Mix design factors and strength prediction of metakaolin-based geopolymer
Mukund Lahotia, Pratik Narangb, Kang Hai Tana, En-Hua Yanga,⁎
a School of Civil and Environmental Engin eering, Nanyang Technological University, Singapore 639798, Singaporeb Department of Computer Science Engineering, School of Engineering and Applied Sciences, Bennett University, Greater Noida, Uttar Pradesh 201310,India
Geopolymer is a promising alternative binder to Portland cement. However, the importance of mix designparameters affecting the mechanical properties of geopolymer has yet to be quantitatively assessed. This workevaluates the significance of the four common mix design parameters, namely Si/Al (molar ratio), water/solids(mass ratio), Al/Na (molar ratio) and H2O/Na2O (molar ratio), in determining compressive strength ofmetakaolin-based geopolymers through experiments and statistical analyses. In addition, machine learning-based classifiers were engaged for strength predictions. Results showed that Si/Al ratio is the most significantparameter followed by Al/Na ratio. Unlike ordinary Portland cement system, water/solids ratio is not the chieffactor governing strength of metakaolin-based geopolymers. Machine learning-based classifiers were able topredict the compressive strength with high precision. The strength predictions can potentially guide preliminarymix proportioning of metakaolin-based geopolymers to achieve required strength grade without going throughtedious (trial and error) mix formulation.
1. Introduction
Geopolymer is a term coined by Joseph Davidovits in 1978 for aclass of inorganic, amorphous to semi-crystalline, three-dimensionalsilico-aluminate materials [1]. Geopolymerization involves chemicalreactions among various alumino-silicate oxides with silicates underhighly alkaline conditions, yielding polymeric Si–O–Al–O bonds [2].The most commonly used alumino-silicate oxide sources are metakao-lin and fly ash and their dissolution in alkaline medium leads toformation of individual alumina and silicate species which then co-polymerize to form geopolymers. An alkali metal salt and hydroxide arerequired for the dissolution of silica and alumina to proceed, as well asfor the catalysis of the condensation reaction.
It has been reported that geopolymers possess excellent mechanicalproperties and fire resistance [3,4]. There has been a wide variety ofresearch and development of geopolymers as heat-resistant materials[5–8], cements and concretes [9–12], thermal insulation [13–17],refractory material [18], high-tech composites [19–21], and formedical applications [22]. Geopolymer cement or binder is a promisingalternative to ordinary Portland cement (OPC). Portland cementproduction is one of the principal causes of greenhouse gas emissionwhereas geopolymer when used as a binder can utilize industrial by-products such as coal fly ash [23,24] and/or ground granulated blast-furnace slag (GGBS) [16,25] as raw materials. In this manner, it serves
as a green construction material with immense potential for sustain-able development.
It is known that water-to-cement ratio is the most significant factorin determining the compressive strength of OPC binders. Unlike OPCbinders, the importance of mix design parameters affecting themechanical properties of geopolymer binder has yet to be quantita-tively assessed. Previous research works on this important topic arelimited and have shortcomings. It has been suggested by Kriven et al.[26] that the Si/Al ratio in the range between 1.75 and 2.0 producesmetakaolin-based geopolymers with the highest compressive strength.Duxson et al. [27] studied the effect of Si/Al ratio on the compressivestrength and microstructure development of metakaolin-based geopo-lymers. He concluded that compressive strength increased with in-creasing Si/Al ratio in the range 1.15–1.90. In that series of mixes, theAl/M (‘M’ being the alkali cation) ratio was kept as unity and thealkalinity (H2O/Na2O) was maintained constant. Water-to-solids ratio,however, reduced with an increase of Si/Al ratio. Thus, it cannot beascertained if the increase in the compressive strength of geopolymerwas due to an increase of Si/Al ratio, a reduction of water-to-solidsratio, or a combination of the two.
Kong et al. [28] observed that the compressive strength ofmetakaolin-based geopolymer varied with Si/Al ratio. Kong et al.’sresults, however, were quite different from Duxson's findings since theAl/M ratio in the former set of tests was not close to unity.
http://dx.doi.org/10.1016/j.ceramint.2017.06.006Received 9 March 2017; Received in revised form 15 May 2017; Accepted 2 June 2017
Theoretically, one alkali cation is required to balance the negativecharge on the tetrahedrally coordinated aluminum atom. Thus, it hasbeen suggested that Al/M ratio should be close to unity [29,30]. Theheat of reaction during geopolymerization which is indicative of thedegree of reaction, is inherently linked to the Al/M ratio and has beenobserved to increase until the Al/M ratio reaches unity, beyond whichno greater heat is released [29]. The importance of Al/M molar ratiohas been highlighted in previous research works [29,30].
