Correlation Curves to Characterize Concretes Used in Rio de Janeiro by Means of Non-destructive Tests

© 2009 IBRACON a COPPE, Programa de Engenharia Civil, Universidade Federal do Rio de Janeiro, mauriciodornellas@hotmail.com, Caixa Postal 68506, CEP 21941-972, Rio de Janeiro, Brasil b Escola de Engenharia, Departamento de Engenharia Civil, Universidade Federal Fluminense, lidiashehata@vm.uff.br, COPPE-UFRJ, lidia@coc.ufrj.br,Caixa Postal 68506, CEP 21941-972, Rio de Janeiro, Brasil c COPPE, Programa de Engenharia Civil, Universidade Federal do Rio de Janeiro, ibrahim@coc.ufrj.br, Caixa Postal 68506, CEP 21941-972, Rio de Janeiro, Brasil.


Introduction
The compressive strength of concrete is of fundamental importance in structural design, being defined as the compressive strength attained by the material under controlled temperature and humidity conditions, at a certain age.The verification that the concrete used in the construction of the structure complies with the design requirements is made from compression strength tests, usually at 28 days, on cylindrical or cubic specimens, moulded, cured and loaded to failure according to the technical standards used in each country.However, for different reasons, many times the investigation of the concrete within a structure is required.The need to evaluate the strength of the material in situ at ages below 28 days, for reasons inherent to the construction stages, or at ages after the construction, to verify the need to carry out repairs and/or strengthening, has led to the development or improvement of several tests for the characterization of the concrete.The extraction of concrete samples from the structure, and its subsequent compressive tests, has the disadvantages of being costly and of the restriction of the places where samples can be cut from, so that the stability of the structure is not impaired.As a result, the cores are usually drilled only from the slabs and in relatively small number, not allowing the full mapping of the strength levels of the concrete in the structure.The use of non-destructive tests comes then as an alternative, given that the structural element to be evaluated undergoes no damage at all or small ones, easily repairable, that do not compromise its performance, therefore allowing a wider investigation of the concrete within the structure.These tests, however, have to be carried out according to adequate procedures and should have their results carefully analyzed, given that they are affected by several factors, some of them related to the compression strength of the concrete and others to the type of test.There is a consensus that obtaining reliable results depends on the qualification of the testing personnel and on the use of adequate correlation curves, developed for the type of concrete under study.Thus, correlation curves to evaluate the compressive strength of ready-mixed concretes used in Rio de Janeiro, using different nondestructive tests, were obtained and are presented here.A non-linear multiple regression study, which aimed at evaluating the accuracy increase in the compressive strength estimation with the use of combined non-destructive tests methods, is also presented in this work.The results of the initial tangent modulus of elasticity tests for the same concretes, obtained in a study that was conducted in parallel, also allowed correlating this property with the ultrasonic wave pulse velocity.

Evaluation of the compressive strength by non-destructive tests
The estimation of the compressive strength (f c ) using non-destructive tests is made with curves that correlate f c with the quantities measured in these tests.Obtaining reliable results depends on the use of adequate correlation curves, developed for the type of concrete under study.
According to Malhotra [1], whenever there are changes in the materials involved in the production of the concrete, a new correlation curve should be developed.Considerable errors may be made in the evaluation of f c if correlation curves provided by the manufacturers of the non-destructive equipment are used, given that they were developed for specific test conditions and materials.
According to ACI 228.1R-03 [2], the use of non-destructive tests in the field should be preceded by the development of correlation curves, from laboratory tests done on standard concrete specimens (cylindrical or cubic) made with the same materials used in the structure's concrete that is under evaluation.Measurements of a particular quantity are carried out on these specimens, using a non-destructive test and, immediately after that, they are submitted to the compressive tests.Finally, the pairs of obtained results are analysed to determine the expressions that best characterize the desired correlation.
In some cases, as in the penetration resistance method, the tests are done on specimens that are different from those that are used in the compressive strength test.In these cases, it is essential that both tests are done on samples of same maturity and compaction conditions.According to Neville [3], the major hurdle for obtaining adequate correlation curves is that the factors that affect the compressive strength do not always affect the quantities obtained from the nondestructive tests in the same proportion or in the same manner.

