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

131

Materials and Structures/Matriaux et Constructions, Vol. 30, April 1997, pp 131-138

0025-5432/97 RILEM

SCIE

NTI

FIC

REP

OR

TSEstimate of concrete cube strength by means of different diameter cores: A statistical approach

F. IndelicatoDepartment of Structural Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy

sake of comparison, the values obtained must be expressedin terms of the strength of standard specimens (generallycubes) as required by the applicable standards.

A simultaneous analysis of the way the tests areaffected by the various parameters involved would beextremely complex. On the other hand, in the interpre-tation of test results and in the estimate of strength ascube strength, provided that the testing process has beencarried out in a reasonably satisfactory manner and withsuitable tools, it is possible to resort to statistical methodswhich may prove quite valuable.

As a matter of fact, resorting to statistical concepts is vir-tually indispensable when analysing any test data that con-cern the mechanical strength of concrete, as obtained in thelaboratory on a specimen tested in compression, even in theform of standard cubes. Under these conditions, from theresults obtained for a sample of size n, it is possible to workout various parameters such as mean strength, standarddeviation, characteristic strength and these may then be

1. INTRODUCTION

Among the various methods employed for the assess-ment of concrete strength in situ, the classical method,involving compression tests on cylindrical specimensproduced from cores drilled out of the structure, shouldsurely be recognised as having primary importance onaccount of the reliability and accuracy of the results.

However, although these tests are quite simple to con-duct, the results obtained may sometimes contain consid-erable errors because of the great variety of parametersinvolved (core diameter, specimen length/diameter ratio,specimen moisture at the time of testing, aggregate size,type of diamond wheel employed, damage caused bydrilling and specimen preparation, size effects). Anothercause of uncertainty lies in the methods adopted to inter-pret the test results, since the measuring process must nec-essarily begin with a more or less accurate estimate ofstrength from tests performed on cores, and then, for the

R S U M

Cet article prsente une mthode dinterprtation des rsultatsdessais permettant destimer, avec des niveaux de confiance suffi-sants, la rsistance sur cube du bton partir de carottes de dia-mtre divers. cet effet, 1 270 rsultats dessais de compressionsur des cubes de 150 mm de ct et sur des carottes types de70 mm de diamtre, de petites carottes de 45 mm de diamtre etdes microcarottes de 28 mm de diamtre sont dvelopps aumoyen de mthodes statistiques pouvant galement tre appliques linterprtation dautres types dessais. Les lois de corrlationentre les rsistances des cubes et des carottes de diffrents diamtressont dtermins et discutes. Les relations qui expriment leslimites infrieures de confiance pour les observations individuellesfutures sont labores, compares entre elles par rapport linfluence des diffrents diamtres des carottes, et proposes pourlestimation in situ de la rsistance sur cube.

A B S T R A C T

This paper describes a method for the interpretationof test results which makes it possible to estimate con-crete cube strength from cores of various diameters withsuitable confidence levels. To this end, 1,270 results ofcompression tests carried out on cubes with 150 mmsides, on typical small and micro-cores (70, 45 and 28mm in diameter, respectively), have been elaboratedwith the aid of statistical methods, which can also beused for different types of test. The laws of correlationbetween cube strength and the strength values obtainedfrom the different diameter cores are determined anddiscussed. The relationships expressing the lower confi-dence limits for future individual observations are devel-oped, compared with one another in relation to theinf luence of core diameters, and proposed for the in situestimate of cube strength.

Editorial noteF. Indelicato works at the Politecnico di Torino, Department of Structural Engineering, Italy, which is a RILEM Titular Member.

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Materials and Structures/Matriaux et Constructions, Vol. 30, April 1997

used as estimators to assess the corresponding parametersfor the entire population being considered.

In this investigation, which relies on a test base of1,270 test results from compressive tests performed on240 cubes with 150-mm sides, 480 microcores with 28-mm diameter, 390 small cores with 45-mm diameter and160 cores with 70-mm diameter, the use of statisticalmethods was indispensable.

