CHAPTER 3: ELECTRICAL MEASUREMENTS IN CONCRETE MATERIALS

Transcription

1 26 CHAPTER 3: ELECTRICAL MEASUREMENTS IN CONCRETE MATERIALS This chaper provides a review of he hisory and applicaion of elecrical measuremens in concree. The definiion of elecrical conduciviy and he principles of direc (DC) and alernaing (AC) conduciviy measuremens are presened. The heoreical principles relaing he conduciviy of a porous media o is microsrucural properies and humidiy condiion is discussed. 3.. A Brief Inroducion o Elecrical Measuremens in Concree In concree maerials research, elecrical measuremens (EM) measure he opposiion of he maerial o flow of elecriciy. For example, one can apply a direc (DC) volage o he ends of a concree sample, and measure he sample s elecrical resisance. Mos early researchers, however, recognized ha DC measuremens may no be accurae due o polarizaion effecs. For example, Hammond and Robson (955) observed a change in he measured resisance when hey reversed he direcion of elecrical curren. For his reason, EM mehods which use alernaing curren (AC) have become more applicable. Hundreds of research sudies have used elecrical measuremens o invesigae differen phenomena in concree maerials. Chrisensen and coworkers (994) used EM o perform an in deph invesigaion on microsrucural changes in hydraing cemen concree. They observed an increase in he measured resisance wih age of he sample and concluded ha his increase is mainly aribued o he consumpion of he liquid phase of he marix and producion of large volumes of solid producs during hydraion process. They showed ha EM can provide valuable informaion abou concree s porous

2 27 microsrucure. Also measuremens can be relaed o facors such as waer permeabiliy and ionic diffusiviy of he marix. Elecrical measuremens have been used o monior moisure ranspor in concree. McCarer and coworkers observed a change in he resisance value when a we sample is oven-dried (McCarer and Garvin 989). Several researchers have sudied waer and ionic peneraion in concree s cover zone and used EM o develop and assess moisure profiles in drying concree (McCarer e al. 996, McCarer 996, McCarer and Wason 997, Weiss e al. 999, and Schieβl e al. 2000). EM has also been widely used o measure corrosion poenials in reinforced concree (examples include ASTM C876 and he sudy by Schieβl and Brei 995). Elecrical mehods provide several advanages for accurae in-siu esing of maerials. These mehods are non-invasive and non-desrucive and do no necessiae waer removal from samples prior o esing. Ye, here are also some disadvanages involved. I is sill unclear how o differeniae beween separae underlying facors responsible for elecrical conducion in concree: Facors such as differen ions dissolved in he pore soluion, heir concenraions, waer conen, and geomery of he microsrucure. Also a widely acceped sandard es procedure does no exis. Each person ends o develop his/her own esing proocols, and as a consequence, i is difficul o compare resuls or replicae ess from differen laboraories (McCarer, 2002) Resisiviy and Conduciviy Ohm s law in is simples form relaes a DC elecrical curren (I), passing hrough a conducive sample, o he volage applied o he sample s ends; V = RI. In his equaion R is elecrical resisance which is a funcion of a maerial propery (so called resisiviy), geomery, and dimensions of he sample. Figure 3. shows a cylindrical specimen under consan DC volage. Measuring resisance of he samples wih differen dimensions shows ha elecrical resisance is proporional o he sample s lengh (L) and inverse o he surface area (Equaion 3.):

3 28 L R = mρ (3.) A when ρ is he maerial s resisiviy and m is a geomeric facor which equals o one (m=) for a cylindrical sample wih disc shape elecrodes a he ends (Figure 3.). As a resul, resisiviy of he maerial can be deermined by measuring he sample s elecrical resisance and muliplying he measured value by a facor represening he dimensions and geomery of he es seup ( in Equaion 3.2): k A ρ = R or ρ = R (3.2) ml k geomery facor Conduciviy () is defined as he inverse of resisiviy (Equaion 3.3): = = ρ k R (3.3) Conduciviy (or resisiviy) is a geomery free parameer ha represens he opposiion of he maerial o flow of elecriciy. Conduciviy of concree, as will be discussed laer in his chaper, is a funcion of he microsrucure s geomery, moisure conen of he sample, and conduciviy of he pore soluion. A Fig. 3.. A cylindrical sample under consan DC volage can be used o see how dimension and geomery influence he measured elecrical resisance

