228.1r-95 in-place methods to estimate concrete · pdf file2.4—pullout test ... in-place...

Guidance is provided on the use of methods to estimate the in-placestrength of concrete in new and existing construction. The methods include:

rebound hammer, penetration resistance, pullout, break-off, ultrasonicpulse velocity, maturity, and cast-in-place cylinders. The principle, inher-ent limitations, and repeatability of each method are reviewed. Procedures

are presented for developing the relationship needed to estimate compres-sive strength from in-place results. Factors to consider in planning in-placetests are discussed, and statistical techniques to interpret test results are

presented. The use of in-place tests for acceptance of concrete is intro-duced. The appendix provides information on the number of strength levelsthat should be used to develop the strength relationship and explains a

regression analysis procedure that accounts for error in the independentvariable.

Keywords: coefficient of variation; compressive strength ; concretes;

construction; nondestructive tests; reviews; safety; sampling; statisticalanalysis

In-Place Methods to Estimate Concrete Strength

Reported by ACI Committee 228

ACI 228.1R-95

Nicholas J. Carino*Chairman

Mary J. SansaloneSecretary

Farhad Ansari F. Dirk Heidbrink Robert W. RossJohn A. Bickley† Kal R. Hindo Thomas J. Rowe

Hermenegildo Caratin Roberto Huyke Bryce P. SimonsKi Ho Choi Robert S. Jenkins† Patrick J. SullivanGerardo G. Clemeña Alexander M. Leshchinsky Bruce A. Suprenant

Neil A. Cumming H. S. Lew Michael A. TaylorAllen G. Davis Kenneth M. Lozen George V. TeodoruRonald L. Dilly V. M. Malhotra Henry T. Thornton, Jr.

Donald E. Dixon Larry D. Olson Woodward L. VogtBoris Dragunsky Sandor Popovics Alexander B. ZoobRichard D. Gaynor Paul H. Read

* Task force Chairman.† Member of task force that prepared revision.

CONTENTS

Chapter 1—Introduction, p. 228.1R-21.1—Scope1.2—Need for in-place testing during construction1.3—Influence of ACI 318-831.4—Existing construction1.5—Objective of report

228.1

ACI Committee Reports, Guides, Standard Practices, and Commentariesare intended for guidance in planning, designing, executing, and inspectingconstruction. This document is intended for the use of individuals whoare competent to evaluate the significance and limitations of its con-tent and recommendations and who will accept responsibility for theapplication of the material it contains. The American Concrete Institutedisclaims any and all responsibility for the stated principles. The Instituteshall not be liable for any loss or damage arising therefrom. Reference to this document shall not be made in contract documents. Ifitems found in this document are desired by the Architect/Engineer to bea part of the contract documents, they shall be restated in mandatory lan-guage for incorporation by the Architect/Engineer.

Chapter 2—Review of methods, p. 228.1R-32.1—Introduction2.2—Rebound number (ASTM C 805)2.3—Penetration resistance (ASTM C 803)2.4—Pullout test (ASTM C 900)2.5—Break-off test (ASTM C 1150)2.6—Ultrasonic pulse velocity (ASTM C 597)2.7—Maturity method (ASTM C 1074)2.8—Cast-in-place cylinders (ASTM C 873)2.9—Combined methods2.10—Summary

Chapter 3—Statistical characteristics of tests, p. 228.1R-12

3.1—Need for statistical analysis3.2—Repeatability of test results

Chapter 4—Development of strength relationship, p.228.1R-18

4.1—General4.2—New construction4.3—Existing construction

ACI 228.1R-95 supersedes ACI 228.1R-89 and became effective October 1, 1995.Extensive revisions have been made throughout the report. The title was changed

and the synopsis expanded. New information was added, and existing information wasexpanded in each chapter. New chapters were added to cover planning and in-placetesting for acceptance. Four new appendixes were added as well.

Copyright © 1995, American Concrete Institute.All rights reserved including rights of reproduction and use in any form or by any

means, including the making of copies by any photo process, or by any electronic ormechanical device, printed, written, or oral, or recording for sound or visual reproduc-tion or for use in any knowledge or retrieval system or device, unless permission inwriting is obtained from the copyright proprietors.

R-1

228.1R-2 ACI COMMITTEE REPORT

Chapter 5—Planning for in-place testing, p. 228.1R-235.1—New construction5.2—Existing construction

Chapter 6—Interpretation of results, p. 228.1R-286.1—Introduction6.2—Statistical methods6.3—Reporting results

Chapter 7—In-place tests for acceptance of concrete, p.228.1R-33

7.1—General7.2—Acceptance criteria7.3—Early-age testing

Chapter 8—References, p. 228.1R-348.1—Recommended references8.2—Cited references

Appendix, p. 228.1R-37A.1—Number of strength levelsA.2—Regression analysis with X-errorA.3—Standard deviation of estimated Y-valueA.4—Example

CHAPTER 1—INTRODUCTION

1.1—ScopeIn-place tests are performed typically on concrete within a

structure in contrast to tests performed on molded specimensmade from the concrete to be used in the structure. Histori-cally, they have been called nondestructive tests becausesome of the early tests did not damage the concrete. Over theyears, however, new methods have developed that result insuperficial local damage. Therefore, the terminology in-place tests is used as a general category that includes thosewhich do not alter the concrete and those which result in mi-nor surface damage. The important characteristic of thesetests is that they measure the properties of the concrete in astructure. In this report, the principal application of in-placetests is to estimate the compressive strength of the concrete.

In-place tests can be used to estimate concrete strengthduring construction, so that operations can be performedsafely or curing procedures can be terminated. They can alsobe used to estimate concrete strength during the evaluationof existing structures. These two applications require slightlydifferent approaches, so parts of this report are separated intosections dealing with new and existing construction.

A variety of techniques are available for estimating the in-place strength of concrete (Malhotra 1976, Bungey 1989,Malhotra and Carino 1991). No attempt is made to review allof these methods in this report; only those methods that havebeen standardized by ASTM are discussed. Teodoru (1989)has prepared a compilation of national standards on in-placetest methods.1.2—Need for in-place tests during construction

For over 70 years in North American practice, the most

widely used test for concrete has been the compression testof the standard cylinder. The test procedure is relatively easyto perform in terms of sampling, preparation of specimens,and the determination of strength. When properly per-formed, this test has low within-test variation and low inter-laboratory variation, and therefore lends itself readily to useas a standard. The compressive strength so obtained is mod-ified by specified factors and used to verify the nominalstrengths of structural members. This strength value is,therefore, an essential parameter in design codes.

When carried out according to standard procedures, how-ever, the cylinder test only represents the potential strengthof the concrete as delivered to a site. The test is used mainlyas a basis for quality control to assure that contract require-ments are met. It is not intended for determining the in-placestrength of the concrete since it makes no allowance for theeffects of placing, compaction, or curing. For example, it isunusual for the concrete in a structure to have the same prop-erties as a standard-cured cylinder at the same test age. In ad-dition, since standard-cured cylinders are usually tested at anage of 28 days, they cannot be used to determine whether ad-equate strength exists at earlier ages for safe removal offormwork or the application of post-tensioning. Concrete inportions of a structure, such as columns, may developstrength equal to the standard 28-day cylinder strength by thetime it is subjected to design loads. However, concrete inmost flexural and prestressed members does not develop its28-day strength before the members are required to acceptlarge percentages of their design loads. For these reasons, in-place tests are needed to determine the concrete strength atcritical locations in a structure and at times when crucial con-struction operations are scheduled.

Traditionally, some measure of the strength of the con-crete in the structure has been obtained by using field-curedcylinders. These are supposedly cured on or in the structureunder the same conditions as the concrete in the structure.However, measured strengths of field-cured cylinders are of-ten significantly different from in-place strengths because itis difficult, and often impossible, to have identical bleeding,compaction, and curing conditions for concrete in cylindersand concrete in structures. Field-cured specimens also lendthemselves to errors due to improper handling or inappropri-ate storage, which may result in misleading data for criticaloperations.

To meet rapid construction schedules, form removal, ap-plication of post-tensioning, termination of curing, and theremoval of reshores must be carried out as early as is safelypossible. To enable these operations to proceed safely at theearliest possible time requires the use of reliable in-placetests to determine the in-place sterngth. The need for suchstrength information is emphasized by several constructionfailures that could have been prevented had in-place testingbeen used (Lew 1980; Carino et al. 1983). The use of in-place tests not only increases safety but can result in substan-tial savings in construction costs by permitting acceleratedconstruction schedules (Bickley 1982b).

IN-PLACE METHODS TO ESTIMATE CONCRETE STRENGTH 228.1R-3

1.3—Influence of ACI 318-83Prior to 1983, ACI 318 required testing of field-cured cyl-

inders to demonstrate the adequacy of concrete strength priorto removal of formwork or reshoring. However, Section6.2.1.1 of ACI 318-83 allowed the use of alternative proce-dures to testing field-cured cylinders. The alternative proce-dures must be approved by the building official prior to use.Subsequent versions of ACI 318 also permit the use of in-place testing as an alternative to testing field-cured speci-mens.

Most provisions in ACI 318 are based on the compressivestrength of standard cylinders. Thus, to evaluate structuralcapacity under construction loading, it is necessary to have ameasure of the cylinder strength of the concrete as it exists inthe structure. If in-place tests are used, it is necessary to es-tablish a valid relationship between the results of in-placetests and the compressive strength of cylinders. At present,there are no standard practices for developing the requiredstrength relationship. There are also no generally acceptedguidelines for interpretation of in-place test results. Thesedeficiencies have been impediments to widespread adoptionof in-place tests.

1.4—Existing constructionReliable estimates of the in-place concrete strength are re-

quired for structural evaluation of existing structures (seeACI 437R). Historically, the in-place strength has been esti-mated by testing cores drilled from the structure. In-placetests can supplement coring and permit more economicalevaluation of the concrete in the structure. The critical stepin such applications is to establish the relationship betweenin-place test results and concrete strength. The present ap-proach is to correlate results of in-place tests performed atselected locations with strength of corresponding cores. In-place testing does not eliminate the need for coring, but it canreduce the total amount of coring needed to evaluate a largevolume of concrete. For success, a sound sampling plan isneeded to acquire the correlation data and for reliable inter-pretation of test results.

1.5—Objective of reportThis report reviews ASTM test methods for estimating the

in-place strength of concrete in new construction and in ex-isting structures. The overall objective is to provide the po-tential user with a guide to assist in planning, conducting,and interpreting the results of in-place tests.

Chapter 2 discusses the underlying principles and inherentlimitations of in-place tests. Chapter 3 reviews the statisticalcharacteristics of in-place tests. Chapter 4 outlines proce-

2.1—IntroductionThe objective of an in-place test is to estimate properties

dures to develop the relationship needed to estimate in-place
compressive strength. Chapter 5 discusses factors to be considered in planning the in-place testing program. Chapter 6presents statistical techniques to interpret in-place test results. Chapter 7 discusses in-place testing for acceptance of concrete. The appendix provides details on the statisticalprinciples discussed in the report and includes an illustrativeexample.
CHAPTER 2—REVIEW OF METHODS

of concrete in the structure. Very often the desired propertyis the compressive strength. To make a strength estimate, itis necessary to have a known relationship between the resultof the in-place test and the strength of the concrete. For newconstruction, this relationship is usually established empiri-cally in the laboratory. For existing construction, the rela-tionship is usually established by performing in-place tests atselected locations in the structure and determining thestrength of cores drilled from adjacent locations. Fig. 2.1 is aschematic of a strength relationship, in which the cylindercompressive strength is plotted as a function of an in-placetest result. This relationship would be used to estimate the

Fig. 2.1—Example of relationship between cylinder com-pressive strength and in-place test value

strength of concrete in a structure based on the value of thein-place test result obtained from testing the structure. Theaccuracy of the strength prediction depends directly on thedegree of correlation between the strength of concrete andthe quantity measured by the in-place test. The user of in-place tests should have an understanding of what quantity ismeasured by the test and how this quantity is related to thestrength of concrete.

The purpose of this chapter is to explain the underlyingprinciples of the widely used in-place test methods, and toidentify those factors, other than concrete strength, that caninfluence the test results. Additional background informa-tion on these methods is available in the references by Mal-hotra (1976), Bungey (1989), and Malhotra and Carino(1991).

The following methods are discussed: • Rebound number• Penetration resistance• Pullout• Break-off• Ultrasonic pulse velocity• Maturity• Cast-in-place cylinder


2.2—Rebound number (ASTM C 805)The operation of the rebound hammer (also called the

Schmidt Hammer or Swiss Hammer) is illustrated in Fig.2.2. The device consists of the following main components:(1) outer body, (2) plunger, (3) hammer, and (4) spring. Toperform the test, the plunger is extended from the body of theinstrument and brought into contact with the concrete sur-face. When the plunger is extended, a latching mechanismengages the hammer to the upper end of the plunger. Thebody of the instrument is then pushed toward the concretemember. This action causes an extension of the spring con-necting the hammer to the body [Fig. 2.2(b)]. When the bodyis pushed to its limit, the latch is released, and the springpulls the hammer toward the concrete member [Fig. 2.2(c)].The hammer impacts the shoulder area of the plunger and re-bounds [Fig. 2.2(d)]. The rebounding hammer moves theslide indicator, which records the rebound distance. The re-bound distance is measured on a scale numbered from 10 to100 and is recorded as the rebound number indicated on thescale.

The key, to understanding the inherent limitations of thistest for strength prediction, is understanding the factors in-fluencing the rebound distance. From a fundamental point ofview, the test is a complex problem of impact loading andstress-wave propagation. The rebound distance depends onthe kinetic energy in the hammer before impact with theshoulder of the plunger and how much of that energy is ab-sorbed during the impact. Part of the energy is absorbed asmechanical friction in the instrument, and part of the energyis absorbed in the interaction of the plunger with the con-crete. It is the latter factor that makes the rebound number anindicator of the concrete properties. The energy absorbed bythe concrete depends on the stress-strain relationship of theconcrete. Therefore, absorbed energy is related to thestrength and the stiffness of the concrete. A low-strength,low-stiffness concrete will absorb more energy than a high-strength, high-stiffness concrete. Thus the low-strength con-

Fig. 2.2—Schematic to illustrate operation of the rebound hammer

crete will result in a lower rebound number. Since it is pos-sible for two concrete mixtures to have the same strength butdifferent stiffnesses, there could be different rebound num-bers though the strengths are equal. Conversely, it is possiblefor two concretes with different strengths to result in thesame rebound numbers if the stiffness of the low-strengthconcrete is greater than the stiffness of the high-strength con-crete. Since aggregate type affects stiffness concrete, it isnecessary to develop the strength relationship on concretemade with the same materials that will be used for the con-crete in the structure.

In rebound-hammer testing, only the concrete near theplunger influences the rebound value. Therefore, the test issensitive to the local conditions where the test is performed.If the plunger is located over a hard aggregate particle, an un-usually high rebound number will result. On the other hand,if the plunger is located over a large air void or over a softaggregate particle, a lower rebound number will occur. Toaccount for these possibilities, ASTM C 805 requires that 10rebound numbers be taken for a test. If a reading differs bymore than seven units from the average, that reading shouldbe discarded and a new average should be computed basedon the remaining readings. If more than two readings differfrom the average by seven units, the entire set of readings isdiscarded.

Because the rebound number test probes only the near-sur-face layer of concrete, the rebound number may not repre-sent the interior concrete. The presence of surface car-bonation can result in higher rebound numbers that are notindicative of the interior concrete. Similarly, a dry surfacewill result in higher rebound numbers than for the moist-in-terior concrete. Absorptive oiled plywood can absorb mois-ture from the concrete and produce a harder surface layerthan concrete cast against steel forms. Similarly, curing con-ditions affect the strength of the surface concrete more thanthe concrete several inches (hundred millimeters) from thesurface. The surface texture may also influence the reboundnumber. When the test is performed on rough concrete, localcrushing occurs under the plunger and the indicated concretestrength will be lower than the true value. Rough surfacesshould be ground before testing. If the formed surfaces aresmooth, grinding is unnecessary. A hard smooth surface,such as produced by trowel finishing, can result in higher re-bound numbers. Finally, the rebound distance is affected bythe orientation of the instrument, and the strength relation-ship must be developed for the same instrument orientationas will be used for in-place testing.

In summary, while the rebound number test is simple toperform, there are many factors other than concrete strengththat influence the test result.

2.3—Penetration resistance (ASTM C 803)In the penetration resistance technique, one measures the

depth of penetration of a rod (probe) or a pin forced into thehardened concrete by a driver unit.

The probe penetration technique involves the use of a spe-cially designed gun to drive a hardened steel probe into theconcrete. (The commercial test system is known as the


Windsor Probe.) The amount of penetration of the probe isan indicator of the concrete strength. This method is similarto the rebound number test, except that the probe impacts theconcrete with much higher energy than the plunger of the re-bound hammer. A theoretical analysis of this test is evenmore complicated than the rebound test, but again the es-sence of the test involves the initial kinetic energy of theprobe and energy absorption by the concrete. The probe pen-etrates into the concrete until its initial kinetic energy is ab-sorbed. The initial kinetic energy is governed by the chargeof smokeless powder used to propel the probe, the locationof the probe in the gun barrel before firing, and frictionallosses as the probe travels through the barrel. An essential re-quirement of this test is that the probes have a consistent val-ue of initial kinetic energy. ASTM C 803 requires that theprobe exit velocities should not have a coefficient of varia-tion greater than 3 percent based on 10 tests by approved bal-listic methods.

As the probe penetrates into the concrete, some energy isabsorbed by friction between the probe and the concrete, andsome is absorbed by crushing and fracturing of the concrete.There are no rigorous studies of the factors affecting the ge-ometry of the fracture zone, but its general shape is probablyas illustrated in Fig. 2.3. Generally, there is an approximately

Fig. 2.3—Approximate shape of failure zone in concrete during probe penetration test

cone-shaped region in which the concrete is heavily frac-tured, and this is the zone where most of the probe energy isabsorbed.

The probe tip can travel through mortar and aggregate; ingeneral, cracks in the fracture zone will be through the mor-tar matrix and the coarse-aggregate particles. Hence, thestrength properties of both the mortar and the aggregates in-fluence the penetration distance. This contrasts with the be-havior of normal-strength concrete in a compression test,where the mortar strength has the predominant influence onthe measured compressive strength. Thus, an important char-acteristic of the probe penetration test is that the type ofcoarse aggregate greatly affects the relationship betweenconcrete strength and probe penetration. For example, Fig.2.4 illustrates empirical relationships between compressive

Fig. 2.4—Effect of aggregate type on relationship between

strength and probe penetration for concretes made with a softaggregate (such as limestone) and with a hard aggregate(such as chert). For equal compressive strengths, the con-crete with the soft aggregate allows greater probe penetrationthan the concrete with the hard aggregate. More detailed in-formation on the influence of aggregate type on strength re-lationships can be found in Malhotra (1976), Bungey (1989),and Malhotra and Carino (1991).

Because the probe penetrates into the concrete, test resultsare not usually affected by local surface conditions such astexture and moisture content. However, a harder surface lay-er, as would occur in trowel finishing, can result in low pen-etration values and excessive scatter of data. In addition, thedirection of penetration into the concrete is unimportant ifthe probe is driven perpendicular to the surface. The penetra-tion will be affected by the presence of reinforcing bars with-in the zone of influence of the penetrating probe. Thus thelocation of the reinforcing steel should be determined beforeselecting test sites.

In practice it is customary to measure the exposed lengthof the probes. However, the fundamental relationship is be-tween concrete strength and depth of penetration. Therefore,when assessing the variability of test results (see Chapter 3),it is preferable to express the coefficient of variation in termsof penetration depth rather than exposed length.

A pin penetration test device, requiring less energy thanthe Windsor Probe system, was developed by Nasser (Nasserand Al-Manaseer 1987a, 1987b), and the procedure for itsuse was subsequently incorporated into ASTM C 803. Aspring-loaded device is used to drive a pointed 0.140-in.(3.56 mm) diameter hardened steel pin into the concrete. Thepenetration by the pin creates a small indentation (or hole) inthe surface of the concrete. The pin is removed from the hole,the hole is cleaned with an air jet, and the hole depth is mea-sured with a suitable depth gage. The penetration depth isused to estimate compressive strength from a previously es-tablished strength relationship. In the current test system, themaximum penetration is limited to 0.30 in. (7.6 mm).