As far as the tests on cubes and those on 28-mm micro-cores are concerned, part of the test data and some consid-erations on the relationships between cube strength andmicrocore strength have already been published in earlierpapers [1, 2]. In this paper, the range of test results studiedhas been widened and the comparison extended to include70-mm diameter cores and small 45-mm diameter cores,with all of them being obtained from the same concretes.

As is known, most international standards recom-mend minimum core diameters of 100 mm [3-5] or 4 in.[6], which are virtually equivalent, whilst smaller diame-ter cores, down to 50 mm [3, 5] or 2 in. [7], are acceptedonly in some particular cases.

In any event, an increase in specimen size entails theuse of heavier, less practical tools, resulting in highercosts and, above all, greater damage to the structurebeing evaluated. This should be viewed as a severe draw-back, especially if we consider that in many cases thesamples are taken precisely out of concern that the con-crete does not possess sufficient strength. The choice oflarge diameters is justified by the need to obtain speci-mens with an internal structure as homogeneous as pos-sible, to be fully representative of the concrete beingtested and to approximate the size of standard specimens[8, 9]; the choice of smaller diameters is motivated bythe need to reduce costs and minimise damage to thestructure, and by the possibility of drilling out the sam-ples more easily by means of smaller tools [10-12].

Whatever the chosen diameter, reliable proceduresmust be available in order to compare the actual resultswith those that would have hypothetically been obtainedon cubes.

The aim of this investigation has been to develop andcompare methods for the in situ estimation of cubestrength by testing and comparing specimens of differentdiameters. The range of tests selected includes microcoretesting, a method which uses 28-mm diameter cores andmay therefore be deemed as virtually non-destructive[13-16], tests on small (45-mm) cores and, f inally,destructive core tests on 70-mm diameter specimens.Obviously, the volume of concrete to be drilled differsgreatly from one type of test to another, and the severityof the damage to the structure also varies considerably.

The strength values measured on cubes and cores pro-duced from the same concrete mixes were then used towork out the correlation curves and the relative confi-dence intervals. The results and the relationships obtainedwere compared and analysed to assess their validity for theestimate of the cube strength of existing structures.

Before we proceed with a description of the testingprocedures and the suggested method for the interpreta-tion of the results, it would seem advisable to explain

what is meant by compressive strength of concrete. Thischaracteristic, in fact, is not an absolute value since itmay vary greatly, even for concrete specimens originat-ing from the same mix. It is known, for instance, thatthe results may be greatly affected by numerous factors,such as specimen shape and size, compacting methodemployed, height/base ratio, age of the casting, curingconditions, type of testing machine, planarity of the sur-faces in contact with the plates, rate of loading, etc.

Hence the need to refer to a conventional definition ofstrength, one which can be obtained by imposing suitableconditions in relation to a greater or lesser number of para-meters. In this manner, it is possible to define, with suffi-cient accuracy, several types of conventional compressivestrengths, such as cylinder and cube strength.

As for the latter, it is obvious that, even when deter-mined on specimens made from the same concrete asthat used to build a structure, this strength will be quitedifferent from the strength that can be determined insitu. This would be true even if we assumed that it werepossible to obtain perfectly-undamaged specimens, geo-metrically identical to those produced ad hoc; even inthese circumstances, however, specimen compacting andcuring would still be different. Thus, the cube strengthobtained on specimens produced and tested according tothe usual methodology will never be the same as the insitu cube strength. This explains why the strength deter-mined on cylindrical specimens obtained from cores andmicrocores drilled in situ will be different from the cubestrength of specimens made at the time of casting; yet insome cases, due to the interaction of parameters ofopposite signs, the values may turn out to be very close.This consideration applies to any type of in situ estimateof strength. In this investigation, since the cores aretaken directly from cubes, the latter represent the struc-ture and hence, in this particular case, cube strengthcoincides with in situ strength. In actual practice, how-ever, in situ cube strength, which is the quantity beingassessed, will necessarily be an estimated cube strength.

