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Research ArticlePrediction of Compressive Strength of Concrete UsingArtificial Neural Network and Genetic Programming

Palika Chopra1 Rajendra Kumar Sharma1 and Maneek Kumar2

1Department of Computer Science and Engineering Thapar University Patiala 147004 India2Department of Civil Engineering Thapar University Patiala 147004 India

Correspondence should be addressed to Palika Chopra palikachoprathaparedu

Received 23 June 2015 Accepted 18 August 2015

Academic Editor Luigi Nicolais

Copyright copy 2016 Palika Chopra et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

An effort has been made to develop concrete compressive strength prediction models with the help of two emerging datamining techniques namely Artificial Neural Networks (ANNs) and Genetic Programming (GP) The data for analysis and modeldevelopment was collected at 28- 56- and 91-day curing periods through experiments conducted in the laboratory under standardcontrolled conditions The developed models have also been tested on in situ concrete data taken from literature A comparisonof the prediction results obtained using both the models is presented and it can be inferred that the ANN model with the trainingfunction Levenberg-Marquardt (LM) for the prediction of concrete compressive strength is the best prediction tool

1 Introduction

Conventional concrete is a mixture of cement water andcoarse and fine aggregates Supplementary components suchas chemical and mineral admixtures may be added to thebasic concrete ingredients to enhance its properties in freshor hardened state The procedure of selecting appropriateingredients for concrete and its relative amount with the aimof producing concrete of obligatory strength workability anddurability as cost-spinning as possible is termed mix designThe development of tools to find the optimized mix propor-tions has been the subject of research during the last morethan four decades The aim of any proportioning process isto determine an ample and cost-effective material to make upthe concrete which can be used in its fabrication as near aspossible to the chosen propertiesThe engineering propertiesof cement-based materials and special concretes depend onvarious parameters including the nonhomogeneous natureof their components and the intrinsically different propertiesof various elements and sometimes on the twin andorcontradictory effects of some ingredients on the overall con-crete performance Therefore a clear understanding of suchcomplex behavior is needed in order to successfully use thesematerials in various engineered structures In recent years

many researchers have been working on developing accurateconcrete compressive strength prediction models [1ndash11] Theprediction of compressive strength of concrete has greatconnotation if it is brisk and consistent because it offers anoption to do the essential modification on themix proportionused to avoid circumstances where concrete does not attainthe mandatory design strength or by avoiding concrete thatis gratuitously sturdy and also for more economic use ofraw material and fewer construction failures hence reducingconstruction cost So prediction of compressive strength ofconcrete has been an active area of research The aim of thepresent study is to compare two emerging soft computingtechniques that is Artificial Neural Network and GeneticProgramming (GP) used for concrete compressive strengthprediction by using the experimental data

2 Materials

The experimental data used for the prediction of concretecompressive strength in the present study have been takenfrom the research work conducted by Kumar [12] Forgenerating a trustworthy information bank on concretecompressive strength variation in five parameters namely

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2016 Article ID 7648467 10 pageshttpdxdoiorg10115520167648467

2 Advances in Materials Science and Engineering

water-cementitious material ratio (WCM) water contentworkability cementitious content (which includes eithercement or both cement and fly ash) and curing ages hasbeen considered The range for the water-cementitious ratiois between 042 and 055 for cement content (C) it is 350ndash475 at 25 kgm3 for water content it is 180ndash230 at 10 kgm3with both medium and high workability and cured at theages of 28 56 and 91 days The experiments were performedunder controlled laboratory conditions As per IS 8112-1989the Ordinary Portland Cement (OPC) is of grade 43 havingspecific gravity of 312 The specific gravity of the aggregate(sand) is 254 with a fineness modulus of 209 The sand con-forms to zone III as per IS 383-1970 Coarse aggregate (CA)used herein consists of two sizes 20mm and 10mm havingspecific gravity of 261 and 263 respectivelymixed in varyingproportionThe details of the proportions for concrete mixeswithout fly ash (FA) are shown in Table 1 and the compressivestrength data at varying curing ages for these mixes is pre-sented in Table 2 Table 3 shows proportions of ingredientsof mixes containing 015 FA as substitution of cement andTable 4 gives the compressive strength data at the above agesfor the FA concrete mixes

3 Methods

31 Artificial Neural Network An Artificial Neural Networkis a network of artificial neurons which can reveal intricateglobal performance determined by the associations betweenthe processing elements and element parameters In a neuralnetwork model simple nodes which are called ldquoneuronsrdquoor ldquoneurodesrdquo or ldquoprocessing elementsrdquo (PEs) or ldquounitsrdquoare linked jointly to form a network of units hence calledldquoArtificial Neural Networkrdquo

ANNs consist of the following three major essentials [13]

Topology organization and interconnection of a neu-ral network into layersLearning related with the information storage in thenetworkRecall retrieval of information from the network

The architecture of an ANN consists of synthetic or artificialneurons These are analogous to natural neurons in the brainof a human which are clumped into layers Atypical neuralnetwork architecture consists of an input layer one hiddenlayer and an output layer [14]

311 Construction of Model 1 (ANN Model) A successfulapplication of an ANN for the prediction of compressivestrength of concrete needs a good conception of the impactof different internal parameters For ANN architectures andtraining of the same the significant internal parametersinclude learning rate initial weights number of trainingepochs number of hidden layers and number of neurons inevery hidden layer and transfer functions for hidden layersand output layers [15] In this work an ANN model is devel-oped through experimental exploration of various internalparameters to predict the compressive strength of concreteThe initial trialing is commenced with certain randomly

Table 1 Details of proportions for concrete mixes without fly ash

S number Mixdesignation

WCMratio

Mix proportions(C sand CA)

