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Journal of Cleaner Production 210 (2019) 837e846

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Journal of Cleaner Production

journal homepage: www.elsevier .com/locate/ jc lepro

Application of statistical analysis to evaluate the corrosion resistanceof steel rebars embedded in concrete with marble and granite wastedust

Iman Taji a, Saeid Ghorbani b, Jorge de Brito c, *, Vivian W.Y. Tam d, e, Sohrab Sharifi b,Ali Davoodi a, Mohammadreza Tavakkolizadeh b

a Ferdowsi University of Mashhad, Faculty of Engineering, Department of Metallurgical and Materials Engineering, Mashhad 91775-1111, Iranb Ferdowsi University of Mashhad, Faculty of Engineering, Department of Civil Engineering, Mashhad 91775-1111, Iranc Department of Civil Engineering, Architecture and Georesources, Instituto Superior T�ecnico, Universidade de Lisboa, Lisbon, Portugald Western Sydney University, School of Computing, Engineering and Mathematics, Locked Bag 1797, Penrith, NSW 2751, Australiae College of Civil Engineering, Shenzhen University, China

a r t i c l e i n f o

Article history:Received 2 October 2018Received in revised form6 November 2018Accepted 9 November 2018Available online 12 November 2018

Keywords:StrengthCorrosion resistanceGranite and marble waste dustStatistical analysis

* Corresponding author.E-mail addresses: Imantaji@um.ac.ir (I. Taji),

(S. Ghorbani), jb@civil.ist.utl.pt (J. de Brito), V(V.W.Y. Tam), sharifi.sohrab@mail.um.ac.ir (S.(A. Davoodi), drt@um.ac.ir (M. Tavakkolizadeh).

https://doi.org/10.1016/j.jclepro.2018.11.0910959-6526/© 2018 Elsevier Ltd. All rights reserved.

a b s t r a c t

In recent years, the production of waste materials has increased due to the growth of industrial activitiesaround the world. Therefore, recycling and reusing these waste materials for different applications wouldmake a tremendous contribution to waste elimination and sustainable building construction. Theobjective of this paper is to investigate the effect of marble and granite waste dust (MGWD) as a result ofmarble and granite stone processing on concrete properties. To achieve this purpose, a total of 15 mixeswere prepared with up to 30% of MGWD cement replacement. After 28-day immersion of specimens inlime-saturated water, they were placed in a NaCl solution with 3.5% by weight for 90 days. Then, splittingtensile and compressive strength, scanning electron microscopy (SEM), open circuit potential (OCP) andelectrochemical impedance spectroscopy (EIS) tests were performed alongside a statistical analysis. Themechanical results indicate that utilizing MGWD as cement replacement at a maximum amount of 20%does not notably influence the mechanical properties of concrete. The OCP assessment revealed thatusing 10% of granite and 10% of marble waste dust instead of cement enhances the corrosion resistance ofsteel rebars embedded in concrete, and also increases the potential compared to the other tested con-crete mixes.

© 2018 Elsevier Ltd. All rights reserved.

1. Introduction

Sustainable construction throughout recent years has become abig target for civil and environmental engineers since the con-struction industry, as a fundamental part of development, is knownas one of the main consumers of unprocessed materials and also amassive producer of waste (Cachim, 2009; Kwan et al., 2012).Moreover, most of these waste materials have serious environ-mental impacts that have motivated researchers to devise varioussolutions to eliminate them (Tabrizi et al., 2018; Rafieizonooz et al.,

Saeid.ghorbani@mail.um.ac.ir.Tam@westernsydney.edu.auSharifi), a.davodi@um.ac.ir

2016). Further depletion of mineral and natural resources can alsobe mentioned as a consequence of increasing the exploitationdrastically (Tabsh and Abdelfatah, 2009). Concrete has been in usefor a very long time, shorter only than bricks from mud and straws(Brostow and Hagg Lobland, 2017). Given the present growth inconstructions activities and societal trend for development, it isanticipated that the demand for concrete will intensify in the nearfuture. Therefore, recycling and reusing waste materials fordifferent applications would make a tremendous contribution toboth environment and economy. Every year 3000Mt of waste areproduced in the European Union (Bravo et al., 2015). For this reason,many researches have utilized different fillers resulting from de-molition waste such as paving blocks, furnace slag, fly ash, hema-tite, marble and granite waste dust (MGWD) (Alyamac and Aydin,2015; Andr�e et al., 2014; Baeza-Brotons et al., 2014; Brostowet al., 2016; Gencel et al., 2010, 2012; Ghorbani et al., 2018a,b,

Table 1Size distribution of the coarse and fine aggregates (Ghorbani et al., 2018a,b, 2019).