Experimental programme
In order to propose curves that correlate the compressive strength or the modulus of elasticity with the quantity obtained from the concrete non-destructive tests, the experimental programme covered specimen tests with concrete supplied to construction work by 5 concrete suppliers and produced in the laboratories of 2 concrete supplier groups.
In the first stage it was sought to obtain from each concrete supplier, previously selected based on their market share, two concretes with nominal f ck values equal to at least 25 MPa and different between themselves.However, with only one exception, in the 180-day period (January to June 2004), it was possible to collect only concretes with a nominal f ck of 25 MPa or 30 MPa, minimum values prescribed by NBR 6118 [4] for moderate and high environmental aggressivity.
In the second stage (July to December 2004), aiming to include concretes with more varied strengths and the two typical coarse aggregates of Rio de Janeiro, specimens moulded in the mentioned laboratories, with concretes of a composition similar to that which would normally be adopted by the concrete supplier plants, were tested.In these concretes the variables were the water-cement ratio (0.40, 0.45, 0.50, 0.55 and 0.60) and the petrographic characteristic of the coarse aggregate (crushed granitic gneiss and syenite).The composition of the concretes of this stage is presented by Machado [12].
The following tests were carried out, both in the 1 st as in the 2 nd stage: compressive strength tests and ultrasonic pulse velocity, rebound hammer and penetration resistance tests.The static modulus of elasticity tests (initial tangent) were done by Nunes [13], using the same concretes of this study, and their results were used to obtain the curve that correlates the modulus of elasticity with the ultrasonic wave pulse velocity.Three combined non-destructive methods were studied here, obtaining of the correlation between the ultrasonic pulse velocity, the rebound number and the compressive strength of the concrete (V x IE x f c ), the correlation between the ultrasonic pulse velocity, the probe penetration length and the compressive strength of the concrete (V x Lp x f c ) and the correlation between the rebound number, the probe penetration length and the compressive strength of the concrete (IE x Lp x f c ).  2, the Brazilian Method has gaps in the procedures that have to be adopted during the execution of the penetration resistance tests.Due to that and to the fact that there is no Brazilian Standard for this type of test, this work followed the recommendations of the American Standard ASTM C803 [9] and, for the selection of valid length of exposed probe measurements, the British Standard BS 1881:Part 207 [10].
In spite of all the precautions taken during the execution of the tests, incoherent exposed probe length values (L e ) were found, that is, L e values in later ages smaller than those obtained in earlier ages, fact also found in the tests carried out by Evangelista [11].
Apart from that, the tests showed coefficients of variation over 5%, limit recommended by ACI 228.1R-03 [2].
Having discarded the possibility that these incoherencies could have occurred due to inadequate procedures during the tests, a decision was made to seek a limit value for the selection of valid L e values that would be more adequate to the length of the probe used in Brazil.The need to establish this new limit comes from the fact that the length of the probe used in Brazil (55 mm) is smaller than the one used in the USA and in Europe (around 80 mm).Besides that, the limit value for the L e difference of one probe to the other in the same region recommended by the British Standard [10], 5mm, is stricter than that set by the USA Standard [9], 8.4mm or 11.7mm, as shown in Table 2.
The criterion used in establishing this new limit, described in detail by Machado [12], consisted of considering the average of only 3 L e values from the 4 obtained, discarding the one that showed the greatest difference in relation to the average value of the 4 obtained.The differences between the L e value of the excluded probe and the greatest or smallest L e value of the remaining 3 probes showed that the value recommended by BS 1881:Part 207 [10], 5mm, was more adequate to use in the analysis of the tests undertaken in this work.

