Crack detection using embedded cement-based piezoelectric sensor

Fracture Mechanics of Concrete and Concrete Structures Assessment, Durability, Monitoring and Retrofitting of Concrete Structures- B. H. Oh, et al. (eds) ⓒ 2010 Korea Concrete Institute, Seoul, ISBN 978-89-5708-181-5

Crack detection using embedded cement-based piezoelectric sensor Y. Lu & Z. Li

Department of Civil and Environmental Engineering, Hong Kong University of Science & Technology, China

ABSTRACT: In this paper, the new methodology to detect the crack propagation in concrete will be presented. The methodology will employ newly developed cement-based piezoelectric sensors that can be embedded into a concrete structure. The new sensors have the advantages of good compatibility with concrete, broad flat response spectrum, and good durability. By employing cement-based piezoelectric sensors, different mode of fractures have been studied, including tension, shear and mixed mode. The experiments results show that such new sensors can detect the formation of micro-crack, propagation of micro or macro crack, and different mode of failure. 1 INTRODUCTION Early researches on the AE analysis mainly rely on the traditional parameter (accumulated events numbers, event rate etc.) elevation. These parameters variation and trend have long been used to predict the onset of damage or sever failure (Reymond 1983, Hamstad 1986, Li & Shah 1994). And the AE source locations have also been estimated on 2-D planar graph by using derived partial differential equations (Li & Shah 1994). Moreover, the recorded AE waveforms have been further used to interpret the mode of micro-fracture by a seismic moment tensor (Li 1996). With the development of modern signal processing technique, AE measurement and evaluation researches have focused on manipulating the advanced technique, such as the frequency domain analysis and wavelet analysis, for fracture mode classification of AE signals from composites materials (Yoon et al. 2000). In this paper, cement-based piezoelectric composites sensors with improved sensitivity and better frequency domain performance were used to detect the damage process of two kinds of static loading conditions. The objective of this research is to verify the feasibility of damage monitoring for concrete by using the brand new piezoelectric sensors array and the signal-based monitoring technique. 3-D localization of AE sources was introduced based on the embedded cement-based piezo sensors array. Further more, the defined signal-based fracture energy index, together with various frequency components of the detected AE signals were figured out to investigate the variation of crack condition throughout concrete fracture process.

2 CEMENT-BASED PIEZOELECTRIC COMPOSITE SENSORS ARRAY The compatibility of the piezoelectric material and matrix material is a critical issue in health monitoring since that it greatly affects the performance of the piezoelectric material in its ability of detection and actuation of acoustic waves. If the compatibility can not meet the request, the detecting sensitivity and SNR (signal to noisy ratio) will be unsatisfactory. In civil engineering, concrete is dominant construction material. However, there exists relatively large difference on stiffness, linear elastic modulus and the acoustic impedance between concrete and metal. The traditional sensors which are especially designed for metal materials may not be suitable for concrete material for achieving optimal performance. In order to ensure perfect compatibility between passive detecting utility and matrix material, three aspects of issues should be paid attention to, including good coupling, matching of the acoustic impedance and consistency. In 2002 Li et al. found that it is possible to overcome these problems using a brand new cement-based piezoelectric composite which has the acoustic impedance value close to that of the concrete matrix by adjusting the mix proportion of ceramic material and portland cement particles. This composite improved the damping characteristic of the sensing element when embedded into the concrete (the acoustic impedance of the cement-based piezo composite is approximately 10) resulting in flat and broad frequency domain response, and the sensitivity enhanced accordingly. Nowadays, cement-based piezo composites with six kinds of connectivity patterns have been developed. In this experiment, cement-based piezoelectric composites of 0-3 connectivity

J = −could D (h, T )∇beh calculated using the The 3-D locations time differences of the first arrival (TDOA) from different monitoringThe channels of an acquisition sys- D(h,T) proportionality coefficient tem. It had been theoretically proved that in order moisture permeability and it is a tononlinea ensure iteration converges on the source hlocation of of the relative humidity and temperature AE, the least required number of channels shall be & Najjar 1972). The moisture mass balanc guaranteed (two that channels for linear localization, the variation in time of the water mas three for planar localization and four for volume of concrete (watervolumetric content w) be eq localization). Additionally, arrival time divergenceaccurate of the moisture flux Jdetermination method must also be available. In our experiments, a 128-point band-pass FIR filter (20 − ∂ =hamming ∇•J KHZ~300 KHz) with windows was used ∂ to smooth the original signal waveform detected by the sensors array in The orderwater to efficiently theexpressed arcontent wmake can be a rival point sharperofand easily be identified. the evaporable water we (capillary wa vapor, and adsorbed water) and the non-e (chemically bound) water wn (Mil 3 HOME-PROGRAMMED HEALTH PantazopouloDECLIN & Mills 1995). It is reas MONITORING SYSTEM assume that the evaporable water is a fu relative humidity, h, degree of hydration The elementary function the reaction, DEcLIN αsys, i.e. w =w degree ofblock silicaoffume tem is illustrated =in Figure 4. The system consistss of e age-dependent sorption/desorption 0-3 cement-based(Norling piezoelectric presented Mjonellsensors 1997). Under this assum previously, voltage pre-amplifier, 8-channel data acby substituting Equation 1 into Equati quisition hardwareobtains and corresponding software. w t

Figure 1. The 0-3 cement-based piezoelectric composite sensor.