Coarse aggregate Sieve size (mm) Passing percentage (%)37.500 10025.000 95.0019.000 57.5012.500 25.009.500 8.504.750 0.00

Fine aggregate 4.750 1002.360 85.501.180 55.250.600 31.750.300 5.750.150 0.750.075 0.10

I. Taji et al. / Journal of Cleaner Production 210 (2019) 837e846838

2019; Vijayalakshmi and Sekar, 2013). The marble reserve in theworld is assessed to be 15 billion cubic meters and just in Turkey2.500.000 tons of marble waste are produced annually (Alyamacand Aydin, 2015). Also, 20e25% of global granite productionreportedly becomes waste (Vijayalakshmi and Sekar, 2013).Therefore, MGWD has been chosen as fillers in this study. Lately, abroad range of waste materials such as demolition and glass wasteand MGWD have been adopted to produce concrete (Elmoaty,2013). Reportedly, the use of such materials in concrete produc-tion may positively affect the mechanical, durability and work-ability properties (Bhanja and Sengupta, 2002; Corinaldesi andMoriconi, 2010; Ghrici et al., 2007; Li and Zhao, 2003; Pacheco-Torgal et al., 2012; Siddique, 2004). Factories around the worldgenerate huge amounts of dust as byproducts of the marble andgranite aggregate production process; thus, as raw material in agreat variety of applications, and particularly as fillers or cementreplacement in the production of concrete, MGWD could be anadvantageous choice (Abukersh and Fairfield, 2011; Aliabdo et al.,2014; Aruntas et al., 2010; Belaidi et al., 2012; Donza et al., 2002;Elmoaty, 2013; Ergün, 2011; Ghrici et al., 2007; Rana et al., 2015;Rao et al., 2012; Singh et al., 2016a, 2016b; Pacheco-Torgal andCastro-Gomes, 2006; Uyguno�glu et al., 2014). The mechanicalproperties of concrete have been reported to improve due to a fillereffect by replacing part of the sand or cement with marble wastedust (MWD) in concrete production (Aliabdo et al., 2014). More-over, as a partial cement replacement, using up to 10% MWD inconcrete is said to be beneficial for specific mechanical properties,namely splitting tensile (fctm) and compressive strength (fcm)(Ergün, 2011). Gencel et al. (2012) studied the characteristics ofconcrete paving blocks comprisingmarble waste. It was shown thatdifferent attributes of concrete were enhanced during this pro-cedure such as freeze-thaw and wear resistance. Belaidi et al.(2012) proved that the replacement of cement with MWD andnatural pozzolan improved the workability of self-compactingconcrete (SCC). Abukersh and Fairfield's (2011) investigationrevealed that, at the level of 20e50%, using granite waste dust(GWD) had a considerable adverse effect on the fcm of samples,although the impact of this replacement on the tensile strengthwasfound to be negligible (Abukersh and Fairfield, 2011). Vijayalakshmiand Sekar (2013) reported that replacing 15% of sand with GWD inconcrete production had no significant effects on the strength anddurability characteristics of concrete. Ramos et al. (2013) showedthat, during the production of concrete, the granite waste sludgeformed a denser cement paste with higher durability than thecontrol mix. M�armol et al. (2010) experimental results demon-strated that using granite slurry as replacement of ordinary sandimproved the strength of concrete. The utilization of granite cuttingpowder in high-strength concrete was studied by Singh et al.(2016a,b). The experimental results illustrated the optimumamount of this material as partial replacement of fine aggregates as30%, which successfully reduced the costs of concrete production.Besides, the emission of CO2 can be reduced by 12% through using10% MWD as cement replacement (Ergün, 2011; Geso�glu et al.,2012). Therefore, to decrease the air polluting impacts of cementproduction, one may actually consider using MGWD as replace-ment of cement as an efficient procedure. Due to numerous me-chanical advantages, reinforced concrete (RC) has replaced plainconcrete; higher resistance to flexural, shear and axial loads, fewercracking, and greater resistance to impact fall into this category(Zhu et al., 2014). The steel rebars' corrosion (SRC) resistance in RCmembers became a serious issue and is considered the most sig-nificant durability problem of RC elements (Fang et al., 2017; Ji et al.,2015). The penetration of harmful elements, such as sulfate ions,chloride ions, and atmospheric carbon dioxide, into a highly