Yunsheng et al. [31] studied the effects of three parameters, viz. Si/Al ratio, H2O/Na2O ratio and Al/Na ratio on the mechanical propertiesand microstructure of calcined kaolin-based geopolymers in accor-dance with orthogonal design but only for a Na-PSDS (Poly-sialate-disiloxo) type geopolymer. Thus, the effect of Si/Al ratio was studiedwithin a narrow range between 2.75 and 3.25 and hence the impor-tance of Si/Al ratio could not be singled out in their test results.According to Rahier et al. [30], the H2O/Na2O ratio affects thegeopolymer reaction. H2O/Na2O ratio determines the alkalinity ofthe system and affects the degree of geopolymerization. Burciaga-Dı´azet al. [32] studied the influence of factors (such as blast furnace slag-to-metakaolin weight ratio, activator concentration and curing time) onthe development of mechanical properties in a composite system basedon blast furnace slag and metakaolin using a statistical approach.However, the effect of water content on geopolymers was not studied.Lyu et al. [33] used statistical analysis to study the factors affecting themechanical characteristics of metakaolin-based geopolymers withoutconsidering the effect of Si/Al ratio.
For fly ash-based geopolymers, Panagiotopoulou et al. [34] usedTaguchi method for experimental design and performed analysis ofvariance (ANOVA) on the results so as to assess the importance of theparameters. Kazemian et al. [35] used multiple linear regressiontechnique to quantitatively assess the parameters for fly ash-basedgeopolymers. However, both studies did not investigate the effect of Si/Al ratio on the compressive strength of fly ash-based geopolymers. Infact, many studies of fly ash-based geopolymers ignored the influenceof Si/Al ratio and suggested that compressive strength of geopolymersis dependent on the water-to-solids ratio similar to that of OPC [36–38].
There is a need to clearly understand the importance of mix designparameters governing the development of compressive strength ofgeopolymers so as to tailor its properties for desired applications. Thispaper evaluates the significance of four inter-independent mix designparameters, namely Si/Al molar ratio, water/solids mass ratio, Al/Namolar ratio and H2O/Na2O molar ratio, in determining compressivestrength of metakaolin-based geopolymers through experiments andstatistical analyses. A total of 35 geopolymers (using metakaolin asprecursor and sodium-based alkali as activator) with a wide range ofmix design parameters were synthesized and compressive strengthswere measured. Attribute evaluation by means of correlation-basedfeature selection (CFS) algorithm and ANOVA were engaged for dataanalyses to evaluate the significance of the four mix design parameterscontributing to compressive strength. Morphology of the specimenswas obtained by means of scanning electron microscope (SEM), whichreveals the influences of four mix design parameters on microstructureof geopolymers and provides physical reasoning and interpretation tothe statistics results. Multiple machine learning-based classifiersincluding the random forests classifier, the Naïve Bayes algorithm,and the k-nearest neighbor (k-nn) classifier were used to predictcompressive strength of metakaolin-based geopolymer based on thefour mix design parameters.
2. Methodology
2.1. Experimental program
A total of 35 metakaolin-based geopolymer mixes with a wide rangeof the four parameters were synthesized in this study as shown in
Table 1. The mixes were prepared by changing the proportions ofmetakaolin and sodium silicate solution. The concentration of sodiumsilicate solution was also varied. In some cases, fine rock powder (d50 =5.7 µm) was added to the geopolymer mix as filler in order to study theinfluence of high Si/Al molar ratio on the compressive strength. Thus,experimental parameters of Table 1 were established.
Metakaolin is rich in SiO2 and Al2O3 and therefore is an idealprecursor for geopolymer formation. Metakaolin easily participates ingeopolymerization compared to other precursors such as fly ash due toits highly amorphous nature. Thus, metakaolin geopolymer system isoften used as a model system to understand geopolymer chemistry[39]. Metakaolin was supplied by BASF and chemical composition ofthe material is included in Table 2. As can be seen, metakaolin used inthis study has about 97% of SiO2 and Al2O3 in total. The mean particlesize of metakaolin was 1.3 µm and its XRD pattern is shown in Fig. 1.In the XRD pattern, a hump could be observed in the 2theta rangebetween 15° and 35°. This hump represents typical amorphous natureof metakaolin. A few peaks corresponding to muscovite, a commonlyfound impurity in metakaolin, were also detected in the diffractogramof metakaolin.