Cementcontent (C)

kgm31 MD-1 053 1 158 305 375002 MD-2 050 1 143 282 400003 MD-3 053 1 154 299 400004 MD-4 047 1 128 258 425005 MD-5 049 1 139 277 425006 MD-6 044 1 114 235 450007 MD-7 047 1 125 254 450008 MD-8 042 1 105 219 475009 MD-9 044 1 119 246 4750010 MD-10 053 1 158 305 3750011 MD-11 050 1 143 282 4000012 MD-12 053 1 154 299 4000013 MD-13 047 1 128 258 4250014 MD-14 049 1 139 277 4250015 MD-15 051 1 151 295 4250016 MD-16 044 1 114 235 4500017 MD-17 047 1 125 254 4500018 MD-18 049 1 137 273 4500019 MD-19 042 1 105 219 4750020 MD-20 044 1 119 246 4750021 MD-21 046 1 123 251 4750022 MD-22 052 1 143 202 4250023 MD-23 049 1 129 186 4500024 MD-24 051 1 0391 19 4500025 MD-25 046 1 117 172 4750026 MD-26 048 1 126 183 4750027 MD-27 051 1 139 326 3500028 MD-28 054 1 149 342 3500029 MD-29 048 1 125 299 3750030 MD-30 051 1 135 319 3750031 MD-31 045 1 110 270 4000032 MD-32 048 1 121 292 4000033 MD-33 042 1 098 247 4250034 MD-34 045 1 109 268 4250035 MD-35 042 1 098 245 4500036 MD-36 054 1 149 342 3500037 MD-37 051 1 135 319 3750038 MD-38 048 1 121 292 4000039 MD-39 045 1 109 268 4250040 MD-40 042 1 098 245 4500041 MD-41 053 1 147 241 3750042 MD-42 050 1 132 221 4000043 MD-43 053 1 144 236 4000044 MD-44 047 1 119 203 4250045 MD-45 049 1 129 218 4250046 MD-46 044 1 107 186 4500047 MD-47 047 1 117 200 4500048 MD-48 042 1 095 168 4750049 MD-49 044 1 106 184 47500

selected parameters on the basis of the technical literatureavailable The ldquotrial and errorrdquo method is used to reach atbest possible parameter values that would generate the truepredictions

In the starting most of the variants are examined for thenetwork performance optimization Levenberg-Marquardt

Advances in Materials Science and Engineering 3

Table 2 Details of compressive strength of concrete mixes withoutfly ash after curing for 28 56 and 91 days


WCMratio

28 d(MPa)

56 d(MPa)

91 d(MPa)

1 MD-1 053 3684 4092 44522 MD-2 050 4313 5022 51973 MD-3 053 3858 4551 47494 MD-4 047 4716 5125 54275 MD-5 049 4505 5072 52856 MD-6 044 4963 5448 58047 MD-7 047 4742 5134 55308 MD-8 042 5401 5791 60159 MD-9 044 5005 5572 583110 MD-10 053 3781 4350 475511 MD-11 050 4411 5098 525612 MD-12 053 4090 4656 510713 MD-13 047 4751 5292 544714 MD-14 049 4530 5147 530915 MD-15 051 4254 4905 511916 MD-16 044 5203 5626 591917 MD-17 047 4874 5342 550318 MD-18 049 4659 5321 536719 MD-19 042 5449 5865 630720 MD-20 044 5306 5667 625721 MD-21 046 4918 5404 571022 MD-22 052 4002 4692 484823 MD-23 049 4525 5043 530924 MD-24 051 4268 4854 496325 MD-25 046 4867 5348 565026 MD-26 048 4552 5097 536327 MD-27 051 3952 4331 461328 MD-28 054 3166 3718 439229 MD-29 048 4273 4823 522330 MD-30 051 4069 4446 464231 MD-31 045 4799 5295 555132 MD-32 048 4489 5120 538533 MD-33 042 5125 5755 595034 MD-34 045 4905 5414 573535 MD-35 042 5369 5777 598936 MD-36 054 3664 4346 465537 MD-37 051 4157 4681 500438 MD-38 048 4622 5258 530739 MD-39 045 5035 5602 583240 MD-40 042 5411 5852 622841 MD-41 053 3730 4351 466342 MD-42 050 4404 5053 525543 MD-43 053 3961 4609 481744 MD-44 047 4737 5131 547745 MD-45 049 4469 5069 527546 MD-46 044 5093 5571 590547 MD-47 047 4808 5263 556148 MD-48 042 5414 5821 611149 MD-49 044 5131 5637 5951

training (LM) was found to be most suitable for the data pat-terns for the prediction of concrete compressive strength dur-ing trail approach In the present study two types of datasetshave been taken dataset 1 has 49 tuples and this dataset iswithout the substitution of cement with FA and dataset 2 has27 tuples and this dataset is with 015 substitution of cement

with FA Further each dataset is categorized according tothe curing time that is 28 days 56 days and 91 days Thefour numbers of input parameters have been engaged thatis water cement coarse aggregate and fine aggregate whenthe output parameter is 28-day compressive strength Thefive numbers of input parameters have been taken includingthe 28-day compressive strength as input parameter that iswater cement coarse aggregate fine aggregate and 28-daycompressive strength when the output parameter is 56-daycompressive strength The six numbers of input parametershave been used including the 28-day compressive strengthand 56-day compressive strength as input parameters that iswater cement coarse aggregate fine aggregate 28-day com-pressive strength and 56-day compressive strength when theoutput parameter is 91-day compressive strength For all theexperiments in model 1 tansig(119909) function is selected for thehidden layer and purelin(119909) function is selected for outputlayer due to their ability to learn complex nonlinear relationbetween the input parameter and output parameter [16] 50numbers of neurons are used at hidden layer and 01 neuronis used at output layer The values of other parameters thatis performance function learning rate performance goaland epochs are ldquomserdquo ldquo001rdquo ldquo0000001rdquo and ldquo10000rdquo whichhave been taken for the construction of ANN model Thearchitecture selected for ANN model is given in Table 5

