Estimate of Concrete Cube Strength by Means of Different Diameter Cores - A Statistical Approach

Materials and Structures/Matériaux et Constructions, Vol.30, April 1997, pp 131-138 F. Indelicato Department of Structural Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy A B S T R A C T This paper describes a method for the interpretation of test results which makes it possible to estimate concrete cube strength from cores of various diameters with suitable confidence levels. To this end, 1,270 results of compression tests carried out on cubes with 150 mm sides, on typical small and micro-cores (70, 45 and 28 mm in diameter, respectively), have been elaborated with the aid of statistical methods, which can also be used for different types of test. The laws of correlation between cube strength and the strength values obtained from the different diameter cores are determined and discussed. The relationships expressing the lower confidence limits for future individual observations are developed, compared with one another in relation to the influence of core diameters, and proposed for the in situ estimate of cube strength. R É S U M É Cet article présente une méthode d’interprétation des résultats d’essais permettant d’estimer, avec des niveaux de confiance suffisants, la résistance sur cube du béton à partir de carottes de diamètre divers. À cet effet, 1 270 résultats d’essais de compression sur des cubes de 150 mm de côté et sur des carottes types de 70 mm de diamètre, de petites carottes de 45 mm de diamètre et des microcarottes de 28 mm de diamètre sont développés au moyen de méthodes statistiques pouvant également être appliquées à l’interprétation d’autres types d’essais. Les lois de corrélation entre les résistances des cubes et des carottes de différents diamètres sont déterminés et discutées. Les relations qui expriment les limites inférieures de confiance pour les observations individuelles futures sont élaborées, comparées entre elles par rapport à l’influence des différents diamètres des carottes, et proposées pour l’estimation in situ de la résistance sur cube. Ⅵ 1. INTRODUCTION Among the various methods employed for the assessment of concrete strength in situ, the classical method, involving compression tests on cylindrical specimens produced from cores drilled out of the structure, should surely be recognised as having primary importance on account of the reliability and accuracy of the results. However, although these tests are quite simple to conduct, the results obtained may sometimes contain considerable errors because of the great variety of parameters involved (core diameter, specimen length/diameter ratio, specimen moisture at the time of testing, aggregate size, type of diamond wheel employed, damage caused by drilling and specimen preparation, size effects). Another cause of uncertainty lies in the methods adopted to interpret the test results, since the measuring process must necessarily begin with a more or less accurate estimate of strength from tests performed on cores, and then, for the sake of comparison, the values obtained must be expressed in terms of the strength of standard specimens (generally cubes) as required by the applicable standards. A simultaneous analysis of the way the tests are affected by the various parameters involved would be extremely complex. On the other hand, in the interpretation of test results and in the estimate of strength as cube strength, provided that the testing process has been carried out in a reasonably satisfactory manner and with suitable tools, it is possible to resort to statistical methods which may prove quite valuable. As a matter of fact, resorting to statistical concepts is virtually indispensable when analysing any test data that concern the mechanical strength of concrete, as obtained in the laboratory on a specimen tested in compression, even in the form of standard cubes. Under these conditions, from the results obtained for a sample of size n, it is possible to work out various parameters – such as mean strength, standard deviation, characteristic strength – and these may then be Editorial note F. Indelicato works at the Politecnico di Torino, Department of Structural Engineering, Italy, which is a RILEM Titular Member. 0025-5432/97 © RILEM 131 SCIENTIFIC REPORTS Estimate of concrete cube strength by means of different diameter cores: A statistical approach which is the quantity being assessed. This explains why the strength determined on cylindrical specimens obtained from cores and microcores drilled in situ will be different from the cube strength of specimens made at the time of casting. Vol. part of the test data and some considerations on the relationships between cube strength and microcore strength have already been published in earlier papers [1. All concrete mixes were produced with siliceous river aggregate. especially if we consider that in many cases the samples are taken precisely out of concern that the concrete does not possess sufficient strength. As for the latter. As is known. 