The kinetic energy delivered by the pin penetration deviceis estimated to be about 1.3 percent of the energy deliveredby the Windsor Probe system (Carino and Tank 1989). Be-cause of the low energy level, the penetration of the pin is re-

concrete strength and depth of probe penetration


Fig. 2.5—Schematic of pullout test

Fig. 2.6—Principle stress trajectories prior to cracking for pullout test in a homogeneous material (Stone and Carino 1984)

duced greatly if the pin encounters a coarse aggregateparticle. Thus the test is intended as a penetration test of themortar fraction of the concrete. Individual test results thatpenetrate coarse aggregates particles are not considered indetermining the average pin penetration resistance (seeASTM C 803). A pin becomes blunted as it is reused. Sincethe blunting affects the penetration depth, ASTM C 803 re-quires that a new pin be used for each penetration test.

The sensitivity of the pin penetration to changes in com-pressive strength decreases for concrete strength above 4000psi (28 MPa) (Carino and Tank 1989). Therefore, the pinpenetration test system is not recommended for testing con-crete having a compressive strength above 4000 psi.

2.4—Pullout test (ASTM C 900)The pullout test measures the maximum force required to

pull an embedded metal insert with an enlarged head from aconcrete specimen or structure. The force is applied by atension jack, or center-hole ram, that reacts against the con-crete surface through a reaction ring concentric with the in-sert (Fig. 2.5). As the insert is pulled out, a roughly cone-shaped fragment of the concrete is also extracted. The largediameter of the conic fragment d2 is determined by the innerdiameter of the reaction ring, and the small diameter d1 isdetermined by the insert-head diameter. Requirements forthe testing configuration are given in ASTM C 900. The em-bedment depth and head diameter must be equal, but thereis no requirement on the magnitude of these dimensions.The inner diameter of the reaction ring can be any size be-tween 2.0 and 2.4 times the insert-head diameter. Thismeans that the apex angle of the conic frustum defined bythe insert-head diameter and the inside diameter of the reac-tion ring can vary between 54 and 70 deg. The same test ge-ometry must be used in developing the strength relationshipand the in-place testing.

Unlike the rebound hammer and probe penetration tests,the pullout test subjects the concrete to a static loading thatis amenable to stress analysis. The finite element method hasbeen used to calculate the stresses induced in the concretebefore cracking (Stone and Carino 1984) and where the con-crete has cracked (Ottosen 1981). In these analyses, the con-crete was assumed to be a homogeneous solid and theinfluence of discrete coarse aggregate particles was not mod-eled. There is agreement that the test subjects the concrete toa highly nonuniform, three-dimensional state of stress. Fig.2.6 shows the approximate directions (trajectories) of theprincipal stresses acting in radial planes (those passingthrough the center of the insert) before cracking and for apexangles of 54 and 70 deg. Because of symmetry, only one-halfof the specimen is shown in the figures. These trajectorieswould be expected to change after cracking develops. It isseen that before cracking there are tensile stresses that areapproximately perpendicular to the eventual failure surface,and that compressive stresses are directed from the inserthead toward the ring. These principal stresses are nonuni-form and are greatest near the top edge of the insert head.


A series of analytical and experimental studies has beencarried out to determine the failure mechanism of the pullouttest, some of which are critically reviewed by Yener andChen (1984). While the conclusions have differed, it is gen-erally agreed that circumferential cracking (producing thefailure cone) begins in the highly stressed region next to theinsert head at a pullout load that is a fraction of the ultimatevalue. With increasing load, the circumferential crackingpropagates toward the reaction ring. However, there is noagreement on the nature of the final failure mechanism gov-erning the magnitude of the ultimate pullout load.

Ottosen (1981) concluded that failure is due to “crushing”of concrete in a narrow band between the insert head and thereaction ring. Thus the pullout load is said to depend directlyupon the compressive strength of the concrete. In another an-alytical study (Yener 1994), failure is said to occur by out-ward crushing of concrete around the perimeter of the failurecone near the reaction ring. Using linear-elastic fracture me-chanics and a two-dimensional model, others (Ballarini,Shah, and Keer 1986) have concluded that ultimate load isgoverned by the fracture toughness of the matrix. In an ex-perimental study (Stone and Carino 1983), it was concludedthat before ultimate load, circumferential cracking extendsfrom the insert head to the reaction ring; additional load is re-sisted by aggregate interlock across the circumferentialcrack. In this case, failure is said to occur when sufficient ag-gregate particles have been pulled out of the mortar matrix.According to the aggregate interlock argument, maximumpullout force is not directly related to the compressivestrength. However, there is good correlation between ulti-mate pullout load and compressive strength of concrete, be-cause both values are influenced by the mortar strength(Stone and Carino 1984). Another study, using nonlinearfracture mechanics and a discrete cracking model, showedexcellent agreement between the predicted and observed in-ternal cracking in the pullout test (Hellier et al. 1987). Fig.2.7 shows the displaced shape of the finite element model

Fig. 2.7—Circumferential cracks predicted by nonlinear fracture mechanics analysis of pullout test by Hellier et al. (1987)

used. The analysis showed that a primary circumferentialcrack developed at the corner of the insert head and propa-gated outward at a shallow angle. This crack ceased to growwhen it penetrated a tensile-free region. A secondary crackdeveloped subsequently and propagated as shown in the fig-ure. The secondary crack coincided with the final fracturesurface observed in test specimens when the conical frag-ment was extracted from the concrete mass. This study alsoconcluded that failure does not occur by uniaxial compres-sive failure in the concrete.

A positive feature of the pullout test is that it produces awell-defined fracture surface in the concrete and measures astatic strength property of the concrete. However, since thereis not a consensus on what this strength property is, it is nec-essary to develop an empirical relationship between the pull-out strength and the compressive strength of the concrete.The relationship is applicable to only the particular test con-figuration and concrete materials used in the correlation test-ing.

The pullout strength is governed primarily by that portionof the concrete located next to the conic frustum defined by

the insert head and reaction ring. Commercial inserts haveembedment depths about 25 to 30 mm (1 to 1.2 in.). Thusonly a small volume of the concrete is tested, and because ofthe inherent heterogeneity of concrete, the typical averagewithin-batch coefficient of variation of these pullout testshas been between 7 and 10 percent, which is about two tothree times that of standard cylinder compression tests.

The most desirable approach for pullout testing is to attachthe inserts to formwork before concrete placement. Howev-er, it is also possible to place inserts into unformed surfaces,such as tops of slabs, by placing the inserts into fresh con-crete that is sufficiently workable. The hardware includes ametal plate attached to the insert to provide a smooth bearingsurface and a plastic cup to allow embedment of the plate be-low the surface. When manually placing inserts, special careis required to maintain representative concrete properties atplacement locations and to reduce the amount of air that be-comes entrapped on the underside of the plates. In an earlystudy, Vogt et al. (1984) reported higher than expected with-in-test variability when using manually-placed inserts. How-ever, later work by Dilly and Vogt (1988) resulted invariability similar to that expected with inserts fastened toformwork. The recommended approach is to push the insertinto fresh concrete and then float it horizontally over a dis-tance of 2 to 4 in. (50 to 100 mm) to allow aggregate to flowinto the pullout failure zone. After insertion, the insertshould be tilted about 20 to 30 deg from the vertical to allowentrapped air to escape from beneath the steel plate. Careshould be exercised to assure that the plate is completely be-low the concrete surface. To prevent movement of the insertbefore setting, fresh concrete can be placed in the cup.


Unlike methods such as rebound number or probe penetra-tion, the standard pullout test is limited to use in new con-struction because the inserts have to be embedded into freshconcrete. However, other types of pullout test configurationsare available for existing construction (Mailhot et al. 1979,Chabowski and Bryden-Smith 1980, Petersen 1984,Domone and Castro 1987). These typically involve drilling ahole and inserting an expanding anchorage device that willengage in the concrete and cause fracture in the concretewhen extracted. These techniques are still under develop-ment and have not been standardized as ASTM tests meth-ods.

2.5—Break-off test (ASTM C 1150)The break-off test measures the force required to break off

a cylindrical core from a larger concrete mass (Johansen1979). The measured force and a pre-established strength re-lationship are used to estimate the in-place compressivestrength. Standard procedures for using this method are giv-en in ASTM C 1150.

A schematic of the break-off test is shown in Fig. 2.8. Fornew construction, the core is formed by inserting a plasticsleeve into the surface of the fresh concrete. The sleeves alsocan be attached to the sides of formwork and filled duringconcrete placement (see Chapter 5 for attachment method).Alternatively, the test specimens can be prepared in hard-ened concrete by using a special core bit to cut the core andthe counterbore. Thus the break-off test can be used to eval-uate concrete in both new and existing construction.

When the in-place compressive strength is to be estimated,the sleeve is removed, and a special loading jack is placedinto the counter bore. A pump supplies hydraulic fluid to thejack that applies a horizontal force to the top of the core asshown in Fig. 2.8. The reaction to the horizontal force is pro-vided by a ring that bears against the counterbore. The forceon the core is gradually increased by operating the pump un-

Fig. 2.8—Schematic of break-off test

til the core ruptures at its base. The hydraulic fluid pressureis monitored with a pressure gage having an indicator to reg-ister the maximum pressure achieved during the test. Themaximum pressure gage reading in units of bars [1 bar = 0.1MPa (14.5 psi)] is called the break-off number of the con-crete.

For new construction, the concrete must be workable toeasily insert the sleeves into the concrete surface. To reduceinterference between the sleeve and coarse aggregate parti-cles, the maximum aggregate size in the concrete is limitedto a fraction of the sleeve diameter. According to ASTM C1150, the break-off test is not recommended for concretehaving a maximum nominal aggregate size greater than 1 in.(25 mm). There is evidence that variability of the break-offnumber increases for larger aggregate sizes (see Chapter 3).Sleeve insertion must be performed carefully to assure goodcompaction around the sleeve and a minimum of disturbanceat the base of the formed core. Some problems have been re-ported in keeping the sleeves from floating out of very fluidconcrete mixtures (Naik et al. 1987).

Like the pullout test, the break-off test subjects the con-crete to a slowly applied force and measures a static strengthproperty of the concrete. The core is loaded as a cantilever,and the concrete at the base of the core is subject to a combi-nation of bending and shear. In the early work (Johansen1979), the results of the break-off test were reported as thebreak-off strength, computed as the flexural stress at the baseof the core corresponding to the ultimate force applied to thecore. This approach required a calibration curve to convertthe pressure gage reading to a force, and it assumed that thestress distribution could be calculated by a simple bendingformula. In ASTM C 1150, the flexural strength is not com-puted, and the break-off number (pressure gage reading) isrelated directly to the compressive strength. This approachsimplifies data analysis, but it is still essential to calibrate theinstrument that will be used for testing on the structure to as-sure that the gage readings correspond to the actual forcesapplied to the cores.

It has been reported that the computed flexural strengthbased on the break-off test is about 30 percent greater thanthe modulus of rupture obtained by standard beam tests (Jo-hansen 1979; Yener and Chen 1985).

The relationships between break-off strength and com-pressive strength have been found to be nonlinear (Johansen1979, Barker and Ramirez 1988), which is in accordancewith the usual practice of relating the modulus of rupture ofconcrete to a power of compressive strength. It has also beenfound that the relationship between break-off strength andmodulus of rupture may be more uncertain than that betweenbreak-off strength and compressive strength (Barker andRamirez 1988).

The break-off test has been used successfully on a varietyof construction projects in the Scandinavian countries, in-cluding major offshore oil platforms (Carlsson et al. 1984).Besides its use for estimating in-place compressive strength,the method has also been used to evaluate the bond strengthbetween concrete and overlay materials (Dahl-Jorgensonand Johansen 1984).


2.6—Ultrasonic pulse velocity (ASTM C 597)The ultrasonic pulse velocity test, as prescribed in ASTM

C 597, determines the propagation velocity of a pulse of vi-brational energy through a concrete member. The operation-al principle of modern testing equipment is illustrated in Fig.2.9. A pulser sends a short-duration, high-voltage signal to a

Fig. 2.9—Schematic of apparatus to measure ultrasonic

transducer, causing the transducer to vibrate at its resonantfrequency. At the start of the electrical pulse, an electronictimer is switched on. The transducer vibrations are trans-ferred to the concrete through a viscous coupling fluid. Thevibrational pulse travels through the member and is detectedby a receiving transducer coupled to the opposite concretesurface. When the pulse is received, the electronic timer isturned off and the elapsed travel time is displayed. The directpath length between the transducers is divided by the traveltime to obtain the pulse velocity through the concrete.

It is also possible to measure the attenuation of the ultra-sonic pulse as it travels from the transmitter to the receiver(Teodoru 1988). Pulse attenuation measurements require anoscilloscope to display the signal from the receiving trans-ducer, and care must be used to obtain identical coupling andcontact pressure on the transducers at each test point. In ad-dition, the travel path length must be the same.

From the physics of elastic wave propagation, the pulsevelocity is proportional to the square root of the elastic mod-ulus and inversely proportional to the square root of the massdensity of the concrete. If it is assumed that the elastic mod-ulus of concrete is proportional to the square root of the com-pressive strength, as suggested by ACI 318, then the pulsevelocity is proportional to the fourth root of the compressivestrength. This means that, for a given concrete mixture, asthe compressive strength increases with age there is a pro-portionately smaller increase in the pulse velocity. For ex-ample, reported data (RILEM 1981) indicate that an increasein early-age compressive strength from 500 to 1500 psi (3.4to 10.3 MPa) may increase the velocity from about 13,100 toabout 15,000 ft/s (4000 to 4600 m/s). On the other hand, atlater ages a gain in compressive strength from 4000 to 5000psi (27.6 to 34.5 MPa) may increase the velocity from about16,700 to only about 17,100 ft/s (5090 to 5220 m/s). Thus, atlater ages, the pulse velocity of concrete is not sensitive togain in strength.

Factors other than concrete strength can affect pulse veloc-ity, and changes in pulse velocity due to these factors mayovershadow changes due to strength (Sturrup, Vecchio, andCaratin 1984). An important factor is moisture content. Asthe moisture content of concrete increases from the air-dry tosaturated condition, it is reported that pulse velocity may in-crease up to 5 percent (Bungey 1989). Thus, if the effects ofmoisture are not considered, erroneous conclusions may bedrawn about in-place strength, especially in mature concrete.It has been found that the relationship between pulse velocityand strength is also affected by the curing process, especiallywhen accelerated methods are used (Teodoru 1986).

Another influencing factor is the presence of steel rein-forcement. Since the pulse velocity through steel is about 40percent greater than through concrete, the pulse velocitythrough a heavily reinforced concrete member may be great-

er than through one with little reinforcement. This is espe-cially troublesome when reinforcing bars are orientedparallel to the pulse-propagation direction. The pulse may berefracted into the bars and transmitted to the receiver at thepulse velocity in steel. The resulting apparent velocitythrough the member will be greater than the actual velocitythrough the concrete. Failure to account for the presence andorientation of reinforcement may lead to incorrect conclu-sions about concrete strength. Correction factors, such asthose discussed in Malhotra (1976) and Bungey (1989), havebeen proposed, but their reliability has not been establishedconclusively.

The measured pulse velocity may also be affected by thepresence of cracks or voids along the propagation path fromtransmitter to receiver. The pulse may be diffracted aroundthe discontinuities, thereby increasing the travel path andtravel time. Without additional knowledge about the interiorcondition of the concrete member, the apparent decrease inpulse velocity could be incorrectly interpreted as a low com-pressive strength.

In this test method, all of the concrete between the trans-mitting and receiving transducers affects the travel time.Test results are, therefore, relatively insensitive to the nor-mal heterogeneity of concrete. Consequently, the test meth-od has been found to have an extremely low within-batchcoefficient of variation. However, this does not mean that thestrength predictions are necessarily highly reliable.

2.7—Maturity method (ASTM C 1074)Freshly-placed concrete gains strength because of the exo-

thermic chemical reactions between the water and cementi-tious materials in the mixture. Provided sufficient moistureis present, the rates of the hydration reactions are influencedby the concrete temperature; an increase in temperature

pulse velocity


causes an increase in the reaction rates. The extent of hydra-tion and, therefore, strength at any age depends on the ther-mal history of the concrete.

The maturity method is a technique to estimate in-placestrength by accounting for the effects of temperature andtime on strength development. The thermal history of theconcrete and a maturity function are used to calculate a ma-turity index that quantifies the combined effects of time andtemperature. The strength of a particular concrete mixture isexpressed as a function of its maturity index by means of astrength-maturity relationship. If samples of the same con-crete are subjected to different temperature conditions, thestrength-maturity relationship for that concrete and the tem-perature histories of the samples can be used to predict theirstrengths.

The maturity function is a mathematical expression thatconverts the temperature history of the concrete to a maturityindex. Several such functions have been proposed and are re-viewed in Malhotra (1971), RILEM (1981), and Malhotraand Carino (1991). The key feature of a maturity function isthe expression used to represent the influence of temperatureon the rate of strength development. Two expressions havefound widespread usage. In one expression it is assumed thatthe rate of strength development is a linear function of tem-perature, and this leads to the simple maturity functionshown in Fig. 2.10. In this case, the maturity index at any ageequals the area between a datum temperature T0 and the tem-perature curve of the concrete. The term temperature-timefactor is used for this area and is calculated as follows

M(t) = Σ (Ta - T0) ∆t (2-1)

whereM(t) = the temperature-time factor at age t, deg-days or

deg-hr∆t = a time interval, days or hrTa = average concrete temperature during time interval

∆tT0 = datum temperature

Traditionally, the datum temperature used in Eq. (2-1) hasbeen the temperature below which strength gain ceases,

Fig. 2.10—Maturity function based on assumption that rate of strength gain varies linearly with temperature

which has been assumed to be about 14 F (-10 C). However,it has been suggested that a single value for the datum tem-perature would not be the most appropriate approach andthat the datum temperature should be evaluated for the spe-cific materials in the concrete mixture (Carino 1984). ASTMC 1074 recommends a datum temperature of 32 F (0 C) forconcrete made with Type I cement when the concrete tem-perature is expected to be between 32 and 104 F (0 and 40C). A procedure is also provided to determine experimental-ly the datum temperature for other types of cement and fordifferent ranges of curing temperature.

In the second expression, the maturity function assumesthat the rate of strength gain varies exponentially with con-crete temperature. This exponential function is used to com-pute an equivalent age of the concrete at some specifiedtemperature as follows

(2-2)

wherete = equivalent age at a specified temperature Ts, days or

hrQ = activation energy divided by the gas constant, KTa = average temperature of concrete during time interval

∆t, KTs = specified temperature, K∆t = time interval, days or hr

In Eq. (2-2), the exponential function converts a time in-terval, ∆t, at the actual concrete temperature to an equivalentinterval (in terms of strength gain) at the specified tempera-ture. In the U.S., the specified temperature is 23 C (≈ 296 K),while in the Scandinavian countries 20 C (≈ 293 K) is used.The exponential function in Eq. (2-2) can be thought of as anage conversion factor. To calculate the equivalent age of aconcrete mixture, one needs the value of a characteristicknown as the activation energy , which depends on the typeof cementitious materials (Carino and Tank 1992). The wa-ter-cement ratio may also influence the activation energy.The Q-value in Eq. (2-2) is the activation energy divided bythe gas constant [≈ 8.31 joules/(mole-K)]. ASTM C 1074recommends a Q-value of 5000 K for concrete made withType I cement. Fig. 2.11 shows how the age conversion fac-

t e ΣeQ

1Ta

----- 1Ts

-----– –

= ∆t

tor varies with concrete temperature for Q=5000 K and aspecified temperature of 23 C.