32 Genetic Programming Genetic Programming (GP) is agroup of instructions and a fitness process to determine howwell a machine has performed a particular task It is a special-ization of genetic algorithm (GA) where each node is a com-puter program It is a technique used to optimize residents ofcomputer program in line with a suitable site determined by aprogramrsquos capability to carry out a prearranged computa-tional condition The three genetic operations are as follows

(1) Crossover operates on two programs that are chosenas per their fitness and produces two subprogramsThe two randomnodes are chosen fromeach programand then the resultant subtrees are swapped produc-ing two new programs These new programs turnedinto a part of the new generation of programs to beparticipated further Population here is increased by2

(2) Reproduction the next important operation isaccomplished by copying an electedmember from thepresent generation to the subsequent generation asper the fitness norm Population here is increased by1

(3) Mutation inGPmutation becomes a significant oper-ator that provides assortment to the population Oneindividual is chosen as per the fitness A subprogramis substituted by another one randomlyThemutant ispopped into the new population Population is thenincreased by 1

Saridemir [10] has explained the whole genetic approachproposed by Koza [17] andGhodratnamaa et al [18] have alsopublished the pseudocode for the same The role of GP infuture computing has been seen as the most potential way to


Table 3 Details of proportions for concrete mixes with 015 fly ash replacement

S number Mix designation WCM ratio Mix proportions(C FA sand CA)

Cement content (C)kgm3

Fly ash content (FA)kgm3

1 MDF-1 045 1 015 110 270 40000 60002 MDF-2 042 1 015 098 246 42500 63753 MDF-3 045 1 015 109 268 42500 63754 MDF-4 047 1 015 128 258 42500 63755 MDF-5 042 1 015 098 245 45000 67506 MDF-6 044 1 015 114 235 45000 67507 MDF-7 047 1 015 125 254 45000 67508 MDF-8 042 1 015 105 219 47500 71259 MDF-9 044 1 015 119 246 47500 712510 MDF-10 045 1 015 109 268 42500 637511 MDF-11 047 1 015 128 258 42500 637512 MDF-12 042 1 015 098 245 45000 675013 MDF-13 044 1 015 114 235 45000 675014 MDF-14 047 1 015 125 254 45000 675015 MDF-15 049 1 015 137 273 45000 675016 MDF-16 042 1 015 105 219 47500 712517 MDF-17 044 1 015 119 246 47500 712518 MDF-18 046 1 015 123 251 47500 712519 MDF-19 047 1 015 119 203 42500 637520 MDF-20 044 1 015 107 186 45000 675021 MDF-21 047 1 015 117 200 45000 675022 MDF-22 049 1 015 129 186 45000 675023 MDF-23 051 1 015 139 198 45000 675024 MDF-24 042 1 015 095 168 47500 712525 MDF-25 044 1 015 106 184 47500 712526 MDF-26 046 1 015 117 172 47500 712527 MDF-27 048 1 015 126 183 47500 7125

automatically write computer programs Nowadays somecommercial Genetic Programming kernels are also availablethat will help to apply the technique and to use the GP kernelsthe user needs to take some decisions before the GP systemto begin Firstly the available genes need to be selected andcreated Secondly the user has to specify a number of controlparameters

321 Construction of Model 2 (GP Model) Koza [17] haslisted some of the important control parameters For theconstruction of GP the initial population size is 49 fordataset 1 without substitution of cement with FA and 27with 015 substitution of cement with FA for dataset 2 As inmodel 1 each dataset is further categorized according to thecuring time the same has been taken for model 2 The fournumbers of input parameters have been taken that is watercement coarse aggregate and fine aggregate when the outputparameter is 28-day compressive strength

The five numbers of input parameters have been engagedincluding the 28-day compressive strength as input param-eter that is water cement coarse aggregate fine aggregateand 28-day compressive strength when the output parameter

is 56-day compressive strength The six numbers of inputparameters have been used including the 28-day compressivestrength and 56-day compressive strength as input param-eters that is water cement fine aggregate coarse aggre-gate 28-day compressive strength and 56-day compressivestrength when the output parameter is 91-day compressivestrength The population size (Mu) and the number of chil-dren produced (Lamda) have been taken 100 and 150 respec-tively The greater the number of generations the greater thechance of evolving a solution so the number of generations istaken as 100000 for this modelThe values for the parameterscrossover rate and mutation rate have been selected as 070and 5119890 minus 002 respectively on the trial and error basis Thevalues of other parameters that is function set training per-centage selection method and tournament size of substitu-tion are ldquo+ minus lowast sqrtrdquo ldquo75rdquo ldquotournamentrdquo and ldquo03rdquo whichhave been selected for the construction of GP model Theparameters settings for model 2 are lodged in Table 6

33 Testing of Model 1 and Model 2 Namyong et al [19]have offered the regression equations for prediction of in situconcrete compressive strength and for this purpose they have


Table 4 Details of compressive strength of concrete mixes with fly ash after curing of 28 56 and 91 days

S number Mix designation WCMratio

28 d(MPa)

56 d(MPa)

91 d(MPa)

