Prediction of Compressive Strength of Geopolymers with Seeded Fly Ash and Rice Husk-Bark Ash by Gene Expression Programming

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Ali Nazari, Shadi Riahi, Gholamreza Khalaj, Hamid Bohlooli and Mohammad Mehdiand Rice Husk-Bark Ash by Gene Expression Programming

Prediction of Compressive Strength of Geopolymers with Seeded Fly Ash

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Prediction of Compressive Strengthof Geopolymers with Seeded Fly Ashand Rice Husk�Bark Ash by Gene

Expression Programming

ALI NAZARI,*,1 SHADI RIAHI,1 GHOLAMREZA KHALAJ,1

HAMID BOHLOOLI1

AND MOHAMMAD MEHDI KAYKHA2

1Department of Mechanical Engineering, Birjand Branch, IslamicAzad University, Birjand, Iran

2Department of Mechanical Engineering, University of Zabol,Zabol, Iran

ABSTRACT: In the present work, compressive strength of inorganic polymers (geo-polymers) made from seeded fly ash and rice husk�bark ash has been predicted bygene expression programming. Different specimens were subjected to compressivestrength tests at 7 and 28 days of curing. One set of the specimens were cured at roomtemperature until reaching to 7 and 28 days and the other sets were oven cured for36 h at the range of 40�90�C and then room cured until 7 and 28 days. A modelbased on gene expression programming for predicting the compressive strength ofthe specimens was presented. To build the model, training and testing using exper-imental results from 120 specimens were conducted. According to the input param-eters, in the gene expression programming models, the compressive strength of eachspecimen was predicted. The training and testing results in the gene expression pro-gramming models have shown a strong potential for predicting the compressivestrength of the geopolymer specimens.

KEY WORDS: compressive strength, fly ash, FTIR, gene expression programming,geopolymer, particle size, rice husk�bark ash, seeded mixture.

INTRODUCTION

GEOPOLYMER WHICH WAS developed by Davidovits (1991) contains bothsilica and alumina which can act as a binder for geopolymerization.

*Author to whom correspondence should be addressed. E-mail: [email protected]

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Various alkali activators also play a key role in producing geopolymers bydissolving silica and alumina from the raw material and forming alumino-silicate structures. Geopolymer is used for a variety of applications such asfor sculpture, building, repairing, and estoration. Numerous research pub-lications related to geopolymers have been released, with some reporting onchemical composition aspects or reaction processes, while others presentresults related to mechanical properties and durability (Wongpa et al.,2010). The general formula to describe the chemical composition of thesemineral polymers is Mn[�(SiO2)z�AlO2]n�wH2O, where z is 1, 2, or 3, M is analkali cation (such as potassium or sodium), and n is the degree of polymer-ization. Accordingly, in order to better describe the geopolymeric structures,a terminology has been proposed: poly(sialate) (�Si�O�Al�O�), poly(sia-late-siloxo) (�Si�O�Al�O�Si�O�), and poly(sialatedisiloxo)(�Si�O�Al�O�Si�O�Si�O�; Davidovits, 1991). The main properties ofgeopolymers are: quick compressive strength development, low permeabil-ity, resistance to acid attack, good resistance to freeze�thaw cycles, andtendency to drastically decrease the mobility of most heavy metal ions con-tained within the geopolymeric structure (van Jaarsveld et al., 1997). Suchproperties make them interesting structural products, such as concretereplacements in various environments, and immobilization systems forheavy metal containment (Alvarez-Ayuso et al., 2008).

The compressive strength of an inorganic polymer depends on both theratio of Si/Al and the types of the utilized raw material. Fly ash (FA) isrecently used as a source material to produce geopolymer because of itssuitable chemical composition along with favorable size and shape. TheFA is a by-product of coal-fired electric power stations. Literature surveyspecifies that FA is primarily composed of SiO2, Al2O3, and Fe2O3. Sincethe quality of FA depends on the type and the quality of coal along with theperformance of the power plant, difficulties sometimes remain to control itschemical composition. In order to achieve a suitable chemical compositionto produce geopolymers, the preferred method is to blend FA with anotherhigh-silica source (Wongpa et al., 2010).

Rice husk�bark ash (RHBA) is a solid waste generated by biomass powerplants using rice husk and eucalyptus bark as fuel. The power plant com-pany providing RHBA for this research reported that about 450 tons/day ofRHBA are produced and discarded. The major chemical constituent ofRHBA is SiO2 (about 75%; Sata et al., 2007; Tangchirapat et al., 2008).Therefore, blending FA and RHBA can adjust the ratio of Si/Al as required.

Genetic programming (GP) has begun to arise for the explicit formulationof the properties and the performances of engineering materials recently(Cevik and Sonebi, 2009; Milani and Nazari, 2011; Nazari et al., 2011).The GP offers many advantages as compared to classical regression

2 A. NAZARI ET AL.




techniques. Regression techniques are often based on predefined functionswhere regression analyses of these functions are later performed. On theother hand, in the case of GP approach, there is no predefined functionto be considered. In this sense, GP can be accepted to be superior to regres-sion techniques and neural networks. The GP has proven to be an effectivetool to model and obtain explicit formulations of experimental studiesincluding multivariate parameters where there are no existing analyticalmodels (Cevik and Sonebi, 2009; Milani and Nazari, 2011; Nazari et al.,2011). There are several works (Cevik, 2007; Cevik and Guzelbey, 2007;Cevik and Sonebi, 2008) in the literature addressing the utilization of geneexpression programming (GEP) for engineering problems.