Isolated Methods
In the studies carried out by Evangelista [11], where the coarse aggregate and water volumes were kept constant, on concrete specimens with the same coarse aggregates used in this work, it was found that the factors that affected the V x f c correlation the most were the density of the coarse aggregate and the type of the cement.According to that same author, these factors were the ones that influenced the IE x f c correlation the most, while the type of cement and the maximum aggregate size were the ones to most affected the Lp x f c correlation.These findings served as the basis to decide for the use, in the simple non-linear regression studies aiming at the selection of the curve that best represented the correlation between the quantities measured in the non-destructive tests and f c , the experimental data obtained in the 1 st and in the 2 nd stage of this work simultaneously; given that in all of the concretes tested the same type of cement and coarse aggregates with nearly identical density and volume and with the same maximum size were used.
In the absence of a detailed study on the factors that affect the V x E c relationship, the decision to use the experimental data obtained in the 1 st and 2 nd stages simultaneously was made by taking into account the work developed by Nunes [13], who studied the same concrete specimens of this study.In it, practically no difference was found between the expressions that relate E c and f c obtained for each concrete group tested and that related to all the obtained experimental data.
In this study, for each correlation, the five most commonly proposed curve models in the literature were tested: linear, power, exponential, polynomial (2 nd degree) and logarithmic.The criterion to select the curve that best fitted the experimental data was based on the coefficient of determination (r 2 ) and the residual standard deviation (S res ), as well as the statistical parameter (α), equal to (S res ) divided by the mean value of f c or E c .The power curves were those that best represented the V x f c and IE x f c correlations, while the 2 nd degree polynomial ones were those that best represented the correlations between Lp and f c and between V and E c .The expressions proposed to correlate the concrete compressive strength with the ultrasonic pulse velocity, with the rebound number and with the probe penetration length, along with the expression proposed to relate the modulus of elasticity with the ultrasonic pulse velocity, are shown in Table 3. Figures 2, 3, 4, and 5 show, respectively, the curves that represent the expressions given in Table 3, along with the 95% prediction intervals, apart from all the obtained experimental data.In order to obtain these expressions, the data that were distant from the mean of a value equal to or greater than three times the standard deviation were discarded (see Figures 4 and 5).
Analysing the results related to the expressions for the evaluation of f c shown in Table 3, it is found that the IE x f c relationship is the one that presented the greatest value of r 2 and the smallest value of (α), followed in decreasing order by the Lp x f c and V x f c relationships, in line with the sequence found by Yun et al [14] and Samarin and Meynink [15].According to Popovics [16], the estimation of the concrete compressive strength cannot be obtained with an acceptable accuracy with the use of expressions where the only variable is the value for V.This fact was verified in this work, given that the V x f c relationship is the one which showed the smallest value of r 2 and the largest value of α amongst all of the studied relationships.According to that author, preliminary studies demonstrated that the inclusion of a new variable (age of the concrete) in the expressions that relate V with f c provides an improvement in the accuracy of the estimated f c value.
Comparing the values of r 2 and of α obtained for the V x f c relationship with those obtained for the V x E c relationship, one finds that the latter leads to more accurate values of the estimated quantity as it presented a greater value of r 2 and a smaller value of α than the V x f c relationship.This fact had been anticipated given that the ultrasound pulse velocity is a measure of elastic stiffness and is directly related to the modulus of elasticity [17].
It should be noticed that the values of f c and E c , obtained from the expressions shown in Table 3, correspond to the mean values located within the range set by the upper (f c,sup or E c,sup ) and lower (f c,inf or E c,inf ) limits of the prediction interval.Since these limits were obtained from 95% prediction intervals, it can be said that there is a 95% chance of the f c or E c value to be inside these limits.The expressions for the calculation of these limits are shown in Table 4.The expressions of this table and the prediction intervals shown in Figures 2, 3, and 4 confirm the previously mentioned conclusion drawn from the values of r 2 and α: the IE x f c relationship is the one which presented the smallest uncertainty range for the values of f c amongst the relationships studied in this work.When conducting an evaluation of the f c by means of non-destructive tests or of E c from the V x E c relation, one should always bear in mind the purpose of such evaluation.One should verify if the uncertainty range for the values of f c or E c inherent to all methods is aligned with the accuracy required by the work to be undertaken.Table 4 Expressions for the calculation of the superior and inferior limits of isolated methods.