Sodium-based alkali was used as the activator for the synthesis of
Table 1Mix design and compressive strength of the thirty-five (35) metakaolin-basedgeopolymers synthesized in this study.
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geopolymer in the current study. To prepare sodium hydroxidesolution, a calculated quantity of NaOH pellets (99.8% in purity,purchased from Schedelco Pte. Ltd) was dissolved in ultrapure waterfrom Milli-Q water filtration station. Various amounts of amorphoussilica (Fumed Silica, CAB-O-SIL® M-5) were dissolved into the freshlyprepared hot sodium hydroxide solution using a magnetic stirrer underroom temperature to obtain desired composition of sodium silicatesolution. The amorphous silica or fumed silica is a manufacturedproduct from Cabot Cooperation, Illinois, USA. It has more than 99.8%SiO2 in a fine powder form. The dissolution of fumed silica in sodiumhydroxide solution by the magnetic stirrer was done till a clear solutionwas obtained. The solution was allowed to cool down and was thenused the next day for geopolymer synthesis.
To prepare geopolymer specimens, metakaolin powder was mixedwith sodium silicate solution of various concentrations in a planetarymixer (Kenwood Titanium Timer Major KMM040) for ten minutes.The fresh paste was poured into 50 mm cube molds in two lifts. Toensure proper compaction and removal of entrapped air bubbles, themolds were vibrated after each lift. The molds were then covered withplastic to avoid water evaporation. The specimens were cured atambient conditions in the temperature range of 25–30 °C for 24 h.After which, the specimens were demolded and sealed in plastic bags atambient conditions till the testing date.
The 7-day compressive strengths were measured using a compres-sion testing machine with a loading rate of 60 kN/min [40]. At leastthree samples were tested for each mix to determine its compressivestrength. The average values and the standard deviation are summar-ized in Table 1. A thermal field emission SEM (JSM-7600F) was usedto observe the microstructure of specimens at magnification levels of10k. Samples were taken from fractured surfaces of cubes after thecompression test. Samples were first oven-dried at 105 °C for 24 h toremove all evaporable water. After which, selected samples weremounted on a stub using a carbon tape and coated with a platinumlayer using a JEOL sputter coater (JFC-1600 Auto fine coater) employ-ing a 20 mA current for a duration of 30 s prior to SEM imaging.
2.2. Statistical analyses
In a geopolymer mix design, it is not possible to keep three of thefour parameters (Si/Al molar ratio, water/solids mass ratio, Al/Namolar ratio and H2O/Na2O molar ratio) constant while varying onlyone parameter to study its influence. Noting the inter-dependency ofthe parameters, statistical analyses were engaged to evaluate therelative importance of the four mix design parameters of metakaolin-based geopolymers. To enhance reliability of the statistical analyses,another 36 metakaolin-based geopolymer mixes using sodium-based
alkali as the activator with complete information of mix designparameters and the corresponding value of compressive strength werecollected from literature as shown in Table A1 in the Appendix[26,29,31,41–44]. Overall, a set of 71 data points (35 from the currentstudy and 36 from published literature) was used for the statisticalanalyses. Two well-known statistical analyses methods, namely attri-bute evaluation and analysis of variance (ANOVA), were used in thecurrent study and have been described below.
2.2.1. Attribute evaluationAttribute evaluation is a data mining procedure which estimates the
utility of attributes for a given task. In this study, correlation-basedfeature selection (CFS) algorithm, a filter method, was adopted as theattribute selection method for feature ranking, i.e. to rank theimportance of the four parameters on compressive strength. Given afull attribute set, CFS searches an optimal subset of attributes whichare highly correlated with the class label, but uncorrelated amongthem. The hypothesis behind attribute correlation evaluation per-formed by CFS is that “a good feature subset contains features highlycorrelated with (predictive of) the classification, yet uncorrelated with(not predictive of) each other” [45]. This hypothesis relies on 'attribute-class' correlation, indicating the correlation of the attribute with thetarget class, and on the 'inter-correlation' amongst the attributes whichindicates correlation between any two attributes.
The merit Ms for each subset of k features is calculated as below.