1 MDF-1 045 3904 4765 52202 MDF-2 042 4509 5021 55753 MDF-3 045 4114 4867 52694 MDF-4 047 3835 4327 50425 MDF-5 042 4613 5101 56516 MDF-6 044 4250 4917 53117 MDF-7 047 3958 4402 51078 MDF-8 042 4734 5230 57709 MDF-9 044 4355 4979 537910 MDF-10 045 4201 4968 533911 MDF-11 047 3885 4496 505012 MDF-12 042 4725 5195 571713 MDF-13 044 4309 5030 536714 MDF-14 047 4026 4530 516215 MDF-15 049 3715 4452 480816 MDF-16 042 4841 5358 581917 MDF-17 044 4402 5181 541218 MDF-18 046 4073 4595 521019 MDF-19 047 3890 4320 505020 MDF-20 044 4322 4993 536221 MDF-21 047 3985 4461 514222 MDF-22 049 3687 4125 473023 MDF-23 051 3523 4005 461124 MDF-24 042 4794 5305 578225 MDF-25 044 4387 5048 543826 MDF-26 046 4034 4561 523927 MDF-27 048 3765 4228 4855

used the information of mixture proportions of ready-mixedconcrete and test results of compressive strength from con-struction sites In their study they have used 1442 compres-sive strength test results obtained from the specimens having68 different kinds of mixtures with specified compressivestrength of 18sim27MPa water-cement ratio of 039sim062 andmaximum aggregate size of 25mm In this study Namyonget al [19] in situ data has been used for the testing of thesuggested model for the prediction of concrete compressivestrength

4 Results and Discussion

The objective of the present study was to explore theapplicability of the suggested models that is model 1 andmodel 2 for the prediction of concrete compressive strengthThis section presents the comparative investigation of resultsobtained from these approaches and quantitative assessmentof the modelsrsquo predictive abilities For model 1 the LMalgorithm is used for training whereas tan-sigmoid is used asan activation function for evaluating the prediction accuracy

parameters The results as presented in Table 7 give thevalues of1198772 andRMSE for prediction of concrete compressivestrength for both types of mixtures namely R1 (dataset withno substitution of cement with FA) and R2 (dataset withsubstitution of cement with 015 FA) From the results inTable 7 it can be observed that for all the curing days in boththe cases either R1 or R2 1198772 is above 090 except for R1 at acuring age of 28 days wherein it is 0898 The low values ofRMSE for all the mixes at different curing ages also indicatethat the model can predict compressive strength of the mixeswith high reliability Also it can be seen that model 1 withLM as the training function retrieves the result in just a fewepochsThemaximum number of epochs taken by the modelis just five which clearly indicates that the time taken for theprediction is also very much less

In model 2 the addition is chosen as the linking utilityThe values of 1198772 and RMSE for prediction of concretecompressive strength for both types of mixtures namelyR3 (dataset with no substitution of cement with FA) andR4 (dataset with substitution of cement with 015 FA)obtainedusing model 2 are provided in Table 7 Prediction


Table 5 Architecture selected for model 1 (ANN model)

Parameters Values Description

Dataset Dataset 1 49 (without fly ash)Dataset 2 27 (with fly ash)

Dataset is of two types One is without anysubstitution of cement by fly ash and the secondone is with 15 of the cement replaced by fly ashDataset 1 is of 49 tuples in total Dataset 2 is of 27tuples in total

Number of inputparameters

04 (cement (C) water (W) fine aggregate (sand)coarse aggregate (CA)) in case of 05 (cement (C)water (W) fine aggregate (sand) coarse aggregate(CA) 28-day compressive strength (CS28)) incase of 06 (cement (C) water (W) fine aggregate(sand) coarse aggregate (CA) 28-day compressivestrength (CS28) 56-day compressive strength(CS56)) Fly ash (FA) is used with dataset 2 onlyall other parameters are the same as dataset 1

When output is 28 days then the number of inputparameters is 04 when output is 56 days thenumber of input parameters is 05 as 28-daycompressive strength is taken as input whenoutput is 91 days the number of input parametersis 06 as 28-day compressive strength and 56-daycompressive strength are also taken as input Indataset 2 FA is replacing 15 of the cement

Activation function 1 tansig(119909) tansig (119909) = 2

(1 + exp (minus2 lowast 119909))minus 1

Activation function 2 purelin(119909) purelin(119909) = 119909

Performance function MSE MSE =sum119899

119894=1(predictedoutput minus actualoutput)2

119899

where 119899 is the input patterns

Nettrainparamlr 001 Learning rateNettrainfcn trainlm Levenberg-Marquardt algorithmNettrainparamepochs 10000 Maximum number of epochs to trainNettrainparamgoal 0000001 Performance goalNumber of hidden layerneurons 50 mdash

Number of output layerneurons 1 mdash

equations ((1)ndash(6)) generated using model 2 are detailed asfollows

11989128= radicCA(((((((((FA + FA)

FA) + (radic(FA) + ((FA + 0640295148) +

((((FA0661794484) + radicCA)))radicFA

)))) + CA) + CA) + FA)

minus radic(radic((radic(((1 + FA) + FA)) lowastW)))))minus1

(1)

11989156= (((

((W + (radic((W +W)) lowastW)) lowast 11989128)

(W lowast (11989128+ ((W + ((119891

28+ radic(119891

28)) +W)) + 119891

28)))

) + (W + 0488720804)) lowast 11989128) (2)

11989191=(

radic

radic

radic

radic

(((11989156lowast

radic(radic((((((11989128W)) W) W) + ((radic(W lowast (CA minus FA)) + 119891

28)))) + 119891

28)

W))lowast ((W + (

11989128

W)) lowast ((W lowastW) + (

11989128

W))))) (3)

1198911015840

28= (radicCA (W + ((((FA lowast radic(((((FA + CA) + FA) + FA) lowast FA))) + ((FA + (radicCA + ((W + CA) +W))) + CA)) + (radicFA + FA)) + (W + FA)))

minus1

) (4)

1198911015840

56=(

(

(

radic

radic

radic

radic

radic

radic

radic

radic

(

(

(((minus643119890 minus 002 + 1198911015840

28) + radic(radic((radic(radicCA)) lowast CA))))

radic(radic((radicCA lowast ((radic((radic(((W119891101584028) lowast (119891

1015840

28plusmn 678119890 minus 002))) + radicFA))radic(radic(radicCA))) + 1198911015840