Combined Methods
In the nonlinear multiple regression studies, aiming at choosing the curves that best represented the V x IE x f c , V x Lp x f c , and IE x Lp x f c correlations, the experimental data obtained in the 1 st and 2 nd stages were used simultaneously, as justified above.
Tests were done with 10 types of curve [12] for each correlation, with the choice being made for those that showed the greatest coefficient of determination (R 2 ).The expressions proposed for the 3 combined methods studied here are shown in Table 5.
Aiming at evaluating whether an increase in the accuracy of the estimate of f c had taken place with the use of the combined meth- In relation to the combined methods, it is found that the analysis of only the values of R 2 does not allow to evaluate which of the 3 tested combinations provides more accurate values of f c , as they showed the same value of R 2 (0.999).Using criterion (B), however, one can say that the values of f c estimated by the IE x Lp x f c relationship are more accurate than those estimated by the other 2 studied combinations, as it led to the smallest values of S res and α.
Using criterion (A) in the evaluation of the increase in accuracy of the estimate of f c with the combined methods, it is found that the 3 studied combinations showed an accuracy that was considerably higher than those observed in the isolated correlations, which would justify the use of the combinations.The combined methods led to values of R 2 above the values of r 2 found for the V x f c (increase of 56%), IE x f c (increase of 11%) and Lp x f c (increase of 28%) relationships.
When performing this same evaluation with criterion (B), one can see that the estimate of f c would be more accurate with the use of combined methods V x Lp x f c and IE x Lp x f c than with the use of the corresponding isolated methods, as the values of S res and α found for the combined methods were below those found for the isolated methods.However, in opposition to the conclusion that criterion (A) pointed, the increase in accuracy would hardly justify the additional time and cost that the use of these combined methods would bring about.This comes from the fact that the smallest values of the difference in percentage terms between the α value found for a combined method and those which were found for the isolated methods (β) are relatively  6.In this same table, one can see that the use of the V x IE x f c combined method is not viable, since it led to values of S res and α above those found for the IE x f c correlation.In the attempt to eliminate doubts about the viability of using the combined methods, as the two criteria led to contradictory conclusions, tables with the errors of the estimate of f c related to each one of the 6 proposed expressions were produced by Machado [12].These errors were calculated by taking into account the difference between the values of f c obtained from a particular expression and those obtained from the standard compressive strength tests.A summary of the analysis of these results is shown in Table 7.Based on the results shown in tables 6 and 7, one can say that: a) As far as the isolated methods is concerned, criteria (A) and (B) showed to be adequate to point, amongst various relations, that where the values of f c are estimated with more accuracy, as the IE x f c relation, pointed by the 2 criteria as being the most accurate, was the one that presented the smallest relative errors, 7.9% against 15.4% of the V x f c relation, and 7.6% against 12% of the Lp x f c relation.b) Criterion (B), in opposition to criterion (A), showed adequacy to point, amongst various combined methods, that where the values of f c are estimated with greatest accuracy.The IE x Lp x f c relationship, pointed by criterion (B) as being the most accurate, was the one that presented the smallest relative errors, 7.1% against 8.9% and 10.9% of the V x IE x f c and V x Lp x f c relationships, respectively.
c) The great difference between the values of R 2 found for the combined methods and those of r 2 found for the respective isolated methods, according to criterion (A), indicates a considerable increase in accuracy for the estimate of f c with the combined methods, which would justify their use.This fact, however, was not confirmed by the results of the percentage differences between the relative error found for the combined method and those which were found for the respective isolated methods, X, seen in Table 7, which shows the inefficiency of this criterion for this type of evaluation.d) Criterion (B), in its turn, proved to be adequate for evaluating the viability of the combined methods.In the comparisons made in Table 7 between a particular combined method and the respective isolated methods, the values for X point that, in general, the combined methods showed a discrete increase in accuracy for the estimate of f c .This was not found only in the comparison between the V x IE x f c and IE x f c relations.The correspondence between these conclusions and those which were obtained with that criterion attests its validity for this type of evaluation.It should be noticed that the values of f c , obtained from the expressions in Table 5, correspond to mean values within the range set by the upper and lower limits of the prediction interval.The expressions for the calculation of these limits are shown in Table 8.From the expressions in this table, one can say that the values of f c estimated with the IE x Lp x f c relation showed an accuracy greater than the ones estimated with the relations of the other 2 studied combinations, given that it had the smallest 95% prediction interval for the values of f c .This same conclusion had already been arrived at from the analysis of the values of S res and α.A comparison between the 95% prediction intervals of the relationships studied in this research is shown in Table 9.From the analysis of the values of this table, one can see that: a) The V x IE x f c relation presented a prediction interval smaller than that found in the V x f c relation albeit greater than that found in the IE x f c relation, which does not justify its use.b) The V x Lp x f c relation presented a prediction interval smaller than those found in the V x f c and Lp x f c relations.Despite  c that, its use may not be economically viable due, especially, to the small difference between its prediction interval and that of the Lp x f c relation.c) The IE x Lp x f c relation presented a prediction interval smaller than those found in the IE x f c and Lp x f c relations but may also not be economically viable due to the small difference between its prediction interval and that of the IE x f c relation.Curves that represent the IE x Lp x f c correlation, combined method that showed the best results, are shown in Figure 6.