Mkr
k k k r=
+ ( − 1)Scf
ii (1)
For each value of k, all possible subsets are chosen and merit valuesare computed. The subset which results in the highest value of themerit is given as the output by CFS. In Eq. (1), rcf is the averagecorrelation between feature and class, and riiis the average inter-correlation between two features. The heuristic metrics rcf and rii arecalculated as the symmetrical uncertainty (SU) given in Eq. (2) [45].
SU H X H Y H X YH X H Y
= 2.0 × ( ) + ( ) − ( , )( ) + ( )
⎡⎣⎢
⎤⎦⎥ (2)
where H(X) is defined as entropy, given by:
∑H X p x p x( ) = − ( )log ( ( ))x X∈
2(3)
Here, p(x) is the probability of an instance x being chosen atrandom from X (x ∈ X). The output of CFS is in the form of a subset (ofthe original attributes) which has the highest merit.
Attribute selection is performed using the implementation of CFSprovided in the Weka machine learning suite. The final output of CFS is
Fig. 1. XRD pattern of metakaolin (star refers to muscovite, a commonly found impurity in metakaolin).
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in the form of a single subset of attributes for each fold of the k-foldcross-validation (k = 5) over the entire dataset. The k-fold cross-validation splits the dataset into k parts. The (k−1) parts are used forbuilding/training the model and the remaining one part is used fortesting it. This is repeated k times and each time a different part is usedfor testing. The final result is an average over all k runs. Since themodel is tested k times with a different test set in every run, thisachieves a better learning model than a common training-testing splitratio of 2:1, i.e. two-third of the ‘labeled’ data is used to build and trainthe detection model while the remaining one-third (which is alsolabeled) is used to determine the accuracy of the model. Given arelatively small dataset of the current study, a 5-fold cross-validationwas performed over the 71 datasets for attribute selection.
oped by Friedman [46] in 1991 was used to model the dependence ofcompressive strength on multiple predictor variables, i.e. Si/Al ratio,water/solids ratio, Al/Na ratio and H2O/Na2O ratio in the currentstudy. MARS is a method for flexible nonparametric regressionmodeling that can help to solve the current problem. For moderatesample size N (50 ≤ N ≤ 1000) and a moderate to high dimension n (3≤ n ≤ 20) as in the current study (N = 71 and n = 4), MARS is a suitablemethodology [46]. ARESLab [47] is a MATLAB Octave toolbox forbuilding piecewise-linear and piecewise-cubic regression models usingMARS technique. Some functions from this toolbox were used to buildthe MARS model in MATLAB and perform analysis of variance(ANOVA) on the collected compressive strength data. The mostsignificant parameter affecting compressive strength was determinedby comparing the value of generalized cross validation (GCV) score andstandard deviation (STD) corresponding to the four parameters.
2.3. Strength prediction
Prediction of the compressive strength was performed usingmachine learning based classifiers. To facilitate easy and intuitiveevaluation of the worth of the four attributes (Si/Al ratio, water/solidsratio, Al/Na ratio and H2O/Na2O ratio), numeric values of strengthwere divided into three categories of low, medium and high strength.Thus, the ‘target class’ for any 4-attribute tuple was represented by oneof these categories. The three categories were made via a simpleapproach of dividing the numeric values of compressive strength intothree equal-sized bins estimated from the full range of strength valuesof the 71 data points, i.e. from 0 to 81 MPa. Thus, the size of each binwas chosen to be 27 MPa and compressive strength less than 27 MPawas given a ‘low’ class label, strength between 27 and 54 MPa wascategorized as ‘medium’, and strength above 54 MPa was labeled as‘high’.
Three classifiers including the random forests classifier, the NaïveBayes algorithm, and the k-nearest neighbor (k-nn) classifier weretrained and the results were compared in this study. While decisiontrees are fast and easy to train, they tend to create complex treestructures and over-fit the data. The random forests classifier createsan ensemble of decision trees and output the final class that is the modeof the classes output by individual trees. The Naïve Bayes theorem is asimple probabilistic classifier based on applying Bayes' theorem. Anadvantage of Naïve Bayes method is that it requires a small amount oftraining data for classification, which is particularly useful for thecurrent task. The k-nn classifier classifies instances based on the classlabel of k nearest neighbors. The k-nn method is a simple approachtowards classification and does not over-fit the training data.