As authors’ knowledge, there are no works on utilizing a mixture of FAand RHBA with seeded distribution of particles to produce geopolymers. Aliterature survey shows that utilizing fine pozzolan materials could producehigh-strength concrete specimens (Chindaprasirt et al., 2004). However, fewworks have been conducted on this fact in geopolymers. In addition, sincethe concept of geopolymers is completely new and there are few works ontheir properties, application of computer programs like GEP to predict theirproperties is rarely reported. The aim of this study is to investigate thecompressive strength of geopolymers produced form seeded FA andRHBA mixture experimentally and presenting suitable model based onGEP to predict their compressive strength. Both FA and RHBA with twodifferent particle size distributions have been mixed with different amountsto produce four classes of geopolymers. Compressive strength of the pro-duced specimens has been investigated after specific times of curing. Totally120 data of compressive strength tests in different conditions were collected,trained, and tested by means of artificial neural networks. The obtainedresults have been compared by experimental ones to evaluate the softwarepower for predicting the compressive strength of the geopolymer specimens.

EXPERIMENTAL PROCEDURE

The cementitious materials used in this work were FA and RHBA. Theirchemical composition has been illustrated in Table 1. In addition, Figure 1shows scanning electron microscopy (SEM) micrograph of the cementitiousmaterials, respectively. The as-received ashes were sieved and the particlespassing the finesses of 150 mm and 33 mm were grinded using Los Angelesmill for 30 and 180min, respectively, which yielded two different samples foreach of FA and RHBA. The average particle sizes obtained for FA were75 mm (coarser FA named cF in this study) and 3 mm (finer FA named fF inthis study) with the BET specific surface of 31.3 and 38.9 m2/g, respectively.

Prediction of Compressive Strength of Geopolymers 3




Figure 1. Scanning electron microscope (SEM) micrograph of (a) fly ash (FA) and (b) ricehusk�bark ash (RHBA) used in this study.

Table 1. Chemical composition of FA, RHBA, and WG (Wt.%).

Material SiO2 Al2O3 Fe2O3 CaO SO3 Na2O Loss on ignition

FA 35.21 23.23 12.36 20.01 2.36 0.36 0.24RHBA 81.36 0.4 0.12 3.23 0.85 — 3.55WG 34.21 — — — — 13.11 —

Note. FA: fly ash, RHBA: rice husk�bark ash, WG: water glass.

4 A. NAZARI ET AL.




The average particle sizes obtained for RHBA were 90 mm (coarser RHBA

named cR in this study) and 7 mm (finer RHBA named fR in this study) with

the BET specific surface of 26 and 33.1 m2/g, respectively. The four pro-

duced samples were used in the experiment. Figure 2 shows the particle size

distribution of the four produced samples.Sodium silicate solution or water glass (WG) and sodium hydroxide

(NaOH) were used as the solution part of the mixture. The WG was used

without following modification, but the NaOH was diluted to different con-

centrations before using. The chemical composition of the utilized WG is

also given in Table 1.Totally four series of geopolymer specimens each contain two different

mixture of FA and RHBA as illustrated in Table 2 were prepared for com-

pressive strength tests. The mixed alkali activator of sodium silicate solution

and NaOH was used. The NaOH was diluted by tap water to have concen-

trations of 4, 8, and 12M. The solution was left under ambient conditions

until the excess heat had completely dissipated to avoid accelerating the

setting of the geopolymeric specimens. The sodium silicate solution without

preparation was mixed with the NaOH solution. The ratio of the sodium

silicate solution to NaOH solution was 2.5 by weight for all mixtures

because this ratio demonstrated the best properties for FA-based geopoly-

mer (Pacheco-Torgal et al., 2005, 2007). For all samples, the mass ratio of

alkali activator to FA�RHA mixture was 0.4. Pastes were mixed by shaking

for 5�10min to give complete homogenization. The mixtures were cast in

ø30mm� 60mm polypropylene cylinders. The mixing was done in an air-

conditioned room at approximately 25�C. The molds were half-filled,

vibrated for 45 s, filled to the top, again vibrated for 45 s, and sealed with

the lid. The mixtures were then precured for 24 h at room temperature (this

precuring time has been found to be beneficial to strength development;

Bakharev, 2005). Precuring time before application of heat induces

0102030405060708090

100

0 20 40 60 80 100 120 140

Per

cen

tag

e fi

ner

th

an

Particle size (µm)

Coarse FA

Fine FA

Coarse RHBA

Fine RHBA

Figure 2. Particle size distribution pattern of the different ashes used in this study.





significant dissolution of silica and alumina from FA and formation of a

continuous matrix phase, increasing, therefore, the homogeneity of the geo-

polymeric materials (Chindaprasirt et al., 2007; Zuhua et al., 2009). After

the precuring process, the samples and molds were placed in a water bath to

prevent moisture loss and the carbonation of the surface. One batch of these

samples was placed in an air-conditioned room at 25�C. The other batch was

put in the oven at elevated temperatures of 50�90�C for 36 h. To determine

the most effective alkali concentration on compressive strength, one set of

the specimens cured at 80�C for 36 h were subjected to compressive strength

tests. Afterwards, the other sets of samples were tested at 7 and 28 days of

curing (for the specimens cured in elevated temperature, the time of oven-

curing were also considered).The compressive strength results of the produced specimens were mea-

sured on the cylindrical samples. The tests were carried out triplicately and

average strength values were obtained.The microstructural characteristic of geopolymeric specimens, which was

made at the optimum condition and had a high compressive strength, was

analyzed using Fourier transform infrared spectroscopy (FTIR). The

powder samples were mixed with KBr at a concentration of 0.2�1.0wt%

Table 2. Mixture proportioning of the utilized FA and RHBA to producegeopolymeric specimens.a

