Research Article Predicting Concrete Compressive Strength ... · Research Article Predicting Concrete Compressive Strength and Modulus of Rupture Using Different NDT Techniques WilfridoMartínez-Molina,

Research ArticlePredicting Concrete Compressive Strength and Modulus ofRupture Using Different NDT Techniques

Wilfrido Martiacutenez-Molina12 Andreacutes Antonio Torres-Acosta23

Juan Carlos Jaacuteuregui2 Hugo Luis Chaacutevez-Garciacutea1 Elia Mercedes Alonso-Guzmaacuten1

Mario Graff4 and Juan Carlos Arteaga-Arcos5

1Facultad de Ingenierıa Civil Laboratorio de Materiales Ciudad Universitaria Universidad Michoacana de San Nicolas de HidalgoAvenida Francisco J Mugica sn Colonia Felicitas del Rıo 58040 Morelia MICH Mexico2Facultad de Ingenierıa Ciudad Universitaria Universidad Autonoma de Queretaro Cerro de las Campanas sn76010 Santiago de Queretaro QRO Mexico3Instituto Mexicano del Transporte 76703 Sanfandila QRO Mexico4INFOTEC Centro de Investigacion e Innovacion en Tecnologıas de la Informacion y Comunicacion Catedras-CONACyTCircuito Tecnopolo Sur No 112 Colonia Fracc Tecnopolo Pocitos 20313 Aguascalientes AGS Mexico5Facultad de Ciencias Universidad Autonoma del Estado de Mexico Campus Universitario ldquoEl CerrillordquoEl Cerrillo Piedras Blancas 50200 Toluca MEX Mexico

Correspondence should be addressed to Wilfrido Martınez-Molina wilfridomartinezmolinagmailcom

Received 13 May 2014 Accepted 6 November 2014 Published 4 December 2014

Academic Editor Jun Liu

Copyright copy 2014 Wilfrido Martınez-Molina et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Quality tests applied to hydraulic concrete such as compressive tension and bending strength are used to guarantee propercharacteristics of materials All these assessments are performed by destructive tests (DTs)The trend is to carry out quality analysisusing nondestructive tests (NDTs) as has been widely used for decades This paper proposes a framework for predicting concretecompressive strength and modulus of rupture by combining data from four NDTs electrical resistivity ultrasonic pulse velocityresonant frequency and hammer test reboundwithDTs dataThemodel determined from themultiple linear regression techniqueproduces accurate indicators predictions and categorizes the importance of each NDT estimate However the model is identifiedfrom all the possible linear combinations of the available NDT and it was selected using a cross-validation technique Furthermorethe generality of the model was assessed by comparing results from additional specimens fabricated afterwards

1 Introduction

In the building industry the measurement of certain physicaland mechanical properties of concrete is particularly impor-tant such as compressive strength (1198911015840119888) and modulus of rup-ture (MOR) Test methods to obtain 1198911015840119888 consist of applyinga compressive axial load to molded cylinders or cores The1198911015840119888 of the specimen is calculated by dividing the maximumload reached during the test by the cross-sectional area ofthe specimen [1] the method to determine MOR includesthe determination of the flexural strength of concrete fromsimply supported unreinforced concrete beams where acentral load is applied to the beam until fracture (also called

a three-point load test the load applied at the center of thebeam and the other two are the supports) The result of suchtest is reported as the MOR and might be used to determinecompliance with the materialsrsquo specifications or as a basisfor proportioning mixing and placement operations forslabs and pavements [2] Traditionally these estimates havebeen obtained following destructive methods which are thestandard ones to determine the mechanical resistance (iecompressive tension and bending strength) [3] Howeverthese tests are often costly and time consuming For exampleto determine the compressive strength of concrete it isnecessary to process a large amount of testing samples (atleast fifteen) [4] then a compressometer is required in order

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2014 Article ID 742129 15 pageshttpdxdoiorg1011552014742129

2 Advances in Materials Science and Engineering

to determine the elasticmodulus these samples are deformedand destroyed in order to determine the compressive strengthand the static modulus of elasticity [5] As it can be seenthis procedure modifies the samples and consequently it isimpossible to repeat the test in the same sample in case itwould be necessary [6]

On the other hand it is not easy to determine themechanical characteristics of the materials using only NDTprocedures This problem is more evident since the mod-els are obtained with laboratory settings and under strictcontrolled conditions As a consequence it is necessary toevaluate the applicability of these models in uncontrolledenvironments and using different conditions from those usedin the formulation of an empirical mechanistic model [7]

One particular characteristic ofmost of theseNDTs is thatthey can be conducted at the work place and can be used todetermine certain properties of already built structures thisprocess is known as in-place testing [8]

In accordance with ACI 228-1R-03 the objective of in-place testing is to estimate the compressive strength ofconcrete by the use of NDTs In order to validate the resultsit is necessary to have a known relationship between theseresults and the mechanical resistance obtained by DTs Thisrelationship is usually established by performing DTs ofdrilled cores taken from adjacent locationswhere the in-placetest is conducted The accuracy of the estimated compressivestrength depends on the correlation between the strengthof the concrete and the quantity measured by the in-placetest As a general index of concrete strength the compressivestrength of concrete 1198911015840119888 is important in the performanceassessment of existing reinforced concrete structures [9]On the other hand the MOR is very useful especially inrelation to road slab design and airfield runways becausethe flexure tension is a critical factor to determine concretersquosperformance in such applications [10]

When NDT first appeared for concrete application it wascommon to model the prediction of the concrete strengthusing only one of the above tests However as found bymany researchers the combination of different NDTs canlead to more accurate and reliable models [9 11ndash13] Inorder to approximate the appropriate estimates of indicators(response variables) for example Ploix et al [14] performeda combination or fusion of NDT data as radar test electricalresistivity and capacity infrared thermography impact echoand ultrasound to predict the simultaneous estimation of thewater saturation and porosity rate in concrete for undamagedconcretes measured in laboratory conditionsTheymeasureddifferent NDT parameters such as frequencies velocitiesand attenuations and after that they conducted an sta-tistical analysis with the purpose of identifying empiricalcorrelations linking each experimental parameter to bothsearched indicators There were identified correlations withbilinear regressions as a first approximation but sincesome different NDT measurements are very sensitive tomaterial heterogeneity variability and experimental noiserelative disagreement or conflict between sources of infor-mation happened (ie measurements) thus the predictionmodels rapidly became ill-conditioned Therefore it wasdecided to combine several NDT techniques (at least three)

providing more suitable information Kaftandjian et al [15]used a data fusion approach to improve weld inspectionby NDT combining the use of evidence theory and fuzzylogic in their framework X-ray and ultrasonic inspectionwere modeled in order to generate 3D images from bothNDTs for evaluating defect detection and defect sizing ofwelded joints for industrial purposes showing that the fusionof data significantly enhances the reliability of the defectrecognition Maierhofer et al [16] used radar ultrasonicimpact echo and thermography data fusion for predictingdeterioration of concrete vehicular bridges noting that thedata fusion technique increases reliability and improved theaccuracy of the quantitative results exploiting the differentand sometimes complementary physical effects provided fordifferent NDTs Shah and Ribakov [17] described a testingprocedure based on the dynamic response of the cracked orflawed concrete structures subjected to impact loading andonanalyzing the ability of the resistivity measurement to detectand to locate cracks and spalling with in situ measurementson a damaged concrete slab Huang et al [9] developed aSonReb (the combination of rebound hammer and ultrasonicpulse velocity tests) for compressive strength prediction ofconcrete samples using a probabilistic multivariate regres-sion model taking into account the data of the proportionsof the concrete mix (curing conditions and the age of theconcrete) assessing the model from Bayesian updating ruleLui et al [18] provide a very wide state-of-the-art reportregarding NDT data fusion techniques They established theuse of multiple NDT methods to increase the reliability andreduce the uncertainty of testing and evaluationNonethelessthere are cases in which the use of all available tests createsa model that only works in the samples used to empiricallycorrelate the obtained data and thus the model does notgeneralize In order to deal with this problem it is necessaryfor an automatic method of variable selection (here variablesare the NDT) to establish a simple model that achievesthe predictionexplanation of the response variable togetherwith an efficient estimation of the coefficients

Given that there are only 6 different variables to createthe model in this contribution a decision was made to testall the linear combinations of these variables that is create64 models The model proposed was selected from these 64models by using a cross-validation technique Furthermoreto illustrate the generality of the model few samples wereremoved from the model formulation and selection processand the results presented on this contribution are computedusing the removed samples to validate the predicted modelClearly there are situationswhere it is not possible to compareall possible models To provide a complete picture of thisscenario it was decided to use a cross-validation techniqueto select the best from the different 64 models

In addition to this in order to compare the proposedmodel against the ones described in the literature a compar-ison was made with more than ten different models againstthe ones proposed hereThe results show that the model pro-posed here is competitive with the ones proposed in previousinvestigations In addition the independent variables usedin this investigation were used also with the other modelsfound in the literatureWith this extended set of independent

Advances in Materials Science and Engineering 3

variables all the possible linear modes were initiated andused the selected mechanism to identify the best modelThe result observed was that this novel model is competitivewhen compared against other models previously reportedHowever the proposed model has a better correlation factorand was simpler in the sense that it has fewer degrees offreedom

In this study different frameworks to predict the 1198911015840119888and the MOR of hydraulic concrete were constructed basedon data from electrical resistivity test (ERT) ultrasonicpulse (UPV) resonance frequency test (RFT) and reboundnumber test (RNT) obtained from cylindrical and prismaticspecimens

The objective of this research was to predict the 1198911015840119888and MOR of concrete since these are index parametersthat determine the quality of the concrete but with the useof models based on NDT By employing more than oneNDT it has been possible to generate highly reliable andaccurate models as demonstrated herein Furthermore theobtained models can help engineers to understand how eachone of the different variables in the determination of thecompressive strength and modulus of rupture is importanteither in laboratory samples or in samples from the place(field samples) This research was conducted in two stagesthe first was controlling workability of the concrete and thesecond one was controlling watercement (wc) ratio

2 Review of the Utilized NDT

21 Electrical Resistivity Test (ERT) The application of DCcurrent to quantify resistivity was performed by ConardSchlumberger in 1912 It was reported as one of the mostsuccessful experimental approach of electrical resistivitysurvey In USA the idea was developed by Frank Wennerin 1915 After that the method has undergone significantimprovement in last three decades [19]