28))))

)

)

)

)

)

lowast1198911015840

28 (5)

1198911015840

91= (radic((((W lowast 0577551961) lowast radic((radic(((W lowast 0572648823)))))))) lowast (1198911015840

28lowast 31462729)) (6)


Table 6 Architecture selected for model 2 (GP model)


Initial population size Dataset 1 49 (without fly ash)Dataset 2 27 (with fly ash)

Dataset is of two types One is without anysubstitution of cement by fly ash and thesecond one is with 015 of the cement replacedby fly ash Dataset 1 is of 49 tuples in totalDataset 2 is of 27 tuples in total


04 (cement (C) water (W) fine aggregate(sand) coarse aggregate (CA)) 05 (cement (C)water (W) fine aggregate (sand) coarseaggregate (CA) 28-day compressive strength(CS28)) 06 (cement (C) water (W) fineaggregate (sand) coarse aggregate (CA)28-day compressive strength (CS28) 56-daycompressive strength (CS56)) Fly ash (FA) isused with dataset 2 only all other parametersare the same as dataset 1

When output is 28 days then the number ofinput parameters is 04 when output is 56 daysthe number of input parameters is 05 as 28-daycompressive strength is taken as input whenoutput is 91 days the number of inputparameters is 06 as 28-day compressivestrength and 56-day compressive strength arealso taken as input In dataset 2 FA is replacing15 of the cement

Function set + minus lowast sqrt Set of functions usedTraining percentage 75 mdashSelection method Tournament mdashTournament size ofreplacement 3 mdash

Maximum generations 100000 Maximum number of iterationsCrossover 07 Probability of crossoverMutation 5119890 minus 002 Probability of mutationMu 100 Population sizeLamda 150 Number of children produced

Objectives COD RMSE Coefficient of determination root mean squareerror

Table 7 Results of model 1 (ANN) and model 2 (GP)

Model 1 Training of the datasetArtificial Neural Network (ANN) Epochs taken Coefficient of determination (1198772) Root mean square error (RMSE)

Result number Curing time

R1 (without fly ash)28 days 04 0898 69762e minus 00656 days 05 0998 12712e minus 00791 days 03 01 73640e minus 009

R2 (with 015 fly ash)28 days 05 0996 38809e minus 00756 days 04 01 36873e minus 00991 days 04 01 22181e minus 010

Model 2 Genetic Programming (GP)28 days

Not applicable

077438 001067R3 (without fly ash) 56 days 099999 000550

91 days 099999 00064428 days 093781 001415

R4 (with 015 fly ash) 56 days 094483 00091091 days 096681 000689

where1198912811989156 and119891

91are the concrete compressive strengths

at curing ages of 28 56 and 91 days respectively when nosubstitution has been done 1198911015840

28 119891101584056 and 1198911015840

91are the concrete

compressive strengths at curing ages of 28 56 and 91 daysrespectively when 015 FA is used as substitution of cement

W is the WCM ratio FA is the FACM and CA is theCACM

From the results tabulated in Table 7 it can be observedthat for R3 mixtures at curing ages of 56 and 91 days thevalues of 1198772 are of the order of 090 and 087 respectively


008900940099010401090114011901240129

0 10 20 30 40 50 60Number of tuples in the dataset

28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa

Pre GP 28d CSExp 28d CSPre ANN 28d CS

Figure 1 Comparison between actual and predicted values of 28 dcompressive strength of concrete

010105

0110115

0120125

0130135

014


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa

Pre GP 56d CSPre ANN 56d CSExp 56d CS


with an RMSE value of 00029 in case of 56 days and 005 incase of 91 days indicating a reasonably good fit of the modelHowever in case of 28-day curing 1198772 obtained is 077 whichis approximately 030 less than the suggested good model fit(1198772more than or equal to 080) In case of prediction of com-pressive strength for R4mixtures with 015 FA1198772 obtained isabove or equal to 092 for all the caseswith the highest value of097with anRMSEvalue of 0009 at curing age of 91 daysThisindicates that model 2 provides the best prediction at 91-daycuring for mixes with FA Figures 1ndash6 provide comparison ofthe predicted results obtained using model 1 model 2 andexperimental laboratory results

It can be clearly observed from these figures that model1 predicts compressive strength values very near to theexperimentally obtained values as compared to model 2results To further test the efficacy and reliability of themodels the in situ compressive strength data at curing age of28 days (as provided in Namyong et al [19]) has been used inthe study Figure 7 shows the results of the testing of modelsfor the in situ dataset of compressive strength It has beenclearly observed that model 1 is more reliable and providesmore accurate prediction for the in situ dataset as well

01

012

014

016

018

02

022

024

0 10 20 30 40 50 60

91 d

com

pres

sive

Number of tuples in the dataset

stren

gth

of co

ncre

te (times

500

) MPa



0075008

0085009

009501

0105011

0115

1 3 5 7 9 11 13 15 17 19 21 23 25 27Number of tuples in the dataset

28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa


Figure 4 Comparison between actual and predicted values of 28 dcompressive strength of concrete with FA

0075008

0085009

009501

0105011

0115012


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



5 Conclusions

On the comparative analysis of GP and ANN techniquesused for the prediction of concrete compressive strengthwithout and with FA it can be concluded that ANN modelis the most reliable technique for the purpose The RMSE