Similar to the attribute selection, all models were trained using a 5-fold cross-validation over the entire dataset, including selecting para-meters for various models such as the value of k for the k-nn classifier.Random forests classifier was trained with multiple values of individualtrees. The number of trees was incremented in each run. Value of ten
trees was judged to be suitable since it achieved highest accuracy ofclassification of compressive strength. The value of k for k-nn was alsodetermined via cross-validation and k = 3 was found to give the highestaccuracy of classification. For performance evaluation, establishedmetrics such as Precision, Recall and False Positive rate were used.These are briefly defined as follows:
1. Precision is the ratio of the number of relevant records retrieved tothe total number of relevant and irrelevant records retrieved. It isgiven by TP / (TP+FP);
2. Recall (or True Positive Rate) is the ratio of the number of relevantrecords retrieved to the total number of relevant records in thecomplete dataset. It is given by TP / (TP+FN); and
3. False Positive rate is given by the total number of relevant recordsmissed over the total number of relevant records in the completedataset. It is given by FP / (FP+TN);
where TP stands for True Positive, a relevant record classified asrelevant; TN stands for True Negative, an irrelevant record classified asirrelevant; FP stands for False Positive, an irrelevant record classifiedas relevant; and FN stands for False Negative, a relevant recordclassified as irrelevant.
3. Results and discussion
3.1. Experimental results
Fig. 2 shows the influence of the four mix design parameters oncompressive strengths of 7-day-old metakaolin-based geopolymerssynthesized in the current study. As can be seen in Fig. 2(a), a cleartrend shows that compressive strength increases with increasing Si/Alratio first, peaks at Si/Al ratio close to 2, and decreases with increasingSi/Al ratio afterwards. It had been shown that as the Si/Al ratio isgradually increased from 1.15 to 2.15, due to an increase in Si-O-Silinkages (which are stronger than Si-O-Al linkages) as well as due to asimultaneous improvement in the geopolymer microstructure, thecompressive strengths would keep increasing up to Si/Al = 1.90 [27].It was also shown that a further increase in Si/Al ratio would cause anincrease in the quantity of unreacted metakaolin. These unreactedmetakaolin particles may in turn act as defect sites causing weakeningof material and reduction in compressive strength [27]. This suggests astrong influence of Si/Al ratio in determining the compressive strengthof metakaolin-based geopolymers. Similar findings have been reportedin previous literatures by Duxson et al. [27] and by Kriven et al. [26].
As for the dependence of compressive strength on water/solidsratio, while a general trend shows the strength decreases with increas-ing water/solids ratio, strong variation in compressive strength at thesame water/solids is also observed as indicated by solid oval inFig. 2(b). This indicates that water/solids ratio alone does notdetermine compressive strength of metakaolin-based geopolymers,which is in contrast to the OPC system where water-to-cement ratiois the chief factor controlling the micro-porosity and compressivestrength. Detailed discussion can be found in Section 3.3. The generaltrend showing decrease in strength with increasing water/solids ratio ismainly attributed to simultaneous change in Si/Al ratio of the mix asshown in Fig. 3. As can be seen, water/solids ratio in the current studygenerally increases with increasing Si/Al ratio. This is particularly truefor Si/Al ratio larger than 2 and thus the strength decreases withincreasing water/solids ratio.
As for the dependence of compressive strength on Al/Na ratio,Fig. 2(c) indicates that the highest compressive strength can beattained when this ratio is close to one (as indicated by the rectangularbox in the figure), which is the theoretical Al/Na ratio allowing chargebalance between alkali cation and tetrahedrally coordinated aluminumas suggested in the literatures [29,30,39]. When the amount of sodiumis high, it causes efflorescence which is unsightly but may not always be
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harmful for the structural performance of the material [48]. However,compressive strength experienced significant variations (from 19.80 to66.67 MPa) even at Al/Na ratio of unity as indicated by the oval inFig. 2(c). This implies that although it is important for Al/Na ratio to beclose to unity, the values of the other three mix design parametersinfluence the development of compressive strength. As can be seenfrom Fig. 2(d), no obvious trend in compressive strengths versus H2O/Na2O ratio is observed indicating that H2O/Na2O ratio did notsignificantly influence the development of compressive strength.