3. The choice of large diameters is justified by the need to obtain specimens with an internal structure as homogeneous as possible. This would be true even if we assumed that it were possible to obtain perfectly-undamaged specimens. the use of statistical methods was indispensable. it is obvious that.Materials and Structures/Matériaux et Constructions. Obviously. with all of them being obtained from the same concretes. originating from different quarries. the range of test results studied has been widened and the comparison extended to include 70-mm diameter cores and small 45-mm diameter cores. even in these circumstances. planarity of the surfaces in contact with the plates. In this paper. Thus. The results and the relationships obtained were compared and analysed to assess their validity for the estimate of the cube strength of existing structures. all of them manufactured at industrial plants and intended for a great variety of building applications. one which can be obtained by imposing suitable conditions in relation to a greater or lesser number of parameters. Whatever the chosen diameter. such as cylinder and cube strength. but the relative humidity was reduced to 65%. resulting in higher costs and. 5] or 2 in. it is possible to define. several types of conventional compressive strengths. In this investigation. 390 small cores with 45-mm diameter and 160 cores with 70-mm diameter. Plasticizers were added to concrete types 2. compacting method employed. which relies on a test base of 1. with a maximum aggregate diameter of 30 mm in twelve cases and 25 mm in the four remaining cases. The aim of this investigation has been to develop and compare methods for the in situ estimation of cube strength by testing and comparing specimens of different diameters. [6]. less practical tools. such as specimen shape and size. April 1997 used as estimators to assess the corresponding parameters for the entire population being considered. type of testing machine. however. tests on small (45-mm) cores and. destructive core tests on 70-mm diameter specimens. The range of tests selected includes microcore testing. 11 and 13. and by the possibility of drilling out the samples more easily by means of smaller tools [10-12]. This characteristic. down to 50 mm [3. from the 29th to the 90th day. f inally. yet in some cases. reliable procedures must be available in order to compare the actual results with those that would have hypothetically been obtained on cubes. were selected so as to obtain concretes of nominal classes ranging from fck = 20 Nmm–2 to fck = 50 Nmm–2. the values may turn out to be very close. It is known. 480 microcores with 28mm diameter. in this particular case. whilst smaller diameter cores. the latter represent the “structure” and hence. curing conditions. In this investigation. 2. most international standards recommend minimum core diameters of 100 mm [3-5] or 4 in. height/base ratio. geometrically identical to those produced ad hoc. cube strength coincides with in situ strength. etc. In this manner. the cube strength obtained on specimens produced and tested according to the usual methodology will never be the same as the in situ cube strength. the choice of smaller diameters is motivated by the need to reduce costs and minimise damage to the structure. the volume of concrete to be drilled differs greatly from one type of test to another. that the results may be greatly affected by numerous factors. are accepted only in some particular cases. which are virtually equivalent. [7]. 2]. even when determined on specimens made from the same concrete as that used to build a structure. in fact.270 test results from compressive tests performed on 240 cubes with 150-mm sides. In any event. 30. In actual practice. a method which uses 28-mm diameter cores and may therefore be deemed as virtually non-destructive [13-16]. greater damage to the structure being evaluated. is not an absolute value since it may vary greatly. since the cores are taken directly from cubes. 132 . even for concrete specimens originating from the same mix. will necessarily be an estimated cube strength. however. above all. This consideration applies to any type of in situ estimate of strength. As far as the tests on cubes and those on 28-mm microcores are concerned. Before we proceed with a description of the testing procedures and the suggested method for the interpretation of the results. Concrete was cured for the first 28 days in a controlled environment at a temperature of 20 ± 1°C and a relative humidity of 90%. due to the interaction of parameters of opposite signs. this strength will be quite different from the strength that can be determined in situ. for instance. characterised by continuous grain size curves. rate of loading. it would seem advisable to explain what is meant by compressive strength of concrete. Hence the need to refer to a conventional definition of strength. specimen compacting and curing would still be different. and the severity of the damage to the structure also varies considerably. in situ cube strength. EXPERIMENTAL PROCEDURE The tests covered sixteen different types of concrete. as listed in Table 1. This should be viewed as a severe drawback. with sufficient accuracy. 