−

Figure 2. The time domain (top) & frequency domain (bottom) response of the cement-based piezo sensor subjected to Hsu pencil lead break (shadow area indicate the flat frequency response range).

patterns were employed as the constituent materials of the piezoelectric sensor (see Fig 1.) The piezo sensors own a broad and flat frequency domain response which covers the frequency region of AE from concrete cracks. The sensitivity calibration results are shown in Figure 2. In each test, totally eight piezoelectric sensors were embedded at the corners of the concrete specimen (see Fig. 3) to constitute the detecting array for health monitoring of concrete specimens during loading. During the tests, at least 5 sensors (or 4 un-coplanar sensors) were required to identify and record the AE effectively in order to localize the AE sources correctly and satisfactorily. A C++ program was coded to carry the job.

∂w ∂h e + ∇ • ( D ∇h) = ∂we h ∂α ∂h ∂t

∂w α&c + e α&s + w ∂α c s

the slope where ∂w e/∂h is system. Figure 4. The block diagram of DEcLIN

of the sorption/ isotherm (also called moisture capac (Equation must be The maximumgoverning sampling equation rate of the designed3)acby appropriate boundary and initial quisition system is 10MHz which is capable of per- conditi the amount fectly reconstructingThe therelation signals between within 2MHz fre- of e water and relative humidity is ‘‘ quency region with negligible distortion, and it called is isotherm” if measured with increasing changeable depending on the monitoring duration humidity and ‘‘desorption isotherm” and information precision required. The software is in th case. Neglecting difference (Xi et al. divided into two components: signaltheir acquisition softthe following, ‘‘sorption isotherm” ware and post-analysis software (Fig. 5.) in order towill be to both sorption and desorption c efficiently preventreference the two individual processes from By the way, if the hysteresis of the interfering with each other and occupying excessive isotherm be taken into account, two RAM storage space. Andwould advanced signal-based relation, evaporable water vs relative humi health monitoring analysis, together with traditional be used according to the sign of be the varia parameter-based health monitoring analysis, can relativity humidity. The shape realized based on this data transmission and process- of the ing framework. isotherm for HPC is influenced by many p especially those that influence extent and chemical reactions and, in turn, determ structure and pore size distribution (water4 EXPERIMENTAL SETUP ratio, cement chemical composition, SF curing time and method, temperature, mix 4.1 etc.). In the literature various formulatio The objective of Splitting was tothe induce a tensile found totest describe sorption isotherm crack dominant failure mode on concrete material concrete (Xi et al. 1994). However, in th specimen. The detected AE signals were usedexpression to ex- pro paper the semi-empirical tract the signal-based information on the fracture process Norling Mjornell (1997) is adopted b Splitting test

Figure 3. The detecting array arrangement inside of the test specimen (left: splitting, right: direct-shear test).

Proceedings of FraMCoS-7, May 23-28, 2010

J

= − D ( h , T ) ∇h

(1)

The proportionality coefficient D(h,T) is called moisture permeability and it is a nonlinear function of the relative humidity h and temperature T (Bažant & Najjar 1972). The moisture mass balance requires that the variation in time of the water mass per unit volume of concrete (water content w) be equal to the divergence of the moisture flux J − ∂ = ∇•J ∂ w t

(2)