Sampledesignation

Weightpercent of

fine FA(fF wt%)

Weightpercent ofcoarse FA(cF wt%)

Weightpercent offine RHBA(fR wt%)

Weightpercent of

coarse RHBA(cR wt%)

SiO2/Al2O3

ratio

fF�fR-1 60 0 40 0 3.81fF�fR-2 70 0 30 0 2.99fF�fR-3 80 0 20 0 2.38fF�cR-1 60 0 0 40 3.81fF�cR-2 70 0 0 30 2.99fF�cR-3 80 0 0 20 2.38cF�fR-1 0 60 40 0 3.81cF�fR-2 0 70 30 0 2.99cF�fR-3 0 80 20 0 2.38cF�cR-1 0 60 0 40 3.81cF�cR-2 0 70 0 30 2.99cF�cR-3 0 80 0 20 2.38

Note. FA: fly ash, RHBA: rice husk�bark ash, fF: fine fly ash, cF: coarse fly ash, fR: fine rice husk�barkash, cR: coarse rice husk�bark ash, WG: water glass, NaOH: sodium hydroxide.aAlkali activator (WGþNaOH) to FA�RHBA mixture ratio is 0.4.

6 A. NAZARI ET AL.




to make the KBr disks. Then the disks were evaluated using a Perkin ElmerFTIR microscope.

EXPERIMENTAL RESULTS AND DISCUSSION

Compressive Strength

To determine the effect of NaOH concentration on compressive strengthof the specimens, one series of the specimens (fF�fR series) were randomlyselected, produced by different concentrations of NaOH (4, 8, and 12M)and subjected to compressive strength tests after 36 h oven curing. Figure 3shows the effects of NaOH concentration on compressive strength of thefF�fR series specimens cured for 36 h at 80�C. As Figure 3 shows, thecompressive strength by the geopolymers synthesized using the most con-centrated alkaline solution (12M NaOH) was the highest for mixtures.Zuhua et al. (2009) reported that the use of high molarities NaOH (suchas 12M) could accelerate dissolution and hydrolysis but obstruct polycon-densation. Thus, 12M NaOH can be considered as the suitable solution forpreparing geopolymer specimens. Therefore, as the way discussed in theexperimental section, the specimens were produced by 12M NaOH solutionand were cured at the mentioned time and temperatures.

The compressive strength of the produced specimens has been illustratedin Figures 4 and 5 for 7 and 28 days of curing. Figures 4 and 5 show that thebest strength has been achieved for fF�fR2 specimen cured at 80�C for 36 h

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12 14

Co

mp

ress

ive

stre

ng

th (

Mp

a)

Concentration of NaOH (M)

fF-fR-1

fF-fR-2

fF-fR-3

Figure 3. The effect of sodium hydroxide (NaOH) concentration on compressive strength offine fly ash (fF)�fine rice husk�bark ash (fR) series specimens cured at 80�C for 36 h.





05

101520253035404550

Co

mp

ress

ive

stre

ng

th (

Mp

a)

Oven curing temperature (°C)

Compressive strength of fF-fR series at 7 days of curing(a)

(b)

fF-fR-1

fF-fR-2

fF-fR-3

05

1015202530354045

Co

mp

ress

ive

stre

ng

th (

Mp

a)


Compressive strength of fF-cR series at 7 days of curing

fF-cR-1

fF-cR-2

fF-cR-3

0 20 40 60 80 100

0 20 40 60 80 100

(c)

(d)

0

5

10

15

20

25

30

35

Co

mp

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Compressive strength of cF-fR series at 7 days of curing

cF-fR-1

cF-fR-2

cF-fR-3

0

5

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25

30

0 20 40 60 80 100

0 20 40 60 80 100

Co

mp

ress

ive

stre

ng

th (

Mp

a)


Compressive strength of cF-cR series at 7 days of curing

cF-cR-1

cF-cR-2

cF-cR-3

Figure 4. In all, 7 days compressive strength of (a) fine fly ash (fF)�fine rice husk�bark ash(fR), (b) fF�coarse rice husk�bark ash (cR), (c) coarse fly ash (cF)�fR, and (d) cF�cR seriesspecimens.

8 A. NAZARI ET AL.




0

10

20

30

40

50

60

70

Co

mp

ress

ive

stre

ng

th (

Mp

a)


Compressive strength of fF-fR series at 28 days of curing(a)

(b)

fF-fR-1

fF-fR-2

fF-fR-3

0

10

20

30

40

50

60

Co

mp

ress

ive

stre

ng

th (

Mp

a)


Compressive strength of fF-cR series at 28 days of curing

fF-cR-1

fF-cR-2

fF-cR-3

0 20 40 60 80 100

0 20 40 60 80 100

(c)

(d)

05

101520253035404550

Co

mp

ress

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Mp

a)


Compressive strength of cF-fR series at 28 days of curing

cF-fR-1

cF-fR-2

cF-fR-3

0

5

10

15

20

25

30

35

40

0 20 40 60 80 100

0 20 40 60 80 100

Co

mp

ress

ive

stre

ng

th (

Mp

a)