9]. an increase in specimen size entails the use of heavier. The strength values measured on cubes and cores produced from the same concrete mixes were then used to work out the correlation curves and the relative confidence intervals. to be fully representative of the concrete being tested and to approximate the size of standard specimens [8. the temperature remained the same. age of the casting. Mix compositions. small cores and 70 mm cores).61 0. 1 – The specimens obtained from one of the eight concretes for which the program was extended to all four specimen types. showed quite effectively that within each single concrete.50 0. This choice was primarily inspired by operational considerations.65 0. a vacuum pump and a portable reservoir (for use when water is not readily available on site). the likelihood of a greater scatter in the results relating to geometrically smaller specimens. but it also made it possible to take into account.50 0. since the testing program has been devised for applications on existing structures. A series of Kolmogorov-Smirnov tests. and especially that of slenderness.62 0.c full sized cores.58 0. Fig.55 Fig. After that. 20 additional 70-mm cores. and .61 0. Initially. 11 daN for the pump and about as much for the reservoir) make it especially suitable for in situ use.59 0. with diameter = 45 mm. to make sure that the specimens would be cut when concrete strength had consolidated sufficiently. for which the testing program was extended to all 4 types of specimen (cubes.56 0.55 0. n = 30 for small 45-mm cores and for the 28mm microcores. In this respect. f 70.50 0. but considerably bigger and heavier. in qualitative terms. 1 shows a photograph – taken before the tests – of all the specimens obtained from one of the 8 concretes. however. To this end. where the mean . A relatively long curing period was selected in order to minimise the local differences associated with young concrete [13]. TEST RESULTS The main results of the compression tests are illustrated in Table 2. we were able to obtain 30 additional small cores. compression tests were performed on cubes and cores 90 days after the date of casting. The small dimensions and weight of the equipment (15 daN for the micro-drill. 45 and 70-mm specimens were obtained with another drilling unit. it should be noted first of all that sample size increases with decreasing geometric dimensions of the specimens. from n = 15 for cubes to n = 20 for 70mm cores.deter. are presented together with the standard deviation values relating to the four different types of specimen. microcores. and from 8 of the concretes.60 0.Indelicato Table 1 – Concrete mix characteristics Concrete No. of similar design.59 0. and finally because it was felt that a 90-day period would be more representative than the classical 28-day period. 133 . we again opted for an ᐍ/d ratio of 1 with the intention of minimising the influence of specimen shape. f . which represents an important simplification for further studies. sc. Cores and microcores were produced by moist cutting and were not capped before testing. s28. f . the plan was to produce 30 cubes with 150-mm sides from each concrete mix. microcores. from each cube. of aggregate (mm) 30 30 30 30 30 30 30 30 30 30 30 30 25 25 25 25 Cement content (kg m-3) 300 320 380 340 250 280 290 320 360 300 300 250 350 350 300 330 W/C 0. for the 28-mm diameter specimens. encompassing all the individual concretes and all types of specimen.58 0. the first step was to evaluate the type of distribution in the results. small cores. 3.strength values mined on cubes. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Type of Portland cement 325 425 425 325 325 425 325 325 325 325 425 325 525 425 325 425 Max diam. it was decided to extend the investigation and increase the number of cubes produced so as to be able to work on bigger diameter cores. Following the tests on the first three concrete types. The drilling equipment. the investigation had been conceived with the aim of studying solely the relationships between cube and microcore strength. half of which would be used for direct compression tests and the other half to produce. the populations being examined were all of the normal type. From each of the newly-manufactured concretes. In the analysis of the experimental data. includes a microcore drilling unit fitted with a suction anchorage device.75 0. a specimen 150 mm in length and 28 mm in diameter. s45 and s70. For