ARTICLE IN PRESS

NDT&E International 43 (2010) 55–61

Contents lists available at ScienceDirect

NDT&E International

0963-86

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/ndteint

NDT measurements for the prediction of 28-day compressive strength

Rui Miguel Ferreira �, Said Jalali

University of Minho, Department of Civil Engineering, Campus de Azurem, 4800-058 Guimar~aes, Portugal

a r t i c l e i n f o

Article history:

Received 10 April 2009

Received in revised form

9 September 2009

Accepted 14 September 2009Available online 25 September 2009

Keywords:

NDT

Electrical resistivity

Strength prediction

Quality control

Four-point electrode

95/$ - see front matter & 2009 Elsevier Ltd. A

016/j.ndteint.2009.09.003

esponding author. Tel.: +351253 510 200/494

ail address: rmf@civil.uminho.pt (R.M. Ferreir

a b s t r a c t

A procedure is proposed for the prediction of the compressive strength of concrete based on the use of

NDT measurements. Prior to formwork removal, electrical resistivity can be assessed and based on an

electrical resistivity versus compressive strength correlation curve, the strength of concrete can be

estimated. This procedure ensures, for example, that the formwork is only removed when the concrete

reaches a predefined compressive strength, dispensing with the calculation of concrete maturity. On the

other hand, the whole surface of the concrete structure can be systematically measured so as to

estimate 28-day compressive strengths and detect areas that could potentially not conform to the

specified requirements. In this manner, a realistic overview of the in situ compressive strength of the

whole structure can be obtained.

The procedure proposed predicts the 28-day strength of concrete based on two models. The first

model is based on an empirical equation used for the maturity assessment of concrete. The second

model is based on a theoretical equation for the nucleation process of cement hydration. The effect of

temperature and different curing conditions (concrete maturity) can be effectively taken into account

by the conversion of all electrical resistivity measurement to the same referential. The models are used

to estimate 28-day compressive strength based on the 7-day electrical resistivity measurements. The

results show that the errors in estimation of the 28-day compressive strength are less than 22% and 10%

for these models, respectively. If 28-day electrical resistivity measurements are used then the error in

estimation is lower, circa 9% and 5% for these models, respectively.

& 2009 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2. Research significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3. Using electrical resistivity measurements to predict compressive strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.1. The empirical approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.2. The theoretical approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.3. Correction of electrical resistivity measurement due to temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4. Experimental work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.1. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.2. Test procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.2.1. Four-probe resistivity measurement technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5. Results and discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.1. Predicting compressive strength with 7-day and 28-day electrical resistivity measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.2. Correcting the effect of temperature of electrical resistivity measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

ll rights reserved.

; fax: +351253 510 217.

a).

1. Introduction

The quality control of the compressive strength of concrete istypically performed on standardized specimens at the age of 28days. However, the pressure to fulfill construction deadline andthe need to reduce costs by reducing construction time has

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resulted in continuous construction, where early age specimens(up to 7 days) are tested to obtain some insight as to what the28-day compressive strength of concrete might be. In addition, theremoval of formwork is usually performed at the earliestconvenient time possible to speed up the construction process.Often, there is no precise knowledge of the quality of the concrete,i.e. strength, and factors such as the influence of the environmenton curing and concrete maturity are not considered. One of theNDT commonly suggested in performance-based quality controlprograms is that of electrical resistivity.

For the specification of concrete quality, current codes andpractice are mostly based on prescriptive requirements forconcrete composition and execution of concrete work, the resultsof which are neither unique nor easy to verify and control duringconcrete construction. As a result, new concrete structures arehanded over to the owners without any documentation ofachieved construction quality and durability [1]. At the sametime, extensive experience demonstrates that a lack of concretedurability can often be related to a lack of proper quality controland problems during concrete construction. Therefore, to ensurebetter construction quality and durability, there has been anincreasing focus in recent years on the development of a betterbasis for performance-based quality control for concrete qualityduring concrete construction [2–4].

The electrical resistivity of the surface concrete can bemeasured non-destructively by several means [6]. Electrodes areplaced on the surface and the resistance is measured. From thecell geometry, the resistivity can be calculated. The resistivity canbe related to corrosion and protection of steel reinforcement andto durability indicators [1]. In general, a low resistivity is relatedto a high risk of corrosion. Electrical resistivity mapping will showthe most permeable areas of a structure, where, for example,chloride penetration may be quickest and where corrosion rates,after depassivation has taken place, may be highest.