permeable matrix as concrete has serious impacts on the service-ability of such structures (Pradhan, 2014). Due to a very thin, denseand stable iron-oxide film, called passive layer, steel rebars (SR) inRC members are in the so-called passive state. This film is para-mount in the protection of SR from corrosion by reducing ionsmobility between them and the surrounding concrete. Thus, theSRC rate becomes negligible.

By knowing the pH value, oxygen concentration, and electro-chemical potential near the rebar surface, the chemical composi-tion of this passive layer can be determined (Ahlstr€om et al., 2016).This passive film on the SR surface tends to dissolve when the RCstructure is exposed to an aggressive agent such as chlorides orsulphates. As a result of this exposure, depassivation takes place, inwhich an active state replaces the passive state of the SR. Therefore,considering the degradation of the passive layer, the SRC rate canincrease drastically. It begins when the chloride content at the SR'ssurface exceeds a critical value (Brenna et al., 2017) or penetrationof carbon dioxide from the atmosphere through concrete poresdecreases the alkalinity of the pore's solution (Berrocal et al., 2016).The SRC process is affected by several factors, e.g. carbon dioxidecontent, chloride content, chemical composition of the SR, concretediffusion properties, concrete pH value, existence of voids in theconcrete/SR interface and electrochemical potential of the surfaceof these rebars (Brenna et al., 2017). Unlike for concrete with con-ventional materials, it is not quite evident in RC structures partiallycomposed of MGWD how embedded rebars will behave from theviewpoint of SRC. Thus, the aim of this investigation is to figure outexperimentally and statistically the effect of MGWD on the SRC andmechanical behaviour of RC specimens.

2. Experimental study

2.1. Materials

The materials used in this research include Portland cement(Type II), water, coarse and fine aggregates for concrete production,all acquired locally.

2.1.1. Natural aggregatesLocally available crushed limestone and river sand were used as

aggregate, with 5e25mm and 0.3e4.75mm ranges, respectivelyfor coarse and fine particles. The particle size distribution andphysical properties of the aggregates are provided in Tables 1 and 2.

2.1.2. Marble and granite waste dustMGWDwas gathered and delivered wet from a local marble and

granite production factory nearMashhad, Iran. Therefore, to controlthe ratio of water/cementitious materials, MGWD was totally driedin an oven at 105 �C before partially replacing cement. In this study,

Table 2Physical properties of the fine and coarse aggregates.

Properties Fine aggregates Coarse aggregates

Water absorption (%) 3.95 1.9Existing moisture (%) 2.90 0.8

I. Taji et al. / Journal of Cleaner Production 210 (2019) 837e846 839

two types of waste were used: marble and granite, with specificgravity 2.50 and 2.61, respectively. The MGWD particle size distri-bution is depicted in Fig. 1, and the chemical composition of MGWDis described in (Ghorbani et al., 2018a,b, 2019). As seen there, theGWD is mostly comprised of silica and alumina, while the MWD ismostly comprised of CaO.

2.1.3. Cement and waterType II Portland cement conforming to ASTM C150, manufac-

tured by Zaveh Cement Company was used. The size grading of thecement particles is shown in Fig. 1 and its chemical composition isdescribed in Ghorbani et al. (2018a,b, 2019). The specific gravity ofthe cement used was 3.2. Tap water was used.

Fig. 1. Particle size distribution of cement particles and MGWD.

Table 3Composition of the concrete mixes.