To use the maturity method requires establishing thestrength-maturity relationship for the concrete that will beused in the structure. The temperature history of the in-placeconcrete is continuously monitored and from this data the in-place maturity index (temperature-time factor or equivalentage) is computed. Knowing the in-place maturity index andstrength-maturity relationship, the in-place strength can beestimated. Instruments are available that automatically com-pute the maturity index, but care should be exercised in theiruse because the value of T0 or Q used by the instrument maynot be applicable to the concrete in the structure. ASTM C


Fig. 2.11—Age conversion factor for Q = 5000 K and speci-fied temperature of 23 C based on Eq. (2-2)

1074 gives the procedure for using the maturity method andprovides examples of how to compute the temperature-timefactor or equivalent age from the recorded temperature his-tory of the concrete. ACI 306R illustrates the use of the ma-turity method to estimate in-place strength during coldweather concreting operations.

The maturity method is intended for estimating strengthdevelopment of concrete. Strength estimates are based ontwo important assumptions: (1) there is sufficient water forcontinued hydration, and (2) the concrete in the structure isthe same as that used to develop the strength-maturity rela-tionship. Proper curing procedures (as provided in ACI 308)will ensure that the first condition is satisfied. The secondcondition requires additional confirmation that the concretein the structure has the correct strength potential. This can beachieved by performing accelerated strength tests on con-crete sampled from the structure or by performing other in-place tests that give positive indications of the strength level.Such verification is essential when estimates of in-placestrength are used for timing critical operations such as form-work removal or application of post-tensioning.

2.8—Cast-in-place cylinders (ASTM C 873)This is a technique for obtaining cylindrical concrete spec-

imens from newly cast slabs without drilling cores. Themethod is described in ASTM C 873 and involves using amold, as illustrated in Fig. 2.12. The outer sleeve is nailed to

Fig. 2.12—Special mold and support hardware to obtain

the formwork and is used to support a cylindrical mold. Thesleeve can be adjusted for different slab thicknesses. Themold is filled when the slab is cast, and the concrete in themold is allowed to cure along with the slab. The objective ofthe technique is to obtain a test sample that has been subject-ed to the same thermal history as the concrete in the struc-ture. When it is desired to know the in-place strength, themold is removed from the sleeve and stripped from the con-crete cylinder. The cylinder is capped and tested in compres-sion. For cases in which the length-to-diameter ratio of thecylinders is less than two, the measured compressivestrengths need to be corrected by the factors in ASTM C 42.

2.9—Combined methodsThe term combined method refers to the use of two or more

in-place test methods to estimate concrete strength. By com-bining results from more than one in-place test, a multi-vari-able correlation can be established to estimate strength.Combined methods are reported to increase the reliability ofthe estimated strength. The underlying concept is that if thetwo methods are influenced in different ways by the samefactor, their combined use results in a canceling effect thatimproves the accuracy of the estimated strength. For exam-ple, an increase in moisture content increases pulse velocitybut decreases the rebound number.

Combined methods were developed and have been used inEastern Europe to evaluate concrete strength in existing con-struction or in precast elements (Fa•ca•oaru; Teodoru 1986,1988). Combinations such as pulse velocity and reboundnumber (or pulse velocity, rebound number, and pulse atten-uation) have been reported to result in strength relationships

with higher correlation coefficients than when the methodsare used individually. However, the improvements have usu-ally only been marginal (Tanigawa et al. 1984; Samarin andDhir 1984; Samarin and Meynink 1984; Teodoru 1988).

It is emphasized that the combining of methods is not an endin itself. A combined method should be used in those caseswhere it is the most economical way to obtain a reliable esti-mate of concrete strength (Leshchinsky 1991). In NorthAmerica, the use of combined methods has aroused little inter-est among researchers and practitioners. As a result, there havebeen no efforts to develop ASTM standards for their use.

2.10—SummaryMethods that can be used to estimate the in-place strength

of concrete have been reviewed. While other procedureshave been proposed (see Malhotra 1976; Bungey 1989; Mal-hotra and Carino 1991), the discussion has been limited tothose techniques that have been standardized as ASTM testmethods.

cast-in-place cylindrical concrete sample


CHAPTER 3—STATISTICAL CHARACTERISTICS OF TEST RESULTS

Table 2.1 summarizes the relative performance of the in-place tests discussed in this report in terms of accuracy of es-timated strength and ease of use. The table also indicatesmethods that are applicable to new construction and thosethat are applicable to existing construction. Generally, thosemethods requiring embedment of hardware are limited to usein new construction. A test method having an entry of “++”means that the method is relatively easy to use or that it re-sults in more accurate estimates of strength compared with atest method having an entry of “+”. In general, those tech-niques that involve preplanning of test locations and embed-ment of hardware require more effort to use. However, thosemethods also tend to give more reliable strength estimates.The user should consider the relative importance of each ofthese attributes in selecting the most appropriate in-placetesting system for a particular application.

In-place tests provide alternatives to core tests for estimat-ing the strength of concrete in a structure, or can supplementthe data obtained from a limited number of cores. Thesemethods are based on measuring a concrete property thatbears some relationship to strength. The accuracy of thesemethods is, in part, determined by the degree of correlationbetween strength and the physical quantity measured by thein-place test. For proper evaluation of test results, the usermust be aware of those factors other than concrete strengththat can affect the test results. Additional fundamental re-search is needed to improve our understanding of how thesemethods are related to concrete strength and how the test re-sults are affected by factors other than strength.

An essential step for using these methods to estimate thein-place strength is the development of a relationship be-tween strength and the quantity measured by the in-placetest. The data acquired for developing the strength relation-ship provide valuable information on the reliability of thepredictions. Subsequent chapters of this report discuss thestatistical characteristics of the tests, methods for developingstrength relationships, planning of in-place tests and inter-pretation of the results. The final chapter deals with the useof in-place tests for acceptance of concrete.

Table 2.1—Relative performance of in-place tests

Accuracy*

Ease of use*Test methodASTM

standardNew

constructionExisting

construction

Reboundnumber C 805 + + ++

Penetrationresistance C 803 + + ++

Pullout C 900 ++ ++† +

Break-off C 1150 ++ ++ +

Pulse velocity C 597 ++ + +

Maturity C 1074 ++‡ N.A. +

Cast-in-placecylinder C 873 ++ N.A. +

* A test method with a “++” results in a more accurate strength estimate or is easier to use than a method with a “+”. “N.A.” indicates that the method is not applicable to existing construction.

† ASTM test method does not exist.‡ Requires verification by other tests.

3.1—Need for statistical analysisIn designing a structure to safely resist the expected loads,

the engineer uses the specified compressive strength fc′ of theconcrete. The strength of the concrete in a structure is vari-able and, as indicated in ACI 214, the specified compressivestrength is generally assumed to represent the strength that isexpected to be exceeded with about 90-percent probability.To ensure that this condition is satisfied, the concrete sup-plied for the structure must have an average standard-curedcylinder strength more than fc′ as specified in Chapter 4 ofACI 318. When the strength of concrete in a structure is un-der scrutiny because of low standard-cured cylinderstrengths or because of suspected curing deficiencies, ACI318 states that the concrete is structurally adequate if the in-place strength, as represented by the average core strength, isnot less than 0.85 fc′.

In assessing the ability of a partially completed structure toresist construction loads, it is therefore reasonable that thetenth-percentile in-place compressive strength (strength ex-ceeded with 90-percent probability) should be equal to atleast 0.85 of the required compressive strength at the time ofapplication of the construction loads. The required strengthmeans the compressive strength used in computing the nom-inal load resistance of structural elements. In-place tests canbe used to estimate the tenth-percentile strength with a highdegree of confidence only if test data are subjected to statis-tical analysis.

The use of the tenth-percentile strength as the level of thein-place strength that should be relied upon to resist appliedconstruction loads is perceived as a reasonable procedure byusers of in-place tests. The critical nature of construction op-erations in partially completed structures, the sensitivity ofearly age strength on the previous thermal history of the con-crete, and the general lack of careful consideration of con-struction loading during the design of a structure, dictate theuse of a conservative procedure for evaluating in-place testresults. However, for situations where the consequences of afailure may not be serious, the estimated mean strength maybe an acceptable measure to assess the adequacy of the in-place strength for proceeding with construction operations.Examples of such situations would include slabs on-grade,pavements, and some repairs. Inadequate strength at the timeof a proposed construction operation can usually be reme-died by simply providing for additional curing before pro-ceeding with the operation.

In-place tests may also be used to evaluate the strength ofan existing structure. Often they are used to answer questionsthat arise because of low strengths of standard-cured cylin-ders. Failure to meet specified acceptance criteria can resultin severe penalties for the builder. In such cases, the use ofthe tenth-percentile strength as the reliable strength level toresist design loads is not the appropriate technique for ana-lyzing in-place test data. The existing ACI-318 criteria forthe acceptance of concrete strength in an existing structureare based on testing cores. Based on ACI 318, if the average


compressive strength of three cores exceeds 85 percent ofthe specified compressive strength and no single corestrength is less than 75 percent of the specified strength, theconcrete strength is deemed to be acceptable. However, thereare no analogous acceptance criteria for the estimated in-place compressive strength based on in-place tests. Chapter7 discusses how in-place testing could be used for accep-tance of concrete.

To arrive at a reliable estimate of the in-place compressivestrength by using in-place tests, one must account for the fol-lowing primary sources of uncertainty.

1. The uncertainty in the average value of the in-place testresults.

2. The uncertainty in the relationship between compres-sive strength and the in-place test results.

3. The inherent variability of the in-place compressivestrength.

The first source of uncertainty is associated with the inher-ent variability (repeatability) of the test method. This subjectis discussed in the remainder of this chapter.

3.2—Repeatability of resultsThe uncertainty of the average value of the in-place test re-

sults is indicated by the standard deviation of the results andby the number of tests. The standard deviation is in turn afunction of the repeatability of the test and the variability ofthe concrete in the structure.

In this report, repeatability means the standard deviationor coefficient of variation of repeated tests by the same oper-ator on the same material. This is often called the within-testvariation and shows the inherent scatter associated with aparticular test method.

Data on the repeatability of some in-place tests are provid-ed in the precision statements of the ASTM standards gov-erning the tests. Some information on the repeatability ofother tests may be found in published reports. Unfortunately,most published data deal with correlations with standardstrength tests, rather than with repeatability. As will be seen,conclusions about repeatability are often in conflict becauseof differences in test designs or in data analysis.

3.2.1 Rebound number—The precision statement ofASTM C 805 states that the within-test standard deviation ofthe rebound hammer test is 2.5 rebound numbers. Teodoru*

reported an average standard deviation of 3.75, for averagerebound numbers ranging from 20 to 40, and the standard de-viation was independent of the average rebound number.

The results of three studies that evaluated the performanceof various in-place tests provide additional insight into therepeatability of the rebound number test. Keiller (1982) usedeight different mixtures and took 12 replicate rebound read-ings at ages of seven and 28 days. Carette and Malhotra(1984) used four mixtures and took 20 replicate readings atages of one, two and three days. Yun et al. (1988) used fivemixtures of concrete and took 15 replicate readings at agesranging from one to 91 days.

* Teodoru, G., “Quelques Aspects du Contrôle Statistique de la Qualité du BétonBasé sur le Essais Nondestructifs,” meeting of RILEM NDT committee, Slough,England, 1970.

Fig. 3.1 shows the standard deviations of the reboundnumbers as a function of the average rebound number. Thedata from the three studies appear to follow the same pattern.In the study by Carette and Malhotra (1984), the maximumaverage rebound number ranged from 15 to 22 and the aver-age standard deviation was 2.4. In the study by Keiller(1982), the average rebound number ranged from 18 to 35,and the average standard deviation was 3.4. In the work byYun et al. the range in average rebound number was 12 to 32,and the average standard deviation was 2.5.

Examination of Fig. 3.1 shows that there may be a trend ofincreasing standard deviation with increasing average re-bound number, in which case the coefficient of variation is abetter measure of repeatability. Fig. 3.2 shows the coeffi-

Fig. 3.1—Within-test standard deviation as a function of the average rebound number

cients of variation plotted as function of average reboundnumber. There does not appear to be any trend with increas-ing rebound number. In contrast, however, Leshchinsky etal. (1990) found that the coefficient of variation and its vari-ability tended to decrease with increasing concrete strength.The average coefficients of variation from the studies byCarette and Malhotra (1984) and by Keiller (1982) haveequal values of 11.9, while the average value from the studyby Yun et al. is 10.4.

In Fig. 3.2, the coefficients of variation are not constant.However, it must be realized that the values are based onsample estimates of the true averages and standard devia-tions. With finite sample sizes there will be variations inthese estimates, and a random variation in the computed co-efficient of variation is expected although the true coefficientof variation may be constant. Thus it appears that the repeat-ability of the rebound number technique may be describedby a constant coefficient of variation, which has an averagevalue of about 10 percent.

3.2.2 Penetration resistance—The precision statement inASTM C 803 states that, for the probe penetration test, thewithin-test standard deviations of exposed probe length forthree replicate tests are:


Fig. 3.2—Within-test coefficient of variation as a function of

Mortar 0.08 in. (2.0 mm)Concrete - 1 in. (25 mm) MSA 0.10 in. (2.5 mm)Concrete - 2 in. (50 mm) MSA 0.14 in. (3.6 mm)

average rebound number

Fig. 3.3—Within-test standard deviation as a function of average exposed length of probes

Fig. 3.4—Within-test coefficient of variation as a function of average exposed length of probe

The data provided by Carette and Malhotra (1984) and byKeiller (1982), which include concrete strengths in the rangeof 1500 to 7000 psi (10 to 50 MPa), give additional insightinto the underlying measure of repeatability for this test. Fig.3.3 shows the standard deviations of the exposed length ofthe probes as a function of the average exposed length. Thevalues from Carette and Malhotra (1984) are based on theaverage of six probes, while Keiller’s (1982) results arebased on three probes. Except for one outlying point, there isa trend of decreasing within-test variability with increasingexposed length. In Fig. 3.4, the coefficients of variation ofexposed length are shown as a function of the average ex-posed length. The decreasing trend with increasing concretestrength is more pronounced than in Fig. 3.3. Thus the re-peatability of the exposed length is neither described by aconstant standard deviation nor a constant coefficient ofvariation.

The customary practice is to measure the exposed lengthof the probes, but concrete strength has a direct effect on thedepth of penetration. A more logical approach is to expressthe coefficient of variation in terms of depth of penetration .Fig. 3.5 shows the coefficient of variation of the penetrationdepth as a function of average penetration. In this case, thereis no clear trend with increasing penetration. The higher scat-ter of the values from Keiller’s (1982) tests may be due totheir smaller sample size compared with the tests of Caretteand Malhotra (1984). Note that the standard deviation hasthe same value whether exposed length or penetration depthis used. However, the value of the coefficient of variation de-pends on whether the standard deviation is divided by aver-age exposed length or average penetration depth.

Hence, it appears that a constant coefficient of variation ofthe penetration depth can be used to describe the within-testvariability of the probe penetration test. The work by Caretteand Malhotra (1984) is the first known study that uses thismethod for defining the repeatability of the penetration test.However, other test data using the probe penetration systemcan be manipulated to yield the coefficient of variation ofpenetration depth provided two of these three quantities are

Fig. 3.5—Within-test coefficient of variation as a function of average penetration depth of probes


given: average exposed length, standard deviation, and/orcoefficient of variation of exposed length. Using the datagiven in Table 6 of Malhotra’s 1976 review, the followingvalues for average coefficients of variation for depth of pen-etration have been calculated:

In the study by Carette and Malhotra (1984), the maximumaggregate size was 3/4 in. (20 mm) and the average coefficientof variation was 5.4 percent, while in the study by Keiller(1982) it was 7.8 percent for the same maximum aggregatesize. Other work (Swamy and Al-Hamad 1984) used 3/8 in.(10 mm) maximum aggregate size, and the coefficients ofvariation ranged between 2.7 and 7 percent. For commonlyused 3/4 in. (19 mm) aggregate, it is concluded that a coeffi-cient of variation of 5 percent is reasonable.

There are limited data on the repeatability of the pin pene-tration test. Nasser and Al-Manaseer (1987b) reported an av-erage coefficient of variation of about 5 percent for replicatetests on 4-in. (100-mm) thick slab specimens and on the bot-tom surfaces of 6 x 12-in. (150 x 300-mm) cylinders. Thevariability was based on the “best five of seven” readings,and the concrete strength varied from about 500 to 3500 psi(3.5 to 25 MPa). In another study (Carino and Tank 1989),eight replicate pin tests were performed at the midheight of4 x 8-in. (100 x 200-mm) cylinders. The compressivestrengths ranged from about 1000 to 5800 psi (7 to 40 MPa).Each set of replicate pin tests was analyzed for outliers dueto penetrations into large air voids or coarse aggregate parti-cles. On average, two of the eight readings were discarded.Fig. 3.6 shows the standard deviations of the valid penetra-tion values plotted as function of the average penetration.(Note that a high penetration corresponds to low concretestrength.) There is no clear trend between the standard devi-ation and the average penetration. The average standard de-viation is 0.016 in. (0.41 mm), which is the value adopted inthe precision statement of ASTM C 803. To compare withthe variability reported by Nasser and Al-Manaseer (1987b),the results in Fig. 3.6 are presented in terms of coefficient of

Maximum aggregate size, in. (mm) Coefficient of variation of penetration depth, percent

2 (50) 141 (25) 8, 63/4 (20) 3.5, 4.7, and 5.6

Fig. 3.6—Standard deviation of pin penetration tests on 4 x 8-in. (100 x 200-mm) cylinders (Carino and Tank 1989)

variation in Fig. 3.7. The average coefficient of variation is

Fig. 3.7—Coefficient of variation of pin penetration tests on 4 x 8-in. (100 x 200-mm) cylinders (Carino and Tank 1989)

7.4 percent.Additional data are needed on the repeatability of the pin

penetration test. Based on available information, a coeffi-cient of variation of 8 percent is recommended for planningpin penetration tests.

3.2.3 Pullout test—Currently, ASTM C 900 does not havea precision statement. However, there are published data onthe within-test variability of this test. Stone, Carino, andReeve (1986) examined whether standard deviation or coef-ficient of variation is the best measure of repeatability. Fourtest series were performed. Three of them used a 70-deg apexangle but different aggregate types: river gravel, crushedlimestone, and expanded lightweight shale. The fourth series

was for a 54-deg angle with river-gravel aggregate. Thesetest series are identified as G70, LS, LW, and G54 in Fig. 3.8and 3.9. The embedment depth was about 1 in. (25 mm), and
compressive strength of concrete ranged from about 1500 to6000 psi (10 to 40 MPa). Fig. 3.8 shows the standard devia-tion, using 11 replications, as a function of the average pull-out load. It is seen that there is a tendency for the standarddeviation to increase with increasing pullout load. Fig. 3.9shows the coefficient of variation as a function of the aver-age pullout load. In this case, there is no trend between thetwo quantities. Thus, it may be concluded that the coefficientof variation should be used as a measure of the repeatabilityof the pullout test.
Table 3.1 gives the reported coefficients of variation from
different laboratory studies of the pullout test. Besides thesedata, the work of Krenchel and Petersen* summarizes the re-peatability obtained in 24 correlation testing programs in-volving an insert with a 1-in. (25-mm) embedment and a 62-
* Krenchel, H., and Petersen, C. G., “In-Place Testing with Lok-Test: Ten YearsExperience,” presented at the International Conference on In Situ/NondestructuveTesting of Concrete, Oct. 2-5, 1984, Ottawa, Ontario, Canada.


Fig. 3.8—Within-test standard deviation as a function of average pullout load (Stone, Carino, and Reeve 1986)

Fig. 3.9—Within-test coefficient of variation as a function of average pullout load (Stone, Carino, and Reeve 1986)

Table 3.1—Summary of within-test coefficient of variation of pullout test

ReferenceApex angle,

degEmbedment

depth, in.Maximum aggre-

gate size, in. Aggregate type Sample size

Coefficient of variation, percent

Range Average

Malhotra and Carette (1980) 67 2 1 Gravel 2 00.9-14.3 5.3

Malhotra (1975) 67 2 1/4 Limestone 3 2.3-6.3 3.9

Bickley (1982) 62 1 3/8 ? 8 3.2-5.3 4.1

Khoo (1984) 70 1 3/4 Granite 6 1.9-12.3 6.9

Carette and Malhotra (1984) 67 2 3/4 Limestone 4 1.9-11.8 7.1

62 1 3/4 Limestone 10 5.2-14.9 8.5

Keiller (1982) 62 1 3/4 Limestone 6 7.4-31 14.8

Stone et al. (1986) 70 1 3/4 Gravel 11 4.6-14.4 10.2

70 1 3/4 Limestone 11 6.3-14.6 9.2

70 1 3/4 Lightweight 11 1.4-8.2 6.0

54 1 3/4 Gravel 11 4.3-15.9 10.0

Bocca (1984) 67 1.2 1/2 ? 24 2.8-6.1 4.3

1 in. = 25.4 mm.

degree apex angle. The reported coefficients of variationranged from 4.1 to 15.2 percent, with an average of 8 per-cent. The tests reported in Table 3.1 and by Krenchel and Pe-tersen have involved different test geometries and differenttypes and sizes of coarse aggregate. In addition, the geome-try of the specimens containing the embedded inserts wasdifferent, with cylinders, cubes, beams, and slabs being com-mon shapes. Because of these testing differences, it is diffi-cult to draw firm conclusions about the repeatability of thepullout test.