In concrete, the current flows through the pore liquid in thecement paste. Aggregate can be considered essentially inert.Consequently, the concrete is not a homogeneous conductor andthe flow of measuring current will be heterogeneous. Concreteelectrical resistivity is a geometry-independent material propertythat describes the electrical resistance, i.e. the ratio betweenapplied voltage and resulting current in a unit cell.

As the current is carried by ions dissolved in the pore liquid,the higher the moisture content of the pores, and the larger theirdimension, the lower the electrical resistivity. For constantmoisture content the electrical resistivity is increased by a lowerwater/cement ratio, longer curing time and by the use ofpozzolanic additions. Local disturbances in electrical resistivitymeasurements may be due to the presence of steel bars or asurface layer with different electrical resistivity. The electricalresistivity increases when the concrete dries out and when itcarbonates, in particular for Portland cement concrete. The effectof the penetration of chloride ions is relatively small [5].

There are different test methods for measuring the electricalresistivity of concrete. Of these, the four-electrode (Wenner)method appears to be a very simple and convenient test method;however, several factors may affect the results of such testing.These factors include: geometrical constraints; surface contact;concrete nonhomogeneity; presence of steel reinforcing bars andsurface layers having different resistivity than the bulk of theconcrete [1,6–9].

2. Research significance

The electrical resistivity of concrete is related to the micro-structure of the cement matrix, its pore structure, porosity and

pore-size distribution. It is also a function of the concentration ofions and their mobility in the pore solution [8]. Cement chemistry,cement content, water/cement ratio and use of admixtures andsupplementary cementitious materials are factors which influencethe microstructure of the cement matrix of concrete as well as thechemistry of the pore solution, and therefore influence its electricalresistivity. Studies show that electrical resistivity of the concretesproduced with different cements develops as different rates [11].The influence of water/cement ratio on concrete resistivity varies asthe moisture content changes. The effect of water/cement ratio isless significant in highly saturated concrete as compared to dryconcrete. Gjørv and Vennesland [15] have shown that the decreasein resistivity from a water/cement ratio of 0.45 to a water/cementratio of 0.70 is more pronounced when the degrees of saturationsare 40% and 60%, as compared to 100%.

The electrical resistivity of concrete may vary over a widerange, from 101 to 105Om, influenced by the moisture content ofthe concrete (direct relation to the environment), the temperatureand concrete quality (composition, cement type, etc.) [3,4,6].

Electrical resistivity measurement of concrete is used mainlyas an indicator of reinforcement corrosion activity. Electricalresistivity plays a significant role in controlling the reinforcementcorrosion rate. The higher the resistivity, the lower the corrosioncurrent passing between anodic and cathodic areas of thereinforcing steel [9,10]. Electrical resistivity can be directly relatedto durability performance parameters based on the theoreticalbackground of the phenomena. For example, with regards to thediffusion coefficient of concrete, the Nernst–Einstein equation canbe used [21,24]. In addition, research has shown correlationsbetween the electrical resistivity and the durability performanceparameters of the given concrete [3,22].

Ambient temperature has a significant effect on the electricalresistivity of concrete. An increase in the temperature results in adecrease in resistivity, provided that moisture is not lost from theconcrete during heating. The temperature dependence of elec-trical resistivity is almost entirely dependent on the behavior ofthe electrolyte [12], which is the fluid filling the pores in concrete.Near temperatures of 40 1C resistivity may be half of what it is at20 1C [13]. The need for correction of resistivity data taken attemperatures other than a standard laboratory condition has beenshown and the necessary procedure outlined [3,14].

The effect of moisture content on electrical resistivity isperhaps the strongest than any of the parameters influencing thisproperty, as most of the current is carried through the poresolution of concrete. The change of electrical resistivity over therange of possible moisture contents is dramatic. Concrete isessentially an insulating material in the oven-dry state and asemiconductor when saturated [8]. For a given level of moisturecontent, the water/cement ratio of the concrete has an effect onresistivity. As the water/cement ratio increases, the resistivitydecreases. The effect is most pronounced at the lower levels ofmoisture content.

In general, electrical resistivity of concrete will increase withtime. Increases will be greater for air curing than the moist curing.This is because, for moist curing the increase in resistivity will occurprimarily due to the increased hydration of cement and filling ofpores with hydration products, while for air curing resistivity willincrease due to loss of moisture from the concrete [6].