Mix No. Marble (%)a Granite (%)a Mix proportion (kg

Cement

1 0 0 4002 5 0 3803 0 5 3804 10 0 3605 0 10 3606 5 5 3607 10 5 3408 5 10 3409 20 0 32010 0 20 32011 10 10 32012 20 5 30013 5 20 30014 20 10 28015 10 20 280

a As cement replacement.b Fine aggregates.c Coarse aggregates.

2.1.4. Steel reinforcementThe steel reinforcement of the RC specimens was made of

16mm (A615) structural rebars.

2.2. Experimental design

The experimental plan was to investigate the SRC and me-chanical behaviour of RC specimens made with MGWD as partialreplacement of cement. For this objective, 15 mixes were designed,including a control mix (No. 1) without MGWD and 14 mixes (No.2e15) with MGWD at various contents/combinations. Thereplacement ratios of cement with waste dust of marble andgranite or a combination of the twowere 0%, 5%, 10%, 15%, 20%, 25%,and 30% (by weight). The composition of the concrete specimens isin Table 3.

2.3. Specimen preparation

A drum mixer was employed to make concrete mixes bypartially replacing cement withMGWD from a control concretemixconsisting of cement, water, fine and coarse aggregates. The ag-gregates were first inserted in the drum mixer. Next the cementmixed with MGWD was added and mixed for about 2 more mi-nutes. Then, the water was added and mixed until the mix washomogenous.

2.4. Testing

2.4.1. Compressive strengthThe fcm of concrete was determined according to ASTM C39.

These specimens were demoulded after 24 h and then cured byimmersion in a water fully saturated by lime. The specimens werecrushed after 7 and 28 days of curing. The fcm of eachmix is equal tothe mean value of three specimens.

2.4.2. Splitting tensile strengthThe fctm of concrete was determined according to ASTM C496.

Similarly to the fcm test, the specimens were prepared and curedunder standard conditions. The specimenswere crushed after 7 and28 days of curing in lime-saturated water. The fctm of each mix isequal to the mean value of three specimens.

2.4.3. Corrosion resistanceThe SRC resistance of RC specimens was determined using

/m3)

Marble Granite Water Fineb Coarsec

0 0 200 714 100020 0 200 709 10000 20 200 709 100040 0 200 699 9950 40 200 699 99520 20 200 699 99540 20 200 691 99220 40 200 691 99280 0 200 685 9890 80 200 685 98940 40 200 685 98980 20 200 682 98820 80 200 682 98880 40 200 680 98740 80 200 680 987

I. Taji et al. / Journal of Cleaner Production 210 (2019) 837e846840

cylindrical steel moulds with 100mm diameter, height of 200mmand a 200mm long SR with a 16mm diameter placed in its middle.The setup of this tests is depicted in Ghorbani et al. (2018a,b, 2019).Like in the fcm test, RC specimens were prepared and cured understandard conditions. After curing 28 days in lime-saturated water,the specimens were immersed in a container containing a solutionof 3.5% NaCl byweight. Using a saturated calomel electrode (SCE) asreference, open circuit potential (OCP) measurements were carriedout for 118 days. To specify the SRC resistance behaviour in con-crete, impedance spectroscopy (EIS) was applied after 14, 28 and 90days of exposure to the NaCl solution by using Zive Lab Potentiostatand a platinum wire as counter electrode. To ensure the repeat-ability of the EIS results, the test was performed three times pertesting age.

3. Results and discussion

3.1. Compressive strength

The results of compression tests conducted on the concretemixes including MGWD as partial cement replacement after 7 and28 days of curing are shown in Fig. 2. Using MGWD positivelyaffected the fcm of mixes No. 2 to No. 9. This higher strength couldbe linked to the filler effect of highly fine MGWD. Another factorthat may be responsible for this is the greater density of mixescaused byMGWDuse. The same factors explain the trend of fctm. Onthe other hand, as seen in Fig. 2, using MGWD led to a significantlynegative influence on the fcm of mixes No. 10 to No. 15. This meansthat, for these mixes, an inverse relationship between incorpora-tion ratio of MGWD and fcm of concrete exists, as previously re-ported (Rana et al., 2015). The reason for this is possibly the lowercontent of cement in the mixes. As seen in Fig. 2, concrete mix No. 6displayed the highest compression strength with an improvementof about 44% and 16% after 7 and 28 days of curing, respectively,relative to the control mix, whilst concrete mix No.15 displayed themaximum reduction in compressive strength of the mixes with 5%cement replacement, the one with MWD displayed the largest ef-fect and had the highest compressive strength. Moreover, from themixes with 10% and 15% cement replacement, No. 6 and No. 7displayed the highest compressive strength. Finally, Fig. 2 showsthat, as curing continued, the compressive strength of all concrete