3.2. Statistical analysis
3.2.1. Attribute evaluationTable 3 shows the results of attribute evaluation performed on the
compressive strengths of the 71 metakaolin-based geopolymers (35from the current study and 36 from published literature). Value in thesecond column (given by N) indicates the number of folds (out of 5) inwhich that particular attribute, which has the highest merit, wasselected by CFS. Since the dataset is small, it is prudent to consideronly those attributes as important which are selected by CFS in all thefive folds of cross-validation. The output of CFS indicates that Si/Al is
0
10
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0 1 2 3 4 5 6 7
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Fig. 2. Dependence of compressive strengths of metakaolin-based geopolymers on (a) Si/Al, (b) W/solids, (c) Al/Na, and (d) H2O/Na2O ratios.
0.3
0.4
0.5
0.6
0.7
0.8
0 1 2 3 4 5 6 7
W/s
olid
s
Si/Al
Fig. 3. Variation of water/solids ratio of the mix with the Si/Al ratio.
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the most significant attribute since it was chosen in all 5 folds. Theattributes Al/Na and water/solids were chosen in one-fold of CFS, andthus their significance is much less compared to Si/Al. The significance
of H2O/Na2O can be considered to be the least based on the CFSattribute evaluation method.
3.2.2. ANOVAThe output of ANOVA decomposition is given in Table 4 below.
ANOVA function number is listed in the first column. Standarddeviation (STD) of the ANOVA function is given in the second column.This value gives a clue of its relative importance to the overall model. Itcan be interpreted in a way similar to a standardized regressioncoefficient in a linear model. Generalized cross validation (GCV) scorefor a model with all the basis functions corresponding to that particularANOVA function removed, is listed in the third column. The GCV scoregives another indication of the importance of corresponding ANOVAfunction. It can help to evaluate whether that ANOVA function makes asignificant contribution to the model, or whether it only slightly helpsto improve the global GCV score [46].
Observing the STD and especially the GCV score in Table 4, the firstand second ANOVA functions (corresponding to Si/Al ratio and Al/Naratios respectively) are very important for the fit. The next two ANOVAfunctions have high standard deviation as well. Hence, removing theseANOVA functions would largely degrade the GCV score. In both thesefunctions, Si/Al ratio is involved in interaction with water/solids andH2O/Na2O ratio respectively. Si/Al ratio is hence very significantparameter. Since last three functions have lower values of standarddeviation and GCV score, the corresponding variables have lesserimportance. Further analysis was carried out to give quantitativeinformation about the relative importance of the variables [47] andthe results are shown in Fig. 4. It can be observed that Si/Al ratio is themost important parameter followed by Al/Na, H2O/Na2O and water/solids ratios.
In summary, both statistical analyses indicate that Si/Al ratio is avery significant parameter followed by Al/Na ratio. Water/solids ratioand H2O/Na2O ratio are of less importance among the four mix designparameters. Since Si/Al and Al/Na were found to be the mostsignificant factors, a contour plot as shown in Fig. 5 was created toreveal the best ranges of Si/Al and Al/Na molar ratios suitable for themix proportioning to design metakaolin-based geopolymers withdesirable compressive strengths for any specific application. It wasfound that high strengths above 60 MPa could be attained by keepingSi/Al and Al/Na molar ratio of the geopolymer mixes roughly in theranges of 1.7–2.2 and 0.8–1.2, respectively.
3.3. Microstructure analysis
SEM micrographs of six geopolymers (mixes 1–3 and 22–24) arepresented in Fig. 6. As can be seen, geopolymers with Si/Al ratio of
Table 3Results of attribute evaluation by CFS.
Attribute name N*
Si/Al 5Al/Na 1water/solids 1H2O/Na2O 0
* N denotes number of folds (out of 5) in which that particular attribute, which has thehighest merit, was selected by CFS.
Table 4ANOVA decomposition results obtained from the MARS model developed for thecompressive strength data.
Fig. 5. Compressive strength of metakaolin-based geopolymer as a function of Si/Al and Al/Na molar ratios (scale bar on the right indicates compressive strength in MPa).
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1.03 (mixes 1–3) have very different microstructures than those withSi/Al of 2.0 (mixes 22–24). Microstructure of geopolymers with Si/Alratio of 1.03 consists of dense particulates and large interconnectedpores, whereas for geopolymers of Si/Al ratio of 2.0, the microstructureis relatively more homogenous with smaller pores. As a result,compressive strength of geopolymers with Si/Al ratio of 2.0 (66–73 MPa) is much higher than that of geopolymers with Si/Al ratio of1.03 (16–30 MPa). Similar findings were reported in previous litera-ture [27]. Changes of other parameters, e.g. water/solids ratio from0.48 to 0.67, only result in slight variation in morphology, porosity, andcompressive strength.