3. Using electrical resistivity measurements to predictcompressive strength

The estimation of electrical resistivity development in time isbased on the use of two models: (i) an empirical equation basedon the linearization of the hyperbola equation used for estimating

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compressive strength and concrete maturity [16] and (ii) atheoretical equation based on the definition of solid phasetransformation [17,18], used to describe the nucleation processof cement during hydration [19,20].

The procedure for predicting compressive strength based onelectrical resistivity measurements is dependent on the determi-nation of a reference curve correlating the electrical resistivitymeasurements with compressive strength. The quality controlprocess is based on the aforementioned relationship. Thereference curve should be defined at a reference temperaturewith electrical resistivity measurement being performed onsaturated concrete.

Although compressive strength is not a durability indicator, itoften correlates well with durability performance parameter. Thetwo models were proposed given the similarities in the timedevelopment of both compressive strength and electrical resis-tivity, and the dependency on the continuous hydration of cementin concrete, therefore varying according to the constant change inpore structure and geometry. In addition, the electrical resistivityis also influenced by the environmental exposure and variesaccording to the concrete’s maturity.

3.1. The empirical approach

Due to the curvature of the compressive strength versus timecurve, Carino proposed the use of the hyperbola equation tocharacterize the evolution [16]. Carino first proposed thisprocedure for predicting compressive strength [16]. From a visualanalysis, the electrical resistivity versus time curve presents asimilar hyperbolic evolution. Therefore, this equation is proposedfor simulating the evolution of electrical resistivity with time.From Eq. (1) it can be seen that the hyperbola equation can belinearized. By curve fitting the data to the linearized form of theequation by the use of the least square error fit, the equationparameters can be defined as

y ¼x

axþb; y ¼ randx ¼ t)

t

r¼ atþb ð1Þ

Table 1Concrete mixes.

Constituents/mix Mix A (CEM I 42.5 R) Mix B (CEM IV 42.5)

Cement (kg/m3) 350 423

Sand (kg/m3) 922 911

Course aggregate (kg/m3) 855 911

Water (kg/m3) 175 169

w/c ratio 0.50 0.40

Superplasticizer (kg/m3) 3.5 5.6

Slump (mm) 90 150

Table 2

Electrical resistivity (Om) and compressive strength (MPa) of concrete mixes A and B.

Days rA (CoV%)

Cube, 20 1C Cylinder, 20 1C Cube, 10 1C, 1 h Cylin

1 16.8 (4.4) 24.1 (3.9) 16.7 (12.7) 33.0

2 27.4 (3.7) 35.9 (9.9) 38.9 (5.6) 41.8

3 33.3 (4.1) 46.9 (2.9) 49.4 (4.0) 49.1

4 35.0 (4.6) 50.2 (5.1) 52.3 (4.0) 51.1

7 45.0 (7.7) 62.0 (2.9) 61.4 (4.9) 62.6

10 47.3 (2.6) 65.4 (3.1) – –

14 51.2 (3.4) 72.8 (3.3) 67.7 (4.2) 69.8

28 56.5 (4.2) 79,1 (3.8) 85,0 (3.8) 92,9

in which r is the electrical resistivity, t is time, b=1/rMAX, and a isa geometrical parameter. This equation can be used for differentcurve shapes, i.e. cement types, since the equation variables aregeometrical parameters.

3.2. The theoretical approach

Avrami and coworkers proposed this equation for solids phasetransformations at constant temperature [17,18]. It can specificallydescribe the kinetics of crystallization and can be appliedgenerally to other changes of phase in materials, like chemicalreaction rates. Using this equation, Jalali [19] has demonstratedthe principles of nucleation and growth mechanism of theformation of cementitious material. In addition, the equationhas been adjusted to strength development prediction [20]:

r¼ rMAX ð1� expð�KtnÞ ð2Þ

in which r is the electrical resistivity, K the rate for growth and istemperature dependent according to Arrhenius equation, n thedominant morphology of the formation process, and rMAX themaximum value when t-N. The parameters rMAX, K, and n

are determined by curve fitting the data.

3.3. Correction of electrical resistivity measurement due to

temperature

When referring to temperature, it is necessary to distinguishbetween two distinct effects. The first is a time dependent effectof temperature on the electrical resistivity measurement. This issimilar to the notion of maturity for concrete. The second is thetemperature of the concrete surface when the electrical resistivitymeasurement is made. It is for this second effect that a correctionfactor is presented.