2. EXPERIMENTAL PROCEDURE

The tests covered sixteen different types of concrete,all of them manufactured at industrial plants and intendedfor a great variety of building applications. Mix composi-tions, as listed in Table 1, were selected so as to obtainconcretes of nominal classes ranging from fck = 20 Nmm2to fck = 50 Nmm2.

All concrete mixes were produced with siliceousriver aggregate, originating from different quarries, char-acterised by continuous grain size curves, with a maxi-mum aggregate diameter of 30 mm in twelve cases and25 mm in the four remaining cases. Plasticizers wereadded to concrete types 2, 3, 11 and 13.

Concrete was cured for the first 28 days in a controlledenvironment at a temperature of 20 1C and a relativehumidity of 90%; from the 29th to the 90th day, the tem-perature remained the same, but the relative humidity wasreduced to 65%.

133

Initially, the investigation had been conceived withthe aim of studying solely the relationships between cubeand microcore strength. To this end, the plan was toproduce 30 cubes with 150-mm sides from each con-crete mix, half of which would be used for direct com-pression tests and the other half to produce, from eachcube, a specimen 150 mm in length and 28 mm in diam-eter. After that, two microcores with length equal todiameter would be produced from each specimen andsubjected to compression tests. Following the tests onthe first three concrete types, however, it was decided toextend the investigation and increase the number ofcubes produced so as to be able to work on bigger diam-eter cores. From each of the newly-manufactured con-cretes, we were able to obtain 30 additional small cores,with diameter = 45 mm, and from 8 of the concretes, 20additional 70-mm cores. For these last two types of spec-imen, we again opted for an /d ratio of 1 with the inten-tion of minimising the inf luence of specimen shape, andespecially that of slenderness, in the comparison of cubeand core strengths.

Fig. 1 shows a photograph taken before the tests of all the specimens obtained from one of the 8 con-cretes, for which the testing program was extended to all4 types of specimen (cubes, microcores, small cores and70 mm cores).

The drilling equipment, for the 28-mm diameterspecimens, includes a microcore drilling unit fitted witha suction anchorage device, a vacuum pump and aportable reservoir (for use when water is not readilyavailable on site). The small dimensions and weight ofthe equipment (15 daN for the micro-drill, 11 daN forthe pump and about as much for the reservoir) make itespecially suitable for in situ use; 45 and 70-mm speci-mens were obtained with another drilling unit, of similardesign, but considerably bigger and heavier.

Cores and microcores were produced by moist cut-ting and were not capped before testing; compression

tests were performed on cubes and cores 90 days afterthe date of casting. A relatively long curing period wasselected in order to minimise the local differences associ-ated with young concrete [13], to make sure that thespecimens would be cut when concrete strength hadconsolidated sufficiently, and finally because it was feltthat a 90-day period would be more representative thanthe classical 28-day period, since the testing program hasbeen devised for applications on existing structures.

3. TEST RESULTS

The main results of the compression tests are illus-trated in Table 2, where the mean strength values deter-mined on cubes, fc

-, microcores, f

-28, small cores, f

-45, and

full sized cores, f-

70, are presented together with the stan-dard deviation values relating to the four different typesof specimen, sc, s28, s45 and s70.

In this respect, it should be noted first of all that sam-ple size increases with decreasing geometric dimensionsof the specimens, from n = 15 for cubes to n = 20 for 70-mm cores, n = 30 for small 45-mm cores and for the 28-mm microcores. This choice was primarily inspired byoperational considerations, but it also made it possible totake into account, in qualitative terms, the likelihood ofa greater scatter in the results relating to geometricallysmaller specimens.

In the analysis of the experimental data, the first stepwas to evaluate the type of distribution in the results. Aseries of Kolmogorov-Smirnov tests, encompassing allthe individual concretes and all types of specimen,showed quite effectively that within each single con-crete, the populations being examined were all of thenormal type, which represents an important simplifica-tion for further studies.