Compressive strength of cF-cR series at 28 days of curing

cF-cR-1

cF-cR-2

cF-cR-3

Figure 5. In all, 28 days compressive strength of (a) fine fly ash (fF)�fine rice husk�bark ash(fR), (b) fF�coarse rice husk�bark ash (cR), (c) coarse fly ash (cF)�fR, and (d) cF�cR seriesspecimens.





in both 7 and 28 days curing regimes. As Figures 4 and 5 show, the optimumcuring condition for the all mixtures is at 80�C. Curing temperature has asignificant effect on the compressive strength development because it affectsspecimens setting and hardening. Synthesized products are known to be verysensitive to experimental conditions (Fernandez-Jimenez et al., 2007).However, compressive strength begins to decrease after curing for a certainperiod of time at higher temperatures. Prolonged curing at higher temper-atures can break down the granular structure of geopolymer mixture. Thisresults in dehydration and excessive shrinkage due to contraction of the gel,which does not transform into a more semicrystalline form (van Jaarsveldet al., 2002).

On the whole, samples made with the fine RHBA and FA particles (fF-fRseries) showed considerably higher strength than the other series. This maybe due to production of more compacted specimens. Fine particles are capa-ble of filling the vacancies and producing more densified specimens, whichmake them stronger to the applied loads. This has been confirmed in someworks done on concrete specimens (Naji Givi et al., 2010), but as authors’knowledge there is not any reports to confirm this matter in geopolymers.On the other hand, the fine particle with high surface areas enabled the silicaand alumina leaching out to the solution and enhanced the geopolymeriza-tion (Chindaprasirt et al., 2011).

FTIR Results

Geopolymers are composed from Si�O tetrahedrons, which are connectedvia corner sharing bridging oxygen. The connectivity of the tetrahedrons isspecified by the number of bridging oxygen. Tetrahedrons with n bridgingoxygens are denoted Qn (n¼ 0, 1, 2, 3, or 4). Thus, silicon in Q3 configura-tion is surrounded by three bridging oxygen and a nonbridging oxygen.Amorphous SiO2 is assumed to consist of only Q4 species forming a contin-uous random network (Karlsson et al., 2005). The FTIR spectra of theinorganic polymers synthesized using different NaOH concentrations areshown in Figure 6. In Figure 6, the IR bands are identified as follows:Si�O stretching is located in the range 1000�1200 cm�1, Si�O bending isfound at 800 cm�1 and between 890 and 975 cm�1. The band at approxi-mately 1100 cm�1 is assigned to the Si�O stretching of Q4 units and the bandat 1050 cm�1 is assigned to Q3 units with a nonbridging oxygen(Si�O�NBO) per SiO4 tetrahedron (Zholobenko et al., 1997).

From Figure 6, it is seen that an increase in the fF particles shifts theposition of the maximum absorbance of Si�O bands toward lower wavenumbers, indicating the transformation of Q4 units to Q3 units. Moreover,the emerging of a new band centered on 900 cm�1 is observed, which is

10 A. NAZARI ET AL.




assigned to Si�O stretching of Q2 unit with two nonbridging oxygen perSiO4 tetrahedron (Serra et al., 2002). The observed increase in the signal at2380 cm�1 can be assigned to CO2 which has reacted with increasingamounts of NaOH leading to the formation of HCO�3 .

GENETIC PROGRAMMING

The GP proposed by Koza (Rosenblatt, 1962) is an extension to geneticalgorithms (GA). Koza (Rosenblatt, 1962) defines GP as a domain indepen-dent problem-solving approach in which computer programs are evolved tosolve, or approximately solve, problems based on the Darwinian principle ofreproduction and survival of the fittest and analogs of naturally occurringgenetic operations such as crossover and mutation. The GP reproducescomputer programs to solve problems by executing the steps as shown inFigure 7. This figure is a flowchart showing the executional steps of a run ofGP. The flowchart demonstrates the genetic operations in addition to thearchitecture chancing operations. Also, this flowchart demonstrates a twooffspring version of the crossover operation.

The GEP software which is used in this study is an extension to GEP thatevolves computer programs of different sizes and shapes encoded in linearchromosomes of fixed length. The chromosomes are composed of multiplegenes, each gene encoding a smaller subprogram. Furthermore, the struc-tural and functional organization of the linear chromosomes allows the

Figure 6. The Fourier transform infrared spectroscopy (FTIR) results of the selectedspecimens: (a) fine fly ash (fF)�fine rice husk�bark ash (fR)-2, (b) fF�coarse rice husk�barkash (cR)-2, (c) coarse fly ash (cF)�fR-2, and (d) cF�cR specimens.





unconstrained operation of important genetic operators such as mutation,transposition, and recombination (Anderson, 1983; Rumelhart et al., 1986;

Liu et al., 2002). The two main parameters of GEP are the chromosomes

and expression trees (ETs; Anderson, 1983; Rumelhart et al., 1986; Liu

et al., 2002). Two languages are utilized in GEP: the language of the

genes and the language of ETs. A significant advantage of GEP is that it

Figure 7. Genetic programming flowchart (Karlsson et al., 2005).

12 A. NAZARI ET AL.




enables to infer exactly the phenotype given the sequence of a gene and viceversa, which is termed as Karva language.

For each problem, the type of linking function, as well as the number ofgenes and the length of each gene, are a priori chosen for each problem.While attempting to solve a problem, one can always start by using a single-gene chromosome and then proceed by increasing the length of the head.If it becomes very large, one can increase the number of genes and obvi-ously choose a function to link the sub-ETs. One can start with additionfor algebraic expressions or for Boolean expressions, but in some cases,another linking function might be more appropriate (like multiplicationor if, for instance). The idea, of course, is to find a good solution,and GEP provides the means of finding one very efficiently (Rumelhartet al., 1986).