Fig. 2. 7- and 28-day fcm of the concrete mixes.

mixes increased but the rate of increase varied as reported in pre-vious researches (Ghorbani et al., 2018a,b, 2019).

3.2. Splitting tensile strength

Fig. 3 illustrates the fctm of mixes with MGWD as partial cementreplacement after 7 and 28 days of curing. As seen there, similarlyto compressive strength, using MGWD had a good effect on thetensile strength of mixes No. 2 to No. 9. The concrete mix with 5%GWD and 5% MWD together displayed the highest tensile strengthof all and improved the tensile strength by about 30% and 23% after7 and 28 days of curing, respectively, relative to the control mix.Also, similarly to compressive strength, using MGWD had a notablynegative effect on the tensile strength of mixes No. 10 to No. 15(mixeswithmore than 20%MGWD). As shown in Fig. 3, the greatestreduction in tensile strength was observed inmix No.15, which hadlower tensile strength by 24% and 20% relative to the control mixafter 7 and 28 days of curing, respectively.

3.3. Open circuit potential

Fig. 4 shows the OCP variation or half-cell potential of differentspecimens over a period of 118 days of immersion including 28 daysin lime-saturated water and 90 days in a NaCl solution at 3.5% byweight. Generally, measuring the potential of an electrode in opencircuit condition is the most elementary electrochemical experi-ment in corrosion studies, used to estimate the probability of SRC(Trejo et al., 2009). Described in ASTM C876, it is generallyemployed in industrial and laboratory applications due to itssimplicity. With OCP, the SRC state in an environmental conditioncan be appraised. This method of measurement only needs a highresistance voltmeter connected to the working electrode and areference one. OCP measurement does not yield information aboutthe rate of SRC. Thus, it is recommended to use it with othermonitoring methods such as the EIS technique. Indeed, electronstransfer is the major characteristic of electrochemical reactionssuch as corrosion. Subsequently, the most reliable technique toquantify SRC is tomeasure the current. According to ASTM C876-91,SR are likely to be in a safe condition if its OCP value remainsabove�126mV/SCE; if it falls below�276mV/SCE, the SR are likelyto be at the risk of corrosion; for OCP values between �126

Fig. 3. 7- and 28-day fctm of the concrete mixes.

Fig. 4. Open circuit potential measurements of steel rebar in different concrete mixesuntil 118 days of immersion.

I. Taji et al. / Journal of Cleaner Production 210 (2019) 837e846 841

and �276 mV/SCE, the SRC probability remains uncertain. Asshown in Fig. 4, two distinct areas can be distinguished, before andafter 28 days of immersion in a 3.5% by weight NaCl solution. Thespecimens were submerged in regular tap water for 28 days to cure.In this period, the values of OCP tend to increase positively. Theincrease in OCP is triggered by the increase of the pH level of thesteel-concrete interface, which can reach the value of 12 (Pradhan,2014), leading to the formation of the protective passive layer.Hence, the SRC rate decreases and the OCP values increase. In theNaCl solution, chloride ions can diffuse into the concrete pores andtherefore reach the surface of the SR and then deteriorate theirpassive layer. The chloride attack of the passive layer results in a fallof the SRC potential as shown in Fig. 4. It could be understood fromFig. 4 that, after exposing the RC specimens to the NaCl solution, theSRC potential in specimens No.1, 2, 3, 7, and 8 decreases rapidly intothe corrosion area, while other specimens hardly enter that area. Itcan be inferred that MGWD partially replacing cement can improvethe passive behaviour of the SR. It was reported that the increase inthe surface alkalinity of the SR in RC specimens is caused by usingcalcareous material such as marble, and even helps to improve theSRC resistance in the long-term (Pacheco-Torgal et al., 2017).