4 The procedure of measuring he maerial s conduciviy is slighly differen when alernaing (AC) currens are used. The equivalen form of Ohm s law for AC currens is V = ZI, in which Z is elecrical impedance and is again a form of opposiion o flow of elecriciy. Elecrical impedance is a complex number composed of real and imaginary componens; Z = Z + jz. The real par of impedance ( Z ) is called resisance, while he imaginary par ( Z ) is called reacance. In AC measuremens, he sign and magniude volage is no consan. For example he volage can oscillae beween posiive and negaive peaks in a sinusoidal manner wih consan frequency. The real and imaginary componens of elecrical impedance are boh funcions of his frequency. In fac, resisance and reacance of a sample can be measured a differen frequencies and ploed agains each oher. Such a graph is called Nyquis plo (Figure 3.2a). Each poin in his graph corresponds o a disinc frequency. The impedance componens ( Z and Z ) can be combined o represen he oal (or absolue) impedance, Z, and he impedance argumen (or phase angle), θ : 29 Z 2 2 = ( Z ) + ( Z ) (3.4) o Z 80 φ = an (3.5) Z π The values of Z and θ for each poin can be ploed agains he volage s frequency o ge Bode plos (Figure 3.2b). A ypical Nyquis plo for concree is shown in Figure 3.3. This graph is composed of wo half arcs, a larger arc, which is ypically in he milliherz o kiloherz range and is aribued o he passive oxide film on he surface of seel elecrodes, and a smaller arc, ypically measured in he kiloherz o megaherz range and is aribued o he sample s bulk properies.

5 Z'' increase in frequency Z θ Z' (a) Z Frequency (Hz) hea Frequency (Hz) (b) Fig (a) Nyquis plo, and (b) Bode plos of elecrical impedance

6 3 Fig Typical Nyquis plo for hardened concree (Chrisensen e al. 994) One of he mos imporan parameers ha can be obained from he Nyquis plo is he bulk resisance ( R ) which is he resisance ( Z ) a he inersecion of he wo arcs. b A his poin he reacance ( Z ) of he sysem is heoreically zero. The frequency corresponds o his poin is called he cu-off frequency. The measured bulk resisance is convered o concree s conduciviy using Equaion 3.3. In he pas, single frequency AC measuremens were made a a frequency in he order of kiloherz o measure he bulk resisance. Chrisensen and coworkers (994) showed ha ha he cu-off frequency can vary over wo orders of magniude as a funcion of hydraion ime, cemen ype, and w/c raio. Weiss e al. (999) showed ha his frequency also varies as a funcion of he moisure conen of concree. As a resul, in order o accuraely measure he bulk resisance, i is necessary o measure impedance over a wide range of frequencies. Such a process is called impedance specroscopy (IS). Impedance specroscopy can be performed by employing a gain-phase analyzer and a personal compuer for daa acquisiion.

7 Conduciviy of Cemeniious Marices According o he Powers-Brownyard model (Taylor 990), cemen pase can be envisioned as parallel layers of differen componens (i.e., capillary porosiy, hydraion producs, unhydraed cemen, ec.) ha exend from one side of a sample o he oher (Figure 3.4). The conduciviy of a se of n parallel layers can be calculaed using he followings approach. The complee elecrical resisance of he se of n layers (R ) is relaed o he resisance of each ih layer (as represened by R i ): R = + + (3.6) R R n Rewriing his expression in erms of conduciviy (s i and A i are respecively conduciviy and cross secional area of he ih layer, and m is he geomery facor ha is he same for all layers) resuls in: R i i Ai = (3.7) ml A = + A + n An (3.8) Direcion of curren I 2... Surface area= A I n Lengh= L Fig Powers-Brownyard model of envisioning cemen pase as parallel layers