As the temperature increases, the viscosity of a fluid decreases,increasing the mobility of the ions, which carry the current. Thisleads to a decrease in electrical resistivity of the porous material.Due to the complex nature of these interactions, an empiricalapproach is followed [6]. Assuming that the conductivity (C=1/r)is a function of the mobility of the ions in the concrete liquidphase, it can be expected that the conductivity varies withtemperature in the same manner in which the diffusion of ionsvary in a liquid phase. This variation is governed by the Arrheniusequation. Therefore, the variation of electrical conductivity withtemperature can be expressed by the following equation [21]:

C ¼ C0 expð�E=RTÞ ð3Þ

where C is the conductivity at any temperature (Om)�1, C0

the conductivity when the temperature tends towards infinity(Om)�1, E the activation energy (J/mol), R is the gas constant,8.314 J/mol K, and T the absolute temperature K.

rB fC,A fC,B

der, 10 1C Cube, 20 1C Cylinder, 20 1C

(2.7) 315.0 (4.7) 320.0 (6.4) 17.5 –

(3.3) 350.0 (9.9) 385.0 (8.4) 26.5 –

(2.8) 365.0 (9.1) 425.0 (3.2) – 45.3

(2.6) 400.0 (7.6) 475.0 (5.1) 33.2 –

(2.7) 450.0 (6.4) 550.0 (8.6) 35.5 52.6

490.0 (4.3) 665.0 (6.8) – –

(3.5) 560.0 (8.3) 760.0 (7.3) 44.7 59.5

(3.0) 835,0 (5.7) 900,0 (7.6) 51.3 68.6

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Fig. 1. Principle of the four-electrode test method with the resulting current flow

and equipotential contours

R.M. Ferreira, S. Jalali / NDT&E International 43 (2010) 55–6158

In order to establish the relationship between electricalresistivity and temperature, and convert electrical resistivitymeasurements at any temperature to a reference temperature(20 1C), E must be determined. These values can be obtained for agiven type of cement, concrete mix and curing conditions bylinear transformation of Eq. (3). This is performed by applying thelogarithm to both sides of the equation.

LnðCÞ ¼ LnðC0Þ � E=RTð4Þ

The activation energy E can be estimated using data fromresistivity measurements at different temperatures [3]. To obtainthe electrical resistivity for a reference temperature, usually 20 1C,the following expression can be used:

rREF ¼ rj ð5Þ

where the conversion factor j is given by

j¼ expð�E=RTÞ=expð�E=RTREFÞ ð6Þ

4. Experimental work

4.1. Materials

To demonstrate the proposed procedure measurements wereperformed on two concrete mixes, one produced with an ordinaryPortland cement (CEM I 42.5 R) with a water/cement ratio of 0.50and the other produced with a fly ash cement (CEM IV 42.5) with awater/cement ratio of 0.40. The composition of these concretemixes is given in Table 1. A naphthalene-based super plasticizerwith a solid content of 40% was used. Two aggregates were used, agranitic coarse aggregate with a maximum particle size of 15 mmand river sand with a maximum particle size of 2.5 mm. A seriesof 150 mm cubes as well as 100 mm�200 mm and150 mm�300 mm cylinders were molded.

The concrete specimens were unmolded the day after castingand then stored in water at 20 1C. For each test, three specimenswere measured, with 6 readings per specimen, according to thelaboratory testing procedure [23]. Prior to testing, the surfacewater of each specimen was removed with a damp cloth andspecimens were placed on a dry wooden support. The effect ofmaturity was assessed on concrete specimens (100 mm�200 mmcylinders) permanently cured in water at 10 1C. The effect of theconcrete temperature on the measurement was assessed onconcrete specimens (100 mm�200 mm cylinders) cured at 20 1Cbut cooled down to 10 1C 1 h prior to testing.

4.2. Test procedure

After casting, all specimens were tested regularly for the firstweek. After this, they were tested weekly until 28 days for theCEM IV concrete and 90 days for the CEM I concrete. The electricalresistivity was measured using the four-electrode method [24].For both concrete mixes, electrical resistivity measurements on

Table 3Best-fit to 7-day electrical resistivity measurements for the empirical and the theoreti

Empirical equation

Specimen m b rEST (Om) Error (%)

rA, Cube 0.0166 0.0424 55.3 2.2

rA, Cylinder 0.0119 0.0303 76.8 2.9

rB, Cube 0.0020 0.0016 477.7 42.8

rB, Cylinder 0.0016 0.0020 608.2 32.4

cubic and cylindrical specimens were performed. For the CEM I42.5 R concrete, cylindrical specimens where cured in 10 1C waterto asses the influence of concrete maturity. In addition, theconcrete compressive strength was also determined in order tocorrelate with the electrical resistivity measurements. Table 2presents all the electrical resistivity readings performed on bothconcrete mixes, the corresponding compressive strengths and theelectrical resistivity measurements performed at 10 1C.