Table 3.2 summarizes the coefficients of variation ob-
tained in a study by Stone and Giza (1985) designed to ex-amine the effects of different variables on test repeatability.The column labeled sample size shows the number of groupsof tests, with each group containing 11 replications. For theconditions studied it was found that embedment depth andapex angle did not greatly affect repeatability. On the otherhand, the maximum nominal aggregate size appeared to havesome effect, with the 3/4-in. (20-mm) aggregate resulting inslightly greater variability than for smaller aggregates. In ad-dition, the aggregate type also appears to be important. For
tests with lightweight aggregate, the variability was lowerthan for tests with normal weight aggregates. In this study,companion mortar specimens were also tested and the coef-ficients of variation varied between 2.8 and 10.6 percent,with an average value of 6.2 percent. Thus the repeatabilitywith lightweight aggregate is similar to that obtained withmortar.

Experimental evidence suggests that the variability of thepullout test should be affected by the ratio of the mortarstrength to coarse aggregate strength and by the maximumaggregate size. As aggregate strength and mortar strengthbecome similar, repeatability is improved. This explainswhy the tests by Stone and Giza (1985) with lightweight ag-gregate performed like tests with plain mortar. Results fromBocca (1984), summarized in Table 3.2, also lend support tothis pattern of behavior. In this case, high-strength concretewas used and the high mortar strength approached that of thecoarse aggregate. This condition, and the use of small maxi-mum aggregate size, may explain why the coefficients ofvariation were lower than typically obtained with similarpullout test configurations on lower strength concrete.


Table 3.2—Summary of results from investigation of pullout test (Stone and Giza 1985)

Test series Apex angle, degEmbedment depth,

in.Maximum aggre-

gate size, in. Aggregate type Sample size


Range Average

Apex angle 30 0.98 3/4 Gravel 2 x 11 9.1-11.4 10.3

46 0.98 3/4 Gravel 4 x 11 5.6-18.7 11.1

54 0.98 3/4 Gravel 2 x 11 6.3-6.7 6.5

58 0.98 3/4 Gravel 2 x 11 8.6-10.0 9.3

62 0.98 3/4 Gravel 2 x 11 7.5-9.6 8.6

70 0.98 3/4 Gravel 4 x 11 8.0-10.1 8.8

86 0.98 3/4 Gravel 2 x 11 9.0-10.8 9.9

Embedment 58 0.47 3/4 Gravel 1 x 11 — 12.9

58 0.78 3/4 Gravel 2 x 11 7.7-14.0 10.9

58 0.91 3/4 Gravel 2 x 11 6.5-6.7 6.6

58 0.98 3/4 Gravel 2 x 11 8.8-10.7 9.8

58 1.06 3/4 Gravel 2 x 11 9.1-11.1 10.1

58 1.69 3/4 Gravel 2 x 11 11.5-11.9 11.7

Aggregate size 70 0.98 1/4 Gravel 2 x 11 6.5-7.0 6.8

70 0.98 3/8 Gravel 5 x 11 4.9-6.5 6.0

70 0.98 1/2 Gravel 5 x 11 3.3-10.6 6.7

70 0.98 3/4 Gravel 4 x 11 8.0-10.1 8.8

Aggregate type 70 0.98 3/4 Lightweight 2 x 11 5.6-5.7 5.7

70 0.98 3/4 Gravel 4 x 11 8.0-10.1 8.8

70 0.98 3/4 Crushed gneiss 2 x 11 7.2-16.8 12.0

70 0.98 3/4 Porous limestone 2 x 11 7.7-10.9 9.3

1 in. = 25.4 mm.

In summary, a variety of test data has been accumulated onthe repeatability of the pullout tests. Differing results can of-ten be explained because of differences in the materials andthe testing conditions. In general, it appears that an averagecoefficient of variation of 8 percent is typical for pullout testsconforming with the requirements of ASTM C 900 and withembedment depths of about 1 in. (25 mm). The actual valueexpected in any particular situation will be affected primarilyby the nature of the coarse aggregate, as discussed in previ-ous paragraphs.

3.2.4 Break-off test—Failure during the break-off test isdue to the formation of a fracture surface at the base of thecore (see Fig. 2.8). The crack passes through the mortar and,usually, around coarse aggregate particles at the base of thecore. The force required to break off the core is influencedby the particular arrangement of aggregate particles withinthe failure region. Because of the small size of the fracturesurface and the heterogeneous nature of concrete, the distri-bution of aggregate particles will be different at each test lo-cation. Hence one would expect the within-test variability ofthe break-off test to be higher than that of other standardstrength tests that involve larger test specimens. One wouldalso expect that the variability might be affected by maxi-mum aggregate size and aggregate shape.

The developer of the break-off test reported a within-testcoefficient of variation of about 9 percent (Johansen 1979).This value has generally been confirmed by other investiga-tors. Table 3.3 summarizes some published data on within-
test variability of the break-off test. The results have beengrouped according to nominal maximum aggregate size and
aggregate type (river gravel and crushed stone). The num-bers of replicate tests are also listed. The following observa-tions can be made:

• The variability tends to increase with increasing maxi-mum aggregate size.

• The variability in concrete made with river gravel tendsto be higher than in concrete made with crushed stone.

In Table 3.3, the variability reported by Barker andRamirez (1988) is lower than that reported by others. Part ofthe difference may be due to the experimental technique. Inmost of the research, break-off tests have been performed onslab specimens. However, Barker and Ramirez inserted theplastic sleeves into the tops of a 6 x 6-in (150 x 150-mm) cyl-inders. It is possible that the confining effects of the cylindermold produced more reproducible conditions at the base ofthe cores.

The results of Naik et al. (1987) suggest that the variabilityof break-off tests on drilled cores is comparable to that ob-tained on cores formed by inserting sleeves into fresh con-crete. However, it should be noted that cores were drilledinto concrete having a compressive strength greater than ap-proximately 3000 psi (20 MPa). Thus additional data areneeded to determine the lowest concrete strength for whichcore drilling does not affect the integrity of the concrete atthe base of the core.

In summary, the results summarized in Table 3.3 supportJohansen’s (1979) claim that the break-off test has a within-test coefficient of variation of about 9 percent. The variabil-ity is expected to be slightly higher for concrete made with


CHAPTER 4—DEVELOPMENT OF STRENGTHRELATIONSHIP

Table 3.3—Within-test coefficient of variation of break-off test

Reference MSA,* in.Coarse aggregate

type Replicate tests


Range Average

Johansen (1976) 1 Unknown 5 Not available 9.7

1 Gravel 5 8.7

11 /2 Unknown 5 12.3

Sand None 5 4.1

Keiller (1982) 3/4 Crushed stone 6 4.2-15.8 9.4

3/4 Gravel 6 8.2

Nishikawa (1983) 1/2 Gravel 10 5.1-13.7 9.9

1/2 Crushed stone 10 † 8.0

3/8 Gravel 10 † 4.7

3/4 Gravel 10 † 9.0

1 Gravel 10 † 13.3

Naik et al. (1987)(sleeves)

(cores)

3/4 Crushed stone 5,6 3.5-11.7 6.8

3/4 Gravel 5,6 3.0-17.9 10.6

3/4 Crushed stone 5 2.8-11.6 6.2

3/4 Gravel 5 3.6-12.9 8.3

Barker and Ramirez (1988)

1/2 Gravel 4 2.4-13.9 6.0

1/2 Crushed stone 4 2.9-7.2 4.8

1 Gravel 4 3.8-14.3 6.8

* MSA = Nominal maximum aggregate size.† Only one test series.1 in. = 25.4 mm.

nominal maximum aggregate size greater then 3/4 in. (20mm).

3.2.5 Pulse velocity—In contrast to the previous test tech-niques that examine a relatively thin layer of the concrete ina structure, the pulse-velocity method examines the entirethickness of concrete between the transducers. Localized dif-ferences in the composition of the concrete because of inher-ent variability are expected to have a negligible effect on themeasured travel times of the ultrasonic pulses. Thus the re-peatability of this method is expected to be much better thanthe previous techniques.

Table 3.4 reports the within-test variability of pulse-veloc-ity measurements obtained by different investigators. ASTMC 597 states that the repeatability of test results is within 2percent, for path lengths from 1 to 20 ft (0.3 to 6 m) throughsound concrete and for different operators using the same in-strument or one operator using different instruments.

3.2.6 Maturity method—In the maturity method, the tem-perature history of the concrete is recorded and used to com-pute a maturity index. Therefore, the repeatability of thematurity indices depends on the instrumentation used. Onewould expect the repeatability to be lower when using anelectronic maturity meter than when maturity is computedfrom temperature readings on a strip-chart recorder. Howev-er, at present there are no published data on repeatability ofmaturity measurements using different instrumentation.

3.2.7 Cast-in-place cylinder—This test method involvesthe determination of the compressive strength of cylindricalspecimens cured in the special molds located in the structure.Thus the repeatability would be expected to be similar to oth-er compression tests on cylinders. Few data have been pub-lished. Bloem (1968) reported a within-test coefficient ofvariation ranging from 2.7 to 5.2 percent with an average of

3.8 percent for three replicate tests at ages from 1 to 91 days.Richards* reported values from 1.2 to 5.8 percent with an av-erage of 2.8 percent for two replicate tests at ages of from 7to 64 days. Data from Carino et al. (1983b), in which threereplicate cylinders were tested at ages ranging from one to 32days, show an average coefficient of variation of 3.8 percent.

ASTM C 873 states that the single-operator coefficient ofvariation is 3.5 percent for a range of compressive strengthbetween 1500 psi (10 MPa) and 6000 psi (40 MPa).

4.1—GeneralManufacturers of in-place testing equipment typically pro-

vide relationships that relate the quantity measured by theparticular test device to the compressive strength of standardspecimens. However, it is recommended that the user estab-lish such a relationship for the specific test instrument thatwill be used in the investigation and for the specific concretein the structure. The general approach is to perform replicatein-place tests and standard strength tests at various strengthlevels, and use statistical procedures to establish the relation-ship. The details, however, will depend on whether the in-place tests are to be used in new construction or in existingstructures.

The standard specimen may be the standard cylinder orstandard cube. Very often, the in-place tests are correlatedwith the compressive strength of cores, since core strength isthe most established and accepted measure of in-placestrength. The statistical techniques for establishing the

* Personal communication from former committee member Owen Richards.


strength relationship are independent of the type of “stan-dard” specimen. However, the specimen type is importantwhen interpreting the results of in-place tests.

4.2—New construction4.2.1 General—For new construction, the preferred ap-

proach is to establish the strength relationship by a laborato-ry testing program that is performed before using the in-place test method in the field. The testing program typicallyinvolves preparing test specimens using the same concretingmaterials to be used in construction. At regular intervals,measurements are made using the in-place test techniques,and the compressive strengths of standard specimens are alsomeasured. The paired data are subjected to regression analy-sis to determine the best-fit estimate of the strength relation-ship.

For some techniques it may be possible to perform the in-place test on standard specimens without damaging them,and the specimens can be subsequently tested for compres-sive strength. Usually, in-place tests are carried out on sepa-rate specimens, and it is extremely important that the in-place tests and standard tests are performed on specimenshaving similar compaction and at the same maturity. Thismay be achieved by using curing conditions that insure sim-ilar internal temperature histories. Alternatively, internaltemperatures can be recorded and test ages can be adjustedso that the in-place and standard tests are performed at thesame maturity index.

In developing the test plan to obtain a reliable strength re-lationship, the user should consider the following questions:

• How many strength levels (i.e., test points) are needed?• How many replicate tests should be performed at each

strength level?• How should the data be analyzed?4.2.2 Number of strength levels—The number of strength

levels required to develop the strength relationship dependson the desired level of precision and the cost of additionaltests. Section A.1 in the appendix discusses how the number

Table 3.4—Within-test coefficient of variation for pulse-velocity tests

Reference


Range Average

Keiller (1982) 0.5-1.5 1.1

Carette and Malhotra (1984)

0.1-0.8 0.4

Bocca (1984) 0.4-1.2 0.7

Yun et al. (1988) 0.4-1.1 0.6

Leshchinsky et al. (1990)

0.2-4 1.9

of test points used to develop the strength relationship affectsthe uncertainty of the estimated strength. From that discus-sion, it was concluded that in planning the correlation testingprogram, six to nine strength levels should be considered.Using fewer than six strength levels may result in high un-certainties in the estimated strength and using more than ninelevels may not be economically justifiable.

The range of strengths used in the correlation testing pro-gram should cover the range of strengths that are to be esti-mated in the structure. This will insure that the strengthrelationship will not be used for extrapolation beyond therange of the correlation data. Therefore, if low in-placestrengths are to be estimated, such as during slipforming, thetesting program must include these low strength levels. Thechosen strength levels should be evenly distributed withinthe strength range.

4.2.3 Number of replications—The number of replicatetests at each strength level affects the uncertainty of the av-erage values. The standard deviation of the computed aver-age varies with the inverse of the square root of the numberof replicate tests used to obtain the average. The effect of thenumber of tests on the precision of the average is similar tothat shown in Fig. A.1 (appendix).

Statistics show (ASTM E 122) that the required number ofreplicate tests depends on: (1) the within-test variability ofthe method; (2) the allowable error between the sample av-erage and the true average; and (3) the confidence level thatthe allowable error is not exceeded. However, the number ofreplicate tests is often based upon customary practice. Forexample, in acceptance testing, ACI 318 considers a test re-sult as the average compressive strength of two molded cyl-inders. Therefore, in correlation testing, two replicatestandard compression tests can be assumed to be adequatefor measuring the average compressive strength at each lev-el.

The number of companion in-place tests at each strengthlevel should be chosen so that the averages of the in-placetests and compressive strengths have similar certainty. Toachieve this condition, the ratio of the number of tests equalsthe square of the ratio of the corresponding within-test coef-ficients of variation. If the number of replicate compressiontests at each strength level is two, the number of replicate in-place tests is

(4-1)

whereni = number of replicate in-place testsVi = coefficient of variation of in-place testVs = coefficient of variation of standard test

For planning purposes, the coefficients of variation givenin Chapter 3 may be used for the in-place tests. For moldedcylinders prepared, cured, and tested according to ASTMstandards, the within-test coefficient of variation can be as-sumed to be 3 percent. For cores a value of 5 percent may beassumed.

4.2.4 Regression analysis—After the data are obtained,the strength relationship must be determined. The usualpractice is to treat the average values of the replicate com-pressive strength and in-place test results at each strengthlevel as one data pair. The data pairs are plotted using the in-place test value as the independent value (or X variable) and

ni 2Vi

Vs

----- 2

=


the compressive strength as the dependent value (or Y vari-able). Regression analysis is performed on the data pairs toobtain the best-fit estimate of the strength relationship.

Historically, most strength relationships have been as-sumed to be straight lines, and ordinary least-squares (OLS)analysis has been used to estimate the corresponding slopesand intercepts. The use of OLS is acceptable if an estimate ofthe uncertainty of the strength relationship is not required toanalyze in-place test results, such as if the procedures in6.2.1 and 6.2.2 are used. However, if more rigorous methods,
such as those in 6.2.3 and 6.2.4, are used to analyze in-place tests results, a procedure that is more exact than OLS shouldbe used to establish the strength relationship and its associat-ed uncertainty.
The limitations of OLS analysis arise from two of its un-derlying assumptions

• There is no error in the X value• The error (standard deviation) in the Y value is constantExcept for measured maturity indices, the first of these as-

sumptions is violated because in-place tests (X value) gener-ally have greater within-test variability than compressiontests (Y value). In addition, it is generally accepted that thewithin-test variability of standard cylinder compression testsis described by a constant coefficient of variation (ACI214R). Therefore, the standard deviation increases with in-creasing compressive strength, and the second of the aboveassumptions is also violated. As a result, OLS analysis willunderestimate the uncertainty of the strength relationship(Carino 1993). There are, however, approaches for dealingwith these problems.

First, the problem of increasing standard deviation with in-creasing average strength is discussed. If test results fromgroups that have the same coefficient of variation are trans-formed by taking their natural logarithms, the standard devi-ations of the logarithm values in each group will have thesame value* (Ku 1969). Thus the second assumption of OLScan be satisfied by performing regression analysis using theaverage of the natural logarithms of the test results at eachstrength level. If a linear relationship is used, its form is asfollows:

ln C = a + B ln I (4-2)

whereln C = average of natural logarithms of compressive

strengthsa = intercept of lineB = slope of lineln I = average of natural logarithms of in-place test results

By obtaining the antilogarithm of ln C, Eq. (4-2) is trans-formed into a power function:

C = ea I B = A I B (4-3)

* In fact, the standard deviation of the transformed values will be approximately the same as the coefficient of variation of the original values, when the coefficient of vari-ation is expressed as a decimal fraction. For example, if the coefficient of variation of a group of numbers equals 0.05, the standard deviation of the transformed values will be approximately 0.05.

The exponent B determines the degree of nonlinearity ofthe power function. If B = 1, the strength relationship is astraight line passing through the origin with a slope = A . If B≠ 1, the relationship has positive or negative curvature, de-pending on whether B is greater than or less than one. Re-gression analysis using the natural logarithms of the testresults provides two benefits: 1) it satisfies an underlying as-sumption of OLS analysis (constant error in Y value), and 2)it allows for a nonlinear strength relationship, if such a rela-tionship is needed. Use of the transformed data implies thatconcrete strength is distributed as a log-normal rather than asnormal distribution. It has been argued that, for the usualvariability of concrete strength, the possible errors from thisassumption are not significant (Stone and Reeve 1986).

Next, a method for dealing with the problem of error in theX values is discussed. Fortunately, regression analysis thataccounts for X error can be performed with little additionalcomputational effort compared with OLS analysis. One suchprocedure was proposed by Mandel (1984) and was used byStone and Reeve (1986) to develop a rigorous procedure toanalyze in-place test results. Mandel's approach involves theuse of a parameter λ defined as the variance (square of thestandard deviation) of the Y variable divided by the varianceof the X variable. For the correlation testing program, thevalue of λ is obtained from the standard deviations of the av-erage compressive strength and in-place test results. If thenumber of replicates for compressive tests and in-place testsare chosen so that average values are measured with compa-rable precision, the value of λ should be close to one.

The parameter λ and the correlation testing results (the av-erages of the logarithms of the in-place results (X values)and the averages of the logarithms of compressive strengths(Y values) are used to determine the strength relationship us-ing the calculations outlined in Section A.2 (appendix). The
calculations involve the usual sums of squares and cross-products used in OLS analysis (Mandel 1984). The proce-dure is well suited for application on a personal computerwith a spreadsheet program.
Fig. 4.1 is a graphical representation of the difference be-
tween OLS analysis and Mandel’s procedure. In OLS analy-sis, the best-fit straight line is the one that minimizes the sumof squares of the vertical deviations of the data points fromthe line, as shown in Fig. 4.1(a). On the other hand, Mandel’sanalysis minimizes the sum of squares of the deviationsalong a direction inclined to the straight line, as shown inFig. 4.1(b). The direction of minimization depends on thevalue of λ, which is in turn dependent on the ratio of the er-rors in the Y and X values. As the error in the X value in-creases, the value of λ decreases and the angle θ in Fig.4.1(b) increases. An important feature of Mandel’s analysisis that the estimated standard deviation of the predicted valueof Y for a new value of X accounts for error in the new X val-ue and the error in the strength relationship (see A.3 in the appendix).
In summary, to establish the strength relationship, regres-sion analysis should be performed using the natural loga-rithms of the test results. This will accommodate the increasein within-test variability with increasing strength. Using a


Fig. 4.1—Direction of error minimization in: a) ordinary least-square analysis, and b) in Mandel’s procedure (Car-ino 1990)

straight line to represent the relationship between logarithmvalues is equivalent to assuming a power function strengthrelationship. The power function can accommodate a nonlin-ear relationship, if necessary. To be rigorous, the regressionanalysis procedure should account for the uncertainty in thein-place test results (X error). Failure to account for X errorwill underestimate the uncertainty of future estimates of in-place compressive strength. However, this rigorous proce-dure is justified only when an equally rigorous method willbe used to interpret in-place test results (see Chapter 6), oth-erwise, OLS analysis is acceptable.