∂w trend of tensile w ∂hand analyze the∂wevariation of ∂test e & + w& & α ) = + ∇ • (D ∇hsources. − e induced crack AE The and (3) c + testαprocedure s n h ∂α ∂α ∂h ∂t c s to ASTM C496apparatus were designed conforming 96, while the dimension of concrete specimen is a of the where ∂we/∂h is the slopecube 300mm*300mm*300mm (seesorption/desorption Fig. 3) which is isotherm (also calledto moisture capacity). The convenient for sensors be embedded in the corgoverning equation (Equation must be completed ners forming a detection array.3)The mixture proporby appropriate boundary the and specimens initial conditions. tions used in preparing (Splitting & The relation the amount of evaporable Direct-shear) are between listed in Table 1. water and relative humidity is called ‘‘adsorption Table 1. Theifmixture proportion concrete specimen in isotherm” measured withof the increasing relativity the experiments. humidity and ‘‘desorption isotherm” in the opposite case. Neglecting (Xi Material cementtheir difference water sandet al. 1994), SP in theMortar following, 1‘‘sorption0.5 isotherm” 1.8 will be used 0.2%with reference to both sorption and desorption conditions. ByTwo theLVDTs way, of if 10mm the hysteresis of were the moisture working range mounted isotherm would be taken into account, two different on the front and back side of the concrete cube in relation, evaporable vs relativetohumidity, horizontal directionwater respectively measure must the be used according to the sign of the variation the horizontal displacement due to expanding in theofcenrelativity humidity. The shape of the sorption ter. The displacement values form LVDTs were also isotherm forcontrol HPC isthe influenced by many parameters, fed back to loading rate for guaranteeing especially those that influence extent and rate of the a stable loading process. chemical reactions and, in turn, determine pore structure and pore size distribution (water-to-cement 4.2 ratio, cement chemical composition, SF content, curing time andofmethod, temperature, The objective Direct-shear test wasmix to additives, induce a etc.). In the literature various formulations be shear crack dominant failure mode on concretecan specifound to describe the sorption isotherm of normal men. Similarly, the detected AE signals were used to concretethe(Xisignal-based et al. 1994). However,and in the present extract information summarize paper the semi-empirical expression proposed by the variation trend of shear crack-induced AE sources. Norling Mjornell (1997) is adopted because ASTM standard D5607-02 (Standard Test Methodit Proceedings of FraMCoS-7, May 23-28, 2010

1

,

,

,

1

1

10

10

,

The water content w can be expressed as the sum of the evaporable water we (capillary water, water vapor, and adsorbed water) and the non-evaporable (chemically bound) water wn (Mills 1966, Pantazopoulo & Mills 1995). It is reasonable to assume that the evaporable water is a function of relative humidity, h, degree of hydration, αc, and degree of silica fume reaction, αs, i.e. we=we(h,αc,αs) = age-dependent sorption/desorption isotherm (Norling Mjonell 1997). Under this assumption and by substituting Equation 1 post-analysis into Equation 2 DEone Figure 5. The acquisition (top) and (bottom) obtains clin software.

Direct-shear Test

explicitly accounts for the evolution of hydration for Performing Laboratory Direct Shear Strength reaction and SFSpecimens content. under This sorption Tests of Rock Constant isotherm Normal reads was introduced as reference for apparatus and Force) test procedure design. The dimension of concrete specimen is a 250mm⎡ long, 200mm wide and ⎤ 200mm high cuboid. A ⎢ 40mm depth and⎥ 2.5mm (α α ) − we (h αnotches + ⎥top and c α s ) = Gwere c pre-casted s⎢ width into both the ∞ (g α ⎢ c − α c )hof⎥⎦ 50mm bottom faces of the cuboid e a distance ⎣ with (4) to the face C (see Fig. 3.). The cement-based piezo∞ − αa little ⎡ ⎤ )h (g α is electric sensorsKarray arrangement different c c ⎢ (α α ) e − ⎥ of into that of Splitting c tests ⎢due to the presence ⎥ duced notches and large⎣ compressive stress⎦ on the face A. The sensors supposed to be at the corners wherebelow the first (gelembedded isotherm)with represents the right face term A were a distance physically waterreason. and the second of 40mm forbound safety(adsorbed) and reliability LVDTs of term (capillary isotherm) represents capillary 25mm working range were installed on the top of the water. This expression is valid for low content concrete cuboid to measure theonly vertical downward the amount of of SF. The coefficient displacement relative to Gthe1 represents stationary reference plate water per unitmachine. volume held in the gel pores at 100% of the loading relative humidity, and it can be expressed (Norling Mjornell 1997) as 5 DAMAGE PROCESS MONITORING cAND ANALYSIS s (α α ) = k α c + k α s G RESULTS (5) c s vg c vg s 5.1 s wheretokcthe vg and k vg are material parameters. From the Prior applied reached around maximum amount ofload waterlevel per unit volume that82% can of ultimate load capacity, the concrete specimen fill all pores (both capillary pores and gel pores), one stayed in the pre-burst is the time peas one region obtainsofwhich can calculate riod with theK1characteristic limited number of AEN (accumulated event number) recorded⎞ and a ⎤ ⎡ ⎛ ∞ − α ⎟h ⎥ ⎜ g αaccompanied stable but low-level of ER (event rate) ⎢ c⎠ ⎥ w − withα cthe s + following α s − G ⎢ − fracture e ⎝ c processes. by compared s ⎥ ⎢ (6) This was defined ⎣as the criteria of⎦ recK (α c characteristic α )= s ⎛ ⎞ ∞ ognizing the pre-burst region (Lu & Li 2008). In our ⎜ g α − α ⎟h c c ⎠was − further divided e ⎝ region experiment, this pre-burst into two subsets marked A c& B accordingly with s and k and g can The material parameters k 24% of ultimate load as the division boundary. vg vg 1 Afbe calibrated by fitting experimental data relevant to terwards, once the load level was over 82% of ultifree load, (evaporable) water emerged content suddenly in concrete mate a major crack and theat various ages Luzioapart & Cusatis 2009b).crack in the specimen was(Dispitted by a brittle middle plane. The corresponding time period was called the burst region featured the significant rise of 2.2 Temperature AEN (see Fig. 6.)evolution recorded with a sharp rise slope Notea that, at early sinceonthethechemical reactions and narrow pulse age, recorded ER diagram (see associated with cement hydration and SF reaction Fig. 7). We also further divided the burst region into reare exothermic, thedetailed temperature is not uniform gimes C, D & E for analysisfield of fracture process. forInnon-adiabatic even if the environmental regime A, thesystems concrete materials deformed estemperature is elastically, constant. Heat canfew be sentially linear with conduction extraordinary described in concrete, at least for temperature not AE being recorded by the DEcLIN health monitorexceeding (Bažant & Kaplangraph 1996), by ing system. 100°C From the 3-D localization of reFourier’s reads8, it can be found that the gime A Blaw, & Ewhich in Figure AE sources dispersedly scattered close to the middle q = − λwhere ∇T the high tensile stress concentrated. The plane (7) AE sources in this regime ought to be micro-cracks primarily fromflux, the casting free where q stemming is the heat T is defects, the absolute water evaporation voids and other pre-existing C-S-H temperature, and λ is the heat conductivity; in this weak links in the hydrated concrete materials. In regime 1