4.2.1. Four-probe resistivity measurement technique

Currently the four-probe method is the most widely usedtechnique for field measurement of concrete resistivity. Thismethod originally was developed by Wenner [25] to measureearth resistivity. The principles of the four-electrode test method(Wenner method) with the resulting current flow andequipotential contours are schematically shown in Fig. 1. Duringtesting, a low frequency alternating electrical current passesbetween the two outer electrodes while the voltage drop betweenthe two inner electrodes is measured. In this research, theelectrical resistivity measurements were performed with acommercially available resistivity meter. This resistivity meter,which had adjustable electrode spacing, used an alternatingtrapezoidal current wave at a frequency of 13 Hz. The apparentelectrical resistivity determined by the equipment is obtainedfrom Eq. (7) considered valid for a homogeneous semi-finitevolume of the material

r¼ 2paV=I ð7Þ

where r is the electrical resistivity (Om), a the electrode spacing (m),V the voltage drop (V), and I the current (A).

According to LMC testing procedure for electrical resistivity[24], on cubic specimens, measurements are made on threeadjacent surfaces with two measurements per surface perpendi-cular to each other. On cylindrical specimens, measurementsare made parallel to the length of the cylinders 1201 apart fromeach other along the circumference of the cylinder. Each readingconsists of two measurements slightly apart from each otherand with opposite headings (1801). The measurements on allspecimens were performed with 30 mm spacing between theelectrodes.

cal equations and the error in estimation of the 28-day electrical resistivity.

Theoretical equation

Su k n rEST (Om) Error (%)

67 0.313 0.663 63.2 �11.7

79.1 0.366 0.758 78.3 1.0

1670 0.321 0.186 750.2 10.2

1800 0.194 0.319 772.9 14.1

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There are several factors that influence the resistivitymeasurement when the four-probe technique is used. Thesefactors include (1) geometrical constraints, (2) surface contact, (3)concrete nonhomogeneity, (4) presence of steel reinforcing bars,

Table 4Estimating 28-day compressive strength based on 7-day electrical resistivity

measurements.

Specimen RC, 28 (%) Empirical equation Theoretical equation

RC, 28, EST. (%) Error (%) RC, 28, EST. (%) Error (%)

A, Cube 51.3 46.5 9.3 52.3 1.9

A, Cylinder 45.8 10.8 46.5 9.4

B, Cube 68.6 53.0 22.8 65.9 4.0

B, Cylinder 54.2 21.1 62.8 8.5

Fig. 2. Regression analysis of compressive strength and electrical resistivity with

28-day data. (a) Mix A and (b) Mix B.

Table 5Best-fit to 28-day electrical resistivity measurements for the empirical and the theoret

Empirical equation

Specimen m b rEST (Om) Error (%)

rA, Cube 0.0162 0.0430 56.4 0.2

rA, Cylinder 0.0116 0.0308 78.8 0.4

rB, Cube 0.0011 0.0056 776.4 7.0

rB, Cylinder 0.0010 0.0040 880.2 2.2

and (5) surface layers having different resistivity than the bulk ofthe concrete. These factors have been thoroughly investigated[1,6–9].

5. Results and discussion

5.1. Predicting compressive strength with 7-day and 28-day

electrical resistivity measurements

The proposed procedure involves the use of the electricalresistivity measurements performed up to 7 days in the predictionof the 28-day compressive strength. The models presentedpreviously are adjusted to the 7-day electrical resistivity datafrom Table 2 using a least square error fit, and the 28-dayelectrical resistivity can be estimated. With prior knowledge ofthe relationship between the compressive strength and theelectrical resistivity, the 28-day compressive strength can bepredicted. Table 3 presents the results of the fit of both equationsto the data as well as the estimate of 28-day electrical resistivity.

From Table 3 it can be seen that the empirical equation doesnot adjust well to CEM IV concretes. The error in estimating the28-day electrical resistivity varies from 32% to 43% for cubic orcylindrical specimens, respectively. Observing the curve shape forboth concrete types, it is clear that the differences are significant.For the CEM IV concrete, the initial electrical resistivity values arevery high with the rate of increase being larger than that of CEM Iconcrete.