Indelicato

Concrete Type of Max diam. CementNo. Portland of aggregate content W/C

cement (mm) (kg m-3)

1 325 30 300 0.752 425 30 320 0.553 425 30 380 0.504 325 30 340 0.615 325 30 250 0.606 425 30 280 0.597 325 30 290 0.618 325 30 320 0.629 325 30 360 0.58

10 325 30 300 0.5911 425 30 300 0.5012 325 30 250 0.6513 525 25 350 0.5014 425 25 350 0.5615 325 25 300 0.5816 425 25 330 0.55

Table 1 Concrete mix characteristics

Fig. 1 The specimens obtained from one of the eight concretesfor which the program was extended to all four specimen types.

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In particular, the maximum absolute differ-ence between the value measured and the theo-retical value in the case of normal distributionapplies to cube group No. 10, for which theleast favourable situation occurs: 0.22435, wellbelow the value of 0.30 corresponding to a risk = 0.1, for 15 specimens [17]. For microcores,the absolute difference applies to concrete type11 (the least favourable case: 0.19838) and forsmall cores to concrete type 8 (0.16289), withboth of these values being lower than 0.22, thevalue corresponding to = 0.1, for 30 speci-mens. Finally, for 70-mm cores, the leastfavourable case is observed for group No. 15,with a difference of 0.23222, lower than thelimit of 0.26 corresponding to = 0.1, and asample size of 20. Thus, the results were quitesatisfactory for tests of this type.

As for the main problem at hand, i.e. toestimate cube strength on the basis of mea-surements obtained on other types of speci-men, the first step consisted of evaluating theanalytical relationships between mean cube strength, fc

-,

and the strength values determined on different types ofspecimens, f

-28, f

-45 and f

-70.

A qualitative examination of the results listed inTable 2 shows that, by taking mean cube strength as thereference value, the other values lie around the referencevalue with relatively small differences, thereby suggestingthe existence of linear correlations.

The theoretical parameter employed to measure thelinear relationship between two variables, X and Y, is thelinear correlation coefficient, ; in order to determine thevalue of this coefficient, we must first of all determine thedensity functions of X and Y. In our case, Y is representedby the fc

-values, whilst X is represented by f

-28, f

-45 and f

-70,

respectively. Consequently, to estimate we must use anestimator ^, on the basis of n pairs of available observations(xi, yi), where i = 1 .....n.

At this point, the correlation coefficient can be esti-mated by means of:

(1)

With our data, the values of the correlation coeffi-cients obtained are, respectively: ^28 = 0.882; ^45 = 0.942;^70 = 0.959. All these values are close to one, and hencequite satisfactory in relation to the number of pairs ofobservations taken into consideration; at f irst glancethey suggest that the hypothesis of a linear correlationbetween mean cube strength and core strength is highlyprobable.

However, since we are dealing with estimates, for amore rigorous comparison between the different corre-lation coefficients and to confirm the hypothesis of alinear correlation, three t tests were performed by takinginto account the different sizes of the samples repre-sented, respectively, by 16, 13 and 8 pairs of data. Thetests confirmed the existence of the correlation, with a

cov

= ( )

X, Y

varX varY

risk of error much lower than 0.1% and no substantialdifference between the three cases [18]. This finding isborne out by a comparison which the estimates of thecorrelation coefficients determined for the eight con-crete types common to all four kinds of specimens,which turned out to be basically equivalent: ^ 28 = 0.935;^ 45 = 0.929; ^ 70 = ^70 = 0.959.

4. CORRELATION LAWS

Having ascertained that the linear regression model issuitable for the representation of the relationshipsbetween mean cube strength and mean core strength forthe three different diameters, let us now turn to the esti-mate of the parameters of the straight lines.

In general, the regression model is given by:

Y = a + bX (2)

In our case, for the three regressions, Y is always rep-resented by fc

-, whilst the variables corresponding to X

are: f-

70, f-45 and f

-28; a and b parameters can be estimated

by means of A and B estimators starting from the pair ofvalues xi, yi determined from the tests through the leastsquares method.