Fig. 5. Comparison of Rct in different mixes after 14, 28 and 90 days of immersion in a3.5% NaCl solution.

3.4. Electrochemical impedance spectroscopy

EIS is considered a capable method to characterize and detect

Fig. 6. SEM images (5000� ) of (a) control mix; (b) mix No. 3 and (c) mix No. 11.

Swap

1 0 1 1 1 0 0 0

1 0 1 1 0 0 0 0

Before Mutation

After Mutation

(a)

Children

1 0 1 1 1 0 1 0 0

0 1 1 1 1 1 0

1 0 1 1 1 0 1 0

0 1 1 1 1 0 0 1

(b)

Parents

Fig. 7. Concept of (a) mutation and (b) Crossover.

I. Taji et al. / Journal of Cleaner Production 210 (2019) 837e846842

corrosion events in metallic parts (Ribeiro and Abrantes, 2016). It isalso a common tool to determine the SRC behaviour of RC members(Ribeiro and Abrantes, 2016; Wang et al., 2014). SRC usually occurswhen the aggressive ions attack the passive layer formed on theinterface of the SR and concrete. Any deterioration of the passivelayer can affect the response of a sinusoidal wave applied by the EISmethod. After exposure to a 3.5% by weight NaCl solution, theimpedance of SR in RC specimens was measured after 14, 28 and 90days. In order to quantitatively compare the EIS data, the resultswere analysed using an EIS analyser and can be found as supple-mentary data. As equivalent circuit as referred in Ghorbani et al.(2018a,b, 2019) was used to model the EIS data. It consists of aparallel resistance (Rc) and capacitance (CPEc) for concrete in serieswith a parallel charge transfer resistance (Rct) and double-layercapacitance (CPEdl) of the metal surface. Because of the

Table 4Results of the ANOVA analysis of the parameters of the steel rebar corrosion tests.

Source Sum of squares df Mean Squa

Model 3.737Eþ11 6 6.228Eþ1t 1.303Eþ11 1 1.303Eþ1m 2.301Eþ08 1 2.301Eþ0g 8.534Eþ09 1 8.534Eþ0

t�m 1.981Eþ10 1 1.981Eþ1t� g 4.122Eþ09 1 4.122Eþ0m� g 1.490Eþ11 1 1.490Eþ1

Residual 3.845Eþ11 38 1.012Eþ1Corrosion total 7.581Eþ11 44

significance of Rct data in comparison with other elements in thecircuit, the fitted results of Rct are represented in Fig. 5. It is clearthere that the value of Rct in mixes No. 1 to No.8 was lower thanthat of the control mix. This may be caused by an increase inporosity of the modified concrete. It is reported that adding granitedust as cement replacement in concrete mixes at 7.5%, 10.0% and15.0% increases their porosity (Elmoaty, 2013). The results alsoshow an advance in SRC resistance of mixes No. 9 to No. 12. How-ever, the Rct value decreased in mixes No. 13 to No. 15. It can bestated that, for high amounts of MGWD, i.e. in mixes No. 13, 14, and15, the content of cement, as the main factor responsible forincreasing the pH and depassivate the SR, decreased remarkably;consequently, a decline of SRC resistance in these mixes was ex-pected. However, using MGWD as partial replacement in mixes No.9 to No. 12 improved the SRC resistance. This situation may beattributed to the reduction of pores, pore diameters and air contentin the concrete microstructure as a result of using fine MGWDparticles. In fact, the MGWD's particle size is smaller than that ofcement particles and, as a result, the coefficient of chloridedispersion decreases. Consequently, it can be inferred that replac-ing cement with up to around 20% MGWD can have beneficial ef-fects on the SRC behaviour of the mix.

3.5. Scanning electron microscope analysis

5000�magnification SEM images of concrete mixes No. 1, asthe control mix, and concrete mixes No. 11 and No. 3, which dis-played the most and the least SRC resistance to a 3.5% by weightNaCl solution, are shown in Fig. 6. As seen there, the highestamount of pores in the concrete structure occurs inmix No. 3, whilethe lowest amount occurs in mix No. 11. This implicates that usingsimultaneously 10% of both GWD and MWD dust as partialreplacement of cement brought a significant improvement of themicrostructure of concrete. This lower porosity probably is a resultof using high fineness MGWD. As depicted in Fig. 6, larger andmorefrequent crystals can be seen in mix No. 11 than in the control mix.