4.2.5 Procedures for correlation testing—Ideally, it is de-sirable to determine the compressive strength and the in-place test result on the same specimen so that companion testresults are obtained at the same maturity. Unfortunately, thisis only possible with those methods that are truly nonde-structive, such as pulse velocity and rebound number. Formethods that cause local damage to the concrete, separatespecimens are needed for obtaining compressive strengthand the in-place test result. In such cases, it is important thatcompanion specimens are tested at the same maturity. Thisis especially critical for early-age tests when strength at agiven age is highly dependent on the previous thermal histo-ry. The problem arises because of differences in early-agetemperatures in specimens of different geometries. An ap-proach for moderating temperature differences is to cure allspecimens in the same water bath. Alternatively, internaltemperatures can be monitored and test ages adjusted so thatcompression tests and in-place tests are performed at equalvalues of the maturity index. Failure to perform companiontests on specimens that are at equal maturities will result inan inaccurate strength relationship that will cause systematicerrors (or bias) when it is used to estimate the in-placestrength in a structure. The following recommendationsshould be used in correlation testing programs.

4.2.5.1 Rebound number—At least 12 standard cylin-ders should be cast. At each test age, a set of ten reboundnumbers (ASTM C 805) should be obtained from each of apair of cylinders held firmly in a compression testing ma-chine or other suitable device at a pressure of about 500 psi(3 MPa). The rebound tests should be made in the same di-rection relative to gravity as they will be made on the struc-ture. The cylinders should then be tested in compression. Ifit is not feasible to test the cylinders with the hammer in thesame orientation that will be used to test the structure, thecorrection factors supplied by the equipment manufacturercan be used to account for differences in orientation. Asmentioned in Section 2.2, the surface produced by the mate-rial of the cylinder molds can differ from the surface pro-duced by the form material for the structure. This factorshould also be considered in the correlation testing. If con-siderable difference is expected between the surfaces of thestructure and the cylinders, additional prismatic specimensshould be prepared for rebound tests. These specimensshould be formed with the same type of forming materialsthat will be used in construction, and they should be similarin size to the cylinders so that they will experience similarthermal histories.

For accurate estimates of in-place strength, the moisturecontent and texture of the surfaces of the cylinders at the timeof the correlation tests should be similar to those anticipatedfor the concrete in the structure at the time of in-place test-ing. Practically, the only easily reproducible moisture condi-tion for concrete surfaces is the saturated condition.

4.2.5.2 Penetration resistance—For the probe penetra-tion test, at least 12 standard cylinders and a test slab largeenough for at least 18 probe penetration tests should be cast.For in-place testing of vertical elements, the recommendedprocedure is to cast a wall specimen and take cores next tothe probe tests. All test specimens should be cured underidentical conditions of moisture and temperature. At eachtest age, two compression tests and three probe penetrationtests should be made. The recommended minimum thicknessfor the test slab is 6 in. (150 mm). The minimum spacing be-tween probe penetrations is 7 in. (175 mm), and the mini-mum distance from a probe to a slab edge is 4 in. (100 mm).

For the pin penetration test, it may be possible to performpenetration tests on the sides of cylinders and subsequently


test the cylinders for compressive strength. Carino and Tank(1989) showed that the surface damage produced by pin pen-etrations into 4 x 8-in. (100 x 200-mm) cylinders did not re-sult in strength reductions. However, comparative tests werenot performed on specimens with concrete strength less than3700 psi (25.5 MPa). Until further studies are conducted toconfirm that pin penetrations do not affect the compressivestrength of cylinders for a wide range of concrete strength, itis recommended that slab specimens be used for pin penetra-tion tests. A minimum of six penetration readings should beperformed at each test age. Discard a result when obviouslyan aggregate particle or a large air void was penetrated. Inaddition, according to ASTM C 803, if the range of penetra-tion values exceeds 0.064 in. (1.6 mm), the result with themaximum deviation from the average should be discardedand a new test performed. Individual penetrations should bespaced between 2 and 6 in. (50 and 150 mm), and the mini-mum distance from an edge should be 2 in. (50 mm).

4.2.5.3 Pullout test—Several techniques have beenused. Pullout inserts have been cast in the bottom of standardcylinders, and a pullout test performed before testing thestandard cylinder in compression (Bickley 1982). In thiscase, the pullout test is stopped when the maximum load (in-dicated by a drop in the load with further displacement) hasbeen attained. The insert is not extracted and the cylinder canbe capped and tested in compression. Alternatively, compan-ion cylinders have been cast with and without inserts, and thepullout test has been performed on one standard cylinder andthe other cylinder tested in compression. Investigators havehad problems with both procedures, particularly at highstrengths, because radial cracking occurs at the end of thecylinder containing the pullout insert. This cracking is be-lieved to result in lower ultimate pullout loads.

A third alternative has been to cast standard cylinders forcompression testing and to place pullout inserts in cubes (orslabs or beams) so that the pullout tests can be made in thecompanion specimen when the standard cylinders are tested.This latter approach is the preferred method, providing com-paction is consistent between the standard cylinders and thecubes or other specimens containing the pullout inserts, andthe maturity of all specimens tested is the same. The recom-mended minimum size for cubes is 8 in. (200 mm) when 1-in. (25-mm)-diameter inserts are used. Four inserts can beplaced in each cube, one in the middle of each vertical side.For each test age, two standard cylinders should be testedand eight pullout tests performed.

4.2.5.4 Break-off test—The procedure for correlationtesting depends on how the system will be used in practice.If the break-off specimens will be formed by insertingsleeves, the correlation testing should involve the fabricationof a slab specimen (or specimens) and companion cylinders.The slabs should have a minimum thickness of 6 in. (150mm). The sleeves should be inserted into the top surface ofthe slab after the concrete has been consolidated and screed-ed. The slabs and cylinders should be subjected to identicalcuring conditions. When tests are performed, the break-offtest locations should be chosen randomly from the availablelocations. For applications in which the sleeves are to be at-

tached to the sides of formwork, the laboratory specimensshould simulate the conditions that will be encountered inthe field. For example, if the sleeves will be used on verticalfaces of the formwork, the laboratory specimens should bemade with the sleeves on the vertical faces of the forms.

When the in-place break-off test specimens will be pre-pared by core drilling, the correlation testing should involvecore drilling into a slab or wall specimen. At each test age,the location of the drilled cores for break-off specimensshould be selected randomly. The recommended minimumthickness of the slab or wall is 6 in. (150 mm).

For either specimen preparation method, at least eightbreak-off specimens and two cylinders should be tested ateach test age. The center-to-center spacing of the break-offspecimens should be at least 6 in. (150 mm), and the distancefrom the edge of the slab or wall and the counterbore shouldbe at least 4 in. (100 mm).

4.2.5.5 Ultrasonic pulse velocity—It is preferable to de-velop the strength relationship from concrete in the structure.Tests should be on cores obtained from the concrete beingevaluated. Tests with standard cylinders can lead to unreli-able correlations because of different moisture conditionsbetween the cylinders and the in-place concrete.

Because the geometry of the test specimens has an effecton the determination of the pulse velocity, the correlationdata should be obtained from a testing configuration that issimilar to the one in the field. The recommended procedureis to select certain areas in the structure that represent differ-ent levels of pulse velocity. At these locations, it is recom-mended that five velocity determinations be made to insurea representative average value of the pulse velocity. For eachmeasurement, the transducers should be uncoupled from thesurface and then recoupled, to avoid systematic errors due topoor coupling (ASTM C 597). Then obtain at least two coresfrom each of the same locations for compressive strengthtesting. Pulse velocity measurements on these cores, oncethey have been removed from the structure, will usually notbe the same as the velocities measured in the structure andare not representative of the pulse velocity of the structure.

4.2.5.6 Maturity method—The following procedure isgiven in ASTM C 1074:

Prepare cylindrical concrete specimens according toASTM C 192 using the mixture proportions for the concreteintended for the structure. Embed temperature sensors at thecenters of at least two specimens. Connect the sensors to ma-turity instruments or to a multichannel temperature record-ing device.

Moist cure the specimens in a water bath or in a moistroom meeting the requirements of ASTM C 511. At ages of1, 3, 7, 14, and 28 days, perform compression tests accordingto ASTM method C 39. Test at least two specimens at eachage.

At each test age, record the average maturity index for theinstrumented specimens. On graph paper, plot the averagecompressive strength as a function of the average maturityindex. Draw a best-fit curve through the data. The resultingcurve is the strength-maturity relationship to be used for es-timating in-place strength.


CHAPTER 5—PLANNING FOR IN-PLACE TESTING

4.2.5.7 Cast-in-place cylinder—Test results should becorrected for the height-diameter ratio using the values givenin ASTM C 42. Otherwise no other correlation is neededsince the specimens represent the concrete in the placementand the test is a uniaxial compression test.

4.3—Existing construction4.3.1 General—There is often a need to evaluate the in-

place strength of concrete in existing structures. For exam-ple, planned renovation or change in the use of a structuremay require determination of the concrete strength for an ac-curate assessment of structural capacity. There also may bea need to evaluate concrete strength after a structural failure,fire damage, or environmental degradation has occurred.Sometimes, errors or unforeseen conditions occur duringnew construction and an evaluation is needed to resolvequestions about concrete strength. These situations are simi-lar because the need to determine the in-place strength of theconcrete was not preplanned. In-place testing methods canbe helpful in these evaluations.

In-place tests can be used in two ways to evaluate existingconstruction. First, they can be used qualitatively to locatethose portions of the structure where the concrete appears tobe different from other portions. In this case, the in-placetests can be used without a strength relationship for the con-crete in the structure. The main purpose of the in-place test-ing is to establish where cores should be taken for strengthdeterminations and other pertinent tests (see ACI 437R). Therebound number and the pulse velocity method are widelyused for this purpose. Second, in-place methods are used fora quantitative assessment of the strength. In this case, astrength relationship must be established for the concrete inthe structure. The relationship can only be developed by per-forming in-place tests at selected locations and taking com-panion cores for strength testing. Thus the use of in-placetesting does not eliminate the need for coring, but it can re-duce the amount of coring required to gain an understandingof the variations of strength in a structure.

4.3.2 Developing strength relationship—Because in-placetesting for evaluations of existing construction is not pre-planned, the techniques generally used are ultrasonic pulsevelocity, rebound number, and probe penetration. The break-off test is also applicable, but because it is a relatively newtest, it has not been widely used in North America. In theUnited Kingdom, the pull-off test is also used (Long 1984).The pull-off test involves gluing a steel disk to the concretesurface and measuring the force required to pull off the disk.In the Scandinavian countries, a drilled-in pullout test iswidely used (Petersen 1984). This test involves drilling ahole into the concrete and cutting out a cylindrical slot to ac-commodate an expandable ring that functions as the inserthead (Fig. 2.5). Efforts are underway to incorporate thismethod into an ASTM standard.

For some test methods, certain factors must be consideredwhen testing existing structures. For example, for surfacetests (rebound number, penetration resistance, and pull-off),the user must give special attention to those factors that mayaffect the near-surface strength, such as carbonation, mois-

ture content, or surface degradation from chemical or physi-cal processes. Surface grinding may be necessary to exposeconcrete that represents the concrete within the structure.

To develop the strength relationship, it is generally neces-sary to correlate the in-place test parameter with the com-pressive strength of cores obtained from the construction. Inselecting the core locations, it is desirable to include the wid-est range of concrete strengths in the structure that is possi-ble. Often rebound numbers or pulse velocity values aredetermined at points spread over a grid pattern establishedon the area being evaluated. When the data are plotted on amap, contour lines can be sketched in to outline the varia-tions in the concrete quality. Based on this initial survey, sixto nine different locations should be selected for coring andmeasurement of the in-place test parameter. At each loca-tion, a minimum of two cores should be obtained to establishthe in-place compressive strength. The number of replicatein-place tests at each location depends on the test method andeconomic considerations, as discussed in Chapter 5. Becauseat least 12 cores are recommended to develop an adequatestrength relationship, the use of in-place testing may only beeconomical if a large volume of concrete is to be evaluated.

The required moisture conditioning of cores beforestrength testing depends on the specific circumstances. If thestructure will always be dry during its service life, the coresshould be tested in the dry condition (ACI 318). If the in-place testing was done when the structure was dry, but thestructure is expected to be more than superficially wet any-time during its service life, the cores should be tested in a wetcondition (see ASTM C 42).

After the averages and standard deviations of the in-placetest parameter and core strength are determined at each testlocation, the strength relationship is developed using thesame approach as for new construction (Section 4.2.4).

In evaluating the average and standard deviation of thereplicate in-place results, the recorded values should bechecked for outliers (ASTM E 178). In general, test resultsthat are more than two standard deviations from the averageshould be scrutinized carefully. Outliers may occur due to animproperly performed test or a localized, abnormal condi-tion. If an obvious cause of the outlier is identified, that resultshould be ignored and the average and standard deviation re-calculated. For correlation purposes, the 90 or 95 percentconfidence limits for the regression equation should also bedetermined. Data points which lie outside the confidenceband should be scrutinized. If a data point is eliminated, theregression should be recalculated.

5.1—New construction5.1.1 Preconstruction consensus—Before starting con-

struction of the components of the structure that are to betested in-place, a meeting should be held among the partieswho are involved. These normally may be the structural en-gineer, testing company representative, general contractor,formwork contractor, post-tensioning contractor (if applica-


ble), and concrete supplier. The objective of the preconstruc-tion meeting is to clarify the test procedures to be used, thecriteria for interpretation of test data, and the interactionamong the engineer, testing company, and the contractors.By having a mutual understanding among the involved par-ties, there is less likelihood of dispute during construction,and the project can move forward as planned.

The purpose of the meeting will be to achieve a consensuson the following critical issues:

• The test procedure(s) to be used, the access require-ments for testing, number and locations of tests, and theassistance to be provided by the contractors in preparingand protecting test locations and testing equipment

• The criteria for acceptable test results for performingcritical operations, such as form removal, post-tension-ing, removal of reshores, or termination of curing

• Procedures for providing access and any modificationsto formwork required to facilitate testing

• Procedures and responsibilities for placement of testinghardware, where required, and protection of test sites

• Procedures for the timing and execution of testing• Reporting procedures to provide timely information to

site personnel• Approval procedures to allow construction operations to

proceed if adequate strength is shown to have beenachieved

• Procedures to be followed if adequate strength is notshown to have been achieved

5.1.2 Strength limitations—Most test procedures havesome limitations regarding the strength of concrete that canbe tested. In some cases, the apparatus has not been designedfor testing very weak or very strong concrete, and in othercases there is limited experience in using the methods to testvery strong concrete. The useful strength ranges for the var-

Table 5.1—Useful strength ranges for in-place test methods

Test method Range of strength*, psi (MPa)

Rebound number 1500-6000 (10-40)

Probe penetration 1500-6000 (10-40)

Pin penetration 500-4000 (3-30)

Pullout 300-19,000† (2-130)

Ultrasonic pulse velocity 100-10,000 (1-70)

Break-off 500-7000 (3-50)

Maturity No limit

Cast-in-place cylinder No limit

* Higher strengths may be tested if satisfactory data are presented for the testmethod and equipment to be used.

† For strengths above 8000 psi (55 MPa), special high-strength bolts are required toextract pullout inserts.

ious methods are summarized in Table 5.1. These ranges areapproximate and may be extended if the user can show a re-liable strength relationship at higher strengths.

5.1.3 Number of test locations—It is important that thetests provide a reliable measure of the strength of the struc-tural component at the time the tests are made. Therefore,sufficient test locations need to be provided so that there aresufficient test results to adequately characterize the concretestrength within the portion of the structure being evaluated.The term test location means a region on the structure wherean in-place test procedure is to be executed. At a test loca-tion, single or replicate in-place tests may be performed.

The number of provided test locations should account forthe following considerations:

• Since these tests will be made at early ages when strengthgain of concrete is highly dependent on temperature, theinitial tests may show that adequate strength has not yetbeen achieved. It will then be necessary to stop testing af-ter the initial tests have been made and to retest at a laterage. Sufficient test locations have to be provided to allowrepeat tests and satisfy the criteria for number of tests re-quired to allow critical operations to proceed.

• If tests are made at ages under 12 hr after the concrete iscast, it is expected that the in-place strength will have

high variability due to variations in temperature at thetest locations. In this case, it is advisable to increase thenumber of provided test locations by 10 to 25 percent.

Tables 5.2 through 5.5 provide recommendations for test-ing various structural components. For each test method, thetables show:

• The number of test locations or access points that shouldbe provided per stated volume of concrete

• The minimum number of test results that should be avail-able for statistical analysis to decide whether critical op-erations can proceed

The numbers in these tables are based on experience con-sidering the criticality of the structure and practicality.

5.1.4 Number of tests per location—The number of in-place tests to be performed at a test location could, in theory,be chosen based on the within-test repeatability of the testmethod, as discussed in section 4.2.3. However, consider-ation must be also given to practicality; otherwise, in-placetesting programs will be avoided because of the financial
burden. Table 5.6 lists the minimum number of individualdeterminations per test location. A lower number is recom-mended for those in-place test methods that require installa-tion of hardware compared with those methods that do not.
5.1.5 Providing access to test locations—To perform in-place tests during construction, it is necessary to provide ac-cess to the hardening concrete. The specific details will de-pend on the test method, the type of structural component,and the type of formwork.

For tests on the soffits of slabs formed with plywood, an
access configuration as shown in Fig. 5.1 can be used. A cir-cular hole is cut in the form and the plug that is cut can beattached to a backup plate that is temporarily fastened to theformwork with screws. Test hardware, such as a pullout in-sert, is attached to the removable assembly. When a test is tobe performed, test hardware, if it exists, is loosened and thebackup plate and plug are removed to expose the test surface.To provide a smooth test surface a sheet metal plate can beattached to the plug. A sealant should be used to seal the gapbetween the plug and backup plate to prevent leakage offresh cement paste. The diameter of the plug will depend onthe specific spacing requirements for the test method, as discussed in 5.1.7, and it should provide at least 1 in. (25 mm)


Table 5.2—Recommendations for slabs, shear walls, and core walls*

Test method

Number of test locations provided Minimum number of locations to test

First 100 yd3 (75 m3) Each additional 20 yd3 (15 m3) First 100 yd3 (75 m3) Each additional 20 yd3 (15 m3)

Rebound number 20 2 10 1

Probe penetration 8 1 6 1

Pin penetration 15 2 10 1

Pullout 15 2 10 1

Ultrasonic pulse velocity 15 2 10 1

Break-off 10 2 8 1

Maturity 5 2 5 1

Cast-in-place cylinder† 5 1 5 1

* Core walls are usually at the center of a building and form the structural backbone of the building. Typically, core walls surround the elevator shafts.† For slabs only.

Table 5.3—Recommendations for other walls per 200 yd3 (150 m3)

Test method

Number of test locations provided Minimum number of locations to test

Walls thinner than 1 ft(300 mm)

Walls 1 ft (300 mm) thick or thicker

Walls thinner than 1 ft(300 mm)

Walls 1 ft (300 mm) thick or thicker

Rebound number 20-25 15-20 10 8

Probe penetration 8-10 6-8 8 6

Pin penetration 10-15 8-12 10 8

Pullout 10-15 8-12 10 8

Ultrasonic pulse velocity 10-15 8-12 10 8

Break-off 10-12 8-12 10 8

Maturity 5 5 5 5

Table 5.4—Recommendations for individual columns*

Test methodNumber of test

locations providedMinimum number of

locations to test

Rebound number 5-8 5

Probe penetration 5-8 5

Pin penetration 5-8 5

Pullout 5-8 6

Ultrasonic pulse velocity 5-8 6

Break-off 5-8 6

Maturity 5 5

* These numbers are based on the assumption that there are 6 to 10 columns in eachtest area and that each column contains about 1.5 yd 3 (1 m 3) of concrete. Greater num-bers of test locations should be provided for larger columns or where the test area con-tains more than 10 columns.