GEP Structure and Parameters

In this study, as seen in Figures 8 and 9, the ETs of two different GEPapproach models, namely GEP-I and GEP-II, were constructed for com-pressive strength values of geopolymers. The d0, d1, d2, d3, d4, and d5 inFigures 8 and 9 represent the values for input layers, which were the per-centage of fine fly ash in the ashes mixture (fF), the percentage of coarse flyash in the ashes mixture (cF), the percentage of fine rice husk bark ash in theashes mixture (fR), the percentage of coarse rice husk bark ash in the ashesmixture (cR), the temperature of curing (T) and the time of water curing (t),respectively. In the GEP-I and GEP-II, the number of genes used three andfour genes (Sub-ETs), and linking function used addition and multiplica-tion, respectively. In training and testing of the GEP-I and GEP-II approachmodels constituted with two different Sub-ETs and linking function fF, cF,fR, cR, T, and t as input data and compressive strength values of geopoly-mers as independent output data. Among 120 experimental sets, 94 sets wererandomly chosen as a training set for the GEP-I and GEP-II modeling andthe remaining 26 sets were used as testing the generalization capacity of theproposed models.

For this problem, firstly, the fitness, fi, of an individual program, i, ismeasured by:

fi ¼XCt

j¼1ðM� jCðij Þ � Tj jÞ ð1Þ

whereM is the range of selection, C(i,j) is the value returned by the individualchromosome i for fitness case j (out of Ct fitness cases), and Tj is the targetvalue for fitness case j. If jCðij Þ � Tj j (the precision) is less than or equal to0.01, then the precision is equal to zero, and fi¼ fmax¼CtM. In this case,





M¼ 100 was used, therefore, fmax¼ 1000. The advantage of this kind offitness functions is that the system can find the optimal solution by itself(Hopfield, 1982; Cevik and Sonebi, 2009).

Afterwards, the set of terminals T and the set of functions F to create thechromosomes are preferred, namely, T¼ {fF, cF, fR, cR, T, t} and fourbasic arithmetic operators (þ, �, �, and /) and some basic mathematicalfunctions (Sqrt, x3) were used.

Another major step is to choose the chromosomal tree, that is, the lengthof the head and the number of genes. The GEP-I and GEP-II approachmodels initially used single gene and two lengths of heads, and increased the

Figure 8. Expression tree with three genes for predicting compressive strength in geneexpression programming-I (GEP-I) model. C0¼ 11.21 and C1¼�6.47.

14 A. NAZARI ET AL.




Figure 9. Expression tree with four genes for predicting compressive strength in geneexpression programming-II (GEP-II) model. C0¼ 3.54, c1¼ 8.99.





number of genes and heads, one after another during each run, and moni-

tored the training and testing sets performance of each model. In this study,

for the GEP-I and GEP-II approach models observed the number of genes 3

and 4, and length of heads 10 and 12, respectively. In addition, for the GEP-

I and GEP-II approach models determined the linking function multiplica-

tion and addition, respectively.Finally, a combination of all genetic operators (mutation, transposition,

and crossover) was utilized as set of genetic operators. Parameters of the

Table 3. Parameters of GEP approach models.

Parameter definition GEP-I GEP-II

P1 Function set þ, �, �, /, sqrt, x3þ, �, �, /, sqrt, x3

P2 Chromosomes 30 40P3 Head size 12 14P4 Number of genes 3 4P5 Linking function Addition MultiplicationP6 Mutation rate 0.044 0.044P7 Inversion rate 0.1 0.1P8 One-point recombination rate 0.3 0.3P9 Two-point recombination rate 0.3 0.3P10 Gene recombination rate 0.1 0.1P11 Gene transposition rate 0.1 0.1

Note. GEP: gene expression programming.

Figure 10. Chromosome with two genes and its decoding in gene expression programming(GEP; Cevik and Sonebi, 2009).

16 A. NAZARI ET AL.




training of the GEP-I and GEP-II approach models are given in Table 3.

For the GEP-I and GEP-II approach models, chromosome 30 and 40

were observed to be the best of generation individuals predicting compres-

sive strength. Explicit formulations based on the GEP-I and GEP-II

approach models for fs were obtained by:

CVN ¼ f fF, cF, fR, cR,T, tð Þ: ð2Þ

The related formulations could be obtained by the procedure shown in

Figure 10 (Cevik and Sonebi, 2009).

y = 0.9057x + 2.5473R² = 0.9624

GEP-I

y = 1.0024x + 0.1424R² = 0.9765

GEP-II

0

10

20

30

40

50

60

70(a)

(b)

Pred

icte

d C

ompr

essi

ve S

tren

gth

(MPa

)

Experimental Compressive Strength (MPa)

GEP-I

GEP-II

y = 0.9057x + 2.5473R² = 0.9624

GEP-I

y = 1.0024x + 0.1424R² = 0.9765

GEP-II

0

10

20

30

40

50

60

70

0 20 40 60 80

0 20 40 60 80

Pred

icte

d C

ompr

essi

ve S

tren

gth

(MPa

)

Experimental Compressive Strength (MPa)

GEP-I

GEP-II

Figure 11. The correlation of the measured and predicted compressive strength values ofgeopolymers in (a) training and (b) testing phase for GEP models.





Tab

le4

.D

ata

sets

for

co

mp

ari

son

of

exp

eri

me

nta

lre

sult

sw

ith

resu

lts

pre

dic

ted

fro

mth

eG

EP

mo

de

ls.