3.6. Statistical analysis

Generating a mathematical model is one of the most essentialtasks of experimental research. By developing a robust model,determining the output of any input becomes possible with anappropriate precision whether it is between the existing range(interpolation) or outside it (extrapolation). Many novel techniqueshave been devised in order to facilitate this part of studiesthroughout recent years. Since describing mathematical expressionof almost every phenomena is complicated, these methods arenormally beneficial but not in all cases. The aim of this statisticalanalysis is to define an equation that can provide the desired out-puts, related to the tests described in the paper. First, an evolu-tionary algorithm named “MEP” (Multi-Expression Programming)

re F-value p-value (Prob> F)

0 6.15 0.0001 significant1 12.88 0.00098 0.023 0.88099 0.84 0.36420 1.96 0.16989 0.41 0.52711 14.72 0.00050

I. Taji et al. / Journal of Cleaner Production 210 (2019) 837e846 843

was used. Regarding the unclear arithmetic structure, evolutionaryalgorithms (EAs) such as GA (genetic algorithm) (Holland, 1992), EP(evolutionary programming) (Fogel et al., 1966) and MEP (Olteanand Grosan, 2003) are well-known methods to face this chal-lenge. They employ multiple operations like crossover and

Fig. 8. Surfaces fitted to the results relative to the

mutation to maintain a constant trend of evolving, which can bereferred as “Learning”. Evolutionary computation encompasses aunique interpretation of possible answers - not necessarily correct -into the form of binary entities (called “chromosome”). Each EAstarts with an initial population of binary individuals (called

corrosion testing days: (a) 7, (b) 14 and (c) 90.

I. Taji et al. / Journal of Cleaner Production 210 (2019) 837e846844

“Parents”); then, during the process, the above-mentioned opera-tions are applied to generate the children populations (off-springs).Based on a predetermined function, namely sum of error, they areranked and the top ones are selected to become parents of the nextgeneration. Thus, this cycle goes on until convergence or themaximum number of iterations is reached, and then calculationstops. Considering the nature of binary entities which are consti-tuted only by one and zero, mutation simply alters a single char-acter to the other one, and crossover cuts the string of each parentin a randomly-selected location and swaps new strings (Fig. 7). Inthis study, hundreds of models were generated using differentcombination of several famous mathematical functions. Nonethe-less, satisfactory accuracy was not reached and also only one of theparameters (inputs of the model) would be involved in the pro-duced models. The highest R2 value attained was about 0.30 (Eq. 1).Eq. 1 Where: m¼Marble (%), g¼Granite (%) and t¼ time (days).Response surface methodology (RSM) was further adopted to ac-quire a relationship between the percentage of GWD and MWD aswell as the time required for processing SRC resistant concrete. RSMis a statistical strategy to enhance a mathematical surface expres-sion, where the average response values are optimized. Several

Table 5Value of the constants in Eq. 3.

P0 ¼ 9:254� 105 � t�1:198 þ 4:525� 104 1

P1 ¼ � 5:952� 104 � t�0:595 � 1794 2

P3 ¼ � 5:148� 105 � t�1:023 � 9662 3

P4 ¼ 1:024� 104 � t�0:976 þ 281:5 4

P5 ¼ 6:795� 104 � t�1:094 � 1123 5

P6 ¼ 9:880� 104 � t�1:196 þ 1283 6

P7 ¼ � 3464 � t�1:207 � 40:12 7

P8 ¼ � 2257 � t�1:008 � 38:26 8

P9 ¼ � 4316 � t�1:427 � 36:51 9

t¼ time (days).