1

1

1

,

1

Splitting test

10

0

0.188

0.22

1

1

,

1

10

1

1

1

J

= − D ( h , T ) ∇h

The proportionality coefficient D(h,T) moisture permeability and it is a nonlinea of the relative humidity h and temperature & Najjar 1972). The moisture mass balanc that the variation in time of the water mas volume of concrete (water content w) be eq divergence of the moisture flux J Figure 6. The AEN diagram of Splitting Test (red broken line as the regime boundary).

Figure 7. The ER diagram of Splitting Test (red broken line as the regime boundary).

B, the AEN began to increase a little bit, but was still in the low level. The AE sources tended to start to be close together towards the center of the specimen, which is called the micro-crack localization in literature. And it was often observed when a major crack was likely to occur (Li & Shah 1994) as the applied load level was close enough to the ultimate load. After the load level was over 80%of ultimate load, both AEN value and ER value grew up abruptly. From regime D, we observed that most of the AE sources concentrated at the center of the specimens showing that a brittle major crack appeared and propagated quickly at the center with a large number of AE sources recorded simultaneously. The 3-D localization diagram of regime E is shown as a representative. It is found that the splitting fracture process of concrete materials is a brittle process with a major crack propagating from inside towards outside very rapidly. Meanwhile it is clearly observed that the brittle process has a very obvious and rapid micro-crack localization behavior from 3D localization of AE. 5.2 The fracture process of the Direct-Shear test was found out to be in an even more brittle way than that of Splitting test. Prior to the load level reaching approximately 96% of ultimate load capacity, AE signals Were seldom detected based on the results of AEN Direct-shear Test

− ∂ = ∇•J ∂ w t

The water content w can be expressed a of the evaporable water we (capillary wa vapor, and adsorbed water) and the non-e (chemically bound) water wn (Mil Pantazopoulo & Mills 1995). It is reas assume that the evaporable water is a fu relative humidity, h, degree of hydration degree of silica fume reaction, αs, i.e. we=w = age-dependent sorption/desorption (Norling Mjonell 1997). Under this assum by substituting Equation 1 into Equati obtains −

∂w ∂h e + ∇ • ( D ∇h) = ∂we h ∂α ∂h ∂t

∂w α&c + e α&s + w ∂α c s

where ∂we/∂h is the slope of the sorption/ isotherm (also called moisture capac governing equation (Equation 3) must be by appropriate boundary and initial conditi The relation between the amount of e water and relative humidity is called ‘‘ isotherm” if measured with increasing humidity and ‘‘desorption isotherm” in th case. Neglecting their difference (Xi et al. the following, ‘‘sorption isotherm” will be reference of to Splitting both sorption desorption c Figure 8. The 3-D localization Test in and respective regime (with projections plane). By onthethe XY way,planeif and theXZhysteresis of the isotherm would be taken into account, two (see Fig. 9) and ER (see Fig. 10). It water was called the humi relation, evaporable vs relative pre-burst region similar that of Splitting test.ofAnd be usedtoaccording to the sign the varia it was subdividedrelativity into two humidity. subsets marked & B of the The A shape accordingly with isotherm 76% of for ultimate as the diviHPC isload influenced by many p sion boundary soespecially as to studythose the that fracture processextent in and influence detail. At the moment the load level was 96% determ chemical reactions and, over in turn, of ultimate load, structure an explicitand curved cracking accom- (waterpore size distribution panied by several tinycement crackingchemical appearedcomposition, rapidly ratio, SF from the tip of the top notch towards the bottom mix curing time and method, temperature, face. We classify etc.). it as the region because the In burst the literature variousof formulatio significant increasing AEN andtheERsorption as defined foundoftothedescribe isotherm previously, and we subdivided this burst region into concrete (Xi et al. 1994). However, in th regimes C, D & paper E. Additionally, we define expression a post- pro the semi-empirical burst region afterNorling the burstMjornell region and(1997) markedis itadopted reb Proceedings of FraMCoS-7, May 23-28, 2010