Th

ep

erc

en

tag

eo

ffi

ne

fly

ash

inth

ea

sh

es

mix

ture

(fF

)

Th

ep

erc

en

tag

eo

fco

ars

efl

ya

sh

inth

ea

sh

es

mix

ture

(cF

)

Th

ep

erc

en

tag

eo

ffi

ne

rice

hu

sk

�b

ark

ash

inth

ea

sh

es

mix

ture

(fR

)

Th

ep

erc

en

tag

eo

fco

ars

eri

ce

hu

sk

�b

ark

ash

inth

ea

sh

es

mix

ture

(cR

)

Th

ete

mp

era

ture

of

cu

rin

g(T

)

Th

eti

me

of

wa

ter

cu

rin

g(t

)

Co

mp

ressiv

estr

en

gth

va

lue

so

bta

ine

dfr

om

exp

eri

me

nts

(MP

a)

Co

mp

ressiv

estr

en

gth

va

lue

sp

red

icte

db

yG

EP

-Im

od

el

(MP

a)

Co

mp

ressiv

estr

en

gth

va

lue

sp

red

icte

db

yG

EP

-II

mo

de

l(M

Pa

)

60

04

00

25

72

7.1

26

.82

5.7

70

03

00

25

73

73

6.1

35

.78

00

20

02

57

33

.43

2.5

32

.86

00

04

02

57

24

.72

4.1

24

.97

00

03

02

57

33

.72

9.4

34

.78

00

02

02

57

30

.53

0.4

30

.90

60

40

02

57

19

.72

2.9

19

.60

70

30

02

57

26

.92

7.4

26

.90

80

20

02

57

24

.32

4.4

20

.70

60

04

02

57

14

.81

5.3

17

.50

70

03

02

57

20

.21

9.8

24

.10

80

02

02

57

18

.21

8.5

18

.96

00

40

04

07

30

.42

9.7

29

.27

00

30

04

07

39

.23

8.7

39

.78

00

20

04

07

35

.43

4.5

35

60

00

40

40

72

7.7

26

.92

6.6

70

00

30

40

73

5.8

30

.23

7.2

80

00

20

40

73

2.3

30

.33

2.5

06

04

00

40

72

2.1

23

.22

0.8

07

03

00

40

72

8.5

28

.22

7.8

08

02

00

40

72

5.8

25

.22

2.9

06

00

40

40

71

6.5

17

17

.50

70

03

04

07

21

.41

9.5

23

.10

80

02

04

07

19

.31

9.3

19

.9

(co

ntin

ue

d)

18 A. NAZARI ET AL.




Ta

ble

4.

Co

ntin

ue

d

Th

ep

erc

en

tag

eo

ffi

ne

fly

ash

inth

ea

sh

es

mix

ture

(fF

)

Th

ep

erc

en

tag

eo

fco

ars

efl

ya

sh

inth

ea

sh

es

mix

ture

(cF

)

Th

ep

erc

en

tag

eo

ffi

ne

rice

hu

sk

�b

ark

ash

inth

ea

sh

es

mix

ture

(fR

)

Th

ep

erc

en

tag

eo

fco

ars

eri

ce

hu

sk

�b

ark

ash

inth

ea

sh

es

mix

ture

(cR

)

Th

ete

mp

era

ture

of

cu

rin

g(T

)

Th

eti

me

of

wa

ter

cu

rin

g(t

)

Co

mp

ressiv

estr

en

gth

va

lue

so

bta

ine

dfr

om

exp

eri

me

nts

(MP

a)

Co

mp

ressiv

estr

en

gth

va

lue

sp

red

icte

db

yG

EP

-Im

od

el

(MP

a)

Co

mp

ressiv

estr

en

gth

va

lue

sp

red

icte

db

yG

EP

-II

mo

de

l(M

Pa

)

60

04

00

60

73

1.9

32

.13

1.3

70

03

00

60

74

1.7

41

.34

2.1

80

02

00

60

73

7.2

37

37

.26

00

04

06

07

29

.13

1.3

28

.77

00

03

06

07

38

34

.44

18

00

02

06

07

33

.93

2.9

34

.20

60

40

06

07

23

.22

4.9

23

.40

70

30

06

07

30

.33

0.9

30

08

02

00

60

72

72

7.8

26

06

00

40

60

71

7.4

19

.11

7.3

07

00

30

60

72

2.7

21

.42

30

80

02

06

07

20

.22

0.4

20

.76

00

40

08

07

34

.83

2.8

34

.57

00

30

08

07

44

.24

2.7

43

.38

00

20

08

07

39

.63

8.3

39

.36

00

04

08

07

31

.83

1.9

32

70

00

30

80

74

0.3

35

.24

3.8

80

00

20

80

73

6.1

33

.33

70

60

40

08

07

25

.32

6.4

26

.30

70

30

08

07

32

.13

2.3

32

.40

80

20

08

07

28

.82

7.8

29

.10

60

04

08

07

19

19

.51

7.7

07

00

30

80

72

4.1

22

22

.30

80

02

08

07

21

.52

0.9

20

60

04

00

90

73

2.4

32

.33

2.3

(co

ntin

ue

d)





Ta

ble

4.