Later Robert W Fox in 1930 observed electric currentsflowing in the copper mines in Cornwall as a result of chem-ical reactions within the veins of the deposits [20] In termsof materials and equipment the ERT can be performed inlaboratory specimens in specimens taken from the analyzedstructure or directly in the structure at the site field [21] ERTmeasurements are made by applying a current to a porousbody through two current electrodes and measuring theresulting difference voltage at two potential electrodes Thetestmust be performed in saturated samples under themech-anism of electrical conductivity through saturated connectedpores which is based on the conductivity of thewater throughthe pores of thematerial [22] Liu et al [23] conducted a studyin soil-cement used to improve the behavior of soft soils inroad construction engineering they built a model to verifythe quality control of soil-cement in the field The modelpredicted the electrical resistivity (ER) of soil-cement undercertain conditions of curing time and the wc ratio It wasfound that the ER had a good relationship with the 1198911015840119888 of thematerial in study Cao andChung [24] presented a research indynamic response of cement mortars subjected to repeatedcycles of1198911015840119888 bymeasuring ER Lataste et al [25] used the ERTtechnique to characterize damage in field concrete structures

associated with the aperture and depth of surface cracks Onthe other hand for routine quality control measures morerapid but also reliable methods are needed Recent studiesconfirm that electrical resistivity measurement is a simplereliable and rapid test method for quality control of concrete[26 27] Concrete has a resistivity varying substantiallydepending on a number of factors The electrical current iscarried by the dissolved charged ions flowing through thepore solution in the concrete Therefore all the factors suchas watercement ratio cement type pozzolanic admixturesand degree of hydration that is affecting the pore structureof the concrete are also affecting the electrical resistivity ofthe concrete Environmental factors such as temperature andmoisture conditions can also have a large impact on theelectrical resistivity of the concrete [26]

22 Ultrasonic Pulse Velocity (UPV) The UPV has beensuccessfully used to evaluate the quality of hydraulic concretefor over 60 years The 1198911015840119888 of concrete specimens and ofconcrete in situ can also be estimated through the test UPV[28 29] Ultrasonic waves are mechanical waves that aregenerated by exciting a piezoelectric crystal with a highvoltage pulseThewave is then transmitted through the testedmaterial which is in contact with the transducer containingthe crystal When this wave impinges upon a receivingtransducer it produces an output voltage [30]There are threepossible ways in which the transducers may be arrangeddirect transmission semidirect transmission and indirecttransmission In the direct method the transducers are placedon opposite faces of the tested element In the semidirectmethod the transducers are placed at a 90∘ angle whereasin the indirect method both transducers are placed on oneface of the tested element Since the transmission path lengthand direction are not well defined in the indirect methodthe results produced are less satisfactory Thus the indirectmethod does not give any information on deeper concrete itonly collects information on the surface [31]

In order to use the UPV a pulse of ultrasonic wavethrough the concrete is created at a point in the test objectsurface and the time it takes to travel from that point toanother is measured Knowing the distance between thesetwo points the pulse wave velocity can be determined [28]A lot of research has been conducted in order to use thistechnique to predict the mechanical properties of concreteand rock for example Wu and Lin [32] and Selleck et al[33] investigated the behavior of UPV associated with thedamage of concrete When a solid medium is altered by adynamic or vibratory load three kinds of mechanical wavesare generated these waves can be classified by the way theypropagate (also called stress waves) (1) compression waves(also called longitudinal or P waves) (2) shear waves (alsocalled Swaves) and (3) surfacewaves (also known asRayleighwaves) [34]The velocity of such waves depends on the elasticproperties of the medium so that knowing the speed ofsound and the solidmass it can estimate the elastic propertiesof the medium which can be associated with the qualityparameters of the material [35]The relationship between the1198911015840119888 and UPV is not unique and it is affected by many factorssuch as the size type and content of aggregate wc ratio


and content of humidity The effect of these factors has beenstudied by many researchers who have clearly indicated thatthere should be estimated 1198911015840119888 of the concrete values fromthe UPV unless these have similar correlations previouslyestablished for the type of concrete studied [36ndash40]

23 The Resonance Frequencies Test (RFT) The method fordetermining the dynamic modulus of elasticity of solidbodies from their resonance frequencies has been used inthe last 55 yearsHowever in recent yearsmethods of theRFThave been used almost exclusively in laboratory studies [28]

In the late 1930s and early 1940s other researchersimproved themethod by using electronic equipment formea-suring the resonant frequency [41ndash43] currently this typeof equipment is required by ASTM C 215-85 Standard TestMethod [44] The apparatus consists mainly of two sectionsone generates mechanical vibrations and the other detectsthese vibrations [45] The mechanical vibrations are detectedby a piezoelectric transducer and it converts the mechanicalvibrations into electric voltage alternating current of the samefrequencies [28]

The great advantage of the vibrational methods of testingapart from their nondestructive nature is that the dynamicvalues are obtained from transient loads far below the elasticlimit so that the results are free from time-dependentinelastic strains and hysteresis and are directly related to theinternal structure of the material [46]

Vibration-based techniques can be used to monitor theconcrete structures Bagchi et al applied cost-effective andeasy to implement vibration-based damage identification(VBDI) techniques for structural health monitoring of abridge based on changes in the dynamic characteristics ofa structure to determine the location and extent of damagein the structure Hsieh et al described the use of vibrationalmonitoring in the field of structural analysis for detectingand locating structural damage for the purpose of structuralhealth monitoring [47 48]

On the other hand the measurement of the dynamicmodulus of elasticity with resonance frequency methodpredictions can be made about the damage degree anddeleterious progress respectively The dynamic moduli andthe damping capacity are the two important properties ofengineering materials obtained from vibrational methods oftesting To ensure stability and long life it is necessary to avoidthe large amplitudes of vibration associated with resonantfrequencies However where the nature of the structure andits environment are beyond the control of the designer theamplitude of vibration at resonance depends on the dampingcapacity of the structure and its mounting Knowledge ofboth the dynamic moduli and the damping characteristicsof cementitious materials is thus an important aid to design[46]

24 Rebound Number Test (RNT) The RNT method isperformed through the device called sclerometer (SchmidtHammer Rebound) It is based on the principle that therebound of an elastic mass depends on the hardness of thesurface against which the hammer hits there is a relationshipof proportionality between the resistance of concrete and the

rebound height of the hammer mass which is measured byan arbitrary scale of integer numbers Within certain limitsempirical correlations have been established between theproperties of strength of concrete and the RNT [45]TheRNTprovides information about the strength of the material nearthe surface where the test is performed rebound number(RN) is an indicator of the mechanical properties of thematerial Although a large rebound number represent aconcrete with a higher compressive strength than a concretewith a low rebound the test is only useful if a relationship canbe established between the rebound number and the analyzedresistance of the concrete assuming that concrete sampleshave been made with the same type of stone aggregates [10]

For estimation of compressive strength of concrete instructures that are using different testing procedures com-pressive strength of concrete can be found as followsdestructive by taking core bore samples from a structurenondestructive by Schmidt rebound hammer or ultrasonicpulse velocity method semidestructive test methods or acombination of destructive and nondestructive testing Stan-dard procedures have been established and are described indetail in European and international standards as Europeanstandards CSN EN 12504-2 [49] and Czech technical stan-dard CSN 731373 [50] and standards as ASTMC 805-97 [51]JGJT 23-2001 [52]

The combination of NDT such as UVP and RNT canbe conducted to assess the resistance of the concrete in situThis combination has an advantage the Sclerometer revealsinformation regarding the concrete surface while ultrasoundprovides information from the inside of the material [9] Intechnical literature there are models proposed by severalauthors [9 11 53ndash62] Table 1 summarizes the proposedequations to have a fair comparison

Carbonation of concrete occurs when the carbon diox-ide in the atmosphere in the presence of moisture reactswith hydrated cement minerals to produce carbonates forexample calcium carbonate In this case the research wascarried out with hydraulic concrete with ages from 3 to28 days Period during which did not exist the necessaryconditions for carbonation should arise in concrete Howeverwe can say that in older concrete the carbonation depthcan be several millimeters thick and in extreme cases upto 20mm thick In such cases the rebound numbers can beup to 50 higher than those obtained on an uncarbonatedconcrete surface In such cases it is necessary to make anadjustment to the obtained rebounds [10]Moisture conditiontype of aggregate and carbonation depth of the material canaffect the strength estimate [63] and some standards (egChinese standards JGJT 23-2001) offer recommendations forcompensating these effects [52]

3 Significance of Current Research

Nowadays it has been recognized that NDT plays an impor-tant role in the condition monitoring of civil infrastructuresTo properly maintain the civil infrastructures integrity engi-neers required new methods of inspection Better inspectiontechniques are needed for damaged infrastructure [64] Beingaware of this problem in this study four nondestructive


Table 1 Evaluation of different models proposed by different authors

Model Formulation Correlation factor (119877)1198720[9] 1198911015840119888 = 120579

0+ 12057911198731198772 + 120579

2UPV + 120579

3119908119888minus05 + 120579

4ln (age) + 120576 0638

1198720119886[9] 1198911015840119888 = 120579

0+ 12057911198731198772 + 120579

2UPV3 + 120576 0614

1198721[53 71] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV 0621

1198722[54] 1198911015840119888 = 120579

0+ 12057911198773 + 120579

2UPV 0616

1198723[11] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV4 0612

1198724[55] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV + 120579

3UPV2 0596

1198725[56 58 61] ln1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV 0613

1198726[59 60] ln1198911015840119888 = 120579

0+ 1205791ln119877 + 120579

2lnUPV 0617

1198727[57] ln1198911015840119888 = 120579

0+ 1205791(radicln (1198731198773 lowast UPV4)) 0599

1198728[62] 1198911015840119888

minus05

= 1205790+ 1205791119877minus1 + 120579

2(UPV lowast 119877minus1) 0600

119864119886

1198911015840119888 = 1205790freq + 120579

1rebound + 120579

2resistiv + 120579

3UPV 0636

119864119887

1198911015840119888 = 1205790+ 12057911198731198772 + 120579

2UPV + 120579

3(wc)minus05 + 120579

4ln (age) + 120579

5resistiv + 120579

6freq + 120576 0642

techniques were used to predict two important properties toconsider in a structure needed for proper maintenance or toknow the service conditions of the structure of hydraulic con-crete (1198911015840119888 and MOR) By combining several nondestructivetechniques robust models that improve the accuracy of themodel were generated In addition in situ performance con-ditions are different from controlled laboratory conditionsand so it is difficult to keep strict quality control

In this paper the conditions of both field and laboratoryfor concrete mixtures under study were obtained as reportedin Section 4 the forecast mathematical frameworks weregenerated taking into account these conditions and finallythey were fed with data from nondestructive and destructivetests so these models will have better attachment to thereality Furthermore a methodology that could be appliedto any situation to generate and apply a particular modelin the prediction of the properties of the structure understudy could be chosen by the particular characteristic of theresearch material

And inasmuch as that we can demonstrate the reliabilityof nondestructive techniques for the analysis and inspectionof concrete structures we will be providing an importanttool for engineers that can be exploited to save and optimizeresources