With the data available, we obtain the followingstraight lines:

fc-

= 0.647 + 1.017 f-

70 (3)

fc-

= 1.048 + 1.059 f-

45 (4)

fc-

= - 4.617 + 1.255 f-

28 (5)

Equations (3), (4) and (5) are represented in graphicform in Fig. 2. In this respect, it should be noted thatequation (5) had already been presented in an earlierpaper [1]. From an examination of equations (3), (4) and(5), it can be seen that all of these straight lines are veryclose to one another, especially the ones relating to the

Concrete f-c f

-28 f

-45 f

-70 sc s28 s45 s70

No. (Nmm-2) (Nmm-2) (Nmm-2) (Nmm-2) (Nmm-2) (Nmm-2) (Nmm-2) (Nmm-2)

1 23.5 18.8 - - 0.59 2.84 - -2 39.4 33.8 - - 1.66 5.89 - -3 47.2 43.6 - - 2.44 7.47 - -4 33.9 34.4 31.2 - 1.11 5.75 5.06 -5 30.0 31.1 33.1 35.1 1.65 6.08 4.93 5.446 34.4 27.7 29.3 - 3.66 5.53 4.12 -7 24.1 29.5 21.8 - 1.96 6.34 2.65 -8 27.4 28.6 24.2 - 1.57 3.60 2.84 -9 28.0 28.0 22.6 24.0 1.22 6.15 2.36 5.22

10 27.8 28.1 24.0 - 2.59 4.49 2.61 -11 49.1 40.8 47.3 48.6 2.01 8.12 5.68 8.3512 24.7 22.4 24.9 23.8 1.71 4.81 3.43 1.8613 52.1 41.2 44.1 47.9 2.12 4.41 6.99 5.4314 42.6 34.1 37.2 40.2 1.67 5.67 4.80 2.9315 30.9 27.3 32.5 30.0 1.09 5.31 4.57 4.7916 41.8 30.9 36.7 39.4 2.60 5.27 3.98 5.08

Table 2 Experimental results

135

specimens with 70 and 45-mm diameters, which havevirtually identical angular coefficients very close to 1.

For our purposes, the ideal situation would occur if itwere possible to work on specimens whose results wouldlead to a relationship of the type:

fc-

= f-

cores (6)

which would imply the identity of cube and core tests, atleast as far as the mean strength is concerned.

In light of the foregoing, on the basis of equations(3), (4), (5) and Fig. 2, it can be stated that with increas-ing specimen diameter we approach the optimal condi-tion expressed in equation (6). The known term, in fact,is seen to decrease in absolute value approaching zero,while the angular coefficient decreases approaching 1.

It can also be noted that the integral of the functionof the square difference between straight lines (3), (4),(5) and (6) decreases with increasing diameter.

In this sense, the results were predictable on the basisof common experience; however, the interesting factherein is that the differences observed are always mini-mal, despite the considerable differences in specimendiameter and, above all, in specimen volume.

A confirmation of the results described above has beenobtained by comparing the regression straight lines deter-mined by processing the data relating to the eight concretemixes used to produce all four types of specimen.

For these mixes, it is possible to plot the three linesshown in Fig. 3, one of which coincides with straightline (3), while the others are rather close to lines (4) and(5), albeit farther from the ideal straight line, i.e. (6).Consequently, it can be inferred that if it were possibleto increase the number of concrete types being tested,the regression lines would come close to line (6).

From an initial examination, it might therefore seemlogical to conclude that the estimate of mean cubestrength can be determined on the basis of tests per-formed on any of the three types of specimen consid-ered, with a progressive, but not substantial, improve-ment with increasing specimen diameter. However, it isobvious that when working on a construction site, thechoice may be heavily affected by considerations as tothe opportunity of making greater or smaller diameterholes, or concerning the number of holes to be drilledand the costs involved.

Since the straight lines represented by equations (3),(4) and (5) are estimates, we should take into account thedifferent scatter in the data around them and assess theconfidence intervals of the straight lines as well as theconfidence intervals of individual observations.