Co

ntin

ue

d

Th

ep

erc

en

tag

eo

ffi

ne

fly

ash

inth

ea

sh

es

mix

ture

(fF

)

Th

ep

erc

en

tag

eo

fco

ars

efl

ya

sh

inth

ea

sh

es

mix

ture

(cF

)

Th

ep

erc

en

tag

eo

ffi

ne

rice

hu

sk

�b

ark

ash

inth

ea

sh

es

mix

ture

(fR

)

Th

ep

erc

en

tag

eo

fco

ars

eri

ce

hu

sk

�b

ark

ash

inth

ea

sh

es

mix

ture

(cR

)

Th

ete

mp

era

ture

of

cu

rin

g(T

)

Th

eti

me

of

wa

ter

cu

rin

g(t

)

Co

mp

ressiv

estr

en

gth

va

lue

so

bta

ine

dfr

om

exp

eri

me

nts

(MP

a)

Co

mp

ressiv

estr

en

gth

va

lue

sp

red

icte

db

yG

EP

-Im

od

el

(MP

a)

Co

mp

ressiv

estr

en

gth

va

lue

sp

red

icte

db

yG

EP

-II

mo

de

l(M

Pa

)

70

03

00

90

74

1.7

42

.14

1.3

80

02

00

90

73

7.7

37

.73

86

00

04

09

07

29

.63

2.1

29

.97

00

03

09

07

38

35

.14

0.2

80

00

20

90

73

4.4

32

.63

5.9

06

04

00

90

72

3.6

25

.52

6.9

07

03

00

90

73

0.3

26

.22

50

80

20

09

07

27

.42

6.8

29

.10

60

04

09

07

17

.72

01

7.7

07

00

30

90

72

2.7

22

.22

1.8

08

00

20

90

72

0.5

21

.51

8.7

60

04

00

25

28

36

.13

5.4

35

70

03

00

25

28

49

.34

7.8

48

.48

00

20

02

52

84

4.5

42

.64

7.7

60

00

40

25

28

32

.53

5.4

32

.57

00

03

02

52

84

4.4

38

.94

3.6

80

00

20

25

28

40

.13

4.8

40

.70

60

40

02

52

82

72

82

7.4

07

03

00

25

28

36

.93

6.2

38

.50

80

20

02

52

83

3.3

33

.43

50

60

04

02

52

82

0.8

23

.72

4.8

07

00

30

25

28

28

.42

6.5

34

.60

80

02

02

52

82

5.6

24

.62

7.7

60

04

00

40

28

40

.53

9.5

39

.57

00

30

04

02

85

2.3

52

.75

2.4

(co

ntin

ue

d)

20 A. NAZARI ET AL.




Ta

ble

4.

Co

ntin

ue

d

Th

ep

erc

en

tag

eo

ffi

ne

fly

ash

inth

ea

sh

es

mix

ture

(fF

)

Th

ep

erc

en

tag

eo

fco

ars

efl

ya

sh

inth

ea

sh

es

mix

ture

(cF

)

Th

ep

erc

en

tag

eo

ffi

ne

rice

hu

sk

�b

ark

ash

inth

ea

sh

es

mix

ture

(fR

)

Th

ep

erc

en

tag

eo

fco

ars

eri

ce

hu

sk

�b

ark

ash

inth

ea

sh

es

mix

ture

(cR

)

Th

ete

mp

era

ture

of

cu

rin

g(T

)

Th

eti

me

of

wa

ter

cu

rin

g(t

)

Co

mp

ressiv

estr

en

gth

va

lue

so

bta

ine

dfr

om

exp

eri

me

nts

(MP

a)

Co

mp

ressiv

estr

en

gth

va

lue

sp

red

icte

db

yG

EP

-Im

od

el

(MP

a)

Co

mp

ressiv

estr

en

gth

va

lue

sp

red

icte

db

yG

EP

-II

mo

de

l(M

Pa

)

80

02

00

40

28

47

.24

5.7

47

.46

00

04

04

02

83

6.5

35

.73

4.4

70

00

30

40

28

47

.14

0.7

47

.18

00

02

04

02

84

2.5

37

.74

3.4

06

04

00

40

28

30

.33

0.3

30

.40

70

30

04

02

83

9.1

38

.44

0.5

08

02

00

40

28

35

.33

53

6.4

06

00

40

40

28

23

.32

3.8

24

.30

70

03

04

02

83

0.1

28

.53

2.4

08

00

20

40

28

27

.22

5.6

28

.86

00

40

06

02

84

2.5

42

.64

1.9

70

03

00

60

28

55

.65

5.5

55

.38

00

20

06

02

84

9.6

48

.24

9.8

60

00

40

60

28

38

.33

9.4

36

.37

00

03

06

02

85

04

55

0.3

80

00

20

60

28

44

.64

4.3

45

.60

60

40

06

02

83

1.8

32

.63

4.3

07

03

00

60

28

41

.54

2.2

42

.70

80

20

06

02

83

73

9.6

37

.10

60

04

06

02

82

4.5

25

.12

5.2

07

00

30

60

28

32

30

.93

2.7

08

00

20

60

28

28

.52

9.1

29

.56

00

40

08

02

84

6.4

44

.24

4.7

70

03

00

80

28

58

.95

5.8

59

.3

(co

ntin

ue

d)





Ta

ble

4.