4 Experimental

The experimental study was divided in two stages Thefirst one developed three types of specimens type I 70cylinders with dimensions of 100mm (394 in) diameter and200mm(787 in) height type II 70 cylinderswith dimensionsof 150mm (591 in) diameter and 300mm (181 in) heighttype III 20 beams with dimensions of 150mm times 150mmtimes 600mm (591 in times 591 in times 2362 in) All samples wereprepared per ASTM C-143 requirements [65] as reported inTable 2Thewc ratio varied from055 to 076 simulatingfieldconcrete specimens In the second stage three other types ofspecimens were developed with the same dimensions to thatin the first stage but with otherwc ratios type I 70 cylinderstype II 70 cylinders and type III 40 beams half of each type

Table 2 Slumps of mixtures made

Mixture wcProjectslumpmm (in)

Obtainedslumpmm (in)

First stage1 055 75 (295) 100 (394)2 061 100 (394) 135 (531)3 057 75 (295) 115 (453)4 076 100 (394) 190 (748)

Second stage1 050 75 (295) 85 (335)2 065 100 (394) 145 (571)

specimens were made up with wc = 065 and the rest withwc = 050 These specimens were labeled as concrete madein the laboratory Table 3 summarizes the measurements ofthe NDT performed on the specimens that is ERT RFTUPV and RNT the DTs values are also included in the table1198911015840119888 and MOR It should be noted that all the test specimenswere performed under saturated conditions for structures insitu special equipment is needed for locating the presence ofthe reinforcing steel and performing the readings of NDT onplaces away from reinforcing steel to avoid possible errors dueto the presence of it [66 67]

WhenNDTs were completed some of the specimens wereselected and scheduled for destructive testing In the firststage of the investigation 5 cylinders type I 5 cylinders typeII and 2 beams from each differentmixture (see Table 2) weretested In the second stage only 3 cylinders type I 3 cylinderstype II and 2 beams were tested due to the assumption thatthese samples were made in laboratory conditions thereforeit can be assumed that there is less dispersion of the datafrom ldquolaboratoryrdquo with respect to the information from theldquofieldrdquoThe tests were performed at 3 7 14 21 and 28 daysThe1198911015840119888 and MOR values of hydraulic concrete were calculatedin accordance with ASTM [1 2] the tests were performed


Table 3 Nondestructive and destructive testing applied to thespecimens

Specimen wc NDTs DTratio ERT UPV RNT RFT 1198911015840119888 MOR

STAGE I

Type I

055 X X X X X057 X X X X X061 X X X X X076 X X X X X

Type II


Beam

055 X X X057 X X X061 X X X076 X X X

STAGE II

Type I 050 X X X X065 X X X X

Type II 050 X X X X065 X X X X

Beam 050 X X X X065 X X X X

Table 4 Materials used in concrete mixtures

Material Type

Cement CPC 30R RS NMX C 414-22010Type II ASTM C150

Sand VolcanicGravel VolcanicWater Potable water

by means of a universal testing machine with a capacity of1471 KN and 010 KN of approximation

41Materials Materials used are summarized in Table 4Theconcrete design was performed as ACI requirements [4]Thecement used was CPC 30R RS according to the Mexicanstandard NMX C 414-22010 [68] being equivalent to TypeII of ASTM C150 [69] The mixtures were designed for 1198911015840119888 =2452MPa and 1198911015840119888 = 1667MPa

5 Modeling the Compressive Strength (1198911015840119888)and Modulus of Rupture (MOR)

As mentioned above the contribution of this paper is topredict the 1198911015840119888 and MOR by proposing a linear equation(1) which combines data obtained through four different

NDTs ERT UPV RFT and RNT The following model wasproposed

119910 = 1198860+ 1198861ERT + 119886

2UPV + 119886

3RFT

+ 1198864RNT + 119886

5age + 119886

6wc

(1)

where 119886119894are the coefficients to be calculated and119910 is either the

compressive strength 1198911015840119888 or the modulus of rupture MOR inMPa

Even though it was decided to produce the model usinga linear equation it is the possibility that one or some ofthese NDTs were not correlated with the characteristic beingmodeled (in this case1198911015840119888 orMOR) If this were the case theirinclusion in the model would not be beneficial For examplelet us suppose that all the available variables are usedhowever one of these is not correlated with the characteristicbeing predicted In this case it would see that the accuracy ofthe model on the specimens used to identify the coefficientis the poorest Unfortunately given that one test is notcorrelated with response then the accuracy of this model ondifferent specimens is not as good as the performance of amodel that does not include this noncorrelated test that is amodel with poor generality can be calculated

In order to overcome this problem was decided to createall the linearmodels that can be built using the available inde-pendent variables Then our proposed model was identifiedby following the next procedure That is in order to identifythe final model a one-leave-out technique [70] is used in asubset of the total number of specimens This is performedas follows let 119899 be the number of specimens in this subsetused to identify the coefficients of a particular model then119899 minus 1 specimens are used to identify the coefficients of thatmodel using ordinary least squares and then this model isused to predict the characteristic of the missing specimenThis process is repeated for all the specimens at the end of thisprocess the predicted values are compared against the actualvalues and as consequence the generality of the modelis assessed This procedure is repeated for all the availablemodels and at the end the model selected is the one thatpresents the best generality

6 Results and Discussion

Comparative graphs of the mechanical properties measure-ments against nondestructive tests carried out were plottedthey were constructed with the point values of the readingsrecorded for each mixture at different ages (3 7 14 21and 28 days) Figure 1(a) shows the scatter plot of the ERTmeasurements versus the 1198911015840119888 values of cylinders types I andII for the concrete considered as made in situ This figure isrepresentative of the results obtained in this stage of researchIn these samples the ERT increases with the age in spiteof the fact that this is a general trend where a substantialdispersion of the plotted data is shown Figure 1(b) showsthe representative results of the cylinders types I and II ofthe second stage (concrete made in the laboratory) unlike theresults shown in Figure 1(a) there is a definite upward trendwhere the mechanical properties of concrete increase withage and therefore also increase the ERT The mixtures of the


5

10

15

20

25

30

Resistivity (Ohm-m)

Com

pres

sive s

treng

th (M

Pa)

20 30 40 50 60 70

05 065-3d05 065-7d05 065-21d05 065-28d057 076-3d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)

Resistivity (Ohm-m)20 30 40 50 60

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)

Figure 1 Compressive strength versus electrical resistivity of cylinder type I with wc ratio = (a) 055 057 061 and 076 (concrete made insitu) and (b) 050 and 065 (concrete made in laboratory) for ages of 3 days to 28 days

15

20

25

30

VPU (kms)

Com

pres

sive s

treng

th (M

Pa)

34 35 36 37 38 39 40 41

055 061-3d055 061-7d055 061-14d055 061-21d055 061-28d

057 076-3d057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)

VPU (kms)34 35 36 37 38 39

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)

Figure 2 Compressive strength versus ultrasonic pulse velocity of cylinder type I with wc ratio = (a) 055 057 061 and 076 (concrete madein situ) and (b) 050 and 065 (concrete made in laboratory) for ages of 3 days to 28 days

second stage with wc = 065 have a lower ERT than mixtureswithwc = 050 due to the content of interconnected saturatedpores through which the electric current flows this is beingreflected in the results shown

The behavior described by the ERT is very similar to theone observed for the UPV (Figure 2) The results obtainedwith the RFT showed no trend Figure 3 shows representative

results obtained on cylinders type I and II at both stages ofthe investigation this graph corresponds to cylinders type IIwith wc ratio = 050 and ages of 3 to 28 days any trend is notobserved in such a graph

On the other hand the graphs that correspond to thebeams of the first stage have a FRT in longitudinal modethat describes an upward trend with respect to the increase


Table 5 Comparison of models obtained to predict 1198911015840119888 and MOR

Samples Models Factorcorrel

Name

Cyl of 1st and 2nd stage 27 cylused for validation

1198911015840119888 = 1205790freq + 120579

1UPV + 120579

2(wc) + 120579

3resistiv 0895 119864

0


1198911015840119888 = 1205790+ 1205791UPV3 + 120579

2(wc)minus05 + 120579

3ln (age) + 120579

4resistiv + 120579

5freq + 120576 0889 119864

1

Beams of 1st and 2nd stage Mr = 1205790age + 120579

1freq long + 120579

2(wc) + 120579

3freq trans 0913 119864

2

5

10

15

20

25

30

Frequency (Hz)

Com

pres

sive s

treng

th (M

Pa)

1000 1200 1400 1600 1800 2000 2200

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

Figure 3 Compressive strength versus resonance frequency inlongitudinalmode obtained in cylinders type II withwc ratio = 050and 065 for ages of 3 days to 28 days (concrete made in laboratory)

of the age (see Figure 4(a)) as in the case of ERT versus1198911015840119888 (Figure 1(a)) and UPV versus 1198911015840119888 (Figure 2(a)) where asubstantial dispersion of the plotted data is shown that alsocan be attributed to not controlling the wc ratio as describedabove (simulating concrete made in situ)

The FRT and longitudinal and transverse mode observedon beams of the second stage showed an increase of both theMOR and the FRT values as the age of the samples increasedthe values for the longitudinal FRT of the beams with awc ratio = 050 are higher than the frequencies measuredon the beams with a wc ratio = 065 Figure 4(b) showsrepresentative results obtained in beams of the second stagethere is an upward trend over the time

The results obtained from 1198911015840119888 versus RNT in cylinderstype I are shown in Figure 5 it is possible to try to definea trend indicating a rebound increase associated with theage of the concrete however it can be observed a significantdispersion of data due to the fact that the wc ratio was notcontrolled to simulate concrete made in situ therefore thereare almost the same values of1198911015840119888 at ages of 14 21 and 28 days

In the common situation where an assessment of materialstrength is required it is unfortunate that the complexity ofcorrelation tends to be greatest for the test methods whichcause the least damage Although rebound hammer testcauses little damage is cheap and quick and is ideal forcomparative and uniformity assessments its correlation toabsolute strength prediction posesmany problems Core testsprovide the most reliable in situ strength assessment but alsocause the most damage and are slow and expensive Howeverone of the advantages of this paper is the combination ofseveral nondestructive tests to get models that provide betterpredictions

Using the data recorded from first stage samples by theNDT different models found in technical literature [9 11 53ndash62 71] were tested in order to compare other frameworksagainst themodels developed hereinThe coefficients of thesemodels are identified using ordinary least squares and thepredictions are computed using the Leave-one-out cross-validation (LOOCV) techniqueTheir respective correlationsfactorswere obtained using the information of the destructivetests (see Table 1) In order to facilitate the comparison in thistable our proposedmodels119864

119886and119864

119887were also included It is

important to note that these proposedmodels were generatedwith the information of the first stage since at this stage wehave the RNT The models proposed in Table 5 (models 119864

0

1198641 and 119864

2) were generated with the information of the two

stages but eliminating the RNT because there were cylinderswith RNT (first stage) and cylinders without RNT (secondstage)