J = −D , T )∇ h region, we could observe that both gime F.(hIn this (1) AEN and ER had a trend of slowing down indicating thatThe the proportionality AE activities were not activeD(h,T) any more. The coefficient is called concrete specimen was considered failed at this momoisture permeability and it is a nonlinear function ment. of the relative humidity h and temperature T (Bažant & Najjar 1972). The moisture mass balance requires that the variation in time of the water mass per unit volume of concrete (water content w) be equal to the divergence of the moisture flux J

we (h α c α s ) = ,

,

⎡ G1 (α c , α s )⎢⎢1 − ⎢ ⎣

1

10

10

(2)

w t

The water content w can be expressed as the sum of the evaporable water we (capillary water, water vapor, and adsorbed water) and the non-evaporable (chemically bound) water wn (Mills 1966, Pantazopoulo & Mills 1995). It is reasonable to assume9. The thatAEN the diagram evaporable water is Test a function of Figure of Direct-shear (red broken relative humidity, h, degree of hydration, αc, and line as the regime boundary). degree of silica fume reaction, αs, i.e. we=we(h,αc,αs) = age-dependent sorption/desorption isotherm (Norling Mjonell 1997). Under this assumption and by substituting Equation 1 into Equation 2 one obtains ∂w ∂h e + ∇ • ( D ∇h) = ∂we h ∂α ∂h ∂t

∂w α&c + e α&s + w&n ∂α c s

(3)

where ∂we/∂h is the slope of the sorption/desorption isotherm (also called moisture capacity). The governing equation (Equation 3) must be completed by appropriate boundary and initial conditions. The relation between the amount of evaporable Figure ER diagram of Direct-shear (red broken water 10. andTherelative humidity is calledTest‘‘adsorption line as the regime boundary). isotherm” if measured with increasing relativity humidity and ‘‘desorption isotherm” in the opposite In regime A, the concrete materials case. Neglecting their difference (Xi etdeformed al. 1994),esin sentially linear‘‘sorption elastically, and thewill AEbesignals rethe following, isotherm” used with ceived were negligible. the 3-D localization reference to both sorptionFrom and desorption conditions. graph of the corresponding regime it could By the way, if the hysteresis inofFigthe11,moisture be found that the AE sources scattered mainly in the isotherm would be taken into account, two different top and bottom region closevstorelative the notch area due to relation, evaporable water humidity, must the local stress concentration induced at tip of the be used according to the sign of the variation of the notch. In regime the AEN to increase relativity humidity.B, The shapebegan of the sorption slowly. And more micro-crack began to appear isotherm for HPC is influenced by many parameters, mainly at the upper of theextent specimen. In regime especially those thatbody influence and rate of the D, the micro-crack localization phenomena became chemical reactions and, in turn, determine pore very obvious and started to move (water-to-cement downwards in a structure and pore size distribution curved trail. Thechemical 3-D localization trail is SF found to be ratio, cement composition, content, consistent eye observation surface curing timewith and the method, temperature, ofmixtheadditives, cracking. It turns out to be a very rapid crack propaetc.). In the literature various formulations can be gation process given that the time period of the two found to describe the sorption isotherm of normal regimes veryet short. In regime E & F,inthe concreteis(Xi al. 1994). However, thelocalizapresent tion disappeared and the proposed AE sources paperphenomena the semi-empirical expression by were foundMjornell out back to scatterisaround the entire curvedit Norling (1997) adopted because seems that after a major crack was formed, the applied Proceedings of FraMCoS-7, May 23-28, 2010

⎤ ⎥ − α c )h ⎥⎥ ⎦

∞ (g α c e ∞ − α )h ⎡ (g α c c − ⎢ K (α c α s ) e ⎢ ,

− ∂ = ∇•J ∂

−

explicitly accounts for the evolution of hydration reaction and SF content. This sorption isotherm reads

1

1

1

⎣

+

(4)

⎤ 1⎥ ⎥ ⎦

where the first term (gel isotherm) represents the physically bound (adsorbed) water and the second term (capillary isotherm) represents the capillary water. This expression is valid only for low content of SF. The coefficient G1 represents the amount of water per unit volume held in the gel pores at 100% relative humidity, and it can be expressed (Norling Mjornell 1997) as c α c+ ks α s G (α c α s ) = k vg c vg s

(5)

,

1

where kcvg and ksvg are material parameters. From the maximum amount of water per unit volume that can fill all pores (both capillary pores and gel pores), one can calculate K1 as one obtains w