Table 5.5—Recommendations for columns with spandrel beams per 50 yd3 (40 m3)*

Test methodNumber of test

locations providedMinimum number of

locations to test

Rebound number 6-9 5

Probe penetration 6-9 5

Pin penetration 6-9 5

Pullout 6-9 6

Ultrasonic pulse velocity 6-9 6

Break-off 6-9 6

Maturity 5 5

* These numbers of tests should be made before removal of forms and again beforeapplication of construction loading from next level of construction. It is assumed thatcorbels, if present, are cast integrally with columns or spandrel beams.

Table 5.6—Number of replicate tests at each test location

Test methodIndividual determinations per

test location

Rebound number 10

Probe penetration 3

Pin penetration 6

Pullout 1

Ultrasonic pulse velocity 2

Break-off 1

Maturity 1

Cast-in-place cylinder 2

of clear space around the perimeter of the plug to avoid test-ing concrete near the edge of the plug. For access throughmetal forms, a similar backup plate assembly can be fabricat-
ed of metal plate. Fig. 5.2 shows a typical access configura-tion for a use on the vertical surface of a metal form. Finally,the user must keep in mind that the water absorption charac-teristics of the form surface at the location of the in-placetesting will affect the results of surface tests, such as the re-bound number and pin penetration methods. Consequently,the in-place test specimens in the correlation testing mustemploy similar form materials as will be used in the con-struction.
The access types shown in Fig. 5.1 and 5.2 are applicableto all the in-place testing methods except for the maturitymethod, the break-off test, and cast-in-place cylinders. Fig.5.3 illustrates typical techniques for installing maturity


Fig. 5.1—Access for use on soffits of slabs with wooden forms

Fig. 5.2—Access for use on vertical surfaces with steel forms

Fig. 5.3—Installation of maturity meters into fresh concrete: a) disposable mini-meter; b) sensor of electronic meter

meters. The disposable mini-maturity meters can be inserteddirectly into the top surfaces of slabs, or they can be embed-ded deeper into the slab using a cup-lid assembly to avoid in-terference with finishing operations. The cup may also beplaced within openings on the sides of vertical forms. Forelectronic maturity meters, temperature probes are insertedinto the structural elements. For meters with reusable probes,the usual practice is to embed an expendable brass tube intothe fresh concrete and to place the probe within the tube [Fig.5.3(b)]. A thermal couplant (a type of grease) should be ap-plied to the probe before insertion into the tube to assure ac-curate measurement of concrete temperature. For meters thatuse thermocouple wires as sensors, the wires are fastened toreinforcing bars before concreting. After testing is complet-ed, the wires are cut flush with the concrete surface, and theremaining wires can be prepared for reuse.

For break-off tests in the top surfaces of slabs, special ac-cess provisions are not necessary. The plastic molds are sim-ply inserted into the fresh concrete after the slab has beenscreeded. Care is needed to avoid disrupting the molds dur-ing subsequent finishing operations.

Cast-in-place cylinders do not require special access pro-visions. The supporting sleeve for the cylinder mold is naileddirectly to the formwork. It is only necessary to assure thatthe top surface of the specimen will coincide with the topsurface of the slab. If the top of the specimen is too low, itwill be difficult to locate and extract the cylinder. If the topof the specimen is too high, finishing operations will disruptthe molds.

Cutting of forms and fabrication of plugs to create accesspoints should be done by the appropriate trades with super-vision by the testing engineer. Installation of pullout inserts,temperature probes, and cast-in-place cylinder molds can bedone by contractor’s forces after direction and demonstra-tion by the testing engineer.

5.1.6 Distribution of tests—Test locations should be dis-tributed throughout the structural component being tested sothat the in-place test results will provide an accurate indica-tion of the strength distribution within that component. In se-lecting the testing locations, consideration should be given tothe most critical locations in the structure in terms of struc-tural strength requirements and exposure conditions, espe-cially during cold weather. When many tests are required forstructural components such as slabs, it is advisable to distrib-


5.1.7 Critical dimensions—Tests such as rebound number,penetration resistance, pullout and break-off produce someform of surface damage to the concrete, and test results areinfluenced by the conditions within the zone of influence ofthe particular test. As a result, the ASTM standards prescribecritical minimum dimensions to assure that test results arenot influenced by neighboring tests, specimen boundaries, orreinforcing steel. Test locations should be positioned to con-form with the critical dimensional limitations in Table 5.7.

Table 5.7—Dimensional requirements for in-place tests according to ASTM standards

Test method Requirements

Rebound number Minimum dimensionsThickness of member: 4 in. (100 mm)Diameter of test area: (300 mm)

Minimum distanceBetween test points: 1 in. (25 mm)

Probe penetration Minimum distanceBetween probes: 7 in. (175 mm)To edge of concrete: 4 in. (100 mm)

Pin penetration Minimum distancesBetween pins: 2 in. (50 mm)To edge of concrete: 2 in. (50 mm)

Maximum distanceBetween pins: 6 in. (150 mm)

Pullout Minimum clear spacingBetween inserts: 10 times insert head diameterTo edge of member: 4 times insert head diameterFrom edge of failure surface to rebar: 1 insert head diameter or maximum aggregate size, whichever is larger

Break-off Minimum clear spacingClear spacing between inserts: 4 in. (100 mm)

ute the test locations in a regular pattern per floor. For testmethods that require few tests, such as cast-in-place cylin-ders, it is advisable to choose locations that are critical ineach placement.

For tests on vertical members, such as columns, walls, anddeep beams, the vertical location within the placement is im-portant. For vertical members, there is a natural tendency forthe strength to be higher at the bottom of the placement andlower at the top of the placement. The magnitude of this vari-ation is influenced by many factors such as mixture compo-sition, type and degree of compaction, aggregate shape, andenvironmental conditions (Munday and Dhir 1984). It is notpossible to predict accurately the magnitude of strength vari-ation expected in a given structural element. Also, code writ-ing committees have not dealt with these strength variations.As a result, engineering judgment is needed in planning andinterpreting the results of in-place tests on vertical members,particularly when testing the top and bottom 12 in. (300mm).

5.2—Existing construction5.2.1 Pretesting meeting—As mentioned in section 4.3,

there are many reasons for in-place determinations of con-crete strength in existing structures. Often in-place testing isone facet of an overall investigation to establish structuraladequacy. The guidelines in ACI 437R should be followed

to develop the complete plan of the investigation and to iden-tify other aspects of the field study to complement concretestrength determination.

The plan for the in-place testing program will depend onthe purpose of the investigation. As for new construction, apretesting meeting should be held among the members of theteam who share a common interest in the test results. At theconclusion of the meeting, there should be a clear under-standing of the objective of the investigation; there should beagreement on the responsibilities of the team members in ac-quiring the test data; and there should be agreement on theprocedures for obtaining and analyzing the test results.When access to the concrete for testing is impeded by archi-tectural coverings, detailed plans should be developed to ac-complish this access.

5.2.2 Sampling plan—In developing the testing programconsideration should be given to the most appropriate sam-pling plan for the specific situation. ASTM C 823 (providesguidelines for developing the sampling plan. Although thestandard deals primarily with the drilling of cores or sawnsamples, there is a section dealing with in-place testing.

In general, two sampling situations may be encountered.In one situation, all of the concrete is believed to be of simi-lar composition and quality. For this case, random samplingshould be spread out over the entire structure and the resultstreated together. ASTM E 105 should be consulted to under-stand the principles of random sampling. The structureshould be partitioned into different regions and a randomnumber table should be used to determine objectively whichareas to test. Objective random sampling is necessary to ap-ply probability theory and make valid inferences about theproperties of the population (all of the concrete in the struc-ture) based upon the sample test results.

The second sampling situation arises when available infor-mation suggests that the concrete in different portions of thestructure may be of different composition or quality, or whenthe purpose of the investigation is to examine failure or dam-age in a specific portion of a structure. In this case, randomsampling should be conducted within each portion of thestructure where the concrete is suspected of being nominallyidentical. Test results from different portions of the structureshould not be combined unless it is shown that there are nostatistically significant differences between the test results.

5.2.3 Number of tests—As was mentioned in Section 4.3,the in-place testing program for an existing structure in-volves two phases. First, the strength relationship must beestablished by testing drilled cores and measuring the corre-sponding in-place test parameter near the core locations. Thelocations for correlation testing should be chosen to providea wide range in concrete strength. As mentioned in section4.3.2, a minimum of six to nine test locations should be se-lected for obtaining the correlation data. In general, coresshould be drilled after the in-place tests are performed. Ateach location two cores should be drilled, and the followingnumber of replicate in-place tests should be performed toprovide the average value of the companion in-place test pa-rameter:


CHAPTER 6—INTERPRETATION ANDREPORTING OF RESULTS

6.2.1 Danish method (Bickley 1982)—This method hasbeen developed for analysis of pullout test results. The pull-out strengths obtained from the field tests are converted toequivalent compressive strengths by means of the strengthrelationship (correlation equation) determined by regressionanalysis of previously generated data for the particular con-crete being used at the construction site. The standard devia-tion of the converted data is then calculated. The tenthpercentile compressive strength of the concrete is obtainedby subtracting the product of the standard deviation and astatistical factor K (which varies with the number of testsmade and the desired level of confidence) from the mean ofthe converted data. Although it has not been stated explicitly,the statistical factor is a one-sided tolerance factor (Natrella1963), as discussed further in Section 6.2.2. The K factors for
different numbers of tests are given in Column 2 of Table6.1. The example in Table 6.2 illustrates how the Danish
Table 6.1—One-sided tolerance factor for ten percent defective level (Natrella 1963)

Number of tests, n

Confidence level

75 percent 90 percent 95 percent

Column 1 Column 2 Column 3 Column 4

3 2.501 4.258 6.158

4 2.134 3.187 4.163

5 1.961 2.742 3.407

6 1.860 2.494 3.006

7 1.791 2.333 2.755

8 1.740 2.219 2.582

9 1.702 2.133 2.454

10 1.671 2.065 2.355

11 1.646 2.012 2.275

12 1.624 1.966 2.210

13 1.606 1.928 2.155

14 1.591 1.895 2.108

15 1.577 1.866 2.068

20 1.528 1.765 1.926

25 1.496 1.702 1.838

30 1.475 1.657 1.778

35 1.458 1.623 1.732

40 1.445 1.598 1.697

50 1.426 1.560 1.646

method is applied. The first column shows the equivalentcompressive strengths corresponding to the individual pull-out test results. The second column shows the values and cal-culations used to obtain the tenth percentile strength. The

These numbers are based on considerations of the within-test variability of the method and the cost of additional test-ing. For example, the within-test repeatability of the ultra-sonic pulse velocity test is low, but the cost of replicatereadings at one location is also low. Therefore, five repli-cate readings are recommended to insure that a representa-tive value will be obtained because of the variability in theefficiency of the coupling of the transducer to the structure.In making the replicate pulse velocity determinations, thetransducers should be moved to nearby locations to evalu-ate the area where cores will be taken. The dimensional re-strictions given in Table 5.7 should be observed for theother test methods.

The second phase of the in-place testing program involvesconducting the in-place tests at other locations and estimat-ing the compressive strength based upon the strength rela-tionship. The number of test locations for this phase willdepend on several factors. First, there are the statistical fac-tors. According to the principles set forth in ASTM E 122,the number of tests depends on the variability of the concretestrength, the acceptable error between the true and sampleaverage, and the acceptable risk that the error will be exceed-ed. Among these factors, the variability of the concrete is apredominant factor in determining the number of requiredtests. For a given acceptable error and level of risk, the num-ber of tests increases with the square of the variability(ASTM E 122).

Economic considerations also influence the testing plan.For some cases, the cost of an extensive investigation mightoutweigh the economic benefit. Because the cost of an inves-tigation is related to the amount of testing performed, a highdegree of confidence, because of a large sample size, is a pre-mium. The selection of a testing plan involves tradeoffs be-tween economics and degree of confidence.

Test method Replicates at each location

Rebound number 10

Probe penetration 3

Break-off 5

Ultrasonic pulse velocity 5

6.1—GeneralInterpretation of in-place tests should be made by using

standard statistical procedures. It is not sufficient to simplyaverage the values of the in-place test results and then com-pute the equivalent compressive strength by means of thepreviously established strength relationship. It is necessaryto account for the uncertainties that exist. While no proce-dure has yet been agreed upon for determining the tenth-per-centile in-place strength based on the results of in-place tests,proponents of in-place testing have developed and are usingstatistically based interpretations.

Four statistical methods for evaluating in-place test resultsare reviewed in the following sections. The first two methods

are similar and are based on the idea of statistical tolerancefactors. These two methods are simple to use, requiring onlytabulated statistical factors and a calculator. However, be-cause of their underlying assumptions, the statistical rigor ofthese methods has been questioned. As a result more rigor-ous methods have been proposed. The rigorous methods aremore complex and require an electronic spreadsheet forpractical use.

6.2—Statistical methods


6.2.2 General tolerance factor method (Hindo and Berg-strom 1985)—The acceptance criteria for strength of con-crete cylinders in ACI 214 are based on the assumption thatthe probability of obtaining a test with strength less than fc′is less than approximately 10 percent. A suggested methodfor evaluating in-place tests of concrete at early ages is to de-termine the lower tenth percentile of strength, with a pre-scribed confidence level.

It has been established that the variation of cylinder com-pressive strength can be modeled by the normal or the log-normal distribution function depending upon the degree ofquality control. In cases of excellent quality control, the dis-tribution of compressive strength results is better modeled bythe normal distribution; in cases of poor control, it is bettermodeled by a lognormal distribution (Hindo and Bergstrom1985).

In the tolerance factor method, the lower tenth percentilecompressive strength is estimated from in-place test resultsby considering quality control, number of tests n, and the re-quired confidence level p. Three quality control levels areconsidered: excellent, average, and poor, with the distribu-tion function of strength assumed as normal, mixed normal-lognormal, and lognormal, respectively. Suggested values ofp are 75 percent for ordinary structures, 90 percent for veryimportant buildings, and 95 percent for crucial parts of nu-clear power plants (Hindo and Bergstrom 1985). However,since safety during construction is the primary concern, asingle value of p may be adequate. A value of p equal to 75percent is widely used in practice.

The tolerance factor K, the sample average Y, and standarddeviation sY are used to establish a lower tolerance limit, thelower tenth percentile strength. For a normal distributionfunction, the estimate of the tenth percentile strength Y0.10

can be determined as follows:

Y0.10 = Y - KsY (6-1)

where

Table 6.2—Example of Danish method

Individual equivalent compressive strength psi

(MPa)* Calculations

3990 (27.5) Mean Y = 3730 psi (25.7 MPa)

3620 (25.0)

3550 (24.5) Standard

3620 (25.0) deviation sY, = 330 psi (2.3 MPa)

3260 (22.5)

3480 (24.0) K = 1.671†

3700 (25.5)

4130 (28.5) Tenth percentile

3620 (25.0) strength = Y - KsY

4350 (30.0) = 3180 psi (21.9 MPa)

* Converted from pullout force measurements using strength relationship.† The values of the constant K are given in Column 2 of Table 6.1.

example uses 10 test results, but another appropriate numbermay be used in larger placements.
Y0.10 = lower tenth percentile of strength (10 percent defec-
tive)Y = sample average strengthK = one-sided tolerance factor (Table 6.1)sY = sample standard deviation

The tolerance factor is determined from statistical charac-teristics of the normal probability distribution and dependsupon the number of tests n, the confidence level p, and thedefect percentage. Values of K are found in reference bookssuch as that by Natrella (1963). Table 6.1 provides one-sidedtolerance factors for confidence levels of 75, 90, and 95 per-cent and a defect level of 10 percent.

For the lognormal distribution, the lower tenth percentileof strength can be calculated in the same manner, but usingthe average and standard deviation of the logarithms ofstrengths in Eq. (6-1).

By dividing both sides of Eq. (6-1) by the average strengthY, the following is obtained

(6-2)

where VY = coefficient of variation (expressed as a decimal).In Eq. (6-2), the tenth-percentile strength is expressed as a

fraction of the average strength. Fig. 6.1 is a plot of Eq. (6-2) for p = 75 percent and for coefficients of variation of 5, 10,15, and 20 percent. This figure shows that as the variabilityof the test results increases or as fewer tests are performed, asmaller fraction of the average strength has to be used for thetenth-percentile strength.

The tolerance factor method is similar to the Danish meth-od. The results of the in-place tests are converted to equiva-lent compressive strengths using the strength relationship,and the equivalent compressive strengths are used to com-pute the sample average and standard deviation.

The example in Table 6.3 illustrates the application of the

Y0.10

Y---------- 1 K V Y–=

Fig. 6.1—Ratio of tenth-percentaile strength to average strength as a function of coefficient of variation and number of tests (normal distribution assumed)

tolerance factor method for probe-penetration tests. Thequestion in the example is whether the in-place strength ofconcrete in a slab is sufficient for the application of post-ten-


6.2.3 Rigorous method (Stone and Reeve 1986)—The pre-ceding methods convert each in-place test result to an equiv-alent compressive strength value by means of the strengthrelationship. The average and standard deviation of theequivalent compressive strength are used to compute thetenth-percentile in-place strength. Two major objectionshave been raised to these methods (Stone, Carino, and Reeve1986; Stone and Reeve 1986): 1) the strength relationship ispresumed to have no error, and 2) the variability of the com-pressive strength in the structure is assumed to be equal tothe variability of the in-place test results. The first factor willmake the estimates of in-place tenth-percentile strength notconservative, while the second factor will make the esti-mates overly conservative.

Stone and Reeve (1986) developed a comprehensive tech-nique for statistical analysis of in-place test results that at-tempted to address the perceived deficiencies of thetolerance factor methods. Only a general summary of themethod is given here. This rigorous method encompasses thefollowing procedures:

1. Regression analysis to establish the strength relation-ship.

2. Estimating the variability of the in-place compressivestrength based on the results of the correlation tests and testson the structure.

3. Calculating the probability distribution of the estimatedin-place, tenth-percentile strength.

6.2.4 Alternative method (Carino 1993)—The rigorousmethod developed by Stone and Reeve (1986) has not re-ceived widespread acceptance among concrete technologistsbecause of its complexity. Carino (1993) proposed an alter-native method that retains the main features of the rigorousmethod, but can be implemented easily with spreadsheetsoftware.

The basic approach of the alternative method is illustrated

Table 6.3—Example of general tolerance factor method

Strength relationship: Y (psi) = -145 + 2540 L (in.) Y (MPa) = -1 + 0.69 L (mm)

Exposed length L, in. (mm) Compressive strength Y, psi (MPa)

1.18 (30) 2850 (19.7)

1.38 (35) 3360 (23.2)

1.34 (34) 3260 (22.5)

1.38 (35) 3360 (23.2)

1.30 (38) 3660 (25.2)

1.42 (36) 3460 (23.9)

1.22 (31) 2950 (20.3)

1.18 (30) 2850 (19.7)

Average = 3220 psi (22.2 MPa)

Standard deviation = 300 psi (2.1 MPa)

Coefficient of variation = 9.3 percent

sioning, if the compressive strength requirement for post-tensioning is 2900 psi (20 MPa). The numbers in the firstcolumn are the measured exposed lengths of each of eightprobes, and the second column gives the corresponding com-pressive strengths based on the previously establishedstrength relationship for the concrete being evaluated. Foreight tests and a confidence level of 75 percent, the tolerancefactor is 1.74. It is assumed that the normal distribution de-scribes the variation of concrete strength. Thus, by substitut-ing the coefficient of variation and the tolerance factor intoEq. (6-2), the ratio of the tenth-percentile strength to the av-erage strength is 0.835. Therefore, the tenth-percentile in-place strength is 2690 psi (18.5 MPa). Since the tenth per-centile strength is greater than 0.85 x 2900 psi (20 MPa) =2465 psi (17 MPa), post-tensioning may be applied.