The model 119864119886corresponds to a proposed model that

takes into consideration only the four NDTs it is a firstdegree equation with four variables and four constants witha correlation factor of 0636 The model 119864

119887was generated

taking the model 1198720[9] as a basis but the ERT and RFT

were added to the model it is a third degree equationwith six variables and seven constants with a correlationfactor of 0642 the variables considered for this model arethe NDT and the age and the wc ratio of the concreteAs can be observed correlation factors for models 119864

119886and

119864119887are very near to the values of the other frameworks

therefore these two models can be considered as accurateenough for the predictions of the mechanical properties ofconcrete

Table 5 summarizes our models for prediction of the 1198911015840119888and MOR the correlation factor values are indicated Themodel was constructed with NDT data from both stagesof the experimental study (90 cylinders randomly selected


30

35

40

45

50

55

60

Longitudinal frequency (Hz)

Mod

ulus

of r

uptu

re (M

Pa)

2500 2600 2700 2800 2900 3000

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

30

35

40

45

50

55

60

Mod

ulus

of r

uptu

re (M

Pa)

Longitudinal frequency (Hz)2500 2600 2700 2800

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)

Figure 4Modulus of rupture versus fundamental resonance frequency in longitudinal mode in beams with dimensions of 150mm times 150mmtimes 600mm with wc ratios = (a) 055 057 061 and 076 (concrete made in situ) and (b) 050 and 065 (concrete made in laboratory) for agesof 7 day to 28 days

15

20

25

30

Hammer rebound

Com

pres

sive s

treng

th (M

Pa)

16 18 20 22 24 26

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d

Figure 5 Compressive strength versus hammer rebound obtainedin cylinders type I with wc ratio = 057 and 076 for ages of 7 day to28 days (concrete made in situ)

of the total of 117) due to the fact that the RNT wasnot performed on the second stage it was necessary toremove such information in order to generate the modelsFigures 6(a) and 6(b) present the correlation coefficient ofthese models in the training phase In order to measure the

generality of the models selected a validation was conductedwith information of NDT and DTs performed in the 27remaining cylinders The best models are summarized inTable 5

Leave-one-out cross-validation (LOOCV) implies isola-tion of the data for each iteration in such a manner thata single sample for the test data and the rest forming thetraining data are obtained The evaluation is given by theerror in this type of cross-validation error is very low but incontrast it is computationally very time consuming becausethemethod has tomake a large number of iterations as manyas n samples and for each test data (test data and training data)[72]

From the cross-validation analysis 64 models wereobtained as a result of all possible combinations of the vari-ables considered 32 of type 119864

119886and 32 of type 119864

119887 the two best

to predict the 1198911015840119888 of the hydraulic concrete (1198640and 119864

1) are

shown in Table 5 The model 1198640is that in which the variables

(NDTdata) aremultiplied by constants the correlation factoris 0886 which is greater than the correlation factor obtainedby the model 119864

1 with a correlation factor of 0858 In case

of the beams models were generated to predict the MOR inthis case all the samples were used to generate and validatethe models due to the small number of specimens 32 mod-els were generated obtaining their correlation coefficients(see Figure 6(c)) The best model is 119864

2with a correlation

factor of 0913 as shown in Table 5 The predictions of the1198911015840119888 obtained with the models 119864

0and 119864

1are shown in

Figures 7(a) and 7(b) the MOR predictions are shown inFigure 7(c)


0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100

Models of type Ea

Correlation factor versus generated models

(a)

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

orN model

3020100

Models of type Eb


(b)

Models of beams

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100


(c)

Figure 6 Correlation factor of the generated models (a) of the type 119864119886and (b) of the type 119864

119887with combined cylinders and (c) on beams

Figure 8 presents the boxplot of the errors produced bythe different models presented on this contribution thatis 1198640 1198641 and 119864

119887 This figure is complemented with the

boxplot of the error presented by model 1198720(see Figure 9)

Comparing the boxplot on Figures 8(a) 8(b) and 9mdashwhichcorrespond to models of 1198911015840119888mdashit is observed that theseboxplots are very similar indicating that these models areequivalent with respect to their error Model 119864

1has a higher

variability indicated by the lines extending from the boxhowever seeing the size of the box one can consider themsimilar

61 Validation of the Models Using Test of HypothesesAccording toWalpole et al [73] ldquoA statistical hypothesis is anassertion or conjecture concerning one ormore populationsrdquo


0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)

Readings taken (MPa)

27 remaining cylinders

30 4020100


(a)

0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)

30 4020100




(b)

Pred

icte

d re

adin

gs (M

Pa)

2

25

3

35

4

45

5

55

6

65

7

2

Predictions with all beams

4 6



(c)

Figure 7 Predictions obtained with the models (a) 1198640and (b) 119864

1for cylinders and (c) with the model 119864

2for beams

in our case this assertion or conjecture is relative to definingwhether or not the information predicted by the differentcalculated models is equivalent to the real values estimatedby destructive testing

In order to determine the validity of the predictionmodels we assumed a paired observations test of hypothesescomputation of the confidence interval for mean1minusmean2 in

the situationwith paired observations is based on the randomvariable presented in (2) [73]

119905 =119889 minus 1198890

119904119889radic119899 (2)

where 119889 and 119904119889

are random variables representing thesample mean and standard deviation of the differences of


10

0

5

minus5

minus10

Tolerance bounds for the model E0

+

1

(a)


1

10

0

5

minus5

minus10

(b)


1

0

05

minus05

(c)

Figure 8 Tolerance bounds for best models proposed 1198640 1198641 and 119864

2

the observations between paired observations 1198890is the

expected differences between means of the two samplesand 119899 is the number of pairs Critical regions are con-structed using the t-distribution with 119899 minus 1 degrees offreedom

The null hypothesis for this model is that the means ofboth samples are equal therefore 119889

0becomes zero (alterna-

tive hypothesis is the means are different) For a confidenceinterval of 95 the critical values from t-distribution areminus2056 lt t gt 2056 and for a confidence interval of 99critical values are minus2779 lt t gt 2779 Table 6 shows thecomputed test statistic (t) for each model

It can be observed from data in Table 6 that the teststatistic lies between critical values for both confidence

intervals therefore the null hypothesis cannot be rejectedand it can be assumed that the mean of the predictedvalues when compared with real data is equivalent there-fore the models are reliable for these two confidenceintervals

7 Conclusions

The measurements of the UPV showed the most uniformdata when compared against other NDTs the samples of thesecond stage indicate velocities of pulse in different rangesfor samples of wc ratio = 050 the velocity is within a rangefrom 36 to 39 kms while for samples of wc ratio = 065 thevelocity is within the range of 33 to 36 kms


Table 6 Computed test statistic (119905) for each of the prediction models

Model 119899 Test statistic (119905) Critical values for different confidence intervals Statistical conclusion95 99

1198640

27 0293minus2056 lt 119905 gt 2056 minus2779 lt 119905 gt 2779 The null hypothesis cannot be rejected119864

127 0229

1198642

35 minus0022

10

0

5

minus5

minus101

Tolerance bounds for the model M0

++

Figure 9 Tolerance bounds of the1198720model model proposed by

other authors

The resonant frequency is the NDT more affected by themorphology or geometry of the analyzed samples Thereforethe resonance frequency should be used only if prismaticsamples that comply with the dimensions indicated in theliterature are tested [31] Otherwise it will be difficult to obtainaccurate frequency values furthermore this test cannot beapplied in the field

The rebound method should be used to determine thehomogeneity of the concrete but not its 1198911015840119888 unless a corre-lation between the rebound number and 1198911015840119888 has been made

The prediction models obtained are 1198640and 119864

1with a

correlation factor of 0895 and 0889 respectively to predictthe 1198911015840119888 and the model 119864

2with a correlation factor of 0913 to

predict the MORThese models are linear and provide betterresults than models formed by higher degree polynomialsand also provide improved estimations than previous modelsproposed in the literature

Nondestructive tests have a fairly wide scope both inengineering and in other areas of knowledge therefore it isrecommended to continue with investigations using nonde-structive techniques for better documentation and reliabilitythereof

With the proposed models it is possible to take readingsof nondestructive testing and predicting 1198911015840119888 or MOR of thestructure in the field and samples are not necessary for thatpurpose

Abbreviations

Resistive Electrical resistivityFreq Resonant frequenciesRebound Rebound numberfreq long Resonance frequency in the longitudinal modefreq trans Resonance frequency in the transverse modeMOR Modulus of rupture1198911015840119888 Compressive strengthLOOCV Leave-one-out cross-validation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] ASTMC39 C39Mndash03 ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo in Annual Book ofASTM Standards ASTM West Conshohocken Pa USA 2003

[2] ASTM C 78-10 ldquoStandard test method for flexural strengthof concrete (using simple beam with third-point loading)rdquoin Annual Book of ASTM Standards vol 0402 ASTM WestConshohocken Pa USA 2002

[3] C Kohl M Krause C Maierhofer and JWostmann ldquo2D- And3D-visualisation of NDT-data using data fusion techniquerdquoMaterials and StructuresMateriaux et Constructions vol 38 no283 pp 817ndash826 2005

[4] ACI 318 Requisitos de Reglamento para Concreto Estructural(ACI 318S-05) y Comentario (ACI 318SR-05) American Con-crete Institute 2005

[5] ASTM C 469-02 ldquoStandard test method for static modulusof elasticity and poissonrsquos ratio of concrete in compressionrdquoin Annual Book of ASTM Standards vol 0402 ASTM WestConshohocken Pa USA 2002

[6] L Kwang-Myong K Dong-Soo and K Jee-Sang ldquoDetermina-tion of dynamic Youngrsquos modulus of concrete at early ages byimpact resonance testrdquo Journal of Civil Engineering vol 1 no 1pp 11ndash18 1997

[7] R Beutel H-W Reinhardt C U Grosse et al ldquoQuantitativerVerfahrensvergleichrdquo in Bergmeister pp 567ndash573 Ernst ampSohn 2007

[8] American Concrete Institute and S P Pessiki American Con-crete Institute Farmington Hills Mich USA 2003

[9] Q Huang P Gardoni and S Hurlebaus ldquoPredicting con-crete compressive strength using ultrasonic pulse velocity andrebound numberrdquo ACI Materials Journal vol 108 no 4 pp403ndash412 2011


[10] IAEA Guidebook on Non-Destructive Testing of Concrete Struc-tures International Atomic Energy Agency Vienna Austria2002

[11] A Samarin and P Meynink ldquoUse of combined ultrasonic andrebound hammer method for determining strength of concretestructural membersrdquo Concrete International vol 3 no 3 pp25ndash29 1981

[12] R Miretti M F Carrasco R O Grether and C R PasserinoldquoCombined non-destructivemethods applied to normal-weightand lightweight-concreterdquo Insight vol 46 no 12 pp 748ndash7532004