Microstructural similarity among the geopolymers with the same Si/Al ratio and a large difference with changes in Si/Al ratio indicates astrong influence of Si/Al ratio on the microstructure of geopolymers andthe influences of the other three parameters (Al/Na, water/solids, andH2O/Na2O ratios) are not as significant. Unlike OPC system where waterparticipates in cement hydration and determines overall porosity ofpaste [49,50], geopolymer system is described as a biphasic gel of waterand alumino-silicate binder where water acts as a reaction intermediateand is released during condensation to form pores and create thebiphasic structure [1,51]. The porosity in geopolymers is determinedby solution chemistry during geopolymerization, which is primarily afunction of Si/Al ratio and alkali metal cation type, while the absolutepore volume is determined by nominal water content [27,51,52]. Therole of water in geopolymer system is therefore not the same as in OPC.
3.4. Strength prediction
The results obtained using Random forests classifier, Naïve Bayesclassifier and k-nn classifier using the 4 attributes are given in Table 5.The precision obtained is as high as 83% indicating a good accuracy ofprediction. Random forests classifier and k-nn classifier show higherprecision than the Naïve Bayes classifier. This is because Naïve Bayestheorem holds a strong (naïve) independence assumption among theattributes; this is not valid for the four mix design parameters in thecurrent study. As pointed out in Section 3.3, the four mix designparameters (Si/Al, water/solids, Al/Na and H2O/Na2O) are inter-dependent and it is not possible to keep three of them constant whilevarying only one parameter to reveal its influence. The false positives(FP) are in the range of 9–22% (with the majority being around 10–12%) indicating not many misclassified instances. This is a moderateresult keeping in view the limited dataset available. These results areencouraging and shed light on the suitability of using the fourattributes (Si/Al, Al/Na, water/solids and H2O/Na2O ratios) in pre-dicting compressive strength of metakaolin-based geopolymersthrough machine learning-based classifiers. The strength predictionpotentially can guide preliminary mix proportioning of metakaolin-based geopolymers to achieve required strength grade without goingthrough tedious (trial and error) mix formulation.
The results obtained through CFS or any other feature selectionapproaches are highly dependent on that particular dataset. Thus, the
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current results should be interpreted only for the current dataset.Availability of a larger dataset shall facilitate a more thorough under-standing of the impact of different parameters in determining com-pressive strength of geopolymers. It should also be noted that thecurrent study evaluated the impact of only four parameters. Furtherstudy is needed to understand the influence of factors such asmetakaolin nature, curing time and temperature on the strengthdevelopment.
4. Conclusions
This study evaluated the significance of four mix design parameters,namely, Si/Al ratio, water/solids ratio, Al/Na ratio and H2O/Na2Oratio, which influence compressive strength of metakaolin-basedgeopolymers through experiments and statistical analyses. Resultsshowed that Si/Al ratio is the most significant parameter in determin-ing compressive strength of geopolymers followed by Al/Na ratio. Itwas also found that unlike OPC, water/solids ratio is not a significantfactor governing compressive strength of metakaolin-based geopoly-
mers. Microstructure observations through SEM facilitated physicalreasoning of the statistics results and revealed that Si/Al ratiosignificantly influences the microstructure of geopolymers, while theother three parameters do have certain minor influence on themorphology of geopolymers. Further, using the four attributes, com-pressive strength of geopolymers could be predicted by means of well-established machine learning approaches. The predictions could clas-sify geopolymers into low, medium and high strength to a reasonableaccuracy with high precision and false positives in range of 8–20%indicating not many misclassified instances. The strength predictionpotentially can guide preliminary mix proportioning of metakaolin-based geopolymers to achieve required strength grade without goingthrough tedious (trial and error) mix formulation.
Acknowledgements
The authors would like to thank the funding support for this projectfrom Land and Livability National Innovation Challenge, Ministry ofNational Development, Singapore (L2NICCFP1-2013-4).
Appendix
see Appendix Table A1.
Table A1Mix design and compressive strength of the thirty-six (36) metakaolin-based geopolymers from published literature.
M. Lahoti et al. Ceramics International 43 (2017) 11433–11441
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M. Lahoti et al. Ceramics International 43 (2017) 11433–11441
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