008

009

01

011

012

013

014


91

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



00620067007200770082008700920097010201070112

0 20 40 60 80Number of tuples in the dataset

28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa


Figure 7 Validation of the proposed model of 28 d compressivestrength of concrete with in situ dataset as per [19]

values so obtained are small enough to indicate that the esti-mates aremost precise and the trained networks supply supe-rior results According to statistics if a proposed model gives1198772gt 08 there is a well-built correlation between predicted

and measured values for the data available in the dataset Ashas been observed for both the models 1198772 is greater than08 for all cases except R3 mixture (in Table 7) strength at 28days which proves that either of the models can be used forprediction purposes However the prediction model usingmodel 1 that is ANNmodel confirms a high degree of steadi-ness with experimentally evaluated concrete compressivestrength specimens used As an outcome ANN may serve asa strong predictive tool for prediction of both experimentaland in situ data and it may provide perfect and valuableexplicit formulation for many civil engineering applicationswherein predictive pronouncements are required

Conflict of Interests

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

References

[1] H-G Ni and J-Z Wang ldquoPrediction of compressive strengthof concrete by neural networksrdquoCement and Concrete Researchvol 30 no 8 pp 1245ndash1250 2000

[2] A Baykasoglu T Dereli and S Tanis ldquoPrediction of cementstrength using soft computing techniquesrdquo Cement and Con-crete Research vol 34 no 11 pp 2083ndash2090 2004

[3] S Akkurt G Tayfur and S Can ldquoFuzzy logic model for theprediction of cement compressive strengthrdquo Cement and Con-crete Research vol 34 no 8 pp 1429ndash1433 2004

[4] A Oztas M Pala E Ozbay E Kanca N Caglar and MA Bhatti ldquoPredicting the compressive strength and slump ofhigh strength concrete using neural networkrdquoConstruction andBuilding Materials vol 20 no 9 pp 769ndash775 2006

[5] M Pala E Ozbay A Oztas and M I Yuce ldquoAppraisal of long-term effects of fly ash and silica fume on compressive strengthof concrete by neural networksrdquo Construction and BuildingMaterials vol 21 no 2 pp 384ndash394 2007

[6] N P Rajamane J A Peter and P S Ambily ldquoPrediction ofcompressive strength of concrete with fly ash as sand replace-ment materialrdquo Cement and Concrete Composites vol 29 no 3pp 218ndash223 2007

[7] M Ozturan B Kutlu and T Ozturan ldquoComparison of concretestrength prediction techniques with artificial neural networkapproachrdquo Building Research Journal vol 56 pp 23ndash36 2008

[8] M M Alshihri A M Azmy and M S El-Bisy ldquoNeuralnetworks for predicting compressive strength of structural lightweight concreterdquo Construction and Building Materials vol 23no 6 pp 2214ndash2219 2009

[9] M Saridemir ldquoPrediction of compressive strength of concretescontaining metakaolin and silica fume by artificial neuralnetworksrdquo Advances in Engineering Software vol 40 no 5 pp350ndash355 2009

[10] M Saridemir ldquoGenetic programming approach for predictionof compressive strength of concretes containing rice husk ashrdquoConstruction and Building Materials vol 24 no 10 pp 1911ndash1919 2010

[11] A M Diab H E Elyamany A E M Abd Elmoaty and AH Shalan ldquoPrediction of concrete compressive strength dueto long term sulfate attack using neural networkrdquo AlexandriaEngineering Journal vol 53 no 3 pp 627ndash642 2014

[12] M Kumar Reliability based design of structural elements [PhDthesis] Thapar Institute of Engineering and Technology PatialaPatiala India 2002

[13] P K Simpson Ed Neural Networks Theory Technology andApplications IEEE New York NY USA 1996

[14] K Knight ldquoConnectionist ideas and algorithmsrdquo Communica-tions of the ACM vol 33 no 11 pp 58ndash74 1990

[15] A K Sharma R K Sharma and H S Kasana ldquoPrediction offirst lactation 305-day milk yield in Karan Fries dairy cattleusing ANN modelingrdquo Applied Soft Computing Journal vol 7no black3 pp 1112ndash1120 2007

[16] A Kamalloo Y Ganjkhanlou S H Aboutalebi and H Noura-nian ldquoModeling of compressive strength of Metakaolin basedgeopolymers by the use of artificial neural networkrdquo Interna-tional Journal of Engineering vol 23 no 2 pp 145ndash152 2010

[17] J R Koza Genetic Programming On the Programming ofComputers by Means of Natural Selection The MIT PressCambridge Mass USA 1992


[18] A Ghodratnamaa R Tavakkoli-Moghaddam and A BabolicldquoComparing three proposed meta-heuristics to solve a newP-HUB location-allocation problemrdquo International Journal ofEngineering vol 26 no 9 pp 1043ndash1058 2013

[19] J Namyong Y Sangchun and C Hongbum ldquoPrediction ofcompressive strength of In-situ concrete based on mixtureproportionsrdquo Journal of Asian Architecture and Building Engi-neering vol 3 no 1 pp 9ndash16 2004

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


water-cementitious material ratio (WCM) water contentworkability cementitious content (which includes eithercement or both cement and fly ash) and curing ages hasbeen considered The range for the water-cementitious ratiois between 042 and 055 for cement content (C) it is 350ndash475 at 25 kgm3 for water content it is 180ndash230 at 10 kgm3with both medium and high workability and cured at theages of 28 56 and 91 days The experiments were performedunder controlled laboratory conditions As per IS 8112-1989the Ordinary Portland Cement (OPC) is of grade 43 havingspecific gravity of 312 The specific gravity of the aggregate(sand) is 254 with a fineness modulus of 209 The sand con-forms to zone III as per IS 383-1970 Coarse aggregate (CA)used herein consists of two sizes 20mm and 10mm havingspecific gravity of 261 and 263 respectivelymixed in varyingproportionThe details of the proportions for concrete mixeswithout fly ash (FA) are shown in Table 1 and the compressivestrength data at varying curing ages for these mixes is pre-sented in Table 2 Table 3 shows proportions of ingredientsof mixes containing 015 FA as substitution of cement andTable 4 gives the compressive strength data at the above agesfor the FA concrete mixes