For the reasons given in section 4.2.4, the logarithms ofthe test results are used in the analysis, and the strength rela-tionship is assumed to be a power function. Regression anal-ysis is performed using Mandel’s procedure discussed inSection 4.2.4 and in Appendix A.2. The errors associatedwith the best-fit strength relationship are used to estimate thein-place, tenth-percentile strength at any desired confidencelevel.

A novelty of the rigorous method is the approach used toestimate the variability of the in-place compressive strength.In Chapter 3, it was shown that the within-test variability ofin-place test results is generally greater than compression-test results. This is why objections have been raised againstassuming that the variability of the in-place compressivestrength equals the variability of the in-place test results. Inthe rigorous method, it is assumed that the variability ofcompressive strength divided by the variability of the in-place test results is a constant. Thus, the ratio obtained dur-ing correlation testing is assumed to be valid for the testsconducted in the field. This provides a means for estimatingthe variability of the in-place compressive strength based onthe results of the in-place tests.

The in-place tenth-percentile strength computed by therigorous procedure accounts for the error associated with thestrength relationship. The user can determine the tenth-per-centile strength at any desired confidence level for a particu-lar group of field test results. In addition, the user can choosethe percentile to be a value other than the tenth percentile.

Stone, Carino, and Reeve (1986) computed the tenth-per-centile strengths by the rigorous method, and compared themwith those computed by the Danish and tolerance factormethods. These calculations used simulated in-place testdata having different mean values and standard deviations. Itwas found that, for an assumed confidence level, thestrengths estimated by the Danish and tolerance factor meth-ods were lower than the values based on the rigorous meth-od. The differences were as high as 40 percent when the in-place tests had high variability (coefficient of variation = 20percent). It was concluded that, compared with the rigorousmethod, the Danish and tolerance factor methods give moreconservative estimates of in-place compressive strength, butthey do not appear to involve a consistent confidence level.Part of the reason for the performance of the tolerance factormethods is the assumption that the variability of the in-placecompressive strength is the same as the variability of the in-place test results. Experimental field studies are needed tocompare the in-place, tenth-percentile strengths estimated bythese methods with the values obtained from many coretests. Only then can the reliability of these methods be eval-uated.


in Fig. 6.2. Mandel’s procedure (as outlined in Appendix
A.2) is used to obtain the strength relationship from correla-tion data. The results of the in-place tests and the strength re-lationship are used to compute the lower confidence limit ofthe estimated average in-place strength at a desired signifi-cance level α. Finally, the tenth-percentile strength is deter-mined assuming a log-normal distribution for the in-placeconcrete strength. Calculations are performed using natural-logarithm values.
In the following paragraphs, the procedure for estimatingthe in-place strength is explained further. When the in-placestrength is to be estimated, replicate tests are performed onthe structure. The average of the logarithms of the in-placetests is used to compute the logarithm of the average in-placecompressive strength using the strength relationship:

Y = a + b X (6-3)

whereY = the logarithm of the estimated average in-place com-

pressive strengthX = the average of the logarithms of the in-place tests per-

formed on the structurea,b = the intercept and slope of the strength relationship

Next, the lower confidence limit for the estimated averagestrength is computed. This lower limit is obtained using Eq.(A-16) in Appendix A.3 for the standard deviation sY of an
estimated value of Y for a new X. The lower confidence limitfor the average concrete strength is as follows:
Ylow = Y - (tm-1,α sY) (6-4)

whereYlow = lower confidence limit at confidence level αtm-1,α= Student t-value for m-1 degrees of freedom and con-

fidence level αm = the number of replicate in-place tests

Table 6.4 lists Student t-values for m-1 degrees of freedomand risk (or confidence) levels of 5 percent and 10 percent.The choice of risk level depends on the criticality of in-placeconcrete strength in the overall assessment. When strength iscritical, a lower risk level, such as 5 percent, should be used.

It is assumed that the distribution of in-place compressivestrength is described by a log-normal distribution, and thetenth-percentile strength is computed as follows:

Y0.10 = Ylow - 1.282 scf (6-5)

whereY0.10 = logarithm of strength expected to be exceeded by 90

percent of the populationscf = standard deviation of the logarithms of concrete

strength in the structureThe value of scf is obtained from the assumption (Stone

and Reeve 1986) that the ratio of the standard deviation ofcompression strength to the standard deviation of in-placetest results has the same value in the field as was obtained

during the laboratory correlation testing. Thus the followingrelationship is assumed:

(6-6)

wherescf, scl = standard deviations of logarithms of compressive

strength in the structure and laboratory, respectivelysX, sil = standard deviation of logarithms of the in-place re-

sults in the structure and laboratory, respectivelyThe final step is to convert the result obtained from Eq. (6-

5) into real units by taking the antilogarithm.A close examination of the alternative procedure shows

scf

scl

si l

-----= sX

Fig. 6.2—Alternative method to estimate compressive strength based on in-place tests (Carino 1993)

Table 6.4—Student t-values for m-1 deg of freedom and risk levels of 0.05 and 0.10 (Natrella 1963)

m-1 t0.05 t0.10

2 2.920 1.886

3 2.353 1.638

4 2.132 1.533

5 2.015 1.476

6 1.943 1.440

7 1.895 1.415

8 1.860 1.397

9 1.833 1.383

10 1.812 1.372

11 1.796 1.363

12 1.782 1.356

13 1.771 1.350

14 1.761 1.345

15 1.753 1.341

16 1.746 1.337

17 1.740 1.333

18 1.734 1.330

19 1.729 1.328


that the average compressive strength estimated by thestrength relationship [Eq. (6-3)] is reduced by two factors.The first factor, which is given by Eq. (6-4), accounts for theuncertainty of the strength relationship and the uncertainty ofthe average of the in-place test results. The second factor,which is given by Eq. (6-5), accounts for the variability ofthe in-place compressive strength. Thus it is felt that the al-ternative procedure strikes a balance between statistical rigorand practicality of use. As mentioned, the procedure is wellsuited for implementation using a computerized spreadsheet.

Fig. 6.3—Example of form used to identify locations of in-place tests in a floor slab of a slab of a multi-story building

Fig. 6.4—Sample form for on-site recording of in-place test results

Appendix A.4 gives examples that compare the estimated in-
place strength using the tolerance factor and alternativemethods.
6.2.5 Summary—Except for testing cast-in-place cylin-ders, in-place tests provide indirect measures of concretestrength. To arrive at a reliable estimate of the in-placestrength, the uncertainties involved in the estimate must beconsidered. This section has discussed some techniques de-veloped for this purpose. The tolerance factor methods dis-cussed in 6.2.1 and 6.2.2 have been used successfully in theanalysis of pullout test data. Therefore, they may be ade-quate for test methods that have good correlation with com-pressive strength, such as the pullout test.

The tolerance factor methods, however, do not account forthe main sources of uncertainty in a rational way. This haslead to the development of more complex procedures as dis-cussed in 6.2.3 and 6.2.4. These new methods are designedto provide reliable estimates of in-place strength for any testprocedure. However, these rigorous methods need to be in-corporated into easy-to-use computer programs before theycan be put to practical use.

6.3—Reporting resultsFor the different tests and for different purposes, a variety

of report forms will be appropriate. Usually, relevant ASTMstandards describe the information required on a report.Where in-place testing is made at early ages, some particularreporting data are desirable. A set of forms, similar to thosedeveloped by an engineer for use in pullout testing, is shownin Fig. 6.3 to 6.5. These may serve as useful models for de-
veloping forms to report the results of other in-place tests.
Briefly, the three forms provide for the following:1. Record of test locations (Fig. 6.3)—This form gives a

plan view of a typical floor in a specific multistory building.The location of each test is noted. The location of maturitymeters, if installed, can also be shown. Location data are im-portant in case of low or variable results. Where tests aremade at very early ages and the time to complete a placementis long, there may be a significant age-strength variationfrom the start to the finish of the placement.

2. Record of field-test results (Fig. 6.4)—This is the formon which test data, the calculated results, and other pertinentdata are recorded at the site. The form shown in Fig. 6.4 hasbeen designed for evaluating the data with the Danish or tol-erance-factor methods (minimum strength is the tenth-per-centile strength). It includes provisions for entering infor-mation on maturity data, protection details, and concrete ap-pearance to corroborate the test data in cold weather. Due tothe critical nature of formwork removal, a recommendedprocedure is for the field technician to phone the data to acontrol office and obtain confirmation of the calculations be-fore giving the results to the contractor.

3. Report of test results (Fig. 6.5)—This form is used to re-port the in-place test results. The example shown in Fig. 6.5is a multicolor self-carbon form designed to be completed atthe site by the technician, with copies given to the contrac-tor's and structural engineer's representatives when the re-sults have been checked. It provides for identification of the


CHAPTER 7—IN-PLACE TESTS FORACCEPTANCE OF CONCRETE

Fig. 6.5—Sample form for reporting in-place test results

placement involved, the individual results, and the calculat-ed mean and minimum strengths. It records the engineer's re-quirements for form removal and states whether theserequirements have been met. It requires the contractor’s rep-resentative's signature on the testing company’s copy.

7.1—GeneralTraditionally, acceptance testing for new construction has

been confined solely to judging the acceptability of the con-crete delivered to the project. It is assumed that acceptableconcrete which is placed, compacted and cured according tostandards of good practice will perform according to designassumptions. Exceptions occur when there is clear visual ev-idence of inadequate compaction or distress (such as exces-sive cracking), or when inadequate protection was providedin cold weather.

It is becoming recognized that the durability of exposedstructures is dependent strongly on the curing history. There-fore, it is desirable to have assurance that the finished struc-ture has the necessary properties to attain the desired level ofperformance. In-place testing offers the opportunity to ob-tain this assurance. The Great Belt Link project in Denmarkis one of the first large-scale construction projects in whichthe owners relied on in-place testing (pullout tests) to assessthe acceptability of the concrete layer protecting the rein-

forcement (Vincentsen and Henriksen 1992). This majorconstruction effort should serve as a model for futureprojects where in-place quality assurance is very important.

In North America, there is a hesitancy to abandon tradi-tional acceptance procedures, which have served their pur-pose. However, in-place testing offers the opportunity tolessen the reliance on the testing of standard-cured cylindersas the only method to judge acceptability of the concrete de-livered to the site. The added benefit of in-place testing isthat it provides assurance that the finished construction hasthe properties specified by the designer. This chapter dis-cusses the potential for in-place testing as an alternative toolfor acceptance testing.

7.2—Acceptance criteriaThe following reviews the current acceptance criteria in

North American practice and proposes how in-place testingmay be used as an alternative to testing standard-cured cyl-inders.

7.2.1 Molded cylinders—According to ACI 318-89, theevaluation and acceptance of concrete are based on tests ofcylinders molded at the job site and subjected to standardlaboratory curing. Section 5.6.2.3 of ACI 318-89 states asfollows:

“Strength level of an individual class of concrete shallbe considered satisfactory if both of the following re-quirements are met:

a) Average of all sets of three consecutive strength testsequal or exceed fc′.

b) No individual strength test (average of two cylin-ders) falls below fc′ by more than 500 psi.”

In addition, according to 5.6.3.1 of ACI 318-89, the Build-ing Official may require testing of field-cured cylinders tocheck the adequacy of curing and protection of the concretein the structure. The acceptability of curing, as indicated bythe field-cured cylinder strengths, is defined in section5.6.3.4:

“Procedures for protecting and curing concrete shallbe improved when strength of field-cured cylinders attest age designated for determination of fc′ is less than 85percent of that of companion laboratory cylinders. The85 percent limitation shall not apply if field-curedstrength exceeds fc′ by more than 500 psi.”

7.2.2 Cores—In the event that a strength test of standard-cured cylinders is more than 500 psi (3.4 MPa) below fc′,ACI 318-89 requires that steps be taken to assure adequacyof the structure. Cores may have to be drilled to verify the in-place strength. Three cores are required for each strength testfailing to meet the specified criteria. In judging the accept-ability of the core strengths, section 5.6.4.4 of ACI 318-89states as follows:

“Concrete in an area represented by core tests shall beconsidered structurally adequate if the average of threecores is equal to at least 85 percent of fc′ and if no singlecore is less than 75 percent of fc′. Additional testing ofcores extracted from locations represented by erraticcore strength results shall be permitted.”

7.2.3 In-place tests—Based on the above requirements for


judging the acceptability of in-place concrete based on corestrengths, the following acceptance criteria based on in-placetesting are proposed:

The concrete in a structure is acceptable if the estimat-ed average, in-place, compressive strength based on a re-liable in-place test procedure equals at least 85 percent offc′ and no test result estimates the compressive strengthto be less than 75 percent of fc′.

However, before these criteria can be put into effect, astandard practice for statistical analysis of in-place test dataneeds to be adopted.

7.3—Early-age testingThe prime reason for using in-place tests in new construc-

tion is to determine whether it is safe to begin critical opera-tions, such as form removal or post-tensioning. The in-placetests provide estimates of compressive strength at ages thatare usually much earlier than the age for attaining the speci-fied strength. The criterion frequently used to judge the ac-ceptability of early-age strengths to permit critical con-struction operations is that the estimated in-place compres-sive strength should be at least 75 percent of fc′. In this con-text, the estimated strength represents an estimate of the 10thpercentile strength. When such a requirement is specified,early-age testing may facilitate final acceptance of concrete.

In high-rise construction, economic factors result in accel-erated schedules in which critical operations may be plannedas early as one to three days after concrete placement. Tomeet the early-age strength requirements, the contractor maychoose to use a concrete mixture that will exceed the speci-fied design strength. Experience has shown that requiring aminimum strength of 75 percent of fc′ at early ages (one tothree days) will usually assure that the in-place strength willbe at least fc′ at 28 days, if proper curing is used and the spec-ifications do not allow mixtures that achieve all theirstrength gain at the time of form removal.

For example, for a specified design strength of 4000 psi(27.6 MPa), the in-place strength to permit form removalmay have to be at least 3000 psi (20.7 MPa). Allowing forthe inherent variation of concrete strength, the average in-place strength may have to be 3700 psi (25.5 MPa) to assurethat the early-age strength criterion is satisfied. In this case,the average early-age, concrete strength has to equal 93 per-

cent of the specified strength. Therefore, it is reasonable toassume that if the early age (one to three days) strength re-quirement is satisfied, then at 28 days the specified designstrength will undoubtedly be achieved. For additional assur-ance, in-place tests can be made on the structure at 28 days.

Bickley (1984) reported on demonstration projects wherein-place testing was used not only for early-age strength de-termination of horizontal elements but also for confirmationof the 28-day design strength. Permission to waive standardcylinder testing was obtained from the Building Official. In-novative project specifications defined the frequency of in-place tests and the procedures to follow in doing the tests andreporting the results. Acceptance of the concrete was basedon the results of pullout tests performed on the structure at 28days. For comparison, standard-cured cylinders were alsotested at 28 days, but these strengths were not reported. Ta-ble 7.1 summarizes the results. The specified design strength

Table 7.1—Results of standard-cured cylinder and in-place tests at 28 days (fc′ = 30 MPa)

Project 1 Project 2

Pullout tests Standard cylinders Pullout tests Standard cylinders

No. of results * 84 84 15 15

Mean strength, psi (MPa) 4990† (34.4) 5630 (38.8) 5210† (35.9) 5540 (38.2)

Standard deviation s, psi (MPa) 390† (2.7) 570 (3.9) 390† (2.7) 510 (3.5)

Range, psi (MPa) 4420-6450 † (30.5-44.5) 4340-6920 (29.9-40.5) 4710-5870† (32.5-40.5) 4480-6310 (30.9-43.5)

Mean strength - fc′ 1.63 s 2.23 s 2.18 s 2.34 s

Expected percentage of results below fc′

4.9 1.2 1.4 1

Actual percentage of results below fc′

None 1.2 None None

* A result is the average of two cylinder tests or the average of two or more pullout tests.† Mean and standard deviation of compressive strength based on strength relationship.

for both projects was 4350 psi (30 MPa). Individual pullouttest results were converted to compressive strengths basedon the strength relationships, and these estimated strengthswere used to compute the statistics shown in the second andfourth columns of the table. Based on the standard devia-tions, the expected percentages of strength below fc′ werecomputed. In all cases, these percentages were less than 10percent, which is the approximate value implied in ACI 318.For both projects, the in-place test results clearly showed thatthe concrete had acceptable strength.

In conclusion, current legal contracts for the sale and pur-chase of ready-mixed concrete are usually based on the 28-day strength of standard-cured cylinders. For the time being,therefore, these cylinders have to be cast. However, when in-place tests are made at an early age, the acceptability of theconcrete can be assessed at that time. If it is satisfactory, thereis no need to test the standard cylinders. If the early in-placetests indicate a problem with concrete in a particular place-ment, the related standard cylinders are available for testing.

CHAPTER 8—REFERENCES

8.1—Recommended referencesThe documents of the various standards-producing organi-

zations referenced in this report are listed below with theirserial designation.


American Concrete Institute214 Recommended Practice for Evaluation of Strength

Test Results of Concrete306R Cold Weather Concreting308 Standard Practice for Curing Concrete318 Building Code Requirements for Reinforced Concrete437R Strength Evaluation of Existing Concrete Buildings

ASTMC 31 Practice for Making and Curing Concrete Test

Specimens in the FieldC 39 Standard Test Method for Compressive Strength of

Cylindrical Concrete SpecimensC 42 Method of Obtaining and Testing Drilled Cores

and Sawed Beams of ConcreteC 192 Method of Making and Curing Concrete Test Spec-

imens in the LaboratoryC 511 Specification for Moist Cabinets, Moist Rooms,

and Water Storage Tanks Used in the Testing ofHydraulic Cements and Concretes

C 597 Test Method for Pulse Velocity Through ConcreteC 803 Test Method for Penetration Resistance of Hard-

ened ConcreteC 805 Test Method for Rebound Number of Hardened

ConcreteC 823 Practice for Examination and Sampling of Hard-

ened Concrete in ConstructionsC 873 Test Method for Compressive Strength of Concrete

Cylinders Cast in Place in Cylindrical MoldsC 900 Test Method for Pullout Strength of Hardened

ConcreteC 1074 Practice for Estimating Concrete Strength by the

Maturity MethodC 1150 Test Method for the Break-Off Number of Con-

creteE 105 Recommended Practice for Probability Sampling

of MaterialsE 122 Recommended Practice for Choice of Sample Size

to Estimate the Average Quality of a Lot or ProcessE 178 Practice for Dealing with Outlying Observations

These documents may be obtained from the following or-ganizations:

American Concrete InstituteP.O. Box 9094Farmington Hills, Mich 48333-9094

ASTM100 Barr Harbor Dr.West Conshohocken, Pa. 19428-2959

8.2—Cited referencesBallarini, R.; Shah, S.P.; and Keer, L.M., “Failure Charac-

teristics of Short Anchor Bolts Embedded in a Brittle Mate-rial,” Proceedings, Royal Society of London, A404, 1986,pp. 35-54.

Barker, M.G., and Ramirez, J.A., “Determination of Con-

crete Strengths Using the Break-Off Tester,” ACI MaterialsJournal, V. 82, No. 6, Jul.-Aug. 1988, pp. 221-228.

Barker, M.G., and Ramirez, J.A., “Determination of Con-crete Strengths Using the Break-Off Tester,” Structural En-gineering Report, #CE-STR-87-22, School of CivilEngineering, Purdue University, 1987, 114 pp.

Bickley, J.A., “Evaluation and Acceptance of ConcreteQuality by In-Place Testing,” In Situ/Nondestructive Testingof Concrete, SP-82, American Concrete Institute, Detroit,1984, pp. 95-109.

Bickley, J.A., “Variability of Pullout Tests and In-PlaceConcrete Strength,” Concrete International: Design & Con-struction, V. 4, No. 4, April 1982, pp. 44-51.

Bickley, J.A., “Concrete Optimization,” Concrete Inter-national: Design & Construction, Vol. 4, No. 6, June 1982b,pp. 38-41.