these last two types of specimen. f 28 45. in the comparison of cube and core strengths. two microcores with length equal to diameter would be produced from each specimen and subjected to compression tests. on the basis of n pairs of available observations estimator ρ (xi.6 23.959. i.43 6.9 40.12 4.7 29.84 2.11 1. However.n. At this point. (4) and (5) are represented in graphic form in Fig.5 36.60 2.3 21.1. Finally. f 45 and f 70. .01 1. and hence quite satisfactory in relation to the number of pairs of observations taken into consideration.1.61 5. to estimate ρ we must use an ^.31 5.6 30.59 2.79 5.9 44. With the data available..8 49.1 24.86 5. well 2 below the value of 0.2 33. to 16 estimate cube strength on the basis of measurements obtained on other types of specimen. the least 10 favourable case is observed for group No. ρ45 = 0.048 + 1.1 42.22435.67 5.16289).57 1.12 1.5 28. it can be seen that all of these straight lines are very close to one another.1 29. let us now turn to the estimate of the parameters of the straight lines. at first glance they suggest that the hypothesis of a linear correlation between mean cube strength and core strength is highly probable. the maximum absolute difference between the value measured and the theoretical value in the case of normal distribution Concrete No. for 30 speci9 mens. we must first of all determine the density-functions of X and Y.0 47. f 45 and f 70.66 1.017 f 70 (4) fc = 1.19838) and for 6 small cores to concrete type 8 (0.27 5.34 3. respectively.96 1. f 45 and f 28.12 2.8 43. lower than the 12 limit of 0. with a 134 .1 24. which turned out to be basically equivalent: ρ 28 ^ ^ ^ ρ 45 ′ = 0. in order to determine the value of this coefficient. From an examination of equations (3).30 corresponding to a risk 3 α = 0. whilst are: f 70.65 2.0 48. Y .0 27. a and b parameters can be estimated by means of A and B estimators starting from the pair of values xi. X and Y. the values of the correlation coeffi^ ^ cients obtained are.2 30. 2. thereby suggesting the existence of linear correlations. 30.4 24.0 34.44 1.4 28. In this respect.1 27.60 6.1.9 30. This finding is borne out by a comparison which the estimates of the correlation coefficients determined for the eight concrete types common to all four kinds of specimens.75 6. In our case. the regression model is given by: Y = a + bX (2) In our case.47 5.68 3.4 31.0 28. the correlation coefficient can be estimated by means of: ˆ= ρ ˆ X.22.67 1. Vol. the 8 value corresponding to α = 0.89 7. and a 13 sample size of 20. f 28..9 41. by taking mean cube strength as the reference value.2 32.93 4. respectively.617 + 1.49 8.57 3.22 2.Materials and Structures/Matériaux et Constructions. for 15 specimens [17].2 33. fc.08 5.8 18.6 24.6 28.59 1.255 f 28 Equations (3). ^ ′ = 0. Y is always represented by f the variables corresponding to X . for a more rigorous comparison between the different correlation coefficients and to confirm the hypothesis of a linear correlation. is the linear correlation coefficient. we obtain the following straight lines: (3) fc = 0. three t tests were performed by taking into account the different sizes of the samples represented.882.values. 13 and 8 pairs of data.35 1. applies to cube group No..71 2.99 4. yi determined from the tests through the least squares method.81 4.3 30. the other values lie around the reference value with relatively small differences. 4.1 40.5 39. and the strength . by 16. All these values are close to one.44 5..1 37. (4) and (5).36 2.65 3. with 7 both of these values being lower than 0.959. Thus.4 41.determined on different types of specimens.15 4.43 2. ^ ρ70 = 0. In general..41 5.647 + 1.935.3 24. The tests confirmed the existence of the correlation.is represented by the fc values.53 6.c. yi).1% and no substantial difference between the three cases [18]. for 70-mm cores. whilst X is represented by f 28. ρ.8 47. 15.9 31. for which the 1 least favourable situation occurs: 0.e.4 47.1 27. The theoretical parameter employed to measure the linear relationship between two variables.08 risk of error much lower than 0. 4 the absolute difference applies to concrete type 5 11 (the least favourable case: 0. Consequently.09 2.2 34. especially the ones relating to the ( ) ˆ ⋅ varY ˆ varX (1) With our data. A qualitative examination of the results listed in Table 2 shows that.942.8 22.23222.8 33. it should be noted that equation (5) had already been presented in an earlier paper [1].7 52.929.06 4.0 39.6 34..4 0. where i = 1 . CORRELATION LAWS Having ascertained that the linear regression model is suitable for the representation of the relationships between mean cube strength and mean core strength for the three different diameters. ρ 70 ′ = ρ70 = 0.26 corresponding to α = 0.059 f 45 (5) fc = .for the three regressions. the results were quite 14 satisfactory for tests of this type.4.7 35.1 27. Y cov Table 2 – Experimental results fc f 28 f 45 f 70 sc s28 s45 s70 -2 -2 -2 (Nmm ) (Nmm ) (Nmm ) (Nmm-2) (Nmm-2) (Nmm-2) (Nmm-2) (Nmm-2) 23. 