Fig. 9. Contours of the model for (a) 7 days, (b)

studies have recently been carried out to develop a robust modelusing the RSM method (Aldahdooh et al., 2013; Alyamac et al.,2017; Güneyisi et al., 2014; Nambiar and Ramamurthy, 2006).Note that an investigation should be first conducted using theANOVA (Analysis of Variance) to investigate the interaction be-tween parameters and how each variable affects the others. Elim-ination of insignificant parameters was done by performing t-testand F-value and p-value were attained by Design-Expert 10.0.3software. The p-value of quartic, cubic and quadratic models turnedout to be significant; however, the R-squared values of thesemodels did not exceed 0.50. Thus, the overall adequacy was notmeteither in this method. The results of the ANOVA for the best modelwith Adjusted R-squared less than 0.2 is tabulated in Table 4 (Eq. 2),where m¼marble (%), g¼ granite (%) and t¼ time (days). Even-tually, a heuristic approach was undertaken. In the first step,polynomial surfaces were fitted to the results with relative to thetesting days (Fig. 8). In other words, three surface expressions weredetermined for 7, 14 and 90 days, equal except for the constants.Separating them per time period had the following advantages:simple like-wise and much more exact models were obtained.

From the viewpoint of mathematical structure (degree ofterms), the similarity between them provided the opportunity ofcombining them with fitting power function to their constants tomerge the three surfaces into one expression (Eq. 3) with R2 of 0.83.This was not feasible in the two previous techniques. The value ofthe constants in Eq. 3 is shown in Table 5 (Eq. 3), where m¼marble(%), g¼ granite (%). According to the shapes of the developedmodel, Fig. 9-a to 9-c illustrate contours of different concrete mixesin various times of the SRC tests. The ridge-line is also drawn foreach one to investigate the behaviour of the surface more accu-rately, and Fig. 9-d depicts all these lines. The ridge-line defines theboundary in which the gradient of the surface changes sign.

In zone I, the slope of the tangent line is positive, which showsan increasing trend of the SRC resistance, but this changes in zone IIwhere it starts to drop. The distance between the contours further

14 days, (c) 90 days and (d) all ridge-lines.

Fig. 10. Surfaces of the developed models for different times of exposure to NaClsolution.

I. Taji et al. / Journal of Cleaner Production 210 (2019) 837e846 845

expresses the higher gradient in zone II compared to zone I.Moreover, plotting the group of surfaces is useful to study the in-fluence of time. Fig. 10 indicates that generally as the days ofexposure to NaCl solution increase, the SRC resistance decreases.The interval between them additionally shows that the reducingrate decreases as exposure to NaCl solution is prolonged. During 7more days (7e14 days), the output decreased approximately asmuch as during 76 more days (14e90 days), which means that theimpact of time on the SRC resistance gradually drops.

4. Conclusions

In this study, it was investigated how the partial use of MGWDinstead of cement in reinforced concrete production may affect itscorrosion and mechanical behaviour. In addition to providing adescribing mathematical model, three different approachesincluding an evolutionary algorithm (call “MEP”), response surfacemethodology (RSM) and a heuristic technique were utilized toconduct the statistical analysis. The following results wereobtained:

- With respect to the partial cement replacement with MGWD,the fctm and fcm of mixes No. 2 to No. 9 improved, while in mixesNo.10 to No.15 it had a negative effect especially in terms of fcm;

- It was also observed that 5% use of both GWD and MWD pro-vided the best results, and caused concrete samples to attainhigher 28-day fctm and fcm by about 25% and 44%, respectively,compared to the control mix;

- By OCP measurements, it was determined that partiallyreplacing cement with MGWD, especially at higher contents,enhanced the passive behaviour and the half-cell potential;

- EIS experiments revealed that using 20e30% partial cementreplacement with MGWD improved the behaviour of embeddedSR in concrete from the standpoint of corrosion and enhancedthe charge transfer resistance;

- The measurements of EIS and OCP also showed that the simul-taneous use of marble and granite waste dust, both at 10%instead of cement led to a higher potential compared to theother concrete mixes and improved the SRC resistance inconcrete;

- The SEM images showed that using 10% waste dust of bothmarble and granite caused the microstructure to improvesignificantly relative to the control mix.

Acknowledgments

The authors gratefully acknowledge the support of the FerdowsiUniversity of Mashhad and the Foundation for Science and Tech-nology, CERIS research centre and Instituto Superior T�ecnico.

Appendix A. Supplementary data

Supplementary data to this article can be found online athttps://doi.org/10.1016/j.jclepro.2018.11.091.

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