[13] J Hoła and K Schabowicz ldquoNew technique of nondestructiveassessment of concrete strength using artificial intelligencerdquoNDT amp E International vol 38 no 4 pp 251ndash259 2005

[14] M A Ploix V Garnier D Breysse and J Moysan ldquoNDT datafusion for evaluating concrete structuresrdquo in Proceedings of the37th Annual Review of Progress in Quantitative NondestructiveEvaluation (QNDE rsquo10) pp 1307ndash1314 San Diego Calif USAJuly 2011

[15] V Kaftandjian Y M Zhu O Dupuis and D Babot ldquoThe com-bined use of the evidence theory and fuzzy logic for improvingmultimodal nondestructive testing systemsrdquo IEEE Transactionson Instrumentation and Measurement vol 54 no 5 pp 1968ndash1977 2005

[16] C Maierhofer G Zacher C Kohl and J Wostmann ldquoEvalu-ation of radar and complementary echo methods for NDT ofconcrete elementsrdquo Journal of Nondestructive Evaluation vol 27no 1ndash3 pp 47ndash57 2008

[17] A A Shah and Y Ribakov ldquoNon-destructive measurements ofcrack assessment and defect detection in concrete structuresrdquoMaterials and Design vol 29 no 1 pp 61ndash69 2008

[18] Z Liu D S Forsyth J P Komorowski K Hanasaki andT Kirubarajan ldquoSurvey state of the art in NDE data fusiontechniquesrdquo IEEE Transactions on Instrumentation and Mea-surement vol 56 no 6 pp 2435ndash2451 2007

[19] A P Aizebeokhai ldquo2D and 3D geoelectrical resistivity imagingtheory and field designrdquo Scientific Research and Essays vol 5no 23 pp 3592ndash3605 2010

[20] S H Ward ldquoElectrical electromagnetic and magnetotelluricmethods geophysicsrdquo Geophysics vol 45 pp 1659ndash1666 1980

[21] T Acosta Andres Antonio M Molina Wilfrido L GonzalezMarıa Guadalupe and P Gallardo Alejandro ldquoCactus basedadmixture as corrosion inhibitor for steel rebars of reinforcedconcreterdquo Tech Rep 328 2010

[22] F Chen J-G Xiu J-Z An C-T Liao and D-Y Chen ldquoDetect-ing rupture precursors and determining the main fracturespread direction of rock with dynamic rock resistivity changeanisotropyrdquoActa Seismologica Sinica English Edition vol 13 no2 pp 234ndash237 2000

[23] S Y Liu Y J Du L H Han and M F Gu ldquoExperimentalstudy on the electrical resistivity of soil-cement admixturesrdquoEnvironmental Geology vol 54 no 6 pp 1227ndash1233 2008

[24] J Cao and D D L Chung ldquoDefect dynamics of cementmortar under repeated loading studied by electrical resistivitymeasurementrdquoCement and Concrete Research vol 32 no 3 pp379ndash385 2002

[25] J F Lataste C Sirieix D Breysse and M Frappa ldquoElectricalresistivitymeasurement applied to cracking assessment on rein-forced concrete structures in civil engineeringrdquoNonDestructiveTesting andEngineering International vol 36 no 6 pp 383ndash3942003

[26] O Sengul ldquoFactors affecting the electrical resistivity of con-creterdquo inNondestructive Testing of Materials and Structures vol6 of RILEM Bookseries pp 263ndash269 Springer 2013

[27] J W Lencioni and M D de Lima ldquoA study of the parametersthat affect the measurements of superficial electrical resistivityof concreterdquo Nondestructive Testing of Materials and Structuresvol 6 pp 271ndash276 2013

[28] V M Malhotra and N J Carino Handbook on NondestructiveTesting of Concrete CRC Press Boca Raton Fla USA 2004

[29] R Jones and I Facaoaru ldquoRecommendations for testing con-crete by the ultrasonic pulse methodrdquo Materiaux et Construc-tions vol 2 no 4 pp 275ndash284 1969

[30] ACI Committee 228 ldquoIn-place methods for determination ofstrength of concreterdquo Manual of Concrete Practice AC12281RAmerican Concrete Institute Detroit Mich USA 1989

[31] R Jones Non-Destructive Testing of Concrete Cambridge Uni-versity Press London UK 1962

[32] T T Wu and T F Lin ldquoThe stress effect on the ultrasonicvelocity variations of concrete under repeated loadingrdquo ACIMaterials Journal vol 95 no 5 pp 519ndash524 1998

[33] S F Selleck E N Landis M L Peterson S P Shah andJ D Achenbach ldquoUltrasonic investigation of concrete withdistributed damagerdquo ACI Materials Journal vol 95 no 1 pp27ndash36 1998

[34] ACICommittee 228Nondestructive TestMethods for Evaluationof Concrete in Structures 1998

[35] J L Rose Ultrasonic Waves in Solid Media 1999[36] V R Sturrup F J Vecchio and H Caratin Pulse Velocity as a

Measure of Concrete Compressive Strengths 1984[37] D A Anderson and R K Seals ldquoPulse velocity as a predictor

of 28 and 90 days strengthrdquo Journal of the American ConcreteInstitute vol 78 no 2 pp 116ndash119 1981

[38] M F Kaplan ldquoCompressive strength and ultrasonic pulsevelocity relationships for concrete in columnsrdquoACI Journal vol29 no 54-37 p 675 1958

[39] M F Kaplan ldquoThe effects of age and water to cement ratio uponthe relation between ultrasonic pulse velocity and compressivestrength of concreterdquoMagazine of Concrete Research vol 11 no32 pp 85ndash92 1959

[40] H Irie Y Yoshida Y Sakurada and T Ito ldquoNon-destructive-testingmethods for concrete structuresrdquoNTTTechnical Reviewvol 6 no 5 pp 1ndash8 2008

[41] F B Hornibrook ldquoApplication of sonic method to freezing andthawing studies of concreterdquo ASTM Bulletin no 101 p 5 1939

[42] W T Thomson ldquoMeasuring changes in physical properties ofconcrete by the dynamicmethodrdquo Proceedings of ASTM vol 40p 1113 1940

[43] L Obert and W I Duvall ldquoDiscussion of dynamic methods oftesting concrete with suggestions for standardizationrdquo ASTMProceedings vol 41 p 1053 1941

[44] ASTM C 215-02 ldquoStandard test method for fundamentaltransverse longitudinal and torsional resonant frequencies ofconcrete specimensrdquo in Annual Book of ASTM Standards vol0402 ASTM West Conshohocken Pa USA 2003

[45] V M Malhotra Testing of Hardened Concrete NondestructiveMethods ACI Monograph no 9 American Concrete InstituteDetroit Mich USA 1976

[46] N Swamy and G Rigby ldquoDynamic properties of hardenedpaste mortar and concreterdquoMateriaux et Constructions vol 4no 1 pp 13ndash40 1971


[47] K H Hsieh M W Halling and P J Barr ldquoOverview ofvibrational structural health monitoring with representativecase studiesrdquo Journal of Bridge Engineering vol 11 no 6 pp707ndash715 2006

[48] A Bagchi J Humar H Xu and A S Noman ldquoModel-baseddamage identification in a continuous bridge using vibrationdatardquo Journal of Performance of Constructed Facilities vol 24no 2 pp 148ndash158 2010

[49] CSN EN 12504-2 ldquoTesting concrete in structuresmdashpart 2 non-destructive testingmdashdetermination of rebound numberrdquo CzechStandards Institute Prague Czech Republic 2002

[50] ldquoTesting of concrete by hardness testing methodrdquo Tech RepCSN731373 Czech Standards Institute Prague CzechRepublic1983

[51] ASTM C 805C805M-08 Standard Test Method for ReboundNumber of Hardened Concrete ASTM International WestConshohocken Pa USA 2008

[52] JGJT 23-2001mdashJ 155-2001 Technical Specification for Inspectionof Concrete Compressive Strength by Rebound Method 2001(Chinese)

[53] K Ramyar and P Kol ldquoDestructive and non-destructive testmethods for estimating the strength of concreterdquo Cement andConcrete World vol 2 pp 46ndash54 1996

[54] U Bellander Testing Methods for Estimating CompressiveStrength in Finished StructuresmdashEvaluation of Accuracy andTesting System 1979

[55] B Hobbs and M T Kebir ldquoNon-destructive testing techniquesfor the forensic engineering investigation of reinforced concretebuildingsrdquo Forensic Science International vol 167 no 2-3 pp167ndash172 2007

[56] J G Wiebenga A Comparison between Various CombinedNon-Destructive Testing Methods to Derive the CompressiveStrength of Concrete Instituut TNO voor Bouwmaterialen enBouwconstructies 1968

[57] E Arioglu O Odbay H Alper and B Arioglu ldquoA new formulaand application results for prediction of concrete compressivestrength by combined non-destructive methodrdquo Concrete Pre-fabrication vol 28 pp 5ndash11 1994

[58] R Sriravindrajah YH Loo andC T Tam ldquoStrength evaluationof recycled-aggregate concrete by in-situ testsrdquo Materials andStructures vol 21 no 4 pp 289ndash295 1988

[59] E Arioglu and O Koyluoglu ldquoPrediction of concrete strengthby destructive and nondestructive methodsrdquo Cement and Con-crete World vol 3 pp 33ndash34 1996

[60] G F Kheder ldquoTwo stage procedure for assessment of in situconcrete strength using combined non-destructive testingrdquoMaterials and Structures vol 32 no 220 pp 410ndash417 1999

[61] E Arioglu and O Manzak Application of ldquoSonRebrdquo Method toConcrete Samples Produced in Yedpa Construction Site 1991

[62] B Postacioglu ldquoNew significations of the reboundhammer testsand the ultrasonic pulse velocityrdquoMaterials and Structures vol18 no 6 pp 447ndash451 1985

[63] J-K Kim C-Y Kim S-T Yi and Y Lee ldquoEffect of carbonationon the rebound number and compressive strength of concreterdquoCement and Concrete Composites vol 31 no 2 pp 139ndash1442009

[64] K L Rens T J Wipf and F W Klaiber ldquoReview of nonde-structive evaluation techniques of civil infrastructurerdquo Journalof Performance of Constructed Facilities vol 11 no 4 pp 152ndash160 1997

[65] ASTM C 143C 143M-03 ldquoStandard test method for slump ofhydraulic-cement concreterdquo in Annual Book of ASTM Stan-dards vol 0402 ASTM West Conshohocken Pa USA 2003

[66] S C Millard J A Harrison and A J Edwards ldquoMeasurementsof electrical resistivity of reinforced concrete structures for theassesment of corrosion riskrdquo British Journal of NDT vol 31 pp617ndash621 1989

[67] R Durar Manual de Inspeccion Evaluacion y Diagnosticode Corrosion en Estructuras de Hormigon Armado CYTEDPrograma Iberoamericano de Ciencia y Tecnologıa para elDesarrollo 1998