15 As for the main problem at hand.8 24.84 5. the first step consisted of evaluating the analytical relationships between mean cube strength.93 4.98 5. respectively: ρ 28 = 0.22 8.2 22.80 4. 11 with a difference of 0. since we are dealing with estimates. April 1997 In particular. For microcores. 10.66 2. vs.of mean cube strength. In light of the foregoing. It can also be noted that the integral of the function of the square difference between straight lines (3). (4). or concerning the number of holes to be drilled and the costs involved. albeit farther from the ideal straight line. f 28. (6). f c.fc = f cores (6) which would imply the identity of cube and core tests. In this sense. while the angular coefficient decreases approaching 1. The known term. but not substantial. The first interval is expressed by the well-known relationship: A + Bx ± t α s y x 2 1 + n ( x − x) ∑ ( x − x) 2 i 2 (7) and the second interval by: A + Bx ± t α s y x 2 1 1+ + n ( x − x) ∑ ( x − x) 2 i 2 (8) 135 . the regression lines would come close to line (6). f c. the choice may be heavily affected by considerations as to the opportunity of making greater or smaller diameter holes. it can be stated that with increasing specimen diameter we approach the optimal condition expressed in equation (6). we should take into account the different scatter in the data around them and assess the confidence intervals of the straight lines as well as the confidence intervals of individual observations.. it is obvious that when working on a construction site. it can be inferred that if it were possible to increase the number of concrete types being tested. however. For our purposes. (4) and (5) are estimates.lines . For these mixes. (4).e. in specimen volume. the results were predictable on the basis of common experience. 2 – Regression straight . f 45. improvement with increasing specimen diameter. the ideal situation would occur if it were possible to work on specimens whose results would lead to a relationship of the type: . is seen to decrease in absolute value approaching zero. it is possible to plot the three lines shown in Fig. on the basis of equations (3). the interesting fact herein is that the differences observed are always minimal. 2. it might therefore seem logical to conclude that the estimate of mean cube strength can be determined on the basis of tests performed on any of the three types of specimen considered. A confirmation of the results described above has been obtained by comparing the regression straight lines determined by processing the data relating to the eight concrete mixes used to produce all four types of specimen. Since the straight lines represented by equations (3). Fig. which have virtually identical angular coefficients very close to 1. i. Consequently. vs mean core strength values as determined by processing the data related to the eight concrete mixes used to produce all four types of specimen. despite the considerable differences in specimen diameter and. with a progressive. 3 – Regression straight lines of mean cube strength. mean core strength: f 70. From an initial examination. (5) and (6) decreases with increasing diameter. above all. while the others are rather close to lines (4) and (5). one of which coincides with straight line (3). at least as far as the mean strength is concerned. However.Indelicato Fig. specimens with 70 and 45-mm diameters. and the straight line which would represent the identity of cube and core tests. in fact. 3. (5) and Fig. α/2)% of the mean strength values lie.. it is not possible to identify .219. even through it yields the most probable value. 4 – Two-sided 80% confidence intervals for mean cube strength. reveals that the width of the intervals is essentially the same for the different specimen diameters.. there is an α/2% chance that t > tα/2. we can identify the limits within . In this connection.029 ) 2 (10) 136 .. Such limits are expressed by the relationships: fce = 0. it might be advisable to concentrate only on the lower limits of these intervals so as to identify the region above which not (1 .straight line (.167 decrease with increasing specimen diameter.-) as a function of mean microcore strength: f 28. if we consider the values of sy|x as a summary estimate of variability around the straight lines. sc|45 = 3.in . and for the regression .α)% but rather (1 .167t α 2 Fig. it should be pointed out that while from the statistical standpoint it might be of greater interest to refer to bilateral confidence intervals. 4.which straight . f c (___). This type. The confidence intervals involved for α = 0. 5 and 6. and for the regression straight line (. 30.of procedure may prove useful when the evaluation of fc though a simple correlation law. where: (9) n−2 and t is such that.