3 Methods

31 Artificial Neural Network An Artificial Neural Networkis a network of artificial neurons which can reveal intricateglobal performance determined by the associations betweenthe processing elements and element parameters In a neuralnetwork model simple nodes which are called ldquoneuronsrdquoor ldquoneurodesrdquo or ldquoprocessing elementsrdquo (PEs) or ldquounitsrdquoare linked jointly to form a network of units hence calledldquoArtificial Neural Networkrdquo

ANNs consist of the following three major essentials [13]

Topology organization and interconnection of a neu-ral network into layersLearning related with the information storage in thenetworkRecall retrieval of information from the network

The architecture of an ANN consists of synthetic or artificialneurons These are analogous to natural neurons in the brainof a human which are clumped into layers Atypical neuralnetwork architecture consists of an input layer one hiddenlayer and an output layer [14]

311 Construction of Model 1 (ANN Model) A successfulapplication of an ANN for the prediction of compressivestrength of concrete needs a good conception of the impactof different internal parameters For ANN architectures andtraining of the same the significant internal parametersinclude learning rate initial weights number of trainingepochs number of hidden layers and number of neurons inevery hidden layer and transfer functions for hidden layersand output layers [15] In this work an ANN model is devel-oped through experimental exploration of various internalparameters to predict the compressive strength of concreteThe initial trialing is commenced with certain randomly

Table 1 Details of proportions for concrete mixes without fly ash


WCMratio

Mix proportions(C sand CA)

Cementcontent (C)

kgm31 MD-1 053 1 158 305 375002 MD-2 050 1 143 282 400003 MD-3 053 1 154 299 400004 MD-4 047 1 128 258 425005 MD-5 049 1 139 277 425006 MD-6 044 1 114 235 450007 MD-7 047 1 125 254 450008 MD-8 042 1 105 219 475009 MD-9 044 1 119 246 4750010 MD-10 053 1 158 305 3750011 MD-11 050 1 143 282 4000012 MD-12 053 1 154 299 4000013 MD-13 047 1 128 258 4250014 MD-14 049 1 139 277 4250015 MD-15 051 1 151 295 4250016 MD-16 044 1 114 235 4500017 MD-17 047 1 125 254 4500018 MD-18 049 1 137 273 4500019 MD-19 042 1 105 219 4750020 MD-20 044 1 119 246 4750021 MD-21 046 1 123 251 4750022 MD-22 052 1 143 202 4250023 MD-23 049 1 129 186 4500024 MD-24 051 1 0391 19 4500025 MD-25 046 1 117 172 4750026 MD-26 048 1 126 183 4750027 MD-27 051 1 139 326 3500028 MD-28 054 1 149 342 3500029 MD-29 048 1 125 299 3750030 MD-30 051 1 135 319 3750031 MD-31 045 1 110 270 4000032 MD-32 048 1 121 292 4000033 MD-33 042 1 098 247 4250034 MD-34 045 1 109 268 4250035 MD-35 042 1 098 245 4500036 MD-36 054 1 149 342 3500037 MD-37 051 1 135 319 3750038 MD-38 048 1 121 292 4000039 MD-39 045 1 109 268 4250040 MD-40 042 1 098 245 4500041 MD-41 053 1 147 241 3750042 MD-42 050 1 132 221 4000043 MD-43 053 1 144 236 4000044 MD-44 047 1 119 203 4250045 MD-45 049 1 129 218 4250046 MD-46 044 1 107 186 4500047 MD-47 047 1 117 200 4500048 MD-48 042 1 095 168 4750049 MD-49 044 1 106 184 47500

selected parameters on the basis of the technical literatureavailable The ldquotrial and errorrdquo method is used to reach atbest possible parameter values that would generate the truepredictions

In the starting most of the variants are examined for thenetwork performance optimization Levenberg-Marquardt




WCMratio

28 d(MPa)

56 d(MPa)

91 d(MPa)























28 d(MPa)

56 d(MPa)

91 d(MPa)




















119899





11989128= radicCA(((((((((FA + FA)

FA) + (radic(FA) + ((FA + 0640295148) +


)))) + CA) + CA) + FA)


(1)

11989156= (((


(W lowast (11989128+ ((W + ((119891

28+ radic(119891

28)) +W)) + 119891

28)))

) + (W + 0488720804)) lowast 11989128) (2)

11989191=(

radic

radic

radic

radic

(((11989156lowast


28)))) + 119891

28)

W))lowast ((W + (

11989128


11989128

W))))) (3)

1198911015840


minus1

) (4)

1198911015840

56=(

(

(

radic

radic

radic

radic

radic

radic

radic

radic

(

(

(((minus643119890 minus 002 + 1198911015840



1015840


28))))

)

)

)

)

)

lowast1198911015840

28 (5)

1198911015840


28lowast 31462729)) (6)


















Not applicable


91 days 099999 00064428 days 093781 001415


where1198912811989156 and119891



28 119891101584056 and 1198911015840

91are the concrete





008900940099010401090114011901240129


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



010105

0110115

0120125

0130135

014


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa





01

012

014

016

018

02

022

024

0 10 20 30 40 50 60

91 d

com

pres

sive


stren

gth

of co

ncre

te (times

500

) MPa



0075008

0085009

009501

0105011

0115


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



0075008

0085009

009501

0105011

0115012


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



5 Conclusions



008

009

01

011

012

013

014


91

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



00620067007200770082008700920097010201070112


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa







References




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






WCMratio

28 d(MPa)

56 d(MPa)

91 d(MPa)























28 d(MPa)

56 d(MPa)

91 d(MPa)




















119899





11989128= radicCA(((((((((FA + FA)