8 33 Muliplying boh sides by he lengh (L) gives: V = + V + nvn (3.9) when V i is he volume of layer i. When he volume fracion of layer i is defined as follows: V i φ i = (3.0) V Equaion 3.9 can be rewrien in erms of volume fracion of layers: = + φ + nφn (3.) If he layers were in series (Figure 3.5), Equaion 3. would ge he following form: = + + φ φ n (3.2) n Since in an acual concree sample, he consiuing componens form a complex sysem of serial and parallel layers, none of he Equaions 3. and 3.2 can be exclusively used. To consider his fac, Chrisensen (993) used a modified equaion in he following form: = + φβ + nφnβ n (3.3) Lengh= L Surface area= A I 2 n I Lengh= L Fig Envisioning cemen pase as serial layers

9 34 In Equaion 3.3 b is called he srucure or he conneciviy facor and represens he oruosiy (wisedness) of he layers. In a concree marix, conduciviy of he sauraed capillary porosiy is several degrees of magniude higher han he conduciviy of oher componens. As a resul, he oal conduciviy of he marix is pracically equal o he conduciviy of he sauraed capillary porosiy: oφcapβ (3.4) In his equaion s is he overall conduciviy of he marix, s o is he conduciviy of pore soluion, f cap is he volume fracion of capillary porosiy, and b is a conneciviy facor. Chrisensen (993) showed ha in a hydraing cemen microsrucure each of hese parameers (s o, f cap, and b) is changing wih ime and as a resul, an overall change can be observed in he sample s conduciviy (Figure 3.6 (a) and (b)) so (s/m) fcap s (s/m) Series2 s o (s/m) Series f cap Age (hr) Age (hr) (a) (b) Fig Variaions in (a) pore soluion conduciviy (s o ) and volume fracion of capillary porosiy (f cap ) and (b) he complee sample s conduciviy (s) as a funcion of age (Chrisensen 993)

10 35 While Chrisensen performed his ess on samples mainained a 00% relaive humidiy, McCarer and coworkers (995 and 996) sudied conduciviy variaions in samples experiencing drying and reweing. They used concree slabs ha were exposed o drying from one surface for a period of 6 weeks. Afer his period, he samples were ponded a he drying face wih waer or a 2 molar NaCl soluion. Conduciviy profiles of slabs were obained before ponding (s B ) and afer 24 hours of ponding wih waer (s W ) or NaCl soluion (s N ), (Figure 3.7). As i s shown in he figure a significan increase in conduciviy was observed afer reweing. The increase was more pronounced for NaCl ponded samples in comparison o waer ponded samples due o dissoluion of sodium and chloride ions in he pore soluion and increasing is conduciviy.. The research eam proposed o link he raio beween conduciviies before ponding and afer waer ponding (s B /s W ) o he degree of sauraion of concree before reweing via he following equaion: B W = (S ) r m (3.5-a) when m is independen from porosiy and moisure conen of he sample and is in he region of.5 o 3.0 for cemen pases and in he range of.2 o 2.5 for concrees and morars (McCarer e al. 995). The research eam also proposed o use he raio beween he conduciviy of he waer ponded sample o he conduciviy of he NaCl ponded sample (s W /s N ) o deermine he concenraion of NaCl dissolved in he pore soluion: W = ow (3.5-b) N on Using Equaion 3.5-b, assuming ha s ow is known; s on can be calculaed and be used o deermine he concenraion of chlorides in he pore soluion of he NaCl ponded sample.

11 Before ponding (B) Waer ponding (W) NaCl ponding (N) 60 s (s/km) Deph from ponding surface (mm) Fig The significan increase in he conduciviy of dried concree slabs due o reweing wih waer and NaCl soluion (McCarer e al. 995) The curren research inends o reframe and exend he previous findings in order o develop a mehod ha accuraely accouns for he humidiy of concree and o propose a procedure ha is able o deermine he inernal humidiy (or moisure conen) of concree based on he measured conduciviy. For his purpose he relaionships used by Chrisensen o relae conduciviy o microsrucural parameers were exended o also accoun for inernal humidiy of he microsrucure. The procedure is as follows. Equaion 3.4 is derived based on he assumpion ha all he capillary pores are sauraed wih pore soluion. In a real life scenario a porion of pores are empy of liquid phase due o drying or self desiccaion. In his case, only he porion of porosiy ha conains pore soluion is conducive. To reflec his fac, he erm f cap in Equaion 3.4 should be subsiued wih f cap-con which represens he volume fracion of capillary porosiy ha is capable of conducing elecrical curren: = φ β (3.6) o cap con