0

K (α c α s ) = ,

1

⎡ ⎢ − ⎢1 − 1 ⎢ ⎣

α s + 0.22α s G

− 0.188

c

s

⎛ 10⎜ ⎝

e

⎛

10⎜

e

g αc − αc h − ∞

1

⎞ ⎟ ⎠

⎝

g α c∞ − α c ⎞⎟h ⎤⎥ 1

⎠

⎥ ⎥ ⎦

(6)

1

The material parameters kcvg and ksvg and g1 can be calibrated by fitting experimental data relevant to free (evaporable) water content in concrete at various ages (Di Luzio & Cusatis 2009b). 2.2 Temperature evolution Note that, at early age, since the chemical reactions associated with cement hydration and SF reaction are exothermic, the temperature field is not uniform for non-adiabatic systems even if the environmental temperature is constant. Heat conduction can be described in concrete, at least for temperature not exceeding 100°C (Bažant & Kaplan 1996), by Fourier’s law, which reads q

= − λ ∇T

where

q

(7) is the heat flux, T is the absolute

Figure 11. The 3-D Direct-shear Test in in respectemperature, andlocalization λ is the of heat conductivity; this tive regime (with projections on the XZ plane).

force was redistributed inside the concrete because of the emergence of a large crack mouth opening. And the friction of the crack surface began to become an important source of AE as shown in the 3D diagram of regime F.

J

The proportionality coefficient D(h,T) moisture permeability and it is a nonlinea of the relative humidity h and temperature & Najjar 1972). The moisture mass balanc that the variation in time of the water mas volume of concrete (water content w) be eq divergence of the moisture flux J

6 SIGNAL-BASED FRACTURE ENERGY INDEX & FREQUENCY DOMAIN COMPONENTS EVOLUTION Since AE signal is usually considered as a function of varying amplitude through time, it seems reasonable that to use the area under the enveloping curve as a good approximate measurement of the energy of an AE signal. The total energy of a signal, , is thus defined as the sum of squared module: f(x)

− ∂ = ∇•J ∂ w t

εf

=

∑ x =0

Test.

2

(1)

f ( x)

x refers to the discrete time point of the detected signal. N represents the total number of the discrete time points.

In digital signal processing, physical unit of the signal energy is routinely discarded, and the signals are renormalized whenever convenient. Therefore, the defined signal-based fracture energy index of an AE signal is introduced as the square root of its total signal energy: f(x)

∆

f ( x)

=

εf

=

∑

N −1 x =0

f ( x)

2

(2)

In experiments, AE signals were caught by the cement-based piezoelectric sensors array and calculated by the home-programmed DEcLIN system using formula (2) to evaluate the signal-based fracture energy index. The 8-channel sensors array was employed simultaneously to record the AE waveforms from 8 directions in order to minimize the probability of energy index error due to micro-cracks and singular points in the wave propagation paths. The signal-based fracture energy index evolution diagrams for Splitting test & Direct-shear test are illustrated in Figures 12,13. In Figure 12, it was found that the variation of signal-based fracture energy index during the Splitting test is quite similar to the variation of ER in Splitting. Before the applied load level approached 82% of the ultimate load, the fracture energy released was very limited and the variation was negligible. Once 82% overcame, the fracture energy released increased very quickly and reached the peak the same time as ER, indicating the AE activities were turning into the most active period, i.e. microcrack localization period. A major crack was formed, and the specimen failed consequently. The fracture

The water content w can be expressed a of the evaporable water we (capillary wa vapor, and adsorbed water) and the non-e (chemically bound) water wn (Mil Pantazopoulo & Mills 1995). It is reas assume that the evaporable water is a fu relative humidity, h, degree of hydration degree of silica fume reaction, αs, i.e. we=w = age-dependent sorption/desorption (Norling Mjonell 1997). Under this assum by substituting Equation 1 into Equati obtains

Figure 12. The signal-based fracture energy index of Splitting

f(x)

∆ N −1

= − D ( h , T ) ∇h

∂w ∂h e + ∇ • ( D ∇h) = ∂we α ∂we h index ∂α of cDirect∂α ∂h ∂tfracture energy signal-based −

Figure 13. The shear Test.