Co

ntin

ue

d

Th

ep

erc

en

tag

eo

ffi

ne

fly

ash

inth

ea

sh

es

mix

ture

(fF

)

Th

ep

erc

en

tag

eo

fco

ars

efl

ya

sh

inth

ea

sh

es

mix

ture

(cF

)

Th

ep

erc

en

tag

eo

ffi

ne

rice

hu

sk

�b

ark

ash

inth

ea

sh

es

mix

ture

(fR

)

Th

ep

erc

en

tag

eo

fco

ars

eri

ce

hu

sk

�b

ark

ash

inth

ea

sh

es

mix

ture

(cR

)

Th

ete

mp

era

ture

of

cu

rin

g(T

)

Th

eti

me

of

wa

ter

cu

rin

g(t

)

Co

mp

ressiv

estr

en

gth

va

lue

so

bta

ine

dfr

om

exp

eri

me

nts

(MP

a)

Co

mp

ressiv

estr

en

gth

va

lue

sp

red

icte

db

yG

EP

-Im

od

el

(MP

a)

Co

mp

ressiv

estr

en

gth

va

lue

sp

red

icte

db

yG

EP

-II

mo

de

l(M

Pa

)

80

02

00

80

28

52

.85

0.9

53

.36

00

04

08

02

84

1.8

41

.74

07

00

03

08

02

85

34

6.3

53

.28

00

02

08

02

84

7.5

43

.94

7.8

06

04

00

80

28

34

.73

4.4

35

.40

70

30

08

02

84

44

3.5

43

.80

80

20

08

02

83

9.4

40

.53

8.3

06

00

40

80

28

26

.72

6.2

25

07

00

30

80

28

33

.93

1.6

32

.10

80

02

08

02

83

0.3

28

.62

86

00

40

09

02

84

3.2

42

.74

3.5

70

03

00

90

28

55

.65

4.6

58

.48

00

20

09

02

85

0.2

50

.35

1.7

60

00

40

90

28

38

.94

1.9

37

.57

00

03

09

02

85

04

5.7

50

.18

00

02

09

02

84

5.2

41

.34

60

60

40

09

02

83

2.3

33

.33

3.7

07

03

00

90

28

41

.54

1.9

42

.10

80

20

09

02

83

7.5

38

.83

6.8

06

00

40

90

28

24

.92

5.8

24

.40

70

03

09

02

83

23

1.2

30

.90

80

02

09

02

82

8.9

27

.92

6.4

No

te.

GE

P:

ge

ne

exp

ress

ion

pro

gra

mm

ing

.

22 A. NAZARI ET AL.




PREDICTED RESULTS AND DISCUSSION

In this study, the error that arose during the training and testing in GEP-Iand GEP-II models can be expressed as absolute fraction of variance (R2),which is calculated by Equation (3) [Topcu and Sarıdemir, 2008]:

R2 ¼ 1�

Pi ðti � oiÞ

2Pi ðoiÞ

2

!ð3Þ

where t is the target value and o is the output value.All of the results obtained from experimental studies and predicted by

using the training and testing results of GEP-I and GEP-II models are givenin Figures 11(a) and (b), respectively. The linear least square fit line, itsequation, and the R2 values were shown in these figures for the trainingand testing data. Also, inputs values and experimental results with trainingand testing results obtained from GEP-I and GEP-II models are given inTable 4. As it is visible in Figure 11, the values obtained from the trainingand testing in GEP-I and GEP-II models are very close to the experimentalresults. The result of testing phase in Figure 11 shows that the GEP-I andGEP-II models are capable of generalizing between input and output vari-ables with reasonably good predictions.

The performance of the GEP-I and GEP-II models is shown in Figure 11.The best value of R2 is 97.650% for training set in the GEP-II model. Theminimum value of R2 is 95.22% for testing set in the GEP-I model. All of R2

values show that the proposed GEP-I and GEP-II models are suitable andcan predict the compressive strength values very close to the experimentalvalues.

CONCLUSIONS

From the experimental procedure, the following results were obtained:

1. The compressive strength of the specimens depends on the particle size ofthe ashes, time of oven curing, and the time of room condition curing.The finer the ashes particle size results in the denser and hence the stron-ger specimen. On the other hand, oven curing of the specimens at 80�Cwas found to be the optimum temperature of curing in geopolymericspecimens.

2. The GEP can be an alternative approach for the evaluation of the effectof seeded mixture of FA and RHBA on compressive strength values ofgeopolymer specimens.





3. Comparison between GEP models in terms of R2 showed that GEP

models are capable of predicting suitable results for compressive strengthvalues of geopolymer specimens.

REFERENCES

Alvarez-Ayuso, E., Querol, X., Plan, F., Alastuey, A., Moreno, N., Izquierdo, M. et al. (2008).Environmental, Physical and Structural Characterisation of Geopolymer MatrixesSynthesised from Coal (Co-)Combustion Fly Ashes, Journal of Hazardous Materials,154: 175�183.

Anderson, J.A. (1983). Cognitive and Psychological Computation with Neural Models, IEEETransactions on Systems, Man, and Cybernetics, SMC-13: 799�814.

Bakharev, T. (2005). Geopolymeric Materials Prepared Using Class F Fly Ash and ElevatedTemperature Curing, Cement and Concrete Research, 35: 1224�1232.

Cevik, A. (2007). A New Formulation for Longitudinally Stiffened Webs Subjected to PatchLoading, Journal of Constructional Steel Research, 63: 1328�1340.

Cevik, A. and Guzelbey, I.H. (2007). A Soft Computing Based Approach for the Prediction ofUltimate Strength of Metal Plates in Compression, Engineering Structures, 29: 383�394.

Cevik, A. and Sonebi, M. (2008). Modelling the Performance of Self-Compacting SIFCON ofCement Slurries Using Genetic Programming Technique, Computers and Concrete, 5:475�490.

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Prediction of Compressive Strength of Geopolymers with Seeded Fly Ash and Rice Husk-Bark Ash by Gene Expression Programming