The f irst interval is expressed by the well-knownrelationship:

(7)

and the second interval by:

(8)

A Bx t sn

x x

x xy x

i

+ + +( )( )2

2

21

1

A Bx t sn

x x

x xy x

i

+ +( )( )2

2

2

1

Indelicato

Fig. 2 Regression straight lines of mean cube strength, f-

c, vs.mean core strength: f

-70, f

-45, f

-28, and the straight line which

would represent the identity of cube and core tests.

Fig. 3 Regression straight lines of mean cube strength, f-

c, vsmean core strength values as determined by processing the datarelated to the eight concrete mixes used to produce all four typesof specimen.

136


where:

(9)

and t is such that, for the t-distribution with n-2 d.f.,there is an /2% chance that t > t/2.

By observing strength relationships from the stand-

sy A Bx

n 2y x

i i

2

i 1

n

=

( )

=

point of the confidence intervals, we can identify thelimits within which straight line (2) and the individualvalues of fc

-as a function of f

-28, f

-45 and f

-70 will lie with a

certain probability. This type of procedure may proveuseful when the evaluation of fc

-though a simple correla-

tion law, even through it yields the most probable value,implies the possibility that 50% of the cases might fallabove or below this value.

The confidence intervals involved for = 0.20 areillustrated in Figs. 4, 5 and 6. A visual examination ofthese figures, verified by a numerical check, reveals thatthe width of the intervals is essentially the same for thedifferent specimen diameters. However, if we considerthe values of sy|x as a summary estimate of variabilityaround the straight lines, we find that the three values:

sc|28 = 4.357; sc|45 = 3.219; and sc|70 = 3.167

decrease with increasing specimen diameter, as could beexpected on the basis of physical considerations. In anyevent, it is not possible to identify a substantial difference inthe validity of the estimates of fc

-obtained from f

-28, f

-45 or f

-70.

In this connection, it should be pointed out thatwhile from the statistical standpoint it might be ofgreater interest to refer to bilateral confidence intervals,from the standpoint of design, it might be advisable toconcentrate only on the lower limits of these intervals soas to identify the region above which not (1 - )% butrather (1 - /2)% of the mean strength values lie. Suchlimits are expressed by the relationships:

(10) f 0.647 1.017f 3.167t

f

662.029ce 70= + +

( )

2

70

2

1 12536 131

..

Fig. 4 Two-sided 80% confidence intervals for mean cubestrength, f

-c (

___), and for the regression straight line (- - -) as afunction of mean core strength: f

-70.


-c (

___), and for the regression straight line (- - -) as afunction of mean microcore strength: f

-28.


-c (

___), and for the regression straight line (- - -) as afunction of mean small core strength: f

-45.

137

(11)

(12))

originating from equation (8), in which the term x, rep-resenting the mean of the mean values of core strength,is in the three cases being considered:

In Fig. 7, equations (10), (11) and (12) are plotted for = 0.20, corresponding to: t/2 = 1.44 for relationship(10) relating to 70-mm diameter cores, t/2 = 1.36 forrelationship (11) relating to small 45-mm diameter cores,and t/2 = 1.34 for microcores; about 90% of the meanstrength values will then fall in the region above them.

Obviously, whether we wish to improve the confi-dence level or accept a lower level, it is possible, by select-ing suitable values of , to introduce into equations (10),(11) and (12) the corresponding values of t/2 to obtainsimilar relationships. In any event, these relationships canbe used with an adequate margin of confidence as empir-ical laws for a rather conservative estimate of mean cubestrength, fc

-, starting from a mean strength value as deter-

mined on microcores, f-

28, on small cores, f-

45, or oncores, f

-70.

In this context, it should be noted that an analysis ofequations (10), (11) and (12) and Fig. 7 clearly shows that

f

n

f

n

f

n70 45 28 = = =36 131 31 470 31 390. ; . ; .

f 4 1.255f 4 t

f

661.76ce 28= + +

( ). . .