c

&+

s

α&s + w

is the consists slope ofaround the sorption/ where ∂we/∂hminute energy released inisotherm the failure (also called moisture capac 71% of the total governing energy released indicating that3)this equation (Equation must be damage process by wasappropriate definitelyboundary brittle. and Figure 13 conditi initial shows the variationThe of energy during Direct-shear relation between the before amount of e test. Similarly, the fracture energy released water and relative humidity called ‘‘ 96% of ultimate isotherm” load was relatively smallwith andishad if measured increasing little variation. However, after 96% of ultimate, the in th humidity and ‘‘desorption isotherm” energy released increased dramatically. The damage case. Neglecting their difference (Xi et al. process was turned out to be even more brittle than the following, ‘‘sorption isotherm” that of Splitting test. And the energy released indesorption thewill bec reference to both sorption and failure minute occupied more than 72% of the totalof the By the way, if the hysteresis energy released before failure. isotherm would be taken into account, two In Figures 12,13 the peak amplitude evolution of humi relation, evaporable water vs relative 40 KHz, 100KHZbe and 200 KHz components were used according to the sign of the varia also plotted to investigate thehumidity. variation The of individual relativity shape of the frequency components of AE signals detected during isotherm for HPC is influenced by many p fracture process. These single frequency components especially those that influence extent and were obtained bychemical filtering the detectedand, original sig- determ reactions in turn, nals using Butterworth 5-order band-pass filter with (waterstructure and100 pore sizeand distribution center frequency ratio, of 40 KHZ, KHz 200 KHz cement30KHz chemical composition, SF respectively and curing bandwidth (gain -3 dB, mix time and method, temperature, about 0.707 relative to In peak). From Figures 12,13formulatio it etc.). the literature various was seen that thefound variation of 40 KHz, KHz and to describe the100 sorption isotherm 200 KHz all bearing relatively the same trend with (Xi et index al. 1994). the evolution of concrete fracturetheenergy statedHowever, previ- inproth paper semi-empirical expression ously. However, by comparing the relative frequency Norling Mjornell (1997) is test, adopted b component magnitude variation ratio in each Proceedings of FraMCoS-7, May 23-28, 2010

J = 100 − D (hKHz , T )∇hcomponent seemed to contribute more the (1) to the variation of detected signal-based fracture energyTheindex regardless ofcoefficient static loading proportionality D(h,T)conditions. is called Clearly, the frequency components around KHz moisture permeability and it is a nonlinear100 function of acoustic signals detected be closely related the relative humidity h andmust temperature T (Bažant to the variation of micro-crack behaviors during & Najjar 1972). The moisture mass balance requires loading. Moreover, micro-crack condition that the variation in time of the water mass perunder unit static loading could (water be further investigated by studyvolume of concrete content w) be equal to the ing the relationship between divergence of the moisture fluxtheJ frequency domain components and the micro-crack mechanism. From the∂ wavelet analysis of AE signals of concrete (2) − = ∇it •was J observed that 100 KHz frequency comcracks, ∂ ponents were exactly within the transition boundary zoneTheofwater P-wave & S-wave components an AE. content w can be expressed of as the sum This transition boundary was found to be not fixed of the evaporable water we (capillary water, water but within region ofwater) 75 KHz~107 KHz (see Fig. vapor, and aadsorbed and the non-evaporable 14). Therefore,bound) when thewater 100 KHz be(Mills 1966, (chemically wn components came very active, it was believed that there existed Pantazopoulo & Mills 1995). It is reasonable to some in the micro-crack behavassumesignificant that the changes evaporable water is a function of iors of concrete at that time. relative humidity, h, degree of hydration, αc, and degree of silica fume reaction, αs, i.e. we=we(h,αc,αs) = age-dependent sorption/desorption isotherm (Norling Mjonell 1997). Under this assumption and by substituting Equation 1 into Equation 2 one obtains w t

−

∂w ∂h e + ∇ • ( D ∇h) = ∂we h ∂α ∂h ∂t

∂w α&c + e α&s + w&n ∂α c s

(3)

where ∂we/∂h is the slope of the sorption/desorption isotherm (also transform called ofmoisture capacity). The Figure 14. Wavelet a typical AE waveform from governing equation (Equation 3) must be completed Splitting test (the red arrow indicates the arrival of P-wave, and by blue appropriate boundary initial conditions. the indicates the arrival ofand S-wave). The relation between the amount of evaporable water and relative humidity is called ‘‘adsorption if measured with increasing relativity 7isotherm” CONCLUSION humidity and ‘‘desorption isotherm” in the opposite case. their difference et al. 1994), in In thisNeglecting paper, different modes of(Xi fractures of conthe following, ‘‘sorption will be used with crete have been studiedisotherm” using embedded cementreference to both sorption desorption conditions. based piezoelectric sensorsandarray. 3-D localization By the way, if the hysteresis of the moisture and signal-based fracture energy index evolution isotherm wouldtobeanalyze taken into different was employed the account, damage two process and relation, evaporable water vs relative humidity, must evaluate the condition of the specimen under static be used according to theconclusions sign of the could variation of the loading. The following be drawn relativity humidity. The shape of the sorption from the study. isotherm for HPC is influenced many parameters, (1) The new sensors have the by advantages of good especially those that of the compatibility withinfluence concrete,extent broadand flatrate response chemical reactions and,durability. in turn, And determine pore spectrum, and good it is capable structure and pore size distribution (water-to-cement of monitoring damage processes under static ratio,loadings. cement The chemical composition, SF concrete content, AE generated from the curing timecould and method, temperature, mixhigh additives, cracks be clearly detected with sensietc.).tivity In the literature various formulations can be and SNR. found to describe the sorption isotherm of normal concrete (Xi et al. 1994). However, in the present paper the semi-empirical expression proposed by Norling Mjornell (1997) is adopted because it Proceedings of FraMCoS-7, May 23-28, 2010

