. This could be due to formation of new crack or propagation of existing crack.
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