FA) + (radic(FA) + ((FA + 0640295148) +


)))) + CA) + CA) + FA)


(1)

11989156= (((


(W lowast (11989128+ ((W + ((119891

28+ radic(119891

28)) +W)) + 119891

28)))

) + (W + 0488720804)) lowast 11989128) (2)

11989191=(

radic

radic

radic

radic

(((11989156lowast


28)))) + 119891

28)

W))lowast ((W + (

11989128


11989128

W))))) (3)

1198911015840


minus1

) (4)

1198911015840

56=(

(

(

radic

radic

radic

radic

radic

radic

radic

radic

(

(

(((minus643119890 minus 002 + 1198911015840



1015840


28))))

)

)

)

)

)

lowast1198911015840

28 (5)

1198911015840


28lowast 31462729)) (6)


















Not applicable


91 days 099999 00064428 days 093781 001415


where1198912811989156 and119891



28 119891101584056 and 1198911015840

91are the concrete





008900940099010401090114011901240129


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



010105

0110115

0120125

0130135

014


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa





01

012

014

016

018

02

022

024

0 10 20 30 40 50 60

91 d

com

pres

sive


stren

gth

of co

ncre

te (times

500

) MPa



0075008

0085009

009501

0105011

0115


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



0075008

0085009

009501

0105011

0115012


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



5 Conclusions



008

009

01

011

012

013

014


91

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



00620067007200770082008700920097010201070112


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa







References




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials

















28 d(MPa)

56 d(MPa)

91 d(MPa)




















119899





11989128= radicCA(((((((((FA + FA)

FA) + (radic(FA) + ((FA + 0640295148) +


)))) + CA) + CA) + FA)


(1)

11989156= (((


(W lowast (11989128+ ((W + ((119891

28+ radic(119891

28)) +W)) + 119891

28)))

) + (W + 0488720804)) lowast 11989128) (2)

11989191=(

radic

radic

radic

radic

(((11989156lowast


28)))) + 119891

28)

W))lowast ((W + (

11989128


11989128

W))))) (3)

1198911015840


minus1

) (4)

1198911015840

56=(

(

(

radic

radic

radic

radic

radic

radic

radic

radic

(

(

(((minus643119890 minus 002 + 1198911015840



1015840


28))))

)

)

)

)

)

lowast1198911015840

28 (5)

1198911015840


28lowast 31462729)) (6)


















Not applicable


91 days 099999 00064428 days 093781 001415


where1198912811989156 and119891



28 119891101584056 and 1198911015840

91are the concrete





008900940099010401090114011901240129


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



010105

0110115

0120125

0130135

014


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa





01

012

014

016

018

02

022

024

0 10 20 30 40 50 60

91 d

com

pres

sive


stren

gth

of co

ncre

te (times

500

) MPa



0075008

0085009

009501

0105011

0115


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



0075008

0085009

009501

0105011

0115012


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



5 Conclusions



008

009

01

011

012

013

014


91

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



00620067007200770082008700920097010201070112


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa







References




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials
















119899





11989128= radicCA(((((((((FA + FA)

FA) + (radic(FA) + ((FA + 0640295148) +


)))) + CA) + CA) + FA)


(1)

11989156= (((


(W lowast (11989128+ ((W + ((119891

28+ radic(119891

28)) +W)) + 119891

28)))

) + (W + 0488720804)) lowast 11989128) (2)

11989191=(

radic

radic

radic

radic

(((11989156lowast


28)))) + 119891

28)

W))lowast ((W + (

11989128


11989128

W))))) (3)

1198911015840


minus1

) (4)

1198911015840

56=(

(

(

radic

radic

radic

radic

radic

radic

radic

radic

(

(

(((minus643119890 minus 002 + 1198911015840



1015840


28))))

)

)

)

)

)

lowast1198911015840

28 (5)

1198911015840


28lowast 31462729)) (6)


















Not applicable


91 days 099999 00064428 days 093781 001415


where1198912811989156 and119891



28 119891101584056 and 1198911015840

91are the concrete





008900940099010401090114011901240129


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



010105

0110115

0120125

0130135

014


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa





01

012

014

016

018

02

022

024

0 10 20 30 40 50 60

91 d

com

pres

sive


stren

gth

of co

ncre

te (times

500

) MPa



0075008

0085009

009501

0105011

0115


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



0075008

0085009

009501

0105011

0115012


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



5 Conclusions



008

009

01

011

012

013

014


91

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



00620067007200770082008700920097010201070112


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa







References




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




















Not applicable


91 days 099999 00064428 days 093781 001415


where1198912811989156 and119891



28 119891101584056 and 1198911015840

91are the concrete





008900940099010401090114011901240129


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



010105

0110115

0120125

0130135

014


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa





01

012

014

016

018

02

022

024

0 10 20 30 40 50 60

91 d

com

pres

sive


stren

gth

of co

ncre

te (times

500

) MPa



0075008

0085009

009501

0105011

0115


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



0075008

0085009

009501

0105011

0115012


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



5 Conclusions



008

009

01

011

012

013

014


91

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



00620067007200770082008700920097010201070112


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa







References




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




008900940099010401090114011901240129


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



010105

0110115

0120125

0130135

014


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa





01

012

014

016

018

02

022

024

0 10 20 30 40 50 60

91 d

com

pres

sive


stren

gth

of co

ncre

te (times

500

) MPa



0075008

0085009

009501

0105011

0115


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



0075008

0085009

009501

0105011

0115012


56

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



5 Conclusions



008

009

01

011

012

013

014


91

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



00620067007200770082008700920097010201070112


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa







References




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




008

009

01

011

012

013

014


91

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa



00620067007200770082008700920097010201070112


28

d co

mpr

essiv

estr

engt

h of

conc

rete

(times500

) MPa







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



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