Bloem, D.L., “Concrete Strength in Structures,” ACI JOUR-

NAL, Proceedings V. 65, No. 3, March 1968, pp. 176-187.Bocca, P., “Application of Pull-Out Test to High Strength

Concrete Strength Estimation,” Materials and Structures,Research and Testing, (RILEM, Paris), V. 17, No. 99, May-June 1984, pp. 211-216.

Bungey, J.H., Testing of Concrete in Structures, 2nd Ed.,Chapman and Hall, New York, 1989, 228 p.

Carino, N.J., “Statistical Methods to Evaluate In-PlaceTest Results,” New Concrete Technology: Robert E. PhilleoSymposium, ACI SP-141, American Concrete Institute,1993, pp. 39-64.

Carino, N.J., and Tank, R.C., “Maturity Functions forConcrete Made with Various Cements and Admixtures,”ACI Materials Journal, V. 89, No. 2, March-April 1992, pp.188-196.

Carino, N.J., and Tank, R.C., “Statistical Characteristicsof New Pin Penetration Test,” ASTM Journal of Cement,Concrete, and Aggregates, V. 11, No. 2, Winter 1989, pp.100-108.

Carino, N.J., “Maturity Method: Theory and Application,”ASTM Journal of Cement, Concrete, and Aggregates, V. 6,No. 2, Winter 1984, pp. 61-73.

Carino, N.J.; Woodward, K.A.; Leyendecker, E.V.; andFattal, S.G., “Review of the Skyline Plaza Collapse,” Con-crete International: Design & Construction, V. 5, No. 7, July1983, pp. 35-42.

Carino, N.J.; Lew, H.S.; and Volz, C.K., “Early Age Tem-perature Effects on Concrete Strength Prediction by the Ma-turity Method,” ACI JOURNAL, Proceedings V. 80, No. 2,March-April 1983b, pp. 93-101.

Carette, G.G., and Malhotra, V.M., “In Situ Tests: Vari-ability and Strength Prediction at Early Ages,” In Situ/Non-destructive Testing of Concrete, SP-82, American ConcreteInstitute, Detroit, 1984, pp. 111-141.

Carlsson, M.; Eeg, I.R.; and Jahren, P., “Field Experiencein the Use of the Break-Off Tester,” In Situ/NondestructiveTesting of Concrete, SP-82, American Concrete Institute,Detroit, 1984, pp. 277-292.

Chabowski, A.J., and Bryden-Smith, D.W., “Assessingthe Strength of Concrete of In-Situ Portland Cement Con-crete by Internal Fracture Tests,” Magazine of Concrete Re-


search , V. 32, No. 112, Sept. 1980, pp. 164-172.Dahl-Jorgenson, E., and Johansen, R., “General and Spe-

cialized Use of the Break-Off Concrete Strength TestingMethod,” In Situ/Nondestructive Testing of Concrete, SP-82,American Concrete Institute, Detroit, 1984, pp. 293-307.

Dilly, R.L., and Vogt, W.L., “Pullout Test, Maturity, andPC Spreadsheet Software,” Nondestructive Testing, SP-112,American Concrete Institute, 1988, pp. 193-218.

Domone, P.L., and Castro, P.F., “An Expanding SleeveTest for In-Situ Concrete and Mortar Strength Evaluation,”Proceedings , Structural Faults and Repairs 87, EngineeringTechnics Press, Edinburgh, 1987.

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Fa∨ca∨oaru, I., “Non-destructive Testing of Concrete inRomania,” Proceedings, Symposium on Non-destructiveTesting of Concrete and Timber, June 11-12, 1969, Institu-tion of Civil Engineers, London, 1970, pp.39-49.

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the confidence interval for an estimate obtained from astrength relationship is affected by the number of points usedto establish that relationship (Carino 1993). Because thestrength relationship is used to estimate compressivestrength from in-place test results, compressive strength istreated as the dependent variable (Y value) and the in-placeresult as the independent variable (X value).

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(A-1)

where

Se

dyx( )2

N 2–--------------=

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APPENDIX

A.1—Number of strength levelsThe number of strength levels needed to develop the

strength relationship depends on statistical considerationsand cost. To gain some insight, it is useful to examine how


Fig. A-1—Effect of number of points used to establish strength relationship on the confidence interval width (in terms of residual standard deviation)

sion analysis procedure to determine the strength relation-ship should account for error in the X-variable. The methodproposed by Mandel (1984) can be used for this purpose.This section provides a step-by-step procedure for carryingout Mandel’s method.

It is assumed that at each strength level for the correlationtests there are nx replicate in-place test results and ny replicatecompression test results. The number of strength levels is N.The objective is to find the best-fit values of a and B (andtheir uncertainties) for the straight line, strength relationship:

ln C = a + B ln I (A-4)

wherea = intercept of straight lineB = slope of straight lineln C = the natural logarithm of compressive strengthln I = the natural logarithm of the in-place test result

After the correlation test data have been obtained, the fol-lowing sequence of calculations is used to establish thestrength relationship and its uncertainty:

1) Transform the data by taking the natural logarithm ofeach test result

x = ln i (A-5a)

y = ln c (A-5b)

where i and c are the individual in-place and compressivestrength test results, respectively.

Se = estimated residual standard deviationdyx = deviation of each test point from the best-fit lineN = number of test points used to establish strength rela-

tionshipWhen the strength relationship is used to estimate the

mean value of Y at a new value of X, the width of the confi-dence interval for the mean is related to the residual standarddeviation by the following expression* (Natrella 1963,Snedecor and Cochran 1967):

(A-2)

whereW = width of the 100(1-α) percent confidence interval

for the estimated mean value of Y for the value XtN-2,α/2= Student t-value for N-2 degrees of freedom and sig-

nificance level = αX = average of X values used to develop strength rela-

tionshipSxx = sum of squares of deviations about X of the X values

used to develop the strength relationship,Sxx = Σ ( X - X)2

The second term under the square root sign in Eq. (A-2)shows that the width of the confidence interval increases asthe distance between X and X increases. This means that theuncertainty of the estimated strength is greater at the extremelimits of the strength relationship than at its center.

To examine how the width of the confidence interval is af-fected by the number of test points, consider the case whereX = X, so that the second term under the square root sign in

* Strictly speaking, Eq. (A-2) is applicable only for the case of where the assump-tions of ordinary least-squares analysis are satisfied. It is used here to demonstrate, ina simplified way, the effects of the number of test points on the width of the confi-dence interval. When using in-place testing, Eq. (A-16) in Appendix A.3 should beused to determine the lower confidence limit of the estimated mean value of Y for anew value of X.

W 2t N 2 α 2⁄,– Se1N---- X X–( )2

Sxx

--------------------+=

Eq. (A-2) equals zero. The width of the confidence intervalrelative to the residual standard deviation is as follows:

(A-3)

Equation (A-3) is plotted in Fig. A.1 to show how thewidth of the 95 percent confidence interval (relative to Se) isaffected by the number of test points used to establish thestrength relationship. It is seen that, for few test points (say,less than 5), by including an additional test point there is asignificant reduction in the relative width of the confidenceinterval. However, for many points, the reduction obtainedby using an additional test point is small. Therefore, the ap-propriate number of strength levels is determined by consid-erations of precision and cost. The user must answer thequestion: “Is the additional precision obtained by using an-other test point worth the additional expense?” From Fig.A.1, it is reasonable to conclude that the minimum numberof test points is about six, while more than nine tests wouldprobably not be economical.

A.2—Regression Analysis with X-error (Mandel 1984)If the procedures in 6.2.3 or 6.2.4 are to be used to estimate

the in-place characteristic strength, the least-squares regres-

W X( )Se

------------- 2 tN 2 α 2⁄,–1N----=


2) For each strength level j compute the average and stan-dard deviation* of the logarithms of the in-place and com-pressive test resultsXj = the average of the logarithms of the in-place tests at

strength level jYj = the average of the logarithms of the compressive

strength tests at strength level jsxj = the standard deviation of the logarithms of the in-

place tests at strength level jsyj = the standard deviation of the logarithms of the com-

pressive strength tests at strength level j3) Calculate (sx)2 and (sy)2, which are the average variances

(squares of the standard deviations) of the logarithms of thein-place tests and of the compression tests, respectively.†

(A-6a)

(A-6b)

4) Compute the value of λ as follows:

(A-7)

The numerator and denominator in Eq. (A-7) are the vari-ances of the average compressive strength and in-place re-sults, respectively. If there are different numbers of replicatetests at each strength level, the average numbers of replica-tions should be used for nx and ny (see Stone and Reeve1986).

5) Find the values of b and k, by solving the following si-multaneous equations:‡

(A-8a)

(A-8b)

In Eq. (A-8a), the terms Sxx, Syy, and Sxy are calculated ac-cording to the following:

* For a small number of replicate tests, the standard deviation may be estimated bymultiplying the range by the following factors: 0.886 for two replicates; 0.591 forthree replicates; and 0.486 for four replicates (Snedecor and Cochran 1967).

† Eq (A-6a) and (A-6b) assume that the same number of replicates were used ateach strength level. If some test results were discarded because they were found to beoutliers, the pooled variances should be computed to account for different numbers ofreplicates at each strength level (see Stone and Reeve 1986 of textbook on introduc-tory statistics).

‡ An iterative procedure can be used to solve for k and b (Mandel 1984). First,assume a value of k, such as k = 0, and solve for b in Eq. (A-8a). Using this value of b,solve for a new value of k in Eq. (A-8b). Substitute the new value of k into Eq. (A-8a)and solve for b. Repeat the procedure until the values of k and b converge, which willusually occur in less than five iterations.

sy( )2 Σ syj( )2

N-----------------=

sx( )2 Σ sxj( )2

N-----------------=

λ

sy( )2

ny

-----------

sx( )2

nx

-----------

-----------=

bSxy k S yy+

Sxx k S xy+-------------------------=

k bλ---=

(A-9a)

(A-9b)

(A-9c)

The terms X and Y are the grand averages of the logarithmsof the in-place and compressive strength test results.

(A-10a)

(A-10b)

6) The best-fit estimates of B and a are as follows:

B = b (A-11a)

(A-11b)

7) Use the following steps to compute the standard errorsof the estimates of a and B.

a) Compute these modified sums of squares:

Suu = Sxx + 2kSxy + k2Syy (A-12a)

Svv = b2Sxx - 2bSxy + Syy (A-12b)

b) Compute the following error of fit, se:

(A-13)

c) The error in a is given by the following:

(A-14)

d) The error in B is given by the following:

(A-15)

In summary, the following general steps are used to obtainthe best-fit strength relationship and account for the error inthe X variable (in-place test results):

• Transform the correlation data by taking their naturallogarithms

Sxx Σ Xj X–( )2

=

Syy Σ Yj Y–( )2=

S xy Σ Xj X–( ) Yj Y–( )=

XΣXj

N--------=

YΣYj

N--------=

a Y b X–=

seSvv

N 2–-------------=

sa se1N---- X

21 k b+( )2

Suu

----------------------------+=

sB se= 1 k b+

Su u

------------------


Reeve 1986)The strength relationship is used to estimate the in-place

compressive strength based on the results of the in-placetests done on the structure. Typically, several in-place testsare done on the structure, the average result is computed, andthe strength relationship is used to estimate the average com-pressive strength. However, to obtain a reliable estimate ofthe average strength, i.e., a value that has a high probabilityof being exceeded, the standard deviation of the estimatemust be known.

The approach developed by Mandel (1984) can be used toestimate the standard deviation of an estimated value of Y(average compressive strength) for a new value of X (averagein-place test results) when there is X-error. Mandel's methodwas modified by Stone and Reeve (1986) so that it also in-corporates the uncertainty of the average in-place result fromtests on the structure. This modification accounts for the factthat the uncertainty in the average of the in-place results istypically greater for tests on the structure compared with thatfrom the laboratory tests used to develop the strength rela-tionship. The standard deviation of the estimated value of Y(average of the logarithm of compressive strength) is ob-tained by the following equation:

2 s2

(A-16)

where

sY1N---- 1 k b+( )2 X X–( )

Su u

--------------------+ se2

b2

+ x

m----=

An example is presented to show the application of Man-del's method and to illustrate the evaluation of in-place testsusing the tolerance factor method discussed in Section 6.2.2and the alternative method discussed in Section 6.2.4. Thecorrelation data are taken from the study of the pullout testby Stone et al. (1986). The pullout test geometry had an apexangle of 70 deg and the concrete was made using river gravelaggregate. Eight strength levels were used to develop thestrength relationship. At each strength level, 11 replicatepullout tests and five replicate cylinder compression testswere done.

The data from the cited reference were converted by tak-ing the natural logarithm of the individual pullout loads andcompressive strengths. The average, standard deviation, andvariance of the transformed pullout loads at each strengthlevel are shown in Columns 1, 3, and 4 of Table A.1. The av-erage, standard deviation, and variance (square of standarddeviation) of the transformed compressive strengths at each
strength level are shown in Columns 5, 7, and 8. For infor-mation, Columns 2 and 6 give the averages of the logarithmvalues transformed into real units.
The average values in Columns 1 and 5 of Table A.1 wereused to calculate the various parameters to establish thestrength relationship according to the procedure in AppendixA.2. A computer spreadsheet was set up to do these calcula-tions. Table A.2 summarizes the calculated values.

The calculated values of a and B are -0.5747 and 1.030, re-spectively. Therefore the equation of the strength relation-
ship is as follows:
C = -0.5747 + 1.030 PO (A-17)

whereC = average of natural logarithms of compressive

strengths, andPO= average of natural logarithms of pullout loads

* The average and standard deviation of the in-place results refer to the average and standard deviation of the logarithms of the test results.

• At each strength level, compute the average and standarddeviation of the transformed values (logarithms)

• Compute the value of λ based on the average (or pooled)variances of the mean compressive and in-place results

• Compute the values of b and k• Compute the slope and intercept of the best-fit relation-

ship• Compute the error of the fitThe error of the fit, se, is needed to calculate the uncertain-

ty in the estimated mean compressive strength when thestrength relationship is used with in-place tests of the struc-ture. This is explained in the next section.

A.3—Standard deviation of estimated Y value (Stone and

sY = standard deviation of estimated value of Y (averageconcrete strength)

N = number of points used to obtain the strength relation-ship

b = estimated slope of the strength relationshipk = b/λ, where λ is obtained from the within-test variabil-

ity during correlation testing, Eq. (A-7)X = average* of in-place tests done on the structureX = average of X values during correlation tests, Eq. (A-

10a)se = error of fit of strength relationship, Eq. (A-13)Suu = modified sum of the squares as given by Eq. A-12a

* The average and standard deviation of the in-place results refer to the average and standard deviation of the logarithms of the test results.

sX = standard deviation*of in-place tests done on the struc-ture

m = number of replicate in-place tests done on the struc-ture

It is seen that there are two sources of the uncertainty in theestimated value of Y: 1) the uncertainty of the strength rela-tionship (se); and 2) the uncertainty (sX) of the in-place testresults obtained from testing the structure. Because Eq. A-16is the sum of two variances, which may have different de-grees of freedom, a formula has been suggested for comput-ing the effective degrees of freedom for sY (Stone and Reeve1986). For simplicity, it can be assumed that there are (m-1)degrees of freedom associated with sY, where m is the num-ber of in-place tests done on the structure. These degrees offreedom are used in choosing the t-value to calculate a lowerconfidence limit for the average value, as discussed in Sec-tion 6.2.4.

A.4—Example


Table A.1—Average, standard deviation, and variance of correlation data from Stone et al. 1986

Average ln(PO) (PO in

lbs)

Real value of PO(lbs)

Stan-dard

devia-tion

ln(PO)Variance ln(PO)

Average ln (C) (C in psi)

Real value of C(psi)

Stan-dard

devia-tion

ln(C)Variance

ln(C)

1 2 3 4 5 6 7 8

7.6842 2174 0.1085 0.0118 7.3183 1508 0.0474 0.0022

7.9138 2735 0.0459 0.0021 7.6292 2057 0.0435 0.0019

8.2229 3725 0.0700 0.0049 7.9043 2709 0.0451 0.0020

8.4040 4465 0.1065 0.0114 8.1047 3310 0.0103 0.0001

8.7098 6062 0.1162 0.0135 8.3209 4109 0.0343 0.0012

8.8100 6701 0.1488 0.0222 8.4321 4592 0.0048 0.0000

8.9397 7629 0.0953 0.0091 8.6660 5802 0.0507 0.0026

8.9877 8004 0.1598 0.0255 8.7358 6222 0.0303 0.0009

Average variance of ln(PO) 0.0125 Average variance of ln(C) 0.0014

1 kN = 224.8 lbs; 1 MPa = 145.1 psi; ln(kN) = ln(lbs) - 5.4153; ln (MPa) = In(psi) - 4.9777.

Table A.2—Summary of results of regression calculations using values in Table A.1 and procedure in Appendix A.2

Parameter Value Parameter Value

N 8 k 4.290

nx 11 b = B 1.030

ny 5 a -0.5747

X 8.4590 ea 0.563

Y 8.1389 Suu 48.211

λ 0.240 Svv 0.0180

Sxx 1.6528 se 0.0548

Syy 1.7424 sa 0.3622

Sxy 1.6883 sB 0.043

Table A.3—Values of pullout force obtained from tests on structure

Case 1 Case2

Pullout force (lbs) ln(PO) Pullout force (lbs) ln(PO)

3010 8.0097 3904 8.2698

3340 8.1137 2873 7.9631

3500 8.1605 3204 8.0722

3080 8.0327 2669 7.8895

2478 7.8152 2332 7.7545

3000 8.0064 3091 8.0362

3290 8.0986 3844 8.2543

3070 8.0294 3140 8.0520

2660 7.8861 2552 7.8446

2660 7.8861 3336 8.1125

Average (X) 8.0038 Average (X) 8.0249

Standard deviation (sX)

0.1108 Standard deviation (sX)

0.1670

1 kN = 224.8 lbs; ln(kN) = ln (lbs) - 5.4153.

Fig. A.2 shows the correlation data (average of loga-rithms) and the best-fit line.

Finally, the strength relationship and the procedures inSection 6.2 are used to estimate the in-place compressivestrength based on in-place test results. Table A.3 shows two

Fig. A.2—Data for strength relationship and best-fit line

Table A.4—Estimate of in-place compressive strength using results in Table A.3

Alternative approach (Section 6.2.4)

Tolerance factor approach (Section 6.2.2)

Case 1 Case 2 Case 1 Case 2

Y(Eq. A-17) 7.6700 7.6917 Y 7.6700 7.6917

exp(Y), psi* 2143 2190 exp(Y), psi 2143 2190

sY(Eq. A-16) 0.0453 0.0607 K (p = 0.75) 1.671 1.671

t9,0.05 1.833 1.833 scf 0.111 0.167

Ylow(Eq. 6-4) 7.5870 7.5804

Y0.10(Eq. 6-1) 7.4845 7.4126

scf (Eq. 6-6) 0.037 0.055exp(Y0.10),

psi 1780 1657

Y0.10(Eq. 6-5) 7.5395 7.5099

exp(Y0.10), psi 1881 1826

* exp(Y) = eY.1 MPa = 145.1 psi.

sets of in-place pullout test results. Both cases have approx-imately the same average value, but Case 2 has higher vari-ability. In each case, there are 10 replicate test results, i.e., m= 10. The pullout loads are transformed by taking their natu-ral logarithms. The averages of the logarithms (PO) are sub-stituted into Eq. (A-17) to obtain the average of the logarithmof in-place compressive strength (C). Estimates of the 10thpercentile strength (Y0.10) corresponding to the two cases areobtained using the tolerance factor method (Section 6.2.2)and the alternative method (Section 6.2.4). The values of thevarious parameters used in the calculations are summarizedin Table A.4, and, where appropriate, the correspondingequation numbers are shown. For the alternative method, thestandard deviation of the in-place compressive strength (scf)was computed using Eq. (6-6), while for the tolerance factormethod it was taken to equal the standard deviation of the in-place test results. For each method, the value of Y0.10 is asmaller fraction of the average strength for Case 2 due to thehigher variability of the in-place tests. The estimates of Y0.10

are lower for the tolerance factor method.

228.1r-95 in-place methods to estimate concrete · pdf file2.4—pullout test ... in-place...

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