On the other hand, the theoretical equation adjusts well toboth concrete types, with a maximum error of 14%. From Fig. 2,the relationship between electrical resistivity and compressivestrength for both concrete type and specimen shape can beobserved. Based on these correlations, Table 4 presents theestimate of 28-day compressive strength and the respectiveerrors. The error in estimating the 28-day compressive strengthis greater for the empirical equation than the theoretical equation.For the first, errors are lower than 23% for mix B and 11% for mix A,whereas for the theoretical equation lower than 9% for mix B and10% for mix A.

The same approach is applied to 28-day electrical resistivitymeasurements to estimate 28-day compressive strength. Theadvantage is that the equation fitting of the data is more preciseand the error associated with the estimation of the 28-day

ical equations and the error in estimation of the 28-day electrical resistivity.

Theoretical equation

Su k n rEST (Om) Error (%)

113.1 0.2155 0.3771 60.0 6.2

158.2 0.2166 0.3731 83.6 5.6

1670 0.1604 0.4050 770.1 7.8

1800 0.1778 0.4087 900.7 0.1

Table 6Estimating 28-day compressive strength based on 28-day electrical resistivity

measurements.

Specimen RC, 28 (%) Empirical equation Theoretical equation

RC, 28, EST. (%) Error (%) RC, 28, EST. (%) Error (%)

A, Cube 51.3 47.4 7.7 50.0 2.5

A, Cylinder 46.8 8.9 49.1 4.2

B, Cube 68.6 67.1 2.2 66.8 2.6

B, Cylinder 66.8 2.6 67.7 1.3

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Fig. 3. Conversion of electrical resistivity measurements to take into account temperature and maturity

R.M. Ferreira, S. Jalali / NDT&E International 43 (2010) 55–6160

compressive strength is lower. This can be seen from Table 5where the results of the fit as well as the estimate of 28-dayelectrical resistivity are presented. Table 6 presents the estimateof 28-day compressive strength and the respective errors.

From Table 5 it can be seen that the empirical equation adjustswell to CEM IV concretes. The error in estimating the 28-dayelectrical resistivity varies from 7% to 2% for cubic or cylindricalspecimens, respectively. However, the theoretical equation dis-plays an over all better fit, with a maximum error of 8%. Table 6presents the estimate of 28-day compressive strength and therespective errors. For the first, errors are lower than 3% for mix Band 9% for mix A, whereas for the theoretical equation lower than3% for mix B and 4% for mix A.

5.2. Correcting the effect of temperature of electrical resistivity

measurements

For the specimens cooled down to 10 1C prior to reading, it isassumed that the maturity is identical to that of the referenceconcrete. For the specimens cured permanently in 10 1C water, thematurity of the concrete has to be taken into account and theequivalent age calculated (age of concrete cured in 20 1C watercured).

Table 2 presents the data from the measurements of thesespecimens. Fig. 3 presents the reference curves for electricalresistivity of cubes and cylinders (at 20 1C), and the curves of themeasurements corrected to take into account temperature usingEq. (5). The determination of the activation energy, E=22.512 kJ/mol for concrete mix A, is published elsewhere [3].

From Fig. 3, it can be observed that Eq. (5) adequately takesinto account the effect of concrete temperature on the electricalresistivity measurement.

6. Conclusions

A procedure based on NDT measurements is used in theprediction of early age compressive strength. The results are basedon limited number of measurements for two concrete mixes (CEMI and CEM IV type cements).

Both compressive strength and electrical resistivity aredependent on the continuous hydration of cement and thereforevary according to the change in pore structure and geometry.

The empirical equation, based on the geometrical similaritiesbetween the time development of electrical resistivity and

compressive strength present promising results for the CEM Itype concrete. With 7-day electrical resistivity measurements, theerror in estimating 28-day compressive strengths was less than11%. The same equation did not perform well for the CEM IVconcrete, in which the errors in estimating 28-day compressivewere 23%.

The theoretical equation showed promising performanceestimating compressive strengths for both concrete types (I andIV) with errors no larger than 14%. This is a promising result.

This approach for compressive strength assessment enablesthe whole structure to be surveyed rapidly with minimum cost,providing crucial information for the quality control.

Furthermore, if 28-day electrical resistivity measurements areused to estimate the compressive strength, the errors associatedare of 9% and 4% for the empirical and the theoretical equations,respectively.

The effect of temperature on the electrical resisitivity mea-surements can be effectively accounted for with an adequateconversion factor. Measurements performed at 10 1C and con-verted into 20 1C coincide with the original measurements takenat the reference temperature.

There is no need to measure the concrete maturity as theelectrical resisitivity measurement is influenced in a similarmanner.

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