explicitly accounts for of estimated hydration (2) 3-D localization of the AE evolution sources was reaction and SF content. sorption isotherm and illustrated accordingThis to the corresponding readsdefined loading stage. Together with the results of AEN and ER, the fracture process under loading could clearly⎡ be recognized and⎤investi⎥ we (hgated. α s )⎢⎢ − + ⎥ introc α s ) = G (α c fracture (3) Aαsignal-based energy index was ∞ (g α − α c )h ⎥ ⎢ c the duced to quantitatively fracture ene ⎣ evaluate ⎦ (4) ergy released throughout the∞ fracture ⎤process. ⎡ (g α By using band pass filtering, that c it− αwas c )h −found ⎥ (α α )⎢e K each frequencyc component of AE signals cons⎢ ⎥ ⎦ tributed differently to⎣ the total energy index and varied with time. where the first term (gel isotherm) represents the physically bound (adsorbed) water and the second term (capillary isotherm) represents the capillary ACKNOWLEDGEMENT water. This expression is valid only for low content amount & of of SF.support The coefficient G1 represents The from China Ministry oftheScience water per unitunder volume held in the gel Technology 2009CB623200 andpores Hongat 100% Kong relative humidity, and it can expressed (Norling Research Grant Council underbe N_HKUST637/9 is Mjornell 1997) as greatly appreciated. 1

,

,

,

1

1

10

10

,

1

1

1

1

c

s

(5)

G (α c α s ) = k vg α c c + k vg α s s REFERENCE ,

1

Carpinteri et al.2007. Structural parameters. Damage Diagnosis ksvg are material From and the where kcvgA.and Life-time Assessment by Acoustic Emission Monitoring. maximum amount water per74,unit volume that can Engineering FractureofMechanics, pp273-289 fill all pores (both capillary pores and pores), one Eric N. L. & Lucie B.2002. Experiments togel Relate Acoustic as one obtains canEmission calculate K 1 Energy to Fracture Energy of Concrete. Journal of Engineering Mechanics, Vol.128, No.6, June 1 Faming L. & Zongjin L.2000. Acoustic Emission Monitoring ⎡ ⎛ ⎞ ⎤ − α ⎟h ⎥ α ∞Tension. ⎜ g in ⎢ of Fracture of Fiber-Reinforced Concrete ACI c c ⎝ ⎠ − α s + α s −G ⎢ −e ⎥ MaterialswJournal Vol.97, No.6 c s November-December ⎥ ⎢ (6) Jochen K (time α αH.) =K. et al.2005. Strategies for⎣ reliable automatic⎦ onset c spicking of acoustic⎛ emissions ⎞ and of ultrasound sig∞ ⎜ g α − α ⎟h nals in concrete. Ultrasonics c pp538-546 c⎠ − e ⎝ 43 Ohtsu M. et al.1991. Determination of Crack Locations, Type and Orientation in Concrete Structures bys Acoustic Emiscan The material kcvg and k43, vg and sion. Magazine parameters of Concrete Research, No.155,g1June, be pp127-134 calibrated by fitting experimental data relevant to Ohtsu M.1996. The History Development of Acoustic free (evaporable) waterandcontent in concrete at Emission in Concrete Engineering. Magazine various ages (Di Luzio & Cusatis 2009b). of Concrete Research, 48, No.17, Dec., pp321-330 Raghu P. & Vidya S.2008. Relationship between AE Energy Fracture Energy of Plain Concrete Beams: Experimen2.2andTemperature evolution tal Study. Journal of Materials in Civil Engineering, Vol.20, 1 age, since the chemical reactions Note that,March at early Youyuan L. & Zongjin L.2008. Cement-based piezoelectric associated with cement hydration and SF reaction for acoustic emission detection inisconcrete strucaresensor exothermic, the temperature field not uniform tures. Proceedings of the 11th International Conference on forEngineering, non-adiabatic systems even if the Science, Construction, andenvironmental Operations in temperature is constant. Heat conduction can be Challenging Environments described in concrete, least for temperature Zongjin L.1996. Micro-crackatCharacterization in Concrete not under Uniaxial100°C Tension.(Bažant Magazine&of Concrete exceeding Kaplan Research, 1996), 48, by No.176, Sep pp219-228 Fourier’s law, which reads Zongjin L. et al.2000. P-wave Arrival Determination and AE Characterization of Concrete. Journal of Engineering Meq =chanics, − λ∇T Vol.126, No.2, February (7) 10

0

0.188

0.22

1

1

1

,

1

10

1

1

where q is the heat flux, T is the absolute temperature, and λ is the heat conductivity; in this