12 37 When he sysem experiences a change in he inernal moisure conen, each of he hree erms s o, f cap-con, and b varies. For example, when a sample loses moisure, he concenraion of ions in he pore soluion increases which in urn causes an increase in he value of s o. On he oher hand, he volume of he liquid phase and consequenly he volume of conducive porosiy decreases (i.e., decrease in f cap-con ). In addiion, conneciviy of pores changes which is refleced in a change in he value of b. Since simulaneous monioring each of hese parameers (s o, f cap-con, and b) as a funcion of he sample s inernal humidiy is difficul, in his sudy i is proposed ha he conduciviy changes caused by humidiy variaions are separaed from he hydraion effecs hrough implemening a humidiy facor (f H ) in Equaion 3.6. The procedure is o selec a reference poin a which he sample s humidiy is known and assign he humidiy facor of one o his reference poin (i.e., f H = a reference poin). Then, he sample s conduciviy a oher humidiies is: = ( φ β ) f (3.7) o cap con ref H when f H is a funcion of he difference beween he curren humidiy and he reference humidiy: f H = f H = H H ) (3.8) H ( ref cur As an example a maure concree can be considered in which changes in s o, f cap-con, and b due o hydraion is negligible. If one selecs he 90% relaive humidiy as he reference poin, conduciviy of he sample a 85%RH can be obained as follows: (3.9) RH = 85 % = ( oφcap conβ ) RH = 90% f H ( RH = + 5%) Figure 3.8 illusraes he idea. The humidiy facor for a given microsrucure can be obained by measuring conduciviy of he sysem a known humidiies and esablishing he humidiy facor funcion (Equaion 3.8). Then, when he inernal humidiy is unknown, measuring he microsrucure s conduciviy can be used along wih he obained humidiy facor funcion o back calculae he inernal humidiy (Equaions 3.7 and 3.8).

13 38 reference sae f H = less humidiy f H < more humidiy f H > Fig 3.8. The humidiy facor represens he inernal humidiy of he sysem This is a valid approach as long as he microsrucure is invarian wih ime. A cemeniious microsrucure experiences coninuous hydraional developmens and as a resul he porosiy and conneciviy of he pores are changing as a funcion of ime. Also, in a cemeniious sysem he hydraion rae and microsrucural developmen are relaed o he microsrucure s humidiy. However, for simplifying he process of calibraion, in his sudy, he wo following assumpions were made o enables applicaion of he aforemenioned approach o cemeniious microsrucures: - The microsrucural developmen is independen of he moisure hisory and is only a funcion of age. 2- The humidiy facor funcion for a given concree mixure is independen of he specimens age. This means ha one can obain he f H funcion a a cerain age and apply his funcion o he samples from he same mixure a differen ages. Using hese assumpions, he conduciviy of wo similar concree samples (from he same mixure) cured a differen relaive humidiies (for example one a 00%RH and he oher a 85%RH) a all ages can be relaed via he following expression: (3.20) RHcur = ( oφcap conβ ) RHref f H ( RH = RHref RHcur)

14 39 As a resul he funcion f H (DRH) can be obained using a se of calibraion specimens and be used o deermine he humidiy of similar concree samples. The comprehensive deails abou obaining and implemening he humidiy facor funcion are described in Chaper Summary This chaper provided a review of he hisory and applicaion of elecrical measuremens in concree. The definiion of elecrical conduciviy and he principles of direc (DC) and alernaing (AC) conduciviy measuremens were presened. Conduciviy of a cemeniious microsrucure is a funcion of he pore soluion conduciviy (s o ), he volume fracion of conducive porosiy (f cap-con ) and he conneciviy of he pores (b). These parameers vary wih he sample s age and inernal humidiy. I is proposed in his sudy o differeniae beween he changes caused by hydraion and he changes caused by variaions in inernal humidiy, hrough inroducing a humidiy facor o Equaion 3.6. This approach can be used o deermine he humidiy of a sample based on is measured conduciviy. The deails of implemening his approach are described in Chaper 5.