[68] Mexican-Standard-NMX-C-414-ONNCCE-2004 Building In-dustry Hydraulic Cement Specifications andTestMethods 2004

[69] ASTMC 150-04 ldquoStandard Specification for Portland Cementrdquoin Annual Book of ASTM Standards ASTM West Consho-hocken Pa USA 2004

[70] E Alpaydin Introduction to Machine Learning 2009[71] Y Tanigawa K Baba and H Mori ldquoEstimation of concrete

strength by combined non-destructive testing methodrdquoSeptember 1984

[72] C Elkan Evaluating Classifiers 2012[73] R EWalpole R H Myers S L Myers and K Ye Probability amp

Statistics for Engineers amp Scientists edited by D Lynch PrenticeHall Boston Mass USA 9th edition 2012

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


to determine the elasticmodulus these samples are deformedand destroyed in order to determine the compressive strengthand the static modulus of elasticity [5] As it can be seenthis procedure modifies the samples and consequently it isimpossible to repeat the test in the same sample in case itwould be necessary [6]

On the other hand it is not easy to determine themechanical characteristics of the materials using only NDTprocedures This problem is more evident since the mod-els are obtained with laboratory settings and under strictcontrolled conditions As a consequence it is necessary toevaluate the applicability of these models in uncontrolledenvironments and using different conditions from those usedin the formulation of an empirical mechanistic model [7]

One particular characteristic ofmost of theseNDTs is thatthey can be conducted at the work place and can be used todetermine certain properties of already built structures thisprocess is known as in-place testing [8]

In accordance with ACI 228-1R-03 the objective of in-place testing is to estimate the compressive strength ofconcrete by the use of NDTs In order to validate the resultsit is necessary to have a known relationship between theseresults and the mechanical resistance obtained by DTs Thisrelationship is usually established by performing DTs ofdrilled cores taken from adjacent locationswhere the in-placetest is conducted The accuracy of the estimated compressivestrength depends on the correlation between the strengthof the concrete and the quantity measured by the in-placetest As a general index of concrete strength the compressivestrength of concrete 1198911015840119888 is important in the performanceassessment of existing reinforced concrete structures [9]On the other hand the MOR is very useful especially inrelation to road slab design and airfield runways becausethe flexure tension is a critical factor to determine concretersquosperformance in such applications [10]

When NDT first appeared for concrete application it wascommon to model the prediction of the concrete strengthusing only one of the above tests However as found bymany researchers the combination of different NDTs canlead to more accurate and reliable models [9 11ndash13] Inorder to approximate the appropriate estimates of indicators(response variables) for example Ploix et al [14] performeda combination or fusion of NDT data as radar test electricalresistivity and capacity infrared thermography impact echoand ultrasound to predict the simultaneous estimation of thewater saturation and porosity rate in concrete for undamagedconcretes measured in laboratory conditionsTheymeasureddifferent NDT parameters such as frequencies velocitiesand attenuations and after that they conducted an sta-tistical analysis with the purpose of identifying empiricalcorrelations linking each experimental parameter to bothsearched indicators There were identified correlations withbilinear regressions as a first approximation but sincesome different NDT measurements are very sensitive tomaterial heterogeneity variability and experimental noiserelative disagreement or conflict between sources of infor-mation happened (ie measurements) thus the predictionmodels rapidly became ill-conditioned Therefore it wasdecided to combine several NDT techniques (at least three)

providing more suitable information Kaftandjian et al [15]used a data fusion approach to improve weld inspectionby NDT combining the use of evidence theory and fuzzylogic in their framework X-ray and ultrasonic inspectionwere modeled in order to generate 3D images from bothNDTs for evaluating defect detection and defect sizing ofwelded joints for industrial purposes showing that the fusionof data significantly enhances the reliability of the defectrecognition Maierhofer et al [16] used radar ultrasonicimpact echo and thermography data fusion for predictingdeterioration of concrete vehicular bridges noting that thedata fusion technique increases reliability and improved theaccuracy of the quantitative results exploiting the differentand sometimes complementary physical effects provided fordifferent NDTs Shah and Ribakov [17] described a testingprocedure based on the dynamic response of the cracked orflawed concrete structures subjected to impact loading andonanalyzing the ability of the resistivity measurement to detectand to locate cracks and spalling with in situ measurementson a damaged concrete slab Huang et al [9] developed aSonReb (the combination of rebound hammer and ultrasonicpulse velocity tests) for compressive strength prediction ofconcrete samples using a probabilistic multivariate regres-sion model taking into account the data of the proportionsof the concrete mix (curing conditions and the age of theconcrete) assessing the model from Bayesian updating ruleLui et al [18] provide a very wide state-of-the-art reportregarding NDT data fusion techniques They established theuse of multiple NDT methods to increase the reliability andreduce the uncertainty of testing and evaluationNonethelessthere are cases in which the use of all available tests createsa model that only works in the samples used to empiricallycorrelate the obtained data and thus the model does notgeneralize In order to deal with this problem it is necessaryfor an automatic method of variable selection (here variablesare the NDT) to establish a simple model that achievesthe predictionexplanation of the response variable togetherwith an efficient estimation of the coefficients

Given that there are only 6 different variables to createthe model in this contribution a decision was made to testall the linear combinations of these variables that is create64 models The model proposed was selected from these 64models by using a cross-validation technique Furthermoreto illustrate the generality of the model few samples wereremoved from the model formulation and selection processand the results presented on this contribution are computedusing the removed samples to validate the predicted modelClearly there are situationswhere it is not possible to compareall possible models To provide a complete picture of thisscenario it was decided to use a cross-validation techniqueto select the best from the different 64 models

In addition to this in order to compare the proposedmodel against the ones described in the literature a compar-ison was made with more than ten different models againstthe ones proposed hereThe results show that the model pro-posed here is competitive with the ones proposed in previousinvestigations In addition the independent variables usedin this investigation were used also with the other modelsfound in the literatureWith this extended set of independent




























0+ 12057911198731198772 + 120579

2UPV + 120579

3119908119888minus05 + 120579

4ln (age) + 120576 0638

1198720119886[9] 1198911015840119888 = 120579

0+ 12057911198731198772 + 120579

2UPV3 + 120576 0614

1198721[53 71] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV 0621

1198722[54] 1198911015840119888 = 120579

0+ 12057911198773 + 120579

2UPV 0616

1198723[11] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV4 0612

1198724[55] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV + 120579

3UPV2 0596

1198725[56 58 61] ln1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV 0613

1198726[59 60] ln1198911015840119888 = 120579

0+ 1205791ln119877 + 120579

2lnUPV 0617

1198727[57] ln1198911015840119888 = 120579


1198728[62] 1198911015840119888

minus05

= 1205790+ 1205791119877minus1 + 120579


119864119886

1198911015840119888 = 1205790freq + 120579

1rebound + 120579

2resistiv + 120579

3UPV 0636

119864119887

1198911015840119888 = 1205790+ 12057911198731198772 + 120579

2UPV + 120579

3(wc)minus05 + 120579

4ln (age) + 120579

5resistiv + 120579

6freq + 120576 0642




4 Experimental





First stage1 055 75 (295) 100 (394)2 061 100 (394) 135 (531)3 057 75 (295) 115 (453)4 076 100 (394) 190 (748)

Second stage1 050 75 (295) 85 (335)2 065 100 (394) 145 (571)






STAGE I

Type I


Type II


Beam

055 X X X057 X X X061 X X X076 X X X

STAGE II





Material Type








119910 = 1198860+ 1198861ERT + 119886

2UPV + 119886

3RFT

+ 1198864RNT + 119886

5age + 119886

6wc

(1)








5

10

15

20

25

30

Resistivity (Ohm-m)

Com

pres

sive s

treng

th (M

Pa)

20 30 40 50 60 70

05 065-3d05 065-7d05 065-21d05 065-28d057 076-3d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

VPU (kms)

Com

pres

sive s

treng

th (M

Pa)

34 35 36 37 38 39 40 41

055 061-3d055 061-7d055 061-14d055 061-21d055 061-28d

057 076-3d057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)

VPU (kms)34 35 36 37 38 39

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)









Name


1198911015840119888 = 1205790freq + 120579

1UPV + 120579

2(wc) + 120579

3resistiv 0895 119864

0


1198911015840119888 = 1205790+ 1205791UPV3 + 120579

2(wc)minus05 + 120579

3ln (age) + 120579

4resistiv + 120579

5freq + 120576 0889 119864

1


1freq long + 120579

2(wc) + 120579

3freq trans 0913 119864

2

5

10

15

20

25

30

Frequency (Hz)

Com

pres

sive s

treng

th (M

Pa)

1000 1200 1400 1600 1800 2000 2200

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d







119886and119864



0

1198641 and 119864





119887was generated



119886and





30

35

40

45

50

55

60


Mod

ulus

of r

uptu

re (M

Pa)

2500 2600 2700 2800 2900 3000

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

30

35

40

45

50

55

60

Mod

ulus

of r

uptu

re (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

Hammer rebound

Com

pres

sive s

treng

th (M

Pa)

16 18 20 22 24 26

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d






119886and 32 of type 119864

119887 the two best


1) are





2with a correlation


0and 119864

1are shown in



0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100

Models of type Ea


(a)

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

orN model

3020100

Models of type Eb


(b)

Models of beams

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100


(c)







1has a higher




0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)



30 4020100


(a)

0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)

30 4020100




(b)

Pred

icte

d re

adin

gs (M

Pa)

2

25

3

35

4

45

5

55

6

65

7

2


4 6



(c)



2for beams




119905 =119889 minus 1198890

119904119889radic119899 (2)

where 119889 and 119904119889



10

0

5

minus5

minus10


+

1

(a)


1

10

0

5

minus5

minus10

(b)


1

0

05

minus05

(c)


2








7 Conclusions





1198640


127 0229

1198642

35 minus0022

10

0

5

minus5

minus101


++


other authors




1with a






Abbreviations




References



















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






























0+ 12057911198731198772 + 120579

2UPV + 120579

3119908119888minus05 + 120579

4ln (age) + 120576 0638

1198720119886[9] 1198911015840119888 = 120579

0+ 12057911198731198772 + 120579

2UPV3 + 120576 0614

1198721[53 71] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV 0621

1198722[54] 1198911015840119888 = 120579

0+ 12057911198773 + 120579

2UPV 0616

1198723[11] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV4 0612

1198724[55] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV + 120579

3UPV2 0596

1198725[56 58 61] ln1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV 0613

1198726[59 60] ln1198911015840119888 = 120579

0+ 1205791ln119877 + 120579

2lnUPV 0617

1198727[57] ln1198911015840119888 = 120579


1198728[62] 1198911015840119888

minus05

= 1205790+ 1205791119877minus1 + 120579


119864119886

1198911015840119888 = 1205790freq + 120579

1rebound + 120579

2resistiv + 120579

3UPV 0636

119864119887

1198911015840119888 = 1205790+ 12057911198731198772 + 120579

2UPV + 120579

3(wc)minus05 + 120579

4ln (age) + 120579

5resistiv + 120579

6freq + 120576 0642




4 Experimental





First stage1 055 75 (295) 100 (394)2 061 100 (394) 135 (531)3 057 75 (295) 115 (453)4 076 100 (394) 190 (748)