-) as a function of mean core strength: f 70. verified by a numerical check. By observing strength relationships from the standsy x = i=1 ∑ (y − A − Bx ) i i n 2 (f 1. April 1997 Fig..017f70 − 3.(2) and . and sc|70 = 3. implies the possibility that 50% of the cases might fall above or below this value.the individual . for the t-distribution with n-2 d. f c (___). we find that the three values: sc|28 = 4. f 45 and f 70 will lie with a certain probability. Vol. 6 – Two-sided 80% confidence intervals for mean cube strength. and for the regression . from the standpoint of design.-) as a function of mean small core strength: f 45. Fig. point of the confidence intervals.357.20 are illustrated in Figs. as could be expected on the basis of physical considerations. f c (___).125 + 70 − 36. 5 – Two-sided 80% confidence intervals for mean cube strength.a substantial-difference the validity of the estimates of fc obtained from f28.131 662. However. f45 or f70.Materials and Structures/Matériaux et Constructions.f.line values of fc as a function of f 28. A visual examination of these figures. In any event.647 + 1.straight line (. fc. the three curves are rather close.Indelicato fce = 1. (11) and (12) the corresponding values of tα/2 to obtain similar relationships. the situation is conceptually different. since the straight lines (3). Consequently. Disregarding the problems pertaining to characteristic strength. we find that with decreasing specimen diameter.as determined.470 803. and therefore express a direct link between the strength values of the two different specimen types. 7. (11) and (12) are plotted for α = 0.357t α ) 2 (f 1. In this context.470 . f 70. it is possible. is in the three cases being considered: ∑f n 70 = 36. for which a partial solution has already been proposed [16] and which are currently being investigated further. the evolution of the . that from an examination of the test results listed in Table 2. to introduce into equations (10). in which the term – x.a rather conservative estimate of mean cube strength.shows that the scatter of the mean values f 70. Incidentally. based on statistical considerations [20]. it should be noted that the methods for interpreting test results proposed in this paper may also be used for tests of different kinds.36 for relationship (11) relating to small 45-mm diameter cores.44 for relationship (10) relating to 70-mm diameter cores. Obviously. provided that the tests are linearly correlated with cube strength.limit . 7 – Lower limits of the . by selecting suitable values of α. on small cores. the variances relating to individual concrete mixes deviate to an ever greater extent from the reference variances of the cubes. f c.390 661. In particular. equations (10). 7 clearly shows that Fig.131 . fck. However. f 45 and f 28. where microcore testing is concerned.strength. that equations (10). ∑f n 45 = 31.931 ) 2 (11) fce = −4.059f45 − 3.617 + 1. (4) and (5) nearly coincide.76 ) 2 (12) originating from equation (8). On the other hand.34 for microcores.curves . as a function of mean core strength: f 70.g. f 45. representing the mean of the mean values of core strength. or on cores. mean cube strength can be estimated almost regardless of the test data relating to the different types of core. The values obtained from such cores will therefore represent an estimated in situ cube strength wherein the term estimated should be construed as having a wider meaning than its purely statistical connotation. since it means that when tests are conducted for practical application purposes on small diameter specimens. whether we wish to improve the confidence level or accept a lower level. about 90% of the mean strength values will then fall in the region above them. when the tests are conducted on a real structure. compacting and curing conditions. it should be noted that an analysis of equations (10). and tα/2 = 1. a solution based on the test data described in this article was worked out through a procedure involving a comparison of the confidence intervals for microcore and cube mean strength values [16]. preferably. 137 .. 19] or. the solution can be empirical [9.077 + 2 ( f45 − 31. starting from. however.062 + 28 − 31.20. such as the estimate of cube strength from the results of other types of tests. ∑f n 28 = 31.048 + 1.219t α 1. corresponding to: tα/2 = 1. In any event. f 45 and f 28 around the regression straight lines remains virtually constant for varying specimen diameters. e. as is the case in all tests aimed at estimating strength on standard samples on the basis of results obtained from tests of a different nature. we should resort to bigger samples if the results are to be sufficiently reliable.390 In Fig.one-sided 90% confidence intervals for cube . (11) and (12) and Fig.255f28 − 4.a mean strength value . the cores are in fact taken from concrete whose characteristics are different from those of the cubes in several respects. This feature