Conclusions
On the basis of the analysis of the obtained results, the following remarks can be made: a) As far as the isolated non-destructive methods is concerned, it was found that the correlation between the rebound number and the compressive strength was that which presented the best results, followed in decreasing order by the Lp x f c and V x f c correlations.The worst results showed by the V x f c relationship could be explained, according to Popovics [16], by the non-existence of a theoretical relation between the compressive strength and the ultrasonic pulse velocity, not even for homogeneous materials and with elastic linear behaviour.This explanation, however, does not seem sufficient to justify that fact, for the simple reason that there is no theoretical relation between the compressive strength and the other quantities (IE and Lp).Analyses made by Machado [12] show that the ultrasonic pulse method is more affected by changes in the concrete  composition than the other methods, and this explanation may be more adequate.
In spite of presenting the worst results in this study, the estimate of f c using the ultrasound pulse method should not be discarded, especially for an evaluation at later ages.In these ages, results obtained using the rebound hammer and the penetration resistance methods are affected by carbonation, and may not represent the concrete located within the element.The influence of carbonation is not as significant in the results obtained by the ultrasound wave propagation method, as the thickness of the surface layer is relatively small in comparison with the total path length of the ultrasound wave (case of direct transmission).
One should always have in mind that, for evaluating the concrete compressive strength by means of non-destructive tests, regardless the method chosen, the greater the knowledge about the composition of the concrete under investigation, thus implying the use of more appropriate curves, the greater will be the accuracy of the obtained results.b) In relation to the combined non-destructive methods, it was found that the correlation between the rebound number, the probe penetration length and the compressive strength was the one which presented the best results.This is in accordance to the assertion in RILEM NDT4 [18] that the combination of 2 or more methods is advantageous when the methods in question provide estimates of the compressive strength with similar accuracy levels.The IE x Lp x f c correlation was obtained from the combination of the 2 isolated methods (IE x f c and Lp x f c ) that individually showed the best results.Despite the fact that the V x Lp x f c and IE x Lp x f c correlations led to an increase in accuracy in the obtained results in comparison to those obtained in the respective isolated methods, this increase may not be enough to justify the time and cost increases produced by the use of the two methods instead of only one.c) The observed differences between the correlation curves proposed in this and in other works [12] highlight the need to obtain the largest possible number of information about the composition of the concrete under investigation, which will allow the choice of more adequate curves and results that are closer to the real ones.It should be pointed out that the use of these curves should be preceded by verification, made with the extraction of cores, to evaluate their validity.Figures 3 and 4 show that the curves indicated by the manufacturer of the used hammer, and by Vieira [8], do not generally lead to an adequate evaluation of f c in the case of the concrete specimens analyzed.d) As regards the statistical procedure adopted, the use of the determination coefficient was proved to be adequate both for the choice of the curve that best represented the correlation studied as for the evaluation, amongst various isolated methods, that one which produced the best results.However, its use does not allow the correct evaluation of the use of combined methods.It is recommended, for the evaluation of the method isolated or combined that provides the best results for a particular data set, that the parameters S res and α are used, apart from the determination coefficient.e) The estimate of the concrete static modulus of elasticity value by means of the ultrasonic pulse velocity presented rather satisfactory results as a consequence of the direct relationship between these two quantities.There is in Brazil a vast field to be explored in relation to the improvement of non-destructive tests for obtaining more reliable results: in the training of qualified personnel; in the modification of adopted procedures; in the inclusion of new variables (as age of the concrete) in the expressions that relate the quantities obtained in the non-destructive tests with the concrete compressive strength.In relation to the penetration resistance method, a broad study is suggested to seek its adaptation to the Brazilian reality, investigating especially the following parameters: minimum number of probes to be fired in a certain region, minimum distance between them, maximum difference between the values of their exposed length, and the ideal driver unit position (power type) as a function of the strength of the concrete under analysis.
Correlation Curves to Characterize Concretes Used in Rio de Janeiro by Means of Non-destructive Tests

Figure 2 -
Figure 2 -Curve that correlates f with the ultrasonic pulse velocity (V) c

Figure 4 -Figure 3 -Figure 5 -
Figure 4 -Curve that correlates f with the probe penetration length (Lp) c calculated from equations in table 5.

*
Difference between the values of f and f ** Obtained from the mean of the differences between the superior and inferior limits of the 95% prediction interval and the predicted values.c,sup c,inf.

Figure 6 -Correlation
Figure 6 -Curves that correlate f with the rebound number (IE) and the probe penetration length (Lp) c

Table 3 -
Proposed expressions to correlate f with V, f with IE, f with Lp and E with V.
** f in MPa, V in km/s, IE dimensionless, Lp in mm and E in GPa.

Table 5 -
Proposed expressions for the combined methods c c

Table 6
res Correlation

Curves to Characterize Concretes Used in Rio de Janeiro by Means of Non-destructive Tests small
, not going beyond 2%, as shown in Table

Table 7
*** No accuracy increase with the use of the combined method.

Table 9 -
Comparison between the 95% prediction intervals of the studied relationships