Second stage1 050 75 (295) 85 (335)2 065 100 (394) 145 (571)






STAGE I

Type I


Type II


Beam

055 X X X057 X X X061 X X X076 X X X

STAGE II





Material Type








119910 = 1198860+ 1198861ERT + 119886

2UPV + 119886

3RFT

+ 1198864RNT + 119886

5age + 119886

6wc

(1)








5

10

15

20

25

30

Resistivity (Ohm-m)

Com

pres

sive s

treng

th (M

Pa)

20 30 40 50 60 70

05 065-3d05 065-7d05 065-21d05 065-28d057 076-3d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

VPU (kms)

Com

pres

sive s

treng

th (M

Pa)

34 35 36 37 38 39 40 41

055 061-3d055 061-7d055 061-14d055 061-21d055 061-28d

057 076-3d057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)

VPU (kms)34 35 36 37 38 39

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)









Name


1198911015840119888 = 1205790freq + 120579

1UPV + 120579

2(wc) + 120579

3resistiv 0895 119864

0


1198911015840119888 = 1205790+ 1205791UPV3 + 120579

2(wc)minus05 + 120579

3ln (age) + 120579

4resistiv + 120579

5freq + 120576 0889 119864

1


1freq long + 120579

2(wc) + 120579

3freq trans 0913 119864

2

5

10

15

20

25

30

Frequency (Hz)

Com

pres

sive s

treng

th (M

Pa)

1000 1200 1400 1600 1800 2000 2200

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d







119886and119864



0

1198641 and 119864





119887was generated



119886and





30

35

40

45

50

55

60


Mod

ulus

of r

uptu

re (M

Pa)

2500 2600 2700 2800 2900 3000

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

30

35

40

45

50

55

60

Mod

ulus

of r

uptu

re (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

Hammer rebound

Com

pres

sive s

treng

th (M

Pa)

16 18 20 22 24 26

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d






119886and 32 of type 119864

119887 the two best


1) are





2with a correlation


0and 119864

1are shown in



0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100

Models of type Ea


(a)

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

orN model

3020100

Models of type Eb


(b)

Models of beams

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100


(c)







1has a higher




0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)



30 4020100


(a)

0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)

30 4020100




(b)

Pred

icte

d re

adin

gs (M

Pa)

2

25

3

35

4

45

5

55

6

65

7

2


4 6



(c)



2for beams




119905 =119889 minus 1198890

119904119889radic119899 (2)

where 119889 and 119904119889



10

0

5

minus5

minus10


+

1

(a)


1

10

0

5

minus5

minus10

(b)


1

0

05

minus05

(c)


2








7 Conclusions





1198640


127 0229

1198642

35 minus0022

10

0

5

minus5

minus101


++


other authors




1with a






Abbreviations




References



















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




















0+ 12057911198731198772 + 120579

2UPV + 120579

3119908119888minus05 + 120579

4ln (age) + 120576 0638

1198720119886[9] 1198911015840119888 = 120579

0+ 12057911198731198772 + 120579

2UPV3 + 120576 0614

1198721[53 71] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV 0621

1198722[54] 1198911015840119888 = 120579

0+ 12057911198773 + 120579

2UPV 0616

1198723[11] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV4 0612

1198724[55] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV + 120579

3UPV2 0596

1198725[56 58 61] ln1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV 0613

1198726[59 60] ln1198911015840119888 = 120579

0+ 1205791ln119877 + 120579

2lnUPV 0617

1198727[57] ln1198911015840119888 = 120579


1198728[62] 1198911015840119888

minus05

= 1205790+ 1205791119877minus1 + 120579


119864119886

1198911015840119888 = 1205790freq + 120579

1rebound + 120579

2resistiv + 120579

3UPV 0636

119864119887

1198911015840119888 = 1205790+ 12057911198731198772 + 120579

2UPV + 120579

3(wc)minus05 + 120579

4ln (age) + 120579

5resistiv + 120579

6freq + 120576 0642




4 Experimental





First stage1 055 75 (295) 100 (394)2 061 100 (394) 135 (531)3 057 75 (295) 115 (453)4 076 100 (394) 190 (748)

Second stage1 050 75 (295) 85 (335)2 065 100 (394) 145 (571)






STAGE I

Type I


Type II


Beam

055 X X X057 X X X061 X X X076 X X X

STAGE II





Material Type








119910 = 1198860+ 1198861ERT + 119886

2UPV + 119886

3RFT

+ 1198864RNT + 119886

5age + 119886

6wc

(1)








5

10

15

20

25

30

Resistivity (Ohm-m)

Com

pres

sive s

treng

th (M

Pa)

20 30 40 50 60 70

05 065-3d05 065-7d05 065-21d05 065-28d057 076-3d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

VPU (kms)

Com

pres

sive s

treng

th (M

Pa)

34 35 36 37 38 39 40 41

055 061-3d055 061-7d055 061-14d055 061-21d055 061-28d

057 076-3d057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)

VPU (kms)34 35 36 37 38 39

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)









Name


1198911015840119888 = 1205790freq + 120579

1UPV + 120579

2(wc) + 120579

3resistiv 0895 119864

0


1198911015840119888 = 1205790+ 1205791UPV3 + 120579

2(wc)minus05 + 120579

3ln (age) + 120579

4resistiv + 120579

5freq + 120576 0889 119864

1


1freq long + 120579

2(wc) + 120579

3freq trans 0913 119864

2

5

10

15

20

25

30

Frequency (Hz)

Com

pres

sive s

treng

th (M

Pa)

1000 1200 1400 1600 1800 2000 2200

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d







119886and119864



0

1198641 and 119864





119887was generated



119886and





30

35

40

45

50

55

60


Mod

ulus

of r

uptu

re (M

Pa)

2500 2600 2700 2800 2900 3000

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

30

35

40

45

50

55

60

Mod

ulus

of r

uptu

re (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

Hammer rebound

Com

pres

sive s

treng

th (M

Pa)

16 18 20 22 24 26

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d






119886and 32 of type 119864

119887 the two best


1) are





2with a correlation


0and 119864

1are shown in



0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100

Models of type Ea


(a)

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

orN model

3020100

Models of type Eb


(b)

Models of beams

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100


(c)







1has a higher




0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)



30 4020100


(a)

0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)

30 4020100




(b)

Pred

icte

d re

adin

gs (M

Pa)

2

25

3

35

4

45

5

55

6

65

7

2


4 6



(c)



2for beams




119905 =119889 minus 1198890

119904119889radic119899 (2)

where 119889 and 119904119889



10

0

5

minus5

minus10


+

1

(a)


1

10

0

5

minus5

minus10

(b)


1

0

05

minus05

(c)


2








7 Conclusions





1198640


127 0229

1198642

35 minus0022

10

0

5

minus5

minus101


++


other authors




1with a






Abbreviations




References



















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






0+ 12057911198731198772 + 120579

2UPV + 120579

3119908119888minus05 + 120579

4ln (age) + 120576 0638

1198720119886[9] 1198911015840119888 = 120579

0+ 12057911198731198772 + 120579

2UPV3 + 120576 0614

1198721[53 71] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV 0621

1198722[54] 1198911015840119888 = 120579

0+ 12057911198773 + 120579

2UPV 0616

1198723[11] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV4 0612

1198724[55] 1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV + 120579

3UPV2 0596

1198725[56 58 61] ln1198911015840119888 = 120579

0+ 1205791119877 + 1205792UPV 0613

1198726[59 60] ln1198911015840119888 = 120579

0+ 1205791ln119877 + 120579

2lnUPV 0617

1198727[57] ln1198911015840119888 = 120579


1198728[62] 1198911015840119888

minus05

= 1205790+ 1205791119877minus1 + 120579


119864119886

1198911015840119888 = 1205790freq + 120579

1rebound + 120579

2resistiv + 120579

3UPV 0636

119864119887

1198911015840119888 = 1205790+ 12057911198731198772 + 120579

2UPV + 120579

3(wc)minus05 + 120579

4ln (age) + 120579

5resistiv + 120579

6freq + 120576 0642




4 Experimental





First stage1 055 75 (295) 100 (394)2 061 100 (394) 135 (531)3 057 75 (295) 115 (453)4 076 100 (394) 190 (748)

Second stage1 050 75 (295) 85 (335)2 065 100 (394) 145 (571)






STAGE I

Type I


Type II


Beam

055 X X X057 X X X061 X X X076 X X X

STAGE II





Material Type








119910 = 1198860+ 1198861ERT + 119886

2UPV + 119886

3RFT

+ 1198864RNT + 119886

5age + 119886

6wc

(1)








5

10

15

20

25

30

Resistivity (Ohm-m)

Com

pres

sive s

treng

th (M

Pa)

20 30 40 50 60 70

05 065-3d05 065-7d05 065-21d05 065-28d057 076-3d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

VPU (kms)

Com

pres

sive s

treng

th (M

Pa)

34 35 36 37 38 39 40 41

055 061-3d055 061-7d055 061-14d055 061-21d055 061-28d

057 076-3d057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)

VPU (kms)34 35 36 37 38 39

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)









Name


1198911015840119888 = 1205790freq + 120579

1UPV + 120579

2(wc) + 120579

3resistiv 0895 119864

0


1198911015840119888 = 1205790+ 1205791UPV3 + 120579

2(wc)minus05 + 120579

3ln (age) + 120579

4resistiv + 120579

5freq + 120576 0889 119864

1


1freq long + 120579

2(wc) + 120579

3freq trans 0913 119864

2

5

10

15

20

25

30

Frequency (Hz)

Com

pres

sive s

treng

th (M

Pa)

1000 1200 1400 1600 1800 2000 2200

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d







119886and119864



0

1198641 and 119864





119887was generated



119886and





30

35

40

45

50

55

60


Mod

ulus

of r

uptu

re (M

Pa)

2500 2600 2700 2800 2900 3000

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

30

35

40

45

50

55

60

Mod

ulus

of r

uptu

re (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

Hammer rebound

Com

pres

sive s

treng

th (M

Pa)

16 18 20 22 24 26

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d






119886and 32 of type 119864

119887 the two best


1) are





2with a correlation


0and 119864

1are shown in



0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100

Models of type Ea


(a)

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

orN model

3020100

Models of type Eb


(b)

Models of beams

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100


(c)







1has a higher




0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)



30 4020100


(a)

0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)

30 4020100




(b)

Pred

icte

d re

adin

gs (M

Pa)

2

25

3

35

4

45

5

55

6

65

7

2


4 6



(c)