.617 357 1 062

31 390

2

28

2

f 1 1.059f 3.219tf

803.931ce 45= + +

( ). .

.048 1 077

31 470

2

45

2

the three curves are rather close. On the other hand,since the straight lines (3), (4) and (5) nearly coincide,the evolution of the limit curves shows that the scatter ofthe mean values f

-70, f

-45 and f

-28 around the regression

straight lines remains virtually constant for varying speci-men diameters.

Consequently, mean cube strength can be estimatedalmost regardless of the test data relating to the differenttypes of core.

It should be borne in mind, however, that from anexamination of the test results listed in Table 2, we findthat with decreasing specimen diameter, the variancesrelating to individual concrete mixes deviate to an evergreater extent from the reference variances of the cubes.This feature has major implications when core testing isused to estimate characteristic cube strength, fck, and italso has considerable implications when this testingmethod is applied to the estimate of mean strength, fc

-, as

discussed in this paper, since it means that when tests areconducted for practical application purposes on smalldiameter specimens, we should resort to bigger samplesif the results are to be sufficiently reliable.

Disregarding the problems pertaining to characteris-tic strength, for which a partial solution has already beenproposed [16] and which are currently being investigatedfurther, it should be noted that the problem of samplesize in this type of test is not to be neglected, as is thecase in all tests aimed at estimating strength on standardsamples on the basis of results obtained from tests of adifferent nature.

As documented in the literature, the solution can beempirical [9, 19] or, preferably, based on statistical con-siderations [20]. In particular, where microcore testing isconcerned, a solution based on the test data described inthis article was worked out through a procedure involv-ing a comparison of the confidence intervals for micro-core and cube mean strength values [16].

For application purposes, it should be kept in mind,however, that equations (10), (11) and (12) representrelationships obtained from a testing campaign con-ducted on cubes and cores taken from cubes producedfrom the same concrete mixes, and therefore express adirect link between the strength values of the two differ-ent specimen types. However, when the tests are con-ducted on a real structure, the situation is conceptuallydifferent. In such circumstances, the cores are in facttaken from concrete whose characteristics are differentfrom those of the cubes in several respects, e.g., com-pacting and curing conditions. The values obtained fromsuch cores will therefore represent an estimated in situcube strength wherein the term estimated should beconstrued as having a wider meaning than its purely sta-tistical connotation.

Incidentally, it should be noted that the methods forinterpreting test results proposed in this paper may alsobe used for tests of different kinds, such as the estimateof cube strength from the results of other types of tests,provided that the tests are linearly correlated with cubestrength.

Indelicato

Fig. 7 Lower limits of the one-sided 90% confidence intervalsfor mean cube strength, f

-c, as a function of mean core strength:

f-

70, f-

45 and f-

28.

138


5. CONCLUSIONS

The results of 1,270 compressive tests performed on240 cubes with 150-mm sides, 480 28-mm diametermicrocores, 390 45-mm diameter cores and 160 70-mmdiameter cores, all of them produced from 16 concretemixes of classes ranging from fck = 20 to fck = 50 Nmm-2and with siliceous river aggregate of different origins anda maximum grain size of 30 mm, have shown that: There are very strong linear correlations betweenmean cube strength values and the mean strength valuesdetermined on cores of the three diameters studied (28,45 and 70 mm), with all of them being characterised bybasically equivalent correlation coefficients. The correlation laws are very close, with straight linesdisplaying angular coefficients very close to 1. It shouldbe noted, however, that with increasing specimen diam-eter, the identity between cube and core mean strengthimproves, albeit slightly. The lower confidence intervals for mean cube strengthmake it possible to estimate the cube strength, fc

-, to the

desired confidence level, starting from a given meanstrength determined on cores, f

-70, on small cores, f

-45, or

on microcores, f-28.