has major implications when core testing is used to estimate characteristic cube strength. It should be borne in mind. and it also has considerable implications when this testing method is applied to the estimate of mean strength. As documented in the literature. these relationships can be used with an adequate margin of confidence as empirical laws for . In such circumstances. however. tα/2 = 1. it should be kept in mind.on microcores. fc.mean . it should be noted that the problem of sample size in this type of test is not to be neglected. as discussed in this paper. For application purposes. (11) and (12) represent relationships obtained from a testing campaign conducted on cubes and cores taken from cubes produced from the same concrete mixes. f 28. London. F. As a consequence. R.. 390 45-mm diameter cores and 160 70-mm diameter cores. 667. [8] Petersons. A. F. for the same confidence level. ‘Properties of Concrete’. have shown that: • There are very strong linear correlations between mean cube strength values and the mean strength values determined on cores of the three diameters studied (28. Mater. 1993) 1-20. • The proposed methods can be used for in situ tests in estimating cube strength on concrete types similar to those discussed above. on small cores. ‘Probability. and Indelicato. in Proceedings of the International Conference on Nondestructive Testing of Concrete in the Infrastructure’. ‘Probability and Statistics in the Engineering and Computing Sciences’ (McGraw-Hill International Editions. Statistics and Decision for Civil Engineers’ (McGraw-Hill Publishing Company. ‘Evaluation of small diameter core tests to determine in situ strength of concrete’. depending on the chosen core diameter. USA. Mater.. J. R... Philadelphia. ‘Prüfverfahren für Beton. in Proceedings of IABSE 13th Congress.. 1970) 466-475. June 1988.. ACI 301-84 (American Concrete Institute. P.. [19] Neville. Struct. with straight lines displaying angular coefficients very close to 1. starting from a given -mean . turn out to be very close to one another. Bestimmung der Bruckfestigkeit von Festbeton in Bauwerken und Bauteilen’ (Deutsches Institut für Normung. • The correlation laws are very close. [12] BS 1881: Part 201. 45 or 28-mm diameters.Taking examination and testing in compression’. or strength determined on cores.Basi teoriche e prime esperienze’. [5] DIN 1048 Teil 2. Malhotra Ed. ‘Nondestructive characterisation of concrete and damage / fracture diagnosis of civil structures and infrastructures’. Magazine of Concrete Research 40 (143) (1988) 99-105. that with increasing specimen diameter. La Prefabbricazione 22 (11) (1986) 651-664. [4] BS 1881: Part 120. 1981) 566 pp. ‘Contract strength requirements . P. Indelicato. ‘In place methods for determination of strength of concrete’. Copenhagen. I. with account being taken of the fact that the choice of core diameter has no significant repercussions on the accuracy of the results... f 45. ACI Journal 74 (4) (1977) 163-172. 1991). J. V. Michigan. 1983). A. 30. [18] Milton. ‘Cores of hardened concrete . 3rd edn. with all of them being characterised by basically equivalent correlation coefficients. April 1997 5. [11] Yip. and Cornell. [7] ACI Committee 301. Draft International Standard (International Organization of Standardization. [15] Bocca. Berlin. New York. and Arnold. ACI Materials Journal 85 (5) (1988) 446-471. ‘Guide to the use of non-destructive methods of test for hardened concrete’ (British Standard Institution. P. fc. [14] Bocca.. 26 (159) (1993) 261267. to the desired confidence level. the identity between cube and core mean strength improves. 379384. J. 1984).C..K. 1983). 480 28-mm diameter microcores. almost indifferently..M. REFERENCES [1] Indelicato. New York. albeit slightly. 45 and 70 mm).M. W. f 70 on microcores.270 compressive tests performed on 240 cubes with 150-mm sides. Detroit. mean cube strength can be estimated. ‘Size effects and statistical problems of microcores in the re-evaluation of existing structures’. f 28. S. Dearborn. London. and Al-Hamed. F. il Cemento 86 (4) (1989) 229-238.M. C. Carpinteri. CONCLUSIONS The results of 1.T. C. all of them produced from 16 concrete mixes of classes ranging from fck = 20 to fck = 50 Nmm-2 and with siliceous river aggregate of different origins and a maximum grain size of 30 mm. F. • The confidence limits being considered are represented by curves which. [2] Indelicato. Iori. [3] ISO/DIS 7032. 4 (24) (1971) 379398. ‘The use of microcores in structural assessment’. in Proceedings of DABI Symposium. [20] ACI Committee 228. it is therefore possible to proceed with tests which.. June 1988.Materials and Structures/Matériaux et Constructions. [17] Benjamin. will range from destructive to virtually non-destructive. and Valente. 1990). on specimens with 70. 1993 (Society for Experimental Mechanics. Vol. Struct. 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