2for beams




119905 =119889 minus 1198890

119904119889radic119899 (2)

where 119889 and 119904119889



10

0

5

minus5

minus10


+

1

(a)


1

10

0

5

minus5

minus10

(b)


1

0

05

minus05

(c)


2








7 Conclusions





1198640


127 0229

1198642

35 minus0022

10

0

5

minus5

minus101


++


other authors




1with a






Abbreviations




References



















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






STAGE I

Type I


Type II


Beam

055 X X X057 X X X061 X X X076 X X X

STAGE II





Material Type








119910 = 1198860+ 1198861ERT + 119886

2UPV + 119886

3RFT

+ 1198864RNT + 119886

5age + 119886

6wc

(1)








5

10

15

20

25

30

Resistivity (Ohm-m)

Com

pres

sive s

treng

th (M

Pa)

20 30 40 50 60 70

05 065-3d05 065-7d05 065-21d05 065-28d057 076-3d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

VPU (kms)

Com

pres

sive s

treng

th (M

Pa)

34 35 36 37 38 39 40 41

055 061-3d055 061-7d055 061-14d055 061-21d055 061-28d

057 076-3d057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)

VPU (kms)34 35 36 37 38 39

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)









Name


1198911015840119888 = 1205790freq + 120579

1UPV + 120579

2(wc) + 120579

3resistiv 0895 119864

0


1198911015840119888 = 1205790+ 1205791UPV3 + 120579

2(wc)minus05 + 120579

3ln (age) + 120579

4resistiv + 120579

5freq + 120576 0889 119864

1


1freq long + 120579

2(wc) + 120579

3freq trans 0913 119864

2

5

10

15

20

25

30

Frequency (Hz)

Com

pres

sive s

treng

th (M

Pa)

1000 1200 1400 1600 1800 2000 2200

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d







119886and119864



0

1198641 and 119864





119887was generated



119886and





30

35

40

45

50

55

60


Mod

ulus

of r

uptu

re (M

Pa)

2500 2600 2700 2800 2900 3000

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

30

35

40

45

50

55

60

Mod

ulus

of r

uptu

re (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

Hammer rebound

Com

pres

sive s

treng

th (M

Pa)

16 18 20 22 24 26

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d






119886and 32 of type 119864

119887 the two best


1) are





2with a correlation


0and 119864

1are shown in



0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100

Models of type Ea


(a)

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

orN model

3020100

Models of type Eb


(b)

Models of beams

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100


(c)







1has a higher




0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)



30 4020100


(a)

0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)

30 4020100




(b)

Pred

icte

d re

adin

gs (M

Pa)

2

25

3

35

4

45

5

55

6

65

7

2


4 6



(c)



2for beams




119905 =119889 minus 1198890

119904119889radic119899 (2)

where 119889 and 119904119889



10

0

5

minus5

minus10


+

1

(a)


1

10

0

5

minus5

minus10

(b)


1

0

05

minus05

(c)


2








7 Conclusions





1198640


127 0229

1198642

35 minus0022

10

0

5

minus5

minus101


++


other authors




1with a






Abbreviations




References



















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




5

10

15

20

25

30

Resistivity (Ohm-m)

Com

pres

sive s

treng

th (M

Pa)

20 30 40 50 60 70

05 065-3d05 065-7d05 065-21d05 065-28d057 076-3d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

VPU (kms)

Com

pres

sive s

treng

th (M

Pa)

34 35 36 37 38 39 40 41

055 061-3d055 061-7d055 061-14d055 061-21d055 061-28d

057 076-3d057 076-7d057 076-14d057 076-21d057 076-28d

(a)

5

10

15

20

25

30

35

Com

pres

sive s

treng

th (M

Pa)

VPU (kms)34 35 36 37 38 39

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)









Name


1198911015840119888 = 1205790freq + 120579

1UPV + 120579

2(wc) + 120579

3resistiv 0895 119864

0


1198911015840119888 = 1205790+ 1205791UPV3 + 120579

2(wc)minus05 + 120579

3ln (age) + 120579

4resistiv + 120579

5freq + 120576 0889 119864

1


1freq long + 120579

2(wc) + 120579

3freq trans 0913 119864

2

5

10

15

20

25

30

Frequency (Hz)

Com

pres

sive s

treng

th (M

Pa)

1000 1200 1400 1600 1800 2000 2200

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d







119886and119864



0

1198641 and 119864





119887was generated



119886and





30

35

40

45

50

55

60


Mod

ulus

of r

uptu

re (M

Pa)

2500 2600 2700 2800 2900 3000

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

30

35

40

45

50

55

60

Mod

ulus

of r

uptu

re (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

Hammer rebound

Com

pres

sive s

treng

th (M

Pa)

16 18 20 22 24 26

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d






119886and 32 of type 119864

119887 the two best


1) are





2with a correlation


0and 119864

1are shown in



0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100

Models of type Ea


(a)

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

orN model

3020100

Models of type Eb


(b)

Models of beams

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100


(c)







1has a higher




0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)



30 4020100


(a)

0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)

30 4020100




(b)

Pred

icte

d re

adin

gs (M

Pa)

2

25

3

35

4

45

5

55

6

65

7

2


4 6



(c)



2for beams




119905 =119889 minus 1198890

119904119889radic119899 (2)

where 119889 and 119904119889



10

0

5

minus5

minus10


+

1

(a)


1

10

0

5

minus5

minus10

(b)


1

0

05

minus05

(c)


2








7 Conclusions





1198640


127 0229

1198642

35 minus0022

10

0

5

minus5

minus101


++


other authors




1with a






Abbreviations




References



















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






Name


1198911015840119888 = 1205790freq + 120579

1UPV + 120579

2(wc) + 120579

3resistiv 0895 119864

0


1198911015840119888 = 1205790+ 1205791UPV3 + 120579

2(wc)minus05 + 120579

3ln (age) + 120579

4resistiv + 120579

5freq + 120576 0889 119864

1


1freq long + 120579

2(wc) + 120579

3freq trans 0913 119864

2

5

10

15

20

25

30

Frequency (Hz)

Com

pres

sive s

treng

th (M

Pa)

1000 1200 1400 1600 1800 2000 2200

05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d







119886and119864



0

1198641 and 119864





119887was generated



119886and





30

35

40

45

50

55

60


Mod

ulus

of r

uptu

re (M

Pa)

2500 2600 2700 2800 2900 3000

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

30

35

40

45

50

55

60

Mod

ulus

of r

uptu

re (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

Hammer rebound

Com

pres

sive s

treng

th (M

Pa)

16 18 20 22 24 26

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d






119886and 32 of type 119864

119887 the two best


1) are





2with a correlation


0and 119864

1are shown in



0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100

Models of type Ea


(a)

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

orN model

3020100

Models of type Eb


(b)

Models of beams

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100


(c)







1has a higher




0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)



30 4020100


(a)

0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)

30 4020100




(b)

Pred

icte

d re

adin

gs (M

Pa)

2

25

3

35

4

45

5

55

6

65

7

2


4 6



(c)



2for beams




119905 =119889 minus 1198890

119904119889radic119899 (2)

where 119889 and 119904119889



10

0

5

minus5

minus10


+

1

(a)


1

10

0

5

minus5

minus10

(b)


1

0

05

minus05

(c)


2








7 Conclusions





1198640


127 0229

1198642

35 minus0022

10

0

5

minus5

minus101


++


other authors




1with a






Abbreviations




References



















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




30

35

40

45

50

55

60


Mod

ulus

of r

uptu

re (M

Pa)

2500 2600 2700 2800 2900 3000

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d

(a)

30

35

40

45

50

55

60

Mod

ulus

of r

uptu

re (M

Pa)


05-3d05-7d05-14d05-21d05-28d

065-3d065-7d065-14d065-21d065-28d

(b)


15

20

25

30

Hammer rebound

Com

pres

sive s

treng

th (M

Pa)

16 18 20 22 24 26

055 061-7d055 061-14d055 061-21d055 061-28d

057 076-7d057 076-14d057 076-21d057 076-28d






119886and 32 of type 119864

119887 the two best


1) are





2with a correlation


0and 119864

1are shown in



0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100

Models of type Ea


(a)

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

orN model

3020100

Models of type Eb


(b)

Models of beams

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100


(c)







1has a higher




0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)



30 4020100


(a)

0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)

30 4020100




(b)

Pred

icte

d re

adin

gs (M

Pa)

2

25

3

35

4

45

5

55

6

65

7

2


4 6



(c)



2for beams




119905 =119889 minus 1198890

119904119889radic119899 (2)

where 119889 and 119904119889



10

0

5

minus5

minus10


+

1

(a)


1

10

0

5

minus5

minus10

(b)


1

0

05

minus05

(c)


2








7 Conclusions





1198640


127 0229

1198642

35 minus0022

10

0

5

minus5

minus101


++


other authors




1with a






Abbreviations




References



















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100

Models of type Ea


(a)

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

orN model

3020100

Models of type Eb


(b)

Models of beams

0

01

02

03

04

05

06

07

08

09

1

Cor

relat

ion

fact

or

N model 3020100


(c)







1has a higher




0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)



30 4020100


(a)

0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)

30 4020100




(b)

Pred

icte

d re

adin

gs (M

Pa)

2

25

3

35

4

45

5

55

6

65

7

2


4 6



(c)



2for beams




119905 =119889 minus 1198890

119904119889radic119899 (2)

where 119889 and 119904119889



10

0

5

minus5

minus10


+

1

(a)


1

10

0

5

minus5

minus10

(b)


1

0

05

minus05

(c)


2








7 Conclusions





1198640


127 0229

1198642

35 minus0022

10

0

5

minus5

minus101


++


other authors




1with a






Abbreviations




References



















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)



30 4020100


(a)

0

5

10

15

20

25

30

35

40

Pred

icte

d re

adin

gs (M

Pa)

30 4020100




(b)

Pred

icte

d re

adin

gs (M

Pa)

2

25

3

35

4

45

5

55

6

65

7

2


4 6



(c)



2for beams




119905 =119889 minus 1198890

119904119889radic119899 (2)

where 119889 and 119904119889



10

0

5

minus5

minus10


+

1

(a)


1

10

0

5

minus5

minus10

(b)


1

0

05

minus05

(c)


2








7 Conclusions





1198640


127 0229

1198642

35 minus0022

10

0

5

minus5

minus101


++


other authors




1with a






Abbreviations




References



















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




10

0

5

minus5

minus10


+

1

(a)


1

10

0

5

minus5

minus10

(b)


1

0

05

minus05

(c)


2








7 Conclusions





1198640


127 0229

1198642

35 minus0022

10

0

5

minus5

minus101


++


other authors




1with a






Abbreviations




References



















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






1198640


127 0229

1198642

35 minus0022

10

0

5

minus5

minus101


++


other authors




1with a






Abbreviations




References



















































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials












































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



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