The confidence limits being considered are repre-sented by curves which, for the same confidence level,turn out to be very close to one another. As a conse-quence, mean cube strength can be estimated, almostindifferently, on specimens with 70, 45 or 28-mm diam-eters, with account being taken of the need to increasesample size with decreasing specimen diameter. The proposed methods can be used for in situ tests inestimating cube strength on concrete types similar tothose discussed above, with account being taken of thefact that the choice of core diameter has no significantrepercussions on the accuracy of the results; it is there-fore possible to proceed with tests which, depending onthe chosen core diameter, will range from destructive tovirtually non-destructive.

REFERENCES

[1] Indelicato, F., A statistical method for the assessment of concretestrength through microcores, Mater. Struct. 26 (159) (1993) 261-267.

[2] Indelicato, F., Microcore testing as a method for the determina-

tion of concrete compressive strength, il Cemento 86 (4) (1989)229-238.

[3] ISO/DIS 7032, Cores of hardened concrete - Taking examina-tion and testing in compression, Draft International Standard(International Organization of Standardization, 1983).

[4] BS 1881: Part 120, Method for determination of the compressivestrength of concrete cores (British Standard Institution, London,1983).

[5] DIN 1048 Teil 2, Prfverfahren fr Beton. Bestimmung derBruckfestigkeit von Festbeton in Bauwerken und Bauteilen(Deutsches Institut fr Normung, Berlin, 1991).

[6] ASTM C42-90, Standard Test Method for Obtaining andTesting Drilled Cores and Sawed Beams of Concrete (AmericanSociety for Testing and Materials, Philadelphia, 1990).

[7] ACI Committee 301, Specification for Structural Concrete forBuildings, ACI 301-84 (American Concrete Institute, Detroit,1984).

[8] Petersons, N., Recommendations for estimation of quality ofconcrete in finished structures, Mater. Struct. 4 (24) (1971) 379-398.

[9] Malhotra, V.M., Contract strength requirements - Cores versusin situ evaluation, ACI Journal 74 (4) (1977) 163-172.

[10] Swamy, R.N. and Al-Hamed, A.H., Evaluation of small diame-ter core tests to determine in situ strength of concrete, in In SituNondestructive Testing of Concrete, V.M. Malhotra Ed. (ACI-SP-82 1984) 411-440.

[11] Yip, W.K. and Tam, C.T., Concrete strength evaluationthrough the use of small diameter cores, Magazine of ConcreteResearch 40 (143) (1988) 99-105.

[12] BS 1881: Part 201, Guide to the use of non-destructive meth-ods of test for hardened concrete (British Standard Institution,London, 1986).

[13] Bocca, P., Sul microcarotaggio - Basi teoriche e prime espe-rienze, La Prefabbricazione 22 (11) (1986) 651-664.

[14] Bocca, P., The use of microcores in structural assessment, inProceedings of IABSE 13th Congress, Helsinki, June 1988, 379-384.

[15] Bocca, P. and Indelicato, F., Size effects and statistical problemsof microcores in the re-evaluation of existing structures, inProceedings of DABI Symposium, Copenhagen, June 1988,463-472.

[16] Bocca, P., Bosco, C., Carpinteri, A., Indelicato, F., Iori, I. andValente, S., Nondestructive characterisation of concrete anddamage / fracture diagnosis of civil structures and infrastructures,in Proceedings of the International Conference onNondestructive Testing of Concrete in the Infrastructure,Dearborn, Michigan, USA, 1993 (Society for ExperimentalMechanics, 1993) 1-20.

[17] Benjamin, J. R. and Cornell, C.A., Probability, Statistics andDecision for Civil Engineers (McGraw-Hill PublishingCompany, New York, 1970) 466-475, 667.

[18] Milton, J.S. and Arnold, J.C., Probability and Statistics in theEngineering and Computing Sciences (McGraw-HillInternational Editions, New York, 1986) 364-371.

[19] Neville, A.M., Properties of Concrete, 3rd edn. (PitmanPublishing Ltd., London, 1981) 566 pp.

[20] ACI Committee 228, In place methods for determination ofstrength of concrete, ACI Materials Journal 85 (5) (1988) 446-471.

Documents

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